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Exploring the Minimum-Energy Pathways and Free-Energy Profiles of Enzymatic Reactions with QM/MM Calculations

  • Kiyoshi Yagi
    Kiyoshi Yagi
    Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
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    Orcidhttp://orcid.org/0000-0003-1120-9355
  • , 
  • Shingo Ito
    Shingo Ito
    Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
    More by Shingo Ito
  • , and 
  • Yuji Sugita*
    Yuji Sugita
    Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
    Computational Biophysics Research Team, RIKEN Center for Computational Science, 7-1-26 minatojima-Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
    Laboratory for Biomolecular Function Simulation, RIKEN Center for Biosystems Dynamics Research, 1-6-5 minatojima-Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
    *[email protected]
    More by Yuji Sugita
    Orcidhttp://orcid.org/0000-0001-9738-9216
Cite this: J. Phys. Chem. B 2021, 125, 18, 4701–4713
Publication Date (Web):April 29, 2021
https://doi.org/10.1021/acs.jpcb.1c01862

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Abstract

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Understanding molecular mechanisms of enzymatic reactions is of vital importance in biochemistry and biophysics. Here, we introduce new functions of hybrid quantum mechanical/molecular mechanical (QM/MM) calculations in the GENESIS program to compute the minimum-energy pathways (MEPs) and free-energy profiles of enzymatic reactions. For this purpose, an interface in GENESIS is developed to utilize a highly parallel electronic structure program, QSimulate-QM (https://qsimulate.com), calling it as a shared library from GENESIS. Second, algorithms to search the MEP are implemented, combining the string method (E et al. J. Chem. Phys. 2007, 126, 164103) with the energy minimization of the buffer MM region. The method implemented in GENESIS is applied to an enzyme, triosephosphate isomerase, which converts dihyroxyacetone phosphate to glyceraldehyde 3-phosphate in four proton-transfer processes. QM/MM-molecular dynamics simulations show performances of greater than 1 ns/day with the density functional tight binding (DFTB), and 10–30 ps/day with the hybrid density functional theory, B3LYP-D3. These performances allow us to compute not only MEP but also the potential of mean force (PMF) of the enzymatic reactions using the QM/MM calculations. The barrier height obtained as 13 kcal mol–1 with B3LYP-D3 in the QM/MM calculation is in agreement with the experimental results. The impact of conformational sampling in PMF calculations and the level of electronic structure calculations (DFTB vs B3LYP-D3) suggests reliable computational protocols for enzymatic reactions without high computational costs.

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 Special Issue

Published as part of The Journal of Physical Chemistry virtual special issue “Computational Advances in Protein Engineering and Enzyme Design”.

1. Introduction

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The role of molecular simulations in life science has been increased rapidly and significantly. (1) The conformational dynamics of membrane proteins, (2) ribosomes, (3) and other biomolecular complexes (4,5) has been investigated in molecular dynamics (MD) simulations based on atomistic (6−9) or coarse-grained (CG) (10−13) molecular models. Biomolecular interactions, such as protein–protein (14,15) or protein–DNA/RNA interactions, (16) are also examined in detail with large-scale biomolecular simulations in the cellular environments (14,17) and viruses. (18,19) MD-special supercomputers like Anton/Anton2 (20) or MD-GRAPE (21) allow us to simulate slow atomic motions of proteins on time scales up to milliseconds. However, most MD simulations are performed on the basis of classical mechanics, relying on the so-called “molecular force fields”, (22−24) which can cause several limitations in the simulations in terms of their accuracy and applicability. The force-field accuracy has long been discussed in simulation communities. (25,26) It is difficult to keep a good balance between the conformational stability of globular proteins and flexible structures of intrinsically disordered proteins/regions (IDP/IDR) even in the latest updates of molecular force fields. (27,28) Divalent cations, namely, Mg2+ or Ca2+, often add another complexity to MD simulations. (29,30) MD simulations using a “molecular force field” cannot describe chemical reactions or enzymatic reactions, since the motion of electrons including bond breaking/formation is totally neglected in the simulations. (31−34)
To overcome those difficulties in MD simulations with “force fields”, a hybrid quantum mechanical/molecular mechanical (QM/MM) calculation was proposed, at first, by Warshal, Levitt, and Karplus more than 40 years ago. (35−37) The electronic structure calculation is applied to a small region where the most interesting chemical reaction happens, while the surrounding buffer regions containing a large number of atoms are treated with molecular force fields. Conventionally, QM/MM calculations were difficult to apply to many interesting biological systems, presumably, due to their high computational costs. The QM region had to be sufficiently small, just containing less than 50 atoms, and only very short-time dynamics (shorter than 100 ps in total) were available if ab initio electronic structure theory was used in the QM calculations. However, recent advances in simulation methodologies and growing computational resources in supercomputers and graphics processing unit (GPU) clusters are opening a new era in the QM/MM calculations. One of the promising future directions is the free-energy calculations using the hybrid QM/MM potential. Yang and co-workers developed methods to compute the free-energy and minimum free-energy path with QM/MM. (38−40) Hayashi and his colleagues decoupled the QM/MM free-energy optimization from atomistic MD simulations to simulate large conformational changes between the reactants, transition states, and products in enzymes or motor proteins. (41,42) Rosta and Hummer applied umbrella sampling (US) based on the QM/MM potentials to describe the free-energy profiles (or potential of mean forces (PMFs)) of adenosine triphosphate (ATP) hydrolysis in solution and in enzymes. (43−45) Hammes-Shiffer and co-workers have also applied the method to various enzymatic reactions. (46−50)
In recent QM/MM simulations, ab initio electronic structure calculations with the QM program are combined with high-performance MD programs, such as AMBER (51,52) and NAMD. (53) We have also developed highly parallel MD software, GENESIS (https://www.r-ccs.riken.jp/labs/cbrt/), for simulating chemical and biological applications. One of the key features in GENESIS is the extensive parallelization for massively parallel supercomputers (54) and GPU-parallel clusters. (55) On the basis of our new computational techniques, such as the midpoint cell method, (56) the volumetric decomposition of three-dimensional (3D) fast Fourier transform (FFT), (57) huge biological systems, such as the cytoplasm of Mycoplasma genetalium, (14) a small bacterial system, or an entire gene locus (GATA4) (16) were simulated on supercomputers like the K computer, Fugaku (both in RIKEN) and Trinity in Los Alamos National Laboratory. The former contains more than 100 million atoms, and the latter includes over 1 billion atoms of biomolecules as well as solvent and ions. The second key feature is the availability of enhanced conformational sampling algorithms for extending the conformational space of biomolecules and accelerating the convergence of free-energy calculations. Replica-exchange MD (REMD), (58,59) replica-exchange US (REUS), (60) generalized replica exchange with solute tempering (gREST), (61) Gaussian accelerated MD (GaMD), (62,63) free-energy perturbation (FEP), (64,65) the string method with mean forces, (66,67) and combinations of these methods are now available. The CHARMM-GUI developed by Im and his colleagues prepares input files of MD simulations and free-energy calculations. (68)
These two key features in GENESIS are also useful in the QM/MM simulation, which has been implemented recently. (69) The well-known QM software, namely, Gaussian, (70) Q-Chem, (71) TeraChem, (72) and DFTB+, (73) is available in GENESIS from the release of 1.5. We did not change the QM programs and just call each binary of the QM software from the QM/MM interface program in GENESIS. This simple approach is sufficient in many QM/MM calculations. However, overhead costs required in the system call and exchanges of information using input/output (I/O) files between GENESIS and QM software are non-negligible when we use DFTB+ in QM simulations. In our previous work, we performed a molecular vibrational analysis using the QM/MM program in GENESIS as well as SINDO, (74) which can introduce the anharmonic effect of molecular vibrations. It was applied to an enzyme, P450 nitric oxide reductase, with the NO molecule bound to a ferric heme. (69)
In this study, we develop two new functions of the QM/MM calculations in GENESIS: (1) the interface with highly parallelized QM software, QSimulate-QM, (75) and (2) a reaction path search algorithm using the string method. (76,77) Note that the original string method in GENESIS (67) can be used with QM/MM calculations as well to compute the minimum free-energy pathway (MFEP). However, the method requires QM/MM-MD simulations to obtain the mean force, which is costly in general. In the present study, we implement an alternative string method (the so-called zero-temperature version), which computes the minimum energy pathway (MEP) on the potential energy. In this method, the buffer MM region is energy minimized with the QM region replaced by atomic charges derived from QM calculation. The QM calculation is required only once in the iteration of string optimization, and thus the computational cost is greatly reduced. The developed method is demonstrated in a conversion reaction of dihyroxyacetone phosphate (DHAP) into glyceraldehyde 3-phosphate (GAP) catalyzed by an enzyme, triosephosphate isomerase (TIM). The mechanism for the reaction has been well-established in previous theoretical works. (38,39,78−82) The whole reaction involves four proton-transfer (PT) processes. The MEP of each process is obtained by the string method, and the free-energy profiles along the PT reactions are calculated using the US method based on the QM/MM MD simulations. The high-performance computations using QSimulate-QM allow us to perform such free-energy calculations of enzymatic reactions in TIM with reasonable computational costs. Different levels of electronic structure calculations suggest promising schemes that are applicable to many other enzymatic reactions based on the QM/MM simulations.

2. Method

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2.1. Interface with QSimulate-QM

We have previously implemented a general interface with electronic structure programs for QM/MM calculations in GENESIS. (69) GENESIS sends the atomic coordinates and the MM charges to an electronic structure program and receives the energy and gradient upon return. The interface exchanges the information through external files. It (1) generates an input file of the electronic structure program, (2) invokes the electronic structure program using a system call function, and (3) reads output files of the electronic structure program. The advantage of such a scheme is that any electronic structure program can be readily adapted once the format of input/output files are known. The current version (ver. 1.6) supports DFTB+, Gaussian, Q-Chem, and TeraChem. However, the drawbacks of this scheme are that the file I/O is intensive and that the system call is not suitable for message passing interface (MPI) parallelized programs.
In this study, we developed an interface that directly combines GENESIS with QSimulate-QM through a library. QSimulate-QM has realized high-accuracy electronic structure calculations of large chemical systems via extensive parallelization. QSimulate-QM is first compiled to create a shared library (libqsimulate.so). Then, the QM/MM routine in GENESIS calls an entry function of QSimulate-QM included in the library to perform electronic structure calculations. Note that GENESIS and QSimulate-QM are written in Fortran and C++, respectively. The interface, therefore, implements a Fortran/C++ interlanguage call, which complies with standardized protocols in Fortran 2003 to be interoperable with C++. In this scheme, all the information is sent and received on memory without requiring the file I/O. GENESIS provides the atomic coordinates and MM charges, and QSimulate-QM returns the energy and gradient. The atomic charges of QM atoms derived from the intrinsic atomic orbitals (IAO) (83) are optionally returned. Furthermore, one of the arguments of the entry function is set to an MPI communicator, which specifies MPI processes assigned to QSimulate-QM. This specification makes it feasible to run multiple electronic structure calculations in parallel, for example, over replicas in REMD or REUS, images in the string method, and so on.
The current QM/MM implementation, not only for QSimulate-QM but for any others, assumes that the system is set up as a cluster system, that is, a nonperiodic system. The electronic structure of a QM system is calculated in the presence of all MM charges. In other words, the electrostatic interaction between electrons, nuclei, and MM charges are included in the electronic Hamiltonian. QM programs solve the electronic Schrödinger equation to obtain the QM energy, the nuclear gradients, and the response of MM charges to the electron density. The information is returned to GENESIS and used as forces to propagate the atomic position.

2.2. Reaction-Path Search

We implemented an algorithm to find the MEP. The procedure is outlined in the following.

Step 0. Setup

The system is divided into three layers: active atoms in a path search, buffer atoms, and fixed atoms. One of the natural choices of these layers is to set the active atoms to QM atoms, the buffer atoms to MM atoms in the vicinity of a QM region (e.g., within ∼8.0 Å), and the fixed atoms to other MM atoms in the outer region. The reaction path is represented by atomic coordinates in a number of discretized images. The definition of three layers, the number of images (Nimg), and the coordinates of images along an initial path must be provided in the input by users.

Step 1. Relax the Buffer Atoms

The first step in the calculation is to relax the structure of buffer atoms with active atoms (QM atoms) held fixed. In this step, the QM/MM interaction is calculated by replacing the QM atoms with atomic charges derived from the electronic structure calculations. The gradient correction is applied by adding the difference between the QM/MM gradient and the approximate one, as is commonly done in the micro-iteration scheme. (69,84)

Step 2. QM/MM Calculations

A single-point QM/MM calculation is performed to update the energy, gradient, and atomic charges.

Step 3. Update the Coordinates of Active Atoms

The coordinates of active atoms are updated in two steps based on the simplified string method by E et al. (77) At first, the image moves along the gradient
(1)
where n is an index of iterations, xin is the Cartesian coordinates of active atoms of the ith image in the nth iteration, V is the potential energy, and δt is a constant. Then, the images are reparameterized to be equidistant. Specifically, the path length is calculated as follows
(2)
and the coordinates, {xi*}, are interpolated as a function of path length, {si}, to construct an interpolation function, I(s). Then, the new coordinates are obtained as
(3)

Step 4. Check the Convergence

If the change in the energy profile and path length are both within threshold values, the calculation is terminated. Otherwise, the calculation goes back to the first step and relaxes the buffer atoms in the updated coordinates.
In the above procedure, the computational bottleneck usually comes from electronic structure calculations in step (2). Therefore, step (2) together with step (1) is parallelized over the image. One can calculate either all images or a subset of images in parallel by setting the number of MPI processes to Nimg × M (M is an integer) or a divisor of Nimg, respectively. The number of MPI processes per image is set to M in the former, while it is 1 in the latter.

2.3. Free-Energy Calculations

The free-energy profile of the enzymatic reaction is computed by an umbrella sampling (US) that uses QM/MM MD simulations after the MEP search. A set of interatomic distances, specified by the user, is used for collective variables (CVs). The window is generated at an equal distance along the MEP in the CV space by interpolation. Then, QM/MM-MD simulations are performed for each window with a bias potential, that is, harmonic restraints to CVs.
The analysis of MD trajectories gives the free-energy profile or PMF. The estimator f̂i is obtained by the multistate Bennett acceptance ratio (MBAR) method (85) as
(4)
where K is the number of windows, Uibias denotes the bias potential of the ith window, Nj is the number of snapshots in the jth window, and xjn is a sample from the nth snapshot and the jth window. Equation 4 is solved iteratively to obtain {f̂i}. Then, the PMF is obtained using MBAR
(5)
(6)
where Z is the partition function. In order to explore the free-energy profile along MEP, it is convenient to introduce pathCV, (67,86,87) which characterizes the component of tangent vector along the path
(7)
where rk is the CV at the kth window, and λ is a constant.
(8)

3. Computational Details

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3.1. Modeling and Equilibration of a System

The atomistic system of TIM was constructed from an X-ray crystal structure (PDBID: 7TIM, resolution 1.90 Å). (88) The crystal structure is a dimer of TIM cocrystallized with an inhibitor, phosphoglycolohydroxamic acid (C2H6NO6P). The two TIM proteins were both included in the simulation system, because the reaction center was located at the interface of the dimer. The nitrogen atom of the inhibitor was replaced with a carbon atom to generate DHAP. All titratable residues were ionized at a neutral pH condition based on pKa values estimated by PROPKA 3.1. (89) An exception is Glu165 with pKa of 7.75, which was kept ionized because it is an acceptor of a proton from DHAP. The proton of His95 was added at the ε position. CHARMM-GUI (90,91) was used to add hydrogen atoms and to solvate the system in a box of water molecules (110 × 90 × 90 Å3). An initial equilibration was performed in a periodic boundary condition (PBC) for 300 ps by the conventional classical MD with positional restraints to heavy atoms of proteins and DHAP. Then, the system was trimmed to 15 Å around a TIM dimer to create a non-PBC system. The system was equilibrated for 2.6 ns by classical MD gradually reducing the force constants of restraint, followed by a further equilibration for 140 ps by QM/MM-MD using scc-DFTB. (92) The protocol of the equilibration is summarized in Tables S1 and S2. Two spherical boundary potentials with a radius of 35 Å were applied around the center of mass of each TIM. The nonbonding interaction was reduced to zero between 16 and 18 Å employing a switching function. The neighbor list was updated every 20 fs. The force field parameters of TIM and water were CHARMM36 (93) and TIP3P, (94) respectively, and those of DHAP were generated using the force field toolkit. (95) The time integration was done using the velocity-Verlet integrator with a time step of 2.0 fs, and the temperature was controlled at 300 K using the Bussi thermostat. (96) The bond length of covalent bonds involving hydrogen atoms was constrained using the RATTLE (97) and SETTLE (98) algorithms.

3.2. QM/MM Calculations

The QM region was set to DHAP and the side chain of Glu165 and His95, which consists of 35 QM atoms. The boundary between QM and MM regions is set between the Cα and Cβ atoms. The link hydrogen atoms were attached to the Cβ atoms excluding the charges of MM atoms that belong to the same group as the Cα atoms. The electronic structure calculations were mainly performed by density functional theory (DFT) at the level of B3LYP hybrid functionals (99,100) with a D3 version of Grimm’s dispersion (101) (B3LYP-D3) using Dunning’s aug-cc-pVDZ for the basis sets. (102) The PBE functional (103) with def2-SVP (104) basis sets was also employed for benchmark calculations. The number of basis sets was 378 and 623 with def2-SVP and aug-cc-pVDZ, respectively. The scc-DFTB calculations were performed using the 3OB parameter sets. (92) The QM/MM calculations were performed using a development version of GENESIS interfaced with QSimulate-QM.

3.3. MEP Search

The structure of a reactant (DHAP) was obtained with the QM/MM energy minimization from the initial one described in Section 3.1. The residues within 6.0 Å of DHAP were relaxed, whereas others were kept fixed. Then, the structure of a product was obtained in two steps. First, the structure was roughly optimized adding distant restraints to X–H bonds with the reference distance set to 1.7–2.0 Å for a dissociating bond and to 1.0 Å for a newly formed bond. Second, the structure was refined by restarting the energy minimization without restraint. In this step, the residues within 3.0 Å of DHAP were relaxed.
Once the reactant and product structures were obtained, the MEP between them was searched using the string method. The initial path was obtained by a linear interpolation of the reactant and product in Cartesian coordinates. The number of images was set to 16. The active atoms in a path search were the same as QM atoms (DHAP and side chains of His95 and Glu165), and the buffer atoms were set to residues within 6.0 Å of DHAP. The step size δt was set to 0.0005 Å. The relaxation of buffer atoms was performed using a limited memory version of Broyden-Fletcher-Goldfarb-Shanno (L-BFGS-B) (105−107) and a macro/micro-iteration scheme. (84) The IAO charges (83) and the self-consistent charges were used for the micro-iteration in B3LYP-D3 and DFTB3, respectively. Convergence thresholds of the energy profile and the path length were set to 0.01 kcal mol–1 and 0.01 Å, respectively.
The procedure was repeated for all four PT reactions to obtain the structures of DHAP, three intermediates, and GAP and the MEPs connecting them.

3.4. Free-Energy Calculations

The umbrella sampling was performed along the MEP predicted from the string-method calculations. The bond distances r(X-H) involved in the reaction are taken as the CVs. The CVs used for each proton-transfer process are illustrated in Figures S1a–S3a. The force constant was set to 100 kcal/mol Å2, and the windows were set with an interval of δr = 0.1 Å following the convention in the literature. (43−47,108) We checked that the probability distribution of each window has a sufficient overlap, as shown in Figures S1c–S3c. QM/MM-MD simulations were performed for 10 ps by DFTB3 and for 12 ps by B3LYP-D3. The hydrogen atoms (protons) involved in the reaction were unconstrained, and thus the time step of the integration was set to δt = 0.5 fs. The canonical ensemble (NVT) simulation was performed at T = 300 K with τT = 0.5 ps for the Bussi thermostat. The structure was sampled every 5 fs in the last 10 ps of the simulation. The trajectory data were analyzed using the MBAR and path CV analyses to obtain the PMF. The MBAR and PMF analyses were performed using the analysis tools of GENESIS.

4. Results

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4.1. Performance

QM/MM calculations were performed for a water droplet (7014 atoms, 2338 water molecules) and TIM in solution (37 QM atoms and 37,182 MM atoms) to study the performance of GENESIS/QSimulate-QM. The timing data were obtained from MD simulations in an NVT condition with a time step of 2 fs for 100 steps (200 fs) and 5000 steps (10 ps) in DFT and DFTB, respectively.
In a water droplet system, water molecules within a radius r of a center were taken as a QM region, which was varied in size by changing r in a range of 3.0–6.0 Å (corresponding to 24–147 atoms). In Figure 1a, QM/MM-MD with DFTB3 shows a performance of more than 1 ns/day up to 114 atoms (or 380 electrons), which is achievable owing to the library interface developed in this work. The DFT calculations are an order of magnitude more expensive than DFTB3. Nonetheless, the performance is found to be more than 10 ps/day with PBE/def2-SVP and B3LYP-D3/aug-cc-pVDZ up to 96 and 45 atoms, respectively, using 2 nodes, and up to 147 and 66 atoms, respectively, using 8 nodes.

Figure 1

Figure 1. Performance of QM/MM-MD simulations combining GENESIS and QSimulate-QM. (a) Visualization of a water droplet and a QM region in the center (left). The timing data for a water droplet with increasing QM size using DFTB3, PBE/def2-SVP, and B3LYP/aug-cc-pVDZ. The total number of atoms is 7014. The computing node has two CPUs of Intel Xeon Gold 6148 (20 core 2.40 GHz), and 10 threads ×4MPI processes were assigned per node. (b) Visualization of TIM and an enlargement of the binding pocket (left). The timing data of TIM using 1 node (7 threads × 8 MPI processes) with various electronic structure methods (middle) and multiple nodes with B3LYP-D3/aug-cc-pVDZ (right). The number of QM and MM atoms are 35 and 37 182, respectively. The number of basis sets is 378 and 623 with def2-SVP and aug-cc-pVDZ, respectively. The computing node has two CPUs of Intel Xeon Platinum 8280 (28 core 2.70 GHz, AVX-512). The timing was measured in NVT condition with a time step of 2 fs.

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The results of TIM are displayed in Figure 1b. QM/MM-MD with DFTB3 shows a performance of 1.42 ns/day. The breakdown has found that portions of 63 and 29% of the time are spent for the calculation of DFTB3 and a nonbonded MM interaction, respectively. Therefore, the cost of MM calculations is non-negligible in a system with more than 30 000 atoms.
Among the DFT results, the pure DFT with moderate basis sets (PBE/def2-SVP) exhibits the best performance of 36.9 ps/day. The performance of PBE/aug-cc-pVDZ is decreased to 20.8 ps/day, because the use of diffuse functions (aug-cc-pVDZ) not only increases the number of basis sets but also makes the self-consistent field (SCF) convergence slower. The hybrid DFT, B3LYP-D3/aug-cc-pVDZ, is the most time-consuming due to the need of the Hartree–Fock exchange. Nonetheless, as shown in Figure 1b, the performance of B3LYP-D3 scales well with respect to the number of nodes. The best performance is obtained as 31.0 ps/day using 16 nodes (28 threads ×32 MPI). Interestingly, the result of 7 threads × 8 MPI reaches the maximum at 4 nodes, and a further increase in nodes leads to a drastic decrease of the performance, indicating the importance of a good balance between the number of threads and MPI processes. These results show that QM/MM-MD simulations of picoseconds and nanoseconds order is feasible at the level of DFT and DFTB, respectively, using GENESIS/QSimulate-QM.

4.2. Proton-Transfer Reactions in TIM

The mechanism of the conversion of DHAP to GAP is illustrated in Figure 2. In the first step, the proton H31 is transferred from DHAP to Glu165 of TIM. It is notable that the proton transfer is coupled with an electron transfer, where the negative charge migrates from Glu165 to the carboxylic acid of DHAP, varying the C2–C3 bond from a single to double bond. The negative charge of O2 drives the subsequent PTs of HE2 from His95 and HO3 from the ligand. Finally, the H31 of Glu165 returns to the ligand at C2 to yield GAP.

Figure 2

Figure 2. Schematic illustration of the conversion of DHAP to GAP with Glu165 and His95 of TIM. Protons are indicated in blue, and the electrons as well as CC/CO double bonds are in red.

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The five structures of the active site of TIM with the ligand, denoted I–V in the following, are shown in Figure 3. The X–H distances are listed in Table S3 of the Supporting Information. It is seen that the current procedure yields the intermediates and the product starting from the reactant. The energy minimization of each structure was converged in 20–50 iterations. These structures were obtained in 76.8 min using four computing nodes in total.

Figure 3

Figure 3. Structures of DHAP (I), intermediates (II–IV), and GAP (V) with His95 and Glu165 obtained by QM/MM calculations at the B3LYP-D3/aug-cc-pVDZ level of theory. The protons before and after the reaction are indicated in green and pink circles, respectively.

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Figure 4 shows the convergence of the string-method calculations in the first PT step (I → II). Both the energy and the pathway rapidly change in the first 10 iterations. The change is less pronounced during 10–50 iterations, and the convergence is achieved at the 93rd iteration. The energy profile of I → II gives a barrier height of 15.5 kcal mol–1 and an endothermic reaction energy of 11.7 kcal mol–1.

Figure 4

Figure 4. Convergence of an MEP search in the first PT step (I → II) with the string-method calculations.

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Although the pathway at the 50th iteration overlaps with the converged path around the transition state (TS) in Figure 4, notable changes are observed in the initial stage of the reaction. This stage corresponds to a rotation of a CH2 group, which makes the C3–H31 bond point toward the OE2 of Glu165 (see Movie S1). The path search in Cartesian coordinates enables to describe smooth changes in the structure space, thereby avoiding discontinuities caused by hidden coordinates.
Figures 5 and 6 compare the results of an MEP search in the whole PT processes obtained in the QM/MM calculations based on B3LYP-D3 and DFTB3. A stark difference is that the intermediate III, where His95 is deprotonated, is not a minimum but a TS in DFTB3. The error is ascribed to a known deficiency in DFTB3 to describe a deprotonated nitrogen due to the lack of d-type orbitals in the basis sets. (92) Furthermore, the energetics obtained by DFTB3 is 2–3 times larger than those obtained by B3LYP-D3 as listed in Table 1. For example, the relative energy of II is 11.7 and 28.0 kcal mol–1 in B3LYP-D3 and DFTB3, respectively. The proton affinity (PA) of DHAP at the level of B3LYP-D3 and DFTB3 is calculated to be different by 15.3 kcal mol–1 (Tables S4–S6), indicating that the error in the PA is not the primary cause. As shown in Figure 6, the N–H group of His95 is hydrogen-bonded with an anionic oxygen and a hydroxyl group of the ligand during II to IV. The hydrogen-bond network presumably leads the nitrogen atom toward a deprotonated state and incurs the error in DFTB3. This is mirrored in the product state (V), where GAP is remote from His95. The relative energy is obtained with a reasonable agreement as 8.0 and 12.0 kcal mol–1 using B3LYP-D3 and DFTB3, respectively.

Figure 5

Figure 5. Interatomic distances (left) and energetics (right) along MEPs obtained by QM/MM calculations at the level of (a) B3LYP-D3 and (b) DFTB3. The definition of r1 – r8 is given in Figure 2.

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Figure 6

Figure 6. Structure of the reactive site along the MEP and the relevant intermolecular distances (in Å) obtained by B3LYP-D3/aug-cc-pVDZ. Those of DFTB3 are also given in parentheses. Note that DFTB3 yields III as a transition state, so that TS2 and TS3 are not characterized.

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Table 1. Relative Energy of Minimum and TS Structures Relative to the Reactant (in kcal mol–1)
  I TS1 II TS2 III TS3 IV TS4 V
B3LYP-D3              
MEP 0.0 15.5 11.7 18.5 17.2 18.7 11.7 13.1 8.0
PMF 0.0 11.8 7.0 13.2 11.8 13.3 5.9 9.3 3.4
DFTB3              
MEP 0.0 31.1 28.0 51.6 49.1 51.7 32.0 33.3 12.0
PMF 0.0 25.6 20.2 50.7 50.5 51.6 33.5 35.7 15.5
Despite the large errors in the energetics, the structural change along the MEP of DFTB3 is found to be similar to that of B3LYP-D3 as shown in the left panel of Figure 5a,b. The difference in the motion of the MEP obtained by B3LYP-D3 and DFTB3 (Movies S1 and S2, respectively) is hardly discernible. The result suggests the possibility of a multilevel approach where the MEP obtained by DFTB may be used to correct the energetics using DFT.
The umbrella sampling simulations were performed for the PT reactions using the distances r1 – r8, shown in Figure 2 as CVs. The details of the CVs, windows, and the probability distribution of path CV are given in Figures S1–S3. The PMFs obtained by B3LYP-D3 and DFTB3 are shown as a function of Path CV in Figure 7. DFTB3 gives the free-energy barrier of ∼50 kcal mol–1, nearly 4 times larger compared to that of B3LYP-D3. The comparison of MEP and PMF summarized in Table 1 indicates that the entropic effect on the energy is less than 10 kcal mol–1. The free-energy barrier is obtained as 13 kcal mol–1 by B3LYP-D3 in good agreement with the experimental result. (109)

Figure 7

Figure 7. PMF as a function of Path CV obtained by B3LYP-D3 (left) and DFTB3 (right).

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Once the weight of each snapshot [eq 6] is obtained from MBAR, it can be used to derive the PMF in arbitrary coordinates. As an example, two-dimensional (2D) PMFs are plotted in Figure 8 as a function of various bond-forming/dissociating coordinates. The contour plots show that the configurations relevant for the reaction are sampled well. It is notable in Figure 8b that the minima around III is shallow and widely spread. The result indicates that two protons (HE2 and HO3) and a deprotonated His95 share an excess electron and stabilize the reactive motion to form a plateau potential. The PMF forms a channel in a diagonal direction, suggesting a concerted double proton transfer. Interestingly, the corresponding figure obtained by DFTB3 shown in Figure S4 shows a channel parallel to the reaction coordinates suggesting a stepwise mechanism.

Figure 8

Figure 8. 2D PMF of PT reactions obtained by QM/MM calculations at the B3LYP-D3/aug-cc-pVDZ level.

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5. Discussion and Perspectives

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In this study, the minimum-energy pathways and the free-energy profiles of enzymatic reactions are predicted using the hybrid QM/MM calculations implemented in GENESIS software. The benchmark calculations using four different electronic structure theories, namely, DFTB3, PBE/def2-SVP, PBE/aug-cc-pVDZ, and B3LYP-D3/aug-cc-pVDZ, have revealed efficient computations using QSimulate-QM as the electronic structure calculations. Since the precompiled binary of QSimulate-QM is linked as a shared library from the QM/MM interface program in GENESIS, we can avoid the large overhead that is required to exchange the energy and gradient information through file I/O between GENESIS and externally coupled electronic structure programs. The direct combination between GENESIS and QSimulate-QM in this way is efficient, in particular, for the DFTB3-level calculations, since the computational cost for the electronic structure calculations is rather comparable to the molecular mechanics calculations. The benchmark performance in the combination of QSimulate-QM/GENESIS suggests that the QM/MM-MD simulations become a useful research tool in chemical and biological problems without spending high computational resources. The free-energy calculations based on the QM/MM umbrella sampling or other enhanced sampling methods are important to take into account the entropic effects in the enzymatic reactions.
Comparisons of free-energy profiles obtained from different levels of the electronic structure calculations (DFTB3 vs B3LYP-D3) give us valuable lessons. To obtain sufficiently accurate energetics, ab initio electronic structure theories, such as B3LYP-D3, are inevitable. If we investigate the other chemical reactions with more complicated changes in the electronic structures, for instance, the reactions involving metal irons in a protein or a heme group, higher-level QM theories are necessary. Interestingly, the structures of TIM obtained in the QM/MM US simulations with DFTB3 and B3LYP-D3 are very similar to each other, suggesting that both of them are able to give us reliable local geometry of the chemical reactions. This suggests a possibility to perform QM/MM MD simulations and free-energy calculations using low-cost electronic structure theories, such as DFTB3. After the simulations, we can calibrate the free-energy profiles, computing more reliable potential energies of simulation snapshots using higher-level calculations (B3LYP-D3). Lee et al. (110−112) already examined the reliability and reproducibility of energetics using such schemes and pointed out the importance of overlapped distributions between high- and low-level QM or QM/MM MD simulations. Since the theoretical framework using MBAR as a reweighting method has been already established, it is important to increase our experiences in such calculations for examining the accuracy and reproducibility of the calibration using different levels of electronic calculations.
The QM/MM interface program in the GENESIS software has two unique features. In our previous paper, (69) a high-precision anharmonic vibrational analysis is shown to be possible in combination with the SINDO program. (74) For this application, a large number of the QM/MM single-point energy calculations on the grids near the energy minima are required to describe the potential energy surface. Accurate and high-performance calculations with QSimulate-QM are powerful for this purpose. Second, the QM/MM MD simulations with the speed of 1 ns/day are realized using DFTB3 as shown in this paper. This opens new possibilities to investigate the conformational dynamics of small- or medium-sized proteins on the time scales of 100 ns or longer using the QM/MM-MD simulations. The free-energy profiles of enzymatic reactions are now able to include the effect of conformational dynamics or an entropic effect more directly in the calculations. Enhanced conformational sampling algorithms and/or free-energy calculation methods in GENESIS, which have been originally implemented just for the classical MD simulations, are all available in the QM/MM calculations. Parallel MD simulation algorithms, such as REMD, gREST, and REUS, seem to be useful in the QM/MM-MD simulations with many replicas using massively parallel supercomputers like Fugaku.
The current version of GENESIS includes two different MD engines: ATDYN and SPDYN. ATDYN has been aimed to develop as a simple MD code with easy modifications for testing novel simulation algorithms. Therefore, CG and hybrid QM/MM models were easily implemented in ATDYN. However, if we aim to extend the simulations toward much larger systems, such as membrane proteins, ribosomes, DNA/RNA polymerases, and so on, the cost of molecular mechanics calculations are non-negligible. Also, the periodic boundary condition for QM/MM calculations (113−116) is more important to simulate membrane proteins and/or long DNA chains. In the future, we plan to implement the QM/MM calculations into SPDYN, allowing efficient spatial decomposition schemes for the parallelization of a whole simulation system and making the QM/MM calculations of huge biological systems possible. These approaches should be more important in understanding molecular mechanisms underlying the enzymatic reactions, designing biomacromolecules with new functions, and developing novel drugs that can control the regulation of functions of proteins related to diseases.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcb.1c01862.

  • Protocols of equilibration, interatomic distances, calculated total energies and proton affinities, Cartesian coordinates, details of umbrella sampling, 2D PMF obtained by DFTB3 (PDF)

  • Animation for the visualization of minimum-energy pathways from DHAP to GAP using QM/MM calculations at the level of B3LYP-D3/aug-cc-pVDZ (MP4)

  • Animation for the visualization of minimum-energy pathways from DHAP to GAP using QM/MM calculations at the levels of DFTB3 (MP4)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
    • Yuji Sugita - Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan;  Computational Biophysics Research Team, RIKEN Center for Computational Science, 7-1-26 minatojima-Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan;  Laboratory for Biomolecular Function Simulation, RIKEN Center for Biosystems Dynamics Research, 1-6-5 minatojima-Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan;  Orcidhttp://orcid.org/0000-0001-9738-9216;  Email: [email protected]
  • Authors
    • Kiyoshi Yagi - Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan;  Orcidhttp://orcid.org/0000-0003-1120-9355
    • Shingo Ito - Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
  • Notes
    The authors declare no competing financial interest.

    Data Availability. The data that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

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This research is partially supported by RIKEN Pioneering Research Projects (Dynamic Structural Biology/Glycolipidologue Initiative) (to Y.S.), RIKEN Incentive Research Project (to K.Y.), Program for Promoting Research on the Supercomputer Fugaku (Biomolecular dynamics in a living cell/MD-driven Precision Medicine), MEXT/KAKENHI Grant No. JP19H05645 (to Y.S.) and JP20H02701 (to K.Y.). We used the computer system HOKUSAI, provided by the RIKEN Information System Division, and Oakbridge-CX and Octopus, provided by the University of Tokyo and Osaka University, respectively, through the HPCI System Research Project (hp200098). We thank Prof. Y. Matsunaga (Saitama Univ.) for his helpful comments on the free-energy calculations. Dr. T. Shiozaki (QSimulate Inc.) is acknowledged for helping us develop the GENESIS/QSimulate-QM interface program. Dr. Y. Akinaga (VINAS Co., Ltd.) is acknowledged for his help to implement the string-method routines into GENESIS.

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    Further Optimization of a Hybrid United-Atom and Coarse-Grained Force Field for Folding Simulations: Improved Backbone Hydration and Interactions between Charged Side Chains
    Han, Wei; Schulten, Klaus
    Journal of Chemical Theory and Computation (2012), 8 (11), 4413-4424CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    PACE, a hybrid force field that couples united-atom protein models with coarse-grained (CG) solvent, has been further optimized, aiming to improve its efficiency for folding simulations. Backbone hydration parameters have been reoptimized based on hydration free energies of polyalanyl peptides through atomistic simulations. Also, atomistic partial charges from all-atom force fields were combined with PACE to provide a more realistic description of interactions between charged groups. Using replica exchange mol. dynamics, ab initio folding using the new PACE has been achieved for seven small proteins (16-23 residues) with different structural motifs. Exptl. data about folded states, such as their stability at room temp., m.p., and NMR nuclear Overhauser effect constraints, were also well reproduced. Moreover, a systematic comparison of folding kinetics at room temp. has been made with expts., through std. mol. dynamics simulations, showing that the new PACE may accelerate the actual folding kinetics 5-10-fold, permitting now the study of folding mechanisms. In particular, we used the new PACE to fold a 73-residue protein, α3D, in multiple 10-30 μs simulations, to its native states (Cα root-mean-square deviation of ∼0.34 nm). Our results suggest the potential applicability of the new PACE for the study of folding and dynamics of proteins.
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  13. 13
    Seo, S.; Shinoda, W. SPICA Force Field for Lipid Membranes: Domain Formation Induced by Cholesterol. J. Chem. Theory Comput. 2019, 15, 762– 774,  DOI: 10.1021/acs.jctc.8b00987
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    13
    SPICA force field for lipid membranes: Domain formation induced by cholesterol
    Seo, Sangjae; Shinoda, Wataru
    Journal of Chemical Theory and Computation (2019), 15 (1), 762-774CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Heterogeneity is essential for multicomponent lipid membranes. Esp., sterol-induced domain formation in membranes has recently attracted attention because of its biol. importance. To investigate such membrane domains at the mol. level, coarse-grained mol. dynamics (CG-MD) simulations are a promising approach since they allow one to consider the temporal and spatial scales involved in domain formation. Here, we present a new CG force field, named SPICA, which can accurately predict domain formation within various lipids in membranes. The SPICA force field was developed as an extension of a previous CG model, known as SDK (Shinoda-DeVane-Klein), in which membrane properties such as tension, elasticity, and structure are well-reproduced. By examg. domain formation in a series of ternary lipid bilayers, we obsd. a sepn. into liq.-ordered and liq.-disordered phases fully consistent with exptl. observations. Importantly, it was shown that the SPICA force field could detect the different phase behavior that results from subtle differences in the lipid compn. of the bilayer.
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  14. 14
    Yu, I.; Mori, T.; Ando, T.; Harada, R.; Jung, J.; Sugita, Y.; Feig, M. Biomolecular Interactions Modulate Macromolecular Structure and Dynamics in Atomistic Model of a Bacterial Cytoplasm. eLife 2016, 5, 18457,  DOI: 10.7554/eLife.19274
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  15. 15
    von Bülow, S.; Siggel, M.; Linke, M.; Hummer, G. Dynamic cluster formation determines viscosity and diffusion in dense protein solutions. Proc. Natl. Acad. Sci. U. S. A. 2019, 116, 9843– 9852,  DOI: 10.1073/pnas.1817564116
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    Jung, J.; Nishima, W.; Daniels, M.; Bascom, G.; Kobayashi, C.; Adedoyin, A.; Wall, M.; Lappala, A.; Phillips, D.; Fischer, W.; Tung, C. S.; Schlick, T.; Sugita, Y.; Sanbonmatsu, K. Y. Scaling molecular dynamics beyond 100,000 processor cores for large-scale biophysical simulations. J. Comput. Chem. 2019, 40, 1919– 1930,  DOI: 10.1002/jcc.25840
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    16
    Scaling molecular dynamics beyond 100,000 processor cores for large-scale biophysical simulations
    Jung, Jaewoon; Nishima, Wataru; Daniels, Marcus; Bascom, Gavin; Kobayashi, Chigusa; Adedoyin, Adetokunbo; Wall, Michael; Lappala, Anna; Phillips, Dominic; Fischer, William; Tung, Chang-Shung; Schlick, Tamar; Sugita, Yuji; Sanbonmatsu, Karissa Y.
    Journal of Computational Chemistry (2019), 40 (21), 1919-1930CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    The growing interest in the complexity of biol. interactions is continuously driving the need to increase system size in biophys. simulations, requiring not only powerful and advanced hardware but adaptable software that can accommodate a large no. of atoms interacting through complex forcefields. To address this, we developed and implemented strategies in the GENESIS mol. dynamics package designed for large nos. of processors. Long-range electrostatic interactions were parallelized by minimizing the no. of processes involved in communication. A novel algorithm was implemented for nonbonded interactions to increase single instruction multiple data (SIMD) performance, reducing memory usage for ultra large systems. Memory usage for neighbor searches in real-space nonbonded interactions was reduced by approx. 80%, leading to significant speedup. Using exptl. data describing phys. 3D chromatin interactions, we constructed the first atomistic model of an entire gene locus (GATA4). Taken together, these developments enabled the first billion-atom simulation of an intact biomol. complex, achieving scaling to 65,000 processes (130,000 processor cores) with 1 ns/day performance. Published 2019. This article is a U. S. Government work and is in the public domain in the USA.
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    Singharoy, A. Atoms to Phenotypes: Molecular Design Principles of Cellular Energy Metabolism. Cell 2019, 179, 1098– 1111,  DOI: 10.1016/j.cell.2019.10.021
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    17
    Atoms to Phenotypes: Molecular Design Principles of Cellular Energy Metabolism
    Singharoy, Abhishek; Maffeo, Christopher; Delgado-Magnero, Karelia H.; Swainsbury, David J. K.; Sener, Melih; Kleinekathofer, Ulrich; Vant, John W.; Nguyen, Jonathan; Hitchcock, Andrew; Isralewitz, Barry; Teo, Ivan; Chandler, Danielle E.; Stone, John E.; Phillips, James C.; Pogorelov, Taras V.; Mallus, M. Ilaria; Chipot, Christophe; Luthey-Schulten, Zaida; Tieleman, D. Peter; Hunter, C. Neil; Tajkhorshid, Emad; Aksimentiev, Aleksei; Schulten, Klaus
    Cell (Cambridge, MA, United States) (2019), 179 (5), 1098-1111.e23CODEN: CELLB5; ISSN:0092-8674. (Cell Press)
    We report a 100-million atom-scale model of an entire cell organelle, a photosynthetic chromatophore vesicle from a purple bacterium, that reveals the cascade of energy conversion steps culminating in the generation of ATP from sunlight. Mol. dynamics simulations of this vesicle elucidate how the integral membrane complexes influence local curvature to tune photoexcitation of pigments. Brownian dynamics of small mols. within the chromatophore probe the mechanisms of directional charge transport under various pH and salinity conditions. Reproducing phenotypic properties from atomistic details, a kinetic model evinces that low-light adaptations of the bacterium emerge as a spontaneous outcome of optimizing the balance between the chromatophore's structural integrity and robust energy conversion. Parallels are drawn with the more universal mitochondrial bioenergetic machinery, from whence mol.-scale insights into the mechanism of cellular aging are inferred. Together, our integrative method and spectroscopic expts. pave the way to first-principles modeling of whole living cells.
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  18. 18
    Zhao, G.; Perilla, J. R.; Yufenyuy, E. L.; Meng, X.; Chen, B.; Ning, J.; Ahn, J.; Gronenborn, A. M.; Schulten, K.; Aiken, C.; Zhang, P. Mature HIV-1 capsid structure by cryo-electron microscopy and all-atom molecular dynamics. Nature 2013, 497, 643– 646,  DOI: 10.1038/nature12162
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    18
    Mature HIV-1 capsid structure by cryo-electron microscopy and all-atom molecular dynamics
    Zhao, Gongpu; Perilla, Juan R.; Yufenyuy, Ernest L.; Meng, Xin; Chen, Bo; Ning, Jiying; Ahn, Jinwoo; Gronenborn, Angela M.; Schulten, Klaus; Aiken, Christopher; Zhang, Peijun
    Nature (London, United Kingdom) (2013), 497 (7451), 643-646CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    Retroviral capsid proteins are conserved structurally but assemble into different morphologies. The mature human immunodeficiency virus-1 (HIV-1) capsid is best described by a fullerene cone' model, in which hexamers of the capsid protein are linked to form a hexagonal surface lattice that is closed by incorporating 12 capsid-protein pentamers. HIV-1 capsid protein contains an amino-terminal domain (NTD) comprising seven α-helixes and a β-hairpin, a carboxy-terminal domain (CTD) comprising four α-helixes, and a flexible linker with a 310-helix connecting the two structural domains. Structures of the capsid-protein assembly units have been detd. by x-ray crystallog.; however, structural information regarding the assembled capsid and the contacts between the assembly units is incomplete. Here we report the cryo-electron microscopy structure of a tubular HIV-1 capsid-protein assembly at 8 Å resoln. and the three-dimensional structure of a native HIV-1 core by cryo-electron tomog. The structure of the tubular assembly shows, at the three-fold interface, a three-helix bundle with crit. hydrophobic interactions. Mutagenesis studies confirm that hydrophobic residues in the center of the three-helix bundle are crucial for capsid assembly and stability, and for viral infectivity. The cryo-electron-microscopy structures enable modeling by large-scale mol. dynamics simulation, resulting in all-atom models for the hexamer-of-hexamer and pentamer-of-hexamer elements as well as for the entire capsid. Incorporation of pentamers results in closer trimer contacts and induces acute surface curvature. The complete at. HIV-1 capsid model provides a platform for further studies of capsid function and for targeted pharmacol. intervention.
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  19. 19
    Casalino, L.; AI-Driven Multiscale Simulations Illuminate Mechanisms of SARS-CoV-2 Spike Dynamics. bioRxiv 2020,  DOI: 10.1101/2020.11.19.390187 .
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    Shaw, D. E.; In Anton 2: Raising the Bar for Performance and Programmability in a Special-Purpose Molecular Dynamics Supercomputer, SC ’14: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, Nov 16–21, 2014; IEEE, 2014; pp 41– 53. DOI: 10.1109/SC.2014.9
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    Ohmura, I.; Morimoto, G.; Ohno, Y.; Hasegawa, A.; Taiji, M. MDGRAPE-4: a special-purpose computer system for molecular dynamics simulations. Philos. Trans. R. Soc., A 2014, 372, 20130387,  DOI: 10.1098/rsta.2013.0387
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    Harder, E.; Damm, W.; Maple, J.; Wu, C.; Reboul, M.; Xiang, J. Y.; Wang, L.; Lupyan, D.; Dahlgren, M. K.; Knight, J. L.; Kaus, J. W.; Cerutti, D. S.; Krilov, G.; Jorgensen, W. L.; Abel, R.; Friesner, R. A. OPLS3: A Force Field Providing Broad Coverage of Drug-like Small Molecules and Proteins. J. Chem. Theory Comput. 2016, 12, 281– 296,  DOI: 10.1021/acs.jctc.5b00864
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    22
    OPLS3: A Force Field Providing Broad Coverage of Drug-like Small Molecules and Proteins
    Harder, Edward; Damm, Wolfgang; Maple, Jon; Wu, Chuanjie; Reboul, Mark; Xiang, Jin Yu; Wang, Lingle; Lupyan, Dmitry; Dahlgren, Markus K.; Knight, Jennifer L.; Kaus, Joseph W.; Cerutti, David S.; Krilov, Goran; Jorgensen, William L.; Abel, Robert; Friesner, Richard A.
    Journal of Chemical Theory and Computation (2016), 12 (1), 281-296CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The parametrization and validation of the OPLS3 force field for small mols. and proteins are reported. Enhancements with respect to the previous version (OPLS2.1) include the addn. of off-atom charge sites to represent halogen bonding and aryl nitrogen lone pairs as well as a complete refit of peptide dihedral parameters to better model the native structure of proteins. To adequately cover medicinal chem. space, OPLS3 employs over an order of magnitude more ref. data and assocd. parameter types relative to other commonly used small mol. force fields (e.g., MMFF and OPLS_2005). As a consequence, OPLS3 achieves a high level of accuracy across performance benchmarks that assess small mol. conformational propensities and solvation. The newly fitted peptide dihedrals lead to significant improvements in the representation of secondary structure elements in simulated peptides and native structure stability over a no. of proteins. Together, the improvements made to both the small mol. and protein force field lead to a high level of accuracy in predicting protein-ligand binding measured over a wide range of targets and ligands (less than 1 kcal/mol RMS error) representing a 30% improvement over earlier variants of the OPLS force field.
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  23. 23
    Huang, J.; Rauscher, S.; Nawrocki, G.; Ran, T.; Feig, M.; de Groot, B. L.; Grubmüller, H.; MacKerell, A. D. CHARMM36m: an improved force field for folded and intrinsically disordered proteins. Nat. Methods 2017, 14, 71– 73,  DOI: 10.1038/nmeth.4067
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    23
    CHARMM36m: an improved force field for folded and intrinsically disordered proteins
    Huang, Jing; Rauscher, Sarah; Nawrocki, Grzegorz; Ran, Ting; Feig, Michael; de Groot, Bert L.; Grubmuller, Helmut; MacKerell, Alexander D. Jr
    Nature Methods (2017), 14 (1), 71-73CODEN: NMAEA3; ISSN:1548-7091. (Nature Publishing Group)
    The all-atom additive CHARMM36 protein force field is widely used in mol. modeling and simulations. We present its refinement, CHARMM36m (http://mackerell.umaryland.edu/charmm_ff.shtml), with improved accuracy in generating polypeptide backbone conformational ensembles for intrinsically disordered peptides and proteins.
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  24. 24
    Tian, C.; Kasavajhala, K.; Belfon, K. A. A.; Raguette, L.; Huang, H.; Migues, A. N.; Bickel, J.; Wang, Y.; Pincay, J.; Wu, Q.; Simmerling, C. ff19SB: Amino-Acid-Specific Protein Backbone Parameters Trained against Quantum Mechanics Energy Surfaces in Solution. J. Chem. Theory Comput. 2020, 16, 528– 552,  DOI: 10.1021/acs.jctc.9b00591
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    24
    ff19SB: Amino-Acid-Specific Protein Backbone Parameters Trained against Quantum Mechanics Energy Surfaces in Solution
    Tian Chuan; Kasavajhala Koushik; Belfon Kellon A A; Raguette Lauren; Huang He; Bickel John; Wang Yuzhang; Pincay Jorge; Simmerling Carlos; Tian Chuan; Kasavajhala Koushik; Belfon Kellon A A; Raguette Lauren; Huang He; Migues Angela N; Wang Yuzhang; Simmerling Carlos; Wu Qin
    Journal of chemical theory and computation (2020), 16 (1), 528-552 ISSN:.
    Molecular dynamics (MD) simulations have become increasingly popular in studying the motions and functions of biomolecules. The accuracy of the simulation, however, is highly determined by the molecular mechanics (MM) force field (FF), a set of functions with adjustable parameters to compute the potential energies from atomic positions. However, the overall quality of the FF, such as our previously published ff99SB and ff14SB, can be limited by assumptions that were made years ago. In the updated model presented here (ff19SB), we have significantly improved the backbone profiles for all 20 amino acids. We fit coupled φ/ψ parameters using 2D φ/ψ conformational scans for multiple amino acids, using as reference data the entire 2D quantum mechanics (QM) energy surface. We address the polarization inconsistency during dihedral parameter fitting by using both QM and MM in aqueous solution. Finally, we examine possible dependency of the backbone fitting on side chain rotamer. To extensively validate ff19SB parameters, and to compare to results using other Amber models, we have performed a total of ∼5 ms MD simulations in explicit solvent. Our results show that after amino-acid-specific training against QM data with solvent polarization, ff19SB not only reproduces the differences in amino-acid-specific Protein Data Bank (PDB) Ramachandran maps better but also shows significantly improved capability to differentiate amino-acid-dependent properties such as helical propensities. We also conclude that an inherent underestimation of helicity is present in ff14SB, which is (inexactly) compensated for by an increase in helical content driven by the TIP3P bias toward overly compact structures. In summary, ff19SB, when combined with a more accurate water model such as OPC, should have better predictive power for modeling sequence-specific behavior, protein mutations, and also rational protein design. Of the explicit water models tested here, we recommend use of OPC with ff19SB.
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    Best, R. B.; Zheng, W.; Mittal, J. Balanced Protein–Water Interactions Improve Properties of Disordered Proteins and Non-Specific Protein Association. J. Chem. Theory Comput. 2014, 10, 5113– 5124,  DOI: 10.1021/ct500569b
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    25
    Balanced Protein-Water Interactions Improve Properties of Disordered Proteins and Non-Specific Protein Association
    Best, Robert B.; Zheng, Wenwei; Mittal, Jeetain
    Journal of Chemical Theory and Computation (2014), 10 (11), 5113-5124CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Some frequently encountered deficiencies in all-atom mol. simulations, such as nonspecific protein-protein interactions being too strong, and unfolded or disordered states being too collapsed, suggest that proteins are insufficiently well solvated in simulations using current state-of-the-art force fields. To address these issues, we make the simplest possible change, by modifying the short-range protein-water pair interactions, and leaving all the water-water and protein-protein parameters unchanged. We find that a modest strengthening of protein-water interactions is sufficient to recover the correct dimensions of intrinsically disordered or unfolded proteins, as detd. by direct comparison with small-angle x-ray scattering (SAXS) and Forster resonance energy transfer (FRET) data. The modification also results in more realistic protein-protein affinities, and av. solvation free energies of model compds. which are more consistent with expt. Most importantly, we show that this scaling is small enough not to affect adversely the stability of the folded state, with only a modest effect on the stability of model peptides forming α-helix and β-sheet structures. The proposed adjustment opens the way to more accurate atomistic simulations of proteins, particularly for intrinsically disordered proteins, protein-protein assocn., and crowded cellular environments.
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  26. 26
    van der Spoel, D. Systematic design of biomolecular force fields. Curr. Opin. Struct. Biol. 2021, 67, 18– 24,  DOI: 10.1016/j.sbi.2020.08.006
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    26
    Systematic design of biomolecular force fields
    van der Spoel, David
    Current Opinion in Structural Biology (2021), 67 (), 18-24CODEN: COSBEF; ISSN:0959-440X. (Elsevier Ltd.)
    A review: Force fields for the study of biomols. have been developed in a predominantly org. manner by regular updates over half a century. Together with better algorithms and advances in computer technol., force fields have improved to yield more robust predictions. However, there are also indications to suggest that intramol. energy functions have not become better and that there still is room for improvement. In this review, systematic efforts toward development of novel force fields from scratch are described. This includes an est. of the complexity of the problem and the prerequisites in the form of data and algorithms. It is suggested that in order to make progress, an effort is needed to standardize ref. data and force field validation benchmarks.
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  27. 27
    Robustelli, P.; Piana, S.; Shaw, D. E. Developing a molecular dynamics force field for both folded and disordered protein states. Proc. Natl. Acad. Sci. U. S. A. 2018, 115, E4758– E4766,  DOI: 10.1073/pnas.1800690115
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    27
    Developing a molecular dynamics force field for both folded and disordered protein states
    Robustelli, Paul; Piana, Stefano; Shaw, David E.
    Proceedings of the National Academy of Sciences of the United States of America (2018), 115 (21), E4758-E4766CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Mol. dynamics (MD) simulation is a valuable tool for characterizing the structural dynamics of folded proteins and should be similarly applicable to disordered proteins and proteins with both folded and disordered regions. It has been unclear, however, whether any phys. model (force field) used in MD simulations accurately describes both folded and disordered proteins. Here, we select a benchmark set of 21 systems, including folded and disordered proteins, simulate these systems with six state-of-the art force fields, and compare the results to over 9000 available exptl. data points. We find that none of the tested force fields simultaneously provided accurate descriptions of folded proteins, of the dimensions of disordered proteins, and of the secondary structure propensities of disordered proteins. Guided by simulation results on a subset of our benchmark, however, we modified parameters of one force field, achieving excellent agreement with expt. for disordered proteins, while maintaining state-of-the-art accuracy for folded proteins. The resulting force field, a99SB-disp, should thus greatly expand the range of biol. systems amenable to MD simulation. A similar approach could be taken to improve other force fields.
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  28. 28
    Piana, S.; Robustelli, P.; Tan, D.; Chen, S.; Shaw, D. E. Development of a Force Field for the Simulation of Single-Chain Proteins and Protein–Protein Complexes. J. Chem. Theory Comput. 2020, 16, 2494– 2507,  DOI: 10.1021/acs.jctc.9b00251
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    28
    Development of a Force Field for the Simulation of Single-Chain Proteins and Protein-Protein Complexes
    Piana, Stefano; Robustelli, Paul; Tan, Dazhi; Chen, Songela; Shaw, David E.
    Journal of Chemical Theory and Computation (2020), 16 (4), 2494-2507CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The accuracy of atomistic physics-based force fields for the simulation of biol. macromols. has typically been benchmarked exptl. using biophys. data from simple, often single-chain systems. In the case of proteins, the careful refinement of force field parameters assocd. with torsion-angle potentials and the use of improved water models have enabled a great deal of progress toward the highly accurate simulation of such monomeric systems in both folded and, more recently, disordered states. In living organisms, however, proteins constantly interact with other macromols., such as proteins and nucleic acids, and these interactions are often essential for proper biol. function. Here, the authors show that state-of-the-art force fields tuned to provide an accurate description of both ordered and disordered proteins can be limited in their ability to accurately describe protein-protein complexes. This observation prompted us to perform an extensive reparameterization of one variant of the Amber protein force field. The objective involved refitting not only the parameters assocd. with torsion-angle potentials, but also the parameters used to model nonbonded interactions, the specification of which is expected to be central to the accurate description of multicomponent systems. The resulting force field, which the authors call DES-Amber, allows for more accurate simulations of protein-protein complexes, while still providing a state-of-the-art description of both ordered and disordered single-chain proteins. Despite the improvements, calcd. protein-protein assocn. free energies still appear to deviate substantially from expt., a result suggesting that more fundamental changes to the force field, such as the explicit treatment of polarization effects, may simultaneously further improve the modeling of single-chain proteins and protein-protein complexes.
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    Li, P.; Merz, K. M. Metal Ion Modeling Using Classical Mechanics. Chem. Rev. 2017, 117, 1564– 1686,  DOI: 10.1021/acs.chemrev.6b00440
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    Metal Ion Modeling Using Classical Mechanics
    Li, Pengfei; Merz, Kenneth M., Jr.
    Chemical Reviews (Washington, DC, United States) (2017), 117 (3), 1564-1686CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
    A review. Metal ions play significant roles in numerous fields including chem., geochem., biochem. and materials science. With computational tools increasingly becoming important in chem. research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aq. and solid phases. Herein we review both quantum and classical modeling strategies for metal ion contg. systems that have been developed over the past few decades. This review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond based models. Quantum mech. studies of metal ion contg. systems at the semiempirical, ab initio and d. functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion contg. systems.
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    Zhang, A.; Yu, H.; Liu, C.; Song, C. The Ca2+ permeation mechanism of the ryanodine receptor revealed by a multi-site ion model. Nat. Commun. 2020, 11, 922,  DOI: 10.1038/s41467-020-14573-w
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    The Ca2+ permeation mechanism of the ryanodine receptor revealed by a multi-site ion model
    Zhang, Aihua; Yu, Hua; Liu, Chunhong; Song, Chen
    Nature Communications (2020), 11 (1), 922CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
    Abstr.: Ryanodine receptors (RyR) are ion channels responsible for the release of Ca2+ from the sarco/endoplasmic reticulum and play a crucial role in the precise control of Ca2+ concn. in the cytosol. The detailed permeation mechanism of Ca2+ through RyR is still elusive. By using mol. dynamics simulations with a specially designed Ca2+ model, we show that multiple Ca2+ ions accumulate in the upper selectivity filter of RyR1, but only one Ca2+ can occupy and translocate in the narrow pore at a time, assisted by electrostatic repulsion from the Ca2+ within the upper selectivity filter. The Ca2+ is nearly fully hydrated with the first solvation shell intact during the whole permeation process. These results suggest a remote knock-on permeation mechanism and one-at-a-time occupation pattern for the hydrated Ca2+ within the narrow pore, uncovering the basis underlying the high permeability and low selectivity of the RyR channels.
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    Senn, H. M.; Thiel, W. QM/MM Methods for Biomolecular Systems. Angew. Chem., Int. Ed. 2009, 48, 1198– 1229,  DOI: 10.1002/anie.200802019
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    QM/MM methods for biomolecular systems
    Senn, Hans Martin; Thiel, Walter
    Angewandte Chemie, International Edition (2009), 48 (7), 1198-1229CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A review. Combined quantum-mechanics/mol.-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomol. systems. Quantum-mech. (QM) methods are required for describing chem. reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based mol. mechanics (MM) methods. Thus to model large biomols. the logical approach is to combine the two techniques and, to use a QM method for the chem. active region (e.g., substrates and co-factors in an enzymic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomol. systems at a reasonable computational effort while providing the necessary accuracy.
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    van der Kamp, M. W.; Mulholland, A. J. Combined Quantum Mechanics/Molecular Mechanics (QM/MM) Methods in Computational Enzymology. Biochemistry 2013, 52, 2708– 2728,  DOI: 10.1021/bi400215w
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    Combined Quantum Mechanics/Molecular Mechanics (QM/MM) Methods in Computational Enzymology
    van der Kamp, Marc W.; Mulholland, Adrian J.
    Biochemistry (2013), 52 (16), 2708-2728CODEN: BICHAW; ISSN:0006-2960. (American Chemical Society)
    A review. Computational enzymol. is a rapidly maturing field that is increasingly integral to understanding mechanisms of enzyme-catalyzed reactions and their practical applications. Combined quantum mechanics/mol. mechanics (QM/MM) methods are important in this field. By treating the reacting species with a quantum mech. method (i.e., a method that calcs. the electronic structure of the active site) and including the enzyme environment with simpler mol. mech. methods, enzyme reactions can be modeled. Here, we review QM/MM methods and their application to enzyme-catalyzed reactions to investigate fundamental and practical problems in enzymol. A range of QM/MM methods is available, from cheaper and more approx. methods, which can be used for mol. dynamics simulations, to highly accurate electronic structure methods. We discuss how modeling of reactions using such methods can provide detailed insight into enzyme mechanisms and illustrate this by reviewing some recent applications. We outline some practical considerations for such simulations. Further, we highlight applications that show how QM/MM methods can contribute to the practical development and application of enzymol., e.g., in the interpretation and prediction of the effects of mutagenesis and in drug and catalyst design.
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    Perspective: Quantum mechanical methods in biochemistry and biophysics
    Cui, Qiang
    Journal of Chemical Physics (2016), 145 (14), 140901/1-140901/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    A review. In this perspective article, I discuss several research topics relevant to quantum mech. (QM) methods in biophys. and biochem. applications. Due to the immense complexity of biol. problems, the key is to develop methods that are able to strike the proper balance of computational efficiency and accuracy for the problem of interest. Therefore, in addn. to the development of novel ab initio and d. functional theory based QM methods for the study of reactive events that involve complex motifs such as transition metal clusters in metalloenzymes, it is equally important to develop inexpensive QM methods and advanced classical or quantal force fields to describe different physicochem. properties of biomols. and their behaviors in complex environments. Maintaining a solid connection of these more approx. methods with rigorous QM methods is essential to their transferability and robustness. Comparison to diverse exptl. observables helps validate computational models and mechanistic hypotheses as well as driving further development of computational methodologies. (c) 2016 American Institute of Physics.
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    Cui, Q.; Pal, T.; Xie, L. Biomolecular QM/MM Simulations: What Are Some of the ″burning Issues″?. J. Phys. Chem. B 2021, 125, 689– 702,  DOI: 10.1021/acs.jpcb.0c09898
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    Biomolecular QM/MM Simulations: What Are Some of the "Burning Issues"?
    Cui, Qiang; Pal, Tanmoy; Xie, Luke
    Journal of Physical Chemistry B (2021), 125 (3), 689-702CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    A review. QM/MM simulations have become an indispensable tool in many chem. and biochem. investigations. Considering the tremendous degree of success, including recognition by a 2013 Nobel Prize in Chem., are there still "burning challenges" in QM/MM methods, esp. for biomol. systems. In this short Perspective, we discuss several issues that we believe greatly impact the robustness and quant. applicability of QM/MM simulations to many, if not all, biomols. We highlight these issues with observations and relevant advances from recent studies in our group and others in the field. Despite such limited scope, we hope the discussions are of general interest and will stimulate addnl. developments that help push the field forward in meaningful directions.
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    Warshel, A.; Karplus, M. Calculation of Ground and Excited State Potential Surfaces of Conjugated Molecules. I. Formulation and Parametrization. J. Am. Chem. Soc. 1972, 94, 5612– 5625,  DOI: 10.1021/ja00771a014
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    Calculation of ground and excited state potential surfaces of conjugated molecules. I. Formulation and parametrization
    Warshel, A.; Karplus, M.
    Journal of the American Chemical Society (1972), 94 (16), 5612-25CODEN: JACSAT; ISSN:0002-7863.
    A formulation is given for the consistent calcn. of ground and excited state potential surfaces of conjugated mols. The method is based on the formal sepn. of σ and π electrons, the former being represented by an empirical potential function and the latter by a semiempirical model of the Pariser-Parr-Pople type cor. for nearest-neighbor orbital overlap. A single parameter set represents all of the mol. properties considered; these include atomization energies, electronic excitation energies, ionization potentials, and the equil. geometries and vibrational frequencies of the ground and excited electronic states, and take account of all bond length and bond angle variations. To permit rapid detn. of the potential surfaces, the σ potential function and SCF-MO-configuration interaction energy of the π electrons are expressed as analytic functions of the mol. coordinates from which the first and second derivs. are obtainable. Applications to 1,3-butadiene, 1,3,5-hexatriene, α,ω-diphenyloctatetraene, and 1,3-cyclohexadiene are given.
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    Warshel, A.; Levitt, M. Theoretical Studies of Enzymic Reactions: Dielectric, Electrostatic and Steric Stabilization of the Carbonium Ion in the Reaction of Lysozyme. J. Mol. Biol. 1976, 103, 227– 249,  DOI: 10.1016/0022-2836(76)90311-9
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    Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme
    Warshel, A.; Levitt, M.
    Journal of Molecular Biology (1976), 103 (2), 227-49CODEN: JMOBAK; ISSN:0022-2836.
    A general method for detailed study of enzymic reactions is presented. The method considers the complete enzyme-substrate complex together with the surrounding solvent and evaluates all the different quantum mech. and classical energy factors that can affect the reaction pathway. These factors include the quantum mech. energies assocd. with bond cleavage and charge redistribution of the substrate and the classical energies of steric and electrostatic interactions between the substrate and the enzyme. The electrostatic polarization of the enzyme atoms and the orientation of the dipoles of the surrounding H2O mols. is simulated by a microscopic dielec. model. The solvation energy resulting from this polarization is considerable and must be included in any realistic calcn. of chem. reactions involving anything more than an isolated mol. in vacuo. Without it, acidic groups can never become ionized and the charge distribution on the substrate will not be reasonable. The same dielec. model can also be used to study the reaction of the substrate in soln. In this way the reaction in soln. can be compared with the enzymic reaction. The stability of the carbonium ion intermediate formed in the cleavage of a glycosidic bond by lysozyme was studied. Electrostatic stabilization is an important factor in increasing the rate of the reaction step that leads to the formation of the carbonium ion intermediate. Steric factors, such as the strain of the substrate on binding to lysozyme, do not seem to contribute significantly.
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    Field, M. J.; Bash, P. A.; Karplus, M. A Combined Quantum Mechanical and Molecular Mechanical Potential for Molecular Dynamics Simulations. J. Comput. Chem. 1990, 11, 700– 733,  DOI: 10.1002/jcc.540110605
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    A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations
    Field, Martin J.; Bash, Paul A.; Karplus, Martin
    Journal of Computational Chemistry (1990), 11 (6), 700-33CODEN: JCCHDD; ISSN:0192-8651.
    A combined quantum mech. (QM) and mol. mech. (MM) potential has been developed for the study of reactions in condensed phases. For the quantum mech. calcns. semiempirical methods of the MNDO and AM1 type are used, while the mol. mechanics part is treated with the HARMM force field. Specific prescriptions are given for the interactions between the QM and MM portions of the system; cases in which the QM and MM methodol. is applied to parts of the same mol. or to different mols. are considered. The details of the method and a range of test calcns., including comparisons with ab initio and exptl. results, are given. In many cases satisfactory results are obtained. However, there are limitations to this type of approach, some of which arise from the AM1 or MNDO methods themselves and others from the present QM/MM implementation. This suggests that it is important to test the applicability of the method to each particular case prior to its use. Possible areas of improvement in the methodol. are discussed.
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    Zhang, Y.; Liu, H.; Yang, W. Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface. J. Chem. Phys. 2000, 112, 3483,  DOI: 10.1063/1.480503
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    Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface
    Zhang, Yingkai; Liu, Haiyan; Yang, Weitao
    Journal of Chemical Physics (2000), 112 (8), 3483-3492CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    A new practical approach to studying enzyme reactions by combining ab initio QM/MM calcns. with free energy perturbation is presented. An efficient iterative optimization procedure has been developed to det. optimized structures and min. energy paths for a system with thousands of atoms on the ab initio QM/MM potential: the small QM sub-system is optimized using a quasi-Newton minimizer in redundant internal coordinates with ab initio QM/MM calcns., while the large MM sub-system is minimized by the truncated Newton method in Cartesian coordinates with only mol. mech. calcns. The above two optimization procedures are performed iteratively until they converge. With the detd. min. energy paths, free energy perturbation calcns. are carried out to det. the change in free energy along the reaction coordinate. Crit. to the success of the iterative optimization procedure and the free energy calcns. is the smooth connection between the QM and MM regions provided by a recently proposed pseudobond QM/MM approach [J. Chem. Phys. 110, 46 (1999)]. The methods have been demonstrated by studying the initial proton transfer step in the reaction catalyzed by the enzyme triosephosphate isomerase (TIM).
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    Hu, H.; Lu, Z.; Yang, W. QM/MM Minimum Free-Energy Path: Methodology and Application to Triosephosphate Isomerase. J. Chem. Theory Comput. 2007, 3, 390– 406,  DOI: 10.1021/ct600240y
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    QM/MM Minimum Free-Energy Path: Methodology and Application to Triosephosphate Isomerase
    Hu, Hao; Lu, Zhenyu; Yang, Weitao
    Journal of Chemical Theory and Computation (2007), 3 (2), 390-406CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Structural and energetic changes are two important characteristic properties of a chem. reaction process. In the condensed phase, studying these two properties is very challenging because of the great computational cost assocd. with the quantum mech. calcns. and phase space sampling. Although the combined quantum mechanics/mol. mechanics (QM/MM) approach significantly reduces the amt. of the quantum mech. calcns. and facilitates the simulation of soln.-phase and enzyme-catalyzed reactions, the required quantum mech. calcns. remain quite expensive and extensive sampling can be achieved routinely only with semiempirical quantum mech. methods. QM/MM simulations with ab initio QM methods, therefore, are often restricted to narrow regions of the potential energy surface such as the reactant, product and transition state, or the min.-energy path. Such ab initio QM/MM calcns. have previously been performed with the QM/MM-free energy (QM/MM-FE) method of Zhang et al. (J. Chem. Phys. 2000, 112, 3483-3492) to generate the free-energy profile along the reaction coordinate using free-energy perturbation calcns. at fixed structures of the QM subsystems. Results obtained with the QM/MM-FE method depend on the detn. of the min.-energy reaction path, which is based on local conformations of the protein/solvent environment and can be difficult to obtain in practice. To overcome the difficulties assocd. with the QM/MM-FE method and to further enhance the sampling of the MM environment conformations, we develop here a new method to det. the QM/MM min. free-energy path (QM/MM-MFEP) for chem.-reaction processes in soln. and in enzymes. Within the QM/MM framework, we express the free energy of the system as a function of the QM conformation, thus leading to a simplified potential of mean force (PMF) description for the thermodn. of the system. The free-energy difference between two QM conformations is evaluated by the QM/MM free-energy perturbation method. The free-energy gradients with respect to the QM degrees of freedom are calcd. from mol. dynamics simulations at given QM conformations. With the free energy and free-energy gradients in hand, we further implement chain-of-conformation optimization algorithms in the search for the reaction path on the free-energy surface without specifying a reaction coordinate. This method thus efficiently provides a unique min. free-energy path for soln. and enzyme reactions, with structural and energetic properties being detd. simultaneously. To further incorporate the dynamic contributions of the QM subsystem into the simulations, we develop the reaction path potential of Lu, et al. (J. Chem. Phys. 2004, 121, 89-100) for the min. free-energy path. The combination of the methods developed here presents a comprehensive and accurate treatment for the simulation of reaction processes in soln. and in enzymes with ab initio QM/MM methods. The method has been demonstrated on the first step of the reaction of the enzyme triosephosphate isomerase with good agreement with previous studies.
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    Hu, H.; Yang, W. Free Energies of Chemical Reactions in Solution and in Enzymes with Ab Initio Quantum Mechanics/Molecular Mechanics Methods. Annu. Rev. Phys. Chem. 2008, 59, 573– 601,  DOI: 10.1146/annurev.physchem.59.032607.093618
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    Free energies of chemical reactions in solution and in enzymes with ab initio quantum mechanics/molecular mechanics methods
    Hu, Hao; Yang, Weitao
    Annual Review of Physical Chemistry (2008), 59 (), 573-601CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews Inc.)
    A review. Combined quantum mechanics/mol. mechanics (QM/MM) methods provide an accurate and efficient energetic description of complex chem. and biol. systems, leading to significant advances in the understanding of chem. reactions in soln. and in enzymes. Here we review progress in QM/MM methodol. and applications, focusing on ab initio QM-based approaches. Ab initio QM/MM methods capitalize on the accuracy and reliability of the assocd. quantum-mech. approaches, however, at a much higher computational cost compared with semiempirical quantum-mech. approaches. Thus reaction-path and activation free-energy calcns. based on ab initio QM/MM methods encounter unique challenges in simulation timescales and phase-space sampling. This review features recent developments overcoming these challenges and enabling accurate free-energy detn. for reaction processes in soln. and in enzymes, along with applications.
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    Kosugi, T.; Hayashi, S. QM/MM Reweighting Free Energy SCF for Geometry Optimization on Extensive Free Energy Surface of Enzymatic Reaction. J. Chem. Theory Comput. 2012, 8, 322– 334,  DOI: 10.1021/ct2005837
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    QM/MM Reweighting Free Energy SCF for Geometry Optimization on Extensive Free Energy Surface of Enzymatic Reaction
    Kosugi, Takahiro; Hayashi, Shigehiko
    Journal of Chemical Theory and Computation (2012), 8 (1), 322-334CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We developed a quantum mech./mol. mech. (QM/MM) free energy geometry optimization method by which the geometry of a quantum chem. treated (QM) mol. is optimized on a free energy surface defined with thermal distribution of the surrounding mol. environment obtained by mol. dynamics simulation with a mol. mechanics (MM) force field. We applied the method to an enzymic reaction of a substrate complex of psychrophilic α-amylase from Antarctic bacterium Pseudoalteromonas haloplanktis and succeeded in geometry optimizations of the reactant and the product of the catalytic reaction that involve large conformational changes of protein loops adjacent to the reaction center on time scales reaching sub-microseconds. We found that the adjacent loops in the reactant and the product form in different conformations and produce catalytic ES potentials on the reaction center. The method called QM/MM reweighting free energy SCF combines a mean field theory of QM/MM free energy geometry optimization developed by Yamamoto with a reweighting scheme for updating the MM distribution introduced by Hu et al. and features high computational efficiency suitable for exploring the reaction free energy surface of extensive protein conformational space. The computational efficiency with improved treatment of a long-range electrostatic (ES) interaction using the Ewald summation technique permits one to take into account global conformational relaxation of an entire protein of an enzyme in the free energy geometry optimization of its reaction center.
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    Hayashi, S.; Uchida, Y.; Hasegawa, T.; Higashi, M.; Kosugi, T.; Kamiya, M. QM/MM Geometry Optimization on Extensive Free-Energy Surfaces for Examination of Enzymatic Reactions and Design of Novel Functional Properties of Proteins. Annu. Rev. Phys. Chem. 2017, 68, 135– 154,  DOI: 10.1146/annurev-physchem-052516-050827
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    QM/MM Geometry Optimization on Extensive Free-Energy Surfaces for Examination of Enzymatic Reactions and Design of Novel Functional Properties of Proteins
    Hayashi, Shigehiko; Uchida, Yoshihiro; Hasegawa, Taisuke; Higashi, Masahiro; Kosugi, Takahiro; Kamiya, Motoshi
    Annual Review of Physical Chemistry (2017), 68 (), 135-154CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)
    Many remarkable mol. functions of proteins use their characteristic global and slow conformational dynamics through coupling of local chem. states in reaction centers with global conformational changes of proteins. To theor. examine the functional processes of proteins in at. detail, a methodol. of quantum mech./mol. mech. (QM/MM) free-energy geometry optimization is introduced. In the methodol., a geometry optimization of a local reaction center is performed with a quantum mech. calcn. on a free-energy surface constructed with conformational samples of the surrounding protein environment obtained by a mol. dynamics simulation with a mol. mechanics force field. Geometry optimizations on extensive free-energy surfaces by a QM/MM reweighting free-energy SCF method designed to be variationally consistent and computationally efficient have enabled examns. of the multiscale mol. coupling of local chem. states with global protein conformational changes in functional processes and anal. and design of protein mutants with novel functional properties.
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    Rosta, E.; Woodcock, H. L.; Brooks, B. R.; Hummer, G. Artificial reaction coordinate “tunneling” in free-energy calculations: The catalytic reaction of RNase H. J. Comput. Chem. 2009, 30, 1634– 1641,  DOI: 10.1002/jcc.21312
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    Artificial reaction coordinate "tunneling" in free-energy calculations: The catalytic reaction of RNase H
    Rosta, Edina; Woodcock, H. Lee; Brooks, Bernard R.; Hummer, Gerhard
    Journal of Computational Chemistry (2009), 30 (11), 1634-1641CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    We describe a method for the systematic improvement of reaction coordinates in quantum mech./mol. mech. (QM/MM) calcns. of reaction free-energy profiles. In umbrella-sampling free-energy calcns., a biasing potential acting on a chosen reaction coordinate is used to sample the system in reactant, product, and transition states. Sharp, nearly discontinuous changes along the resulting reaction path are used to identify coordinates that are relevant for the reaction but not properly sampled. These degrees of freedom are then included in an extended reaction coordinate. The general formalism is illustrated for the catalytic cleavage of the RNA backbone of an RNA/DNA hybrid duplex by the RNase H enzyme of Bacillus halodurans. We find that in the initial attack of the phosphate diester by water, the oxygen-phosphorus distances alone are not sufficient as reaction coordinates, resulting in substantial hysteresis in the proton degrees of freedom and a barrier that is too low (∼10 kcal/mol). If the proton degrees of freedom are included in an extended reaction coordinate, we obtain a barrier of 21.6 kcal/mol consistent with the exptl. rates. As the barrier is approached, the attacking water mol. transfers one of its protons to the O1P oxygen of the phosphate group. At the barrier top, the resulting hydroxide ion forms a penta-coordinated phosphate intermediate. The method used to identify important degrees of freedom, and the procedure to optimize the reaction coordinate are general and should be useful both in classical and in QM/MM free-energy calcns. © 2009 Wiley Periodicals, Inc. J Comput Chem 30, 1634-1641, 2009.
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    Rosta, E.; Nowotny, M.; Yang, W.; Hummer, G. Catalytic Mechanism of RNA Backbone Cleavage by Ribonuclease H from Quantum Mechanics/Molecular Mechanics Simulations. J. Am. Chem. Soc. 2011, 133, 8934– 8941,  DOI: 10.1021/ja200173a
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    Catalytic Mechanism of RNA Backbone Cleavage by Ribonuclease H from Quantum Mechanics/Molecular Mechanics Simulations
    Rosta, Edina; Nowotny, Marcin; Yang, Wei; Hummer, Gerhard
    Journal of the American Chemical Society (2011), 133 (23), 8934-8941CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    We use quantum mechanics/mol. mechanics simulations to study the cleavage of the RNA (RNA) backbone catalyzed by RNase H. This protein is a prototypical member of a large family of enzymes that use two-metal catalysis to process nucleic acids. By combining Hamiltonian replica exchange with a finite-temp. string method, we calc. the free energy surface underlying the RNA-cleavage reaction and characterize its mechanism. We find that the reaction proceeds in two steps. In a first step, catalyzed primarily by magnesium ion A and its ligands, a water mol. attacks the scissile phosphate. Consistent with thiol-substitution expts., a water proton is transferred to the downstream phosphate group. The transient phosphorane formed as a result of this nucleophilic attack decays by breaking the bond between the phosphate and the ribose oxygen. In the resulting intermediate, the dissocd. but unprotonated leaving group forms an alkoxide coordinated to magnesium ion B. In a second step, the reaction is completed by protonation of the leaving group, with a neutral Asp132 as a likely proton donor. The overall reaction barrier of ∼15 kcal mol-1, encountered in the first step, together with the cost of protonating Asp132, is consistent with the slow measured rate of ∼1-100/min. The two-step mechanism is also consistent with the bell-shaped pH dependence of the reaction rate. The nonmonotonic relative motion of the magnesium ions along the reaction pathway agrees with X-ray crystal structures. Proton-transfer reactions and changes in the metal ion coordination emerge as central factors in the RNA-cleavage reaction.
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    Rosta, E.; Yang, W.; Hummer, G. Calcium Inhibition of Ribonuclease H1 Two-Metal Ion Catalysis. J. Am. Chem. Soc. 2014, 136, 3137– 3144,  DOI: 10.1021/ja411408x
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    Calcium inhibition of ribonuclease H1 two-metal ion catalysis
    Rosta, Edina; Yang, Wei; Hummer, Gerhard
    Journal of the American Chemical Society (2014), 136 (8), 3137-3144CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Most phosphate-processing enzymes require Mg2+ as a cofactor to catalyze nucleotide cleavage and transfer reactions. Ca2+ ions inhibit many of these enzymic activities, despite Ca2+ and Mg2+ having comparable binding affinities and overall biol. abundances. Here, the authors studied the mol. details of the Ca2+ inhibition mechanism for phosphodiester cleavage, an essential reaction in the metab. of nucleic acids and nucleotides, by comparing Ca2+- and Mg2+-catalyzed reactions. The authors studied the functional roles of specific metal ion sites A and B in enabling the catalytic cleavage of an RNA/DNA hybrid substrate by Bacillus halodurans RNase H1 using hybrid quantum-mechanics/mol. mechanics (QM/MM) free energy calcns. The authors found that Ca2+ substitution of either of the 2 active site Mg2+ ions substantially increased the height of the reaction barrier and thereby abolished the catalytic activity. Remarkably, Ca2+ at the A site was inactive also in Mg2+-optimized active site structures along the reaction path, whereas Mg2+ substitution recovered activity in Ca2+-optimized structures. Geometric changes resulting from Ca2+ substitution at metal ion site A may thus be a secondary factor in the loss of catalytic activity. By contrast, at metal ion site B geometry played a more important role, with only a partial recovery of activity after Mg2+ substitution in Ca2+-optimized structures. Ca2+-substitution also led to a change in mechanism, with deprotonation of the water nucleophile requiring a closer approach to the scissile phosphate, which in turn increased the barrier. As a result, Ca2+ was less efficient in activating the water. As a likely cause for the different reactivities of Mg2+ and Ca2+ ions in site A, the authors identified differences in charge transfer to the ions and the assocd. decrease in the pKa of the oxygen nucleophile attacking the phosphate group.
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  46. 46
    Ganguly, A.; Thaplyal, P.; Rosta, E.; Bevilacqua, P. C.; Hammes-Schiffer, S. Quantum mechanical/molecular mechanical free energy simulations of the self-cleavage reaction in the hepatitis delta virus ribozyme. J. Am. Chem. Soc. 2014, 136, 1483– 1496,  DOI: 10.1021/ja4104217
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    46
    Quantum Mechanical/Molecular Mechanical Free Energy Simulations of the Self-Cleavage Reaction in the Hepatitis Delta Virus Ribozyme
    Ganguly, Abir; Thaplyal, Pallavi; Rosta, Edina; Bevilacqua, Philip C.; Hammes-Schiffer, Sharon
    Journal of the American Chemical Society (2014), 136 (4), 1483-1496CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The hepatitis delta virus (HDV) ribozyme catalyzes a self-cleavage reaction using a combination of nucleobase and metal ion catalysis. Both divalent and monovalent ions can catalyze this reaction, although the rate is slower with monovalent ions alone. Herein, we use quantum mech./mol. mech. (QM/MM) free energy simulations to investigate the mechanism of this ribozyme and to elucidate the roles of the catalytic metal ion. With Mg2+ at the catalytic site, the self-cleavage mechanism is obsd. to be concerted with a phosphorane-like transition state and a free energy barrier of ∼13 kcal/mol, consistent with free energy barrier values extrapolated from exptl. studies. With Na+ at the catalytic site, the mechanism is obsd. to be sequential, passing through a phosphorane intermediate, with free energy barriers of 2-4 kcal/mol for both steps; moreover, proton transfer from the exocyclic amine of protonated C75 to the nonbridging oxygen of the scissile phosphate occurs to stabilize the phosphorane intermediate in the sequential mechanism. To explain the slower rate obsd. exptl. with monovalent ions, we hypothesize that the activation of the O2' nucleophile by deprotonation and orientation is less favorable with Na+ ions than with Mg2+ ions. To explore this hypothesis, we exptl. measure the pKa of O2' by kinetic and NMR methods and find it to be lower in the presence of divalent ions rather than only monovalent ions. The combined theor. and exptl. results indicate that the catalytic Mg2+ ion may play three key roles: assisting in the activation of the O2' nucleophile, acidifying the general acid C75, and stabilizing the nonbridging oxygen to prevent proton transfer to it.
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  47. 47
    Zhang, S.; Ganguly, A.; Goyal, P.; Bingaman, J. L.; Bevilacqua, P. C.; Hammes-Schiffer, S. Role of the active site guanine in the glmS ribozyme self-cleavage mechanism: Quantum mechanical/molecular mechanical free energy simulations. J. Am. Chem. Soc. 2015, 137, 784– 798,  DOI: 10.1021/ja510387y
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    Role of the Active Site Guanine in the glmS Ribozyme Self-Cleavage Mechanism: Quantum Mechanical/Molecular Mechanical Free Energy Simulations
    Zhang, Sixue; Ganguly, Abir; Goyal, Puja; Bingaman, Jamie L.; Bevilacqua, Philip C.; Hammes-Schiffer, Sharon
    Journal of the American Chemical Society (2015), 137 (2), 784-798CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The glmS ribozyme catalyzes a self-cleavage reaction at the phosphodiester bond between residues A-1 and G1. This reaction is thought to occur by an acid-base mechanism involving the glucosamine-6-phosphate cofactor and G40 residue. Herein quantum mech./mol. mech. free energy simulations and pKa calcns., as well as exptl. measurements of the rate const. for self-cleavage, are utilized to elucidate the mechanism, particularly the role of G40. Our calcns. suggest that an external base deprotonates either G40(N1) or possibly A-1(O2'), which would be followed by proton transfer from G40(N1) to A-1(O2'). After this initial deprotonation, A-1(O2') starts attacking the phosphate as a hydroxyl group, which is hydrogen-bonded to deprotonated G40, concurrent with G40(N1) moving closer to the hydroxyl group and directing the in-line attack. Proton transfer from A-1(O2') to G40 is concomitant with attack of the scissile phosphate, followed by the remainder of the cleavage reaction. A mechanism in which an external base does not participate, but rather the proton transfers from A-1(O2') to a nonbridging oxygen during nucleophilic attack, was also considered but deemed to be less likely due to its higher effective free energy barrier. The calcd. rate const. for the favored mechanism is in agreement with the exptl. rate const. measured at biol. Mg2+ ion concn. According to these calcns., catalysis is optimal when G40 has an elevated pKa rather than a pKa shifted toward neutrality, although a balance among the pKa's of A-1, G40, and the nonbridging oxygen is essential. These results have general implications, as the hammerhead, hairpin, and twister ribozymes have guanines at a similar position as G40.
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    Li, P.; Soudackov, A. V.; Hammes-Schiffer, S. Fundamental Insights into Proton-Coupled Electron Transfer in Soybean Lipoxygenase from Quantum Mechanical/Molecular Mechanical Free Energy Simulations. J. Am. Chem. Soc. 2018, 140, 3068– 3076,  DOI: 10.1021/jacs.7b13642
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    Fundamental Insights into Proton-Coupled Electron Transfer in Soybean Lipoxygenase from Quantum Mechanical/Molecular Mechanical Free Energy Simulations
    Li, Pengfei; Soudackov, Alexander V.; Hammes-Schiffer, Sharon
    Journal of the American Chemical Society (2018), 140 (8), 3068-3076CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The proton-coupled electron transfer (PCET) reaction catalyzed by soybean lipoxygenase has served as a prototype for understanding hydrogen tunneling in enzymes. Herein this PCET reaction is studied with mixed quantum mech./mol. mech. (QM/MM) free energy simulations. The free energy surfaces are computed as functions of the proton donor-acceptor (C-O) distance and the proton coordinate, and the potential of mean force is computed as a function of the C-O distance, inherently including anharmonicity. The simulation results are used to calc. the kinetic isotope effects for the wild-type enzyme (WT) and the L546A/L754A double mutant (DM), which have been measured exptl. to be ∼80 and ∼700, resp. The PCET reaction is found to be exoergic for WT and slightly endoergic for the DM, and the equil. C-O distance for the reactant is found to be ∼0.2 Å greater for the DM than for WT. The larger equil. distance for the DM, which is due mainly to less optimal substrate binding in the expanded binding cavity, is primarily responsible for its higher kinetic isotope effect. The calcd. potentials of mean force are anharmonic and relatively soft at shorter C-O distances, allowing efficient thermal sampling of the shorter distances required for effective hydrogen tunneling. The primarily local electrostatic field at the transferring hydrogen is ∼100 MV/cm in the direction to facilitate proton transfer and increases dramatically as the C-O distance decreases. These simulations suggest that the overall protein environment is important for conformational sampling of active substrate configurations aligned for proton transfer, but the PCET reaction is influenced primarily by local electrostatic effects that facilitate conformational sampling of shorter proton donor-acceptor distances required for effective hydrogen tunneling.
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    Stevens, D. R.; Hammes-Schiffer, S. Exploring the Role of the Third Active Site Metal Ion in DNA Polymerase η with QM/MM Free Energy Simulations. J. Am. Chem. Soc. 2018, 140, 8965– 8969,  DOI: 10.1021/jacs.8b05177
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    Exploring the Role of the Third Active Site Metal Ion in DNA Polymerase η with QM/MM Free Energy Simulations
    Stevens, David R.; Hammes-Schiffer, Sharon
    Journal of the American Chemical Society (2018), 140 (28), 8965-8969CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The enzyme human DNA polymerase η (Pol η) is crit. for bypassing lesions during DNA replication. In addn. to the two Mg2+ ions aligning the active site, expts. suggest that a third Mg2+ ion could play an essential catalytic role. Herein the role of this third metal ion is investigated with quantum mech./mol. mech. (QM/MM) free energy simulations of the phosphoryl transfer reaction and a proposed self-activating proton transfer from the incoming nucleotide to the pyrophosphate leaving group. The simulations with only two metal ions in the active site support a sequential mechanism, with phosphoryl transfer followed by relatively fast proton transfer. The simulations with three metal ions in the active site suggest that the third metal ion may play a catalytic role through electrostatic interactions with the leaving group. These electrostatic interactions stabilize the product, making the phosphoryl transfer reaction more thermodynamically favorable with a lower free energy barrier relative to the activated state corresponding to the deprotonated 3'OH nucleophile, and also inhibit the subsequent proton transfer.
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    Li, P.; Rangadurai, A.; Al-Hashimi, H. M.; Hammes-Schiffer, S. Environmental Effects on Guanine-Thymine Mispair Tautomerization Explored with Quantum Mechanical/Molecular Mechanical Free Energy Simulations. J. Am. Chem. Soc. 2020, 142, 11183– 11191,  DOI: 10.1021/jacs.0c03774
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    Environmental Effects on Guanine-Thymine Mispair Tautomerization Explored with Quantum Mechanical/Molecular Mechanical Free Energy Simulations
    Li, Pengfei; Rangadurai, Atul; Al-Hashimi, Hashim M.; Hammes-Schiffer, Sharon
    Journal of the American Chemical Society (2020), 142 (25), 11183-11191CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    DNA bases can adopt energetically unfavorable tautomeric forms that enable the formation of Watson-Crick-like (WC-like) mispairs, which have been proposed to give rise to spontaneous mutations in DNA and misincorporation errors in DNA replication and translation. Previous NMR and computational studies have indicated that the population of WC-like guanine-thymine (G-T) mispairs depends on the environment, such as the local nucleic acid sequence and solvation. To investigate these environmental effects, herein G-T mispair tautomerization processes are studied computationally in aq. soln., in A-form and B-form DNA duplexes, and within the active site of a DNA polymerase λ variant. The wobble G-T (wG-T), WC-like G-T*, and WC-like G*-T forms are considered, where * indicates the enol tautomer of the base. The min. free energy paths for the tautomerization from the wG-T to the WC-like G-T* and from the WC-like G-T* to the WC-like G*-T are computed with mixed quantum mech./mol. mech. (QM/MM) free energy simulations. The reaction free energies and free energy barriers are found to be significantly influenced by the environment. The wG-T→ G-T* tautomerization is predicted to be endoergic in aq. soln. and the DNA duplexes but slightly exoergic in the polymerase, with Arg517 and Asn513 providing electrostatic stabilization of G-T*. The G-T*→ G*-T tautomerization is also predicted to be slightly more thermodynamically favorable in the polymerase relative to these DNA duplexes. These simulations are consistent with an exptl. driven kinetic misincorporation model suggesting that G-T mispair tautomerization occurs in the ajar polymerase conformation or concertedly with the transition from the ajar to the closed polymerase conformation. Furthermore, the order of the assocd. two proton transfer reactions is predicted to be different in the polymerase than in aq. soln. and the DNA duplexes. These studies highlight the impact of the environment on the thermodn., kinetics, and fundamental mechanisms of G-T mispair tautomerization, which plays a role in a wide range of biochem. important processes.
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    Walker, R. C.; Crowley, M. F.; Case, D. A. The Implementation of a Fast and Accurate QM/MM Potential Method in Amber. J. Comput. Chem. 2008, 29, 1019– 1031,  DOI: 10.1002/jcc.20857
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    The implementation of a fast and accurate QM/MM potential method in Amber
    Walker, Ross C.; Crowley, Michael F.; Case, David A.
    Journal of Computational Chemistry (2008), 29 (7), 1019-1031CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    Version 9 of the Amber simulation programs includes a new semiempirical hybrid QM/MM functionality. This includes support for implicit solvent (generalized Born) and for periodic explicit solvent simulations using a newly developed QM/MM implementation of the particle mesh Ewald (PME) method. The code provides sufficiently accurate gradients to run const. energy QM/MM MD simulations for many nanoseconds. The link atom approach used for treating the QM/MM boundary shows improved performance, and the user interface has been rewritten to bring the format into line with classical MD simulations. Support is provided for the PM3, PDDG/PM3, PM3CARB1, AM1, MNDO, and PDDG/MNDO semiempirical Hamiltonians as well as the self-consistent charge d. functional tight binding (SCC-DFTB) method. Performance has been improved to the point where using QM/MM, for a QM system of 71 atoms within an explicitly solvated protein using periodic boundaries and PME requires less than twice the cpu time of the corresponding classical simulation.
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    Götz, A. W.; Clark, M. A.; Walker, R. C. An Extensible Interface for QM/MM Molecular Dynamics Simulations with AMBER. J. Comput. Chem. 2014, 35, 95– 108,  DOI: 10.1002/jcc.23444
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    An extensible interface for QM/MM molecular dynamics simulations with AMBER
    Gotz Andreas W; Clark Matthew A; Walker Ross C
    Journal of computational chemistry (2014), 35 (2), 95-108 ISSN:.
    We present an extensible interface between the AMBER molecular dynamics (MD) software package and electronic structure software packages for quantum mechanical (QM) and mixed QM and classical molecular mechanical (MM) MD simulations within both mechanical and electronic embedding schemes. With this interface, ab initio wave function theory and density functional theory methods, as available in the supported electronic structure software packages, become available for QM/MM MD simulations with AMBER. The interface has been written in a modular fashion that allows straight forward extensions to support additional QM software packages and can easily be ported to other MD software. Data exchange between the MD and QM software is implemented by means of files and system calls or the message passing interface standard. Based on extensive tests, default settings for the supported QM packages are provided such that energy is conserved for typical QM/MM MD simulations in the microcanonical ensemble. Results for the free energy of binding of calcium ions to aspartate in aqueous solution comparing semiempirical and density functional Hamiltonians are shown to demonstrate features of this interface.
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    Melo, M. C. R.; Bernardi, R. C.; Rudack, T.; Scheurer, M.; Riplinger, C.; Phillips, J. C.; Maia, J. D. C.; Rocha, G. B.; Ribeiro, J. V.; Stone, J. E.; Neese, F.; Schulten, K.; Luthey-Schulten, Z. NAMD goes quantum: an integrative suite for hybrid simulations. Nat. Methods 2018, 15, 351– 354,  DOI: 10.1038/nmeth.4638
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    NAMD goes quantum: an integrative suite for hybrid simulations
    Melo, Marcelo C. R.; Bernardi, Rafael C.; Rudack, Till; Scheurer, Maximilian; Riplinger, Christoph; Phillips, James C.; Maia, Julio D. C.; Rocha, Gerd B.; Ribeiro, Joao V.; Stone, John E.; Neese, Frank; Schulten, Klaus; Luthey-Schulten, Zaida
    Nature Methods (2018), 15 (5), 351-354CODEN: NMAEA3; ISSN:1548-7091. (Nature Research)
    Hybrid methods that combine quantum mechanics (QM) and mol. mechanics (MM) can be applied to studies of reaction mechanisms in locations ranging from active sites of small enzymes to multiple sites in large bioenergetic complexes. By combining the widely used mol. dynamics and visualization programs NAMD and VMD with the quantum chem. packages ORCA and MOPAC, we created an integrated, comprehensive, customizable, and easy-to-use suite (http://www.ks.uiuc.edu/Research/qmmm). Through the QwikMD interface, setup, execution, visualization, and anal. are streamlined for all levels of expertise.
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    Jung, J.; Kobayashi, C.; Kasahara, K.; Tan, C.; Kuroda, A.; Minami, K.; Ishiduki, S.; Nishiki, T.; Inoue, H.; Ishikawa, Y.; Feig, M.; Sugita, Y. New parallel computing algorithm of molecular dynamics for extremely huge scale biological systems. J. Comput. Chem. 2021, 42, 231– 241,  DOI: 10.1002/jcc.26450
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    New parallel computing algorithm of molecular dynamics for extremely huge scale biological systems
    Jung, Jaewoon; Kobayashi, Chigusa; Kasahara, Kento; Tan, Cheng; Kuroda, Akiyoshi; Minami, Kazuo; Ishiduki, Shigeru; Nishiki, Tatsuo; Inoue, Hikaru; Ishikawa, Yutaka; Feig, Michael; Sugita, Yuji
    Journal of Computational Chemistry (2021), 42 (4), 231-241CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    In this paper, we address high performance extreme-scale mol. dynamics (MD) algorithm in the GENESIS software to perform cellular-scale mol. dynamics (MD) simulations with more than 100,000 CPU cores. It includes (1) the new algorithm of real-space nonbonded interactions maximizing the performance on ARM CPU architecture, (2) reciprocal-space nonbonded interactions minimizing communicational cost, (3) accurate temp./pressure evaluations that allows a large time step, and (4) effective parallel file inputs/outputs (I/O) for MD simulations of extremely huge systems. The largest system that contains 1.6 billion atoms was simulated using MD with a performance of 8.30 ns/day on Fugaku supercomputer. It extends the available size and time of MD simulations to answer unresolved questions of biomacromols. in a living cell.
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    Jung, J.; Naurse, A.; Kobayashi, C.; Sugita, Y. Graphics Processing Unit Acceleration and Parallelization of GENESIS for Large-Scale Molecular Dynamics Simulations. J. Chem. Theory Comput. 2016, 12, 4947– 4958,  DOI: 10.1021/acs.jctc.6b00241
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    Graphics Processing Unit Acceleration and Parallelization of GENESIS for Large-Scale Molecular Dynamics Simulations
    Jung, Jaewoon; Naurse, Akira; Kobayashi, Chigusa; Sugita, Yuji
    Journal of Chemical Theory and Computation (2016), 12 (10), 4947-4958CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Graphics processing unit (GPU) has become a popular computational platform for mol. dynamics (MD) simulations of biomols. A significant speedup in the simulations of small- or medium-size systems using only a few computer nodes with a single or multiple GPUs has been reported. Due to GPU memory limitation and slow communication between GPUs on different computer nodes, it is not straightforward to accelerate MD simulations of large biol. systems that contain a few million or more atoms on massively parallel supercomputers with GPUs. The authors develop a new scheme in their MD software, GENESIS, to reduce the total computational time on such computers. Computationally intensive real-space non-bonded interactions are computed mainly on GPUs in the scheme, while less intensive bonded interactions and communication-intensive reciprocal-space interactions were performed on CPUs. Based on the midpoint cell method as a domain decompn. scheme, the authors invent the single particle interaction list for reducing the GPU memory usage. Since total computational time is limited by the reciprocal-space computation, the authors use the RESPA multiple time-step integration and reduce the CPU resting time by assigning a subset of non-bonded interactions on CPUs as well as on GPUs when the reciprocal-space computation is skipped. The authors validated their GPU implementations in GENESIS on BPTI and a membrane protein, porin, by MD simulations and an alanine-tripeptide by REMD simulations. Benchmark calcns. on TSUBAME supercomputer showed that an MD simulation of a million atoms system was scalable up to 256 computer nodes with GPUs.
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    Jung, J.; Mori, T.; Sugita, Y. Midpoint cell method for hybrid (MPI+OpenMP) parallelization of molecular dynamics simulations. J. Comput. Chem. 2014, 35, 1064– 1072,  DOI: 10.1002/jcc.23591
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    Midpoint cell method for hybrid (MPI+OpenMP) parallelization of molecular dynamics simulations
    Jung, Jaewoon; Mori, Takaharu; Sugita, Yuji
    Journal of Computational Chemistry (2014), 35 (14), 1064-1072CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    We have developed a new hybrid (MPI+OpenMP) parallelization scheme for mol. dynamics (MD) simulations by combining a cell-wise version of the midpoint method with pair-wise Verlet lists. In this scheme, which we call the midpoint cell method, simulation space is divided into subdomains, each of which is assigned to a MPI processor. Each subdomain is further divided into small cells. The interaction between two particles existing in different cells is computed in the subdomain contg. the midpoint cell of the two cells where the particles reside. In each MPI processor, cell pairs are distributed over OpenMP threads for shared memory parallelization. The midpoint cell method keeps the advantages of the original midpoint method, while filtering out unnecessary calcns. of midpoint checking for all the particle pairs by single midpoint cell detn. prior to MD simulations. Distributing cell pairs over OpenMP threads allows for more efficient shared memory parallelization compared with distributing atom indexes over threads. Furthermore, cell grouping of particle data makes better memory access, reducing the no. of cache misses. The parallel performance of the midpoint cell method on the K computer showed scalability up to 512 and 32,768 cores for systems of 20,000 and 1 million atoms, resp. One MD time step for long-range interactions could be calcd. within 4.5 ms even for a 1 million atoms system with particle-mesh Ewald electrostatics. © 2014 Wiley Periodicals, Inc.
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    Jung, J.; Kobayashi, C.; Imamura, T.; Sugita, Y. Parallel implementation of 3D FFT with volumetric decomposition schemes for efficient molecular dynamics simulations. Comput. Phys. Commun. 2016, 200, 57– 65,  DOI: 10.1016/j.cpc.2015.10.024
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    Parallel implementation of 3D FFT with volumetric decomposition schemes for efficient molecular dynamics simulations
    Jung, Jaewoon; Kobayashi, Chigusa; Imamura, Toshiyuki; Sugita, Yuji
    Computer Physics Communications (2016), 200 (), 57-65CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    Three-dimensional Fast Fourier Transform (3D FFT) plays an important role in a wide variety of computer simulations and data analyses, including mol. dynamics (MD) simulations. In this study, we develop hybrid (MPI+OpenMP) parallelization schemes of 3D FFT based on two new volumetric decompns., mainly for the particle mesh Ewald (PME) calcn. in MD simulations. In one scheme, (1d_Alltoall), five all-to-all communications in one dimension are carried out, and in the other, (2d_Alltoall), one two-dimensional all-to-all communication is combined with two all-to-all communications in one dimension. 2d_Alltoall is similar to the conventional volumetric decompn. scheme. We performed benchmark tests of 3D FFT for the systems with different grid sizes using a large no. of processors on the K computer in RIKEN AICS. The two schemes show comparable performances, and are better than existing 3D FFTs. The performances of 1d_Alltoall and 2d_Alltoall depend on the supercomputer network system and no. of processors in each dimension. There is enough leeway for users to optimize performance for their conditions. In the PME method, short-range real-space interactions as well as long-range reciprocal-space interactions are calcd. Our volumetric decompn. schemes are particularly useful when used in conjunction with the recently developed midpoint cell method for short-range interactions, due to the same decompns. of real and reciprocal spaces. The 1d_Alltoall scheme of 3D FFT takes 4.7 ms to simulate one MD cycle for a virus system contg. more than 1 million atoms using 32,768 cores on the K computer.
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    Sugita, Y.; Okamoto, Y. Replica-exchange molecular dynamics method for protein folding. Chem. Phys. Lett. 1999, 314, 141– 151,  DOI: 10.1016/S0009-2614(99)01123-9
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    Replica-exchange molecular dynamics method for protein folding
    Sugita, Y.; Okamoto, Y.
    Chemical Physics Letters (1999), 314 (1,2), 141-151CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
    We have developed a formulation for mol. dynamics algorithm for the replica-exchange method. The effectiveness of the method for the protein-folding problem is tested with the penta-peptide Met-enkephalin. The method can overcome the multiple-min. problem by exchanging non-interacting replicas of the system at several temps. From only one simulation run, one can obtain probability distributions in canonical ensemble for a wide temp. range using multiple-histogram re-weighting techniques, which allows the calcn. of any thermodn. quantity as a function of temp. in that range.
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    Sugita, Y.; Okamoto, Y. Replica-exchange multicanonical algorithm and multicanonical replica-exchange method for simulating systems with rough energy landscape. Chem. Phys. Lett. 2000, 329, 261– 270,  DOI: 10.1016/S0009-2614(00)00999-4
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    Replica-exchange multicanonical algorithm and multicanonical replica-exchange method for simulating systems with rough energy landscape
    Sugita, Y.; Okamoto, Y.
    Chemical Physics Letters (2000), 329 (3,4), 261-270CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
    We propose two efficient algorithms for configurational sampling of systems with rough energy landscape. The first one is a new method for the detn. of the multi-canonical wt. factor. In this method, a short replica-exchange simulation is performed and the multi-canonical wt. factor is obtained by the multiple histogram reweighting techniques. The second one is a further extension of the first in which a replica-exchange multi-canonical simulation is performed with a small no. of replicas. These new algorithms are particularly useful for studying the protein folding problem.
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    Sugita, Y.; Kitao, A.; Okamoto, Y. Multidimensional replica-exchange method for free-energy calculations. J. Chem. Phys. 2000, 113, 6042– 6051,  DOI: 10.1063/1.1308516
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    Multidimensional replica-exchange method for free-energy calculations
    Sugita, Yuji; Kitao, Akio; Okamoto, Yuko
    Journal of Chemical Physics (2000), 113 (15), 6042-6051CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We have developed a new simulation algorithm for free-energy calcns. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temps. are exchanged during the simulation in the original replica-exchange method, pairs of replicas with different temps. and/or different parameters of the potential energy are exchanged in the new algorithm. This greatly enhances the sampling of the conformational space and allows accurate calcns. of free energy in a wide temp. range from a single simulation run, using the weighted histogram anal. method.
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    Kamiya, M.; Sugita, Y. Flexible selection of the solute region in replica exchange with solute tempering: Application to protein-folding simulations. J. Chem. Phys. 2018, 149, 72304,  DOI: 10.1063/1.5016222
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    Flexible selection of the solute region in replica exchange with solute tempering: Application to protein-folding simulations
    Kamiya, Motoshi; Sugita, Yuji
    Journal of Chemical Physics (2018), 149 (7), 072304/1-072304/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Replica-exchange mol. dynamics (REMD) and their variants have been widely used in simulations of the biomol. structure and dynamics. Replica exchange with solute tempering (REST) is one of the methods where temp. of a pre-defined solute mol. is exchanged between replicas, while solvent temps. in all the replicas are kept const. REST greatly reduces the no. of replicas compared to the temp. REMD, while replicas at low temps. are often trapped under their conditions, interfering with the conformational sampling. Here, the authors introduce a new scheme of REST, referred to as generalized REST (gREST), where the solute region is defined as a part of a mol. or a part of the potential energy terms, such as the dihedral-angle energy term or Lennard-Jones energy term. The authors applied this new method to folding simulations of a β-hairpin (16 residues) and a Trp-cage (20 residues) in explicit water. The protein dihedral-angle energy term is chosen as the solute region in the simulations. gREST reduces the no. of replicas necessary for good random walks in the solute-temp. space and covers a wider conformational space compared to the conventional REST2. Considering the general applicability, gREST should become a promising tool for the simulations of protein folding, conformational dynamics, and an in silico drug design. (c) 2018 American Institute of Physics.
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    Miao, Y.; Feher, V. A.; McCammon, J. A. Gaussian Accelerated Molecular Dynamics: Unconstrained Enhanced Sampling and Free Energy Calculation. J. Chem. Theory Comput. 2015, 11, 3584– 3595,  DOI: 10.1021/acs.jctc.5b00436
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    Gaussian Accelerated Molecular Dynamics: Unconstrained Enhanced Sampling and Free Energy Calculation
    Miao, Yinglong; Feher, Victoria A.; McCammon, J. Andrew
    Journal of Chemical Theory and Computation (2015), 11 (8), 3584-3595CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    A Gaussian accelerated mol. dynamics (GaMD) approach for simultaneous enhanced sampling and free energy calcn. of biomols. is presented. By constructing a boost potential that follows Gaussian distribution, accurate reweighting of the GaMD simulations is achieved using cumulant expansion to the second order. Here, GaMD is demonstrated on three biomol. model systems: alanine dipeptide, chignolin folding, and ligand binding to the T4-lysozyme. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of these biomols. Furthermore, the free energy profiles obtained from reweighting of the GaMD simulations allow the authors to identify distinct low-energy states of the biomols. and characterize the protein-folding and ligand-binding pathways quant.
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    Oshima, H.; Re, S.; Sugita, Y. Replica-Exchange Umbrella Sampling Combined with Gaussian Accelerated Molecular Dynamics for Free-Energy Calculation of Biomolecules. J. Chem. Theory Comput. 2019, 15, 5199– 5208,  DOI: 10.1021/acs.jctc.9b00761
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    Replica-Exchange Umbrella Sampling Combined with Gaussian Accelerated Molecular Dynamics for Free-Energy Calculation of Biomolecules
    Oshima, Hiraku; Re, Suyong; Sugita, Yuji
    Journal of Chemical Theory and Computation (2019), 15 (10), 5199-5208CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We have developed an enhanced conformational sampling method combining replica-exchange umbrella sampling (REUS) with Gaussian accelerated mol. dynamics (GaMD). REUS enhances the sampling along predefined reaction coordinates, while GaMD accelerates the conformational dynamics by adding a boost potential to the system energy. The method, which we call GaREUS (Gaussian accelerated replica-exchange umbrella sampling), enhances the sampling more efficiently than REUS or GaMD, while the computational resource for GaREUS is the same as that required for REUS. The two-step reweighting procedure using the multistate Bennett acceptance ratio method and the cumulant expansion for the exponential av. is applied to the simulation trajectories for obtaining the unbiased free-energy landscapes. We apply GaREUS to the calcns. of free-energy landscapes for three different cases: conformational equil. of N-glycan, folding of chignolin, and conformational change of adenyl kinase. We show that GaREUS speeds up the convergences of free-energy calcns. using the same amt. of computational resources as REUS. The free-energy landscapes reweighted from the trajectories of GaREUS agree with previously reported ones. GaREUS is applicable to free-energy calcns. of various biomol. dynamics and functions with reasonable computational costs.
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    Tembre, B. L.; Mc Cammon, J. A. Ligand-receptor interactions. Comput. Chem. 1984, 8, 281– 283,  DOI: 10.1016/0097-8485(84)85020-2
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    Oshima, H.; Re, S.; Sugita, Y. Prediction of Protein-Ligand Binding Pose and Affinity Using the gREST+FEP Method. J. Chem. Inf. Model. 2020, 60, 5382– 5394,  DOI: 10.1021/acs.jcim.0c00338
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    Prediction of Protein-Ligand Binding Pose and Affinity Using the gREST+FEP Method
    Oshima, Hiraku; Re, Suyong; Sugita, Yuji
    Journal of Chemical Information and Modeling (2020), 60 (11), 5382-5394CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    The accurate prediction of protein-ligand binding affinity is a central challenge in computational chem. and in-silico drug discovery. The free energy perturbation (FEP) method based on mol. dynamics (MD) simulation provides reasonably accurate results only if a reliable structure is available via high-resoln. x-ray crystallog. To overcome the limitation, the authors propose a sequential prediction protocol using generalized replica exchange with solute tempering (gREST) and FEP. At first, ligand binding poses are predicted using gREST, which weakens protein-ligand interactions at high temps. to sample multiple binding poses. To avoid ligand dissocn. at high temps., a flat-bottom restraint potential centered on the binding site is applied in the simulation. The binding affinity of the most reliable pose is then calcd. using FEP. The protocol is applied to the bindings of ten ligands to FK506 binding proteins (FKBP), showing the excellent agreement between the calcd. and exptl. binding affinities. The present protocol, which is referred to as the gREST+FEP method, would help to predict the binding affinities without high-resoln. structural information on the ligand-bound state.
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    Maragliano, L.; Fischer, A.; Vanden-Eijnden, E.; Ciccotti, G. String method in collective variables: Minimum free energy paths and isocommittor surfaces. J. Chem. Phys. 2006, 125, 24106,  DOI: 10.1063/1.2212942
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    String method in collective variables: Minimum free energy paths and isocommittor surfaces
    Maragliano, Luca; Fischer, Alexander; Vanden-Eijnden, Eric; Ciccotti, Giovanni
    Journal of Chemical Physics (2006), 125 (2), 024106/1-024106/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    A computational technique is proposed which combines the string method with a sampling technique to det. min. free energy paths. The technique only requires to compute the mean force and another conditional expectation locally along the string, and therefore can be applied even if the no. of collective variables kept in the free energy calcn. is large. This is in contrast with other free energy sampling techniques which aim at mapping the full free energy landscape and whose cost increases exponentially with the no. of collective variables kept in the free energy. Provided that the no. of collective variables is large enough, the new technique captures the mechanism of transition in that it allows to det. the committor function for the reaction and, in particular, the transition state region. The new technique is illustrated on the example of alanine dipeptide, in which we compute the min. free energy path for the isomerization transition using either two or four dihedral angles as collective variables. It is shown that the mechanism of transition can be captured using the four dihedral angles, but it cannot be captured using only two of them.
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    Matsunaga, Y.; Komuro, Y.; Kobayashi, C.; Jung, J.; Mori, T.; Sugita, Y. Dimensionality of Collective Variables for Describing Conformational Changes of a Multi-Domain Protein. J. Phys. Chem. Lett. 2016, 7, 1446– 1451,  DOI: 10.1021/acs.jpclett.6b00317
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    Dimensionality of Collective Variables for Describing Conformational Changes of a Multi-Domain Protein
    Matsunaga, Yasuhiro; Komuro, Yasuaki; Kobayashi, Chigusa; Jung, Jaewoon; Mori, Takaharu; Sugita, Yuji
    Journal of Physical Chemistry Letters (2016), 7 (8), 1446-1451CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Collective variables (CVs) are often used in mol. dynamics simulations based on enhanced sampling algorithms to investigate large conformational changes of a protein. The choice of CVs in these simulations is essential because it affects simulation results and impacts the free-energy profile, the min. free-energy pathway (MFEP), and the transition-state structure. Here we examine how many CVs are required to capture the correct transition-state structure during the open-to-close motion of adenylate kinase using a coarse-grained model in the mean forces string method to search the MFEP. Various nos. of large amplitude principal components are tested as CVs in the simulations. The incorporation of local coordinates into CVs, which is possible in higher dimensional CV spaces, is important for capturing a reliable MFEP. The Bayesian measure proposed by Best and Hummer is sensitive to the choice of CVs, showing sharp peaks when the transition-state structure is captured. We thus evaluate the required no. of CVs needed in enhanced sampling simulations for describing protein conformational changes.
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    Kim, S.; Oshima, H.; Zhang, H.; Kern, N. R.; Re, S.; Lee, J.; Roux, B.; Sugita, Y.; Jiang, W.; Im, W. CHARMM-GUI Free Energy Calculator for Absolute and Relative Ligand Solvation and Binding Free Energy Simulations. J. Chem. Theory Comput. 2020, 16, 7207– 7218,  DOI: 10.1021/acs.jctc.0c00884
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    68
    CHARMM-GUI Free Energy Calculator for Absolute and Relative Ligand Solvation and Binding Free Energy Simulations
    Kim, Seonghoon; Oshima, Hiraku; Zhang, Han; Kern, Nathan R.; Re, Suyong; Lee, Jumin; Roux, Benoit; Sugita, Yuji; Jiang, Wei; Im, Wonpil
    Journal of Chemical Theory and Computation (2020), 16 (11), 7207-7218CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Alchem. free energy simulations have long been utilized to predict free energy changes for binding affinity and soly. of small mols. However, while the theor. foundation of these methods is well established, seamlessly handling many of the practical aspects regarding the prepn. of the different thermodn. end states of complex mol. systems and the numerous processing scripts often remains a burden for successful applications. In this work, we present CHARMM-GUI Free Energy Calculator (http://www.charmm-gui.org/input/fec) that provides various alchem. free energy perturbation mol. dynamics (FEP/MD) systems with input and post-processing scripts for NAMD and GENESIS. Four submodules are available: Abs. Ligand Binder (for abs. ligand binding FEP/MD), Relative Ligand Binder (for relative ligand binding FEP/MD), Abs. Ligand Solvator (for abs. ligand solvation FEP/MD), and Relative Ligand Solvator (for relative ligand solvation FEP/MD). Each module is designed to build multiple systems of a set of selected ligands at once for high-throughput FEP/MD simulations. The capability of Free Energy Calculator is illustrated by abs. and relative solvation FEP/MD of a set of ligands and abs. and relative binding FEP/MD of a set of ligands for T4-lysozyme in soln. and the adenosine A2A receptor in a membrane. The calcd. free energy values are overall consistent with the exptl. and published free energy results (within ∼ 1 kcal/mol). We hope that Free Energy Calculator is useful to carry out high-throughput FEP/MD simulations in the field of biomol. sciences and drug discovery.
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    Yagi, K.; Yamada, K.; Kobayashi, C.; Sugita, Y. Anharmonic Vibrational Analysis of Biomolecules and Solvated Molecules Using Hybrid QM/MM Computations. J. Chem. Theory Comput. 2019, 15, 1924– 1938,  DOI: 10.1021/acs.jctc.8b01193
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    Anharmonic Vibrational Analysis of Biomolecules and Solvated Molecules Using Hybrid QM/MM Computations
    Yagi, Kiyoshi; Yamada, Kenta; Kobayashi, Chigusa; Sugita, Yuji
    Journal of Chemical Theory and Computation (2019), 15 (3), 1924-1938CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Quantum mechanics/mol. mechanics (QM/MM) calcns. are applied for anharmonic vibrational analyses of biomols. and solvated mols. The QM/MM method is implemented into a mol. dynamics (MD) program, GENESIS, by interfacing with external electronic structure programs. Following the geometry optimization and the harmonic normal-mode anal. based on a partial Hessian, the anharmonic potential energy surface (PES) is generated from QM/MM energies and gradients calcd. at grid points. The PES is used for vibrational SCF (VSCF) and post-VSCF calcns. to compute the vibrational spectrum. The method is first applied to a phosphate ion in soln. With both the ion and neighboring water mols. taken as a QM region, IR spectra of representative hydration structures are calcd. by the second-order vibrational quasi-degenerate perturbation theory (VQDPT2) at the level of B3LYP/cc-pVTZ and TIP3P force field. A wt.-av. of IR spectra over the structures reproduces the exptl. spectrum with a mean abs. deviation of 16 cm-1. Then, the method is applied to an enzyme, P 450 nitric oxide reductase (P450nor), with the NO mol. bound to a ferric (FeIII) heme. Starting from snapshot structures obtained from MD simulations of P450nor in soln., QM/MM calcns. have been carried out at the level of B3LYP-D3/def2-SVP(D). The spin state of FeIII(NO) is likely a closed-shell singlet state based on a ratio of N-O and Fe-NO stretching frequencies (νN-O and νFe-NO) calcd. for closed- and open-shell singlet states. The calcd. νN-O and νFe-NO overestimate the exptl. ones by 120 and 75 cm-1, resp. The electronic structure and solvation of FeIII(NO) affect the structure around the heme of P450nor leading to an increase in νN-O and νFe-NO.
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    Frisch, M. J.; Gaussian 16, rev. C.01; Gaussian, Inc.: Wallingford, CT, 2016.
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    Shao, Y. Advances in molecular quantum chemistry contained in the Q-Chem 4 program package. Mol. Phys. 2015, 113, 184– 215,  DOI: 10.1080/00268976.2014.952696
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    Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
    Shao, Yihan; Gan, Zhengting; Epifanovsky, Evgeny; Gilbert, Andrew T. B.; Wormit, Michael; Kussmann, Joerg; Lange, Adrian W.; Behn, Andrew; Deng, Jia; Feng, Xintian; Ghosh, Debashree; Goldey, Matthew; Horn, Paul R.; Jacobson, Leif D.; Kaliman, Ilya; Khaliullin, Rustam Z.; Kus, Tomasz; Landau, Arie; Liu, Jie; Proynov, Emil I.; Rhee, Young Min; Richard, Ryan M.; Rohrdanz, Mary A.; Steele, Ryan P.; Sundstrom, Eric J.; Woodcock, H. Lee, III; Zimmerman, Paul M.; Zuev, Dmitry; Albrecht, Ben; Alguire, Ethan; Austin, Brian; Beran, Gregory J. O.; Bernard, Yves A.; Berquist, Eric; Brandhorst, Kai; Bravaya, Ksenia B.; Brown, Shawn T.; Casanova, David; Chang, Chung-Min; Chen, Yunquing; Chien, Siu Hung; Closser, Kristina D.; Crittenden, Deborah L.; Diedenhofen, Michael; DiStasio, Robert A., Jr.; Do, Hainam; Dutoi, Anthony D.; Edgar, Richard G.; Fatehi, Shervin; Fusti-Molnar, Laszlo; Ghysels, An; Golubeva-Zadorozhnaya, Anna; Gomes, Joseph; Hanson-Heine, Magnus W. D.; Harbach, Philipp H. P.; Hauser, Andreas W.; Hohenstein, Edward G.; Holden, Zachary C.; Jagau, Thomas-C.; Ji, Hyunjun; Kaduk, Ben; Khistyaev, Kirill; Kim, Jaehoon; Kim, Jihan; King, Rollin A.; Klunzinger, Phil; Kosenkov, Dmytro; Kowalczyk, Tim; Krauter, Caroline M.; Lao, Ka Un; Laurent, Adele; Lawler, Keith V.; Levchenko, Sergey V.; Lin, Ching Yeh; Liu, Fenglai; Livshits, Ester; Lochan, Rohini C.; Luenser, Arne; Manohar, Prashant; Manzer, Samuel F.; Mao, Shan-Ping; Mardirossian, Narbe; Marenich, Aleksandr V.; Maurer, Simon A.; Mayhall, Nicholas J.; Neuscamman, Eric; Oana, C. Melania; Olivares-Amaya, Roberto; O'Neill, Darragh P.; Parkhill, John A.; Perrine, Trilisa M.; Peverati, Roberto; Prociuk, Alexander; Rehn, Dirk R.; Rosta, Edina; Russ, Nicholas J.; Sharada, Shaama M.; Sharma, Sandeep; Small, David W.; Sodt, Alexander; Stein, Tamar; Stuck, David; Su, Yu-Chuan; Thom, Alex J. W.; Tsuchimochi, Takashi; Vanovschi, Vitalii; Vogt, Leslie; Vydrov, Oleg; Wang, Tao; Watson, Mark A.; Wenzel, Jan; White, Alec; Williams, Christopher F.; Yang, Jun; Yeganeh, Sina; Yost, Shane R.; You, Zhi-Qiang; Zhang, Igor Ying; Zhang, Xing; Zhao, Yan; Brooks, Bernard R.; Chan, Garnet K. L.; Chipman, Daniel M.; Cramer, Christopher J.; Goddard, William A., III; Gordon, Mark S.; Hehre, Warren J.; Klamt, Andreas; Schaefer, Henry F., III; Schmidt, Michael W.; Sherrill, C. David; Truhlar, Donald G.; Warshel, Arieh; Xu, Xin; Aspuru-Guzik, Alan; Baer, Roi; Bell, Alexis T.; Besley, Nicholas A.; Chai, Jeng-Da; Dreuw, Andreas; Dunietz, Barry D.; Furlani, Thomas R.; Gwaltney, Steven R.; Hsu, Chao-Ping; Jung, Yousung; Kong, Jing; Lambrecht, Daniel S.; Liang, WanZhen; Ochsenfeld, Christian; Rassolov, Vitaly A.; Slipchenko, Lyudmila V.; Subotnik, Joseph E.; Van Voorhis, Troy; Herbert, John M.; Krylov, Anna I.; Gill, Peter M. W.; Head-Gordon, Martin
    Molecular Physics (2015), 113 (2), 184-215CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)
    A review. A summary of the tech. advances that are incorporated in the fourth major release of the Q-Chem quantum chem. program is provided, covering approx. the last seven years. These include developments in d. functional theory methods and algorithms, NMR (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, anal. tools, energy and electron transfer modeling, parallel computing capabilities, and graphical user interfaces. In addn., a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern d. functionals for bonded and non-bonded interactions, tests of attenuated second order Moller-Plesset (MP2) methods for intermol. interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chem. examples include calcns. on the strongly correlated Cr2 dimer, exploring zeolite-catalyzed ethane dehydrogenation, energy decompn. anal. of a charged ter-mol. complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.
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    Seritan, S.; Bannwarth, C.; Fales, B. S.; Hohenstein, E. G.; Isborn, C. M.; Kokkila-Schumacher, S. I. L.; Li, X.; Liu, F.; Luehr, N.; Snyder, J. W., Jr; Song, C.; Titov, A. V.; Ufimtsev, I. S.; Wang, L.-P.; Martínez, T. J. TeraChem: A graphical processing unit-accelerated electronic structure package for large-scale ab initio molecular dynamics. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1494,  DOI: 10.1002/wcms.1494
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    TeraChem: A graphical processing unit-accelerated electronic structure package for large-scale ab initio molecular dynamics
    Seritan, Stefan; Bannwarth, Christoph; Fales, Bryan S.; Hohenstein, Edward G.; Isborn, Christine M.; Kokkila-Schumacher, Sara I. L.; Li, Xin; Liu, Fang; Luehr, Nathan; Snyder, James W., Jr.; Song, Chenchen; Titov, Alexey V.; Ufimtsev, Ivan S.; Wang, Lee-Ping; Martinez, Todd J.
    Wiley Interdisciplinary Reviews: Computational Molecular Science (2021), 11 (2), e1494CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
    TeraChem was born in 2008 with the goal of providing fast on-the-fly electronic structure calcns. to facilitate ab initio mol. dynamics studies of large biochem. systems such as photoswitchable proteins and multichromophoric antenna complexes. Originally developed for videogaming applications, graphics processing units (GPUs) offered a low-cost parallel computer architecture that became more accessible for general-purpose GPU computing with the release of CUDA in 2007. Thus, highly efficient routines for evaluation of and contractions between the ERIs and d. matrixes were implemented in TeraChem. Electronic structure methods were developed and implemented to leverage these integral contraction routines, resulting in the first quantum chem. package designed from the ground up for GPUs. This GPU acceleration makes TeraChem capable of performing large-scale ground and excited state calcns. in the gas and condensed phase. Today, TeraChem's speed forms the basis for a suite of quantum chem. applications, including optimization and dynamics of proteins, automated and interactive chem. discovery tools, and large-scale nonadiabatic dynamics simulations.
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    Hourahine, B. DFTB+, a software package for efficient approximate density functional theory based atomistic simulations. J. Chem. Phys. 2020, 152, 124101,  DOI: 10.1063/1.5143190
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    DFTB+, a software package for efficient approximate density functional theory based atomistic simulations
    Hourahine, B.; Aradi, B.; Blum, V.; Bonafe, F.; Buccheri, A.; Camacho, C.; Cevallos, C.; Deshaye, M. Y.; Dumitrica, T.; Dominguez, A.; Ehlert, S.; Elstner, M.; van der Heide, T.; Hermann, J.; Irle, S.; Kranz, J. J.; Kohler, C.; Kowalczyk, T.; Kubar, T.; Lee, I. S.; Lutsker, V.; Maurer, R. J.; Min, S. K.; Mitchell, I.; Negre, C.; Niehaus, T. A.; Niklasson, A. M. N.; Page, A. J.; Pecchia, A.; Penazzi, G.; Persson, M. P.; Rezac, J.; Sanchez, C. G.; Sternberg, M.; Stohr, M.; Stuckenberg, F.; Tkatchenko, A.; Yu, V. W.-z.; Frauenheim, T.
    Journal of Chemical Physics (2020), 152 (12), 124101CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mech. simulations. By implementing various methods approximating d. functional theory (DFT), such as the d. functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long time-scales with reasonable accuracy while being considerably faster for typical simulations than the resp. ab initio methods. Based on the DFTB framework, it addnl. offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equil. Green's functions, and many more. DFTB+ can be used as a user-friendly standalone application in addn. to being embedded into other software packages as a library or acting as a calcn.-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives. (c) 2020 American Institute of Physics.
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    QSimulate-QM. Quantum Simulation Technologies, Inc. 2020, https://qsimulate.com/.
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    E, W.; Ren, W.; Vanden-Eijnden, E. String method for the study of rare events. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 66, 52301,  DOI: 10.1103/PhysRevB.66.052301
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    String method for the study of rare events
    E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
    Physical Review B: Condensed Matter and Materials Physics (2002), 66 (5), 052301/1-052301/4CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    We present an efficient method for computing the transition pathways, free energy barriers, and transition rates in complex systems with relatively smooth energy landscapes. The method proceeds by evolving strings, i.e., smooth curves with intrinsic parametrization whose dynamics takes them to the most probable transition path between two metastable regions in configuration space. Free energy barriers and transition rates can then be detd. by a std. umbrella sampling around the string. Applications to Lennard-Jones cluster rearrangement and thermally induced switching of a magnetic film are presented.
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    E, W.; Ren, W.; Vanden-Eijnden, E. Simplified and improved string method for computing the minimum energy paths in barrier-crossing events. J. Chem. Phys. 2007, 126, 164103,  DOI: 10.1063/1.2720838
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    Simplified and improved string method for computing the minimum energy paths in barrier-crossing events
    E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
    Journal of Chemical Physics (2007), 126 (16), 164103/1-164103/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We present a simplified and improved version of the string method, originally proposed by W.E.W. Ren and E. Vanden-Eijnden [Phys. Rev. B 66, 052301 (2002)] for identifying the min. energy paths in barrier-crossing events. In this new version, the step of projecting the potential force to the direction normal to the string is eliminated and the full potential force is used in the evolution of the string. This not only simplifies the numerical procedure, but also makes the method more stable and accurate. We discuss the algorithmic details of the improved string method, analyze its stability, accuracy and efficiency, and illustrate it via numerical examples. We also show how the string method can be combined with the climbing image technique for the accurate calcn. of saddle points and we present another algorithm for the accurate calcn. of the unstable directions at the saddle points.
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    Cui, Q.; Karplus, M. Quantum mechanics/molecular mechanics studies of triosephosphate isomerase-catalyzed reactions: Effect of geometry and tunneling on proton-transfer rate constants. J. Am. Chem. Soc. 2002, 124, 3093– 3124,  DOI: 10.1021/ja0118439
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    Quantum Mechanics/Molecular Mechanics Studies of Triosephosphate Isomerase-Catalyzed Reactions: Effect of Geometry and Tunneling on Proton-Transfer Rate Constants
    Cui, Qiang; Karplus, Martin
    Journal of the American Chemical Society (2002), 124 (12), 3093-3124CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The role of tunneling for two proton-transfer steps in the reactions catalyzed by triosephosphate isomerase (TIM) has been studied. One step is the rate-limiting proton transfer from Cα in the substrate to Glu 165, and the other is an intrasubstrate proton transfer proposed for the isomerization of the enediolate intermediate. The latter, which is not important in the wild-type enzyme but is a useful model system because of its simplicity, has also been examd. in the gas phase and in soln. Variational transition-state theory with semiclassical ground-state tunneling was used for the calcn. with potential energy surface detd. by an AM1 method specifically parametrized for the TIM system. The effect of tunneling on the reaction rate was found to be less than a factor of 10 at room temp.; the tunneling becomes more important at lower temp., as expected. The imaginary frequency (barrier) mode and modes that have large contributions to the reaction path curvature are localized on the atoms in the active site, within 4 Å of the substrate. This suggests that only a small no. of atoms that are close to the substrate and their motions (e.g., donor-acceptor vibration) directly det. the magnitude of tunneling. Atoms that are farther away influence the effect of tunneling indirectly by modulating the energetics of the proton transfer. For the intramol. proton transfer, tunneling was found to be most important in the gas phase, to be similar in the enzyme, and to be the smallest in water. The major reason for this trend is that the barrier frequency is substantially lower in soln. than in the gas phase and enzyme; the broader soln. barrier is caused by the strong electrostatic interaction between the highly charged solute and the polar solvent mols. Anal. of isotope effects showed that the conventional Arrenhius parameters are more useful as exptl. criteria for detg. the magnitude of tunneling than the widely used Swain-Schaad exponent (SSE). For the primary SSE, although values larger than the transition-state theory limit (3.3) occur when tunneling is included, there is no clear relationship between the calcd. magnitudes of tunneling and the SSE. Also, the temp. dependence of the primary SSE is rather complex; the value of SSE tends to decrease as the temp. is lowered (i.e., when tunneling becomes more significant). For the secondary SSE, the results suggest that it is more relevant for evaluating the "coupled motion" between the secondary hydrogen and the reaction coordinate than the magnitude of tunneling. Although tunneling makes a significant contribution to the rate of proton transfer, it appears not to be a major aspect of the catalysis by TIM at room temp.; i.e., the tunneling factor of 10 is "small" relative to the overall rate acceleration by 109. For the intramol. proton transfer, the tunneling in the enzyme is larger by a factor of 5 than in soln.
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    Zhang, X.; Harrison, D. H. T.; Cui, Q. Functional specificities of methylglyoxal synthase and triosephosphate isomerase: A combined QM/MM analysis. J. Am. Chem. Soc. 2002, 124, 14871– 14878,  DOI: 10.1021/ja027063x
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    Functional Specificities of Methylglyoxal Synthase and Triosephosphate Isomerase: A Combined QM/MM Analysis
    Zhang, Xiaodong; Harrison, David H. T.; Cui, Qiang
    Journal of the American Chemical Society (2002), 124 (50), 14871-14878CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Combined SCC-DFTB/CHARMM calcns. were carried out to analyze the origin for the functional specificities of triosephosphate isomerase (TIM) and methylglyoxal synthase (MGS). The two enzymes bind to the same substrate, dihydroxyacetone phosphate (DHAP), and have rather similar active sites. However, they catalyze different reactions; TIM catalyzes the isomerization of DHAP to glyceraldehyde 3-phosphate (GAP), while MGS catalyzes the elimination of phosphate from DHAP. Similar to previous suggestions, the calcns. confirmed that GAP formation is prohibited in MGS due primarily to the reduced flexibility of the catalytic base (Asp 71) compared to that in TIM (Glu 165). For the suppression of phosphate elimination in TIM, the calcns. show that the widely accepted stereoelectronic argument that invokes the different phosphoryl torsion angles obsd. in the x-ray structures of inhibitor complexes of the two enzymes is not as important as electrostatic contributions from the protein and water mols. surrounding the phosphoryl.
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    Cui, Q.; Karplus, M. Quantum mechanical/molecular mechanical studies of the triosephosphate isomerase-catalyzed reaction: Verification of methodology and analysis of reaction mechanisms. J. Phys. Chem. B 2002, 106, 1768– 1798,  DOI: 10.1021/jp012659c
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    80
    Quantum Mechanical/Molecular Mechanical Studies of the Triosephosphate Isomerase-Catalyzed Reaction: Verification of Methodology and Analysis of Reaction Mechanisms
    Cui, Qiang; Karplus, Martin
    Journal of Physical Chemistry B (2002), 106 (7), 1768-1798CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
    Three possible mechanisms for the reactions catalyzed by triosephosphate isomerase (TIM) have been studied by the combined quantum mech./mol. mech. (QM/MM) approach at a no. of QM levels including AM1, AM1 with specific reaction parameters (SRP), and B3LYP/6-31+G(d,p). The comparison of the various QM levels is used to verify the adequacy of our recent B3LYP/MM anal. of the reaction mechanism (Cui et al. J. Am. Chem. Soc. 2001, 123, 2284), which showed that the intramol. proton transfer pathway is ruled out, due largely to the unfavorable interaction between the transition state and His 95. The relative contributions from the two other proposed pathways, however, are difficult to det. at the present level of theory; both pathways are also consistent with available expts. To obtain information about the role of the enzyme, d. functional calcns. were made for model systems in the gas phase and in soln.; selected models were also studied with ab initio calcns. at the levels of MP2 and CCSD to confirm the B3LYP results. Mulliken population anal. of the transition states demonstrates that hydrogen transfers essentially as proton for all the reactions in TIM, with an electron population between +0.33 and +0.44. Adiabatic mapping calcns. for path A indicate that the two relevant proton-transfer steps between the substrate and His 95 proceed in a nearly concerted manner. The QM model calcns. in soln. and a QM/MM perturbation anal. shows that a no. of factors combine to yield the rate enhancement by a factor of 109 in TIM. These include orienting catalytic groups (e.g., Glu 165, His 95) in good positions for the proton transfers, employing charged and polar groups (e.g., Lys 12, Asn 10) that stabilize the reaction intermediates and permitting flexibility of the catalytic groups (e.g., Glu 165 along path C). Some residues far from the active site, such as the main-chain atoms in Gly 210, as well as certain water mols., also make significant contributions. For the electrostatic interaction and polarization to function effectively, the active site of TIM has a relatively low effective dielec. "const.", which reflects the structural integrity of the enzyme active site as compared with soln. Short hydrogen bonds occur during the reaction (e.g., between the reactant substrate and Glu 165), but the calcd. energetics indicate that they do not have a specific role in catalysis; i.e., no contribution was found from the rather short hydrogen bond between His 95 and the substrate in path A.
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    Lennartz, C.; Schäfer, A.; Terstegen, F.; Thiel, W. Enzymatic reactions of triosephosphate isomerase: A theoretical calibration study. J. Phys. Chem. B 2002, 106, 1758– 1767,  DOI: 10.1021/jp012658k
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    Enzymatic Reactions of Triosephosphate Isomerase: A Theoretical Calibration Study
    Lennartz, C.; Schaefer, A.; Terstegen, F.; Thiel, W.
    Journal of Physical Chemistry B (2002), 106 (7), 1758-1767CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
    Combined quantum mech. (QM) and mol. mech. (MM) calcns. are reported for the triosephosphate isomerase-catalyzed conversion of dihydroxyacetone phosphate into glyceraldehyde 3-phosphate. The min. and transition states for the relevant proton-transfer reactions have been located on QM/MM potential surfaces. The primary objective of this work is to study the sensitivity of optimized structures and relative energies toward variations in the QM/MM model, including the choice of the QM method, the size of the QM region, the size of the optimized MM region, and the treatment of the QM/MM boundary. The QM methods that have been applied in combination with the CHARMm force field range from semiempirical (AM1) to d. functional (BP86, B3LYP) and ab initio (MP2) methods, the most extensive QM calcns. involving 275 atoms and 2162 basis functions at the d. functional level. Implications of the different choices of QM/MM options on the energy profile are discussed. From a mechanistic point of view, the present QM/MM results support a four-step proton-transfer pathway via an enediol, with involvement of neutral His95 acting as a proton donor, since the alternative direct intramol. proton transfer in the enediolate is disfavored by the protein environment.
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    Mendieta-Moreno, J. I.; Walker, R. C.; Lewis, J. P.; Gómez-Puertas, P.; Mendieta, J.; Ortega, J. FIREBALL/AMBER: An Efficient Local-Orbital DFT QM/MM Method for Biomolecular Systems. J. Chem. Theory Comput. 2014, 10, 2185– 2193,  DOI: 10.1021/ct500033w
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    FIREBALL/AMBER: An Efficient Local-Orbital DFT QM/MM Method for Biomolecular Systems
    Mendieta-Moreno, Jesus I.; Walker, Ross C.; Lewis, James P.; Gomez-Puertas, Paulino; Mendieta, Jesus; Ortega, Jose
    Journal of Chemical Theory and Computation (2014), 10 (5), 2185-2193CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    In recent years, quantum mechanics/mol. mechanics (QM/MM) methods have become an important computational tool for the study of chem. reactions and other processes in biomol. systems. In the QM/MM technique, the active region is described by means of QM calcns., while the remainder of the system is described using a MM approach. Because of the complexity of biomols. and the desire to achieve converged sampling, it is important that the QM method presents a good balance between accuracy and computational efficiency. Here, we report on the implementation of a QM/MM technique that combines a DFT approach specially designed for the study of complex systems using first-principles mol. dynamics simulations (FIREBALL) with the AMBER force fields and simulation programs. We also present examples of the application of this QM/MM approach to three representative biomol. systems: the anal. of the effect of electrostatic embedding in the behavior of a salt bridge between an aspartic acid and a lysine residue, a study of the intermediate states for the triosephosphate isomerase catalyzed conversion of dihydroxyacetone phosphate into glyceraldehyde 3-phosphate, and the detailed description, using DFT QM/MM mol. dynamics, of the cleavage of a phosphodiester bond in RNA catalyzed by the enzyme RNase A.
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    Knizia, G. Intrinsic atomic orbitals: An unbiased bridge between quantum theory and chemical concepts. J. Chem. Theory Comput. 2013, 9, 4834– 4843,  DOI: 10.1021/ct400687b
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    Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts
    Knizia, Gerald
    Journal of Chemical Theory and Computation (2013), 9 (11), 4834-4843CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Modern quantum chem. can make quant. predictions on an immense array of chem. systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an exceptionally simple algebraic construction allows for defining at. core and valence orbitals, polarized by the mol. environment, which can exactly represent SCF wave functions. This construction provides an unbiased and direct connection between quantum chem. and empirical chem. concepts, and can be used, for example, to calc. the nature of bonding in mols., in chem. terms, from first principles. In particular, we find consistency with electronegativities (χ), C 1s core-level shifts, resonance substituent parameters (σR), Lewis structures, and oxidn. states of transition-metal complexes.
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    Kästner, J.; Thiel, S.; Senn, H. M.; Sherwood, P.; Thiel, W. Exploiting QM/MM Capabilities in Geometry Optimization: A Microiterative Approach Using Electrostatic Embedding. J. Chem. Theory Comput. 2007, 3, 1064– 1072,  DOI: 10.1021/ct600346p
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    Exploiting QM/MM Capabilities in Geometry Optimization: A Microiterative Approach Using Electrostatic Embedding
    Kastner Johannes; Thiel Stephan; Senn Hans Martin; Sherwood Paul; Thiel Walter
    Journal of chemical theory and computation (2007), 3 (3), 1064-72 ISSN:1549-9618.
    We present a microiterative adiabatic scheme for quantum mechanical/molecular mechanical (QM/MM) energy minimization that fully optimizes the MM part in each QM macroiteration. This scheme is applicable not only to mechanical embedding but also to electrostatic and polarized embedding. The electrostatic QM/MM interactions in the microiterations are calculated from electrostatic potential charges fitted on the fly to the QM density. Corrections to the energy and gradient expressions ensure that macro- and microiterations are performed on the same energy surface. This results in excellent convergence properties and no loss of accuracy compared to standard optimization. We test our implementation on water clusters and on two enzymes using electrostatic embedding, as well as on a surface example using polarized embedding with a shell model. Our scheme is especially well-suited for systems containing large MM regions, since the computational effort for the optimization is almost independent of the MM system size. The microiterations reduce the number of required QM calculations typically by a factor of 2-10, depending on the system.
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    Shirts, M. R.; Chodera, J. D. Statistically optimal analysis of samples from multiple equilibrium states. J. Chem. Phys. 2008, 129, 124105,  DOI: 10.1063/1.2978177
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    Statistically optimal analysis of samples from multiple equilibrium states
    Shirts, Michael R.; Chodera, John D.
    Journal of Chemical Physics (2008), 129 (12), 124105/1-124105/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We present a new estimator for computing free energy differences and thermodn. expectations as well as their uncertainties from samples obtained from multiple equil. states via either simulation or expt. The estimator, which we call the multistate Bennett acceptance ratio estimator (MBAR) because it reduces to the Bennett acceptance ratio estimator (BAR) when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a soln. to the estg. equations in many cases. Addnl., an est. of the statistical uncertainty is provided for all estd. quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equil. data collected from multiple states. We illustrate this method by producing a highly precise est. of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under const. force bias. (c) 2008 American Institute of Physics.
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    Branduardi, D.; Gervasio, F. L.; Parrinello, M. From A to B in free energy space. J. Chem. Phys. 2007, 126, 054103,  DOI: 10.1063/1.2432340
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    From A to B in free energy space
    Branduardi, Davide; Gervasio, Francesco Luigi; Parrinello, Michele
    Journal of Chemical Physics (2007), 126 (5), 054103/1-054103/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The authors present a new method for searching low free energy paths in complex mol. systems at finite temp. They introduce two variables that are able to describe the position of a point in configurational space relative to a preassigned path. With the help of these two variables the authors combine features of approaches such as metadynamics or umbrella sampling with those of path based methods. This allows global searches in the space of paths to be performed and a new variational principle for the detn. of low free energy paths to be established. Contrary to metadynamics or umbrella sampling the path can be described by an arbitrary large no. of variables, still the energy profile along the path can be calcd. The authors exemplify the method numerically by studying the conformational changes of alanine dipeptide.
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    Bonomi, M.; Branduardi, D.; Bussi, G.; Camilloni, C.; Provasi, D.; Raiteri, P.; Donadio, D.; Marinelli, F.; Pietrucci, F.; Broglia, R. A.; Parrinello, M. PLUMED: A portable plugin for free-energy calculations with molecular dynamics. Comput. Phys. Commun. 2009, 180, 1961– 1972,  DOI: 10.1016/j.cpc.2009.05.011
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    PLUMED: A portable plugin for free-energy calculations with molecular dynamics
    Bonomi, Massimiliano; Branduardi, Davide; Bussi, Giovanni; Camilloni, Carlo; Provasi, Davide; Raiteri, Paolo; Donadio, Davide; Marinelli, Fabrizio; Pietrucci, Fabio; Broglia, Ricardo A.; Parrinello, Michele
    Computer Physics Communications (2009), 180 (10), 1961-1972CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    A program aimed at free-energy calcns. in mol. systems is presented. It consists of a series of routines that can be interfaced with the most popular classical mol. dynamics (MD) codes through a simple patching procedure. This leaves the possibility for the user to exploit many different MD engines depending on the system simulated and on the computational resources available. Free-energy calcns. can be performed as a function of many collective variables, with a particular focus on biol. problems, and using state-of-the-art methods such as metadynamics, umbrella sampling, and Jarzynski-equation based steered MD. The present software, written in ANSI-C language, can be easily interfaced with both Fortran and C/C++ codes.
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    Davenport, R. C.; Bash, P. A.; Seaton, B. A.; Karplus, M.; Petsko, G. A.; Ringe, D. Structure of the Triosephosphate Isomerase-Phosphoglycolohydroxamate Complex: An Analogue of the Intermediate on the Reaction Pathway. Biochemistry 1991, 30, 5821– 5826,  DOI: 10.1021/bi00238a002
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    Structure of the triosephosphate isomerase-phosphoglycolohydroxamate complex: an analog of the intermediate on the reaction pathway
    Davenport, Robert C.; Bash, Paul A.; Seaton, Barbara A.; Karplus, Martin; Petsko, Gregory A.; Ringe, Dagmar
    Biochemistry (1991), 30 (24), 5821-6CODEN: BICHAW; ISSN:0006-2960.
    The 3-dimensional structure of triosephosphate isomerase (TIM) complexed with a reactive intermediate analog, phosphoglycolohydroxamate (PGH), was solved at 1.9-Å resoln. and the structure was refined to an R-factor of 18%. Anal. of the refined structure revealed the geometry of the active-site residues and the interactions they make with the inhibitor and, by analogy, the substrates. The structure was consistent with an acid-base mechanism in which the carboxylate of Glu-165 abstrs. a proton from the substrate C atom while His-95 donates a proton to a substrate O atom to form an enediol (or enediolate) intermediate. The conformation of the bound substrate stereoelectronically favored proton transfer from the substrate C atom to the syn orbital of Glu-165. The crystal structure suggested that His-95 is neutral rather than cationic in the ground state and therefore would have to function as an imidazole acid instead of the usual imidazolium. Lys-12 was oriented so as to polarize the substrate O atoms by H-bonding and/or electrostatic interaction, providing stabilization for the charged transition state. Asn-10 may play a similar role.
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    Olsson, M. H. M.; Søndergaard, C. R.; Rostkowski, M.; Jensen, J. H. PROPKA3: Consistent Treatment of Internal and Surface Residues in Empirical pKa predictions. J. Chem. Theory Comput. 2011, 7, 525– 537,  DOI: 10.1021/ct100578z
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    PROPKA3: Consistent Treatment of Internal and Surface Residues in Empirical pKa Predictions
    Olsson, Mats H. M.; Sondergaard, Chresten R.; Rostkowski, Michal; Jensen, Jan H.
    Journal of Chemical Theory and Computation (2011), 7 (2), 525-537CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The authors have revised the rules and parameters for one of the most commonly used empirical pKa predictors, PROPKA, based on better phys. description of the desolvation and dielec. response for the protein. The authors have introduced a new and consistent approach to interpolate the description between the previously distinct classifications into internal and surface residues, which otherwise is found to give rise to an erratic and discontinuous behavior. Since the goal of this study is to lay out the framework and validate the concept, it focuses on Asp and Glu residues where the protein pKa values and structures are assumed to be more reliable. The new and improved implementation is evaluated and discussed; it is found to agree better with expt. than the previous implementation (in parentheses): rmsd = 0.79 (0.91) for Asp and Glu, 0.75 (0.97) for Tyr, 0.65 (0.72) for Lys, and 1.00 (1.37) for His residues. The most significant advance, however, is in reducing the no. of outliers and removing unreasonable sensitivity to small structural changes that arise from classifying residues as either internal or surface.
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  90. 90
    Jo, S.; Kim, T.; Iyer, V. G.; Im, W. CHARMM-GUI: A web-based graphical user interface for CHARMM. J. Comput. Chem. 2008, 29, 1859– 1865,  DOI: 10.1002/jcc.20945
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    CHARMM-GUI: a web-based graphical user interface for CHARMM
    Jo, Sunhwan; Kim, Taehoon; Iyer, Vidyashankara G.; Im, Wonpil
    Journal of Computational Chemistry (2008), 29 (11), 1859-1865CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    CHARMM is an academic research program used widely for macromol. mechanics and dynamics with versatile anal. and manipulation tools of at. coordinates and dynamics trajectories. CHARMM-GUI, http://www.charmm-gui.org, has been developed to provide a web-based graphical user interface to generate various input files and mol. systems to facilitate and standardize the usage of common and advanced simulation techniques in CHARMM. The web environment provides an ideal platform to build and validate a mol. model system in an interactive fashion such that, if a problem is found through visual inspection, one can go back to the previous setup and regenerate the whole system again. In this article, we describe the currently available functional modules of CHARMM-GUI Input Generator that form a basis for the advanced simulation techniques. Future directions of the CHARMM-GUI development project are also discussed briefly together with other features in the CHARMM-GUI website, such as Archive and Movie Gallery.
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  91. 91
    Lee, J.; Cheng, X.; Swails, J. M.; Yeom, M. S.; Eastman, P. K.; Lemkul, J. A.; Wei, S.; Buckner, J.; Jeong, J. C.; Qi, Y.; Jo, S.; Pande, V. S.; Case, D. A.; Brooks, C. L.; MacKerell, A. D.; Klauda, J. B.; Im, W. CHARMM-GUI Input Generator for NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM Simulations Using the CHARMM36 Additive Force Field. J. Chem. Theory Comput. 2016, 12, 405– 413,  DOI: 10.1021/acs.jctc.5b00935
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    CHARMM-GUI Input Generator for NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM Simulations Using the CHARMM36 Additive Force Field
    Lee, Jumin; Cheng, Xi; Swails, Jason M.; Yeom, Min Sun; Eastman, Peter K.; Lemkul, Justin A.; Wei, Shuai; Buckner, Joshua; Jeong, Jong Cheol; Qi, Yifei; Jo, Sunhwan; Pande, Vijay S.; Case, David A.; Brooks, Charles L.; MacKerell, Alexander D.; Klauda, Jeffery B.; Im, Wonpil
    Journal of Chemical Theory and Computation (2016), 12 (1), 405-413CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Proper treatment of nonbonded interactions is essential for the accuracy of mol. dynamics (MD) simulations, esp. in studies of lipid bilayers. The use of the CHARMM36 force field (C36 FF) in different MD simulation programs can result in disagreements with published simulations performed with CHARMM due to differences in the protocols used to treat the long-range and 1-4 nonbonded interactions. In this study, we systematically test the use of the C36 lipid FF in NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM. A wide range of Lennard-Jones (LJ) cutoff schemes and integrator algorithms were tested to find the optimal simulation protocol to best match bilayer properties of six lipids with varying acyl chain satn. and head groups. MD simulations of a 1,2-dipalmitoyl-sn-phosphatidylcholine (DPPC) bilayer were used to obtain the optimal protocol for each program. MD simulations with all programs were found to reasonably match the DPPC bilayer properties (surface area per lipid, chain order parameters, and area compressibility modulus) obtained using the std. protocol used in CHARMM as well as from expts. The optimal simulation protocol was then applied to the other five lipid simulations and resulted in excellent agreement between results from most simulation programs as well as with exptl. data. AMBER compared least favorably with the expected membrane properties, which appears to be due to its use of the hard-truncation in the LJ potential vs. a force-based switching function used to smooth the LJ potential as it approaches the cutoff distance. The optimal simulation protocol for each program has been implemented in CHARMM-GUI. This protocol is expected to be applicable to the remainder of the additive C36 FF including the proteins, nucleic acids, carbohydrates, and small mols.
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    Gaus, M.; Cui, Q.; Elstner, M. DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB). J. Chem. Theory Comput. 2011, 7, 931– 948,  DOI: 10.1021/ct100684s
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    DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB)
    Gaus, Michael; Cui, Qiang; Elstner, Marcus
    Journal of Chemical Theory and Computation (2011), 7 (4), 931-948CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The self-consistent-charge d.-functional tight-binding method (SCC-DFTB) is an approx. quantum chem. method derived from d. functional theory (DFT) based on a second-order expansion of the DFT total energy around a ref. d. In the present study, we combine earlier extensions and improve them consistently with, first, an improved Coulomb interaction between at. partial charges and, second, the complete third-order expansion of the DFT total energy. These modifications lead us to the next generation of the DFTB methodol. called DFTB3, which substantially improves the description of charged systems contg. elements C, H, N, O, and P, esp. regarding hydrogen binding energies and proton affinities. As a result, DFTB3 is particularly applicable to biomol. systems. Remaining challenges and possible solns. are also briefly discussed.
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    Best, R. B.; Zhu, X.; Shim, J.; Lopes, P. E. M.; Mittal, J.; Feig, M.; Mackerell, A. D. Optimization of the Additive CHARMM All-Atom Protein Force Field Targeting Improved Sampling of the Backbone φ, ψ and Side-Chain χ1 and χ2 Dihedral Angles. J. Chem. Theory Comput. 2012, 8, 3257– 3273,  DOI: 10.1021/ct300400x
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    Optimization of the Additive CHARMM All-Atom Protein Force Field Targeting Improved Sampling of the Backbone .vphi., ψ and Side-Chain χ1 and χ2 Dihedral Angles
    Best, Robert B.; Zhu, Xiao; Shim, Jihyun; Lopes, Pedro E. M.; Mittal, Jeetain; Feig, Michael; MacKerell, Alexander D.
    Journal of Chemical Theory and Computation (2012), 8 (9), 3257-3273CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    While the quality of the current CHARMM22/CMAP additive force field for proteins has been demonstrated in a large no. of applications, limitations in the model with respect to the equil. between the sampling of helical and extended conformations in folding simulations have been noted. To overcome this, as well as make other improvements in the model, we present a combination of refinements that should result in enhanced accuracy in simulations of proteins. The common (non-Gly, -Pro) backbone CMAP potential has been refined against exptl. soln. NMR data for weakly structured peptides, resulting in a rebalancing of the energies of the α-helix and extended regions of the Ramachandran map, correcting the α-helical bias of CHARMM22/CMAP. The Gly and Pro CMAPs have been refitted to more accurate quantum-mech. energy surfaces. Side-chain torsion parameters have been optimized by fitting to backbone-dependent quantum-mech. energy surfaces, followed by addnl. empirical optimization targeting NMR scalar couplings for unfolded proteins. A comprehensive validation of the revised force field was then performed against a collection of exptl. data: (i) comparison of simulations of eight proteins in their crystal environments with crystal structures; (ii) comparison with backbone scalar couplings for weakly structured peptides; (iii) comparison with NMR residual dipolar couplings and scalar couplings for both backbone and side-chains in folded proteins; (iv) equil. folding of mini-proteins. The results indicate that the revised CHARMM 36 parameters represent an improved model for modeling and simulation studies of proteins, including studies of protein folding, assembly, and functionally relevant conformational changes.
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    Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 1983, 79, 926– 935,  DOI: 10.1063/1.445869
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    Comparison of simple potential functions for simulating liquid water
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    Journal of Chemical Physics (1983), 79 (2), 926-35CODEN: JCPSA6; ISSN:0021-9606.
    Classical Monte Carlo simulations were carried out for liq. H2O in the NPT ensemble at 25° and 1 atm using 6 of the simpler intermol. potential functions for the dimer. Comparisons were made with exptl. thermodn. and structural data including the neutron diffraction results of Thiessen and Narten (1982). The computed densities and potential energies agree with expt. except for the original Bernal-Fowler model, which yields an 18% overest. of the d. and poor structural results. The discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons were made for the self-diffusion coeffs. obtained from mol. dynamics simulations.
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    Mayne, C. G.; Saam, J.; Schulten, K.; Tajkhorshid, E.; Gumbart, J. C. Rapid parameterization of small molecules using the force field toolkit. J. Comput. Chem. 2013, 34, 2757– 2770,  DOI: 10.1002/jcc.23422
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    Rapid parameterization of small molecules using the force field toolkit
    Mayne, Christopher G.; Saam, Jan; Schulten, Klaus; Tajkhorshid, Emad; Gumbart, James C.
    Journal of Computational Chemistry (2013), 34 (32), 2757-2770CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    The inability to rapidly generate accurate and robust parameters for novel chem. matter continues to severely limit the application of mol. dynamics simulations to many biol. systems of interest, esp. in fields such as drug discovery. Although the release of generalized versions of common classical force fields, for example, General Amber Force Field and CHARMM General Force Field, have posited guidelines for parameterization of small mols., many tech. challenges remain that have hampered their wide-scale extension. The Force Field Toolkit (ffTK), described herein, minimizes common barriers to ligand parameterization through algorithm and method development, automation of tedious and error-prone tasks, and graphical user interface design. Distributed as a VMD plugin, ffTK facilitates the traversal of a clear and organized workflow resulting in a complete set of CHARMM-compatible parameters. A variety of tools are provided to generate quantum mech. target data, setup multidimensional optimization routines, and analyze parameter performance. Parameters developed for a small test set of mols. using ffTK were comparable to existing CGenFF parameters in their ability to reproduce exptl. measured values for pure-solvent properties (<15% error from expt.) and free energy of solvation (±0.5 kcal/mol from expt.). © 2013 Wiley Periodicals, Inc.
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    Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126, 014101,  DOI: 10.1063/1.2408420
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    Canonical sampling through velocity rescaling
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    Journal of Chemical Physics (2007), 126 (1), 014101/1-014101/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The authors present a new mol. dynamics algorithm for sampling the canonical distribution. In this approach the velocities of all the particles are rescaled by a properly chosen random factor. The algorithm is formally justified and it is shown that, in spite of its stochastic nature, a quantity can still be defined that remains const. during the evolution. In numerical applications this quantity can be used to measure the accuracy of the sampling. The authors illustrate the properties of this new method on Lennard-Jones and TIP4P water models in the solid and liq. phases. Its performance is excellent and largely independent of the thermostat parameter also with regard to the dynamic properties.
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    Andersen, H. C. Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculations. J. Comput. Phys. 1983, 52, 24– 34,  DOI: 10.1016/0021-9991(83)90014-1
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    RATTLE: a "velocity" version of the SHAKE algorithm for molecular dynamics calculations
    Andersen, Hans C.
    Journal of Computational Physics (1983), 52 (1), 24-34CODEN: JCTPAH; ISSN:0021-9991.
    An algorithm, called RATTLE, for integrating the equations of motion in mol. dynamics calcns. for mol. models with internal constraints is presented. RATTLE calcs. the positions and velocities at the next time from the positions and velocities at the present time step, without requiring information about the earlier history. It is based on the Verlet algorithm and retains the simplicity of using Cartesian coordinates for each of the atoms to describe the configuration of a mol. with internal constraints. RATTLE guarantees that the coordinates and velocities of the atoms in a mol. satisfy the internal constraints at each time step.
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    Miyamoto, S.; Kollman, P. A. Settle: An analytical version of the SHAKE and RATTLE algorithm for rigid water models. J. Comput. Chem. 1992, 13, 952– 962,  DOI: 10.1002/jcc.540130805
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    SETTLE: an analytical version of the SHAKE and RATTLE algorithm for rigid water models
    Miyamoto, Shuichi; Kollman, Peter A.
    Journal of Computational Chemistry (1992), 13 (8), 952-62CODEN: JCCHDD; ISSN:0192-8651.
    An anal. algorithm, called SETTLE, for resetting the positions and velocities to satisfy the holonomic constraints on the rigid water model is presented. This method is based on the Cartesian coordinate system and can be used in place of SHAKE and RATTLE. The authors implemented this algorithm in the SPASMS package of mol. mechanics and dynamics. Several series of mol. dynamics simulations were carried out to examine the performance of the new algorithm in comparison with the original RATTLE method. SETTLE is of higher accuracy and is faster than RATTLE with reasonable tolerances by three to nine times on a scalar machine. The performance improvement ranged from factors of 26 to 98 on a vector machine since the method presented is not iterative.
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    Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785– 789,  DOI: 10.1103/PhysRevB.37.785
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    Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
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    A correlation-energy formula due to R. Colle and D. Salvetti (1975), in which the correlation energy d. is expressed in terms of the electron d. and a Laplacian of the 2nd-order Hartree-Fock d. matrix, is restated as a formula involving the d. and local kinetic-energy d. On insertion of gradient expansions for the local kinetic-energy d., d.-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calcns. on a no. of atoms, pos. ions, and mols., of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.
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    Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648– 5652,  DOI: 10.1063/1.464913
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    Density-functional thermochemistry. III. The role of exact exchange
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    Journal of Chemical Physics (1993), 98 (7), 5648-52CODEN: JCPSA6; ISSN:0021-9606.
    Despite the remarkable thermochem. accuracy of Kohn-Sham d.-functional theories with gradient corrections for exchange-correlation, the author believes that further improvements are unlikely unless exact-exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange-correlation functional (contg. local-spin-d., gradient, and exact-exchange terms) is tested for 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total at. energies of first- and second-row systems. This functional performs better than previous functionals with gradient corrections only, and fits expt. atomization energies with an impressively small av. abs. deviation of 2.4 kcal/mol.
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    Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104,  DOI: 10.1063/1.3382344
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    A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
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    The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
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    Dunning, T. H., Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90, 1007– 1023,  DOI: 10.1063/1.456153
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    Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
    Dunning, Thom H., Jr.
    Journal of Chemical Physics (1989), 90 (2), 1007-23CODEN: JCPSA6; ISSN:0021-9606.
    Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.
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    Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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    Weigend, F.; Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297– 3305,  DOI: 10.1039/b508541a
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    Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy
    Weigend, Florian; Ahlrichs, Reinhart
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    Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 mols. representing (nearly) all elements-except lanthanides-in their common oxidn. states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, d. functional theory and correlated methods, for which we had chosen Moller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.
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    QM/MM simulations identify the determinants of catalytic activity differences between type II dehydroquinase enzymes
    Lence, Emilio; van der Kamp, Marc W.; Gonzalez-Bello, Concepcion; Mulholland, Adrian J.
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    Type II dehydroquinase enzymes (DHQ2), recognized targets for antibiotic drug discovery, show significantly different activities dependent on the species: DHQ2 from Mycobacterium tuberculosis (MtDHQ2) and Helicobacter pylori (HpDHQ2) show a 50-fold difference in catalytic efficiency. Revealing the determinants of this activity difference is important for our understanding of biol. catalysis and further offers the potential to contribute to tailoring specificity in drug design. Mol. dynamics simulations using a quantum mechanics/mol. mechanics potential, with correlated ab initio single point corrections, identify and quantify the subtle determinants of the exptl. obsd. difference in efficiency. The rate-detg. step involves the formation of an enolate intermediate: more efficient stabilization of the enolate and transition state of the key step in MtDHQ2, mainly by the essential residues Tyr24 and Arg19, makes it more efficient than HpDHQ2. Further, a water mol., which is absent in MtDHQ2 but involved in generation of the catalytic Tyr22 tyrosinate in HpDHQ2, was found to destabilize both the transition state and the enolate intermediate. The quantification of the contribution of key residues and water mols. in the rate-detg. step of the mechanism also leads to improved understanding of higher potencies and specificity of known inhibitors, which should aid ongoing inhibitor design.
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    The exptl. results on the interconversion of dihydroxyacetone phosphate and D-glyceraldehyde 3-phosphate catalyzed by triose phosphate isomerase that are presented in 5 previous papers are collected here and analyzed according to the theory presented in the 1st paper (Albery, W. J., and Knowles, J. R. (1976)). The rate consts. and fractionation factors so derived allow the construction of the Gibbs free-energy profile for this enzyme-catalyzed reaction.
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    Carrying out free energy simulations (FES) using quantum mech. (QM) Hamiltonians remains an attractive, albeit elusive goal. Renewed efforts in this area have focused on using "indirect" thermodn. cycles to connect "low level" simulation results to "high level" free energies. The main obstacle to computing converged free energy results between mol. mech. (MM) and QM (ΔAMM→QM), as recently demonstrated by us and others, is differences in the so-called "stiff" degrees of freedom (e.g., bond stretching) between the resp. energy surfaces. Herein, we demonstrate that this problem can be efficiently circumvented using nonequil. work (NEW) techniques, i.e., Jarzynski's and Crooks' equations. Initial applications of computing ΔAMM→QMNEW, for blocked amino acids alanine and serine as well as to generate butane's potentials of mean force via the indirect QM/MM FES method, showed marked improvement over traditional FES approaches.
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    We demonstrate that Jarzynski's equation can be used to reliably compute free energy differences between low and high level representations of systems. The need for such a calcn. arises when employing the so-called "indirect" approach to free energy simulations with mixed quantum mech./mol. mech. (QM/MM) Hamiltonians; a popular technique for circumventing extensive simulations involving quantum chem. computations. We have applied this methodol. to several small and medium sized org. mols., both in the gas phase and explicit solvent. Test cases include several systems for which the std. approach; i.e., free energy perturbation between low and high level description, fails to converge. Finally, we identify three major areas in which the difference between low and high level representations make the calcn. of ΔA(low→high) difficult: bond stretching and angle bending, different preferred conformations, and the response of the MM region to the charge distribution of the QM region. © 2016 Wiley Periodicals, Inc.
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    The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost assocd. with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the ''indirect'' approach is generally taken, necessitating a free energy calcn. between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with std. free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approxns. have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and anal. demonstrate that this ''interaction energy approxn.'' (IEA) is theor. incorrect, and the implicit approxn. invoked is spurious at best. Herein, we demonstrate this via solvation free energy calcns. using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼ 1.5 kcal/mol from the rigorously obtained value.
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    An implementation of Ewald summation for use in mixed quantum mechanics/mol. mechanics (QM/MM) calcns. is presented, which builds upon previous work by others that was limited to semi-empirical electronic structure for the QM region. Unlike previous work, our implementation describes the wave function's periodic images using "ChElPG" at. charges, which are detd. by fitting to the QM electrostatic potential evaluated on a real-space grid. This implementation is stable even for large Gaussian basis sets with diffuse exponents, and is thus appropriate when the QM region is described by a correlated wave function. Derivs. of the ChElPG charges with respect to the QM d. matrix are a potentially serious bottleneck in this approach, so we introduce a ChElPG algorithm based on atom-centered Lebedev grids. The ChElPG charges thus obtained exhibit good rotational invariance even for sparse grids, enabling significant cost savings. Detailed anal. of the optimal choice of user-selected Ewald parameters, as well as timing breakdowns, is presented. (c) 2013 American Institute of Physics.
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    Giese, Timothy J.; York, Darrin M.
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    A new approach for performing Particle Mesh Ewald in ab initio quantum mech./mol. mech. (QM/MM) simulations with extended AO basis sets is presented. The new approach, the Ambient-Potential Composite Ewald (CEw) method, does not perform the QM/MM interaction with Mulliken charges nor electrostatically fit charges. Instead the nuclei and electron d. interact directly with the MM environment, but in a manner that avoids the use of dense Fourier transform grids. By performing the electrostatics with the underlying QM d., the CEw method avoids SCF instabilities that have been encountered with simple charge mapping procedures. Potential of mean force (PMF) profiles of the p-nitrophenyl phosphate dissocn. reaction in explicit solvent are computed from PBE0/6-31G* QM/MM mol. dynamics simulations with various electrostatic protocols. The CEw profiles are shown to be stable with respect to real-space Ewald cutoff, whereas the PMFs computed from truncated and switched electrostatics produce artifacts. PBE0/6-311G**, AM1/d-PhoT, and DFTB2 QM/MM simulations are performed to generate two-dimensional PMF profiles of the phosphoryl transesterification reactions with ethoxide and phenoxide leaving groups. The semiempirical models incorrectly produce a concerted ethoxide mechanism, whereas PBE0 correctly produces a stepwise mechanism. The ab initio reaction barriers agree more closely to expt. than the semiempirical models. The failure of Mulliken-charge QM/MM-Ewald is analyzed.
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    Vasilevskaya, T.; Thiel, W. Periodic Boundary Conditions in QM/MM Calculations: Implementation and Tests. J. Chem. Theory Comput. 2016, 12, 3561– 3570,  DOI: 10.1021/acs.jctc.6b00269
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    Periodic Boundary Conditions in QM/MM Calculations: Implementation and Tests
    Vasilevskaya, Tatiana; Thiel, Walter
    Journal of Chemical Theory and Computation (2016), 12 (8), 3561-3570CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Quantum mechanics/mol. mechanics (QM/MM) simulations of reactions in solns. and in solvated enzymes can be performed using the QM/MM-Ewald approach with periodic boundary conditions (PBC) or a nonperiodic treatment with a finite solvent shell (droplet model). To avoid the changes in QM codes that are required in std. QM/MM-Ewald implementations, we present a general method (Gen-Ew) for periodic QM/MM calcns. that can be used with any QM method in the QM/MM framework. The Gen-Ew approach approximates the QM/MM-Ewald method by representing the PBC potential by virtual charges on a sphere and the QM d. by electrostatic potential (ESP) charges. Test calcns. show that the deviations between Gen-Ew and QM/MM-Ewald results are generally small enough to justify the application of the Gen-Ew method in the absence of a suitable QM/MM-Ewald implementation. We compare the results from periodic QM/MM calcns. (QM/MM-Ewald, Gen-Ew) to their nonperiodic counterparts (droplet model) for five test reactions in water and for the Claisen rearrangement in chorismate mutase. The periodic and nonperiodic QM/MM treatments give similar free energy profiles for the reactions in soln. (umbrella sampling, free energy deviations of the order of 1 kcal/mol) and essentially the same energy profile (constrained geometry optimizations) for the Claisen rearrangement in chorismate mutase. In all cases considered, long-range electrostatic interactions are thus well captured by nonperiodic QM/MM calcns. in a water droplet of reasonable size (radius of 15-20 Å). This provides further justification for the widespread use of the computationally efficient droplet model in QM/MM studies of reactions in soln. and in enzymes.
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    Ab initio quantum mechanics/molecular mechanics method with periodic boundaries employing Ewald summation technique to electron-charge interaction: Treatment of the surface-dipole term
    Kawashima, Y.; Ishimura, K.; Shiga, M.
    Journal of Chemical Physics (2019), 150 (12), 124103/1-124103/14CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We have developed a combined quantum mechanics/mol. mechanics (QM/MM) method with periodic boundary condition (PBC) treatment of explicit electron-charge interactions in a theor. rigorous manner, for an accurate description of electronic structures for mols. in the condensed phase. The Ewald summation technique is employed for the calcn. of the one-electron Hamiltonian in an ab initio framework. We decomp. the Coulomb interactions into two components: those within the same cell and those between different cells. The former is calcd. in the same way as the conventional QM/MM calcn. for isolated systems; this article focuses on our novel method for calcg. the latter type of Coulomb interactions. The detailed formulation of the Hamiltonian of this new QM/MM-PBC method, as well as the necessary one-electron integrals and their gradients, is given. The novel method is assessed by applying it to the dil. water system and a system with a coumarin mol. in water solvent; it successfully reproduces the electronic energies, frontier orbital energies, and Mulliken population charge of the real-space limit calcd. by QM/MM using large isolated systems. We investigated the contribution from each term of the Hamiltonian and found that the surface-dipole term in the Ewald summation technique is indispensable for QM/MM-PBC calcns. The newly developed QM/MM-PBC method is promising for tackling chem. reactions and excited states of mols. in the condensed phase. (c) 2019 American Institute of Physics.
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    Figure 1

    Figure 1. Performance of QM/MM-MD simulations combining GENESIS and QSimulate-QM. (a) Visualization of a water droplet and a QM region in the center (left). The timing data for a water droplet with increasing QM size using DFTB3, PBE/def2-SVP, and B3LYP/aug-cc-pVDZ. The total number of atoms is 7014. The computing node has two CPUs of Intel Xeon Gold 6148 (20 core 2.40 GHz), and 10 threads ×4MPI processes were assigned per node. (b) Visualization of TIM and an enlargement of the binding pocket (left). The timing data of TIM using 1 node (7 threads × 8 MPI processes) with various electronic structure methods (middle) and multiple nodes with B3LYP-D3/aug-cc-pVDZ (right). The number of QM and MM atoms are 35 and 37 182, respectively. The number of basis sets is 378 and 623 with def2-SVP and aug-cc-pVDZ, respectively. The computing node has two CPUs of Intel Xeon Platinum 8280 (28 core 2.70 GHz, AVX-512). The timing was measured in NVT condition with a time step of 2 fs.

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    Figure 2

    Figure 2. Schematic illustration of the conversion of DHAP to GAP with Glu165 and His95 of TIM. Protons are indicated in blue, and the electrons as well as CC/CO double bonds are in red.

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    Figure 3

    Figure 3. Structures of DHAP (I), intermediates (II–IV), and GAP (V) with His95 and Glu165 obtained by QM/MM calculations at the B3LYP-D3/aug-cc-pVDZ level of theory. The protons before and after the reaction are indicated in green and pink circles, respectively.

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    Figure 4

    Figure 4. Convergence of an MEP search in the first PT step (I → II) with the string-method calculations.

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    Figure 5

    Figure 5. Interatomic distances (left) and energetics (right) along MEPs obtained by QM/MM calculations at the level of (a) B3LYP-D3 and (b) DFTB3. The definition of r1 – r8 is given in Figure 2.

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    Figure 6

    Figure 6. Structure of the reactive site along the MEP and the relevant intermolecular distances (in Å) obtained by B3LYP-D3/aug-cc-pVDZ. Those of DFTB3 are also given in parentheses. Note that DFTB3 yields III as a transition state, so that TS2 and TS3 are not characterized.

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    Figure 7

    Figure 7. PMF as a function of Path CV obtained by B3LYP-D3 (left) and DFTB3 (right).

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    Figure 8

    Figure 8. 2D PMF of PT reactions obtained by QM/MM calculations at the B3LYP-D3/aug-cc-pVDZ level.

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  • References

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    This article references 116 other publications.

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      A review. The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely assocd. with the membrane. The heterogeneity of lipid compn. of biol. membranes and the effect of lipid mols. on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with exptl. techniques is however still prohibitively challenging. Mol. dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolns. to gain at.-level structural information and energetics on lipid-protein interactions. In this review, the authors aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.
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    3. 3
      Whitford, P. C.; Geggier, P.; Altman, R. B.; Blanchard, S. C.; Onuchic, J. N.; Sanbonmatsu, K. Y. Accommodation of aminoacyl-tRNA into the ribosome involves reversible excursions along multiple pathways. RNA 2010, 16, 1196– 1204,  DOI: 10.1261/rna.2035410
      3
      Accommodation of aminoacyl-tRNA into the ribosome involves reversible excursions along multiple pathways
      Whitford, Paul C.; Geggier, Peter; Altman, Roger B.; Blanchard, Scott C.; Onuchic, Jose N.; Sanbonmatsu, Karissa Y.
      RNA (2010), 16 (6), 1196-1204CODEN: RNARFU; ISSN:1355-8382. (Cold Spring Harbor Laboratory Press)
      The ribosome is a massive ribonucleoprotein complex (∼2.4 MDa) that uses large-scale structural fluctuations to produce unidirectional protein synthesis. Accommodation is a key conformational change during tRNA selection that allows movement of tRNA into the ribosome. Here, the authors address the structure-function relation that governs accommodation using all-atom mol. simulations and single-mol. fluorescence resonance energy transfer (smFRET). Simulations that employ an all-atom, structure-based (G‾o-like) model illuminate the interplay between configurational entropy and effective enthalpy during the accommodation process. This delicate balance leads to spontaneous reversible accommodation attempts, which are corroborated by smFRET measurements. The dynamics about the endpoints of accommodation (the A/T and A/A conformations) obtained from structure-based simulations are validated by multiple 100-200 ns explicit-solvent simulations (3.2 million atoms for a cumulative 1.4 μs) and previous crystallog. anal. The configurational entropy of the 3'-CCA end of aminoacyl-tRNA resists accommodation, leading to a multistep accommodation process that encompasses a distribution of parallel pathways. The calcd. mechanism is robust across simulation methods and protocols, suggesting that the structure of the accommodation corridor imposes stringent limitations on the accessible pathways. The identified mechanism and obsd. parallel pathways establish an atomistic framework for interpreting a large body of biochem. data and demonstrate that conformational changes during translation occur through a stochastic trial-and-error process, rather than in concerted lock-step motions.
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    4. 4
      Wang, B.; Opron, K.; Burton, Z. F.; Cukier, R. I.; Feig, M. Five checkpoints maintaining the fidelity of transcription by RNA polymerases in structural and energetic details. Nucleic Acids Res. 2015, 43, 1133– 1146,  DOI: 10.1093/nar/gku1370
      4
      ImmuCo: a database of gene co-expression in immune cells
      Wang, Pingzhang; Qi, Huiying; Song, Shibin; Li, Shuang; Huang, Ningyu; Han, Wenling; Ma, Dalong
      Nucleic Acids Research (2015), 43 (D1), D1133-D1139CODEN: NARHAD; ISSN:0305-1048. (Oxford University Press)
      Current gene co-expression databases and correlation networks do not support cell-specific anal. Gene co-expression and expression correlation are subtly different phenomena, although both are likely to be functionally significant. Here, we report a new database, ImmuCo, which is a cell-specific database that contains information about gene co-expression in immune cells, identifying co-expression and correlation between any two genes. The strength of co-expression of queried genes is indicated by signal values and detection calls, whereas expression correlation and strength are reflected by Pearson correlation coeffs. A scatter plot of the signal values is provided to directly illustrate the extent of co-expression and correlation. In addn., the database allows the anal. of cell-specific gene expression profile across multiple exptl. conditions and can generate a list of genes that are highly correlated with the queried genes. Currently, the database covers 18 human cell groups and 10 mouse cell groups, including 20283 human genes and 20963 mouse genes. More than 8.6 × 108 and 7.4 × 108 probe set combinations are provided for querying each human and mouse cell group, resp. Sample applications support the distinctive advantages of the database.
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    5. 5
      Da, L.-T.; Pardo-Avila, F.; Xu, L.; Silva, D.-A.; Zhang, L.; Gao, X.; Wang, D.; Huang, X. Bridge helix bending promotes RNA polymerase II backtracking through a critical and conserved threonine residue. Nat. Commun. 2016, 7, 11244,  DOI: 10.1038/ncomms11244
      5
      Bridge helix bending promotes RNA polymerase II backtracking through a critical and conserved threonine residue
      Da, Lin-Tai; Pardo-Avila, Fatima; Xu, Liang; Silva, Daniel-Adriano; Zhang, Lu; Gao, Xin; Wang, Dong; Huang, Xuhui
      Nature Communications (2016), 7 (), 11244CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      The dynamics of the RNA polymerase II (Pol II) backtracking process is poorly understood. Here, the authors built a Markov State Model from extensive mol. dynamics simulations to identify metastable intermediate states and the dynamics of backtracking at atomistic detail. The results revealed that Pol II backtracking occurred in a stepwise mode where 2 intermediate states were involved. The authors found that the continuous bending motion of the bridge helix (BH) served as a crit. checkpoint, using the highly conserved BH residue, Thr-831, as a sensing probe for the 3'-terminal base paring of RNA:DNA hybrid. If the base pair was mismatched, BH bending could promote the RNA 3'-end nucleotide into a frayed state that further led to the backtracked state. These computational observations were validated by site-directed mutagenesis and transcript cleavage assays, and provided insights into the key factors that regulate the preferences of the backward translocation.
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    6. 6
      Brooks, B. R. CHARMM: The biomolecular simulation program. J. Comput. Chem. 2009, 30, 1545– 1614,  DOI: 10.1002/jcc.21287
      6
      CHARMM: The biomolecular simulation program
      Brooks, B. R.; Brooks, C. L., III; Mackerell, A. D., Jr.; Nilsson, L.; Petrella, R. J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S.; Caflisch, A.; Caves, L.; Cui, Q.; Dinner, A. R.; Feig, M.; Fischer, S.; Gao, J.; Hodoscek, M.; Im, W.; Kuczera, K.; Lazaridis, T.; Ma, J.; Ovchinnikov, V.; Paci, E.; Pastor, R. W.; Post, C. B.; Pu, J. Z.; Schaefer, M.; Tidor, B.; Venable, R. M.; Woodcock, H. L.; Wu, X.; Yang, W.; York, D. M.; Karplus, M.
      Journal of Computational Chemistry (2009), 30 (10), 1545-1614CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      A review. CHARMM (Chem. at HARvard Mol. Mechanics) is a highly versatile and widely used mol. simulation program. It has been developed over the last three decades with a primary focus on mols. of biol. interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small mol. ligands, as they occur in soln., crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, mol. minimization, dynamics, and anal. techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calcns. with CHARMM can be performed using a no. of different energy functions and models, from mixed quantum mech.-mol. mech. force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009.
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    7. 7
      Lee, T.-S.; Cerutti, D. S.; Mermelstein, D.; Lin, C.; LeGrand, S.; Giese, T. J.; Roitberg, A.; Case, D. A.; Walker, R. C.; York, D. M. GPU-Accelerated Molecular Dynamics and Free Energy Methods in Amber18: Performance Enhancements and New Features. J. Chem. Inf. Model. 2018, 58, 2043– 2050,  DOI: 10.1021/acs.jcim.8b00462
      7
      GPU-Accelerated Molecular Dynamics and Free Energy Methods in Amber18: Performance Enhancements and New Features
      Lee, Tai-Sung; Cerutti, David S.; Mermelstein, Dan; Lin, Charles; LeGrand, Scott; Giese, Timothy J.; Roitberg, Adrian; Case, David A.; Walker, Ross C.; York, Darrin M.
      Journal of Chemical Information and Modeling (2018), 58 (10), 2043-2050CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      The authors report progress in graphics processing unit (GPU)-accelerated mol. dynamics and free energy methods in Amber18. Of particular interest is the development of alchem. free energy algorithms, including free energy perturbation and thermodn. integration methods with support for nonlinear soft-core potential and parameter interpolation transformation pathways. These methods can be used in conjunction with enhanced sampling techniques such as replica exchange, const.-pH mol. dynamics, and new 12-6-4 potentials for metal ions. Addnl. performance enhancements have been made that enable appreciable speed-up on GPUs relative to the previous software release.
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    8. 8
      Abraham, M. J.; Murtola, T.; Schulz, R.; Páll, S.; Smith, J. C.; Hess, B.; Lindahl, E. GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 2015, 1–2, 19– 25,  DOI: 10.1016/j.softx.2015.06.001
      There is no corresponding record for this reference.
    9. 9
      Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kalé, L.; Schulten, K. Scalable Molecular Dynamics with NAMD. J. Comput. Chem. 2005, 26, 1781– 1802,  DOI: 10.1002/jcc.20289
      9
      Scalable molecular dynamics with NAMD
      Phillips, James C.; Braun, Rosemary; Wang, Wei; Gumbart, James; Tajkhorshid, Emad; Villa, Elizabeth; Chipot, Christophe; Skeel, Robert D.; Kale, Laxmikant; Schulten, Klaus
      Journal of Computational Chemistry (2005), 26 (16), 1781-1802CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      NAMD is a parallel mol. dynamics code designed for high-performance simulation of large biomol. systems. NAMD scales to hundreds of processors on high-end parallel platforms, as well as tens of processors on low-cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats. This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical mol. dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temp. and pressure controls used. Features for steering the simulation across barriers and for calcg. both alchem. and conformational free energy differences are presented. The motivations for and a roadmap to the internal design of NAMD, implemented in C++ and based on Charm++ parallel objects, are outlined. The factors affecting the serial and parallel performance of a simulation are discussed. Finally, typical NAMD use is illustrated with representative applications to a small, a medium, and a large biomol. system, highlighting particular features of NAMD, for example, the Tcl scripting language. The article also provides a list of the key features of NAMD and discusses the benefits of combining NAMD with the mol. graphics/sequence anal. software VMD and the grid computing/collab. software BioCoRE. NAMD is distributed free of charge with source code at www.ks.uiuc.edu.
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    10. 10
      Marrink, S. J.; Risselada, H. J.; Yefimov, S.; Tieleman, D. P.; de Vries, A. H. The MARTINI Force Field: Coarse Grained Model for Biomolecular Simulations. J. Phys. Chem. B 2007, 111, 7812– 7824,  DOI: 10.1021/jp071097f
      10
      The MARTINI Force Field: Coarse Grained Model for Biomolecular Simulations
      Marrink, Siewert J.; Risselada, H. Jelger; Yefimov, Serge; Tieleman, D. Peter; De Vries, Alex H.
      Journal of Physical Chemistry B (2007), 111 (27), 7812-7824CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      We present an improved and extended version of our coarse grained lipid model. The new version, coined the MARTINI force field, is parametrized in a systematic way, based on the reprodn. of partitioning free energies between polar and apolar phases of a large no. of chem. compds. To reproduce the free energies of these chem. building blocks, the no. of possible interaction levels of the coarse-grained sites has increased compared to those of the previous model. Application of the new model to lipid bilayers shows an improved behavior in terms of the stress profile across the bilayer and the tendency to form pores. An extension of the force field now also allows the simulation of planar (ring) compds., including sterols. Application to a bilayer/cholesterol system at various concns. shows the typical cholesterol condensation effect similar to that obsd. in all atom representations.
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    11. 11
      Kenzaki, H.; Koga, N.; Hori, N.; Kanada, R.; Li, W.; Okazaki, K.-i.; Yao, X.-Q.; Takada, S. CafeMol: A Coarse-Grained Biomolecular Simulator for Simulating Proteins at Work. J. Chem. Theory Comput. 2011, 7, 1979– 1989,  DOI: 10.1021/ct2001045
      11
      CafeMol: A Coarse-Grained Biomolecular Simulator for Simulating Proteins at Work
      Kenzaki, Hiroo; Koga, Nobuyasu; Hori, Naoto; Kanada, Ryo; Li, Wenfei; Okazaki, Kei-ichi; Yao, Xin-Qiu; Takada, Shoji
      Journal of Chemical Theory and Computation (2011), 7 (6), 1979-1989CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      For simulating proteins at work in millisecond time scale or longer, the authors develop a coarse-grained (CG) mol. dynamics (MD) method and software, CafeMol. At the resoln. of one-particle-per-residue, CafeMol equips four structure-based protein models: (1) the off-lattice Go model, (2) the at. interaction based CG model for native state and folding dynamics, (3) the multiple-basin model for conformational change dynamics, and (4) the elastic network model for quasiharmonic fluctuations around the native structure. Ligands can be treated either explicitly or implicitly. For mimicking functional motions of proteins driven by some external force, CafeMol has various and flexible means to "switch" the energy functions that induce active motions of the proteins. CafeMol can do parallel computation with modest sized PC clusters. The authors describe CafeMol methods and illustrate it with several examples, such as rotary motions of F1-ATPase and drug exports from a transporter. The CafeMol source code is available at www.cafemol.org.
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    12. 12
      Han, W.; Schulten, K. Further Optimization of a Hybrid United-Atom and Coarse-Grained Force Field for Folding Simulations: Improved Backbone Hydration and Interactions between Charged Side Chains. J. Chem. Theory Comput. 2012, 8, 4413– 4424,  DOI: 10.1021/ct300696c
      12
      Further Optimization of a Hybrid United-Atom and Coarse-Grained Force Field for Folding Simulations: Improved Backbone Hydration and Interactions between Charged Side Chains
      Han, Wei; Schulten, Klaus
      Journal of Chemical Theory and Computation (2012), 8 (11), 4413-4424CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      PACE, a hybrid force field that couples united-atom protein models with coarse-grained (CG) solvent, has been further optimized, aiming to improve its efficiency for folding simulations. Backbone hydration parameters have been reoptimized based on hydration free energies of polyalanyl peptides through atomistic simulations. Also, atomistic partial charges from all-atom force fields were combined with PACE to provide a more realistic description of interactions between charged groups. Using replica exchange mol. dynamics, ab initio folding using the new PACE has been achieved for seven small proteins (16-23 residues) with different structural motifs. Exptl. data about folded states, such as their stability at room temp., m.p., and NMR nuclear Overhauser effect constraints, were also well reproduced. Moreover, a systematic comparison of folding kinetics at room temp. has been made with expts., through std. mol. dynamics simulations, showing that the new PACE may accelerate the actual folding kinetics 5-10-fold, permitting now the study of folding mechanisms. In particular, we used the new PACE to fold a 73-residue protein, α3D, in multiple 10-30 μs simulations, to its native states (Cα root-mean-square deviation of ∼0.34 nm). Our results suggest the potential applicability of the new PACE for the study of folding and dynamics of proteins.
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    13. 13
      Seo, S.; Shinoda, W. SPICA Force Field for Lipid Membranes: Domain Formation Induced by Cholesterol. J. Chem. Theory Comput. 2019, 15, 762– 774,  DOI: 10.1021/acs.jctc.8b00987
      13
      SPICA force field for lipid membranes: Domain formation induced by cholesterol
      Seo, Sangjae; Shinoda, Wataru
      Journal of Chemical Theory and Computation (2019), 15 (1), 762-774CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Heterogeneity is essential for multicomponent lipid membranes. Esp., sterol-induced domain formation in membranes has recently attracted attention because of its biol. importance. To investigate such membrane domains at the mol. level, coarse-grained mol. dynamics (CG-MD) simulations are a promising approach since they allow one to consider the temporal and spatial scales involved in domain formation. Here, we present a new CG force field, named SPICA, which can accurately predict domain formation within various lipids in membranes. The SPICA force field was developed as an extension of a previous CG model, known as SDK (Shinoda-DeVane-Klein), in which membrane properties such as tension, elasticity, and structure are well-reproduced. By examg. domain formation in a series of ternary lipid bilayers, we obsd. a sepn. into liq.-ordered and liq.-disordered phases fully consistent with exptl. observations. Importantly, it was shown that the SPICA force field could detect the different phase behavior that results from subtle differences in the lipid compn. of the bilayer.
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    14. 14
      Yu, I.; Mori, T.; Ando, T.; Harada, R.; Jung, J.; Sugita, Y.; Feig, M. Biomolecular Interactions Modulate Macromolecular Structure and Dynamics in Atomistic Model of a Bacterial Cytoplasm. eLife 2016, 5, 18457,  DOI: 10.7554/eLife.19274
      There is no corresponding record for this reference.
    15. 15
      von Bülow, S.; Siggel, M.; Linke, M.; Hummer, G. Dynamic cluster formation determines viscosity and diffusion in dense protein solutions. Proc. Natl. Acad. Sci. U. S. A. 2019, 116, 9843– 9852,  DOI: 10.1073/pnas.1817564116
      There is no corresponding record for this reference.
    16. 16
      Jung, J.; Nishima, W.; Daniels, M.; Bascom, G.; Kobayashi, C.; Adedoyin, A.; Wall, M.; Lappala, A.; Phillips, D.; Fischer, W.; Tung, C. S.; Schlick, T.; Sugita, Y.; Sanbonmatsu, K. Y. Scaling molecular dynamics beyond 100,000 processor cores for large-scale biophysical simulations. J. Comput. Chem. 2019, 40, 1919– 1930,  DOI: 10.1002/jcc.25840
      16
      Scaling molecular dynamics beyond 100,000 processor cores for large-scale biophysical simulations
      Jung, Jaewoon; Nishima, Wataru; Daniels, Marcus; Bascom, Gavin; Kobayashi, Chigusa; Adedoyin, Adetokunbo; Wall, Michael; Lappala, Anna; Phillips, Dominic; Fischer, William; Tung, Chang-Shung; Schlick, Tamar; Sugita, Yuji; Sanbonmatsu, Karissa Y.
      Journal of Computational Chemistry (2019), 40 (21), 1919-1930CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      The growing interest in the complexity of biol. interactions is continuously driving the need to increase system size in biophys. simulations, requiring not only powerful and advanced hardware but adaptable software that can accommodate a large no. of atoms interacting through complex forcefields. To address this, we developed and implemented strategies in the GENESIS mol. dynamics package designed for large nos. of processors. Long-range electrostatic interactions were parallelized by minimizing the no. of processes involved in communication. A novel algorithm was implemented for nonbonded interactions to increase single instruction multiple data (SIMD) performance, reducing memory usage for ultra large systems. Memory usage for neighbor searches in real-space nonbonded interactions was reduced by approx. 80%, leading to significant speedup. Using exptl. data describing phys. 3D chromatin interactions, we constructed the first atomistic model of an entire gene locus (GATA4). Taken together, these developments enabled the first billion-atom simulation of an intact biomol. complex, achieving scaling to 65,000 processes (130,000 processor cores) with 1 ns/day performance. Published 2019. This article is a U. S. Government work and is in the public domain in the USA.
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    17. 17
      Singharoy, A. Atoms to Phenotypes: Molecular Design Principles of Cellular Energy Metabolism. Cell 2019, 179, 1098– 1111,  DOI: 10.1016/j.cell.2019.10.021
      17
      Atoms to Phenotypes: Molecular Design Principles of Cellular Energy Metabolism
      Singharoy, Abhishek; Maffeo, Christopher; Delgado-Magnero, Karelia H.; Swainsbury, David J. K.; Sener, Melih; Kleinekathofer, Ulrich; Vant, John W.; Nguyen, Jonathan; Hitchcock, Andrew; Isralewitz, Barry; Teo, Ivan; Chandler, Danielle E.; Stone, John E.; Phillips, James C.; Pogorelov, Taras V.; Mallus, M. Ilaria; Chipot, Christophe; Luthey-Schulten, Zaida; Tieleman, D. Peter; Hunter, C. Neil; Tajkhorshid, Emad; Aksimentiev, Aleksei; Schulten, Klaus
      Cell (Cambridge, MA, United States) (2019), 179 (5), 1098-1111.e23CODEN: CELLB5; ISSN:0092-8674. (Cell Press)
      We report a 100-million atom-scale model of an entire cell organelle, a photosynthetic chromatophore vesicle from a purple bacterium, that reveals the cascade of energy conversion steps culminating in the generation of ATP from sunlight. Mol. dynamics simulations of this vesicle elucidate how the integral membrane complexes influence local curvature to tune photoexcitation of pigments. Brownian dynamics of small mols. within the chromatophore probe the mechanisms of directional charge transport under various pH and salinity conditions. Reproducing phenotypic properties from atomistic details, a kinetic model evinces that low-light adaptations of the bacterium emerge as a spontaneous outcome of optimizing the balance between the chromatophore's structural integrity and robust energy conversion. Parallels are drawn with the more universal mitochondrial bioenergetic machinery, from whence mol.-scale insights into the mechanism of cellular aging are inferred. Together, our integrative method and spectroscopic expts. pave the way to first-principles modeling of whole living cells.
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    18. 18
      Zhao, G.; Perilla, J. R.; Yufenyuy, E. L.; Meng, X.; Chen, B.; Ning, J.; Ahn, J.; Gronenborn, A. M.; Schulten, K.; Aiken, C.; Zhang, P. Mature HIV-1 capsid structure by cryo-electron microscopy and all-atom molecular dynamics. Nature 2013, 497, 643– 646,  DOI: 10.1038/nature12162
      18
      Mature HIV-1 capsid structure by cryo-electron microscopy and all-atom molecular dynamics
      Zhao, Gongpu; Perilla, Juan R.; Yufenyuy, Ernest L.; Meng, Xin; Chen, Bo; Ning, Jiying; Ahn, Jinwoo; Gronenborn, Angela M.; Schulten, Klaus; Aiken, Christopher; Zhang, Peijun
      Nature (London, United Kingdom) (2013), 497 (7451), 643-646CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      Retroviral capsid proteins are conserved structurally but assemble into different morphologies. The mature human immunodeficiency virus-1 (HIV-1) capsid is best described by a fullerene cone' model, in which hexamers of the capsid protein are linked to form a hexagonal surface lattice that is closed by incorporating 12 capsid-protein pentamers. HIV-1 capsid protein contains an amino-terminal domain (NTD) comprising seven α-helixes and a β-hairpin, a carboxy-terminal domain (CTD) comprising four α-helixes, and a flexible linker with a 310-helix connecting the two structural domains. Structures of the capsid-protein assembly units have been detd. by x-ray crystallog.; however, structural information regarding the assembled capsid and the contacts between the assembly units is incomplete. Here we report the cryo-electron microscopy structure of a tubular HIV-1 capsid-protein assembly at 8 Å resoln. and the three-dimensional structure of a native HIV-1 core by cryo-electron tomog. The structure of the tubular assembly shows, at the three-fold interface, a three-helix bundle with crit. hydrophobic interactions. Mutagenesis studies confirm that hydrophobic residues in the center of the three-helix bundle are crucial for capsid assembly and stability, and for viral infectivity. The cryo-electron-microscopy structures enable modeling by large-scale mol. dynamics simulation, resulting in all-atom models for the hexamer-of-hexamer and pentamer-of-hexamer elements as well as for the entire capsid. Incorporation of pentamers results in closer trimer contacts and induces acute surface curvature. The complete at. HIV-1 capsid model provides a platform for further studies of capsid function and for targeted pharmacol. intervention.
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    19. 19
      Casalino, L.; AI-Driven Multiscale Simulations Illuminate Mechanisms of SARS-CoV-2 Spike Dynamics. bioRxiv 2020,  DOI: 10.1101/2020.11.19.390187 .
      There is no corresponding record for this reference.
    20. 20
      Shaw, D. E.; In Anton 2: Raising the Bar for Performance and Programmability in a Special-Purpose Molecular Dynamics Supercomputer, SC ’14: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, Nov 16–21, 2014; IEEE, 2014; pp 41– 53. DOI: 10.1109/SC.2014.9
      There is no corresponding record for this reference.
    21. 21
      Ohmura, I.; Morimoto, G.; Ohno, Y.; Hasegawa, A.; Taiji, M. MDGRAPE-4: a special-purpose computer system for molecular dynamics simulations. Philos. Trans. R. Soc., A 2014, 372, 20130387,  DOI: 10.1098/rsta.2013.0387
      There is no corresponding record for this reference.
    22. 22
      Harder, E.; Damm, W.; Maple, J.; Wu, C.; Reboul, M.; Xiang, J. Y.; Wang, L.; Lupyan, D.; Dahlgren, M. K.; Knight, J. L.; Kaus, J. W.; Cerutti, D. S.; Krilov, G.; Jorgensen, W. L.; Abel, R.; Friesner, R. A. OPLS3: A Force Field Providing Broad Coverage of Drug-like Small Molecules and Proteins. J. Chem. Theory Comput. 2016, 12, 281– 296,  DOI: 10.1021/acs.jctc.5b00864
      22
      OPLS3: A Force Field Providing Broad Coverage of Drug-like Small Molecules and Proteins
      Harder, Edward; Damm, Wolfgang; Maple, Jon; Wu, Chuanjie; Reboul, Mark; Xiang, Jin Yu; Wang, Lingle; Lupyan, Dmitry; Dahlgren, Markus K.; Knight, Jennifer L.; Kaus, Joseph W.; Cerutti, David S.; Krilov, Goran; Jorgensen, William L.; Abel, Robert; Friesner, Richard A.
      Journal of Chemical Theory and Computation (2016), 12 (1), 281-296CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The parametrization and validation of the OPLS3 force field for small mols. and proteins are reported. Enhancements with respect to the previous version (OPLS2.1) include the addn. of off-atom charge sites to represent halogen bonding and aryl nitrogen lone pairs as well as a complete refit of peptide dihedral parameters to better model the native structure of proteins. To adequately cover medicinal chem. space, OPLS3 employs over an order of magnitude more ref. data and assocd. parameter types relative to other commonly used small mol. force fields (e.g., MMFF and OPLS_2005). As a consequence, OPLS3 achieves a high level of accuracy across performance benchmarks that assess small mol. conformational propensities and solvation. The newly fitted peptide dihedrals lead to significant improvements in the representation of secondary structure elements in simulated peptides and native structure stability over a no. of proteins. Together, the improvements made to both the small mol. and protein force field lead to a high level of accuracy in predicting protein-ligand binding measured over a wide range of targets and ligands (less than 1 kcal/mol RMS error) representing a 30% improvement over earlier variants of the OPLS force field.
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    23. 23
      Huang, J.; Rauscher, S.; Nawrocki, G.; Ran, T.; Feig, M.; de Groot, B. L.; Grubmüller, H.; MacKerell, A. D. CHARMM36m: an improved force field for folded and intrinsically disordered proteins. Nat. Methods 2017, 14, 71– 73,  DOI: 10.1038/nmeth.4067
      23
      CHARMM36m: an improved force field for folded and intrinsically disordered proteins
      Huang, Jing; Rauscher, Sarah; Nawrocki, Grzegorz; Ran, Ting; Feig, Michael; de Groot, Bert L.; Grubmuller, Helmut; MacKerell, Alexander D. Jr
      Nature Methods (2017), 14 (1), 71-73CODEN: NMAEA3; ISSN:1548-7091. (Nature Publishing Group)
      The all-atom additive CHARMM36 protein force field is widely used in mol. modeling and simulations. We present its refinement, CHARMM36m (http://mackerell.umaryland.edu/charmm_ff.shtml), with improved accuracy in generating polypeptide backbone conformational ensembles for intrinsically disordered peptides and proteins.
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    24. 24
      Tian, C.; Kasavajhala, K.; Belfon, K. A. A.; Raguette, L.; Huang, H.; Migues, A. N.; Bickel, J.; Wang, Y.; Pincay, J.; Wu, Q.; Simmerling, C. ff19SB: Amino-Acid-Specific Protein Backbone Parameters Trained against Quantum Mechanics Energy Surfaces in Solution. J. Chem. Theory Comput. 2020, 16, 528– 552,  DOI: 10.1021/acs.jctc.9b00591
      24
      ff19SB: Amino-Acid-Specific Protein Backbone Parameters Trained against Quantum Mechanics Energy Surfaces in Solution
      Tian Chuan; Kasavajhala Koushik; Belfon Kellon A A; Raguette Lauren; Huang He; Bickel John; Wang Yuzhang; Pincay Jorge; Simmerling Carlos; Tian Chuan; Kasavajhala Koushik; Belfon Kellon A A; Raguette Lauren; Huang He; Migues Angela N; Wang Yuzhang; Simmerling Carlos; Wu Qin
      Journal of chemical theory and computation (2020), 16 (1), 528-552 ISSN:.
      Molecular dynamics (MD) simulations have become increasingly popular in studying the motions and functions of biomolecules. The accuracy of the simulation, however, is highly determined by the molecular mechanics (MM) force field (FF), a set of functions with adjustable parameters to compute the potential energies from atomic positions. However, the overall quality of the FF, such as our previously published ff99SB and ff14SB, can be limited by assumptions that were made years ago. In the updated model presented here (ff19SB), we have significantly improved the backbone profiles for all 20 amino acids. We fit coupled φ/ψ parameters using 2D φ/ψ conformational scans for multiple amino acids, using as reference data the entire 2D quantum mechanics (QM) energy surface. We address the polarization inconsistency during dihedral parameter fitting by using both QM and MM in aqueous solution. Finally, we examine possible dependency of the backbone fitting on side chain rotamer. To extensively validate ff19SB parameters, and to compare to results using other Amber models, we have performed a total of ∼5 ms MD simulations in explicit solvent. Our results show that after amino-acid-specific training against QM data with solvent polarization, ff19SB not only reproduces the differences in amino-acid-specific Protein Data Bank (PDB) Ramachandran maps better but also shows significantly improved capability to differentiate amino-acid-dependent properties such as helical propensities. We also conclude that an inherent underestimation of helicity is present in ff14SB, which is (inexactly) compensated for by an increase in helical content driven by the TIP3P bias toward overly compact structures. In summary, ff19SB, when combined with a more accurate water model such as OPC, should have better predictive power for modeling sequence-specific behavior, protein mutations, and also rational protein design. Of the explicit water models tested here, we recommend use of OPC with ff19SB.
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    25. 25
      Best, R. B.; Zheng, W.; Mittal, J. Balanced Protein–Water Interactions Improve Properties of Disordered Proteins and Non-Specific Protein Association. J. Chem. Theory Comput. 2014, 10, 5113– 5124,  DOI: 10.1021/ct500569b
      25
      Balanced Protein-Water Interactions Improve Properties of Disordered Proteins and Non-Specific Protein Association
      Best, Robert B.; Zheng, Wenwei; Mittal, Jeetain
      Journal of Chemical Theory and Computation (2014), 10 (11), 5113-5124CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Some frequently encountered deficiencies in all-atom mol. simulations, such as nonspecific protein-protein interactions being too strong, and unfolded or disordered states being too collapsed, suggest that proteins are insufficiently well solvated in simulations using current state-of-the-art force fields. To address these issues, we make the simplest possible change, by modifying the short-range protein-water pair interactions, and leaving all the water-water and protein-protein parameters unchanged. We find that a modest strengthening of protein-water interactions is sufficient to recover the correct dimensions of intrinsically disordered or unfolded proteins, as detd. by direct comparison with small-angle x-ray scattering (SAXS) and Forster resonance energy transfer (FRET) data. The modification also results in more realistic protein-protein affinities, and av. solvation free energies of model compds. which are more consistent with expt. Most importantly, we show that this scaling is small enough not to affect adversely the stability of the folded state, with only a modest effect on the stability of model peptides forming α-helix and β-sheet structures. The proposed adjustment opens the way to more accurate atomistic simulations of proteins, particularly for intrinsically disordered proteins, protein-protein assocn., and crowded cellular environments.
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    26. 26
      van der Spoel, D. Systematic design of biomolecular force fields. Curr. Opin. Struct. Biol. 2021, 67, 18– 24,  DOI: 10.1016/j.sbi.2020.08.006
      26
      Systematic design of biomolecular force fields
      van der Spoel, David
      Current Opinion in Structural Biology (2021), 67 (), 18-24CODEN: COSBEF; ISSN:0959-440X. (Elsevier Ltd.)
      A review: Force fields for the study of biomols. have been developed in a predominantly org. manner by regular updates over half a century. Together with better algorithms and advances in computer technol., force fields have improved to yield more robust predictions. However, there are also indications to suggest that intramol. energy functions have not become better and that there still is room for improvement. In this review, systematic efforts toward development of novel force fields from scratch are described. This includes an est. of the complexity of the problem and the prerequisites in the form of data and algorithms. It is suggested that in order to make progress, an effort is needed to standardize ref. data and force field validation benchmarks.
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    27. 27
      Robustelli, P.; Piana, S.; Shaw, D. E. Developing a molecular dynamics force field for both folded and disordered protein states. Proc. Natl. Acad. Sci. U. S. A. 2018, 115, E4758– E4766,  DOI: 10.1073/pnas.1800690115
      27
      Developing a molecular dynamics force field for both folded and disordered protein states
      Robustelli, Paul; Piana, Stefano; Shaw, David E.
      Proceedings of the National Academy of Sciences of the United States of America (2018), 115 (21), E4758-E4766CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      Mol. dynamics (MD) simulation is a valuable tool for characterizing the structural dynamics of folded proteins and should be similarly applicable to disordered proteins and proteins with both folded and disordered regions. It has been unclear, however, whether any phys. model (force field) used in MD simulations accurately describes both folded and disordered proteins. Here, we select a benchmark set of 21 systems, including folded and disordered proteins, simulate these systems with six state-of-the art force fields, and compare the results to over 9000 available exptl. data points. We find that none of the tested force fields simultaneously provided accurate descriptions of folded proteins, of the dimensions of disordered proteins, and of the secondary structure propensities of disordered proteins. Guided by simulation results on a subset of our benchmark, however, we modified parameters of one force field, achieving excellent agreement with expt. for disordered proteins, while maintaining state-of-the-art accuracy for folded proteins. The resulting force field, a99SB-disp, should thus greatly expand the range of biol. systems amenable to MD simulation. A similar approach could be taken to improve other force fields.
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    28. 28
      Piana, S.; Robustelli, P.; Tan, D.; Chen, S.; Shaw, D. E. Development of a Force Field for the Simulation of Single-Chain Proteins and Protein–Protein Complexes. J. Chem. Theory Comput. 2020, 16, 2494– 2507,  DOI: 10.1021/acs.jctc.9b00251
      28
      Development of a Force Field for the Simulation of Single-Chain Proteins and Protein-Protein Complexes
      Piana, Stefano; Robustelli, Paul; Tan, Dazhi; Chen, Songela; Shaw, David E.
      Journal of Chemical Theory and Computation (2020), 16 (4), 2494-2507CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The accuracy of atomistic physics-based force fields for the simulation of biol. macromols. has typically been benchmarked exptl. using biophys. data from simple, often single-chain systems. In the case of proteins, the careful refinement of force field parameters assocd. with torsion-angle potentials and the use of improved water models have enabled a great deal of progress toward the highly accurate simulation of such monomeric systems in both folded and, more recently, disordered states. In living organisms, however, proteins constantly interact with other macromols., such as proteins and nucleic acids, and these interactions are often essential for proper biol. function. Here, the authors show that state-of-the-art force fields tuned to provide an accurate description of both ordered and disordered proteins can be limited in their ability to accurately describe protein-protein complexes. This observation prompted us to perform an extensive reparameterization of one variant of the Amber protein force field. The objective involved refitting not only the parameters assocd. with torsion-angle potentials, but also the parameters used to model nonbonded interactions, the specification of which is expected to be central to the accurate description of multicomponent systems. The resulting force field, which the authors call DES-Amber, allows for more accurate simulations of protein-protein complexes, while still providing a state-of-the-art description of both ordered and disordered single-chain proteins. Despite the improvements, calcd. protein-protein assocn. free energies still appear to deviate substantially from expt., a result suggesting that more fundamental changes to the force field, such as the explicit treatment of polarization effects, may simultaneously further improve the modeling of single-chain proteins and protein-protein complexes.
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    29. 29
      Li, P.; Merz, K. M. Metal Ion Modeling Using Classical Mechanics. Chem. Rev. 2017, 117, 1564– 1686,  DOI: 10.1021/acs.chemrev.6b00440
      29
      Metal Ion Modeling Using Classical Mechanics
      Li, Pengfei; Merz, Kenneth M., Jr.
      Chemical Reviews (Washington, DC, United States) (2017), 117 (3), 1564-1686CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      A review. Metal ions play significant roles in numerous fields including chem., geochem., biochem. and materials science. With computational tools increasingly becoming important in chem. research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aq. and solid phases. Herein we review both quantum and classical modeling strategies for metal ion contg. systems that have been developed over the past few decades. This review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond based models. Quantum mech. studies of metal ion contg. systems at the semiempirical, ab initio and d. functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion contg. systems.
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    30. 30
      Zhang, A.; Yu, H.; Liu, C.; Song, C. The Ca2+ permeation mechanism of the ryanodine receptor revealed by a multi-site ion model. Nat. Commun. 2020, 11, 922,  DOI: 10.1038/s41467-020-14573-w
      30
      The Ca2+ permeation mechanism of the ryanodine receptor revealed by a multi-site ion model
      Zhang, Aihua; Yu, Hua; Liu, Chunhong; Song, Chen
      Nature Communications (2020), 11 (1), 922CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
      Abstr.: Ryanodine receptors (RyR) are ion channels responsible for the release of Ca2+ from the sarco/endoplasmic reticulum and play a crucial role in the precise control of Ca2+ concn. in the cytosol. The detailed permeation mechanism of Ca2+ through RyR is still elusive. By using mol. dynamics simulations with a specially designed Ca2+ model, we show that multiple Ca2+ ions accumulate in the upper selectivity filter of RyR1, but only one Ca2+ can occupy and translocate in the narrow pore at a time, assisted by electrostatic repulsion from the Ca2+ within the upper selectivity filter. The Ca2+ is nearly fully hydrated with the first solvation shell intact during the whole permeation process. These results suggest a remote knock-on permeation mechanism and one-at-a-time occupation pattern for the hydrated Ca2+ within the narrow pore, uncovering the basis underlying the high permeability and low selectivity of the RyR channels.
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    31. 31
      Senn, H. M.; Thiel, W. QM/MM Methods for Biomolecular Systems. Angew. Chem., Int. Ed. 2009, 48, 1198– 1229,  DOI: 10.1002/anie.200802019
      31
      QM/MM methods for biomolecular systems
      Senn, Hans Martin; Thiel, Walter
      Angewandte Chemie, International Edition (2009), 48 (7), 1198-1229CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A review. Combined quantum-mechanics/mol.-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomol. systems. Quantum-mech. (QM) methods are required for describing chem. reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based mol. mechanics (MM) methods. Thus to model large biomols. the logical approach is to combine the two techniques and, to use a QM method for the chem. active region (e.g., substrates and co-factors in an enzymic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomol. systems at a reasonable computational effort while providing the necessary accuracy.
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    32. 32
      van der Kamp, M. W.; Mulholland, A. J. Combined Quantum Mechanics/Molecular Mechanics (QM/MM) Methods in Computational Enzymology. Biochemistry 2013, 52, 2708– 2728,  DOI: 10.1021/bi400215w
      32
      Combined Quantum Mechanics/Molecular Mechanics (QM/MM) Methods in Computational Enzymology
      van der Kamp, Marc W.; Mulholland, Adrian J.
      Biochemistry (2013), 52 (16), 2708-2728CODEN: BICHAW; ISSN:0006-2960. (American Chemical Society)
      A review. Computational enzymol. is a rapidly maturing field that is increasingly integral to understanding mechanisms of enzyme-catalyzed reactions and their practical applications. Combined quantum mechanics/mol. mechanics (QM/MM) methods are important in this field. By treating the reacting species with a quantum mech. method (i.e., a method that calcs. the electronic structure of the active site) and including the enzyme environment with simpler mol. mech. methods, enzyme reactions can be modeled. Here, we review QM/MM methods and their application to enzyme-catalyzed reactions to investigate fundamental and practical problems in enzymol. A range of QM/MM methods is available, from cheaper and more approx. methods, which can be used for mol. dynamics simulations, to highly accurate electronic structure methods. We discuss how modeling of reactions using such methods can provide detailed insight into enzyme mechanisms and illustrate this by reviewing some recent applications. We outline some practical considerations for such simulations. Further, we highlight applications that show how QM/MM methods can contribute to the practical development and application of enzymol., e.g., in the interpretation and prediction of the effects of mutagenesis and in drug and catalyst design.
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    33. 33
      Cui, Q. Perspective: Quantum Mechanical Methods in Biochemistry and Biophysics. J. Chem. Phys. 2016, 145, 140901,  DOI: 10.1063/1.4964410
      33
      Perspective: Quantum mechanical methods in biochemistry and biophysics
      Cui, Qiang
      Journal of Chemical Physics (2016), 145 (14), 140901/1-140901/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      A review. In this perspective article, I discuss several research topics relevant to quantum mech. (QM) methods in biophys. and biochem. applications. Due to the immense complexity of biol. problems, the key is to develop methods that are able to strike the proper balance of computational efficiency and accuracy for the problem of interest. Therefore, in addn. to the development of novel ab initio and d. functional theory based QM methods for the study of reactive events that involve complex motifs such as transition metal clusters in metalloenzymes, it is equally important to develop inexpensive QM methods and advanced classical or quantal force fields to describe different physicochem. properties of biomols. and their behaviors in complex environments. Maintaining a solid connection of these more approx. methods with rigorous QM methods is essential to their transferability and robustness. Comparison to diverse exptl. observables helps validate computational models and mechanistic hypotheses as well as driving further development of computational methodologies. (c) 2016 American Institute of Physics.
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    34. 34
      Cui, Q.; Pal, T.; Xie, L. Biomolecular QM/MM Simulations: What Are Some of the ″burning Issues″?. J. Phys. Chem. B 2021, 125, 689– 702,  DOI: 10.1021/acs.jpcb.0c09898
      34
      Biomolecular QM/MM Simulations: What Are Some of the "Burning Issues"?
      Cui, Qiang; Pal, Tanmoy; Xie, Luke
      Journal of Physical Chemistry B (2021), 125 (3), 689-702CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      A review. QM/MM simulations have become an indispensable tool in many chem. and biochem. investigations. Considering the tremendous degree of success, including recognition by a 2013 Nobel Prize in Chem., are there still "burning challenges" in QM/MM methods, esp. for biomol. systems. In this short Perspective, we discuss several issues that we believe greatly impact the robustness and quant. applicability of QM/MM simulations to many, if not all, biomols. We highlight these issues with observations and relevant advances from recent studies in our group and others in the field. Despite such limited scope, we hope the discussions are of general interest and will stimulate addnl. developments that help push the field forward in meaningful directions.
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    35. 35
      Warshel, A.; Karplus, M. Calculation of Ground and Excited State Potential Surfaces of Conjugated Molecules. I. Formulation and Parametrization. J. Am. Chem. Soc. 1972, 94, 5612– 5625,  DOI: 10.1021/ja00771a014
      35
      Calculation of ground and excited state potential surfaces of conjugated molecules. I. Formulation and parametrization
      Warshel, A.; Karplus, M.
      Journal of the American Chemical Society (1972), 94 (16), 5612-25CODEN: JACSAT; ISSN:0002-7863.
      A formulation is given for the consistent calcn. of ground and excited state potential surfaces of conjugated mols. The method is based on the formal sepn. of σ and π electrons, the former being represented by an empirical potential function and the latter by a semiempirical model of the Pariser-Parr-Pople type cor. for nearest-neighbor orbital overlap. A single parameter set represents all of the mol. properties considered; these include atomization energies, electronic excitation energies, ionization potentials, and the equil. geometries and vibrational frequencies of the ground and excited electronic states, and take account of all bond length and bond angle variations. To permit rapid detn. of the potential surfaces, the σ potential function and SCF-MO-configuration interaction energy of the π electrons are expressed as analytic functions of the mol. coordinates from which the first and second derivs. are obtainable. Applications to 1,3-butadiene, 1,3,5-hexatriene, α,ω-diphenyloctatetraene, and 1,3-cyclohexadiene are given.
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    36. 36
      Warshel, A.; Levitt, M. Theoretical Studies of Enzymic Reactions: Dielectric, Electrostatic and Steric Stabilization of the Carbonium Ion in the Reaction of Lysozyme. J. Mol. Biol. 1976, 103, 227– 249,  DOI: 10.1016/0022-2836(76)90311-9
      36
      Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme
      Warshel, A.; Levitt, M.
      Journal of Molecular Biology (1976), 103 (2), 227-49CODEN: JMOBAK; ISSN:0022-2836.
      A general method for detailed study of enzymic reactions is presented. The method considers the complete enzyme-substrate complex together with the surrounding solvent and evaluates all the different quantum mech. and classical energy factors that can affect the reaction pathway. These factors include the quantum mech. energies assocd. with bond cleavage and charge redistribution of the substrate and the classical energies of steric and electrostatic interactions between the substrate and the enzyme. The electrostatic polarization of the enzyme atoms and the orientation of the dipoles of the surrounding H2O mols. is simulated by a microscopic dielec. model. The solvation energy resulting from this polarization is considerable and must be included in any realistic calcn. of chem. reactions involving anything more than an isolated mol. in vacuo. Without it, acidic groups can never become ionized and the charge distribution on the substrate will not be reasonable. The same dielec. model can also be used to study the reaction of the substrate in soln. In this way the reaction in soln. can be compared with the enzymic reaction. The stability of the carbonium ion intermediate formed in the cleavage of a glycosidic bond by lysozyme was studied. Electrostatic stabilization is an important factor in increasing the rate of the reaction step that leads to the formation of the carbonium ion intermediate. Steric factors, such as the strain of the substrate on binding to lysozyme, do not seem to contribute significantly.
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    37. 37
      Field, M. J.; Bash, P. A.; Karplus, M. A Combined Quantum Mechanical and Molecular Mechanical Potential for Molecular Dynamics Simulations. J. Comput. Chem. 1990, 11, 700– 733,  DOI: 10.1002/jcc.540110605
      37
      A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations
      Field, Martin J.; Bash, Paul A.; Karplus, Martin
      Journal of Computational Chemistry (1990), 11 (6), 700-33CODEN: JCCHDD; ISSN:0192-8651.
      A combined quantum mech. (QM) and mol. mech. (MM) potential has been developed for the study of reactions in condensed phases. For the quantum mech. calcns. semiempirical methods of the MNDO and AM1 type are used, while the mol. mechanics part is treated with the HARMM force field. Specific prescriptions are given for the interactions between the QM and MM portions of the system; cases in which the QM and MM methodol. is applied to parts of the same mol. or to different mols. are considered. The details of the method and a range of test calcns., including comparisons with ab initio and exptl. results, are given. In many cases satisfactory results are obtained. However, there are limitations to this type of approach, some of which arise from the AM1 or MNDO methods themselves and others from the present QM/MM implementation. This suggests that it is important to test the applicability of the method to each particular case prior to its use. Possible areas of improvement in the methodol. are discussed.
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    38. 38
      Zhang, Y.; Liu, H.; Yang, W. Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface. J. Chem. Phys. 2000, 112, 3483,  DOI: 10.1063/1.480503
      38
      Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface
      Zhang, Yingkai; Liu, Haiyan; Yang, Weitao
      Journal of Chemical Physics (2000), 112 (8), 3483-3492CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      A new practical approach to studying enzyme reactions by combining ab initio QM/MM calcns. with free energy perturbation is presented. An efficient iterative optimization procedure has been developed to det. optimized structures and min. energy paths for a system with thousands of atoms on the ab initio QM/MM potential: the small QM sub-system is optimized using a quasi-Newton minimizer in redundant internal coordinates with ab initio QM/MM calcns., while the large MM sub-system is minimized by the truncated Newton method in Cartesian coordinates with only mol. mech. calcns. The above two optimization procedures are performed iteratively until they converge. With the detd. min. energy paths, free energy perturbation calcns. are carried out to det. the change in free energy along the reaction coordinate. Crit. to the success of the iterative optimization procedure and the free energy calcns. is the smooth connection between the QM and MM regions provided by a recently proposed pseudobond QM/MM approach [J. Chem. Phys. 110, 46 (1999)]. The methods have been demonstrated by studying the initial proton transfer step in the reaction catalyzed by the enzyme triosephosphate isomerase (TIM).
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    39. 39
      Hu, H.; Lu, Z.; Yang, W. QM/MM Minimum Free-Energy Path: Methodology and Application to Triosephosphate Isomerase. J. Chem. Theory Comput. 2007, 3, 390– 406,  DOI: 10.1021/ct600240y
      39
      QM/MM Minimum Free-Energy Path: Methodology and Application to Triosephosphate Isomerase
      Hu, Hao; Lu, Zhenyu; Yang, Weitao
      Journal of Chemical Theory and Computation (2007), 3 (2), 390-406CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Structural and energetic changes are two important characteristic properties of a chem. reaction process. In the condensed phase, studying these two properties is very challenging because of the great computational cost assocd. with the quantum mech. calcns. and phase space sampling. Although the combined quantum mechanics/mol. mechanics (QM/MM) approach significantly reduces the amt. of the quantum mech. calcns. and facilitates the simulation of soln.-phase and enzyme-catalyzed reactions, the required quantum mech. calcns. remain quite expensive and extensive sampling can be achieved routinely only with semiempirical quantum mech. methods. QM/MM simulations with ab initio QM methods, therefore, are often restricted to narrow regions of the potential energy surface such as the reactant, product and transition state, or the min.-energy path. Such ab initio QM/MM calcns. have previously been performed with the QM/MM-free energy (QM/MM-FE) method of Zhang et al. (J. Chem. Phys. 2000, 112, 3483-3492) to generate the free-energy profile along the reaction coordinate using free-energy perturbation calcns. at fixed structures of the QM subsystems. Results obtained with the QM/MM-FE method depend on the detn. of the min.-energy reaction path, which is based on local conformations of the protein/solvent environment and can be difficult to obtain in practice. To overcome the difficulties assocd. with the QM/MM-FE method and to further enhance the sampling of the MM environment conformations, we develop here a new method to det. the QM/MM min. free-energy path (QM/MM-MFEP) for chem.-reaction processes in soln. and in enzymes. Within the QM/MM framework, we express the free energy of the system as a function of the QM conformation, thus leading to a simplified potential of mean force (PMF) description for the thermodn. of the system. The free-energy difference between two QM conformations is evaluated by the QM/MM free-energy perturbation method. The free-energy gradients with respect to the QM degrees of freedom are calcd. from mol. dynamics simulations at given QM conformations. With the free energy and free-energy gradients in hand, we further implement chain-of-conformation optimization algorithms in the search for the reaction path on the free-energy surface without specifying a reaction coordinate. This method thus efficiently provides a unique min. free-energy path for soln. and enzyme reactions, with structural and energetic properties being detd. simultaneously. To further incorporate the dynamic contributions of the QM subsystem into the simulations, we develop the reaction path potential of Lu, et al. (J. Chem. Phys. 2004, 121, 89-100) for the min. free-energy path. The combination of the methods developed here presents a comprehensive and accurate treatment for the simulation of reaction processes in soln. and in enzymes with ab initio QM/MM methods. The method has been demonstrated on the first step of the reaction of the enzyme triosephosphate isomerase with good agreement with previous studies.
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    40. 40
      Hu, H.; Yang, W. Free Energies of Chemical Reactions in Solution and in Enzymes with Ab Initio Quantum Mechanics/Molecular Mechanics Methods. Annu. Rev. Phys. Chem. 2008, 59, 573– 601,  DOI: 10.1146/annurev.physchem.59.032607.093618
      40
      Free energies of chemical reactions in solution and in enzymes with ab initio quantum mechanics/molecular mechanics methods
      Hu, Hao; Yang, Weitao
      Annual Review of Physical Chemistry (2008), 59 (), 573-601CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews Inc.)
      A review. Combined quantum mechanics/mol. mechanics (QM/MM) methods provide an accurate and efficient energetic description of complex chem. and biol. systems, leading to significant advances in the understanding of chem. reactions in soln. and in enzymes. Here we review progress in QM/MM methodol. and applications, focusing on ab initio QM-based approaches. Ab initio QM/MM methods capitalize on the accuracy and reliability of the assocd. quantum-mech. approaches, however, at a much higher computational cost compared with semiempirical quantum-mech. approaches. Thus reaction-path and activation free-energy calcns. based on ab initio QM/MM methods encounter unique challenges in simulation timescales and phase-space sampling. This review features recent developments overcoming these challenges and enabling accurate free-energy detn. for reaction processes in soln. and in enzymes, along with applications.
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    41. 41
      Kosugi, T.; Hayashi, S. QM/MM Reweighting Free Energy SCF for Geometry Optimization on Extensive Free Energy Surface of Enzymatic Reaction. J. Chem. Theory Comput. 2012, 8, 322– 334,  DOI: 10.1021/ct2005837
      41
      QM/MM Reweighting Free Energy SCF for Geometry Optimization on Extensive Free Energy Surface of Enzymatic Reaction
      Kosugi, Takahiro; Hayashi, Shigehiko
      Journal of Chemical Theory and Computation (2012), 8 (1), 322-334CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We developed a quantum mech./mol. mech. (QM/MM) free energy geometry optimization method by which the geometry of a quantum chem. treated (QM) mol. is optimized on a free energy surface defined with thermal distribution of the surrounding mol. environment obtained by mol. dynamics simulation with a mol. mechanics (MM) force field. We applied the method to an enzymic reaction of a substrate complex of psychrophilic α-amylase from Antarctic bacterium Pseudoalteromonas haloplanktis and succeeded in geometry optimizations of the reactant and the product of the catalytic reaction that involve large conformational changes of protein loops adjacent to the reaction center on time scales reaching sub-microseconds. We found that the adjacent loops in the reactant and the product form in different conformations and produce catalytic ES potentials on the reaction center. The method called QM/MM reweighting free energy SCF combines a mean field theory of QM/MM free energy geometry optimization developed by Yamamoto with a reweighting scheme for updating the MM distribution introduced by Hu et al. and features high computational efficiency suitable for exploring the reaction free energy surface of extensive protein conformational space. The computational efficiency with improved treatment of a long-range electrostatic (ES) interaction using the Ewald summation technique permits one to take into account global conformational relaxation of an entire protein of an enzyme in the free energy geometry optimization of its reaction center.
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    42. 42
      Hayashi, S.; Uchida, Y.; Hasegawa, T.; Higashi, M.; Kosugi, T.; Kamiya, M. QM/MM Geometry Optimization on Extensive Free-Energy Surfaces for Examination of Enzymatic Reactions and Design of Novel Functional Properties of Proteins. Annu. Rev. Phys. Chem. 2017, 68, 135– 154,  DOI: 10.1146/annurev-physchem-052516-050827
      42
      QM/MM Geometry Optimization on Extensive Free-Energy Surfaces for Examination of Enzymatic Reactions and Design of Novel Functional Properties of Proteins
      Hayashi, Shigehiko; Uchida, Yoshihiro; Hasegawa, Taisuke; Higashi, Masahiro; Kosugi, Takahiro; Kamiya, Motoshi
      Annual Review of Physical Chemistry (2017), 68 (), 135-154CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)
      Many remarkable mol. functions of proteins use their characteristic global and slow conformational dynamics through coupling of local chem. states in reaction centers with global conformational changes of proteins. To theor. examine the functional processes of proteins in at. detail, a methodol. of quantum mech./mol. mech. (QM/MM) free-energy geometry optimization is introduced. In the methodol., a geometry optimization of a local reaction center is performed with a quantum mech. calcn. on a free-energy surface constructed with conformational samples of the surrounding protein environment obtained by a mol. dynamics simulation with a mol. mechanics force field. Geometry optimizations on extensive free-energy surfaces by a QM/MM reweighting free-energy SCF method designed to be variationally consistent and computationally efficient have enabled examns. of the multiscale mol. coupling of local chem. states with global protein conformational changes in functional processes and anal. and design of protein mutants with novel functional properties.
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    43. 43
      Rosta, E.; Woodcock, H. L.; Brooks, B. R.; Hummer, G. Artificial reaction coordinate “tunneling” in free-energy calculations: The catalytic reaction of RNase H. J. Comput. Chem. 2009, 30, 1634– 1641,  DOI: 10.1002/jcc.21312
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      Artificial reaction coordinate "tunneling" in free-energy calculations: The catalytic reaction of RNase H
      Rosta, Edina; Woodcock, H. Lee; Brooks, Bernard R.; Hummer, Gerhard
      Journal of Computational Chemistry (2009), 30 (11), 1634-1641CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      We describe a method for the systematic improvement of reaction coordinates in quantum mech./mol. mech. (QM/MM) calcns. of reaction free-energy profiles. In umbrella-sampling free-energy calcns., a biasing potential acting on a chosen reaction coordinate is used to sample the system in reactant, product, and transition states. Sharp, nearly discontinuous changes along the resulting reaction path are used to identify coordinates that are relevant for the reaction but not properly sampled. These degrees of freedom are then included in an extended reaction coordinate. The general formalism is illustrated for the catalytic cleavage of the RNA backbone of an RNA/DNA hybrid duplex by the RNase H enzyme of Bacillus halodurans. We find that in the initial attack of the phosphate diester by water, the oxygen-phosphorus distances alone are not sufficient as reaction coordinates, resulting in substantial hysteresis in the proton degrees of freedom and a barrier that is too low (∼10 kcal/mol). If the proton degrees of freedom are included in an extended reaction coordinate, we obtain a barrier of 21.6 kcal/mol consistent with the exptl. rates. As the barrier is approached, the attacking water mol. transfers one of its protons to the O1P oxygen of the phosphate group. At the barrier top, the resulting hydroxide ion forms a penta-coordinated phosphate intermediate. The method used to identify important degrees of freedom, and the procedure to optimize the reaction coordinate are general and should be useful both in classical and in QM/MM free-energy calcns. © 2009 Wiley Periodicals, Inc. J Comput Chem 30, 1634-1641, 2009.
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    44. 44
      Rosta, E.; Nowotny, M.; Yang, W.; Hummer, G. Catalytic Mechanism of RNA Backbone Cleavage by Ribonuclease H from Quantum Mechanics/Molecular Mechanics Simulations. J. Am. Chem. Soc. 2011, 133, 8934– 8941,  DOI: 10.1021/ja200173a
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      Catalytic Mechanism of RNA Backbone Cleavage by Ribonuclease H from Quantum Mechanics/Molecular Mechanics Simulations
      Rosta, Edina; Nowotny, Marcin; Yang, Wei; Hummer, Gerhard
      Journal of the American Chemical Society (2011), 133 (23), 8934-8941CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      We use quantum mechanics/mol. mechanics simulations to study the cleavage of the RNA (RNA) backbone catalyzed by RNase H. This protein is a prototypical member of a large family of enzymes that use two-metal catalysis to process nucleic acids. By combining Hamiltonian replica exchange with a finite-temp. string method, we calc. the free energy surface underlying the RNA-cleavage reaction and characterize its mechanism. We find that the reaction proceeds in two steps. In a first step, catalyzed primarily by magnesium ion A and its ligands, a water mol. attacks the scissile phosphate. Consistent with thiol-substitution expts., a water proton is transferred to the downstream phosphate group. The transient phosphorane formed as a result of this nucleophilic attack decays by breaking the bond between the phosphate and the ribose oxygen. In the resulting intermediate, the dissocd. but unprotonated leaving group forms an alkoxide coordinated to magnesium ion B. In a second step, the reaction is completed by protonation of the leaving group, with a neutral Asp132 as a likely proton donor. The overall reaction barrier of ∼15 kcal mol-1, encountered in the first step, together with the cost of protonating Asp132, is consistent with the slow measured rate of ∼1-100/min. The two-step mechanism is also consistent with the bell-shaped pH dependence of the reaction rate. The nonmonotonic relative motion of the magnesium ions along the reaction pathway agrees with X-ray crystal structures. Proton-transfer reactions and changes in the metal ion coordination emerge as central factors in the RNA-cleavage reaction.
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    45. 45
      Rosta, E.; Yang, W.; Hummer, G. Calcium Inhibition of Ribonuclease H1 Two-Metal Ion Catalysis. J. Am. Chem. Soc. 2014, 136, 3137– 3144,  DOI: 10.1021/ja411408x
      45
      Calcium inhibition of ribonuclease H1 two-metal ion catalysis
      Rosta, Edina; Yang, Wei; Hummer, Gerhard
      Journal of the American Chemical Society (2014), 136 (8), 3137-3144CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Most phosphate-processing enzymes require Mg2+ as a cofactor to catalyze nucleotide cleavage and transfer reactions. Ca2+ ions inhibit many of these enzymic activities, despite Ca2+ and Mg2+ having comparable binding affinities and overall biol. abundances. Here, the authors studied the mol. details of the Ca2+ inhibition mechanism for phosphodiester cleavage, an essential reaction in the metab. of nucleic acids and nucleotides, by comparing Ca2+- and Mg2+-catalyzed reactions. The authors studied the functional roles of specific metal ion sites A and B in enabling the catalytic cleavage of an RNA/DNA hybrid substrate by Bacillus halodurans RNase H1 using hybrid quantum-mechanics/mol. mechanics (QM/MM) free energy calcns. The authors found that Ca2+ substitution of either of the 2 active site Mg2+ ions substantially increased the height of the reaction barrier and thereby abolished the catalytic activity. Remarkably, Ca2+ at the A site was inactive also in Mg2+-optimized active site structures along the reaction path, whereas Mg2+ substitution recovered activity in Ca2+-optimized structures. Geometric changes resulting from Ca2+ substitution at metal ion site A may thus be a secondary factor in the loss of catalytic activity. By contrast, at metal ion site B geometry played a more important role, with only a partial recovery of activity after Mg2+ substitution in Ca2+-optimized structures. Ca2+-substitution also led to a change in mechanism, with deprotonation of the water nucleophile requiring a closer approach to the scissile phosphate, which in turn increased the barrier. As a result, Ca2+ was less efficient in activating the water. As a likely cause for the different reactivities of Mg2+ and Ca2+ ions in site A, the authors identified differences in charge transfer to the ions and the assocd. decrease in the pKa of the oxygen nucleophile attacking the phosphate group.
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    46. 46
      Ganguly, A.; Thaplyal, P.; Rosta, E.; Bevilacqua, P. C.; Hammes-Schiffer, S. Quantum mechanical/molecular mechanical free energy simulations of the self-cleavage reaction in the hepatitis delta virus ribozyme. J. Am. Chem. Soc. 2014, 136, 1483– 1496,  DOI: 10.1021/ja4104217
      46
      Quantum Mechanical/Molecular Mechanical Free Energy Simulations of the Self-Cleavage Reaction in the Hepatitis Delta Virus Ribozyme
      Ganguly, Abir; Thaplyal, Pallavi; Rosta, Edina; Bevilacqua, Philip C.; Hammes-Schiffer, Sharon
      Journal of the American Chemical Society (2014), 136 (4), 1483-1496CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The hepatitis delta virus (HDV) ribozyme catalyzes a self-cleavage reaction using a combination of nucleobase and metal ion catalysis. Both divalent and monovalent ions can catalyze this reaction, although the rate is slower with monovalent ions alone. Herein, we use quantum mech./mol. mech. (QM/MM) free energy simulations to investigate the mechanism of this ribozyme and to elucidate the roles of the catalytic metal ion. With Mg2+ at the catalytic site, the self-cleavage mechanism is obsd. to be concerted with a phosphorane-like transition state and a free energy barrier of ∼13 kcal/mol, consistent with free energy barrier values extrapolated from exptl. studies. With Na+ at the catalytic site, the mechanism is obsd. to be sequential, passing through a phosphorane intermediate, with free energy barriers of 2-4 kcal/mol for both steps; moreover, proton transfer from the exocyclic amine of protonated C75 to the nonbridging oxygen of the scissile phosphate occurs to stabilize the phosphorane intermediate in the sequential mechanism. To explain the slower rate obsd. exptl. with monovalent ions, we hypothesize that the activation of the O2' nucleophile by deprotonation and orientation is less favorable with Na+ ions than with Mg2+ ions. To explore this hypothesis, we exptl. measure the pKa of O2' by kinetic and NMR methods and find it to be lower in the presence of divalent ions rather than only monovalent ions. The combined theor. and exptl. results indicate that the catalytic Mg2+ ion may play three key roles: assisting in the activation of the O2' nucleophile, acidifying the general acid C75, and stabilizing the nonbridging oxygen to prevent proton transfer to it.
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    47. 47
      Zhang, S.; Ganguly, A.; Goyal, P.; Bingaman, J. L.; Bevilacqua, P. C.; Hammes-Schiffer, S. Role of the active site guanine in the glmS ribozyme self-cleavage mechanism: Quantum mechanical/molecular mechanical free energy simulations. J. Am. Chem. Soc. 2015, 137, 784– 798,  DOI: 10.1021/ja510387y
      47
      Role of the Active Site Guanine in the glmS Ribozyme Self-Cleavage Mechanism: Quantum Mechanical/Molecular Mechanical Free Energy Simulations
      Zhang, Sixue; Ganguly, Abir; Goyal, Puja; Bingaman, Jamie L.; Bevilacqua, Philip C.; Hammes-Schiffer, Sharon
      Journal of the American Chemical Society (2015), 137 (2), 784-798CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The glmS ribozyme catalyzes a self-cleavage reaction at the phosphodiester bond between residues A-1 and G1. This reaction is thought to occur by an acid-base mechanism involving the glucosamine-6-phosphate cofactor and G40 residue. Herein quantum mech./mol. mech. free energy simulations and pKa calcns., as well as exptl. measurements of the rate const. for self-cleavage, are utilized to elucidate the mechanism, particularly the role of G40. Our calcns. suggest that an external base deprotonates either G40(N1) or possibly A-1(O2'), which would be followed by proton transfer from G40(N1) to A-1(O2'). After this initial deprotonation, A-1(O2') starts attacking the phosphate as a hydroxyl group, which is hydrogen-bonded to deprotonated G40, concurrent with G40(N1) moving closer to the hydroxyl group and directing the in-line attack. Proton transfer from A-1(O2') to G40 is concomitant with attack of the scissile phosphate, followed by the remainder of the cleavage reaction. A mechanism in which an external base does not participate, but rather the proton transfers from A-1(O2') to a nonbridging oxygen during nucleophilic attack, was also considered but deemed to be less likely due to its higher effective free energy barrier. The calcd. rate const. for the favored mechanism is in agreement with the exptl. rate const. measured at biol. Mg2+ ion concn. According to these calcns., catalysis is optimal when G40 has an elevated pKa rather than a pKa shifted toward neutrality, although a balance among the pKa's of A-1, G40, and the nonbridging oxygen is essential. These results have general implications, as the hammerhead, hairpin, and twister ribozymes have guanines at a similar position as G40.
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    48. 48
      Li, P.; Soudackov, A. V.; Hammes-Schiffer, S. Fundamental Insights into Proton-Coupled Electron Transfer in Soybean Lipoxygenase from Quantum Mechanical/Molecular Mechanical Free Energy Simulations. J. Am. Chem. Soc. 2018, 140, 3068– 3076,  DOI: 10.1021/jacs.7b13642
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      Fundamental Insights into Proton-Coupled Electron Transfer in Soybean Lipoxygenase from Quantum Mechanical/Molecular Mechanical Free Energy Simulations
      Li, Pengfei; Soudackov, Alexander V.; Hammes-Schiffer, Sharon
      Journal of the American Chemical Society (2018), 140 (8), 3068-3076CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The proton-coupled electron transfer (PCET) reaction catalyzed by soybean lipoxygenase has served as a prototype for understanding hydrogen tunneling in enzymes. Herein this PCET reaction is studied with mixed quantum mech./mol. mech. (QM/MM) free energy simulations. The free energy surfaces are computed as functions of the proton donor-acceptor (C-O) distance and the proton coordinate, and the potential of mean force is computed as a function of the C-O distance, inherently including anharmonicity. The simulation results are used to calc. the kinetic isotope effects for the wild-type enzyme (WT) and the L546A/L754A double mutant (DM), which have been measured exptl. to be ∼80 and ∼700, resp. The PCET reaction is found to be exoergic for WT and slightly endoergic for the DM, and the equil. C-O distance for the reactant is found to be ∼0.2 Å greater for the DM than for WT. The larger equil. distance for the DM, which is due mainly to less optimal substrate binding in the expanded binding cavity, is primarily responsible for its higher kinetic isotope effect. The calcd. potentials of mean force are anharmonic and relatively soft at shorter C-O distances, allowing efficient thermal sampling of the shorter distances required for effective hydrogen tunneling. The primarily local electrostatic field at the transferring hydrogen is ∼100 MV/cm in the direction to facilitate proton transfer and increases dramatically as the C-O distance decreases. These simulations suggest that the overall protein environment is important for conformational sampling of active substrate configurations aligned for proton transfer, but the PCET reaction is influenced primarily by local electrostatic effects that facilitate conformational sampling of shorter proton donor-acceptor distances required for effective hydrogen tunneling.
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    49. 49
      Stevens, D. R.; Hammes-Schiffer, S. Exploring the Role of the Third Active Site Metal Ion in DNA Polymerase η with QM/MM Free Energy Simulations. J. Am. Chem. Soc. 2018, 140, 8965– 8969,  DOI: 10.1021/jacs.8b05177
      49
      Exploring the Role of the Third Active Site Metal Ion in DNA Polymerase η with QM/MM Free Energy Simulations
      Stevens, David R.; Hammes-Schiffer, Sharon
      Journal of the American Chemical Society (2018), 140 (28), 8965-8969CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The enzyme human DNA polymerase η (Pol η) is crit. for bypassing lesions during DNA replication. In addn. to the two Mg2+ ions aligning the active site, expts. suggest that a third Mg2+ ion could play an essential catalytic role. Herein the role of this third metal ion is investigated with quantum mech./mol. mech. (QM/MM) free energy simulations of the phosphoryl transfer reaction and a proposed self-activating proton transfer from the incoming nucleotide to the pyrophosphate leaving group. The simulations with only two metal ions in the active site support a sequential mechanism, with phosphoryl transfer followed by relatively fast proton transfer. The simulations with three metal ions in the active site suggest that the third metal ion may play a catalytic role through electrostatic interactions with the leaving group. These electrostatic interactions stabilize the product, making the phosphoryl transfer reaction more thermodynamically favorable with a lower free energy barrier relative to the activated state corresponding to the deprotonated 3'OH nucleophile, and also inhibit the subsequent proton transfer.
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    50. 50
      Li, P.; Rangadurai, A.; Al-Hashimi, H. M.; Hammes-Schiffer, S. Environmental Effects on Guanine-Thymine Mispair Tautomerization Explored with Quantum Mechanical/Molecular Mechanical Free Energy Simulations. J. Am. Chem. Soc. 2020, 142, 11183– 11191,  DOI: 10.1021/jacs.0c03774
      50
      Environmental Effects on Guanine-Thymine Mispair Tautomerization Explored with Quantum Mechanical/Molecular Mechanical Free Energy Simulations
      Li, Pengfei; Rangadurai, Atul; Al-Hashimi, Hashim M.; Hammes-Schiffer, Sharon
      Journal of the American Chemical Society (2020), 142 (25), 11183-11191CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      DNA bases can adopt energetically unfavorable tautomeric forms that enable the formation of Watson-Crick-like (WC-like) mispairs, which have been proposed to give rise to spontaneous mutations in DNA and misincorporation errors in DNA replication and translation. Previous NMR and computational studies have indicated that the population of WC-like guanine-thymine (G-T) mispairs depends on the environment, such as the local nucleic acid sequence and solvation. To investigate these environmental effects, herein G-T mispair tautomerization processes are studied computationally in aq. soln., in A-form and B-form DNA duplexes, and within the active site of a DNA polymerase λ variant. The wobble G-T (wG-T), WC-like G-T*, and WC-like G*-T forms are considered, where * indicates the enol tautomer of the base. The min. free energy paths for the tautomerization from the wG-T to the WC-like G-T* and from the WC-like G-T* to the WC-like G*-T are computed with mixed quantum mech./mol. mech. (QM/MM) free energy simulations. The reaction free energies and free energy barriers are found to be significantly influenced by the environment. The wG-T→ G-T* tautomerization is predicted to be endoergic in aq. soln. and the DNA duplexes but slightly exoergic in the polymerase, with Arg517 and Asn513 providing electrostatic stabilization of G-T*. The G-T*→ G*-T tautomerization is also predicted to be slightly more thermodynamically favorable in the polymerase relative to these DNA duplexes. These simulations are consistent with an exptl. driven kinetic misincorporation model suggesting that G-T mispair tautomerization occurs in the ajar polymerase conformation or concertedly with the transition from the ajar to the closed polymerase conformation. Furthermore, the order of the assocd. two proton transfer reactions is predicted to be different in the polymerase than in aq. soln. and the DNA duplexes. These studies highlight the impact of the environment on the thermodn., kinetics, and fundamental mechanisms of G-T mispair tautomerization, which plays a role in a wide range of biochem. important processes.
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    51. 51
      Walker, R. C.; Crowley, M. F.; Case, D. A. The Implementation of a Fast and Accurate QM/MM Potential Method in Amber. J. Comput. Chem. 2008, 29, 1019– 1031,  DOI: 10.1002/jcc.20857
      51
      The implementation of a fast and accurate QM/MM potential method in Amber
      Walker, Ross C.; Crowley, Michael F.; Case, David A.
      Journal of Computational Chemistry (2008), 29 (7), 1019-1031CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      Version 9 of the Amber simulation programs includes a new semiempirical hybrid QM/MM functionality. This includes support for implicit solvent (generalized Born) and for periodic explicit solvent simulations using a newly developed QM/MM implementation of the particle mesh Ewald (PME) method. The code provides sufficiently accurate gradients to run const. energy QM/MM MD simulations for many nanoseconds. The link atom approach used for treating the QM/MM boundary shows improved performance, and the user interface has been rewritten to bring the format into line with classical MD simulations. Support is provided for the PM3, PDDG/PM3, PM3CARB1, AM1, MNDO, and PDDG/MNDO semiempirical Hamiltonians as well as the self-consistent charge d. functional tight binding (SCC-DFTB) method. Performance has been improved to the point where using QM/MM, for a QM system of 71 atoms within an explicitly solvated protein using periodic boundaries and PME requires less than twice the cpu time of the corresponding classical simulation.
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    52. 52
      Götz, A. W.; Clark, M. A.; Walker, R. C. An Extensible Interface for QM/MM Molecular Dynamics Simulations with AMBER. J. Comput. Chem. 2014, 35, 95– 108,  DOI: 10.1002/jcc.23444
      52
      An extensible interface for QM/MM molecular dynamics simulations with AMBER
      Gotz Andreas W; Clark Matthew A; Walker Ross C
      Journal of computational chemistry (2014), 35 (2), 95-108 ISSN:.
      We present an extensible interface between the AMBER molecular dynamics (MD) software package and electronic structure software packages for quantum mechanical (QM) and mixed QM and classical molecular mechanical (MM) MD simulations within both mechanical and electronic embedding schemes. With this interface, ab initio wave function theory and density functional theory methods, as available in the supported electronic structure software packages, become available for QM/MM MD simulations with AMBER. The interface has been written in a modular fashion that allows straight forward extensions to support additional QM software packages and can easily be ported to other MD software. Data exchange between the MD and QM software is implemented by means of files and system calls or the message passing interface standard. Based on extensive tests, default settings for the supported QM packages are provided such that energy is conserved for typical QM/MM MD simulations in the microcanonical ensemble. Results for the free energy of binding of calcium ions to aspartate in aqueous solution comparing semiempirical and density functional Hamiltonians are shown to demonstrate features of this interface.
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    53. 53
      Melo, M. C. R.; Bernardi, R. C.; Rudack, T.; Scheurer, M.; Riplinger, C.; Phillips, J. C.; Maia, J. D. C.; Rocha, G. B.; Ribeiro, J. V.; Stone, J. E.; Neese, F.; Schulten, K.; Luthey-Schulten, Z. NAMD goes quantum: an integrative suite for hybrid simulations. Nat. Methods 2018, 15, 351– 354,  DOI: 10.1038/nmeth.4638
      53
      NAMD goes quantum: an integrative suite for hybrid simulations
      Melo, Marcelo C. R.; Bernardi, Rafael C.; Rudack, Till; Scheurer, Maximilian; Riplinger, Christoph; Phillips, James C.; Maia, Julio D. C.; Rocha, Gerd B.; Ribeiro, Joao V.; Stone, John E.; Neese, Frank; Schulten, Klaus; Luthey-Schulten, Zaida
      Nature Methods (2018), 15 (5), 351-354CODEN: NMAEA3; ISSN:1548-7091. (Nature Research)
      Hybrid methods that combine quantum mechanics (QM) and mol. mechanics (MM) can be applied to studies of reaction mechanisms in locations ranging from active sites of small enzymes to multiple sites in large bioenergetic complexes. By combining the widely used mol. dynamics and visualization programs NAMD and VMD with the quantum chem. packages ORCA and MOPAC, we created an integrated, comprehensive, customizable, and easy-to-use suite (http://www.ks.uiuc.edu/Research/qmmm). Through the QwikMD interface, setup, execution, visualization, and anal. are streamlined for all levels of expertise.
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    54. 54
      Jung, J.; Kobayashi, C.; Kasahara, K.; Tan, C.; Kuroda, A.; Minami, K.; Ishiduki, S.; Nishiki, T.; Inoue, H.; Ishikawa, Y.; Feig, M.; Sugita, Y. New parallel computing algorithm of molecular dynamics for extremely huge scale biological systems. J. Comput. Chem. 2021, 42, 231– 241,  DOI: 10.1002/jcc.26450
      54
      New parallel computing algorithm of molecular dynamics for extremely huge scale biological systems
      Jung, Jaewoon; Kobayashi, Chigusa; Kasahara, Kento; Tan, Cheng; Kuroda, Akiyoshi; Minami, Kazuo; Ishiduki, Shigeru; Nishiki, Tatsuo; Inoue, Hikaru; Ishikawa, Yutaka; Feig, Michael; Sugita, Yuji
      Journal of Computational Chemistry (2021), 42 (4), 231-241CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      In this paper, we address high performance extreme-scale mol. dynamics (MD) algorithm in the GENESIS software to perform cellular-scale mol. dynamics (MD) simulations with more than 100,000 CPU cores. It includes (1) the new algorithm of real-space nonbonded interactions maximizing the performance on ARM CPU architecture, (2) reciprocal-space nonbonded interactions minimizing communicational cost, (3) accurate temp./pressure evaluations that allows a large time step, and (4) effective parallel file inputs/outputs (I/O) for MD simulations of extremely huge systems. The largest system that contains 1.6 billion atoms was simulated using MD with a performance of 8.30 ns/day on Fugaku supercomputer. It extends the available size and time of MD simulations to answer unresolved questions of biomacromols. in a living cell.
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    55. 55
      Jung, J.; Naurse, A.; Kobayashi, C.; Sugita, Y. Graphics Processing Unit Acceleration and Parallelization of GENESIS for Large-Scale Molecular Dynamics Simulations. J. Chem. Theory Comput. 2016, 12, 4947– 4958,  DOI: 10.1021/acs.jctc.6b00241
      55
      Graphics Processing Unit Acceleration and Parallelization of GENESIS for Large-Scale Molecular Dynamics Simulations
      Jung, Jaewoon; Naurse, Akira; Kobayashi, Chigusa; Sugita, Yuji
      Journal of Chemical Theory and Computation (2016), 12 (10), 4947-4958CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Graphics processing unit (GPU) has become a popular computational platform for mol. dynamics (MD) simulations of biomols. A significant speedup in the simulations of small- or medium-size systems using only a few computer nodes with a single or multiple GPUs has been reported. Due to GPU memory limitation and slow communication between GPUs on different computer nodes, it is not straightforward to accelerate MD simulations of large biol. systems that contain a few million or more atoms on massively parallel supercomputers with GPUs. The authors develop a new scheme in their MD software, GENESIS, to reduce the total computational time on such computers. Computationally intensive real-space non-bonded interactions are computed mainly on GPUs in the scheme, while less intensive bonded interactions and communication-intensive reciprocal-space interactions were performed on CPUs. Based on the midpoint cell method as a domain decompn. scheme, the authors invent the single particle interaction list for reducing the GPU memory usage. Since total computational time is limited by the reciprocal-space computation, the authors use the RESPA multiple time-step integration and reduce the CPU resting time by assigning a subset of non-bonded interactions on CPUs as well as on GPUs when the reciprocal-space computation is skipped. The authors validated their GPU implementations in GENESIS on BPTI and a membrane protein, porin, by MD simulations and an alanine-tripeptide by REMD simulations. Benchmark calcns. on TSUBAME supercomputer showed that an MD simulation of a million atoms system was scalable up to 256 computer nodes with GPUs.
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    56. 56
      Jung, J.; Mori, T.; Sugita, Y. Midpoint cell method for hybrid (MPI+OpenMP) parallelization of molecular dynamics simulations. J. Comput. Chem. 2014, 35, 1064– 1072,  DOI: 10.1002/jcc.23591
      56
      Midpoint cell method for hybrid (MPI+OpenMP) parallelization of molecular dynamics simulations
      Jung, Jaewoon; Mori, Takaharu; Sugita, Yuji
      Journal of Computational Chemistry (2014), 35 (14), 1064-1072CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      We have developed a new hybrid (MPI+OpenMP) parallelization scheme for mol. dynamics (MD) simulations by combining a cell-wise version of the midpoint method with pair-wise Verlet lists. In this scheme, which we call the midpoint cell method, simulation space is divided into subdomains, each of which is assigned to a MPI processor. Each subdomain is further divided into small cells. The interaction between two particles existing in different cells is computed in the subdomain contg. the midpoint cell of the two cells where the particles reside. In each MPI processor, cell pairs are distributed over OpenMP threads for shared memory parallelization. The midpoint cell method keeps the advantages of the original midpoint method, while filtering out unnecessary calcns. of midpoint checking for all the particle pairs by single midpoint cell detn. prior to MD simulations. Distributing cell pairs over OpenMP threads allows for more efficient shared memory parallelization compared with distributing atom indexes over threads. Furthermore, cell grouping of particle data makes better memory access, reducing the no. of cache misses. The parallel performance of the midpoint cell method on the K computer showed scalability up to 512 and 32,768 cores for systems of 20,000 and 1 million atoms, resp. One MD time step for long-range interactions could be calcd. within 4.5 ms even for a 1 million atoms system with particle-mesh Ewald electrostatics. © 2014 Wiley Periodicals, Inc.
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    57. 57
      Jung, J.; Kobayashi, C.; Imamura, T.; Sugita, Y. Parallel implementation of 3D FFT with volumetric decomposition schemes for efficient molecular dynamics simulations. Comput. Phys. Commun. 2016, 200, 57– 65,  DOI: 10.1016/j.cpc.2015.10.024
      57
      Parallel implementation of 3D FFT with volumetric decomposition schemes for efficient molecular dynamics simulations
      Jung, Jaewoon; Kobayashi, Chigusa; Imamura, Toshiyuki; Sugita, Yuji
      Computer Physics Communications (2016), 200 (), 57-65CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      Three-dimensional Fast Fourier Transform (3D FFT) plays an important role in a wide variety of computer simulations and data analyses, including mol. dynamics (MD) simulations. In this study, we develop hybrid (MPI+OpenMP) parallelization schemes of 3D FFT based on two new volumetric decompns., mainly for the particle mesh Ewald (PME) calcn. in MD simulations. In one scheme, (1d_Alltoall), five all-to-all communications in one dimension are carried out, and in the other, (2d_Alltoall), one two-dimensional all-to-all communication is combined with two all-to-all communications in one dimension. 2d_Alltoall is similar to the conventional volumetric decompn. scheme. We performed benchmark tests of 3D FFT for the systems with different grid sizes using a large no. of processors on the K computer in RIKEN AICS. The two schemes show comparable performances, and are better than existing 3D FFTs. The performances of 1d_Alltoall and 2d_Alltoall depend on the supercomputer network system and no. of processors in each dimension. There is enough leeway for users to optimize performance for their conditions. In the PME method, short-range real-space interactions as well as long-range reciprocal-space interactions are calcd. Our volumetric decompn. schemes are particularly useful when used in conjunction with the recently developed midpoint cell method for short-range interactions, due to the same decompns. of real and reciprocal spaces. The 1d_Alltoall scheme of 3D FFT takes 4.7 ms to simulate one MD cycle for a virus system contg. more than 1 million atoms using 32,768 cores on the K computer.
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    58. 58
      Sugita, Y.; Okamoto, Y. Replica-exchange molecular dynamics method for protein folding. Chem. Phys. Lett. 1999, 314, 141– 151,  DOI: 10.1016/S0009-2614(99)01123-9
      58
      Replica-exchange molecular dynamics method for protein folding
      Sugita, Y.; Okamoto, Y.
      Chemical Physics Letters (1999), 314 (1,2), 141-151CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
      We have developed a formulation for mol. dynamics algorithm for the replica-exchange method. The effectiveness of the method for the protein-folding problem is tested with the penta-peptide Met-enkephalin. The method can overcome the multiple-min. problem by exchanging non-interacting replicas of the system at several temps. From only one simulation run, one can obtain probability distributions in canonical ensemble for a wide temp. range using multiple-histogram re-weighting techniques, which allows the calcn. of any thermodn. quantity as a function of temp. in that range.
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    59. 59
      Sugita, Y.; Okamoto, Y. Replica-exchange multicanonical algorithm and multicanonical replica-exchange method for simulating systems with rough energy landscape. Chem. Phys. Lett. 2000, 329, 261– 270,  DOI: 10.1016/S0009-2614(00)00999-4
      59
      Replica-exchange multicanonical algorithm and multicanonical replica-exchange method for simulating systems with rough energy landscape
      Sugita, Y.; Okamoto, Y.
      Chemical Physics Letters (2000), 329 (3,4), 261-270CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
      We propose two efficient algorithms for configurational sampling of systems with rough energy landscape. The first one is a new method for the detn. of the multi-canonical wt. factor. In this method, a short replica-exchange simulation is performed and the multi-canonical wt. factor is obtained by the multiple histogram reweighting techniques. The second one is a further extension of the first in which a replica-exchange multi-canonical simulation is performed with a small no. of replicas. These new algorithms are particularly useful for studying the protein folding problem.
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    60. 60
      Sugita, Y.; Kitao, A.; Okamoto, Y. Multidimensional replica-exchange method for free-energy calculations. J. Chem. Phys. 2000, 113, 6042– 6051,  DOI: 10.1063/1.1308516
      60
      Multidimensional replica-exchange method for free-energy calculations
      Sugita, Yuji; Kitao, Akio; Okamoto, Yuko
      Journal of Chemical Physics (2000), 113 (15), 6042-6051CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We have developed a new simulation algorithm for free-energy calcns. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temps. are exchanged during the simulation in the original replica-exchange method, pairs of replicas with different temps. and/or different parameters of the potential energy are exchanged in the new algorithm. This greatly enhances the sampling of the conformational space and allows accurate calcns. of free energy in a wide temp. range from a single simulation run, using the weighted histogram anal. method.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXntFSrt7w%253D&md5=066cf45c629b341bbd2fc4d92c7778a6
    61. 61
      Kamiya, M.; Sugita, Y. Flexible selection of the solute region in replica exchange with solute tempering: Application to protein-folding simulations. J. Chem. Phys. 2018, 149, 72304,  DOI: 10.1063/1.5016222
      61
      Flexible selection of the solute region in replica exchange with solute tempering: Application to protein-folding simulations
      Kamiya, Motoshi; Sugita, Yuji
      Journal of Chemical Physics (2018), 149 (7), 072304/1-072304/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Replica-exchange mol. dynamics (REMD) and their variants have been widely used in simulations of the biomol. structure and dynamics. Replica exchange with solute tempering (REST) is one of the methods where temp. of a pre-defined solute mol. is exchanged between replicas, while solvent temps. in all the replicas are kept const. REST greatly reduces the no. of replicas compared to the temp. REMD, while replicas at low temps. are often trapped under their conditions, interfering with the conformational sampling. Here, the authors introduce a new scheme of REST, referred to as generalized REST (gREST), where the solute region is defined as a part of a mol. or a part of the potential energy terms, such as the dihedral-angle energy term or Lennard-Jones energy term. The authors applied this new method to folding simulations of a β-hairpin (16 residues) and a Trp-cage (20 residues) in explicit water. The protein dihedral-angle energy term is chosen as the solute region in the simulations. gREST reduces the no. of replicas necessary for good random walks in the solute-temp. space and covers a wider conformational space compared to the conventional REST2. Considering the general applicability, gREST should become a promising tool for the simulations of protein folding, conformational dynamics, and an in silico drug design. (c) 2018 American Institute of Physics.
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    62. 62
      Miao, Y.; Feher, V. A.; McCammon, J. A. Gaussian Accelerated Molecular Dynamics: Unconstrained Enhanced Sampling and Free Energy Calculation. J. Chem. Theory Comput. 2015, 11, 3584– 3595,  DOI: 10.1021/acs.jctc.5b00436
      62
      Gaussian Accelerated Molecular Dynamics: Unconstrained Enhanced Sampling and Free Energy Calculation
      Miao, Yinglong; Feher, Victoria A.; McCammon, J. Andrew
      Journal of Chemical Theory and Computation (2015), 11 (8), 3584-3595CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      A Gaussian accelerated mol. dynamics (GaMD) approach for simultaneous enhanced sampling and free energy calcn. of biomols. is presented. By constructing a boost potential that follows Gaussian distribution, accurate reweighting of the GaMD simulations is achieved using cumulant expansion to the second order. Here, GaMD is demonstrated on three biomol. model systems: alanine dipeptide, chignolin folding, and ligand binding to the T4-lysozyme. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of these biomols. Furthermore, the free energy profiles obtained from reweighting of the GaMD simulations allow the authors to identify distinct low-energy states of the biomols. and characterize the protein-folding and ligand-binding pathways quant.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhtFOmsLjE&md5=f5e4df19cf7fe1c4cb9fa4bac2f2b219
    63. 63
      Oshima, H.; Re, S.; Sugita, Y. Replica-Exchange Umbrella Sampling Combined with Gaussian Accelerated Molecular Dynamics for Free-Energy Calculation of Biomolecules. J. Chem. Theory Comput. 2019, 15, 5199– 5208,  DOI: 10.1021/acs.jctc.9b00761
      63
      Replica-Exchange Umbrella Sampling Combined with Gaussian Accelerated Molecular Dynamics for Free-Energy Calculation of Biomolecules
      Oshima, Hiraku; Re, Suyong; Sugita, Yuji
      Journal of Chemical Theory and Computation (2019), 15 (10), 5199-5208CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We have developed an enhanced conformational sampling method combining replica-exchange umbrella sampling (REUS) with Gaussian accelerated mol. dynamics (GaMD). REUS enhances the sampling along predefined reaction coordinates, while GaMD accelerates the conformational dynamics by adding a boost potential to the system energy. The method, which we call GaREUS (Gaussian accelerated replica-exchange umbrella sampling), enhances the sampling more efficiently than REUS or GaMD, while the computational resource for GaREUS is the same as that required for REUS. The two-step reweighting procedure using the multistate Bennett acceptance ratio method and the cumulant expansion for the exponential av. is applied to the simulation trajectories for obtaining the unbiased free-energy landscapes. We apply GaREUS to the calcns. of free-energy landscapes for three different cases: conformational equil. of N-glycan, folding of chignolin, and conformational change of adenyl kinase. We show that GaREUS speeds up the convergences of free-energy calcns. using the same amt. of computational resources as REUS. The free-energy landscapes reweighted from the trajectories of GaREUS agree with previously reported ones. GaREUS is applicable to free-energy calcns. of various biomol. dynamics and functions with reasonable computational costs.
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    64. 64
      Tembre, B. L.; Mc Cammon, J. A. Ligand-receptor interactions. Comput. Chem. 1984, 8, 281– 283,  DOI: 10.1016/0097-8485(84)85020-2
      There is no corresponding record for this reference.
    65. 65
      Oshima, H.; Re, S.; Sugita, Y. Prediction of Protein-Ligand Binding Pose and Affinity Using the gREST+FEP Method. J. Chem. Inf. Model. 2020, 60, 5382– 5394,  DOI: 10.1021/acs.jcim.0c00338
      65
      Prediction of Protein-Ligand Binding Pose and Affinity Using the gREST+FEP Method
      Oshima, Hiraku; Re, Suyong; Sugita, Yuji
      Journal of Chemical Information and Modeling (2020), 60 (11), 5382-5394CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      The accurate prediction of protein-ligand binding affinity is a central challenge in computational chem. and in-silico drug discovery. The free energy perturbation (FEP) method based on mol. dynamics (MD) simulation provides reasonably accurate results only if a reliable structure is available via high-resoln. x-ray crystallog. To overcome the limitation, the authors propose a sequential prediction protocol using generalized replica exchange with solute tempering (gREST) and FEP. At first, ligand binding poses are predicted using gREST, which weakens protein-ligand interactions at high temps. to sample multiple binding poses. To avoid ligand dissocn. at high temps., a flat-bottom restraint potential centered on the binding site is applied in the simulation. The binding affinity of the most reliable pose is then calcd. using FEP. The protocol is applied to the bindings of ten ligands to FK506 binding proteins (FKBP), showing the excellent agreement between the calcd. and exptl. binding affinities. The present protocol, which is referred to as the gREST+FEP method, would help to predict the binding affinities without high-resoln. structural information on the ligand-bound state.
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    66. 66
      Maragliano, L.; Fischer, A.; Vanden-Eijnden, E.; Ciccotti, G. String method in collective variables: Minimum free energy paths and isocommittor surfaces. J. Chem. Phys. 2006, 125, 24106,  DOI: 10.1063/1.2212942
      66
      String method in collective variables: Minimum free energy paths and isocommittor surfaces
      Maragliano, Luca; Fischer, Alexander; Vanden-Eijnden, Eric; Ciccotti, Giovanni
      Journal of Chemical Physics (2006), 125 (2), 024106/1-024106/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      A computational technique is proposed which combines the string method with a sampling technique to det. min. free energy paths. The technique only requires to compute the mean force and another conditional expectation locally along the string, and therefore can be applied even if the no. of collective variables kept in the free energy calcn. is large. This is in contrast with other free energy sampling techniques which aim at mapping the full free energy landscape and whose cost increases exponentially with the no. of collective variables kept in the free energy. Provided that the no. of collective variables is large enough, the new technique captures the mechanism of transition in that it allows to det. the committor function for the reaction and, in particular, the transition state region. The new technique is illustrated on the example of alanine dipeptide, in which we compute the min. free energy path for the isomerization transition using either two or four dihedral angles as collective variables. It is shown that the mechanism of transition can be captured using the four dihedral angles, but it cannot be captured using only two of them.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xnt1Khurk%253D&md5=b3a7b0b167df6980ac6c8e7bb36b16fc
    67. 67
      Matsunaga, Y.; Komuro, Y.; Kobayashi, C.; Jung, J.; Mori, T.; Sugita, Y. Dimensionality of Collective Variables for Describing Conformational Changes of a Multi-Domain Protein. J. Phys. Chem. Lett. 2016, 7, 1446– 1451,  DOI: 10.1021/acs.jpclett.6b00317
      67
      Dimensionality of Collective Variables for Describing Conformational Changes of a Multi-Domain Protein
      Matsunaga, Yasuhiro; Komuro, Yasuaki; Kobayashi, Chigusa; Jung, Jaewoon; Mori, Takaharu; Sugita, Yuji
      Journal of Physical Chemistry Letters (2016), 7 (8), 1446-1451CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Collective variables (CVs) are often used in mol. dynamics simulations based on enhanced sampling algorithms to investigate large conformational changes of a protein. The choice of CVs in these simulations is essential because it affects simulation results and impacts the free-energy profile, the min. free-energy pathway (MFEP), and the transition-state structure. Here we examine how many CVs are required to capture the correct transition-state structure during the open-to-close motion of adenylate kinase using a coarse-grained model in the mean forces string method to search the MFEP. Various nos. of large amplitude principal components are tested as CVs in the simulations. The incorporation of local coordinates into CVs, which is possible in higher dimensional CV spaces, is important for capturing a reliable MFEP. The Bayesian measure proposed by Best and Hummer is sensitive to the choice of CVs, showing sharp peaks when the transition-state structure is captured. We thus evaluate the required no. of CVs needed in enhanced sampling simulations for describing protein conformational changes.
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    68. 68
      Kim, S.; Oshima, H.; Zhang, H.; Kern, N. R.; Re, S.; Lee, J.; Roux, B.; Sugita, Y.; Jiang, W.; Im, W. CHARMM-GUI Free Energy Calculator for Absolute and Relative Ligand Solvation and Binding Free Energy Simulations. J. Chem. Theory Comput. 2020, 16, 7207– 7218,  DOI: 10.1021/acs.jctc.0c00884
      68
      CHARMM-GUI Free Energy Calculator for Absolute and Relative Ligand Solvation and Binding Free Energy Simulations
      Kim, Seonghoon; Oshima, Hiraku; Zhang, Han; Kern, Nathan R.; Re, Suyong; Lee, Jumin; Roux, Benoit; Sugita, Yuji; Jiang, Wei; Im, Wonpil
      Journal of Chemical Theory and Computation (2020), 16 (11), 7207-7218CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Alchem. free energy simulations have long been utilized to predict free energy changes for binding affinity and soly. of small mols. However, while the theor. foundation of these methods is well established, seamlessly handling many of the practical aspects regarding the prepn. of the different thermodn. end states of complex mol. systems and the numerous processing scripts often remains a burden for successful applications. In this work, we present CHARMM-GUI Free Energy Calculator (http://www.charmm-gui.org/input/fec) that provides various alchem. free energy perturbation mol. dynamics (FEP/MD) systems with input and post-processing scripts for NAMD and GENESIS. Four submodules are available: Abs. Ligand Binder (for abs. ligand binding FEP/MD), Relative Ligand Binder (for relative ligand binding FEP/MD), Abs. Ligand Solvator (for abs. ligand solvation FEP/MD), and Relative Ligand Solvator (for relative ligand solvation FEP/MD). Each module is designed to build multiple systems of a set of selected ligands at once for high-throughput FEP/MD simulations. The capability of Free Energy Calculator is illustrated by abs. and relative solvation FEP/MD of a set of ligands and abs. and relative binding FEP/MD of a set of ligands for T4-lysozyme in soln. and the adenosine A2A receptor in a membrane. The calcd. free energy values are overall consistent with the exptl. and published free energy results (within ∼ 1 kcal/mol). We hope that Free Energy Calculator is useful to carry out high-throughput FEP/MD simulations in the field of biomol. sciences and drug discovery.
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    69. 69
      Yagi, K.; Yamada, K.; Kobayashi, C.; Sugita, Y. Anharmonic Vibrational Analysis of Biomolecules and Solvated Molecules Using Hybrid QM/MM Computations. J. Chem. Theory Comput. 2019, 15, 1924– 1938,  DOI: 10.1021/acs.jctc.8b01193
      69
      Anharmonic Vibrational Analysis of Biomolecules and Solvated Molecules Using Hybrid QM/MM Computations
      Yagi, Kiyoshi; Yamada, Kenta; Kobayashi, Chigusa; Sugita, Yuji
      Journal of Chemical Theory and Computation (2019), 15 (3), 1924-1938CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Quantum mechanics/mol. mechanics (QM/MM) calcns. are applied for anharmonic vibrational analyses of biomols. and solvated mols. The QM/MM method is implemented into a mol. dynamics (MD) program, GENESIS, by interfacing with external electronic structure programs. Following the geometry optimization and the harmonic normal-mode anal. based on a partial Hessian, the anharmonic potential energy surface (PES) is generated from QM/MM energies and gradients calcd. at grid points. The PES is used for vibrational SCF (VSCF) and post-VSCF calcns. to compute the vibrational spectrum. The method is first applied to a phosphate ion in soln. With both the ion and neighboring water mols. taken as a QM region, IR spectra of representative hydration structures are calcd. by the second-order vibrational quasi-degenerate perturbation theory (VQDPT2) at the level of B3LYP/cc-pVTZ and TIP3P force field. A wt.-av. of IR spectra over the structures reproduces the exptl. spectrum with a mean abs. deviation of 16 cm-1. Then, the method is applied to an enzyme, P 450 nitric oxide reductase (P450nor), with the NO mol. bound to a ferric (FeIII) heme. Starting from snapshot structures obtained from MD simulations of P450nor in soln., QM/MM calcns. have been carried out at the level of B3LYP-D3/def2-SVP(D). The spin state of FeIII(NO) is likely a closed-shell singlet state based on a ratio of N-O and Fe-NO stretching frequencies (νN-O and νFe-NO) calcd. for closed- and open-shell singlet states. The calcd. νN-O and νFe-NO overestimate the exptl. ones by 120 and 75 cm-1, resp. The electronic structure and solvation of FeIII(NO) affect the structure around the heme of P450nor leading to an increase in νN-O and νFe-NO.
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    70. 70
      Frisch, M. J.; Gaussian 16, rev. C.01; Gaussian, Inc.: Wallingford, CT, 2016.
      There is no corresponding record for this reference.
    71. 71
      Shao, Y. Advances in molecular quantum chemistry contained in the Q-Chem 4 program package. Mol. Phys. 2015, 113, 184– 215,  DOI: 10.1080/00268976.2014.952696
      71
      Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
      Shao, Yihan; Gan, Zhengting; Epifanovsky, Evgeny; Gilbert, Andrew T. B.; Wormit, Michael; Kussmann, Joerg; Lange, Adrian W.; Behn, Andrew; Deng, Jia; Feng, Xintian; Ghosh, Debashree; Goldey, Matthew; Horn, Paul R.; Jacobson, Leif D.; Kaliman, Ilya; Khaliullin, Rustam Z.; Kus, Tomasz; Landau, Arie; Liu, Jie; Proynov, Emil I.; Rhee, Young Min; Richard, Ryan M.; Rohrdanz, Mary A.; Steele, Ryan P.; Sundstrom, Eric J.; Woodcock, H. Lee, III; Zimmerman, Paul M.; Zuev, Dmitry; Albrecht, Ben; Alguire, Ethan; Austin, Brian; Beran, Gregory J. O.; Bernard, Yves A.; Berquist, Eric; Brandhorst, Kai; Bravaya, Ksenia B.; Brown, Shawn T.; Casanova, David; Chang, Chung-Min; Chen, Yunquing; Chien, Siu Hung; Closser, Kristina D.; Crittenden, Deborah L.; Diedenhofen, Michael; DiStasio, Robert A., Jr.; Do, Hainam; Dutoi, Anthony D.; Edgar, Richard G.; Fatehi, Shervin; Fusti-Molnar, Laszlo; Ghysels, An; Golubeva-Zadorozhnaya, Anna; Gomes, Joseph; Hanson-Heine, Magnus W. D.; Harbach, Philipp H. P.; Hauser, Andreas W.; Hohenstein, Edward G.; Holden, Zachary C.; Jagau, Thomas-C.; Ji, Hyunjun; Kaduk, Ben; Khistyaev, Kirill; Kim, Jaehoon; Kim, Jihan; King, Rollin A.; Klunzinger, Phil; Kosenkov, Dmytro; Kowalczyk, Tim; Krauter, Caroline M.; Lao, Ka Un; Laurent, Adele; Lawler, Keith V.; Levchenko, Sergey V.; Lin, Ching Yeh; Liu, Fenglai; Livshits, Ester; Lochan, Rohini C.; Luenser, Arne; Manohar, Prashant; Manzer, Samuel F.; Mao, Shan-Ping; Mardirossian, Narbe; Marenich, Aleksandr V.; Maurer, Simon A.; Mayhall, Nicholas J.; Neuscamman, Eric; Oana, C. Melania; Olivares-Amaya, Roberto; O'Neill, Darragh P.; Parkhill, John A.; Perrine, Trilisa M.; Peverati, Roberto; Prociuk, Alexander; Rehn, Dirk R.; Rosta, Edina; Russ, Nicholas J.; Sharada, Shaama M.; Sharma, Sandeep; Small, David W.; Sodt, Alexander; Stein, Tamar; Stuck, David; Su, Yu-Chuan; Thom, Alex J. W.; Tsuchimochi, Takashi; Vanovschi, Vitalii; Vogt, Leslie; Vydrov, Oleg; Wang, Tao; Watson, Mark A.; Wenzel, Jan; White, Alec; Williams, Christopher F.; Yang, Jun; Yeganeh, Sina; Yost, Shane R.; You, Zhi-Qiang; Zhang, Igor Ying; Zhang, Xing; Zhao, Yan; Brooks, Bernard R.; Chan, Garnet K. L.; Chipman, Daniel M.; Cramer, Christopher J.; Goddard, William A., III; Gordon, Mark S.; Hehre, Warren J.; Klamt, Andreas; Schaefer, Henry F., III; Schmidt, Michael W.; Sherrill, C. David; Truhlar, Donald G.; Warshel, Arieh; Xu, Xin; Aspuru-Guzik, Alan; Baer, Roi; Bell, Alexis T.; Besley, Nicholas A.; Chai, Jeng-Da; Dreuw, Andreas; Dunietz, Barry D.; Furlani, Thomas R.; Gwaltney, Steven R.; Hsu, Chao-Ping; Jung, Yousung; Kong, Jing; Lambrecht, Daniel S.; Liang, WanZhen; Ochsenfeld, Christian; Rassolov, Vitaly A.; Slipchenko, Lyudmila V.; Subotnik, Joseph E.; Van Voorhis, Troy; Herbert, John M.; Krylov, Anna I.; Gill, Peter M. W.; Head-Gordon, Martin
      Molecular Physics (2015), 113 (2), 184-215CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)
      A review. A summary of the tech. advances that are incorporated in the fourth major release of the Q-Chem quantum chem. program is provided, covering approx. the last seven years. These include developments in d. functional theory methods and algorithms, NMR (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, anal. tools, energy and electron transfer modeling, parallel computing capabilities, and graphical user interfaces. In addn., a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern d. functionals for bonded and non-bonded interactions, tests of attenuated second order Moller-Plesset (MP2) methods for intermol. interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chem. examples include calcns. on the strongly correlated Cr2 dimer, exploring zeolite-catalyzed ethane dehydrogenation, energy decompn. anal. of a charged ter-mol. complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.
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    72. 72
      Seritan, S.; Bannwarth, C.; Fales, B. S.; Hohenstein, E. G.; Isborn, C. M.; Kokkila-Schumacher, S. I. L.; Li, X.; Liu, F.; Luehr, N.; Snyder, J. W., Jr; Song, C.; Titov, A. V.; Ufimtsev, I. S.; Wang, L.-P.; Martínez, T. J. TeraChem: A graphical processing unit-accelerated electronic structure package for large-scale ab initio molecular dynamics. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1494,  DOI: 10.1002/wcms.1494
      72
      TeraChem: A graphical processing unit-accelerated electronic structure package for large-scale ab initio molecular dynamics
      Seritan, Stefan; Bannwarth, Christoph; Fales, Bryan S.; Hohenstein, Edward G.; Isborn, Christine M.; Kokkila-Schumacher, Sara I. L.; Li, Xin; Liu, Fang; Luehr, Nathan; Snyder, James W., Jr.; Song, Chenchen; Titov, Alexey V.; Ufimtsev, Ivan S.; Wang, Lee-Ping; Martinez, Todd J.
      Wiley Interdisciplinary Reviews: Computational Molecular Science (2021), 11 (2), e1494CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
      TeraChem was born in 2008 with the goal of providing fast on-the-fly electronic structure calcns. to facilitate ab initio mol. dynamics studies of large biochem. systems such as photoswitchable proteins and multichromophoric antenna complexes. Originally developed for videogaming applications, graphics processing units (GPUs) offered a low-cost parallel computer architecture that became more accessible for general-purpose GPU computing with the release of CUDA in 2007. Thus, highly efficient routines for evaluation of and contractions between the ERIs and d. matrixes were implemented in TeraChem. Electronic structure methods were developed and implemented to leverage these integral contraction routines, resulting in the first quantum chem. package designed from the ground up for GPUs. This GPU acceleration makes TeraChem capable of performing large-scale ground and excited state calcns. in the gas and condensed phase. Today, TeraChem's speed forms the basis for a suite of quantum chem. applications, including optimization and dynamics of proteins, automated and interactive chem. discovery tools, and large-scale nonadiabatic dynamics simulations.
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    73. 73
      Hourahine, B. DFTB+, a software package for efficient approximate density functional theory based atomistic simulations. J. Chem. Phys. 2020, 152, 124101,  DOI: 10.1063/1.5143190
      73
      DFTB+, a software package for efficient approximate density functional theory based atomistic simulations
      Hourahine, B.; Aradi, B.; Blum, V.; Bonafe, F.; Buccheri, A.; Camacho, C.; Cevallos, C.; Deshaye, M. Y.; Dumitrica, T.; Dominguez, A.; Ehlert, S.; Elstner, M.; van der Heide, T.; Hermann, J.; Irle, S.; Kranz, J. J.; Kohler, C.; Kowalczyk, T.; Kubar, T.; Lee, I. S.; Lutsker, V.; Maurer, R. J.; Min, S. K.; Mitchell, I.; Negre, C.; Niehaus, T. A.; Niklasson, A. M. N.; Page, A. J.; Pecchia, A.; Penazzi, G.; Persson, M. P.; Rezac, J.; Sanchez, C. G.; Sternberg, M.; Stohr, M.; Stuckenberg, F.; Tkatchenko, A.; Yu, V. W.-z.; Frauenheim, T.
      Journal of Chemical Physics (2020), 152 (12), 124101CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mech. simulations. By implementing various methods approximating d. functional theory (DFT), such as the d. functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long time-scales with reasonable accuracy while being considerably faster for typical simulations than the resp. ab initio methods. Based on the DFTB framework, it addnl. offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equil. Green's functions, and many more. DFTB+ can be used as a user-friendly standalone application in addn. to being embedded into other software packages as a library or acting as a calcn.-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives. (c) 2020 American Institute of Physics.
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    74. 74
      Yagi, K. SINDO 4.0 beta. 2020, https://tms.riken.jp/en/research/software/sindo/.
      There is no corresponding record for this reference.
    75. 75
      QSimulate-QM. Quantum Simulation Technologies, Inc. 2020, https://qsimulate.com/.
      There is no corresponding record for this reference.
    76. 76
      E, W.; Ren, W.; Vanden-Eijnden, E. String method for the study of rare events. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 66, 52301,  DOI: 10.1103/PhysRevB.66.052301
      76
      String method for the study of rare events
      E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
      Physical Review B: Condensed Matter and Materials Physics (2002), 66 (5), 052301/1-052301/4CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      We present an efficient method for computing the transition pathways, free energy barriers, and transition rates in complex systems with relatively smooth energy landscapes. The method proceeds by evolving strings, i.e., smooth curves with intrinsic parametrization whose dynamics takes them to the most probable transition path between two metastable regions in configuration space. Free energy barriers and transition rates can then be detd. by a std. umbrella sampling around the string. Applications to Lennard-Jones cluster rearrangement and thermally induced switching of a magnetic film are presented.
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    77. 77
      E, W.; Ren, W.; Vanden-Eijnden, E. Simplified and improved string method for computing the minimum energy paths in barrier-crossing events. J. Chem. Phys. 2007, 126, 164103,  DOI: 10.1063/1.2720838
      77
      Simplified and improved string method for computing the minimum energy paths in barrier-crossing events
      E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
      Journal of Chemical Physics (2007), 126 (16), 164103/1-164103/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We present a simplified and improved version of the string method, originally proposed by W.E.W. Ren and E. Vanden-Eijnden [Phys. Rev. B 66, 052301 (2002)] for identifying the min. energy paths in barrier-crossing events. In this new version, the step of projecting the potential force to the direction normal to the string is eliminated and the full potential force is used in the evolution of the string. This not only simplifies the numerical procedure, but also makes the method more stable and accurate. We discuss the algorithmic details of the improved string method, analyze its stability, accuracy and efficiency, and illustrate it via numerical examples. We also show how the string method can be combined with the climbing image technique for the accurate calcn. of saddle points and we present another algorithm for the accurate calcn. of the unstable directions at the saddle points.
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    78. 78
      Cui, Q.; Karplus, M. Quantum mechanics/molecular mechanics studies of triosephosphate isomerase-catalyzed reactions: Effect of geometry and tunneling on proton-transfer rate constants. J. Am. Chem. Soc. 2002, 124, 3093– 3124,  DOI: 10.1021/ja0118439
      78
      Quantum Mechanics/Molecular Mechanics Studies of Triosephosphate Isomerase-Catalyzed Reactions: Effect of Geometry and Tunneling on Proton-Transfer Rate Constants
      Cui, Qiang; Karplus, Martin
      Journal of the American Chemical Society (2002), 124 (12), 3093-3124CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The role of tunneling for two proton-transfer steps in the reactions catalyzed by triosephosphate isomerase (TIM) has been studied. One step is the rate-limiting proton transfer from Cα in the substrate to Glu 165, and the other is an intrasubstrate proton transfer proposed for the isomerization of the enediolate intermediate. The latter, which is not important in the wild-type enzyme but is a useful model system because of its simplicity, has also been examd. in the gas phase and in soln. Variational transition-state theory with semiclassical ground-state tunneling was used for the calcn. with potential energy surface detd. by an AM1 method specifically parametrized for the TIM system. The effect of tunneling on the reaction rate was found to be less than a factor of 10 at room temp.; the tunneling becomes more important at lower temp., as expected. The imaginary frequency (barrier) mode and modes that have large contributions to the reaction path curvature are localized on the atoms in the active site, within 4 Å of the substrate. This suggests that only a small no. of atoms that are close to the substrate and their motions (e.g., donor-acceptor vibration) directly det. the magnitude of tunneling. Atoms that are farther away influence the effect of tunneling indirectly by modulating the energetics of the proton transfer. For the intramol. proton transfer, tunneling was found to be most important in the gas phase, to be similar in the enzyme, and to be the smallest in water. The major reason for this trend is that the barrier frequency is substantially lower in soln. than in the gas phase and enzyme; the broader soln. barrier is caused by the strong electrostatic interaction between the highly charged solute and the polar solvent mols. Anal. of isotope effects showed that the conventional Arrenhius parameters are more useful as exptl. criteria for detg. the magnitude of tunneling than the widely used Swain-Schaad exponent (SSE). For the primary SSE, although values larger than the transition-state theory limit (3.3) occur when tunneling is included, there is no clear relationship between the calcd. magnitudes of tunneling and the SSE. Also, the temp. dependence of the primary SSE is rather complex; the value of SSE tends to decrease as the temp. is lowered (i.e., when tunneling becomes more significant). For the secondary SSE, the results suggest that it is more relevant for evaluating the "coupled motion" between the secondary hydrogen and the reaction coordinate than the magnitude of tunneling. Although tunneling makes a significant contribution to the rate of proton transfer, it appears not to be a major aspect of the catalysis by TIM at room temp.; i.e., the tunneling factor of 10 is "small" relative to the overall rate acceleration by 109. For the intramol. proton transfer, the tunneling in the enzyme is larger by a factor of 5 than in soln.
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    79. 79
      Zhang, X.; Harrison, D. H. T.; Cui, Q. Functional specificities of methylglyoxal synthase and triosephosphate isomerase: A combined QM/MM analysis. J. Am. Chem. Soc. 2002, 124, 14871– 14878,  DOI: 10.1021/ja027063x
      79
      Functional Specificities of Methylglyoxal Synthase and Triosephosphate Isomerase: A Combined QM/MM Analysis
      Zhang, Xiaodong; Harrison, David H. T.; Cui, Qiang
      Journal of the American Chemical Society (2002), 124 (50), 14871-14878CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Combined SCC-DFTB/CHARMM calcns. were carried out to analyze the origin for the functional specificities of triosephosphate isomerase (TIM) and methylglyoxal synthase (MGS). The two enzymes bind to the same substrate, dihydroxyacetone phosphate (DHAP), and have rather similar active sites. However, they catalyze different reactions; TIM catalyzes the isomerization of DHAP to glyceraldehyde 3-phosphate (GAP), while MGS catalyzes the elimination of phosphate from DHAP. Similar to previous suggestions, the calcns. confirmed that GAP formation is prohibited in MGS due primarily to the reduced flexibility of the catalytic base (Asp 71) compared to that in TIM (Glu 165). For the suppression of phosphate elimination in TIM, the calcns. show that the widely accepted stereoelectronic argument that invokes the different phosphoryl torsion angles obsd. in the x-ray structures of inhibitor complexes of the two enzymes is not as important as electrostatic contributions from the protein and water mols. surrounding the phosphoryl.
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    80. 80
      Cui, Q.; Karplus, M. Quantum mechanical/molecular mechanical studies of the triosephosphate isomerase-catalyzed reaction: Verification of methodology and analysis of reaction mechanisms. J. Phys. Chem. B 2002, 106, 1768– 1798,  DOI: 10.1021/jp012659c
      80
      Quantum Mechanical/Molecular Mechanical Studies of the Triosephosphate Isomerase-Catalyzed Reaction: Verification of Methodology and Analysis of Reaction Mechanisms
      Cui, Qiang; Karplus, Martin
      Journal of Physical Chemistry B (2002), 106 (7), 1768-1798CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
      Three possible mechanisms for the reactions catalyzed by triosephosphate isomerase (TIM) have been studied by the combined quantum mech./mol. mech. (QM/MM) approach at a no. of QM levels including AM1, AM1 with specific reaction parameters (SRP), and B3LYP/6-31+G(d,p). The comparison of the various QM levels is used to verify the adequacy of our recent B3LYP/MM anal. of the reaction mechanism (Cui et al. J. Am. Chem. Soc. 2001, 123, 2284), which showed that the intramol. proton transfer pathway is ruled out, due largely to the unfavorable interaction between the transition state and His 95. The relative contributions from the two other proposed pathways, however, are difficult to det. at the present level of theory; both pathways are also consistent with available expts. To obtain information about the role of the enzyme, d. functional calcns. were made for model systems in the gas phase and in soln.; selected models were also studied with ab initio calcns. at the levels of MP2 and CCSD to confirm the B3LYP results. Mulliken population anal. of the transition states demonstrates that hydrogen transfers essentially as proton for all the reactions in TIM, with an electron population between +0.33 and +0.44. Adiabatic mapping calcns. for path A indicate that the two relevant proton-transfer steps between the substrate and His 95 proceed in a nearly concerted manner. The QM model calcns. in soln. and a QM/MM perturbation anal. shows that a no. of factors combine to yield the rate enhancement by a factor of 109 in TIM. These include orienting catalytic groups (e.g., Glu 165, His 95) in good positions for the proton transfers, employing charged and polar groups (e.g., Lys 12, Asn 10) that stabilize the reaction intermediates and permitting flexibility of the catalytic groups (e.g., Glu 165 along path C). Some residues far from the active site, such as the main-chain atoms in Gly 210, as well as certain water mols., also make significant contributions. For the electrostatic interaction and polarization to function effectively, the active site of TIM has a relatively low effective dielec. "const.", which reflects the structural integrity of the enzyme active site as compared with soln. Short hydrogen bonds occur during the reaction (e.g., between the reactant substrate and Glu 165), but the calcd. energetics indicate that they do not have a specific role in catalysis; i.e., no contribution was found from the rather short hydrogen bond between His 95 and the substrate in path A.
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    81. 81
      Lennartz, C.; Schäfer, A.; Terstegen, F.; Thiel, W. Enzymatic reactions of triosephosphate isomerase: A theoretical calibration study. J. Phys. Chem. B 2002, 106, 1758– 1767,  DOI: 10.1021/jp012658k
      81
      Enzymatic Reactions of Triosephosphate Isomerase: A Theoretical Calibration Study
      Lennartz, C.; Schaefer, A.; Terstegen, F.; Thiel, W.
      Journal of Physical Chemistry B (2002), 106 (7), 1758-1767CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
      Combined quantum mech. (QM) and mol. mech. (MM) calcns. are reported for the triosephosphate isomerase-catalyzed conversion of dihydroxyacetone phosphate into glyceraldehyde 3-phosphate. The min. and transition states for the relevant proton-transfer reactions have been located on QM/MM potential surfaces. The primary objective of this work is to study the sensitivity of optimized structures and relative energies toward variations in the QM/MM model, including the choice of the QM method, the size of the QM region, the size of the optimized MM region, and the treatment of the QM/MM boundary. The QM methods that have been applied in combination with the CHARMm force field range from semiempirical (AM1) to d. functional (BP86, B3LYP) and ab initio (MP2) methods, the most extensive QM calcns. involving 275 atoms and 2162 basis functions at the d. functional level. Implications of the different choices of QM/MM options on the energy profile are discussed. From a mechanistic point of view, the present QM/MM results support a four-step proton-transfer pathway via an enediol, with involvement of neutral His95 acting as a proton donor, since the alternative direct intramol. proton transfer in the enediolate is disfavored by the protein environment.
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    82. 82
      Mendieta-Moreno, J. I.; Walker, R. C.; Lewis, J. P.; Gómez-Puertas, P.; Mendieta, J.; Ortega, J. FIREBALL/AMBER: An Efficient Local-Orbital DFT QM/MM Method for Biomolecular Systems. J. Chem. Theory Comput. 2014, 10, 2185– 2193,  DOI: 10.1021/ct500033w
      82
      FIREBALL/AMBER: An Efficient Local-Orbital DFT QM/MM Method for Biomolecular Systems
      Mendieta-Moreno, Jesus I.; Walker, Ross C.; Lewis, James P.; Gomez-Puertas, Paulino; Mendieta, Jesus; Ortega, Jose
      Journal of Chemical Theory and Computation (2014), 10 (5), 2185-2193CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      In recent years, quantum mechanics/mol. mechanics (QM/MM) methods have become an important computational tool for the study of chem. reactions and other processes in biomol. systems. In the QM/MM technique, the active region is described by means of QM calcns., while the remainder of the system is described using a MM approach. Because of the complexity of biomols. and the desire to achieve converged sampling, it is important that the QM method presents a good balance between accuracy and computational efficiency. Here, we report on the implementation of a QM/MM technique that combines a DFT approach specially designed for the study of complex systems using first-principles mol. dynamics simulations (FIREBALL) with the AMBER force fields and simulation programs. We also present examples of the application of this QM/MM approach to three representative biomol. systems: the anal. of the effect of electrostatic embedding in the behavior of a salt bridge between an aspartic acid and a lysine residue, a study of the intermediate states for the triosephosphate isomerase catalyzed conversion of dihydroxyacetone phosphate into glyceraldehyde 3-phosphate, and the detailed description, using DFT QM/MM mol. dynamics, of the cleavage of a phosphodiester bond in RNA catalyzed by the enzyme RNase A.
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    83. 83
      Knizia, G. Intrinsic atomic orbitals: An unbiased bridge between quantum theory and chemical concepts. J. Chem. Theory Comput. 2013, 9, 4834– 4843,  DOI: 10.1021/ct400687b
      83
      Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts
      Knizia, Gerald
      Journal of Chemical Theory and Computation (2013), 9 (11), 4834-4843CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Modern quantum chem. can make quant. predictions on an immense array of chem. systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an exceptionally simple algebraic construction allows for defining at. core and valence orbitals, polarized by the mol. environment, which can exactly represent SCF wave functions. This construction provides an unbiased and direct connection between quantum chem. and empirical chem. concepts, and can be used, for example, to calc. the nature of bonding in mols., in chem. terms, from first principles. In particular, we find consistency with electronegativities (χ), C 1s core-level shifts, resonance substituent parameters (σR), Lewis structures, and oxidn. states of transition-metal complexes.
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    84. 84
      Kästner, J.; Thiel, S.; Senn, H. M.; Sherwood, P.; Thiel, W. Exploiting QM/MM Capabilities in Geometry Optimization: A Microiterative Approach Using Electrostatic Embedding. J. Chem. Theory Comput. 2007, 3, 1064– 1072,  DOI: 10.1021/ct600346p
      84
      Exploiting QM/MM Capabilities in Geometry Optimization: A Microiterative Approach Using Electrostatic Embedding
      Kastner Johannes; Thiel Stephan; Senn Hans Martin; Sherwood Paul; Thiel Walter
      Journal of chemical theory and computation (2007), 3 (3), 1064-72 ISSN:1549-9618.
      We present a microiterative adiabatic scheme for quantum mechanical/molecular mechanical (QM/MM) energy minimization that fully optimizes the MM part in each QM macroiteration. This scheme is applicable not only to mechanical embedding but also to electrostatic and polarized embedding. The electrostatic QM/MM interactions in the microiterations are calculated from electrostatic potential charges fitted on the fly to the QM density. Corrections to the energy and gradient expressions ensure that macro- and microiterations are performed on the same energy surface. This results in excellent convergence properties and no loss of accuracy compared to standard optimization. We test our implementation on water clusters and on two enzymes using electrostatic embedding, as well as on a surface example using polarized embedding with a shell model. Our scheme is especially well-suited for systems containing large MM regions, since the computational effort for the optimization is almost independent of the MM system size. The microiterations reduce the number of required QM calculations typically by a factor of 2-10, depending on the system.
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    85. 85
      Shirts, M. R.; Chodera, J. D. Statistically optimal analysis of samples from multiple equilibrium states. J. Chem. Phys. 2008, 129, 124105,  DOI: 10.1063/1.2978177
      85
      Statistically optimal analysis of samples from multiple equilibrium states
      Shirts, Michael R.; Chodera, John D.
      Journal of Chemical Physics (2008), 129 (12), 124105/1-124105/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We present a new estimator for computing free energy differences and thermodn. expectations as well as their uncertainties from samples obtained from multiple equil. states via either simulation or expt. The estimator, which we call the multistate Bennett acceptance ratio estimator (MBAR) because it reduces to the Bennett acceptance ratio estimator (BAR) when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a soln. to the estg. equations in many cases. Addnl., an est. of the statistical uncertainty is provided for all estd. quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equil. data collected from multiple states. We illustrate this method by producing a highly precise est. of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under const. force bias. (c) 2008 American Institute of Physics.
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    86. 86
      Branduardi, D.; Gervasio, F. L.; Parrinello, M. From A to B in free energy space. J. Chem. Phys. 2007, 126, 054103,  DOI: 10.1063/1.2432340
      86
      From A to B in free energy space
      Branduardi, Davide; Gervasio, Francesco Luigi; Parrinello, Michele
      Journal of Chemical Physics (2007), 126 (5), 054103/1-054103/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The authors present a new method for searching low free energy paths in complex mol. systems at finite temp. They introduce two variables that are able to describe the position of a point in configurational space relative to a preassigned path. With the help of these two variables the authors combine features of approaches such as metadynamics or umbrella sampling with those of path based methods. This allows global searches in the space of paths to be performed and a new variational principle for the detn. of low free energy paths to be established. Contrary to metadynamics or umbrella sampling the path can be described by an arbitrary large no. of variables, still the energy profile along the path can be calcd. The authors exemplify the method numerically by studying the conformational changes of alanine dipeptide.
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    87. 87
      Bonomi, M.; Branduardi, D.; Bussi, G.; Camilloni, C.; Provasi, D.; Raiteri, P.; Donadio, D.; Marinelli, F.; Pietrucci, F.; Broglia, R. A.; Parrinello, M. PLUMED: A portable plugin for free-energy calculations with molecular dynamics. Comput. Phys. Commun. 2009, 180, 1961– 1972,  DOI: 10.1016/j.cpc.2009.05.011
      87
      PLUMED: A portable plugin for free-energy calculations with molecular dynamics
      Bonomi, Massimiliano; Branduardi, Davide; Bussi, Giovanni; Camilloni, Carlo; Provasi, Davide; Raiteri, Paolo; Donadio, Davide; Marinelli, Fabrizio; Pietrucci, Fabio; Broglia, Ricardo A.; Parrinello, Michele
      Computer Physics Communications (2009), 180 (10), 1961-1972CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      A program aimed at free-energy calcns. in mol. systems is presented. It consists of a series of routines that can be interfaced with the most popular classical mol. dynamics (MD) codes through a simple patching procedure. This leaves the possibility for the user to exploit many different MD engines depending on the system simulated and on the computational resources available. Free-energy calcns. can be performed as a function of many collective variables, with a particular focus on biol. problems, and using state-of-the-art methods such as metadynamics, umbrella sampling, and Jarzynski-equation based steered MD. The present software, written in ANSI-C language, can be easily interfaced with both Fortran and C/C++ codes.
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    88. 88
      Davenport, R. C.; Bash, P. A.; Seaton, B. A.; Karplus, M.; Petsko, G. A.; Ringe, D. Structure of the Triosephosphate Isomerase-Phosphoglycolohydroxamate Complex: An Analogue of the Intermediate on the Reaction Pathway. Biochemistry 1991, 30, 5821– 5826,  DOI: 10.1021/bi00238a002
      88
      Structure of the triosephosphate isomerase-phosphoglycolohydroxamate complex: an analog of the intermediate on the reaction pathway
      Davenport, Robert C.; Bash, Paul A.; Seaton, Barbara A.; Karplus, Martin; Petsko, Gregory A.; Ringe, Dagmar
      Biochemistry (1991), 30 (24), 5821-6CODEN: BICHAW; ISSN:0006-2960.
      The 3-dimensional structure of triosephosphate isomerase (TIM) complexed with a reactive intermediate analog, phosphoglycolohydroxamate (PGH), was solved at 1.9-Å resoln. and the structure was refined to an R-factor of 18%. Anal. of the refined structure revealed the geometry of the active-site residues and the interactions they make with the inhibitor and, by analogy, the substrates. The structure was consistent with an acid-base mechanism in which the carboxylate of Glu-165 abstrs. a proton from the substrate C atom while His-95 donates a proton to a substrate O atom to form an enediol (or enediolate) intermediate. The conformation of the bound substrate stereoelectronically favored proton transfer from the substrate C atom to the syn orbital of Glu-165. The crystal structure suggested that His-95 is neutral rather than cationic in the ground state and therefore would have to function as an imidazole acid instead of the usual imidazolium. Lys-12 was oriented so as to polarize the substrate O atoms by H-bonding and/or electrostatic interaction, providing stabilization for the charged transition state. Asn-10 may play a similar role.
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    89. 89
      Olsson, M. H. M.; Søndergaard, C. R.; Rostkowski, M.; Jensen, J. H. PROPKA3: Consistent Treatment of Internal and Surface Residues in Empirical pKa predictions. J. Chem. Theory Comput. 2011, 7, 525– 537,  DOI: 10.1021/ct100578z
      89
      PROPKA3: Consistent Treatment of Internal and Surface Residues in Empirical pKa Predictions
      Olsson, Mats H. M.; Sondergaard, Chresten R.; Rostkowski, Michal; Jensen, Jan H.
      Journal of Chemical Theory and Computation (2011), 7 (2), 525-537CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The authors have revised the rules and parameters for one of the most commonly used empirical pKa predictors, PROPKA, based on better phys. description of the desolvation and dielec. response for the protein. The authors have introduced a new and consistent approach to interpolate the description between the previously distinct classifications into internal and surface residues, which otherwise is found to give rise to an erratic and discontinuous behavior. Since the goal of this study is to lay out the framework and validate the concept, it focuses on Asp and Glu residues where the protein pKa values and structures are assumed to be more reliable. The new and improved implementation is evaluated and discussed; it is found to agree better with expt. than the previous implementation (in parentheses): rmsd = 0.79 (0.91) for Asp and Glu, 0.75 (0.97) for Tyr, 0.65 (0.72) for Lys, and 1.00 (1.37) for His residues. The most significant advance, however, is in reducing the no. of outliers and removing unreasonable sensitivity to small structural changes that arise from classifying residues as either internal or surface.
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    90. 90
      Jo, S.; Kim, T.; Iyer, V. G.; Im, W. CHARMM-GUI: A web-based graphical user interface for CHARMM. J. Comput. Chem. 2008, 29, 1859– 1865,  DOI: 10.1002/jcc.20945
      90
      CHARMM-GUI: a web-based graphical user interface for CHARMM
      Jo, Sunhwan; Kim, Taehoon; Iyer, Vidyashankara G.; Im, Wonpil
      Journal of Computational Chemistry (2008), 29 (11), 1859-1865CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      CHARMM is an academic research program used widely for macromol. mechanics and dynamics with versatile anal. and manipulation tools of at. coordinates and dynamics trajectories. CHARMM-GUI, http://www.charmm-gui.org, has been developed to provide a web-based graphical user interface to generate various input files and mol. systems to facilitate and standardize the usage of common and advanced simulation techniques in CHARMM. The web environment provides an ideal platform to build and validate a mol. model system in an interactive fashion such that, if a problem is found through visual inspection, one can go back to the previous setup and regenerate the whole system again. In this article, we describe the currently available functional modules of CHARMM-GUI Input Generator that form a basis for the advanced simulation techniques. Future directions of the CHARMM-GUI development project are also discussed briefly together with other features in the CHARMM-GUI website, such as Archive and Movie Gallery.
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    91. 91
      Lee, J.; Cheng, X.; Swails, J. M.; Yeom, M. S.; Eastman, P. K.; Lemkul, J. A.; Wei, S.; Buckner, J.; Jeong, J. C.; Qi, Y.; Jo, S.; Pande, V. S.; Case, D. A.; Brooks, C. L.; MacKerell, A. D.; Klauda, J. B.; Im, W. CHARMM-GUI Input Generator for NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM Simulations Using the CHARMM36 Additive Force Field. J. Chem. Theory Comput. 2016, 12, 405– 413,  DOI: 10.1021/acs.jctc.5b00935
      91
      CHARMM-GUI Input Generator for NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM Simulations Using the CHARMM36 Additive Force Field
      Lee, Jumin; Cheng, Xi; Swails, Jason M.; Yeom, Min Sun; Eastman, Peter K.; Lemkul, Justin A.; Wei, Shuai; Buckner, Joshua; Jeong, Jong Cheol; Qi, Yifei; Jo, Sunhwan; Pande, Vijay S.; Case, David A.; Brooks, Charles L.; MacKerell, Alexander D.; Klauda, Jeffery B.; Im, Wonpil
      Journal of Chemical Theory and Computation (2016), 12 (1), 405-413CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Proper treatment of nonbonded interactions is essential for the accuracy of mol. dynamics (MD) simulations, esp. in studies of lipid bilayers. The use of the CHARMM36 force field (C36 FF) in different MD simulation programs can result in disagreements with published simulations performed with CHARMM due to differences in the protocols used to treat the long-range and 1-4 nonbonded interactions. In this study, we systematically test the use of the C36 lipid FF in NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM. A wide range of Lennard-Jones (LJ) cutoff schemes and integrator algorithms were tested to find the optimal simulation protocol to best match bilayer properties of six lipids with varying acyl chain satn. and head groups. MD simulations of a 1,2-dipalmitoyl-sn-phosphatidylcholine (DPPC) bilayer were used to obtain the optimal protocol for each program. MD simulations with all programs were found to reasonably match the DPPC bilayer properties (surface area per lipid, chain order parameters, and area compressibility modulus) obtained using the std. protocol used in CHARMM as well as from expts. The optimal simulation protocol was then applied to the other five lipid simulations and resulted in excellent agreement between results from most simulation programs as well as with exptl. data. AMBER compared least favorably with the expected membrane properties, which appears to be due to its use of the hard-truncation in the LJ potential vs. a force-based switching function used to smooth the LJ potential as it approaches the cutoff distance. The optimal simulation protocol for each program has been implemented in CHARMM-GUI. This protocol is expected to be applicable to the remainder of the additive C36 FF including the proteins, nucleic acids, carbohydrates, and small mols.
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    92. 92
      Gaus, M.; Cui, Q.; Elstner, M. DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB). J. Chem. Theory Comput. 2011, 7, 931– 948,  DOI: 10.1021/ct100684s
      92
      DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB)
      Gaus, Michael; Cui, Qiang; Elstner, Marcus
      Journal of Chemical Theory and Computation (2011), 7 (4), 931-948CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The self-consistent-charge d.-functional tight-binding method (SCC-DFTB) is an approx. quantum chem. method derived from d. functional theory (DFT) based on a second-order expansion of the DFT total energy around a ref. d. In the present study, we combine earlier extensions and improve them consistently with, first, an improved Coulomb interaction between at. partial charges and, second, the complete third-order expansion of the DFT total energy. These modifications lead us to the next generation of the DFTB methodol. called DFTB3, which substantially improves the description of charged systems contg. elements C, H, N, O, and P, esp. regarding hydrogen binding energies and proton affinities. As a result, DFTB3 is particularly applicable to biomol. systems. Remaining challenges and possible solns. are also briefly discussed.
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    93. 93
      Best, R. B.; Zhu, X.; Shim, J.; Lopes, P. E. M.; Mittal, J.; Feig, M.; Mackerell, A. D. Optimization of the Additive CHARMM All-Atom Protein Force Field Targeting Improved Sampling of the Backbone φ, ψ and Side-Chain χ1 and χ2 Dihedral Angles. J. Chem. Theory Comput. 2012, 8, 3257– 3273,  DOI: 10.1021/ct300400x
      93
      Optimization of the Additive CHARMM All-Atom Protein Force Field Targeting Improved Sampling of the Backbone .vphi., ψ and Side-Chain χ1 and χ2 Dihedral Angles
      Best, Robert B.; Zhu, Xiao; Shim, Jihyun; Lopes, Pedro E. M.; Mittal, Jeetain; Feig, Michael; MacKerell, Alexander D.
      Journal of Chemical Theory and Computation (2012), 8 (9), 3257-3273CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      While the quality of the current CHARMM22/CMAP additive force field for proteins has been demonstrated in a large no. of applications, limitations in the model with respect to the equil. between the sampling of helical and extended conformations in folding simulations have been noted. To overcome this, as well as make other improvements in the model, we present a combination of refinements that should result in enhanced accuracy in simulations of proteins. The common (non-Gly, -Pro) backbone CMAP potential has been refined against exptl. soln. NMR data for weakly structured peptides, resulting in a rebalancing of the energies of the α-helix and extended regions of the Ramachandran map, correcting the α-helical bias of CHARMM22/CMAP. The Gly and Pro CMAPs have been refitted to more accurate quantum-mech. energy surfaces. Side-chain torsion parameters have been optimized by fitting to backbone-dependent quantum-mech. energy surfaces, followed by addnl. empirical optimization targeting NMR scalar couplings for unfolded proteins. A comprehensive validation of the revised force field was then performed against a collection of exptl. data: (i) comparison of simulations of eight proteins in their crystal environments with crystal structures; (ii) comparison with backbone scalar couplings for weakly structured peptides; (iii) comparison with NMR residual dipolar couplings and scalar couplings for both backbone and side-chains in folded proteins; (iv) equil. folding of mini-proteins. The results indicate that the revised CHARMM 36 parameters represent an improved model for modeling and simulation studies of proteins, including studies of protein folding, assembly, and functionally relevant conformational changes.
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    94. 94
      Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 1983, 79, 926– 935,  DOI: 10.1063/1.445869
      94
      Comparison of simple potential functions for simulating liquid water
      Jorgensen, William L.; Chandrasekhar, Jayaraman; Madura, Jeffry D.; Impey, Roger W.; Klein, Michael L.
      Journal of Chemical Physics (1983), 79 (2), 926-35CODEN: JCPSA6; ISSN:0021-9606.
      Classical Monte Carlo simulations were carried out for liq. H2O in the NPT ensemble at 25° and 1 atm using 6 of the simpler intermol. potential functions for the dimer. Comparisons were made with exptl. thermodn. and structural data including the neutron diffraction results of Thiessen and Narten (1982). The computed densities and potential energies agree with expt. except for the original Bernal-Fowler model, which yields an 18% overest. of the d. and poor structural results. The discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons were made for the self-diffusion coeffs. obtained from mol. dynamics simulations.
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    95. 95
      Mayne, C. G.; Saam, J.; Schulten, K.; Tajkhorshid, E.; Gumbart, J. C. Rapid parameterization of small molecules using the force field toolkit. J. Comput. Chem. 2013, 34, 2757– 2770,  DOI: 10.1002/jcc.23422
      95
      Rapid parameterization of small molecules using the force field toolkit
      Mayne, Christopher G.; Saam, Jan; Schulten, Klaus; Tajkhorshid, Emad; Gumbart, James C.
      Journal of Computational Chemistry (2013), 34 (32), 2757-2770CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      The inability to rapidly generate accurate and robust parameters for novel chem. matter continues to severely limit the application of mol. dynamics simulations to many biol. systems of interest, esp. in fields such as drug discovery. Although the release of generalized versions of common classical force fields, for example, General Amber Force Field and CHARMM General Force Field, have posited guidelines for parameterization of small mols., many tech. challenges remain that have hampered their wide-scale extension. The Force Field Toolkit (ffTK), described herein, minimizes common barriers to ligand parameterization through algorithm and method development, automation of tedious and error-prone tasks, and graphical user interface design. Distributed as a VMD plugin, ffTK facilitates the traversal of a clear and organized workflow resulting in a complete set of CHARMM-compatible parameters. A variety of tools are provided to generate quantum mech. target data, setup multidimensional optimization routines, and analyze parameter performance. Parameters developed for a small test set of mols. using ffTK were comparable to existing CGenFF parameters in their ability to reproduce exptl. measured values for pure-solvent properties (<15% error from expt.) and free energy of solvation (±0.5 kcal/mol from expt.). © 2013 Wiley Periodicals, Inc.
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    96. 96
      Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126, 014101,  DOI: 10.1063/1.2408420
      96
      Canonical sampling through velocity rescaling
      Bussi, Giovanni; Donadio, Davide; Parrinello, Michele
      Journal of Chemical Physics (2007), 126 (1), 014101/1-014101/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The authors present a new mol. dynamics algorithm for sampling the canonical distribution. In this approach the velocities of all the particles are rescaled by a properly chosen random factor. The algorithm is formally justified and it is shown that, in spite of its stochastic nature, a quantity can still be defined that remains const. during the evolution. In numerical applications this quantity can be used to measure the accuracy of the sampling. The authors illustrate the properties of this new method on Lennard-Jones and TIP4P water models in the solid and liq. phases. Its performance is excellent and largely independent of the thermostat parameter also with regard to the dynamic properties.
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    97. 97
      Andersen, H. C. Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculations. J. Comput. Phys. 1983, 52, 24– 34,  DOI: 10.1016/0021-9991(83)90014-1
      97
      RATTLE: a "velocity" version of the SHAKE algorithm for molecular dynamics calculations
      Andersen, Hans C.
      Journal of Computational Physics (1983), 52 (1), 24-34CODEN: JCTPAH; ISSN:0021-9991.
      An algorithm, called RATTLE, for integrating the equations of motion in mol. dynamics calcns. for mol. models with internal constraints is presented. RATTLE calcs. the positions and velocities at the next time from the positions and velocities at the present time step, without requiring information about the earlier history. It is based on the Verlet algorithm and retains the simplicity of using Cartesian coordinates for each of the atoms to describe the configuration of a mol. with internal constraints. RATTLE guarantees that the coordinates and velocities of the atoms in a mol. satisfy the internal constraints at each time step.
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    98. 98
      Miyamoto, S.; Kollman, P. A. Settle: An analytical version of the SHAKE and RATTLE algorithm for rigid water models. J. Comput. Chem. 1992, 13, 952– 962,  DOI: 10.1002/jcc.540130805
      98
      SETTLE: an analytical version of the SHAKE and RATTLE algorithm for rigid water models
      Miyamoto, Shuichi; Kollman, Peter A.
      Journal of Computational Chemistry (1992), 13 (8), 952-62CODEN: JCCHDD; ISSN:0192-8651.
      An anal. algorithm, called SETTLE, for resetting the positions and velocities to satisfy the holonomic constraints on the rigid water model is presented. This method is based on the Cartesian coordinate system and can be used in place of SHAKE and RATTLE. The authors implemented this algorithm in the SPASMS package of mol. mechanics and dynamics. Several series of mol. dynamics simulations were carried out to examine the performance of the new algorithm in comparison with the original RATTLE method. SETTLE is of higher accuracy and is faster than RATTLE with reasonable tolerances by three to nine times on a scalar machine. The performance improvement ranged from factors of 26 to 98 on a vector machine since the method presented is not iterative.
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    99. 99
      Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785– 789,  DOI: 10.1103/PhysRevB.37.785
      99
      Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
      Lee, Chengteh; Yang, Weitao; Parr, Robert G.
      Physical Review B: Condensed Matter and Materials Physics (1988), 37 (2), 785-9CODEN: PRBMDO; ISSN:0163-1829.
      A correlation-energy formula due to R. Colle and D. Salvetti (1975), in which the correlation energy d. is expressed in terms of the electron d. and a Laplacian of the 2nd-order Hartree-Fock d. matrix, is restated as a formula involving the d. and local kinetic-energy d. On insertion of gradient expansions for the local kinetic-energy d., d.-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calcns. on a no. of atoms, pos. ions, and mols., of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.
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    100. 100
      Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648– 5652,  DOI: 10.1063/1.464913
      100
      Density-functional thermochemistry. III. The role of exact exchange
      Becke, Axel D.
      Journal of Chemical Physics (1993), 98 (7), 5648-52CODEN: JCPSA6; ISSN:0021-9606.
      Despite the remarkable thermochem. accuracy of Kohn-Sham d.-functional theories with gradient corrections for exchange-correlation, the author believes that further improvements are unlikely unless exact-exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange-correlation functional (contg. local-spin-d., gradient, and exact-exchange terms) is tested for 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total at. energies of first- and second-row systems. This functional performs better than previous functionals with gradient corrections only, and fits expt. atomization energies with an impressively small av. abs. deviation of 2.4 kcal/mol.
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    101. 101
      Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104,  DOI: 10.1063/1.3382344
      101
      A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
      Grimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, Helge
      Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
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    102. 102
      Dunning, T. H., Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90, 1007– 1023,  DOI: 10.1063/1.456153
      102
      Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
      Dunning, Thom H., Jr.
      Journal of Chemical Physics (1989), 90 (2), 1007-23CODEN: JCPSA6; ISSN:0021-9606.
      Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.
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    103. 103
      Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865– 3868,  DOI: 10.1103/PhysRevLett.77.3865
      103
      Generalized gradient approximation made simple
      Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
      Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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    104. 104
      Weigend, F.; Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297– 3305,  DOI: 10.1039/b508541a
      104
      Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy
      Weigend, Florian; Ahlrichs, Reinhart
      Physical Chemistry Chemical Physics (2005), 7 (18), 3297-3305CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 mols. representing (nearly) all elements-except lanthanides-in their common oxidn. states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, d. functional theory and correlated methods, for which we had chosen Moller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.
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    105. 105
      Byrd, R. H.; Lu, P.; Nocedal, J.; Zhu, C. A Limited Memory Algorithm for Bound Constrained Optimization. SIAM J. Sci. Stat. Comp. 1995, 16, 1190– 1208,  DOI: 10.1137/0916069
      There is no corresponding record for this reference.
    106. 106
      Zhu, C.; Byrd, R.; Nocedal, J.; Morales, J. L. L-BFGS-B (ver. 3.0), http://users.iems.northwestern.edu/~nocedal/lbfgsb.html.
      There is no corresponding record for this reference.
    107. 107
      Zhu, C.; Byrd, R. H.; Lu, P.; Nocedal, J. L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization. ACM Transactions on Mathematical Software 1997, 23, 550– 560,  DOI: 10.1145/279232.279236
      There is no corresponding record for this reference.
    108. 108
      Lence, E.; van der Kamp, M. W.; González-Bello, C.; Mulholland, A. J. QM/MM simulations identify the determinants of catalytic activity differences between type II dehydroquinase enzymes. Org. Biomol. Chem. 2018, 16, 4443– 4455,  DOI: 10.1039/C8OB00066B
      108
      QM/MM simulations identify the determinants of catalytic activity differences between type II dehydroquinase enzymes
      Lence, Emilio; van der Kamp, Marc W.; Gonzalez-Bello, Concepcion; Mulholland, Adrian J.
      Organic & Biomolecular Chemistry (2018), 16 (24), 4443-4455CODEN: OBCRAK; ISSN:1477-0520. (Royal Society of Chemistry)
      Type II dehydroquinase enzymes (DHQ2), recognized targets for antibiotic drug discovery, show significantly different activities dependent on the species: DHQ2 from Mycobacterium tuberculosis (MtDHQ2) and Helicobacter pylori (HpDHQ2) show a 50-fold difference in catalytic efficiency. Revealing the determinants of this activity difference is important for our understanding of biol. catalysis and further offers the potential to contribute to tailoring specificity in drug design. Mol. dynamics simulations using a quantum mechanics/mol. mechanics potential, with correlated ab initio single point corrections, identify and quantify the subtle determinants of the exptl. obsd. difference in efficiency. The rate-detg. step involves the formation of an enolate intermediate: more efficient stabilization of the enolate and transition state of the key step in MtDHQ2, mainly by the essential residues Tyr24 and Arg19, makes it more efficient than HpDHQ2. Further, a water mol., which is absent in MtDHQ2 but involved in generation of the catalytic Tyr22 tyrosinate in HpDHQ2, was found to destabilize both the transition state and the enolate intermediate. The quantification of the contribution of key residues and water mols. in the rate-detg. step of the mechanism also leads to improved understanding of higher potencies and specificity of known inhibitors, which should aid ongoing inhibitor design.
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    109. 109
      Albery, W. J.; Knowles, J. R. Free-Energy Profile for the Reaction Catalyzed by Triosephosphate Isomerase. Biochemistry 1976, 15, 5627– 5631,  DOI: 10.1021/bi00670a031
      109
      Free-energy profile for the reaction catalyzed by triosephosphate isomerase
      Albery, W. John; Knowles, Jeremy R.
      Biochemistry (1976), 15 (25), 5627-31CODEN: BICHAW; ISSN:0006-2960.
      The exptl. results on the interconversion of dihydroxyacetone phosphate and D-glyceraldehyde 3-phosphate catalyzed by triose phosphate isomerase that are presented in 5 previous papers are collected here and analyzed according to the theory presented in the 1st paper (Albery, W. J., and Knowles, J. R. (1976)). The rate consts. and fractionation factors so derived allow the construction of the Gibbs free-energy profile for this enzyme-catalyzed reaction.
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    110. 110
      Hudson, P. S.; Woodcock, H. L.; Boresch, S. Use of Nonequilibrium Work Methods to Compute Free Energy Differences Between Molecular Mechanical and Quantum Mechanical Representations of Molecular Systems. J. Phys. Chem. Lett. 2015, 6, 4850– 4856,  DOI: 10.1021/acs.jpclett.5b02164
      110
      Use of Nonequilibrium Work Methods to Compute Free Energy Differences Between Molecular Mechanical and Quantum Mechanical Representations of Molecular Systems
      Hudson, Phillip S.; Woodcock, H. Lee; Boresch, Stefan
      Journal of Physical Chemistry Letters (2015), 6 (23), 4850-4856CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Carrying out free energy simulations (FES) using quantum mech. (QM) Hamiltonians remains an attractive, albeit elusive goal. Renewed efforts in this area have focused on using "indirect" thermodn. cycles to connect "low level" simulation results to "high level" free energies. The main obstacle to computing converged free energy results between mol. mech. (MM) and QM (ΔAMM→QM), as recently demonstrated by us and others, is differences in the so-called "stiff" degrees of freedom (e.g., bond stretching) between the resp. energy surfaces. Herein, we demonstrate that this problem can be efficiently circumvented using nonequil. work (NEW) techniques, i.e., Jarzynski's and Crooks' equations. Initial applications of computing ΔAMM→QMNEW, for blocked amino acids alanine and serine as well as to generate butane's potentials of mean force via the indirect QM/MM FES method, showed marked improvement over traditional FES approaches.
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    111. 111
      Kearns, F. L.; Hudson, P. S.; Woodcock, H. L.; Boresch, S. Computing Converged Free Energy Differences between Levels of Theory via Nonequilibrium Work Methods: Challenges and Opportunities. J. Comput. Chem. 2017, 38, 1376– 1388,  DOI: 10.1002/jcc.24706
      111
      Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities
      Kearns, Fiona L.; Hudson, Phillip S.; Woodcock, Henry L.; Boresch, Stefan
      Journal of Computational Chemistry (2017), 38 (16), 1376-1388CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      We demonstrate that Jarzynski's equation can be used to reliably compute free energy differences between low and high level representations of systems. The need for such a calcn. arises when employing the so-called "indirect" approach to free energy simulations with mixed quantum mech./mol. mech. (QM/MM) Hamiltonians; a popular technique for circumventing extensive simulations involving quantum chem. computations. We have applied this methodol. to several small and medium sized org. mols., both in the gas phase and explicit solvent. Test cases include several systems for which the std. approach; i.e., free energy perturbation between low and high level description, fails to converge. Finally, we identify three major areas in which the difference between low and high level representations make the calcn. of ΔA(low→high) difficult: bond stretching and angle bending, different preferred conformations, and the response of the MM region to the charge distribution of the QM region. © 2016 Wiley Periodicals, Inc.
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    112. 112
      Hudson, P. S.; Woodcock, H. L.; Boresch, S. Use of Interaction Energies in QM/MM Free Energy Simulations. J. Chem. Theory Comput. 2019, 15, 4632– 4645,  DOI: 10.1021/acs.jctc.9b00084
      112
      Use of Interaction Energies in QM/MM Free Energy Simulations
      Hudson, Phillip S.; Woodcock, H. Lee; Boresch, Stefan
      Journal of Chemical Theory and Computation (2019), 15 (8), 4632-4645CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost assocd. with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the ''indirect'' approach is generally taken, necessitating a free energy calcn. between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with std. free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approxns. have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and anal. demonstrate that this ''interaction energy approxn.'' (IEA) is theor. incorrect, and the implicit approxn. invoked is spurious at best. Herein, we demonstrate this via solvation free energy calcns. using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼ 1.5 kcal/mol from the rigorously obtained value.
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    113. 113
      Holden, Z. C.; Richard, R. M.; Herbert, J. M. Periodic boundary conditions for QM/MM calculations: Ewald summation for extended Gaussian basis sets. J. Chem. Phys. 2013, 139, 244108,  DOI: 10.1063/1.4850655
      113
      Periodic boundary conditions for QM/MM calculations: Ewald summation for extended Gaussian basis sets
      Holden, Zachary C.; Richard, Ryan M.; Herbert, John M.
      Journal of Chemical Physics (2013), 139 (24), 244108/1-244108/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      An implementation of Ewald summation for use in mixed quantum mechanics/mol. mechanics (QM/MM) calcns. is presented, which builds upon previous work by others that was limited to semi-empirical electronic structure for the QM region. Unlike previous work, our implementation describes the wave function's periodic images using "ChElPG" at. charges, which are detd. by fitting to the QM electrostatic potential evaluated on a real-space grid. This implementation is stable even for large Gaussian basis sets with diffuse exponents, and is thus appropriate when the QM region is described by a correlated wave function. Derivs. of the ChElPG charges with respect to the QM d. matrix are a potentially serious bottleneck in this approach, so we introduce a ChElPG algorithm based on atom-centered Lebedev grids. The ChElPG charges thus obtained exhibit good rotational invariance even for sparse grids, enabling significant cost savings. Detailed anal. of the optimal choice of user-selected Ewald parameters, as well as timing breakdowns, is presented. (c) 2013 American Institute of Physics.
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    114. 114
      Giese, T. J.; York, D. M. Ambient-Potential Composite Ewald Method for ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulation. J. Chem. Theory Comput. 2016, 12, 2611– 2632,  DOI: 10.1021/acs.jctc.6b00198
      114
      Ambient-Potential Composite Ewald Method for ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulation
      Giese, Timothy J.; York, Darrin M.
      Journal of Chemical Theory and Computation (2016), 12 (6), 2611-2632CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      A new approach for performing Particle Mesh Ewald in ab initio quantum mech./mol. mech. (QM/MM) simulations with extended AO basis sets is presented. The new approach, the Ambient-Potential Composite Ewald (CEw) method, does not perform the QM/MM interaction with Mulliken charges nor electrostatically fit charges. Instead the nuclei and electron d. interact directly with the MM environment, but in a manner that avoids the use of dense Fourier transform grids. By performing the electrostatics with the underlying QM d., the CEw method avoids SCF instabilities that have been encountered with simple charge mapping procedures. Potential of mean force (PMF) profiles of the p-nitrophenyl phosphate dissocn. reaction in explicit solvent are computed from PBE0/6-31G* QM/MM mol. dynamics simulations with various electrostatic protocols. The CEw profiles are shown to be stable with respect to real-space Ewald cutoff, whereas the PMFs computed from truncated and switched electrostatics produce artifacts. PBE0/6-311G**, AM1/d-PhoT, and DFTB2 QM/MM simulations are performed to generate two-dimensional PMF profiles of the phosphoryl transesterification reactions with ethoxide and phenoxide leaving groups. The semiempirical models incorrectly produce a concerted ethoxide mechanism, whereas PBE0 correctly produces a stepwise mechanism. The ab initio reaction barriers agree more closely to expt. than the semiempirical models. The failure of Mulliken-charge QM/MM-Ewald is analyzed.
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    115. 115
      Vasilevskaya, T.; Thiel, W. Periodic Boundary Conditions in QM/MM Calculations: Implementation and Tests. J. Chem. Theory Comput. 2016, 12, 3561– 3570,  DOI: 10.1021/acs.jctc.6b00269
      115
      Periodic Boundary Conditions in QM/MM Calculations: Implementation and Tests
      Vasilevskaya, Tatiana; Thiel, Walter
      Journal of Chemical Theory and Computation (2016), 12 (8), 3561-3570CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Quantum mechanics/mol. mechanics (QM/MM) simulations of reactions in solns. and in solvated enzymes can be performed using the QM/MM-Ewald approach with periodic boundary conditions (PBC) or a nonperiodic treatment with a finite solvent shell (droplet model). To avoid the changes in QM codes that are required in std. QM/MM-Ewald implementations, we present a general method (Gen-Ew) for periodic QM/MM calcns. that can be used with any QM method in the QM/MM framework. The Gen-Ew approach approximates the QM/MM-Ewald method by representing the PBC potential by virtual charges on a sphere and the QM d. by electrostatic potential (ESP) charges. Test calcns. show that the deviations between Gen-Ew and QM/MM-Ewald results are generally small enough to justify the application of the Gen-Ew method in the absence of a suitable QM/MM-Ewald implementation. We compare the results from periodic QM/MM calcns. (QM/MM-Ewald, Gen-Ew) to their nonperiodic counterparts (droplet model) for five test reactions in water and for the Claisen rearrangement in chorismate mutase. The periodic and nonperiodic QM/MM treatments give similar free energy profiles for the reactions in soln. (umbrella sampling, free energy deviations of the order of 1 kcal/mol) and essentially the same energy profile (constrained geometry optimizations) for the Claisen rearrangement in chorismate mutase. In all cases considered, long-range electrostatic interactions are thus well captured by nonperiodic QM/MM calcns. in a water droplet of reasonable size (radius of 15-20 Å). This provides further justification for the widespread use of the computationally efficient droplet model in QM/MM studies of reactions in soln. and in enzymes.
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    116. 116
      Kawashima, Y.; Ishimura, K.; Shiga, M. Ab initio quantum mechanics/molecular mechanics method with periodic boundaries employing Ewald summation technique to electron-charge interaction: Treatment of the surface-dipole term. J. Chem. Phys. 2019, 150, 124103,  DOI: 10.1063/1.5048451
      116
      Ab initio quantum mechanics/molecular mechanics method with periodic boundaries employing Ewald summation technique to electron-charge interaction: Treatment of the surface-dipole term
      Kawashima, Y.; Ishimura, K.; Shiga, M.
      Journal of Chemical Physics (2019), 150 (12), 124103/1-124103/14CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We have developed a combined quantum mechanics/mol. mechanics (QM/MM) method with periodic boundary condition (PBC) treatment of explicit electron-charge interactions in a theor. rigorous manner, for an accurate description of electronic structures for mols. in the condensed phase. The Ewald summation technique is employed for the calcn. of the one-electron Hamiltonian in an ab initio framework. We decomp. the Coulomb interactions into two components: those within the same cell and those between different cells. The former is calcd. in the same way as the conventional QM/MM calcn. for isolated systems; this article focuses on our novel method for calcg. the latter type of Coulomb interactions. The detailed formulation of the Hamiltonian of this new QM/MM-PBC method, as well as the necessary one-electron integrals and their gradients, is given. The novel method is assessed by applying it to the dil. water system and a system with a coumarin mol. in water solvent; it successfully reproduces the electronic energies, frontier orbital energies, and Mulliken population charge of the real-space limit calcd. by QM/MM using large isolated systems. We investigated the contribution from each term of the Hamiltonian and found that the surface-dipole term in the Ewald summation technique is indispensable for QM/MM-PBC calcns. The newly developed QM/MM-PBC method is promising for tackling chem. reactions and excited states of mols. in the condensed phase. (c) 2019 American Institute of Physics.
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    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcb.1c01862.

    • Protocols of equilibration, interatomic distances, calculated total energies and proton affinities, Cartesian coordinates, details of umbrella sampling, 2D PMF obtained by DFTB3 (PDF)

    • Animation for the visualization of minimum-energy pathways from DHAP to GAP using QM/MM calculations at the level of B3LYP-D3/aug-cc-pVDZ (MP4)

    • Animation for the visualization of minimum-energy pathways from DHAP to GAP using QM/MM calculations at the levels of DFTB3 (MP4)


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