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Routine Access to Millisecond Time Scale Events with Accelerated Molecular Dynamics

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† Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, Urey Hall, La Jolla, California 92093-0365, United States
‡ San Diego Supercomputer Center, University of California, San Diego, La Jolla, California 92093-0505, United States
§ Howard Hughes Medical Institute, University of California, San Diego, La Jolla, California 92093, United States
*E-mail: [email protected]
Cite this: J. Chem. Theory Comput. 2012, 8, 9, 2997–3002
Publication Date (Web):July 27, 2012
https://doi.org/10.1021/ct300284c
Copyright © 2012 American Chemical Society
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Abstract

In this work, we critically assess the ability of the all-atom enhanced sampling method accelerated molecular dynamics (aMD) to investigate conformational changes in proteins that typically occur on the millisecond time scale. We combine aMD with the inherent power of graphics processor units (GPUs) and apply the implementation to the bovine pancreatic trypsin inhibitor (BPTI). A 500 ns aMD simulation is compared to a previous millisecond unbiased brute force MD simulation carried out on BPTI, showing that the same conformational space is sampled by both approaches. To our knowledge, this represents the first implementation of aMD on GPUs and also the longest aMD simulation of a biomolecule run to date. Our implementation is available to the community in the latest release of the Amber software suite (v12), providing routine access to millisecond events sampled from dynamics simulations using off the shelf hardware.

Introduction

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Conventional molecular dynamics allows one to access time scales on the order of tens to hundreds of nanoseconds; however, many biological processes of interest occur on longer time scales of up to milliseconds or more. (1-6) Efforts to explore these long time scales have led to the development of several advanced sampling techniques such as conformational flooding, (7, 8) hyperdynamics, (9, 10) metadynamics, (11-13) and the adaptive biasing force method. (13-15) Inspired by Voter, accelerated molecular dynamics (aMD) is an additional enhanced conformational sampling method that provides access to events beyond those obtainable with conventional molecular dynamics (cMD). (9) Here, we emphasize one of the great advantages of aMD, which is that no prior knowledge of the potential energy landscape needs to be known and, consequently, no reaction coordinate needs to be defined prior to running the simulation.
In addition to advances in algorithms to achieve dynamics on longer time scales, recent efforts by D. E. Shaw Research have focused on building a specialized computer, Anton, with the sole purpose of simulating protein dynamics. (16) With this great engineering achievement, simulation time scales have been pushed into the range of hundreds of microseconds to milliseconds using unbiased brute force cMD. (17, 18) While time on an Anton machine has been generously granted to the scientific community, access is still limited, and many researchers are stuck waiting in queues on crowded super computers or local clusters. Recently, the advancement of computational science on conventional graphic processing units (GPU) has allowed researchers efficient and inexpensive access to microseconds of simulation time on just a single desktop computer. (18-21) By combining the advanced sampling method of aMD and the inherent power of the GPU, we present the synthesis of a tool that allows researchers access to inexpensive efficient exploration of long time scale events. Here, we point out that a time scale cannot be directly determined from an aMD simulation, but we can correlate events which occur on long time scales from either experimental results or long conventional molecular dynamics simulations. However, future work using the conformational space explored by aMD as a seed for other methods, namely, Markov models, (22) would allow one access to time dependent properties, such as NMR relaxation data, which was shown can be computed directly from the Anton millisecond trajectory. (23)
In its original form, the aMD method modifies the potential energy landscape by raising energy minima that lie below a defined threshold level, while leaving those areas lying above the threshold unmodified. As a result, barriers separating adjacent energy basins are effectively reduced, providing the simulation access to conformational space that cannot be easily accessed in a cMD simulation. Historically, aMD was first implemented by Hamelberg et al. within the framework of the sander module in the AMBER 7 package and used to study several small peptide and protein systems. (24, 25) Since the original implementation, there have been several notable variations of the aMD method, (26-28) but no official implementation has been released. However, Wang et al. recently ported the aMD method to NAMD, (29) and following this approach, we have ported aMD to the three main MD engines included in Amber 12: (30) the CPU versions sander and pmemd and the GPU version pmemd.cuda. The performance enhancements for cMD on GPUs obtained with pmemd.cuda alone are remarkable and can be found on the Amber Web site (ambermd.org) and in the following publications. (21, 31) For this work, we have used our implementation of aMD in the pmemd.cuda MD engine and will refer to it simply as aMD.
Bovine pancreatic trypsin inhibitor (BPTI) is a small protein with 58 residues that has been extensively studied experimentally, being the first subject of NMR experiments to characterize individual hydration water molecules in proteins, (32) and also the first protein to be simulated with molecular dynamics. (33) D. E. Shaw Research reported in 2010 a remarkable 1.03 ms MD simulation of BPTI in explicit water. (34) Using our aMD implementation in pmemd.cuda, we have performed a 500 ns aMD simulation of BPTI in explicit water, maintaining the same conditions as the simulation on Anton. In order to mimic the force field used in the Anton simulation, we modified the ff99SB-ILDN force field removing the modifications to leucine, aspartic acid, and asparagine, which we refer to as ff99SB-I.
Using the 1.03 ms simulation of BPTI provided by D. E. Shaw Research throughout our analysis, we have shown that both methodologies sample the same conformational space. Additionally, we performed a 500 ns cMD simulation to use as a measure of the amount of sampling attainable by conventional MD with the same computational effort. To the best of our knowledge, our aMD implementation is the first to support GPU acceleration, and the work presented here represents the longest single aMD simulation of a biomolecule run to date. Both Amber simulations were completed in two weeks on individual desktop computers containing single $500 GTX580 GPUs. Details of the simulations can be found in the Supporting Information.

Results

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Structural Analysis

In the millisecond Anton simulation, five long-lived structural states were identified that persisted for 6–26 μs with deviations of up to 3.5 Å from the crystal structure, 5PTI. (34, 35) Using these same five structures and the crystal structure as references, we calculated RMSD values (heavy backbone atoms) along our 500 ns aMD simulation, shown in Figure 1. We color each point according to which of the five structures it is closest to in terms of RMSD, allowing one to see the transitions from the different structural states. RMSD results show we sample structures from all five states but spend the majority of the time near the blue state and the least amount of time close to the green state. The RMSD with respect to the X-ray structure shows that the protein moves away from the crystal structure 49 ns into the simulation and achieves a maximum RMSD of 2.7 Å before coming back to within 0.89 Å, emphasizing that the system is sampling states both far from and near to the crystal structure, as was seen in the long 1 ms cMD simulation. The largest deviation from the crystal structure is 3.29 Å, which occurs at 195 ns.

Figure 1

Figure 1. RMSD of the aMD trajectory from the crystal structure. Red, blue, green, purple, and black colors correspond to the kinetic clusters identified in the 1 ms cMD BPTI simulation. (34) For each frame, we identify what cluster we are closest to and color it accordingly. Only a handful of transitions to the green state were observed, and we highlight them with diamond markers.

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To characterize the conformational states explored in more detail, principal component analysis was carried out on the 1 ms simulation using Bio3D. (36) Figure 2a displays the two-dimensional representation of the structural data set as a projection of the Boltzmann reweighted distribution onto the subspace defined by the first and second principal component vectors (PC1 and PC2) built from the C-α atoms spanning residues 4 to 54. In this analysis, PC1 and PC2 describe 35% and 21%, respectively, of the total variance of the motions in the simulation (Movies S1 and S2). The five long-lived structures and the crystal structure were then projected into this space. The 500 ns cMD control simulation and the 500 ns aMD simulation were also projected into the subspace defined by the 1 ms simulation (Figure 2b,c). It is clear from Figure 2b that the 500 ns cMD control simulation does not explore the amount of conformational space that the aMD simulation does and remains trapped in the basin localized around the crystal structure.

Figure 2

Figure 2. The free energy principal component projection of (a) 1 ms simulation, (b) 500 ns cMD ff99SB-I simulation, and (c) 500 ns aMD ff99SB-I simulation onto (PC1, PC2) defined by the 1 ms simulation. The long-lived structures are projected onto the free energy surface and are labeled as red, blue, green, purple, and black triangles. The crystal structure, 5PTI, is demarked by the red diamond (see also Movies S1 and S2).

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The aMD simulation (Figure 2c) exhibits a rather broad pathway from the crystallographic basin (0.0, −5.0) to the region (−10.0, −5.0) which is not present in the 1 ms simulation (Figure 2a). Flattening of the potential energy surface in the two basins could promote transitions over a large barrier separating them, but the 1 ms simulation may also not have sampled these regions frequently enough to explore this pathway. The 1 ms simulation spent the majority of the time in the basin around (2.5, 1.0) which is ultimately responsible for the observed populations in the 1 ms cMD simulation differing substantially from experiment. In the Shaw et al. paper, this is attributed to inaccuracies in the underlying force field, and indeed we also spend a considerable amount of our 500 ns simulation in the same basin, as one would expect using the same force field. In future work, to determine accurately the conformational changes mapped out by the PC space using an aMD simulation, one could use the technique employed by Wereszczynski and McCammon. (37)

NMR Observables

The recent analysis carried out by Xue et al. examined in detail the χ1, χ2, and χ3 dihedral angles associated with the disulfide bond formed between cysteine 14 and cysteine 38 during the course of the 1 ms cMD BPTI simulation. (23) In this manuscript, a similar analysis was performed. Figure 3c shows the Boltzmann reweighted χ1(C14) vs χ1(C38) free energy surface explored throughout the 500 ns aMD simulation. In contrast, the 500 ns control cMD simulation never visits the minima explored by the aMD simulation and remains trapped in a state close to the crystal structure (Figure 3b), as was seen in the PC projections. Comparing the free energy surface explored by the 1 ms cMD simulation (Figure 3a) to that of our aMD simulation, it is clear the aMD simulation explores the same states as the unbiased simulation.

Figure 3

Figure 3. The χ1–C14 vs χ1–C38 dihedral angle free energy surfaces of (a) 1 ms cMD simulation, (b) 500 ns cMD ff99SB-I simulation, and (c) 500 ns aMD ff99SB-I simulation. The long-lived stable states are plotted onto the free energy surface and are labeled as red, blue, green, purple, and black triangles. The crystal structure, 5PTI, is demarked by the red diamond. The major state M is labeled along with the minor states mC14 and mC38.

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The χ2 and χ3 dihedral angles associated with Cys14 and Cys38 can be used to further describe isomerization configurations of the disulfide bond: the major state M, which consists of three substates (M1, M2, and M3), and the two minor or excited states mC38 and mC14. (23) A detailed description of these states is included in the Supporting Information (Figure S1), which can be compared to those analyzed by Xue et al. for the 1 ms cMD simulation. In contrast with the 1 ms cMD simulation, which predicts the excited state mC14 to be the most populated, we find the major state M to be the most populated in the aMD simulations after Boltzmann reweighting our distribution (Table S1); however, to fully converge the population distribution would require a longer simulation than was used in this study.
Structures from states M1, mC38, and mC14 were extracted from the trajectory by using the lowest energy structure in the M1 state as a reference to select an ensemble of structures with similar energy from each of the three basins for performing the chemical shift analysis. Using the SHIFTX2 software package, (38) chemical shift differences were computed between the ensembles representing the different substates (Table 1). A RMS deviation of 2.1 ppm was obtained from the ff99SB-I aMD simulation (computed for the shifts with known sign) compared to 2.7 ppm computed from the 1 ms cMD simulation. In general, good agreement is achieved from the aMD simulation compared to values calculated from the 1 ms cMD simulation and the experimental values. (39, 40) We would like to highlight the fact that one cannot compute these differences using only 500 ns of cMD since the simulation never explores the excited states during the course of such a short simulation (Figure 3b).
Table 1. 15N Chemical Shift Differences between the Conformational States M1(M), mC14, and mC38
  ΔδM1,mC14 (ppm) ΔδM1,mC38 (ppm)
res. exptl (37) 500 ns cMD 1 ms cMD23 500 ns aMD exptl (32) 500 ns cMD 1 ms cMD (23) 500 ns aMD
C14 3.6   1.8 5.0 –0.4   0.6 0.6
K15 4.7   –1.4 1.6 –0.5   –1.5 0.1
C38 |0.8|   –2.2 –0.6 –1.7   –1.9 –3.7
R39 |1.2|   –0.5 0.2 –3.7   –2.6 –2.5

Water Occupancy

Examination of the water occupancy throughout the aMD simulation correctly identifies the four long-lived waters in agreement with experimental results. (41) The longest-lived water, W122, is identified by the 1 ms cMD simulation as having a lifetime of 14 μs. During the course of the aMD simulation, several exchange events are captured at this location and an interesting “revolving door” mechanism is identified, whereby the disulfide bond rotates around and pushes the water out of the pocket (highlighted in Movie S3). The longest binding events of water molecules at this site occur when in the crystallographic basin of the aMD simulation, consistent with the 1 ms cMD simulation.

Conclusion

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This work shows that, using conventional off the shelf GPU hardware combined with an enhanced sampling algorithm, events taking place on the millisecond time scale can be effectively sampled with dynamics simulations orders of magnitude shorter (2000×) than those time scales. The implementation is validated in this work by comparison with a long unbiased cMD simulation and experimental data. Structurally, we show the long-lived states identified by the 1 ms cMD simulation have been sampled both in terms of RMSD and coverage in PC space. We demonstrate that access to these states cannot be obtained with the same length of simulation carried out using conventional MD. Important structural waters were preserved and found to exhibit the same occupancies as those experimentally. Chemical shift differences computed from the aMD simulations were found to be in agreement with those calculated from the long 1 ms cMD simulation, and similar dihedral populations were also observed. However, we point out that, while aMD is great for exploration of conformational space, it does not reproduce the exact dynamics of the system. We conclude by emphasizing never before has the aMD been benchmarked against a long cMD simulation, and we commend D. E. Shaw Research for providing their data to the community.

Supporting Information

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Simulation setup, theory of aMD, details of how aMD parameters were selected, and reweighting protocol. Movies S1–S3, Figure S1, and Table S1. This information is available free of charge via the Internet at http://pubs.acs.org/.

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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
    • Ross C. Walker - Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, Urey Hall, La Jolla, California 92093-0365, United States;  San Diego Supercomputer Center, University of California, San Diego, La Jolla, California 92093-0505, United States;  Email: [email protected]
  • Authors
    • Levi C.T. Pierce - Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, Urey Hall, La Jolla, California 92093-0365, United States
    • Romelia Salomon-Ferrer - San Diego Supercomputer Center, University of California, San Diego, La Jolla, California 92093-0505, United States
    • Cesar Augusto F. de Oliveira - Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, Urey Hall, La Jolla, California 92093-0365, United States;  Howard Hughes Medical Institute, University of California, San Diego, La Jolla, California 92093, United States
    • J. Andrew McCammon - Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, Urey Hall, La Jolla, California 92093-0365, United States;  Howard Hughes Medical Institute, University of California, San Diego, La Jolla, California 92093, United States
  • Notes
    The authors declare no competing financial interest.

Acknowledgment

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This research used resources of the Keeneland Computing Facility at the Georgia Institute of Technology, which is supported by the National Science Foundation under contract OCI-0910735. This work was funded in part by the National Science Foundation through the Scientific Software Innovations Institutes program—NSF SI2-SSE (NSF1047875 & NSF1148276) grants to R.C.W, the NSF XSEDE program, and also by a University of California (UC Lab 09-LR-06-117792) grant to R.C.W. Computer time was provided by the San Diego Supercomputer Center through National Science Foundation award TGMCB090110 to R.C.W. The work was also supported by a CUDA fellowship to R.C.W. from NVIDIA. The J.A.M group is supported by NSF, NIH, HHMI, NBCR, and CTBP.

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    A review. Metadynamics calcns. allow investigating structure, plasticity, and energetics in a variety of biol. processes spanning from mol. docking to protein folding. Recent theor. developments have led to applications to increasingly complex systems and processes stepping up the biol. relevance of the problem solved. Here, after summarizing recent tech. advances and applications, we give a perspective of the method as a tool for enzymol. and for the prediction of NMR and other spectroscopic data.
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    Darve, E.; Pohorille, A. Calculating free energies using average force J. Chem. Phys. 2001, 115, 9169– 9183
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    13
    Calculating free energies using average force
    Darve, Eric; Pohorille, Andrew
    Journal of Chemical Physics (2001), 115 (20), 9169-9183CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    A new, general formula that connects the derivs. of the free energy along the selected, generalized coordinates of the system with the instantaneous force acting on these coordinates is derived. The instantaneous force is defined as the force acting on the coordinate of interest so that when it is subtracted from the equations of motion the acceleration along this coordinate is zero. The formula applies to simulations in which the selected coordinates are either unconstrained or constrained to fixed values. It is shown that in the latter case the formula reduces to the expression previously derived by den Otter and Briels [Mol. Phys. 98, 773 (2000)]. If simulations are carried out without constraining the coordinates of interest, the formula leads to a new method for calcg. the free energy changes along these coordinates. This method is tested in two examples - rotation around the C-C bond of 1,2-dichloroethane immersed in water and transfer of fluoromethane across the water-hexane interface. The calcd. free energies are compared with those obtained by two commonly used methods. One of them relies on detg. the probability d. function of finding the system at different values of the selected coordinate and the other requires calcg. the av. force at discrete locations along this coordinate in a series of constrained simulations. The free energies calcd. by these three methods are in excellent agreement. The relative advantages of each method are discussed.
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    Darve, E.; Rodriguez-Gomez, D.; Pohorille, A. Adaptive biasing force method for scalar and vector free energy calculations J. Chem. Phys. 2008, 128 (14) 144120
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    14
    Adaptive biasing force method for scalar and vector free energy calculations
    Darve, Eric; Rodriguez-Gomez, David; Pohorille, Andrew
    Journal of Chemical Physics (2008), 128 (14), 144120/1-144120/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    In free energy calcns. based on thermodn. integration, it is necessary to compute the derivs. of the free energy as a function of one (scalar case) or several (vector case) order parameters. We derive in a compact way a general formulation for evaluating these derivs. as the av. of a mean force acting on the order parameters, which involves first derivs. with respect to both Cartesian coordinates and time. This is in contrast with the previously derived formulas, which require first and second derivs. of the order parameter with respect to Cartesian coordinates. As illustrated in a concrete example, the main advantage of this new formulation is the simplicity of its use, esp. for complicated order parameters. It is also straightforward to implement in a mol. dynamics code, as can be seen from the pseudo-code given at the end. We further discuss how the approach based on time derivs. can be combined with the adaptive biasing force method, an enhanced sampling technique that rapidly yields uniform sampling of the order parameters, and by doing so greatly improves the efficiency of free energy calcns. Using the backbone dihedral angles Φ and Ψ in N-acetylalanyl-N'-methylamide as a numerical example, we present a technique to reconstruct the free energy from its derivs., a calcn. that presents some difficulties in the vector case because of the statistical errors affecting the derivs. (c) 2008 American Institute of Physics.
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    Henin, J.; Fiorin, G.; Chipot, C.; Klein, M. L. Exploring Multidimensional Free Energy Landscapes Using Time-Dependent Biases on Collective Variables J. Chem. Theory Comput. 2009, 6, 35– 47
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    Shaw, D. E.; Deneroff, M. M.; Dror, R. O.; Kuskin, J. S.; Larson, R. H.; Salmon, J. K.; Young, C.; Batson, B.; Bowers, K. J.; Chao, J. C.; Eastwood, M. P.; Gagliardo, J.; Grossman, J. P.; Ho, C. R.; Ierardi, D. J.; Kolossvary, I.; Klepeis, J. L.; Layman, T.; McLeavey, C.; Moraes, M. A.; Mueller, R.; Priest, E. C.; Shan, Y.; Spengler, J.; Theobald, M.; Towles, B.; Wang, S. C. Anton, a special-purpose machine for molecular dynamics simulation Commun. ACM 2008, 51, 91– 97
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    Dror, R. O.; Arlow, D. H.; Maragakis, P.; Mildorf, T. J.; Pan, A. C.; Xu, H.; Borhani, D. W.; Shaw, D. E. Activation mechanism of the β2-adrenergic receptor Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 18684– 18689
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    Activation mechanism of the β2-adrenergic receptor
    Dror, Ron O.; Arlow, Daniel H.; Maragakis, Paul; Mildorf, Thomas J.; Pan, Albert C.; Xu, Huafeng; Borhani, David W.; Shaw, David E.
    Proceedings of the National Academy of Sciences of the United States of America (2011), 108 (46), 18684-18689, S18684/1-S18684/12CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    A third of marketed drugs act by binding to a G-protein-coupled, receptor (GPCR) and either triggering or preventing receptor activation. Although recent crystal structures have provided snapshots of both active and inactive functional states of GPCRs, these structures do not reveal the mechanism by which GPCRs transition between these states. Here we propose an activation mechanism for the β2-adrenergic receptor, a prototypical GPCR, based on at.-level simulations in which an agonist-bound receptor transitions spontaneously from the active to the inactive crystallog. obsd. conformation. A loosely coupled allosteric network, comprising three regions that can each switch individually between multiple distinct conformations, links small perturbations at the extracellular drug-binding site to large conformational changes at the intracellular G-protein-binding site. Our simulations also exhibit an intermediate that may represent a receptor conformation to which a G protein binds during activation, and suggest that the first structural changes during receptor activation often take place on the intracellular side of the receptor, far from the drug-binding site. By capturing this fundamental signaling process in at. detail, our results may provide a foundation for the design of drugs that control receptor signaling more precisely by stabilizing specific receptor conformations.
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    Shan, Y.; Kim, E. T.; Eastwood, M. P.; Dror, R. O.; Seeliger, M. A.; Shaw, D. E. How Does a Drug Molecule Find Its Target Binding Site? J. Am. Chem. Soc. 2011, 133, 9181– 9183
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    How Does a Drug Molecule Find Its Target Binding Site?
    Shan, Yibing; Kim, Eric T.; Eastwood, Michael P.; Dror, Ron O.; Seeliger, Markus A.; Shaw, David E.
    Journal of the American Chemical Society (2011), 133 (24), 9181-9183CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Although the thermodn. principles that control the binding of drug mols. to their protein targets are well understood, detailed exptl. characterization of the process by which such binding occurs has proven challenging. We conducted relatively long, unguided mol. dynamics simulations in which a ligand (the cancer drug dasatinib or the kinase inhibitor PP1) was initially placed at a random location within a box that also contained a protein (Src kinase) to which that ligand was known to bind. In several of these simulations, the ligand correctly identified its target binding site, forming a complex virtually identical to the crystallog. detd. bound structure. The simulated trajectories provide a continuous, at.-level view of the entire binding process, revealing persistent and noteworthy intermediate conformations and shedding light on the role of water mols. The technique we employed, which does not assume any prior knowledge of the binding site's location, may prove particularly useful in the development of allosteric inhibitors that target previously undiscovered binding sites.
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    Harvey, M. J.; Giupponi, G.; Fabritiis, G. D. ACEMD: Accelerating Biomolecular Dynamics in the Microsecond Time Scale J. Chem. Theory Comput. 2009, 5, 1632– 1639
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    ACEMD: Accelerating Biomolecular Dynamics in the Microsecond Time Scale
    Harvey, M. J.; Giupponi, G.; De Fabritiis, G.
    Journal of Chemical Theory and Computation (2009), 5 (6), 1632-1639CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The high arithmetic performance and intrinsic parallelism of recent graphical processing units (GPUs) can offer a technol. edge for mol. dynamics simulations. ACEMD is a prodn.-class biomol. dynamics (MD) engine supporting CHARMM and AMBER force fields. Designed specifically for GPUs it is able to achieve supercomputing scale performance of 40 ns/day for all-atom protein systems with over 23,000 atoms. The authors provide a validation and performance evaluation of the code and run a microsecond-long trajectory for an all-atom mol. system in explicit TIP3P water on a single workstation computer equipped with just 3 GPUs. The authors believe that microsecond time scale mol. dynamics on cost-effective hardware will have important methodol. and scientific implications.
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  20. 20
    Friedrichs, M. S.; Eastman, P.; Vaidyanathan, V.; Houston, M.; Legrand, S.; Beberg, A. L.; Ensign, D. L.; Bruns, C. M.; Pande, V. S. Accelerating molecular dynamic simulation on graphics processing units J. Comput. Chem. 2009, 30, 864– 72
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    Accelerating molecular dynamic simulation on graphics processing units
    Friedrichs, Mark S.; Eastman, Peter; Vaidyanathan, Vishal; Houston, Mike; Legrand, Scott; Beberg, Adam L.; Ensign, Daniel L.; Bruns, Christopher M.; Pande, Vijay S.
    Journal of Computational Chemistry (2009), 30 (6), 864-872CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    The authors describe a complete implementation of all-atom protein mol. dynamics running entirely on a graphics processing unit (GPU), including all std. force field terms, integration, constraints, and implicit solvent. The authors discuss the design of their algorithms and important optimizations needed to fully take advantage of a GPU. The authors evaluate its performance, and show that it can be more than 700 times faster than a conventional implementation running on a single CPU core.
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    Gotz, A. W.; Williamson, M. J.; Xu, D.; Poole, D.; Le Grand, S.; Walker, R. C. Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born J. Chem. Theory Comput. 2012, 8, 1542– 1555
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    Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born
    Gotz, Andreas W.; Williamson, Mark J.; Xu, Dong; Poole, Duncan; Le Grand, Scott; Walker, Ross C.
    Journal of Chemical Theory and Computation (2012), 8 (5), 1542-1555CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We present an implementation of generalized Born implicit solvent all-atom classical mol. dynamics (MD) within the AMBER program package that runs entirely on CUDA enabled NVIDIA graphics processing units (GPUs). We discuss the algorithms that are used to exploit the processing power of the GPUs and show the performance that can be achieved in comparison to simulations on conventional CPU clusters. The implementation supports three different precision models in which the contributions to the forces are calcd. in single precision floating point arithmetic but accumulated in double precision (SPDP), or everything is computed in single precision (SPSP) or double precision (DPDP). In addn. to performance, we have focused on understanding the implications of the different precision models on the outcome of implicit solvent MD simulations. We show results for a range of tests including the accuracy of single point force evaluations and energy conservation as well as structural properties pertaining to protein dynamics. The numerical noise due to rounding errors within the SPSP precision model is sufficiently large to lead to an accumulation of errors which can result in unphys. trajectories for long time scale simulations. We recommend the use of the mixed-precision SPDP model since the numerical results obtained are comparable with those of the full double precision DPDP model and the ref. double precision CPU implementation but at significantly reduced computational cost. Our implementation provides performance for GB simulations on a single desktop that is on par with, and in some cases exceeds, that of traditional supercomputers.
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    Pande, V. S.; Beauchamp, K.; Bowman, G. R. Everything you wanted to know about Markov State Models but were afraid to ask Methods 2010, 52, 99– 105
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    Everything you wanted to know about Markov State Models but were afraid to ask
    Pande, Vijay S.; Beauchamp, Kyle; Bowman, Gregory R.
    Methods (Amsterdam, Netherlands) (2010), 52 (1), 99-105CODEN: MTHDE9; ISSN:1046-2023. (Elsevier B.V.)
    A review. Simulating protein folding has been a challenging problem for decades due to the long timescales involved (compared with what is possible to simulate) and the challenges of gaining insight from the complex nature of the resulting simulation data. Markov State Models (MSMs) present a means to tackle both of these challenges, yielding simulations on exptl. relevant timescales, statistical significance, and coarse grained representations that are readily humanly understandable. Here, we review this method with the intended audience of non-experts, in order to introduce the method to a broader audience. We review the motivations, methods, and caveats of MSMs, as well as some recent highlights of applications of the method. We conclude by discussing how this approach is part of a paradigm shift in how one uses simulations, away from anecdotal single-trajectory approaches to a more comprehensive statistical approach.
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  23. 23
    Xue, Y.; Ward, J. M.; Yuwen, T.; Podkorytov, I. S.; Skrynnikov, N. R. Microsecond time-scale conformational exchange in proteins: using long molecular dynamics trajectory to simulate NMR relaxation dispersion data J. Am. Chem. Soc. 2012, 134, 2555– 62
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    Microsecond Time-Scale Conformational Exchange in Proteins: Using Long Molecular Dynamics Trajectory To Simulate NMR Relaxation Dispersion Data
    Xue, Yi; Ward, Joshua M.; Yuwen, Tairan; Podkorytov, Ivan S.; Skrynnikov, Nikolai R.
    Journal of the American Chemical Society (2012), 134 (5), 2555-2562CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    With the advent of ultra-long MD simulations it becomes possible to model microsecond time-scale protein dynamics and, in particular, the exchange broadening effects (Rex) as probed by NMR relaxation dispersion measurements. This new approach allows one to identify the exchanging species, including the elusive "excited states". It further helps to map out the exchange network, which is potentially far more complex than the commonly assumed 2- or 3-site schemes. Under fast exchange conditions, this method can be useful for sepg. the populations of exchanging species from their resp. chem. shift differences, thus paving the way for structural analyses. In this study, recent millisecond-long MD trajectory of protein BPTI is employed to simulate the time variation of amide 15N chem. shifts. The results are used to predict the exchange broadening of 15N lines and, more generally, the outcome of the relaxation dispersion measurements using Carr-Purcell-Meiboom-Gill sequence. The simulated Rex effect stems from the fast (∼10-100 μs) isomerization of the C14-C38 disulfide bond, in agreement with the prior exptl. findings.
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    Hamelberg, D.; Mongan, J.; McCammon, J. A. Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules J. Chem. Phys. 2004, 120, 11919– 29
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    Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules
    Hamelberg, Donald; Mongan, John; McCammon, J. Andrew
    Journal of Chemical Physics (2004), 120 (24), 11919-11929CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Many interesting dynamic properties of biol. mols. cannot be simulated directly using mol. dynamics because of nanosecond time scale limitations. These systems are trapped in potential energy min. with high free energy barriers for large nos. of computational steps. The dynamic evolution of many mol. systems occurs through a series of rare events as the system moves from one potential energy basin to another. Therefore, we have proposed a robust bias potential function that can be used in an efficient accelerated mol. dynamics approach to simulate the transition of high energy barriers without any advance knowledge of the location of either the potential energy wells or saddle points. In this method, the potential energy landscape is altered by adding a bias potential to the true potential such that the escape rates from potential wells are enhanced, which accelerates and extends the time scale in mol. dynamics simulations. Our definition of the bias potential echoes the underlying shape of the potential energy landscape on the modified surface, thus allowing for the potential energy min. to be well defined, and hence properly sampled during the simulation. We have shown that our approach, which can be extended to biomols., samples the conformational space more efficiently than normal mol. dynamics simulations, and converges to the correct canonical distribution.
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    Hamelberg, D.; de Oliveira, C. A.; McCammon, J. A. Sampling of slow diffusive conformational transitions with accelerated molecular dynamics J. Chem. Phys. 2007, 127, 155102
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    Sampling of slow diffusive conformational transitions with accelerated molecular dynamics
    Hamelberg, Donald; de Oliveira, Cesar Augusto F.; McCammon, J. Andrew
    Journal of Chemical Physics (2007), 127 (15), 155102/1-155102/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Slow diffusive conformational transitions play key functional roles in biomol. systems. Our ability to sample these motions with mol. dynamics simulation in explicit solvent is limited by the slow diffusion of the solvent mols. around the biomols. Previously, we proposed an accelerated mol. dynamics method that has been shown to efficiently sample the torsional degrees of freedom of biomols. beyond the millisecond timescale. However, in our previous approach, large-amplitude displacements of biomols. are still slowed by the diffusion of the solvent. Here we present a unified approach of efficiently sampling both the torsional degrees of freedom and the diffusive motions concurrently. We show that this approach samples the configuration space more efficiently than normal mol. dynamics and that ensemble avs. converge faster to the correct values.
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    Fajer, M.; Hamelberg, D.; McCammon, J. A. Replica-Exchange Accelerated Molecular Dynamics (REXAMD) Applied to Thermodynamic Integration J. Chem. Theory Comput. 2008, 4, 1565– 1569
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    Replica-Exchange Accelerated Molecular Dynamics (REXAMD) Applied to Thermodynamic Integration
    Fajer, Mikolai; Hamelberg, Donald; McCammon, J. Andrew
    Journal of Chemical Theory and Computation (2008), 4 (10), 1565-1569CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Accelerated mol. dynamics (AMD) is an efficient strategy for accelerating the sampling of mol. dynamics simulations, and observable quantities such as free energies derived on the biased AMD potential can be reweighted to yield results consistent with the original, unmodified potential. In conventional AMD the reweighting procedure has an inherent statistical problem in systems with large acceleration, where the points with the largest biases will dominate the reweighted result and reduce the effective no. of data points. We propose a replica exchange of various degrees of acceleration (REXAMD) to retain good statistics while achieving enhanced sampling. The REXAMD method is validated and benchmarked on two simple gas-phase model systems, and two different strategies for computing reweighted avs. over a simulation are compared.
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    Wereszczynski, J.; McCammon, J. A. Using Selectively Applied Accelerated Molecular Dynamics to Enhance Free Energy Calculations J. Chem. Theory Comput. 2010, 6, 3285– 3292
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    Using Selectively Applied Accelerated Molecular Dynamics to Enhance Free Energy Calculations
    Wereszczynski, Jeff; McCammon, J. Andrew
    Journal of Chemical Theory and Computation (2010), 6 (11), 3285-3292CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Accelerated mol. dynamics (aMD) has been shown to enhance conformational space sampling relative to classical mol. dynamics; however, the exponential reweighting of aMD trajectories, which is necessary for the calcn. of free energies relating to the classical system, is oftentimes problematic, esp. for systems larger than small poly peptides. Here, we propose a method of accelerating only the degrees of freedom most pertinent to sampling, thereby reducing the total acceleration added to the system and improving the convergence of calcd. ensemble avs., which we term selective aMD. Its application is highlighted in two biomol. cases. First, the model system alanine dipeptide is simulated with classical MD, all-dihedral aMD, and selective aMD, and these results are compared to the infinite sampling limit as calcd. with metadynamics. We show that both forms of aMD enhance the convergence of the underlying free energy landscape by 5-fold relative to classical MD; however, selective aMD can produce improved statistics over all-dihedral aMD due to the improved reweighting. Then we focus on the pharmaceutically relevant case of computing the free energy of the decoupling of oseltamivir in the active site of neuraminidase. Results show that selective aMD greatly reduces the cost of this alchem. free energy transformation, whereas all-dihedral aMD produces unreliable free energy ests.
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    Sinko, W.; de Oliveira, C. A. F.; Pierce, L. C. T.; McCammon, J. A. Protecting High Energy Barriers: A New Equation to Regulate Boost Energy in Accelerated Molecular Dynamics Simulations J. Chem. Theory Comput. 2012, 8, 17– 23
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    Protecting High Energy Barriers: A New Equation to Regulate Boost Energy in Accelerated Molecular Dynamics Simulations
    Sinko, William; de Oliveira, Cesar Augusto F.; Pierce, Levi C. T.; McCammon, J. Andrew
    Journal of Chemical Theory and Computation (2012), 8 (1), 17-23CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Mol. dynamics (MD) is one of the most common tools in computational chem. Recently, our group has employed accelerated mol. dynamics (aMD) to improve the conformational sampling over conventional mol. dynamics techniques. In the original aMD implementation, sampling is greatly improved by raising energy wells below a predefined energy level. Recently, our group presented an alternative aMD implementation where simulations are accelerated by lowering energy barriers of the potential energy surface. When coupled with thermodn. integration simulations, this implementation showed very promising results. However, when applied to large systems, such as proteins, the simulation tends to be biased to high energy regions of the potential landscape. The reason for this behavior lies in the boost equation used since the highest energy barriers are dramatically more affected than the lower ones. To address this issue, in this work, we present a new boost equation that prevents oversampling of unfavorable high energy conformational states. The new boost potential provides not only better recovery of statistics throughout the simulation but also enhanced sampling of statistically relevant regions in explicit solvent MD simulations.
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    Wang, Y.; Harrison, C. B.; Schulten, K.; McCammon, J. A. Implementation of Accelerated Molecular Dynamics in NAMD Comput. Sci. Discovery 2011, 4
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    Case, D. A.; Darden, T. A.; Cheatham, T. E., III; Simmerling, C. L.; Wang, J.; Duke, R. E.; Luo, R.; Walker, R. C.; Zhang, W.; Merz, K. M.; Roberts, B.; Hayik, S.; Roitberg, A.; Seabra, G.; Swails, J.; Goetz, A. W.; Kolossvai, I.; Wong, K. F.; Paesani, F.; Vanicek, J.; Wolf, R. M.; Liu, J.; Wu, X.; Brozell, S.R.; Steinbrecher, T.; Gohlke, H.; Cai, Q.; Ye, X.; Wang, J.; Hsieh, M.-J.; Cui, G.; Roe, D.R.; Mathews, D.H.; Seetin, M.G.; Salomon-Ferrer, R.; Sagui, C.; Babin, V.; Luchko, T.; Gusarov, S.; Kovalenko, A.; ; Kollman, P. A. Amber 12; University of California: San Francisco, CA, 2012.
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    Le Grand, S.; Walker, R. C. SPFP: Speed without compromise - a mixed precision model for GPU accelerated molecular dynamics simulations. Comput. Phys. Commun. 2012, not supplied.
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    Dynamics of folded proteins
    McCammon, J. Andrew; Gelin, Bruce R.; Karplus, Martin
    Nature (London, United Kingdom) (1977), 267 (5612), 585-90CODEN: NATUAS; ISSN:0028-0836.
    The dynamics of a folded globular protein (bovine pancreatic trypsin inhibitor) have been studied by solving the equations of motions for the atoms with an empirical potential energy function. They provide the magnitude, correlations, and decay of fluctuations about the av. structure. The protein interior may therefore be fluidlike in that the local atom motions have a diffusional character.
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    Shaw, D. E.; Maragakis, P.; Lindorff-Larsen, K.; Piana, S.; Dror, R. O.; Eastwood, M. P.; Bank, J. A.; Jumper, J. M.; Salmon, J. K.; Shan, Y.; Wriggers, W. Atomic-Level Characterization of the Structural Dynamics of Proteins Science 2010, 330, 341– 346
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    Atomic-Level Characterization of the Structural Dynamics of Proteins
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    Nanosecond to Microsecond Protein Dynamics Probed by Magnetic Relaxation Dispersion of Buried Water Molecules
    Persson, Erik; Halle, Bertil
    Journal of the American Chemical Society (2008), 130 (5), 1774-1787CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Large-scale protein conformational motions on nanosecond-microsecond time scales are important for many biol. processes, but remain largely unexplored because of methodol. limitations. NMR relaxation methods can access these time scales if protein tumbling is prevented, but the isotropy required for high-resoln. soln. NMR is then lost. However, if the immobilized protein mols. are randomly oriented, the water 2H and 17O spins relax as in a soln. of freely tumbling protein mols., with the crucial difference that they now sample motions on all time scales up to ∼100 μs. In particular, the exchange rates of internal water mols. can be detd. directly from the 2H or 17O magnetic relaxation dispersion (MRD) profile. This possibility opens up a new window for characterizing the motions of individual internal water mols. as well as the large-scale protein conformational fluctuations that govern the exchange rates of structural water mols. The authors introduce and validate this new NMR method by presenting and analyzing an extensive set of 2H and 17O MRD data from cross-linked gels of two model proteins: bovine pancreatic trypsin inhibitor and ubiquitin. The authors det. residence times and order parameters of four internal water mols. in these proteins and show that they are quant. consistent with the information available from crystallog. and soln. MRD. The authors also show how slow motions of side-chains bearing labile hydrogens can be monitored by the same approach. Proteins of any size can be studied at physiol. hydration levels with this method.
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  • Figure 1

    Figure 1. RMSD of the aMD trajectory from the crystal structure. Red, blue, green, purple, and black colors correspond to the kinetic clusters identified in the 1 ms cMD BPTI simulation. (34) For each frame, we identify what cluster we are closest to and color it accordingly. Only a handful of transitions to the green state were observed, and we highlight them with diamond markers.

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    Figure 2

    Figure 2. The free energy principal component projection of (a) 1 ms simulation, (b) 500 ns cMD ff99SB-I simulation, and (c) 500 ns aMD ff99SB-I simulation onto (PC1, PC2) defined by the 1 ms simulation. The long-lived structures are projected onto the free energy surface and are labeled as red, blue, green, purple, and black triangles. The crystal structure, 5PTI, is demarked by the red diamond (see also Movies S1 and S2).

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    Figure 3

    Figure 3. The χ1–C14 vs χ1–C38 dihedral angle free energy surfaces of (a) 1 ms cMD simulation, (b) 500 ns cMD ff99SB-I simulation, and (c) 500 ns aMD ff99SB-I simulation. The long-lived stable states are plotted onto the free energy surface and are labeled as red, blue, green, purple, and black triangles. The crystal structure, 5PTI, is demarked by the red diamond. The major state M is labeled along with the minor states mC14 and mC38.

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      Hyperdynamics: accelerated molecular dynamics of infrequent events
      Voter, Arthur F.
      Physical Review Letters (1997), 78 (20), 3908-3911CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      I derive a general method for accelerating the mol.-dynamics (MD) simulation of infrequent events in solids. A bias potential (ΔVb) raises the energy in regions other than the transition states between potential basins. Transitions occur at an accelerated rate and the elapsed time becomes a statistical property of the system. ΔVb can be constructed without knowing the location of the transition states and implementation requires only first derivs. I examine the diffusion mechanisms of a 10-atom Ag cluster on the Ag(111) surface using a 220 μs hyper-MD simulation.
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    10. 10
      Voter, A. F. A method for accelerating the molecular dynamics simulation of infrequent events J. Chem. Phys. 1997, 106, 4665– 4677
      10
      A method for accelerating the molecular dynamics simulation of infrequent events
      Voter, Arthur F.
      Journal of Chemical Physics (1997), 106 (11), 4665-4677CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      For infrequent-event systems, transition state theory (TST) is a powerful approach for overcoming the time scale limitations of the mol. dynamics (MD) simulation method, provided one knows the location of the potential-energy basins (states) and the TST dividing surfaces (or the saddle points) between them. Often, however, the states to which the system will evolve are not known in advance. We present a new, TST-based method for extending the MD time scale that does not require advanced knowledge of the states of the system or the transition states that sep. them. The potential is augmented by a bias potential, designed to raise the energy in regions other than at the dividing surfaces. State to state evolution on the biased potential occurs in the proper sequence, but at an accelerated rate with a nonlinear time scale. Time is no longer an independent variable, but becomes a statistically estd. property that converges to the exact result at long times. The long-time dynamical behavior is exact if there are no TST-violating correlated dynamical events, and appears to be a good approxn. even when this condition is not met. We show that for strongly coupled (i.e., solid state) systems, appropriate bias potentials can be constructed from properties of the Hessian matrix. This new "hyper-MD" method is demonstrated on two model potentials and for the diffusion of a Ni atom on a Ni(100) terrace for a duration of 20 μs.
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    11. 11
      Bussi, G.; Laio, A.; Parrinello, M. Equilibrium Free Energies from Nonequilibrium Metadynamics Phy. Rev. Lett. 2006, 96, 090601
      There is no corresponding record for this reference.
    12. 12
      Leone, V.; Marinelli, F.; Carloni, P.; Parrinello, M. Targeting biomolecular flexibility with metadynamics Curr. Opin. Struct. Biol. 2010, 20, 148– 154
      12
      Targeting biomolecular flexibility with metadynamics
      Leone, Vanessa; Marinelli, Fabrizio; Carloni, Paolo; Parrinello, Michele
      Current Opinion in Structural Biology (2010), 20 (2), 148-154CODEN: COSBEF; ISSN:0959-440X. (Elsevier Ltd.)
      A review. Metadynamics calcns. allow investigating structure, plasticity, and energetics in a variety of biol. processes spanning from mol. docking to protein folding. Recent theor. developments have led to applications to increasingly complex systems and processes stepping up the biol. relevance of the problem solved. Here, after summarizing recent tech. advances and applications, we give a perspective of the method as a tool for enzymol. and for the prediction of NMR and other spectroscopic data.
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    13. 13
      Darve, E.; Pohorille, A. Calculating free energies using average force J. Chem. Phys. 2001, 115, 9169– 9183
      13
      Calculating free energies using average force
      Darve, Eric; Pohorille, Andrew
      Journal of Chemical Physics (2001), 115 (20), 9169-9183CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      A new, general formula that connects the derivs. of the free energy along the selected, generalized coordinates of the system with the instantaneous force acting on these coordinates is derived. The instantaneous force is defined as the force acting on the coordinate of interest so that when it is subtracted from the equations of motion the acceleration along this coordinate is zero. The formula applies to simulations in which the selected coordinates are either unconstrained or constrained to fixed values. It is shown that in the latter case the formula reduces to the expression previously derived by den Otter and Briels [Mol. Phys. 98, 773 (2000)]. If simulations are carried out without constraining the coordinates of interest, the formula leads to a new method for calcg. the free energy changes along these coordinates. This method is tested in two examples - rotation around the C-C bond of 1,2-dichloroethane immersed in water and transfer of fluoromethane across the water-hexane interface. The calcd. free energies are compared with those obtained by two commonly used methods. One of them relies on detg. the probability d. function of finding the system at different values of the selected coordinate and the other requires calcg. the av. force at discrete locations along this coordinate in a series of constrained simulations. The free energies calcd. by these three methods are in excellent agreement. The relative advantages of each method are discussed.
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    14. 14
      Darve, E.; Rodriguez-Gomez, D.; Pohorille, A. Adaptive biasing force method for scalar and vector free energy calculations J. Chem. Phys. 2008, 128 (14) 144120
      14
      Adaptive biasing force method for scalar and vector free energy calculations
      Darve, Eric; Rodriguez-Gomez, David; Pohorille, Andrew
      Journal of Chemical Physics (2008), 128 (14), 144120/1-144120/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      In free energy calcns. based on thermodn. integration, it is necessary to compute the derivs. of the free energy as a function of one (scalar case) or several (vector case) order parameters. We derive in a compact way a general formulation for evaluating these derivs. as the av. of a mean force acting on the order parameters, which involves first derivs. with respect to both Cartesian coordinates and time. This is in contrast with the previously derived formulas, which require first and second derivs. of the order parameter with respect to Cartesian coordinates. As illustrated in a concrete example, the main advantage of this new formulation is the simplicity of its use, esp. for complicated order parameters. It is also straightforward to implement in a mol. dynamics code, as can be seen from the pseudo-code given at the end. We further discuss how the approach based on time derivs. can be combined with the adaptive biasing force method, an enhanced sampling technique that rapidly yields uniform sampling of the order parameters, and by doing so greatly improves the efficiency of free energy calcns. Using the backbone dihedral angles Φ and Ψ in N-acetylalanyl-N'-methylamide as a numerical example, we present a technique to reconstruct the free energy from its derivs., a calcn. that presents some difficulties in the vector case because of the statistical errors affecting the derivs. (c) 2008 American Institute of Physics.
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    15. 15
      Henin, J.; Fiorin, G.; Chipot, C.; Klein, M. L. Exploring Multidimensional Free Energy Landscapes Using Time-Dependent Biases on Collective Variables J. Chem. Theory Comput. 2009, 6, 35– 47
      There is no corresponding record for this reference.
    16. 16
      Shaw, D. E.; Deneroff, M. M.; Dror, R. O.; Kuskin, J. S.; Larson, R. H.; Salmon, J. K.; Young, C.; Batson, B.; Bowers, K. J.; Chao, J. C.; Eastwood, M. P.; Gagliardo, J.; Grossman, J. P.; Ho, C. R.; Ierardi, D. J.; Kolossvary, I.; Klepeis, J. L.; Layman, T.; McLeavey, C.; Moraes, M. A.; Mueller, R.; Priest, E. C.; Shan, Y.; Spengler, J.; Theobald, M.; Towles, B.; Wang, S. C. Anton, a special-purpose machine for molecular dynamics simulation Commun. ACM 2008, 51, 91– 97
      There is no corresponding record for this reference.
    17. 17
      Dror, R. O.; Arlow, D. H.; Maragakis, P.; Mildorf, T. J.; Pan, A. C.; Xu, H.; Borhani, D. W.; Shaw, D. E. Activation mechanism of the β2-adrenergic receptor Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 18684– 18689
      17
      Activation mechanism of the β2-adrenergic receptor
      Dror, Ron O.; Arlow, Daniel H.; Maragakis, Paul; Mildorf, Thomas J.; Pan, Albert C.; Xu, Huafeng; Borhani, David W.; Shaw, David E.
      Proceedings of the National Academy of Sciences of the United States of America (2011), 108 (46), 18684-18689, S18684/1-S18684/12CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      A third of marketed drugs act by binding to a G-protein-coupled, receptor (GPCR) and either triggering or preventing receptor activation. Although recent crystal structures have provided snapshots of both active and inactive functional states of GPCRs, these structures do not reveal the mechanism by which GPCRs transition between these states. Here we propose an activation mechanism for the β2-adrenergic receptor, a prototypical GPCR, based on at.-level simulations in which an agonist-bound receptor transitions spontaneously from the active to the inactive crystallog. obsd. conformation. A loosely coupled allosteric network, comprising three regions that can each switch individually between multiple distinct conformations, links small perturbations at the extracellular drug-binding site to large conformational changes at the intracellular G-protein-binding site. Our simulations also exhibit an intermediate that may represent a receptor conformation to which a G protein binds during activation, and suggest that the first structural changes during receptor activation often take place on the intracellular side of the receptor, far from the drug-binding site. By capturing this fundamental signaling process in at. detail, our results may provide a foundation for the design of drugs that control receptor signaling more precisely by stabilizing specific receptor conformations.
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    18. 18
      Shan, Y.; Kim, E. T.; Eastwood, M. P.; Dror, R. O.; Seeliger, M. A.; Shaw, D. E. How Does a Drug Molecule Find Its Target Binding Site? J. Am. Chem. Soc. 2011, 133, 9181– 9183
      18
      How Does a Drug Molecule Find Its Target Binding Site?
      Shan, Yibing; Kim, Eric T.; Eastwood, Michael P.; Dror, Ron O.; Seeliger, Markus A.; Shaw, David E.
      Journal of the American Chemical Society (2011), 133 (24), 9181-9183CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Although the thermodn. principles that control the binding of drug mols. to their protein targets are well understood, detailed exptl. characterization of the process by which such binding occurs has proven challenging. We conducted relatively long, unguided mol. dynamics simulations in which a ligand (the cancer drug dasatinib or the kinase inhibitor PP1) was initially placed at a random location within a box that also contained a protein (Src kinase) to which that ligand was known to bind. In several of these simulations, the ligand correctly identified its target binding site, forming a complex virtually identical to the crystallog. detd. bound structure. The simulated trajectories provide a continuous, at.-level view of the entire binding process, revealing persistent and noteworthy intermediate conformations and shedding light on the role of water mols. The technique we employed, which does not assume any prior knowledge of the binding site's location, may prove particularly useful in the development of allosteric inhibitors that target previously undiscovered binding sites.
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    19. 19
      Harvey, M. J.; Giupponi, G.; Fabritiis, G. D. ACEMD: Accelerating Biomolecular Dynamics in the Microsecond Time Scale J. Chem. Theory Comput. 2009, 5, 1632– 1639
      19
      ACEMD: Accelerating Biomolecular Dynamics in the Microsecond Time Scale
      Harvey, M. J.; Giupponi, G.; De Fabritiis, G.
      Journal of Chemical Theory and Computation (2009), 5 (6), 1632-1639CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The high arithmetic performance and intrinsic parallelism of recent graphical processing units (GPUs) can offer a technol. edge for mol. dynamics simulations. ACEMD is a prodn.-class biomol. dynamics (MD) engine supporting CHARMM and AMBER force fields. Designed specifically for GPUs it is able to achieve supercomputing scale performance of 40 ns/day for all-atom protein systems with over 23,000 atoms. The authors provide a validation and performance evaluation of the code and run a microsecond-long trajectory for an all-atom mol. system in explicit TIP3P water on a single workstation computer equipped with just 3 GPUs. The authors believe that microsecond time scale mol. dynamics on cost-effective hardware will have important methodol. and scientific implications.
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    20. 20
      Friedrichs, M. S.; Eastman, P.; Vaidyanathan, V.; Houston, M.; Legrand, S.; Beberg, A. L.; Ensign, D. L.; Bruns, C. M.; Pande, V. S. Accelerating molecular dynamic simulation on graphics processing units J. Comput. Chem. 2009, 30, 864– 72
      20
      Accelerating molecular dynamic simulation on graphics processing units
      Friedrichs, Mark S.; Eastman, Peter; Vaidyanathan, Vishal; Houston, Mike; Legrand, Scott; Beberg, Adam L.; Ensign, Daniel L.; Bruns, Christopher M.; Pande, Vijay S.
      Journal of Computational Chemistry (2009), 30 (6), 864-872CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      The authors describe a complete implementation of all-atom protein mol. dynamics running entirely on a graphics processing unit (GPU), including all std. force field terms, integration, constraints, and implicit solvent. The authors discuss the design of their algorithms and important optimizations needed to fully take advantage of a GPU. The authors evaluate its performance, and show that it can be more than 700 times faster than a conventional implementation running on a single CPU core.
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    21. 21
      Gotz, A. W.; Williamson, M. J.; Xu, D.; Poole, D.; Le Grand, S.; Walker, R. C. Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born J. Chem. Theory Comput. 2012, 8, 1542– 1555
      21
      Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born
      Gotz, Andreas W.; Williamson, Mark J.; Xu, Dong; Poole, Duncan; Le Grand, Scott; Walker, Ross C.
      Journal of Chemical Theory and Computation (2012), 8 (5), 1542-1555CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We present an implementation of generalized Born implicit solvent all-atom classical mol. dynamics (MD) within the AMBER program package that runs entirely on CUDA enabled NVIDIA graphics processing units (GPUs). We discuss the algorithms that are used to exploit the processing power of the GPUs and show the performance that can be achieved in comparison to simulations on conventional CPU clusters. The implementation supports three different precision models in which the contributions to the forces are calcd. in single precision floating point arithmetic but accumulated in double precision (SPDP), or everything is computed in single precision (SPSP) or double precision (DPDP). In addn. to performance, we have focused on understanding the implications of the different precision models on the outcome of implicit solvent MD simulations. We show results for a range of tests including the accuracy of single point force evaluations and energy conservation as well as structural properties pertaining to protein dynamics. The numerical noise due to rounding errors within the SPSP precision model is sufficiently large to lead to an accumulation of errors which can result in unphys. trajectories for long time scale simulations. We recommend the use of the mixed-precision SPDP model since the numerical results obtained are comparable with those of the full double precision DPDP model and the ref. double precision CPU implementation but at significantly reduced computational cost. Our implementation provides performance for GB simulations on a single desktop that is on par with, and in some cases exceeds, that of traditional supercomputers.
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    22. 22
      Pande, V. S.; Beauchamp, K.; Bowman, G. R. Everything you wanted to know about Markov State Models but were afraid to ask Methods 2010, 52, 99– 105
      22
      Everything you wanted to know about Markov State Models but were afraid to ask
      Pande, Vijay S.; Beauchamp, Kyle; Bowman, Gregory R.
      Methods (Amsterdam, Netherlands) (2010), 52 (1), 99-105CODEN: MTHDE9; ISSN:1046-2023. (Elsevier B.V.)
      A review. Simulating protein folding has been a challenging problem for decades due to the long timescales involved (compared with what is possible to simulate) and the challenges of gaining insight from the complex nature of the resulting simulation data. Markov State Models (MSMs) present a means to tackle both of these challenges, yielding simulations on exptl. relevant timescales, statistical significance, and coarse grained representations that are readily humanly understandable. Here, we review this method with the intended audience of non-experts, in order to introduce the method to a broader audience. We review the motivations, methods, and caveats of MSMs, as well as some recent highlights of applications of the method. We conclude by discussing how this approach is part of a paradigm shift in how one uses simulations, away from anecdotal single-trajectory approaches to a more comprehensive statistical approach.
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    23. 23
      Xue, Y.; Ward, J. M.; Yuwen, T.; Podkorytov, I. S.; Skrynnikov, N. R. Microsecond time-scale conformational exchange in proteins: using long molecular dynamics trajectory to simulate NMR relaxation dispersion data J. Am. Chem. Soc. 2012, 134, 2555– 62
      23
      Microsecond Time-Scale Conformational Exchange in Proteins: Using Long Molecular Dynamics Trajectory To Simulate NMR Relaxation Dispersion Data
      Xue, Yi; Ward, Joshua M.; Yuwen, Tairan; Podkorytov, Ivan S.; Skrynnikov, Nikolai R.
      Journal of the American Chemical Society (2012), 134 (5), 2555-2562CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      With the advent of ultra-long MD simulations it becomes possible to model microsecond time-scale protein dynamics and, in particular, the exchange broadening effects (Rex) as probed by NMR relaxation dispersion measurements. This new approach allows one to identify the exchanging species, including the elusive "excited states". It further helps to map out the exchange network, which is potentially far more complex than the commonly assumed 2- or 3-site schemes. Under fast exchange conditions, this method can be useful for sepg. the populations of exchanging species from their resp. chem. shift differences, thus paving the way for structural analyses. In this study, recent millisecond-long MD trajectory of protein BPTI is employed to simulate the time variation of amide 15N chem. shifts. The results are used to predict the exchange broadening of 15N lines and, more generally, the outcome of the relaxation dispersion measurements using Carr-Purcell-Meiboom-Gill sequence. The simulated Rex effect stems from the fast (∼10-100 μs) isomerization of the C14-C38 disulfide bond, in agreement with the prior exptl. findings.
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    24. 24
      Hamelberg, D.; Mongan, J.; McCammon, J. A. Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules J. Chem. Phys. 2004, 120, 11919– 29
      24
      Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules
      Hamelberg, Donald; Mongan, John; McCammon, J. Andrew
      Journal of Chemical Physics (2004), 120 (24), 11919-11929CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Many interesting dynamic properties of biol. mols. cannot be simulated directly using mol. dynamics because of nanosecond time scale limitations. These systems are trapped in potential energy min. with high free energy barriers for large nos. of computational steps. The dynamic evolution of many mol. systems occurs through a series of rare events as the system moves from one potential energy basin to another. Therefore, we have proposed a robust bias potential function that can be used in an efficient accelerated mol. dynamics approach to simulate the transition of high energy barriers without any advance knowledge of the location of either the potential energy wells or saddle points. In this method, the potential energy landscape is altered by adding a bias potential to the true potential such that the escape rates from potential wells are enhanced, which accelerates and extends the time scale in mol. dynamics simulations. Our definition of the bias potential echoes the underlying shape of the potential energy landscape on the modified surface, thus allowing for the potential energy min. to be well defined, and hence properly sampled during the simulation. We have shown that our approach, which can be extended to biomols., samples the conformational space more efficiently than normal mol. dynamics simulations, and converges to the correct canonical distribution.
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    25. 25
      Hamelberg, D.; de Oliveira, C. A.; McCammon, J. A. Sampling of slow diffusive conformational transitions with accelerated molecular dynamics J. Chem. Phys. 2007, 127, 155102
      25
      Sampling of slow diffusive conformational transitions with accelerated molecular dynamics
      Hamelberg, Donald; de Oliveira, Cesar Augusto F.; McCammon, J. Andrew
      Journal of Chemical Physics (2007), 127 (15), 155102/1-155102/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Slow diffusive conformational transitions play key functional roles in biomol. systems. Our ability to sample these motions with mol. dynamics simulation in explicit solvent is limited by the slow diffusion of the solvent mols. around the biomols. Previously, we proposed an accelerated mol. dynamics method that has been shown to efficiently sample the torsional degrees of freedom of biomols. beyond the millisecond timescale. However, in our previous approach, large-amplitude displacements of biomols. are still slowed by the diffusion of the solvent. Here we present a unified approach of efficiently sampling both the torsional degrees of freedom and the diffusive motions concurrently. We show that this approach samples the configuration space more efficiently than normal mol. dynamics and that ensemble avs. converge faster to the correct values.
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    26. 26
      Fajer, M.; Hamelberg, D.; McCammon, J. A. Replica-Exchange Accelerated Molecular Dynamics (REXAMD) Applied to Thermodynamic Integration J. Chem. Theory Comput. 2008, 4, 1565– 1569
      26
      Replica-Exchange Accelerated Molecular Dynamics (REXAMD) Applied to Thermodynamic Integration
      Fajer, Mikolai; Hamelberg, Donald; McCammon, J. Andrew
      Journal of Chemical Theory and Computation (2008), 4 (10), 1565-1569CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Accelerated mol. dynamics (AMD) is an efficient strategy for accelerating the sampling of mol. dynamics simulations, and observable quantities such as free energies derived on the biased AMD potential can be reweighted to yield results consistent with the original, unmodified potential. In conventional AMD the reweighting procedure has an inherent statistical problem in systems with large acceleration, where the points with the largest biases will dominate the reweighted result and reduce the effective no. of data points. We propose a replica exchange of various degrees of acceleration (REXAMD) to retain good statistics while achieving enhanced sampling. The REXAMD method is validated and benchmarked on two simple gas-phase model systems, and two different strategies for computing reweighted avs. over a simulation are compared.
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    27. 27
      Wereszczynski, J.; McCammon, J. A. Using Selectively Applied Accelerated Molecular Dynamics to Enhance Free Energy Calculations J. Chem. Theory Comput. 2010, 6, 3285– 3292
      27
      Using Selectively Applied Accelerated Molecular Dynamics to Enhance Free Energy Calculations
      Wereszczynski, Jeff; McCammon, J. Andrew
      Journal of Chemical Theory and Computation (2010), 6 (11), 3285-3292CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Accelerated mol. dynamics (aMD) has been shown to enhance conformational space sampling relative to classical mol. dynamics; however, the exponential reweighting of aMD trajectories, which is necessary for the calcn. of free energies relating to the classical system, is oftentimes problematic, esp. for systems larger than small poly peptides. Here, we propose a method of accelerating only the degrees of freedom most pertinent to sampling, thereby reducing the total acceleration added to the system and improving the convergence of calcd. ensemble avs., which we term selective aMD. Its application is highlighted in two biomol. cases. First, the model system alanine dipeptide is simulated with classical MD, all-dihedral aMD, and selective aMD, and these results are compared to the infinite sampling limit as calcd. with metadynamics. We show that both forms of aMD enhance the convergence of the underlying free energy landscape by 5-fold relative to classical MD; however, selective aMD can produce improved statistics over all-dihedral aMD due to the improved reweighting. Then we focus on the pharmaceutically relevant case of computing the free energy of the decoupling of oseltamivir in the active site of neuraminidase. Results show that selective aMD greatly reduces the cost of this alchem. free energy transformation, whereas all-dihedral aMD produces unreliable free energy ests.
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    28. 28
      Sinko, W.; de Oliveira, C. A. F.; Pierce, L. C. T.; McCammon, J. A. Protecting High Energy Barriers: A New Equation to Regulate Boost Energy in Accelerated Molecular Dynamics Simulations J. Chem. Theory Comput. 2012, 8, 17– 23
      28
      Protecting High Energy Barriers: A New Equation to Regulate Boost Energy in Accelerated Molecular Dynamics Simulations
      Sinko, William; de Oliveira, Cesar Augusto F.; Pierce, Levi C. T.; McCammon, J. Andrew
      Journal of Chemical Theory and Computation (2012), 8 (1), 17-23CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Mol. dynamics (MD) is one of the most common tools in computational chem. Recently, our group has employed accelerated mol. dynamics (aMD) to improve the conformational sampling over conventional mol. dynamics techniques. In the original aMD implementation, sampling is greatly improved by raising energy wells below a predefined energy level. Recently, our group presented an alternative aMD implementation where simulations are accelerated by lowering energy barriers of the potential energy surface. When coupled with thermodn. integration simulations, this implementation showed very promising results. However, when applied to large systems, such as proteins, the simulation tends to be biased to high energy regions of the potential landscape. The reason for this behavior lies in the boost equation used since the highest energy barriers are dramatically more affected than the lower ones. To address this issue, in this work, we present a new boost equation that prevents oversampling of unfavorable high energy conformational states. The new boost potential provides not only better recovery of statistics throughout the simulation but also enhanced sampling of statistically relevant regions in explicit solvent MD simulations.
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    29. 29
      Wang, Y.; Harrison, C. B.; Schulten, K.; McCammon, J. A. Implementation of Accelerated Molecular Dynamics in NAMD Comput. Sci. Discovery 2011, 4
      There is no corresponding record for this reference.
    30. 30
      Case, D. A.; Darden, T. A.; Cheatham, T. E., III; Simmerling, C. L.; Wang, J.; Duke, R. E.; Luo, R.; Walker, R. C.; Zhang, W.; Merz, K. M.; Roberts, B.; Hayik, S.; Roitberg, A.; Seabra, G.; Swails, J.; Goetz, A. W.; Kolossvai, I.; Wong, K. F.; Paesani, F.; Vanicek, J.; Wolf, R. M.; Liu, J.; Wu, X.; Brozell, S.R.; Steinbrecher, T.; Gohlke, H.; Cai, Q.; Ye, X.; Wang, J.; Hsieh, M.-J.; Cui, G.; Roe, D.R.; Mathews, D.H.; Seetin, M.G.; Salomon-Ferrer, R.; Sagui, C.; Babin, V.; Luchko, T.; Gusarov, S.; Kovalenko, A.; ; Kollman, P. A. Amber 12; University of California: San Francisco, CA, 2012.
      There is no corresponding record for this reference.
    31. 31
      Le Grand, S.; Walker, R. C. SPFP: Speed without compromise - a mixed precision model for GPU accelerated molecular dynamics simulations. Comput. Phys. Commun. 2012, not supplied.
      There is no corresponding record for this reference.
    32. 32
      Otting, G.; Liepinsh, E.; Wuethrich, K. Proton exchange with internal water molecules in the protein BPTI in aqueous solution J. Am. Chem. Soc. 1991, 113, 4363– 4364
      There is no corresponding record for this reference.
    33. 33
      McCammon, J. A.; Gelin, B. R.; Karplus, M. Dynamics of folded proteins Nature 1977, 267, 585– 590
      33
      Dynamics of folded proteins
      McCammon, J. Andrew; Gelin, Bruce R.; Karplus, Martin
      Nature (London, United Kingdom) (1977), 267 (5612), 585-90CODEN: NATUAS; ISSN:0028-0836.
      The dynamics of a folded globular protein (bovine pancreatic trypsin inhibitor) have been studied by solving the equations of motions for the atoms with an empirical potential energy function. They provide the magnitude, correlations, and decay of fluctuations about the av. structure. The protein interior may therefore be fluidlike in that the local atom motions have a diffusional character.
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    34. 34
      Shaw, D. E.; Maragakis, P.; Lindorff-Larsen, K.; Piana, S.; Dror, R. O.; Eastwood, M. P.; Bank, J. A.; Jumper, J. M.; Salmon, J. K.; Shan, Y.; Wriggers, W. Atomic-Level Characterization of the Structural Dynamics of Proteins Science 2010, 330, 341– 346
      34
      Atomic-Level Characterization of the Structural Dynamics of Proteins
      Shaw, David E.; Maragakis, Paul; Lindorff-Larsen, Kresten; Piana, Stefano; Dror, Ron O.; Eastwood, Michael P.; Bank, Joseph A.; Jumper, John M.; Salmon, John K.; Shan, Yibing; Wriggers, Willy
      Science (Washington, DC, United States) (2010), 330 (6002), 341-346CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      Mol. dynamics (MD) simulations are widely used to study protein motions at an at. level of detail, but they have been limited to time scales shorter than those of many biol. crit. conformational changes. We examd. two fundamental processes in protein dynamics-protein folding and conformational change within the folded state-by means of extremely long all-atom MD simulations conducted on a special-purpose machine. Equil. simulations of a WW protein domain captured multiple folding and unfolding events that consistently follow a well-defined folding pathway; sep. simulations of the protein's constituent substructures shed light on possible determinants of this pathway. A 1-ms simulation of the folded protein BPTI reveals a small no. of structurally distinct conformational states whose reversible interconversion is slower than local relaxations within those states by a factor of more than 1000.
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    35. 35
      Wlodawer, A.; Walter, J.; Huber, R.; Sjolin, L. Structure of bovine pancreatic trypsin inhibitor. Results of joint neutron and X-ray refinement of crystal form II J. Mol. Biol. 1984, 180, 301– 29
      35
      Structure of bovine pancreatic trypsin inhibitor. Results of joint neutron and x-ray refinement of crystal form II
      Wlodawer, Alexander; Walter, Jochen; Huber, Robert; Sjoelin, Lennart
      Journal of Molecular Biology (1984), 180 (2), 301-29CODEN: JMOBAK; ISSN:0022-2836.
      The structure of form II crystals of bovine pancreatic trypsin inhibitor was investigated by joint refinement of x-ray and neutron data. Crystallog. R factors for the final model were 0-200 for the x-ray data extending to 1-Å resoln. and 0.197 for the 1.8 Å neutron data. This model was strongly restrained, with 0.020 Å root-mean-square (r.m.s.) departure of bond lengths from their ideal values and 0.019 Å r.m.s. departure of planar groups from planarity. The resulting structure was very similar to that of crystal form I (r.m.s. deviation for main-chain atoms was 0.40 Å); larger deviations were obsd. in particular regions of the chain. Twenty of 63 ordered H2O mols. occupy similar positions (deviation <1 Å) in both models. Eleven amide atoms were protected from exchange after 3 mo of soaking the crystals in deuterated mother liquor at pH 8.2. Their locations were in excellent agreement with the results obtained by 2-dimensional NMR, but the rates of exchange are much lower in the cryst. state.
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    36. 36
      Grant, B. J.; Rodrigues, A. P.; ElSawy, K. M.; McCammon, J. A.; Caves, L. S. Bio3d: an R package for the comparative analysis of protein structures Bioinformatics 2006, 22, 2695– 6
      36
      Bio3d: an R package for the comparative analysis of protein structures
      Grant, Barry J.; Rodrigues, Ana P. C.; ElSawy, Karim M.; McCammon, J. Andrew; Caves, Leo S. D.
      Bioinformatics (2006), 22 (21), 2695-2696CODEN: BOINFP; ISSN:1367-4803. (Oxford University Press)
      An automated procedure for the anal. of homologous protein structures has been developed. The method facilitates the characterization of internal conformational differences and inter-conformer relationships and provides a framework for the anal. of protein structural evolution. The method is implemented in bio3d, an R package for the exploratory anal. of structure and sequence data.
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    37. 37
      Wereszczynski, J.; McCammon, J. A. Nucleotide-dependent mechanism of Get3 as elucidated from free energy calculations. Proc. Natl. Acad. Sci. U. S. A. 2012, not supplied.
      There is no corresponding record for this reference.
    38. 38
      Han, B.; Liu, Y.; Ginzinger, S. W.; Wishart, D. S. SHIFTX2: significantly improved protein chemical shift prediction J. Biomol. NMR 2011, 50, 43– 57
      38
      SHIFTX2: significantly improved protein chemical shift prediction
      Han, Beomsoo; Liu, Yifeng; Ginzinger, Simon W.; Wishart, David S.
      Journal of Biomolecular NMR (2011), 50 (1), 43-57CODEN: JBNME9; ISSN:0925-2738. (Springer)
      A new computer program, called SHIFTX2, is described which is capable of rapidly and accurately calcg. diamagnetic 1H, 13C and 15N chem. shifts from protein coordinate data. Compared to its predecessor (SHIFTX) and to other existing protein chem. shift prediction programs, SHIFTX2 is substantially more accurate (up to 26% better by correlation coeff. with an RMS error that is up to 3.3× smaller) than the next best performing program. It also provides significantly more coverage (up to 10% more), is significantly faster (up to 8.5×) and capable of calcg. a wider variety of backbone and side chain chem. shifts (up to 6×) than many other shift predictors. In particular, SHIFTX2 is able to attain correlation coeffs. between exptl. obsd. and predicted backbone chem. shifts of 0.9800 (15N), 0.9959 (13Cα), 0.9992 (13Cβ), 0.9676 (13C'), 0.9714 (1HN), 0.9744 (1Hα) and RMS errors of 1.1169, 0.4412, 0.5163, 0.5330, 0.1711, and 0.1231 ppm, resp. The correlation between SHIFTX2's predicted and obsd. side chain chem. shifts is 0.9787 (13C) and 0.9482 (1H) with RMS errors of 0.9754 and 0.1723 ppm, resp. SHIFTX2 is able to achieve such a high level of accuracy by a large, high quality database of training proteins (> 190), by utilizing advanced machine learning techniques, by incorporating many more features (χ2 and χ3 angles, solvent accessibility, H-bond geometry, pH, temp.), and by combining sequence-based with structure-based chem. shift prediction techniques. With this substantial improvement in accuracy we believe that SHIFTX2 will open the door to many long-anticipated applications of chem. shift prediction to protein structure detn., refinement and validation. SHIFTX2 is available both as a standalone program and as a web server.
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    39. 39
      Grey, M. J.; Wang, C.; Palmer, A. G., 3rd. Disulfide bond isomerization in basic pancreatic trypsin inhibitor: multisite chemical exchange quantified by CPMG relaxation dispersion and chemical shift modeling J. Am. Chem. Soc. 2003, 125, 14324– 35
      39
      Disulfide Bond Isomerization in Basic Pancreatic Trypsin Inhibitor: Multisite Chemical Exchange Quantified by CPMG Relaxation Dispersion and Chemical Shift Modeling
      Grey, Michael J.; Wang, Chunyu; Palmer, Arthur G.
      Journal of the American Chemical Society (2003), 125 (47), 14324-14335CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Conformational changes occurring on the microsecond-millisecond time scale in basic pancreatic trypsin inhibitor (BPTI) are investigated using NMR spectroscopy. The rczz CPMG expt. (Wang, C.; Gray, M. J.; Palmer, A. G. J. Biomol. NMR 2001, 21, 361-366) is used to record 15N spin relaxation dispersion data, Rex(1/τcp), in which 1/τcp is the pulsing rate in the CPMG sequence, at two static magnetic fields, 11.7 and 14.1 T, and three temps., 280, 290, and 300 K. These data are used to characterize the kinetics and mechanism of chem. exchange line broadening of the backbone 15N spins of Cys 14, Lys 15, Cys 38, and Arg 39 in BPTI. Line broadening is found to result from two processes: the previously identified isomerization of the Cys 38 side chain between χ1 rotamers (Otting, G.; Liepinsh, E.; Wuethrich, K. Biochem. 1993, 32, 3571-3582) and a previously uncharacterized process on a faster time scale. At 300 K, both processes contribute significantly to the relaxation dispersion for Cys 14 and an anal. expression for a linear three-site exchange model is used to analyze the data. At 280 K, isomerization of the Cys 38 side chain is negligibly slow and the faster process dominates the relaxation dispersion for all four spins. Global anal. of the temp. and static field dependence of Rex(1/τcp) for Cys 14 and Lys 15 is used to det. the activation parameters and chem. shift changes for the previously uncharacterized chem. exchange process. Through an anal. of a database of chem. shifts, 15N chem. shift changes for Cys 14 and Lys 15 are interpreted to result from a χ1 rotamer transition of Cys 14 that converts the Cys 14-Cys 38 disulfide bond between right- and left-handed conformations. At 290 K, isomerization of Cys 14 occurs with a forward and reverse rate const. of 35 s-1 and 2500 s-1, resp., a time scale more than 30-fold faster than the Cys 38 χ1 isomerization. A comparison of the kinetics and thermodn. for the transitions between the two alternative Cys 14-Cys 38 conformations highlights the factors that affect the contribution of disulfide bonds to protein stability.
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    40. 40
      Berndt, K. D.; Beunink, J.; Schroeder, W.; Wuethrich, K. Designed replacement of an internal hydration water molecule in BPTI: structural and functional implications of a Gly-to-Ser mutation Biochemistry 1993, 32, 4564– 4570
      There is no corresponding record for this reference.
    41. 41
      Persson, E.; Halle, B. Nanosecond to microsecond protein dynamics probed by magnetic relaxation dispersion of buried water molecules J. Am. Chem. Soc. 2008, 130, 1774– 87
      41
      Nanosecond to Microsecond Protein Dynamics Probed by Magnetic Relaxation Dispersion of Buried Water Molecules
      Persson, Erik; Halle, Bertil
      Journal of the American Chemical Society (2008), 130 (5), 1774-1787CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Large-scale protein conformational motions on nanosecond-microsecond time scales are important for many biol. processes, but remain largely unexplored because of methodol. limitations. NMR relaxation methods can access these time scales if protein tumbling is prevented, but the isotropy required for high-resoln. soln. NMR is then lost. However, if the immobilized protein mols. are randomly oriented, the water 2H and 17O spins relax as in a soln. of freely tumbling protein mols., with the crucial difference that they now sample motions on all time scales up to ∼100 μs. In particular, the exchange rates of internal water mols. can be detd. directly from the 2H or 17O magnetic relaxation dispersion (MRD) profile. This possibility opens up a new window for characterizing the motions of individual internal water mols. as well as the large-scale protein conformational fluctuations that govern the exchange rates of structural water mols. The authors introduce and validate this new NMR method by presenting and analyzing an extensive set of 2H and 17O MRD data from cross-linked gels of two model proteins: bovine pancreatic trypsin inhibitor and ubiquitin. The authors det. residence times and order parameters of four internal water mols. in these proteins and show that they are quant. consistent with the information available from crystallog. and soln. MRD. The authors also show how slow motions of side-chains bearing labile hydrogens can be monitored by the same approach. Proteins of any size can be studied at physiol. hydration levels with this method.
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    Simulation setup, theory of aMD, details of how aMD parameters were selected, and reweighting protocol. Movies S1–S3, Figure S1, and Table S1. This information is available free of charge via the Internet at http://pubs.acs.org/.


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