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Conformational Strain of Macrocyclic Peptides in Ligand–Receptor Complexes Based on Advanced Refinement of Bound-State Conformers

Cite this: J. Med. Chem. 2021, 64, 6, 3282–3298
Publication Date (Web):March 16, 2021
https://doi.org/10.1021/acs.jmedchem.0c02159

Copyright © 2021 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

Macrocyclic peptides are an important modality in drug discovery, but molecular design is limited due to the complexity of their conformational landscape. To better understand conformational propensities, global strain energies were estimated for 156 protein-macrocyclic peptide cocrystal structures. Unexpectedly large strain energies were observed when the bound-state conformations were modeled with positional restraints. Instead, low-energy conformer ensembles were generated using xGen that fit experimental X-ray electron density maps and gave reasonable strain energy estimates. The ensembles featured significant conformational adjustments while still fitting the electron density as well or better than the original coordinates. Strain estimates suggest the interaction energy in protein–ligand complexes can offset a greater amount of strain for macrocyclic peptides than for small molecules and non-peptidic macrocycles. Across all molecular classes, the approximate upper bound on global strain energies had the same relationship with molecular size, and bound-state ensembles from xGen yielded favorable binding energy estimates.

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Introduction

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Protein–protein associations are often mediated through large and relatively flat surfaces (1500–3000 Å2), to which drug-like small molecules (<500 Da) are often unable to bind tightly and selectively. (1−6) Peptides, however, can bind potently and selectively to these challenging drug targets due to their size and atomic composition. By mimicking endogenous bioactive molecules and protein secondary structure, a network of interactions between the peptide and the flat protein surface results in sufficient interaction energy to overcome major costs to binding. (7−15)
Unfortunately, linear acyclic peptides suffer several disadvantages, such as weak binding affinity (large entropic penalty), low bioavailability, and poor in vivo stability (13) that have historically rendered them difficult to develop into marketed drugs. On the other hand, macrocyclic peptides represent a therapeutic modality that has the potential to combine the best properties of small molecule ligands (oral bioavailability and cell permeability) and antibodies (high specificity and the ability to target shallow or flat protein surfaces). (4,9,16−22) Macrocyclization of peptides constrains conformational space and imparts some structural preorganization, thereby decreasing the number of low-energy conformations. (4,7,16,23−31) This reduces the entropic penalty of binding and increases proteolytic stability compared to acyclic peptides. (32−34)
Although properties of macrocyclic peptides (so-called beyond Rule of 5; bRo5) lie outside the range of small molecule physical properties expected for “drug-likeness”, (35−39) they have gained substantial interest in pharmaceutical development. (4,40−47) Ease of synthesis, large-scale library exploration, diversity, (48,49) and rapid screening capabilities (e.g., phage and mRNA display) have all been contributing factors to the increased pursuit of macrocyclic peptides as drug candidates. Increased adoption of peptides as a therapeutic modality in recent years is evidenced by steadily increasing numbers of publications, (16) as well as several cyclic peptides entering clinical trials. (50)
Computational modeling has been widely adopted by pharmaceutical companies to aid drug design efforts. (51) However, computational investigation of macrocyclic peptides is hampered by the challenges associated with exploring their conformational space. Efficient enumeration of conformers is difficult due to the constraints imposed by the closure of the macrocyclic ring systems, treatment of standard and nonstandard amino acids, incorporation of non-peptidic chemical content, and molecular size. Additionally, the vast number of possible conformers (52−57) creates challenges in ensemble interpretation, identification of the relevant populations, and downstream calculations including prediction of drug-like attributes such as cell permeability, solubility, and other physicochemical properties. (15,58)
Understanding the energetic strain window for peptidic macrocycles that can be compensated through interaction with protein targets would facilitate design efforts that employ conformationally-dependent modeling workflows. In the absence of experimental constraints on the bioactive conformer space, it remains a significant challenge to establish realistic limits on allowable conformational ensemble energy windows. A recent study reported by Zivanovic et al. quantified the global strain energy, defined as the difference between the global minimum solution-state and bound-state conformational energy, tolerated by drug-like small molecules using high-accuracy quantum mechanical calculations. (59) They found that the global strain energy for a data set of 123 small molecules (200–700 Da) ranged from 0 to 7.1 kcal/mol, where 73% of the ligands fell below 1.8 kcal/mol. A similar understanding of global strain for macrocyclic peptides would allow conformational workflows to filter out high-energy conformers, which otherwise exceed the relevant threshold value. This significant reduction in conformational space would mitigate challenges in design and in computational complexity (both concerning time and hardware memory).
Global strain energy values depend directly on the method used to estimate the energy of the bound-state and global minimum solution-state conformation. Here, we used an iterative implementation of ForceGen to locate the global minimum solution-state conformation as it is uniquely positioned to handle macrocyclic peptides by non-stochastically searching the conformational space with physical movements. (60,61) For bound-state ligand conformations, atomic coordinates from X-ray crystallographic models generally require some type of re-refinement to overcome small coordinate deviations that lead to erroneously high force field-based energy values. (62) Historically, ligand heavy atoms have been restrained to their original positions with a square-welled quadratic positional penalty. (63) However, Perola and Charifson’s influential study (62) facilitated the discussion around bound-state ligand modeling, including studies benchmarking modeling methodologies, (64) data set re-analyses, (65) and new techniques to better model the bioactive conformation including quantum mechanics/molecular mechanics (QM/MM) (66) and electron-density fitting. (67)
Here, the newly introduced xGen (68) methodology is used to model the bound-state conformations and estimate the global strain energy for a data set of 156 macrocyclic peptide cocrystal structures. xGen uses a unique real-space refinement approach to identify low-energy conformer ensembles that fit the experimental electron density better than a single ligand conformer. The global strain energies and occupancy-weighted conformer ensembles resulting from the xGen procedure are compared to those of several other bound-state modeling methodologies and discussed in detail, including major implications for the design of macrocyclic peptidic drug candidates.

Results and Discussion

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Macrocyclic Peptide Data Set Composition

A macrocyclic peptide data set containing 156 cocrystal structures with a total of 311 ligand-binding site pairs was curated (Figure 1). Hydrolases make up nearly a quarter of the protein classifications represented, followed by those associated with the immune system (e.g., antigen-binding fragments—Fabs) and isomerases (Figure 1A). The majority of the structures were deposited between 2010 and 2017, highlighting the increased interest in macrocyclic peptides as therapeutics in recent years (Figure 1B). (4,40−44) Peptide sizes ranged from 4 to 24 residues with the bulk of the data set between 5 and 14 residues (Figure 1C). This size range bridges the gap between small molecules (<500 Da) and therapeutic proteins (e.g., insulin; >3000 Da), agreeing with the bRo5 classification by Doak et al. (12) Crystal structure resolutions ranged from 1.0 to 3.0 Å with only a few structures outside this range (Figure 1D). Additional details can be found in the Experimental Section.

Figure 1

Figure 1. Composition of the macrocyclic peptide data set. See the Experimental Section for a list of PDB IDs. (A) Classification of proteins. Only sectors >5% of the total population are labeled. Distribution of (B) deposited structures by year and (C) ligands by size. (D) Cumulative population of PDB structures within resolution cutoffs.

Refining Modeled Bound-State Conformations Using Conformational Ensembles

When ligands bind to protein targets, some adopt conformations very similar to low-energy solution-state conformers (e.g., stapled peptides rigidified by design (69)), while most require some degree of conformer reorganization, which can be characterized in terms of strain energy: the difference in energy between these two reference points. Calculated strain energy is dependent on the precise coordinates used to model the bound-state conformation. Owing to variations between force fields and techniques used to solve ligand-bound cocrystal structures, some form of atomic coordinate adjustment is required to accurately estimate strain energy. A widely used approach has been to restrain the ligand’s heavy atoms to their original positions with a square-welled quadratic positional penalty while performing a local minimization using a force field. (63) For example, Perola and Charifson (62) used this method for a small molecule data set, using a 0.5 Å half-width with a 500 kcal/mol/Å2 force constant. The nominal energy of the bound-state conformer is assigned based on the relaxed version, whose atomic deviations from the starting conformer are generally small.
The implicit assumption underlying such an approach is that the bound-state ligand coordinates are inherently correct. A gross error in a modeled ligand conformation, for example, a 90° dihedral angle for an amide bond, will impart high strain energy, owing to positional restraint penalties. Peptidic macrocycles are among the most challenging ligands to fit into X-ray electron density, which raises concerns about strain estimates based on the nominal modeled ligand coordinates. The xGen real-space ligand refinement approach is integrated within the ForceGen conformational search procedures, which have been optimized for application to macrocyclic ligands. (68) The method seeks to build conformer ensembles that are simultaneously low in energy and provide a better fit to the experimental electron density [real-space correlation coefficient (RSCC) and real-space residual (RSR)].
In some cases, fitting the electron density perfectly with a single conformer results in large geometric distortions of the ligand, leading to artificially high-energy conformations. In contrast, xGen (68) first generates conformers that balance fit to the electron density and geometric distortions. The resulting conformers are re-minimized in two ways to form a “conformer trio”: one being the original conformer, one with a focus on fitting the electron density, and one with a focus on resolving geometric distortions. Conformer neighborhoods are then formed from a subset of the conformers in the resulting pool: those that fit the electron density up to a certain cutoff (90% of the maximum density fit), are within 3.0 kcal/mol of the minimum energy, and are geometrically similar to other neighborhood members (scaled root-mean-square deviation (rmsd) ≤ 0.65 Å). The final xGen conformer ensemble is optimized by selecting from the members of the conformer neighborhoods to fit real-space electron density. The ensemble is weighted by occupancy per conformer, without using B-factors to model atomic motion or uncertainty. The results of applying the xGen procedure on a small macrocyclic inhibitor of BACE1 are shown in Figure 2. Note that overfitting can be a concern when modeling X-ray electron density with conformational ensembles, and this aspect was analyzed and discussed extensively in a method-focused study. (68)

Figure 2

Figure 2. Conformational search and ensemble derivation. (A) All conformers resulting from a restrained search of the 3DV1 ligand, blending force field energetics with a quantitative reward for matching electron density. (B) Single high-quality conformer trio, representing both good fit to the density (orange) and low energy (yellow) along with a conformer with low rmsd to both (slate). (C) Occupancy-weighted conformer ensemble with the 1.0σ experimental density contour (gray mesh) and the corresponding calculated real-space density contour (cyan dots).

xGen was applied using standard parameters on all 311 macrocyclic peptide binding sites (see the Experimental Section for additional details). This process provided conformer ensembles with an average of 3.5 conformers per peptidic macrocycle. Just under one-fifth of the cases had a single conformer, the largest ensemble had 11 members, and around three-quarters fell into the 3–7 conformer range. The RSCC values improved marginally but consistently (average increase of 0.010 and p < 10–7 by paired t-test), and the RSR values also improved consistently but very slightly (average decrease of 0.003 and p < 0.05 by paired t-test). The improvement in RSCC and RSR values indicates that nearly all the xGen conformer ensembles fit the experimental electron density as well, or better than, the deposited structures.
The qualitative difference between the deposited ligand coordinates of 5O4Y (green) and the 5-member xGen conformer ensemble (orange) is illustrated in Figure 3. The positions labeled 1–3 each show places where the deposited ligand contained a cis-amide, where the optimal xGen ensemble produced a lower energy trans-amide within the macrocyclic ring backbone. The xGen trans-amide 2 also introduced a conformational change in the neighboring thioether linkage. While one might observe experimental support for cis-amide configurations (e.g., assay data for N-methylated variants), no such data were provided in the original publication, and it seems likely that these high-energy amide geometries simply resulted from the difficulty in fitting large macrocyclic peptides into X-ray density using commonly available tools. (70) The positions labeled 4–6 each show side chain rotameric variations. As will be discussed later, both the deposited single-conformer model and the alternative ensemble fit the electron density equally well, but the conformers comprising the latter model yield much lower strain estimates. Global strain estimation based on the original model of the bound-state ligand produces erroneously high values, even when making use of standard approaches for local relaxation.

Figure 3

Figure 3. Example of alternative fits to electron density for5O4Y. The atomic coordinates of the deposited ligand model are shown in green sticks, with a set of five conformers comprising an xGen ensemble shown in orange. The electron density contour from the 2|Fo| – |Fc| map is shown at 1.0σ. Red numbers 1–3 mark a position where a high-energy cis-amide in the deposited coordinates is flipped to a low-energy trans-amide in the xGen ensemble. Red numbers 4–6 show alternative side chain rotamers in the xGen ensemble compared to the deposited coordinates.

In addition to the standard square-welled quadratic restraint and xGen methods, two additional methods for ligand refinement were studied for improving strain estimates. Each placed a square-welled quadratic restraint on heavy-atom positions to hold them near the original modeled atomic coordinates (see the Experimental Section for additional details). Rather than applying the same half-widths to all heavy atoms, for one (termed “B-factor binning”) the half-widths of the flat wells were set based on three classes for atomic B-factors: low, medium, and high uncertainty. For the other (termed “coordinate uncertainty”) the half-widths were set based on explicitly calculated atomic-coordinate uncertainty. The diffraction precision index is a global measure of the precision of atomic positions from experimental crystallographic parameters, from which the coordinate error of each atom can be calculated using its B-factor. (71)

Defining the Global Minimum Conformation

Exploring conformational space for peptide macrocycles is challenging and identifying the true global minimum energy value under any force field is computationally infeasible, as doing so requires exhaustive search at relatively fine granularity in dihedral angle space. Here, an estimate for the global minimum was determined using an iterative application of the fast and accurate ForceGen method, (60,61) beginning from two different input conformers for each ligand. The first conformer was defined by the deposited crystal structure ligand coordinates while the second was a randomized conformation (see the Experimental Section for additional details).
The nominal global minima identified using this procedure is limited by the accuracy of the MMFF94sf force field and the thoroughness with which the conformational landscape is traversed. The lower bound on success in finding true global minima can be estimated based on the relationship between total molecular flexibility (the number of rotatable macrocyclic ring bonds plus the total number of rotatable exocyclic bonds) and success in identifying close matches to experimentally determined ligand conformations (either bound to proteins or within small-molecule crystal structures). Beginning from a randomized input conformer, the previously documented success rate for identifying a deposited ligand conformer (with 2.0 Å rmsd) with ForceGen was over 90% for cases with total flexibility up to 36, (60,61) which accounts for half of the current data set. For the remaining half, the success rate was slightly under 60%. Overall, given the iterative and more thorough procedure employed here than in the original benchmark studies, the lower bound for which estimates of global minima will be accurate is projected to be 75–85%. Note, however, the central practical goal of this study is to identify energy windows for conformational exploration, where the low-energy reference point is defined by the specific application and procedure of the conformational search to locate the global minima. In practical (non-iterative) applications of the ForceGen search procedure, the size of the energy windows will likely be larger than required as the extensive procedure employed here is expected to find the global minimum more often.

Strain Energy of Macrocyclic Peptides

The procedure described above for identifying a global minimum conformation produces a single final conformer and associated energy. A complication with such a procedure is that force field energy landscapes are notoriously frustrated surfaces, and it is possible to find singularities where small changes in coordinates lead to large changes in energy. To mitigate this issue, a Boltzmann-weighted ensemble energy value was calculated by a stochastic sampling of small coordinate perturbations followed by minimization (see the Experimental Section for details). This increased the estimate of the global minimum energy by an average of 0.9 kcal/mol across the 156 individual complexes. The largest such change was 4.5 kcal/mol.
The procedure for identifying optimal bound-state conformer ensembles produces a small number of conformers, each of which is somewhat biased toward fitting electron density rather than minimizing internal energy. Recall, however, that these conformers are part of neighborhoods in which another neighborhood member was biased toward low energy (see Figure 2, yellow conformer). We applied the same Boltzmann-weighted ensemble procedure to the collection of low-energy biased conformers with a square-welled quadratic restraint on heavy atoms to prevent excessive deviation from the original ensemble. In each case, the smallest rmsd of any conformer in the final Boltzmann-weighted ensemble to a conformer within the xGen ensemble was noted to quantify the distance between the locally optimal minimum and a conformer with direct experimental support from the X-ray data.
Figure 4 (blue lines) shows the cumulative histograms of rmsd from the crystallographic support (A) and strain energy (B) for the xGen ensembles. The deviations from the xGen ensembles by the Boltzmann-weighted minima were typically 0.25 Å (90th percentile rmsd = 0.45 Å). Median strain energy was 8.0 kcal/mol (90th percentile strain energy = 21.5 kcal/mol). A truncated data set where duplicate peptides were removed (e.g., cyclosporin) contained 116 cocrystal structures compared with 156 in the full data set. The median and the 90th percentile strain energy with the xGen method in the truncated data set shifted from 8.0 to 10.0 and 21.5 to 24.5 kcal/mol, respectively, indicating that duplicate peptides in the data set did not bias the results to a meaningful degree. The widely used square-welled restraint approach for ligand coordinate relaxation was also employed beginning from the originally modeled PDB ligand coordinates (see the Experimental Section for details), with results shown in red-dotted lines in Figure 4. The quadratic restraint approach on deposited coordinates yielded slightly larger deviations than seen with the xGen method, but 90% of the deviations were 0.45 Å or less. However, strain energy values using the standard approach were roughly double the magnitude of those seen using the xGen ensembles (Figure 4B). The fraction of cases with strain values of 20.0 kcal/mol or higher was 29%, compared with just 12% for the xGen ensembles. The changes in estimated strain magnitude were large enough to have clear practical implications, and the changes were also consistent (90th percentile global strain = 21.5 vs 32.5 kcal/mol, respectively; paired t-test, p < 10–12).

Figure 4

Figure 4. (A) Deviation from the crystallographic experimental support for the macrocyclic peptide data set. (B) Cumulative histogram of global strain energy. Red-dotted lines are for the square-welled quadratic positional restraint approach. Blue solid lines are for the xGen electron density fitting approach. Yellow dot-dashed lines are for the B-factor binning approach. Gray-dashed lines are for the coordinate uncertainty approach. The xGen electron density fitting retained high fidelity to the crystallographic data while producing the lowest strain estimates.

The B-factor binning approach (Figure 4; yellow dot-dashed lines) produced slightly lower strain estimates than the xGen ensemble approach; however, the magnitude of deviation from the modeled bound-state coordinates was more than twice as high. The coordinate uncertainty approach (Figure 4; gray-dashed lines) produced larger structural deviations than either the xGen ensemble or standard positional restraint methods (though less than the B-factor binning approach), but it yielded strain estimates midway between those of the xGen and the standard positional restraint approaches. The xGen method re-fits the electron density with chemically sensible conformational ensembles, and it produced the lowest strain estimates of the approaches that retained high fidelity to the crystallographic data.
The case illustrated in Figure 3 is one of several cases where ligands with extremely large strain energies estimated from the standard positional restraint method (>100 kcal/mol) had significantly reduced strain energy estimates derived from the xGen methodology. The deposited coordinates for the macrocyclic peptide ligand in 5O4Y (15-residues; MW = 1869.2 Da) fit the electron density well (RSCC = 0.92). However, when the square-welled quadratic positional restraint approach was applied, the strain energy was 111.2 kcal/mol, both an outlier and a physically unrealistic value. The xGen ensemble fits the electron density as well as the deposited coordinates (RSCC = 0.92). However, the strain energy dropped nearly 10-fold to 11.6 kcal/mol. Additional qualitative analysis of the xGen conformer ensembles is described below, including a detailed discussion on the major conformational changes that led to the dramatic energy change in 5O4Y.

Effects of Force Field and Dielectric Constant

The ForceGen and xGen methods employ a variant of the MMFF94s force field, typically applied using a dielectric constant consistent with an aqueous solution (80.0). (60,61) Because the macrocyclic search procedure makes use of force field calculations as a tightly coupled aspect of the search process, it was not possible to test other force fields in a directly comparable manner. As an approximation, OPLS3e was used to locally optimize the xGen ensembles (with a positional restraint) and the global minimum conformer pools (without a positional restraint), with the difference between the minima from the two being an alternative estimate of the global strain energy. While the OPLS3e force field yielded slightly higher strain estimates, the magnitude and trends were similar.
Solvent-exposed ligands experience a range of dielectric constants, (72) from bulk solvent to the peptidic target background, which influences conformational energies. Within the macrocyclic peptide data set, there is a wide variation in the degree of binding-site contact area, which would suggest modeling the bound ligand states using a lower dielectric constant. On a randomly selected subset for 10% of cases, strain estimates were calculated with a series of different dielectric constants (ranging from 2.0 to 20.0) for the bound ligand states, with the energy for the global minima unchanged (reflecting the nominal solution conformational ensembles). While the results varied, generally, the bound conformation energy estimates decreased with decreasing dielectric values. However, given the large variation in protein–ligand contact areas, all-atom simulations in an explicit solvent would appear to be a better approach, and these are planned for future work.

Conformational Strain for Different Molecular Classes

The xGen electron density fitting procedure was applied to a non-peptidic macrocycle set and a small molecule set to contextualize macrocyclic peptide strain energy with other molecular classes (see the Experimental Section for details on the latter two data sets). Analogous plots to those shown in Figure 4 for the xGen results but with data from all three data sets included are in Figure 5. The rmsd distribution was nearly identical for all data sets despite the diversity in size, topology, and chemical composition of the different molecular classes (Figure 5A). However, strain energies were observed to have significantly larger values for some of the macrocyclic peptides compared to the non-peptidic macrocycles, or small molecules (Figure 5B, vertical lines; 90th percentile = 21.5 vs 7.0 vs 5.0 kcal/mol, respectively). Note that this is also true when normalized by the heavy atom count (HAC), with the median strain per HAC being roughly 0.05–0.06 kcal/mol/atom for the small molecules and non-peptidic macrocycles but roughly double that for the peptide macrocycles. Importantly, not all peptide macrocycles have high strain. Rather, the allowable strain energy range is broader for this class of compounds, and, as will be discussed, can be balanced by favorable intermolecular interactions with the protein.

Figure 5

Figure 5. (A) Deviations from the xGen ensembles by the Boltzmann-weighted minima were identical for all molecular classes. (B) Cumulative histogram of strain energy. Blue solid lines are for the macrocyclic peptide data set, green-dotted lines are for the non-peptidic macrocycle data set, and the purple-dashed lines are for the small molecule data set. All results are obtained from the electron density fitting approach (xGen). Vertical lines correspond to the 90th percentile for each data set, colored respectively. Strain energy estimates suggest the interaction energy in protein–ligand complexes can offset a greater amount of strain for macrocyclic peptides than for non-peptidic macrocycles or small molecules.

For all three molecular classes, a lower-right triangular distribution was observed when the global strain energies were plotted against HAC (Figure 6). More than 95% of the strain energies fit under a linear upper bound [y = 0.3 × (HAC-10)] and a lower bound of 0. Note that strain values calculated using the Boltzmann-weighted approach can be slightly negative (up to −0.6 kcal/mol) when the members of the conformational ensemble each have energy close to the global minimum. This simple relationship provides a means to quickly estimate the allowable energy window required for a thorough conformational search to identify conformers close to the bound-state ensemble. For example, if a ligand has 120 heavy atoms, the bound-state conformation is estimated to be within 33 kcal/mol of the global minimum (y = 0.3 × (120 – 10) = 33 kcal/mol).

Figure 6

Figure 6. Relationship between HAC and global strain energy featuring a lower-right triangular distribution. Blue squares are for the macrocyclic peptide data set, green circles are for the non-peptidic macrocycle data set, and purple triangles are for the small molecule data set. The black-dashed line is an approximate upper bound of the estimated strain energy.

The HAC range where molecules from all three data sets overlap (HAC of 65 or less) can be captured by an energy window of 16.5 kcal/mol, though very few examples exceeded the common conformational search energy window default value of 10.0 kcal/mol (Figure 6). Within this size range, there does not appear to be a distributional difference in strain energy as it relates to the molecular size, regardless of molecular class. Above 65 heavy atoms, only peptidic macrocycles remain, and the size range of 66–110 was well populated in the data set, exhibiting a similar lower-right triangular character to that with the smaller ligands. For the largest examples, with more than 110 heavy atoms, it is not clear whether the lack of a population with very low strain energy is due to the scarcity of ligands in this size range or some other effect.
The relationship between global strain and HAC was highly statistically significant as measured by Kendall‘s τ (73) (p ≪ 0.001) whether considering the entire set (341 cases, τ = 0.58), the small molecule set (38 cases, τ = 0.46), the non-peptide macrocycles (147 cases, τ = 0.37), or just the peptide macrocycles (156 cases, τ = 0.44). HAC is very strongly correlated with molecular weight, and it is also correlated with other characteristics such as the total atom count or the number of rotatable bonds. Particularly for the peptide macrocycle class, HAC is also correlated with the number of hydrogen-bond donors and acceptors. Due to its simplicity and the invariance of the relationship to global strain across molecular classes, HAC is preferable to other surrogates for estimating the energetic window size given a molecule.

Structural Characteristics of the Modeled Bound-State Conformational Ensembles

Several striking differences between the deposited coordinates and the occupancy-weighted conformer ensembles from xGen were observed. For 81% of the data set, the experimental electron density was better described by the inclusion of more than one conformer (Figure 7A). 1H0I contains a 5-residue macrocyclic peptide bound to chitinase B. The macrocycle in the deposited structure and final xGen ensemble overlay nearly perfectly—the only difference is an alternative side chain rotamer for a second conformer in the xGen ensemble (Figure 7B). Both the deposited structure and the xGen ensemble fit the electron density well, with the xGen ensemble fitting marginally better (RSCC = 0.89 and 0.92, respectively). The crystal structure for 1MF8 (an 11-residue macrocyclic peptide bound to cyclophilin) was solved at 3.10 Å resolution. The lower resolution is reflected in less detail in the electron density and leads to an ensemble of nine conformers better explaining the electron density than the single deposited conformer (RSCC = 0.89 and 0.80, respectively). For the 19% of xGen ensembles containing a single conformer, the distribution of crystal structure resolution and peptide size was nearly identical to the full data set; the single conformer ensembles were not clearly indicative of any particular type of example.

Figure 7

Figure 7. Number of conformers in the xGen ensembles. (A) Roughly 80% of the data set had more than one conformer in the final xGen ensemble. (B) Overlay of the deposited ligand conformer for1H0I (green) and the two alternative conformers in the xGen ensemble (orange). (C) Overlay of the deposited ligand conformer for1MF8 (green) and the nine alternative conformers in the xGen ensemble (orange). Isosurface contour for ρcalc corresponding to 1.0σ for the xGen ensemble is shown as cyan dots. Epos. res. and ExGen are the estimated global strain energies for the positional restraint and density fitting methodologies, respectively. Energies are in kcal/mol.

Not only do the xGen ensembles account for the electron density as well or better than the deposited conformers, but they also offer additional possibilities for ligand design. In 27% of the data set, backbone residues in the xGen ensemble were flipped relative to the deposited conformer coordinates (Figure 8A). Residue flipping produces alternative conformations that present different modification vectors and can, therefore, offer additional design opportunities. The consequence could be even more detrimental if a less relevant (or incorrect) conformer was suggested from standard ligand fitting methods and subsequent design ideas were misinformed.

Figure 8

Figure 8. Backbone residue flipping. (A) 27% of the data set featured a backbone residue flip in the final xGen ensemble relative to the deposited conformer. (B) Overlay of the deposited ligand conformer for 5O4Y (green) and the five alternative conformers in the xGen ensemble (orange). (C) Detailed view of a selection of backbone residues in the deposited conformer featuring cis-amide 1 from Figure 3 (red text). (D) Detailed view of the same residues in the final xGen ensemble, now featuring a trans-amide (green text) and a new intramolecular hydrogen bond. Isosurface contour for ρcalc corresponding to 1.0σ for the xGen ensemble is shown as cyan dots. Epos. res. and ExGen are the estimated global strain energies for the positional restraint and density fitting methodologies, respectively. Distances are in Å and energies are in kcal/mol.

For example, the xGen ensemble for the 5O4Y ligand discussed earlier features five backbone residues in a different isomeric state relative to the deposited conformation (Figure 8B). In the deposited conformer, the backbone features a high energy cis-amide where the nitrogen points outside of the macrocyclic ring (Figure 8C; amide 1 in Figure 3). In the xGen ensemble, the same backbone residue is flipped to a low energy trans-amide where the nitrogen now engages in a new trans-annular hydrogen bond (Figure 8D). Although the deposited conformer and the xGen ensemble represent equivalent numerical fits to the electron density (RSCC = 0.92 for both), the xGen ensemble features conformers that are vastly lower in energy and differentially informs ligand design. Although 5O4Y contains several N-methylated residues, the cis-amide nitrogen from the deposited ligand model is solvent-exposed and could be proposed as another site for N-methylation if improving permeability was of interest. However, the xGen ensemble shows the same residue participating in an intramolecular hydrogen bond where N-methylation at this position would disrupt the bound-state configuration and be detrimental to binding affinity. In contrast, targeting a cross-link to enforce this conformation may improve both potency and permeability.
In total, 49% of the data set featured non-peptidic linkers to close the macrocyclic ring (i.e., disulfide bonds, alkyl chains, etc.). Of this subset, 44% of the xGen ensembles had alternative linker rotamers to the deposited conformers (Figure 9A). This was a surprisingly large portion of the ligands. However, the linker atoms were generally solvent-exposed in the bound state, and often had the largest B-factors, implying a large degree of structural disorder. xGen’s approach is to explicitly model the alternate low-energy conformational variants, leading to the large percentage of alternative linker rotamers observed.

Figure 9

Figure 9. Alternative linker rotamers. (A) 44% of the data set with non-peptidic linkers had alternative linker rotamers. (B) Overlay of deposited ligand conformer for 4ZQW (green) and the five alternative conformers in the xGen ensemble (orange). (C) Overlay of the deposited ligand conformer for 1VWM (green) and the two alternative conformers in the xGen ensemble (orange). Major linker rotamers are noted in the red text. Isosurface contour for ρcalc corresponding to 1.0σ for the xGen ensemble is shown as cyan dots. Epos. res. and ExGen are the estimated global strain energies for the positional restraint and density fitting methodologies, respectively. Energies are in kcal/mol.

For example, the xGen final ensemble for the ligand in 4ZQW (a 13-residue macrocyclic peptide bound to immunity protein CdiI) features five alternative conformers where much of the difference from the deposited coordinates is in the alkyl linker (Figure 9B). Alternative positions for the neighboring amide hydrogen bond donor and acceptor groups are a direct result of the linker rotamers, with major implications for protein–ligand or solvent–ligand interactions. An example where the xGen ensemble dramatically improves the fit to the electron density is 1VWM, a 6-residue macrocyclic peptide bound to streptavidin solved at a high resolution (1.60 Å). The ligand in 1VWM features a disulfide linker with two alternative rotamers in the xGen ensemble. The linker’s deposited coordinates place the acetyl group on the N-terminus outside the electron density envelope. The two alternative xGen conformers place the disulfide linker in different regions of the electron density, allowing the acetyl group to fit back within the electron density. This leads to a significantly better fit to the electron density overall for the xGen ensemble (RSCC = 0.63 and 0.77, respectively). It is important to note that, besides improving electron density fit, the calculated strain energy was also significantly reduced from 14.3 to 7.2 kcal/mol for the positional restraint method and xGen method, respectively. Disulfide linkers—a common motif in therapeutic cyclic peptides—were often found in a high-energy conformation in the deposited coordinates. The 1VWM ligand example demonstrates that re-refining ligands with xGen yields much lower-energy disulfide linker conformers while improving the fit to electron density.
Finally, in 90% of the data set, alternative macrocycle side chain rotamers were observed in the final xGen ensembles (Figure 10A). Side chains are often directly involved in interactions with the protein, so this frequency of alternative conformers was notable with major implications for drug design. Hydrophobic groups were among the most prevalent to have alternative rotamers in the data set. The xGen ensemble for 1C5F (an 11-residue macrocyclic peptide bound to cyclophilin) explains the electron density equally well as the deposited coordinates (RSCC = 0.94 and 0.93, respectively). However, the xGen ensemble with three alternative conformations shows rotamers for the Leu and Bmt. In terms of ligand design, hydrophobic group rotamers may be in solvent-exposed regions or may contact flexible regions of the protein target. Although less common, hydrophilic groups were also observed to have alternative rotamers. 4X6S is an 11-residue macrocyclic peptide bound to GRB7. The xGen six-conformer ensemble explained the electron density equally well to the deposited coordinates (RSCC = 0.88 for both). However, several hydrophilic side chains featured alternative rotamers in the xGen ensemble, including the C-terminal amide, the carboxyphenylalanine, and the Trp side chain (Figure 10). The Trp side chain is particularly interesting in that while all rotamers fit the electron density, there is a rotamer-dependent hydrogen bond donor, and the implications for protein–ligand or solvent–ligand interactions are significant. These additional rotamers may influence the design of viable variants and impart a better understanding of the thermodynamics of binding.

Figure 10

Figure 10. Alternative side chain rotamers. (A) 90% of the data set had alternative side chain rotamers. (B) Overlay of the deposited ligand conformer for 1C5F (green) and the three alternative conformers in the xGen ensemble (orange). (C) Overlay of the deposited ligand conformer for 4X6S (green) and the six alternative conformers in the xGen ensemble (orange). Major side chain rotamers are noted in the red text. Isosurface contour for ρcalc corresponding to 1.0σ for the xGen ensemble is shown as cyan dots. Epos. res. and ExGen are the estimated global strain energies for the positional restraint and density fitting methodologies, respectively. Energies are in kcal/mol.

Although the xGen methodology, in its current implementation, does not directly consider the protein, better intermolecular interactions were often observed when the aforementioned conformational adjustments were compared to the deposited ligand coordinates. For example, the deposited 16-residue macrocyclic peptide ligand in 5B4W fits the electron density well (RSCC = 0.91). The arginine side chain featured one strong and one weak intermolecular hydrogen bond with the Asp414 residue of the Plexin B1 protein target (Figure 11B; yellow- and red-dotted lines, respectively). The xGen ensemble, generated in the absence of Plexin B1, fits the electron density equally well (RSCC = 0.91) but features an arginine rotamer that engages with the Asp414 residue with two strong hydrogen bonds (Figure 11C; yellow-dotted lines). Looking at the deposited coordinates from a design perspective, modifications to enhance the weak hydrogen bond could be pursued. However, the xGen ensemble shows that such modifications may not be necessary, and efforts should be directed toward other regions of the peptide.

Figure 11

Figure 11. Alternative intermolecular interactions. (A) Overlay of the deposited ligand conformer for 5B4W (green) and the three alternative conformers in the xGen ensemble (orange) in the crystal structure. Plexin B1 is shown in purple. (B) Detailed view of the deposited peptide arginine side chain and Plexin B1 Asp414 featuring one strong and one weak hydrogen bond (yellow- and red-dotted lines, respectively). (C) Detailed view of the same residues in the final xGen ensemble, now featuring an arginine side chain rotamer with two strong intermolecular hydrogen bonds (yellow-dotted lines). Isosurface contour for ρcalc corresponding to 1.0σ for the xGen ensemble is shown as cyan dots. Epos. res. and ExGen are the estimated global strain energies for the positional restraint and density fitting methodologies, respectively. Distances are in Å and energies are in kcal/mol.

More broadly with respect to the structural characteristics of macrocyclic peptides, the comprehensive review by Malde et al. (57) points out that there are a substantial number of reported macrocyclic peptide structures for which ϕ/ψ angles deviate widely from well-established expectations. Indeed, the case of 2BCD described earlier actually contained a 90° Ω angle, which was remedied through the xGen refinement procedure. Given the difficulty of exploring different explanations to X-ray density fitting for large peptide macrocycles, making use of systematic search and fitting procedures such as those presented here are suggested for cases in which aberrant geometries are identified. A comprehensive analysis of ϕ/ψ angle distributions is beyond the scope of the present study, but such an analysis is enabled by the data archive associated with this paper (see Supporting Information).

Global Strain Energy Compared to Estimated Binding Enthalpy

The foregoing discussion of energetics has focused exclusively on internal ligand strain induced by the movement from a solvated environment to one bound to a protein. Strain energy estimates for all three molecular classes decreased using the xGen ensemble approach compared with deposited ligand model coordinates. Apart from the practical issue of estimating the size of energy windows for conformational search, there remains a basic thermodynamic question: are the estimated strain energy values small enough such that the energy of protein–ligand association can overcome the cost of pushing the ligands away from their energetically preferred conformations?
To estimate the net binding enthalpy, the xGen ensembles were subjected to local optimization within their cognate binding sites using a scoring function for molecular docking (see the Experimental Section for details). Figure 12 shows the cumulative histograms of the difference between the optimized intermolecular interaction energy values (in kcal/mol) and the strain values, both derived from the final xGen conformer ensembles. For the non-macrocyclic small molecules and the non-peptide macrocycles, close to 90% of cases had net energy values of −10 kcal/mol or lower, with all cases but a handful of the non-peptide macrocycles producing negative values.

Figure 12

Figure 12. Cumulative histogram of enthalpy. Blue solid lines are for the macrocyclic peptide data set, green-dotted lines are for the non-peptidic macrocycle data set, and the purple-dashed lines are for the small molecule data set. All results are from docking the electron density fitting approach ensembles (xGen).

However, 10% of the peptide macrocycle cases yielded positive values. Upon further inspection, most positive enthalpy cases arose from multiple neighboring proteins or biological assemblies in the larger unit cell binding with the ligand. The range of −10 to 0 kcal/mol showed a deviation between the enthalpy estimate for the macrocyclic peptides compared with the other two data sets. As with the positive enthalpy cases, some were affected by binding with multiple neighboring proteins or biological assemblies in the larger unit cell. Overall, there was a weak correlation between estimated enthalpy and strain energy (R2 = 0.33) across the combined data set, as would be expected given that both quantities were related to the ligand size. Perhaps most remarkably, nearly 70% of the peptide macrocycle cases followed essentially the same distribution of net estimated enthalpy as the other two molecular classes, with a value of −10 kcal/mol or better.
The xGen-based enthalpy estimates were consistently more favorable than those derived from the deposited crystallographic ligand coordinates: a net improvement of 2.2 kcal/mol from the small molecules (p < 10–4 by paired t-test), 2.0 kcal/mol for non-peptide macrocycles (p < 10–8), and 6.6 kcal/mol for the peptide macrocycles (p < 10–11). Nearly 30% of the peptide macrocycle examples had net positive estimated enthalpy when beginning from the deposited ligand coordinates.

Conclusions

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The xGen methodology was used to refine bound-state conformations of macrocyclic peptide cocrystal structures by building conformational ensembles that are low-energy and fit experimental electron density, ultimately providing more explicit possibilities for ligand design. Iterative conformational searches were used to identify the ForceGen global minimum conformations. The resulting estimates of global strain were substantially lower than those obtained using the originally deposited ligand coordinates, and they provide an upper-bound on ligand strain, applicable across molecular classes, that depends only on the molecular size as approximated by HAC. Applying xGen to deposited macrocyclic peptide coordinates resulted in conformational adjustments for the peptide backbones in 27%, the non-peptidic linkers in 44%, and the side chains in 90% of the data set. Estimates of binding energy revealed that the strain values were low enough in nearly all cases to yield net favorable values for the difference between intermolecular enthalpy and ligand strain.
Computational enumeration of conformational space is ubiquitous in computer-aided drug design, and it poses serious challenges for macrocyclic peptides with their vast conformational landscapes. This work offers a simple-to-calculate estimate for the maximal strain to be incurred for a macrocycle of a given size. Additionally, the broader workflow described here may help to address the enduring problem of understanding permeability and other properties of macrocyclic peptides, as extensive efforts have gone into studying the relationship between their permeability and conformational flexibility. (1,7,14,15,24,48,49,74,75)

Experimental Section

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The data archive for this paper contains all molecular structural data and detailed computational procedures underlying the foregoing results (available to researchers at https://www.jainlab.org among the downloadable data sets as the “Peptide Strain Archive”). Here, descriptions of newly curated data and key procedures will be presented, with additional details present within the data archive. Crystal structures were obtained from the Protein Data Bank (PDB). (76) All compounds described in this study have been previously disclosed and have been characterized by X-ray crystallographic experiments, with details regarding purity available in the original publications or associated with the RCSB PDB deposition codes.

Molecular Data Sets

The review by Malde et al. (57) in 2019 provides a good overview of available macrocyclic peptide cocrystal structures with protein targets. After extraction of all structures referenced in the review, 156 cocrystal structures of macrocyclic peptides complexed with protein targets with available density map coefficients were identified. Duplicate ligands across different PDB codes were retained in the data set given that different conditions were often used in the crystallization processes (different proteins, pH, etc.). Of the structures, 77 of the PDBs contained multiple copies of the ligand in the asymmetric unit. Each copy was extracted, providing 311 complexes in the data set. The strain energies reported represent the minimum strain calculated across the asymmetric unit copies. The list of macrocyclic peptide-containing PDB entries is:
Perola and Charifson’s small molecule data set (62) was used to compare strain energy determined for canonical small molecules to strain energy estimated for macrocyclic peptides. Because the strain energy calculations reported here rely on electron density maps, it is noted that only 38 protein–ligand complexes from the original small-molecule data set had map coefficient files available. Each asymmetric unit ligand copy was extracted, amounting to 52 complexes in the data set. The list of small molecule-containing PDB entries is:
Jain et al. (68) previously investigated the xGen methodology on 147 non-peptidic macrocycles, and the same data set was used here.

Ligand Preparation

All peptide and small-molecule ligands were extracted from the PDB files using PyMOL version 2.3.1. (77) Ligands were protonated as expected at physiological pH using automated procedures within the Surflex Tools module, as previously described. (68) Resulting structures were manually checked for correct bond orders, protonation states, and atom types with their original publications. Several ligands were missing atoms or side chain residues in the deposited ligand coordinates. To retain a direct comparison between experimental data and computational structures, the missing atoms were not added. Non-peptide macrocycles were prepared as previously described. (68)

Real-Space Refinement of Ligands into Bound-State Conformational Ensembles

The xGen methodology and validation have been presented previously. (68) Here, the standard “strict” procedure was employed to produce parsimonious conformational ensembles beginning from the deposited ligand and protein coordinates. The procedure first builds an idealized approximation to real-space X-ray electron density on a 0.25 Å grid surrounding the ligand (the xgen_build procedure). Next, beginning from the original crystallographic coordinates, the ligand is subjected to a conformational search using an objective function that combines force field energy with a measure of fit to electron density (the xgen_refine procedure). The resulting conformer pool is then expanded by taking each conformer and optimizing one copy toward better density congruence and another copy toward lower energy (the xgen_expand procedure). Finally, an occupancy-weighted conformer ensemble is generated (the xgen_ensemble procedure).
As described earlier, the conformers of the final ensemble are each part of a conformer neighborhood, all of whose members have small coordinate deviations from one another. Within each ensemble conformer’s neighborhood is at least one member that was optimized toward low energy. It is the set of lowest energy neighborhood members corresponding to each of the xGen ensemble members that form the input to the Boltzmann weighting procedure. The conformational ensemble that optimally fits the electron density is also provided to that procedure, and it is used to measure the deviation of the minima from the direct crystallographic experimental support.

Re-refining of Deposited Ligand Coordinates

For the deposited ligand coordinates, the standard approach is to employ a flat-bottomed quadratic penalty during an energy minimization, preventing atoms from deviating much from their original positions. One common parameterization is to use a half-width of 0.5 Å a penalty of 500.0 kcal/mol/Å2 (i.e., as used by Perola and Charifson). Here, we employed a half-width of 0.2 Å and a penalty of 1.0 kcal/mol/Å2 to avoid excessively acute penalties on atoms that were questionably fit into electron density in their deposited coordinates. While there were differences between the two different parameterizations on a case by case basis, the overall results were statistically indistinguishable for the resulting estimates of both strain energy and deviation from the crystallographic support. Note that the single conformer emerging from the de-straining procedure was subjected to the same Boltzmann weighting procedure for final global strain estimation as were the xGen ensembles.

Search Procedures to Estimate Global Minima

Each prepared ligand was subjected to an iterative conformational search beginning from its deposited coordinates and also beginning from a randomized conformer. Iterative searches were performed to ensure the global minimum was located, with each successive round being initiated from the prior round’s lowest energy conformer. Iterations terminated when either: (1) the same lowest energy structure was identified for three successive iterations, or (2) no new minimum was found for three consecutive rounds. Conformers identified during this search were combined into a single pool for the input to the Boltzmann weighting procedure.

Boltzmann Weighting Procedure

To avoid energetic singularities and to make robust estimates of energy for conformers, we employed a procedure that repeatedly perturbs and minimizes input conformers. The Boltzmann weighting procedure first identifies the N lowest energy non-redundant conformers from an input pool (default N = 100 and default redundancy rmsd = 0.01 Å). For each such conformer, atomic coordinates are perturbed by a random value uniformly distributed at the interval [−0.01,+0.01], and minimization is performed, optionally with restraints to deter excessive deviation from the original coordinates. Five such perturbations and minimizations are performed. The energy for each conformer is computed as the Boltzmann average of the five local minima. The final reported energy value is computed as the Boltzmann average of each of these values for the N conformers. For the global minimum procedure, no positional restraints were used. For the bound-state energy estimates, this same procedure was applied, however, a flat-bottomed quadratic positional restraint was employed using a 0.1 Å half-width and a penalty of 1.0 kcal/mol/Å2.

Intermolecular Energy Estimation

The Surflex-Dock scoring function has been extensively validated for both pose prediction and virtual screening. (78−82) The function has been tuned to predict binding affinities, though the accuracy of such predictions is not thought to be sufficient to rank-order compounds for lead optimization. However, gross estimates of intermolecular binding free energy can be obtained by docking a ligand beginning with an agnostic initial state, or, when the bound ligand configuration has been determined, through local optimization. Here, given either xGen ensembles or deposited ligand coordinates, estimates were derived for the interaction energy between the protein and the ligand (using the Surflex Docking module’s opt procedure). The procedure provides both the total nominally predicted free energy of binding and the energy attributable to the hydrophobic and polar scoring function terms, without including terms for entropic fixation of rotatable bonds and rigid-body movement. The latter value was used as a rough guide to identify cases where estimates of global strain energy for a ligand were clearly too large to be supported by the interactions apparent in the bound complex.

Alternative Methods to Re-refine Bound-State Conformers

As mentioned earlier, in addition to the standard positional restraint approach with local minimization and the xGen ensemble fitting approach, two additional methods were tried. These were effectively a combination of the two other methods, where specific restraints were placed on each ligand atom based on its assigned B-factor from the deposited PDB structure. B-factors (also called the temperature factors, Debye–Waller factors, or atomic displacement parameters) derive their theoretical basis from the expected impact of the thermal motion of atoms on X-ray scattering. (55) In practice, B-factors reflect broader aspects of the uncertainty in an atomic position, and they are assigned to minimize the deviation between calculated and experimental electron density. The xGen approach conducts a full conformational search subject to force field energy and a term that rewards fit to electron density. These two alternative methods conduct a full conformational search subject to the same force field and use a term that penalizes deviation from the original ligand coordinates.
The penalty is, again, a flat-bottomed quadratic potential (with a force constant of 1.0 kcal/mol/Å2), but the half-widths were assigned in a manner dependent on atomic B-factors. For the B-factor binning approach, the half-widths were set at 0.5 Å for B-factors ≤ 30, 1.0 Å B-factors > 30 and ≤60, and 5.0 Å for B-factors > 60. For the coordinate uncertainty approach, half-widths were set according to the calculated coordinated error, derived from the overall diffraction precision index of the structure, (71) combined with each atom’s B-factor using the standard formula.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jmedchem.0c02159.

  • High-level overview of available data archive (PDF)

  • Molecular formula strings (CSV)

Terms & Conditions

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

Author Information

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  • Corresponding Authors
  • Authors
    • Qiaolin Deng - Computational & Structural Chemistry, Merck & Co Inc, 2000 Galloping Hill Road, Kenilworth, New Jersey 07033, United StatesOrcidhttp://orcid.org/0000-0001-6378-3872
    • Ann E. Cleves - Bioengineering and Therapeutic Sciences, University of California San Francisco, Box 0128, San Francisco, California 94158, United StatesOrcidhttp://orcid.org/0000-0002-1622-2770
    • Charles A. Lesburg - Computational and Structural Chemistry, Merck and Co Inc, 33 Avenue Louis Pasteur, Boston, Massachusetts 02115, United StatesOrcidhttp://orcid.org/0000-0001-7245-7331
    • Juan C. Alvarez - Computational and Structural Chemistry, Merck and Co Inc, 33 Avenue Louis Pasteur, Boston, Massachusetts 02115, United States
    • Mikhail Y. Reibarkh - Analytical Research and Development, Merck & Co Inc, 126 East Lincoln Avenue, Rahway, New Jersey 07065, United StatesOrcidhttp://orcid.org/0000-0002-6589-707X
    • Edward C. Sherer - Analytical Research and Development, Merck & Co Inc, 126 East Lincoln Avenue, Rahway, New Jersey 07065, United StatesOrcidhttp://orcid.org/0000-0001-8178-9186
  • Notes
    The authors declare the following competing financial interest(s): A.N.J. and A.E.C. have a financial interest in BioPharmics LLC, a biotechnology company whose main focus is in the development of methods for computational modeling in drug discovery.

Abbreviations

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bRo5

beyond Rule of 5

Da

Dalton

QM/MM

quantum mechanics/molecular mechanics

Fab

antigen-binding fragments

RSCC

real-space correlation coefficient

RSR

real-space residual

BACE1

beta-site APP cleaving enzyme 1

HAC

heavy atom count

Bmt

4-methyl-4-[(E)-2-butenyl]-4,N-methyl-threonine

GRB7

growth factor receptor bound protein 7

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  • Abstract

    Figure 1

    Figure 1. Composition of the macrocyclic peptide data set. See the Experimental Section for a list of PDB IDs. (A) Classification of proteins. Only sectors >5% of the total population are labeled. Distribution of (B) deposited structures by year and (C) ligands by size. (D) Cumulative population of PDB structures within resolution cutoffs.

    Figure 2

    Figure 2. Conformational search and ensemble derivation. (A) All conformers resulting from a restrained search of the 3DV1 ligand, blending force field energetics with a quantitative reward for matching electron density. (B) Single high-quality conformer trio, representing both good fit to the density (orange) and low energy (yellow) along with a conformer with low rmsd to both (slate). (C) Occupancy-weighted conformer ensemble with the 1.0σ experimental density contour (gray mesh) and the corresponding calculated real-space density contour (cyan dots).

    Figure 3

    Figure 3. Example of alternative fits to electron density for5O4Y. The atomic coordinates of the deposited ligand model are shown in green sticks, with a set of five conformers comprising an xGen ensemble shown in orange. The electron density contour from the 2|Fo| – |Fc| map is shown at 1.0σ. Red numbers 1–3 mark a position where a high-energy cis-amide in the deposited coordinates is flipped to a low-energy trans-amide in the xGen ensemble. Red numbers 4–6 show alternative side chain rotamers in the xGen ensemble compared to the deposited coordinates.

    Figure 4

    Figure 4. (A) Deviation from the crystallographic experimental support for the macrocyclic peptide data set. (B) Cumulative histogram of global strain energy. Red-dotted lines are for the square-welled quadratic positional restraint approach. Blue solid lines are for the xGen electron density fitting approach. Yellow dot-dashed lines are for the B-factor binning approach. Gray-dashed lines are for the coordinate uncertainty approach. The xGen electron density fitting retained high fidelity to the crystallographic data while producing the lowest strain estimates.

    Figure 5

    Figure 5. (A) Deviations from the xGen ensembles by the Boltzmann-weighted minima were identical for all molecular classes. (B) Cumulative histogram of strain energy. Blue solid lines are for the macrocyclic peptide data set, green-dotted lines are for the non-peptidic macrocycle data set, and the purple-dashed lines are for the small molecule data set. All results are obtained from the electron density fitting approach (xGen). Vertical lines correspond to the 90th percentile for each data set, colored respectively. Strain energy estimates suggest the interaction energy in protein–ligand complexes can offset a greater amount of strain for macrocyclic peptides than for non-peptidic macrocycles or small molecules.

    Figure 6

    Figure 6. Relationship between HAC and global strain energy featuring a lower-right triangular distribution. Blue squares are for the macrocyclic peptide data set, green circles are for the non-peptidic macrocycle data set, and purple triangles are for the small molecule data set. The black-dashed line is an approximate upper bound of the estimated strain energy.

    Figure 7

    Figure 7. Number of conformers in the xGen ensembles. (A) Roughly 80% of the data set had more than one conformer in the final xGen ensemble. (B) Overlay of the deposited ligand conformer for1H0I (green) and the two alternative conformers in the xGen ensemble (orange). (C) Overlay of the deposited ligand conformer for1MF8 (green) and the nine alternative conformers in the xGen ensemble (orange). Isosurface contour for ρcalc corresponding to 1.0σ for the xGen ensemble is shown as cyan dots. Epos. res. and ExGen are the estimated global strain energies for the positional restraint and density fitting methodologies, respectively. Energies are in kcal/mol.

    Figure 8

    Figure 8. Backbone residue flipping. (A) 27% of the data set featured a backbone residue flip in the final xGen ensemble relative to the deposited conformer. (B) Overlay of the deposited ligand conformer for 5O4Y (green) and the five alternative conformers in the xGen ensemble (orange). (C) Detailed view of a selection of backbone residues in the deposited conformer featuring cis-amide 1 from Figure 3 (red text). (D) Detailed view of the same residues in the final xGen ensemble, now featuring a trans-amide (green text) and a new intramolecular hydrogen bond. Isosurface contour for ρcalc corresponding to 1.0σ for the xGen ensemble is shown as cyan dots. Epos. res. and ExGen are the estimated global strain energies for the positional restraint and density fitting methodologies, respectively. Distances are in Å and energies are in kcal/mol.

    Figure 9

    Figure 9. Alternative linker rotamers. (A) 44% of the data set with non-peptidic linkers had alternative linker rotamers. (B) Overlay of deposited ligand conformer for 4ZQW (green) and the five alternative conformers in the xGen ensemble (orange). (C) Overlay of the deposited ligand conformer for 1VWM (green) and the two alternative conformers in the xGen ensemble (orange). Major linker rotamers are noted in the red text. Isosurface contour for ρcalc corresponding to 1.0σ for the xGen ensemble is shown as cyan dots. Epos. res. and ExGen are the estimated global strain energies for the positional restraint and density fitting methodologies, respectively. Energies are in kcal/mol.

    Figure 10

    Figure 10. Alternative side chain rotamers. (A) 90% of the data set had alternative side chain rotamers. (B) Overlay of the deposited ligand conformer for 1C5F (green) and the three alternative conformers in the xGen ensemble (orange). (C) Overlay of the deposited ligand conformer for 4X6S (green) and the six alternative conformers in the xGen ensemble (orange). Major side chain rotamers are noted in the red text. Isosurface contour for ρcalc corresponding to 1.0σ for the xGen ensemble is shown as cyan dots. Epos. res. and ExGen are the estimated global strain energies for the positional restraint and density fitting methodologies, respectively. Energies are in kcal/mol.

    Figure 11

    Figure 11. Alternative intermolecular interactions. (A) Overlay of the deposited ligand conformer for 5B4W (green) and the three alternative conformers in the xGen ensemble (orange) in the crystal structure. Plexin B1 is shown in purple. (B) Detailed view of the deposited peptide arginine side chain and Plexin B1 Asp414 featuring one strong and one weak hydrogen bond (yellow- and red-dotted lines, respectively). (C) Detailed view of the same residues in the final xGen ensemble, now featuring an arginine side chain rotamer with two strong intermolecular hydrogen bonds (yellow-dotted lines). Isosurface contour for ρcalc corresponding to 1.0σ for the xGen ensemble is shown as cyan dots. Epos. res. and ExGen are the estimated global strain energies for the positional restraint and density fitting methodologies, respectively. Distances are in Å and energies are in kcal/mol.

    Figure 12

    Figure 12. Cumulative histogram of enthalpy. Blue solid lines are for the macrocyclic peptide data set, green-dotted lines are for the non-peptidic macrocycle data set, and the purple-dashed lines are for the small molecule data set. All results are from docking the electron density fitting approach ensembles (xGen).

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