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Rapid and Reliable Binding Affinity Prediction of Bromodomain Inhibitors: A Computational Study

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† Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, United Kingdom
‡ GlaxoSmithKline, Gunnels Wood Road, Stevenage, Hertfordshire, SG1 2NY, United Kingdom
*E-mail: [email protected]
Cite this: J. Chem. Theory Comput. 2017, 13, 2, 784–795
Publication Date (Web):December 22, 2016
https://doi.org/10.1021/acs.jctc.6b00794

Copyright © 2016 American Chemical Society. This publication is licensed under CC-BY.

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Abstract

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Binding free energies of bromodomain inhibitors are calculated with recently formulated approaches, namely ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent) and TIES (thermodynamic integration with enhanced sampling). A set of compounds is provided by GlaxoSmithKline, which represents a range of chemical functionality and binding affinities. The predicted binding free energies exhibit a good Spearman correlation of 0.78 with the experimental data from the 3-trajectory ESMACS, and an excellent correlation of 0.92 from the TIES approach where applicable. Given access to suitable high end computing resources and a high degree of automation, we can compute individual binding affinities in a few hours with precisions no greater than 0.2 kcal/mol for TIES, and no larger than 0.34 and 1.71 kcal/mol for the 1- and 3-trajectory ESMACS approaches.

1 Introduction

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Computational chemistry has been an established tool in drug discovery for a number of years. The number of crystal structures available in the public domain and within pharmaceutical companies on which to base computational studies continues to rise rapidly. Despite the increase in resources applied and in experimental data on which to base the studies, industrial structure-based design approaches have evolved very little in recent times. (1) In particular, the approaches are largely qualitative and largely dependent on the experience and knowledge of the practitioner. (2, 3) Attempts to quantify protein–ligand binding affinities are rare. Expert practitioners have little confidence in existing tools to make robust predictions and certainly not to do so on a time scale that can substantially impact medicinal chemistry programmes.
Recently, there has been a renewed interest in the use of free energy calculations in drug discovery programmes. In particular, the FEP+ implementation of Free Energy Perturbation (FEP) has shown potential to improve the ability to predict protein–ligand binding affinities on an industrially relevant time scale. (4) Research is ongoing to understand how broadly applicable the method is, and how accurate its predictions are when applied to active drug discovery programmes.
Although FEP+ applies replica exchange solute tempering (REST) in which exchange moves are made between different λ windows, its predictions, like those from many other approaches, are generated from a single output for each pair of mutations. Advances in high-end computing capabilities offer the opportunity to run vast numbers of calculations in parallel. The application of these computational capabilities to free energy calculations allows results to be returned quickly and multiple replicas of simulations (5) to be run, leading to tighter control of standard errors. If such an approach could be validated and implemented in an industrial setting it would represent a major step forward in structure-based design capabilities. The first step in this process is to validate the performance on an industrially relevant data set.
Depending on the reliability, rapidity, and throughput of these calculations, they might find application at various stages of the drug discovery and development process across the wider pharmaceutical industry. As these methods require significant compute resources beyond existing in-house industrial capacity, assessment (and any subsequent adoption) of the methodology requires access to high performance computing resources.
Research into epigenetic proteins is currently a major and rapidly evolving focus for the pharmaceutical industry. (6-8) Bromodomain-containing proteins, and in particular the four members of the BET (bromodomain and extra terminal domain) family, each containing two bromodomains, have been widely studied. Small molecule inhibitors able to competitively antagonize the binding of acetylated histone tails to these modules have been shown to exert profound effects on gene expression and have shown promising preclinical efficacy in pathologies ranging from cancer to inflammation. Indeed, several compounds are progressing through early stage clinical trials and are showing exciting early results. (9) Most inhibitors reported show similar binding potencies to all BET family bromodomains. A representative inhibitor-protein structure is given in Figure 1, showing the key elements for the inhibitor binding. This study will concentrate on the first bromodomain of bromodomain-containing protein 4 (BRD4-BD1) for which extensive crystallographic and ligand binding data are available. (10-12)

Figure 1

Figure 1. Bromodomain inhibitor I-BET726 and its binding mode in BRD4-BD1. Two views are displayed for the binding mode (PDB ID: 4BJX (15)), in which I-BET726 (16) is represented as stick in cyan/blue/red/green, the protein is shown as cartoon in silver, the crystallographic water molecules are shown as red balls, and clipped protein surfaces are shown in orange.

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The purpose of the present study is to assess the potential for rapid, accurate, precise, and reproducible binding affinity calculations based on the use of a Binding Affinity Calculator (BAC) (13) software tool and associated services including a Python-based toolkit, FabSim, (14) to automate data transfer and job submission. The approach is based on the use of high performance computing in an automated workflow which builds models, runs large numbers of replica calculations, and analyzes the output data in order to place reliable standard error bounds on predicted binding affinities.

2 Computational Section

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Models

In this study, chemical structures of 16 BRD4-BD1 ligands based on a single tetrahydroquinoline (THQ) template (16) were provided by GSK (Table 1). The compound set was designed to represent a range of chemical functionality and binding affinities, but also to contain sets of closely related compounds with key SAR trends. Specifically, there are two growth vectors which cause a drop off in potency, a growth vector where substantial structural variation is tolerated and an enantiomeric pair where one isomer is significantly more potent than the other. These will be described below. The calculations were then performed by the UCL group, initially blind, to investigate the ability of BAC to reproduce the SAR trends. The experimental binding affinities were not released to the UCL group until all of the computations had been completed and the estimation of binding free energies were reported (see Figure 3 below). These predictions were subsequently compared with the independently measured experimental free energies of binding (Table 1) as part of the assessment of the reliability of the method.
Table 1. Compounds Used in This Study, Ordered According to Their R4 Group, and Their Experimental IC50s with Standard Deviations Converted into Binding Free Energies ΔG (kcal/mol)
Table a

Compounds 1–9 are electrostatically neutral, compounds 10–12 and 16 are positively charged, and compounds 13–15 are negatively charged.

Table b

Statistical errors were calculated from repeated IC50 measurements.

Table c

There was no activity at the highest concentration (50 μM) tested.

Table d

All compounds are the 2-(S) 4-(R) isomers (Figure 1) except compound 16 which is 2-(R) 4-(S).

The X-ray crystal structure used to represent BRD4-BD1 (published coordinates PDB ID: 4BJX (15)) is a complex with a THQ (I-BET726 (16)) chosen in order to reproduce the likely conditions for which free-energy calculations might be used in a real drug discovery program. The binding mode of I-BET726 is shown in Figure 1. Both of the significant protein–ligand hydrogen-bonding interactions take place through the THQ N1-acetamide carbonyl group, which interacts directly with the Asn140 side chain of the acetyl-lysine binding site and also through the W1 water to the side chain of Tyr97. The W1 water forms part of a chain of water molecules buried within the site (W2–W4, Figure 1). Substituents larger than acetamide at the N1-position extend into the water-filled part of the site. Our ligand data set included a small series of increasing size at N1 (1, 8, and 9, see Table 1) to probe whether the computer methodology can accurately predict the outcome of growing into this region.
The THQ R2-position (S)-methyl group occupies a small lipophilic site between the side chains of three residues of the BRD4-BD1 ZA-loop (Val87, Leu92, and Tyr97). Carbon–carbon contacts for all three lie within 4.25 Å, apparently offering little room for extension of this group without some structural reorganization. Our ligand data set includes a small number of analogues exploring larger substituents at the R2-position (10–14) to see whether the simulation can accurately predict the consequences of pushing on these residues.
The THQ 6-phenyl substituent fills the narrow “ZA channel” between Trp81 and Leu92. This ring can be substituted at the R3- and R4-positions, but R2-substitution is detrimental because this causes an increase in the inter-ring torsion. The ZA channel does not seem to accommodate the resulting wider 6-substituents. The remainder of our data set includes a variety of substituents probing electrostatic and steric changes at this position.
The THQ 4-anilino substituent projects onto the “WPF-shelf” subsite outside the acetyl-lysine pocket, close to Trp81. SAR around this ring has been published previously, (16) showing that substitution had small effects on potency, probably because one edge of the aniline ring is solvent-exposed. Therefore, we did not attempt to vary substituents at this position in our data set, preferring to keep it as constant as possible while exploring changes elsewhere.
In this series the 2-(S) 4-(R) isomers (see Figure 1) are significantly more potent than their alternative trans enantiomers. We included an enantiomeric pair of 2-(S) 4-(R) (compound 10) and 2-(R) 4-(S) (compound 16) isomers to explore whether the simulations were capable of distinguishing between them.
The ligand-protein complexes were constructed by replacing the ligand in the PDB file with the ligands of interest (see structures in Supporting Information). For the congeneric compounds studied here, it is plausible to assume that they bind in the same mode in which all key compound-protein interactions are preserved (Figure 1). For compounds with significant structural differences, computational docking may be required to generate reasonable complex structures. (17) Preparation and setup of the simulations were implemented using BAC, (13) including parametrization of the compounds, solvation of the complexes, electrostatic neutralization of the systems by adding counterions and generation of configurations files for the simulations. The AMBER ff99SB-ILDN (18) force field was used for the protein, and TIP3P was used for water molecules. Standard protonation states were assigned to all titratable residues at pH 7, with histidines protonated on the ε position (HIE). Compound parameters were produced using the general AMBER force field (GAFF) (19) with Gaussian 03 (20) to optimize compound geometries and to determine electrostatic potentials at the Hartree–Fock level with 6-31G** basis functions. The restrained electrostatic potential (RESP) module in the AMBER package (21) was used to calculate the partial atomic charges for the compounds. All systems were solvated in orthorhombic water boxes with a minimum extension from the protein of 14 Å.
Some of the ligands could adopt several rotamers for the R4 group (Table 1) in solution, which due to the constrained environment of the active site are unlikely to be sampled in a single bound simulation run with the protocol used (see Simulations subsection). To decide which rotamer(s) with which to start, metadynamics simulations (22) were employed which used a history-dependent biasing potential to explore the conformational space of the chosen degrees of freedom, here the rotatable bond(s) involving groups R2 and R4 (see details in the Supporting Information). Five replicas were used for each metadynamics study to have a reasonable convergence of the potential profile of the chosen dihedral angle(s) of a ligand in complexed form. The calculated potential of mean force (PMF) was used to determine the most favorable rotamer(s) from which ESMACS simulations initiate. When unambiguous results ensued, the energetically most favorable rotamer was chosen. For some ligands, more than one rotamer showed similar free energies. In these cases, multiple initial structures were prepared using the rotamers suggested by the metadynamics study. The ligands with multiple rotamers were: 4, 7, 10, 11, 12, and 16. There are two rotamers for each of these, except for 7 for which there are three generated by the flip and twist between the two ring planes. This resulted in a total number of 23 complexes being simulated in the ESMACS study.
For each ligand with multiple rotamers, the energetic properties were analyzed and the most favorable rotamer was chosen as the final result of the ESMACS study (see Results section) and was used as the initial structure in the TIES study. For the latter, three subsets of the ligands were selected, within which relative binding free energies were calculated with the TIES approach. The subsets of the ligands were as follows: set 1 including ligands 1–9; set 2 including ligands 10, 11, and 12 which are positively charged; and set 3 including ligands 13, 14, and 15 which are negatively charged. The division of the full set of the cognate ligands into subsets is necessary because TIES, just as any other TI and FEP based method, encounters specific difficulties owing to major adjustments in long-range electrostatic interactions for the “congeners” where the net charges change. (23) For each subset, ligands were paired based on their similarities, and TIES calculations were performed to alchemically mutate one ligand to another (see Theoretical Basis below).

Theoretical Basis

The UCL group have recently introduced new protocols for binding free energy calculations, termed “enhanced sampling of molecular dynamics with approximation of continuum solvent” (ESMACS) (24) and “thermodynamic integration with enhanced sampling” (TIES). (25) ESMACS is based on the molecular mechanics Poisson–Boltzmann surface area method (MMPBSA) (26) which makes a continuum approximation for the aqueous solvent, while TIES centers, as the abbreviation indicates, on thermodynamic integration (TI). Although the approaches are built around the standard MMPBSA and TI methodologies, our abbreviations are used to emphasize the central importance of the ensemble-based nature of the protocols employed as well as, in the case of ESMACS the wider generality and flexibility of the protocol. (5, 24) The size of the statistical mechanical ensembles is determined systematically so that predictions are accurate, precise, and reliable. (24, 27) Moreover, the term “MMPBSA” is used to mean very different things (28) in numerous journal articles and textbooks, including calculations based on single docked structures (4) or on simulation trajectories, calculations with or without the inclusion of configurational entropies, and almost wholly using the so-called 1-trajectory approach. In the ESMACS protocol, we always mean a fully converged, ensemble-based determination of the free energy of binding from either a one-, two-, or three-trajectory method: this includes both the configurational entropy and the association free energy, (27, 29) and (where appropriate) the relative or absolute adaptation energy. (24) Statistical analyses (30) were performed throughout the study for all of the quantities obtained. A Binding Affinity Calculator (BAC) (13) was used to perform ESMACS and TIES studies. BAC constitutes a computational pipeline built from selected software tools and services (see Supporting Information), and relies on access to a range of computing resources. It automates much of the complexity of building, running, and marshalling the molecular dynamics simulations, as well as collecting and analyzing data. Integration and automation are central to the reliability of the method, ensuring that the results are reproducible and can be delivered rapidly.
In ESMACS, the free energy is evaluated approximately based on the extended MMPBSA method, (24, 27) including configurational entropy, and the free energy of association. (29) Free energy changes (ΔGbinding) are determined for the molecules in their solvated states. The binding free energy change is then calculated as(1)where Gcomplex, Greceptor, and Gligand are free energies of the complex, the receptor and the ligands, respectively. The Possion–Boltzmann calculation is performed here using the Amber built-in PBSA solver (31) with radii taken from the parameter/topology files, and the configurational entropy is calculated by a normal mode (NMODE) method.
The three terms on the right-hand side of eq 1 can be generated from single simulations of the complexes or from separated simulations of complexes, receptor(s), and ligand(s). The former is the so-called 1-trajectory (1-traj) method of which the trajectories of the receptor(s) and the ligand(s) are extracted from those of the complexes. The latter is the so-called 3-trajectory (3-traj) method of which the trajectories are generated from separate simulations of the three components. In the drug development field, binding is usually investigated for a set of ligands bound to the same protein target. The free energy of the receptor Greceptor will then be the same for all ligands in the 3-traj method. In the current study, we employ three approaches to calculate the binding free energies ΔGbinding: (A) using single simulations of the complexes (1-traj); (B) same as (A) but using the average of the receptor free energies ⟨Greceptor⟩ from the 1-traj method (denoted as 2-traj); and (C) the same as (B) but invoking separated ligand simulations for the derivation of Gligand (denoted as 3-traj).
In TIES, an alchemical transformation for the mutated entity, either the ligand or the protein, is used in both aqueous solution and within the ligand–protein complex. The free energy changes of the alchemical mutation processes, ΔGaqalch and ΔGcomplexalch, are calculated by(2)and the binding free energy difference is calculated from(3)Here λ (0 ≤ λ ≤ 1) is a coupling parameter such that λ = 0 and λ = 1 correspond to the initial and final thermodynamic states, and V(λ) is the potential energy of an intermediate state λ. ⟨···⟩λ denotes an ensemble average over configurations representative of the state λ. To avoid the well-known “end-point catastrophe”, (32) a soft-core potential is used, along with an approach to decouple at different rates the electrostatic and van der Waals interactions of the perturbed atoms with their environment (for more details see the Supporting Information). The foregoing is a textbook account of thermodynamic integration; TIES differs by virtue of performing ensemble based calculations, (25, 33) in the same manner as for ESMACS, thereby providing control of standard errors based on length of simulation and number of ensembles used. Indeed, it is important to note that the energy derivatives (eq 2) calculated for all λ windows are well described by Gaussian random processes, which makes it possible to draw on the theory of stochastic calculus to compute relevant properties reliably. (5)

Simulations

The ESMACS and TIES studies follow the protocol developed recently (24, 25) (see Supporting Information). The Amber package (21) was used for the setup of the systems and analyses of the results, and the MD package NAMD2.9 (34) was used throughout the equilibration and production runs of all simulations, including the metadynamics. An ensemble simulation was performed for each molecular system with identical atomic coordinates for all replicas. Energy minimizations were first performed with heavy protein atoms restrained at their initial positions. The initial velocities were then generated independently from a Maxwell–Boltzmann distribution at 50 K, and the systems were heated up to and kept at 300 K within 60 ps. A series of equilibration runs, totalling 2 ns, were conducted, while the restraints on heavy atoms were gradually reduced. Finally, 4 ns production simulations were run for each replica for all ESMACS and TIES simulations. In ESMACS, we used 25 replicas in an ensemble calculation for each ligand. In TIES, 5 replicas were used for each pair of the ligands. Simulation of each replica consists of 2 ns for equilibration and 4 ns for production run. Previous studies (24, 27, 30, 35) have shown that the combination of the simulation length and the size of the ensemble provides a trade off between computational cost and precision.
Two independent ESMACS runs were performed to assess the reproducibility of the calculations. One was run on ARCHER, a Cray XC30 supercomputer (equipped with ca 118 000 cores), the UK’s National High Performance Computing Service located in Edinburgh; the other run on the BlueWonder2 supercomputer, an IBM NextScale Cluster (8640 cores) located in Science and Technology Facilities Council’s (STFC’s) Hartree Centre. A comparison between the two runs is very instructive, both in terms of performance and time to solution as well as providing an opportunity to conduct a valuable reproducibility study. Thanks to the large number of cores on ARCHER, we ran the entire set of ESMACS binding affinity calculations concurrently and had the findings available within 7 h. On BlueWonder2, we were hampered by a number of issues, resulting in the calculations taking significantly longer than on ARCHER. On BlueWonder2 and ARCHER, about 440 000 and 335 000 core hours were consumed in the course of this study, including 300 000 and 225 000 core hours for production molecular dynamics simulations and 140 000 and 110 000 core hours for free energy calculations, respectively.
The TIES study was performed entirely on ARCHER. TIES simulations of 7 out of 12 pairs were packed together (the currently enforced limit of maximum tasks for one job in ARCHER) and submitted as one single job, requiring 43 680 cores, which has high priority and executes rapidly on the machine (waiting time in the ARCHER queue was around 8 h). This made it possible to complete the entire TIES study of seven pairs within 1 day including queuing time. Further speed up is feasible on supercomputers with hybrid architectures which would permit for example GPU acceleration for some parts of these calculations.

3 Results

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To assess the accuracy and precision of the method, we evaluated the binding affinities of the ligands (Table 1) to BRD4 and compared the computed results with experimental data. ESMACS was used for the full set of the ligands, including the stereoisomer which cannot be considered as a perturbation of any others. TIES was applied to three subsets of the ligands, of which each includes congeners with the same net charge.

Reproducibility

It is well-known that many complex systems exhibit sensitive dependence on initial conditions. (5, 36) The differences of the initial velocities among individual simulations lead to rapid divergence of trajectories. The calculated thermodynamic properties from individual simulations will therefore inevitably differ. Two sets of ESMACS simulations were performed for the complexes independently on ARCHER and BlueWonder2 (see the Computational Section above). The results are compared by linear regression. Figure 2 shows the variances and correlation of the calculated binding free energies from the two sets of simulations. The correlation coefficient r is 0.98 ± 0.01, with no statistical differences between slopes and intercepts of the calculated regression line and the ideal line (x = y) (Figure 2a). The two studies produce consistent results, with an average difference of 0.07 ± 0.10 kcal/mol, and an average unsigned difference of 0.39 ± 0.06 kcal/mol. Only 3 out of 16 predictions do not overlap within their variances (Figure 2b). For the purpose of ranking compound selectivity, the Spearman correlation coefficient (rS) is also calculated, which shows that the rankings from the two studies are very close to one another, with a highly significant Spearman correlation of 0.98 ± 0.02. In the following analyses, only the results from BlueWonder2 simulations are reported. The ARCHER-based calculations produced very similar results.

Figure 2

Figure 2. Correlation and standard errors of the calculated binding free energies from two independent studies of the BRD4-ligand models performed on BlueWonder2 and ARCHER. (a) Correlation of the predictions, including all rotamers, from 1-traj calculations performed on BlueWonder2 (BW2, horizontal axis) and ARCHER (vertical axis). Solid line, regression of the data using means of the calculated free energies; dotted line, 1:1 ideal regression. (b) the averages and their standard errors from the two separate calculations. One rotamer is used for each ligand.

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Choosing Rotamers

Some of the ligands (Table 1) would be able to adopt more than one rotamer in solution. When the ligands are complexed with the protein, they are usually trapped in a specific rotameric state. The energy barriers between rotamers are sufficiently high, especially for groups occupying the narrow ZA channel (Figure 1), that it is not feasible to achieve equilibrated populations of rotamers using the current protocol. We therefore initiated molecular dynamics simulations of complexes from all possible rotamers for six out of the 16 ligands. Simulations including different rotamers are only applied to the complexes, as the free ligands in water are able to fully sample all rotamers. The most favorable rotamer is selected (Figure 3) for each ligand in its complex form, based on the lowest ligand energy of the rotamer, which is approximated by (Gligand + ΔGbinding).

Figure 3

Figure 3. Calculated binding free energies from simulations on BlueWonder2 and ARCHER. The ligands are numbered as per Table 1. Circles with red/blue colors are the results based on studies with different rotamers. The circles with crosses are the final results with selected rotamers which are chosen on the basis of the sum of energies Gligand and ΔGbinding (see eq 1). All of the calculated binding free energies are associated with standard errors of less than 1.7 kcal/mol, and are not shown in the figures for reasons of clarity.

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Comparison between ESMACS Calculations and Experiments

The predicted binding free energies from the 1-traj approach exhibit a weak Spearman correlation with the experimental data (Figure 4a). In the current study, as commonly employed in pharmaceutical drug development projects, a series of ligands are investigated for the same protein target. The energy of the protein therefore does not affect the ranking of the binding affinities (eq 1). Treating it as a constant, the 2-traj approach significantly improves the correlation between the predictions and experimental data (Figure 4b). Incorporating the free energies of the ligands from their individual simulations in free form, the 3-traj approach, further improves the correlation (Figure 4c). The most significant improvement appears in the compounds involving modifications at the R2 position of the tetrahydroquinoline (Table 1), for which the 1-traj approach predicts an increase (compound 11 to 12) or no change (compound 14 to 13) in the binding affinities when an ethyl is replaced by an n-propyl. The 2- and 3-traj approaches correctly rank the binding potencies of the two pairs, and indeed of these four compounds. Although the improvement is most evident for the listed four compounds, it is indeed applied to the overall correlation for the whole set (Figure 4). It should be noted, however, that although the 2- and 3-traj methods significantly improve the correlations between predictions and experimental data, relatively large standard deviations, up to 1.7 kcal/mol, are associated with the calculated free energies. This indicates that the binding free energies must differ by no less than 3.4 kcal/mol to be statistically significant to a 95% confidence level. With the experimental free energy differences ranging from 0.0 to 4.9 kcal/mol, a larger ensemble would be required to reduce the relatively large uncertainties in order to render all the predictions statistically significant. It is important to mention here that experimental binding affinities usually contain errors to a greater extent (37) than are implied by Table 1. Generating reproducible binding free energies from experiments is as important as that from simulations to make the comparisons statistically significant.

Figure 4

Figure 4. Spearman ranking correlations of the calculated binding free energies and the experimental data from 1-traj (left panel), 2-traj (center), and 3-traj (right panel) ESMACS approaches. The equations on the subfigures indicate the calculations used in each case. The subscripts (com/rec/lig) and the superscripts (com/lig) in the equations indicate the components (complexes, receptor, and ligands) and the simulations (complexes and free ligands), respectively. The ligands with modifications at the R2-position of the tetrahydroquinoline are marked with crosses; they are all significantly improved in the 2- and 3-trajectory version. The standard errors, which are 0.19–0.34 kcal/mol for the 1-traj and 1.02–1.71 kcal/mol for the 2- and 3-traj approaches, are not shown for reasons of clarity. They are calculated using a bootstrapping method (see Supporting Information). The 2- and 3-traj approaches have similar errors because the energy of the receptor is treated as a constant and hence the uncertainties are dominated by the energies of the complexes.

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The improvements are achieved by including the adaptation energies of the receptor and the ligands (Figure 5). While the adaptation energies for the ligands are calculated as the differences between the free energies in their bound and free states, those for the receptor are calculated relative to the average of the receptor free energies in the bound states. The absolute adaptation energies of protein for each ligand binding would require a converged ensemble simulation of protein in solvent, preferably initiated from structures of the protein in its free state. As the ranking of the ligand binding is the main concern of the study, and the relative adaptation energies of the protein are energetically as informative as the absolute ones in the binding affinity comparison, no attempt has been made here to compute accurate absolute adaptation energies for the protein (all adaptation energies for the protein are relative ones in the current paper). Unfavorable adaptation energies are usually induced within the protein by the introduction of larger functional groups at R2 and R3 positions of the compounds (Figure 5c). It is interesting to note that, for the ligands with higher binding affinities (ΔGbinding < −8 kcal/mol), only small adaptation energies arise for both the receptor and the ligands, which makes the binding apparently closer to a “lock and key” recognition mechanism; while for the ligands with lower binding affinities, non-negligible adaptation energies are found for both the receptor and the ligands (Figure 5b). The one exception is the stereoisomer ligand 16 (Table 1) whose binding induces the smallest relative adaptation energy of the receptor but the largest adaptation energy for the ligand (Figure 5c). This compound was included in the set as a negative control to investigate the ability of the computational procedure to highlight the weak activity of the enantiomer of compound 10. Compound 16 has a very high ligand strain, suggesting that this isomer has the wrong shape for the binding site and must adopt a high energy conformation to interact with the protein.

Figure 5

Figure 5. Improvement of the predictions by inclusion of the adaptation free energies of the receptor and the ligands: (a) the binding free energy changes between the 1-traj (black circles) and 2-traj (magenta circles) indicate the relative adaptation energies of the receptor; those between the 2-traj (magenta circles) and 3-traj (orange circles) show the adaptation energies of the ligands. The adaptation energies can be seen more clearly in panels b as a function of binding affinities, and in panels c for each ligand.

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The ESMACS predictions are precise and accurate in terms of ranking the binding free energies, and are so in a reproducible way. However, ESMACS does not provide accurate absolute free energies. In our study, the 3-traj ESMACS protocol yields a much better correlation than the 1-traj ESMACS approach, while they have similar mean absolute deviations (1.97 ± 1.33 kcal/mol and 1.74 ± 0.29 kcal/mol, respectively). The mean absolute deviations can be significantly larger for more flexible ligands such as peptides binding to a major histocompatibility complex (MHC). (24) Some studies show that improved binding free energy prediction could be obtained by including important water molecules between ligands and protein. (38) Inclusion of the bridging water molecules (Figure 1) in the current ESMACS study, however, does not improve the correlation between the calculated binding free energies and the experimental measurements (see Figure S3 in the Supporting Information). Indeed, ours is a “generic” methodology which treats solvent implicitly and works well as such. Embarking on any approaches for treating water molecules explicitly would lead to a loss of simplicity in the method without conferring any benefit.
Component analyses of the binding free energies could provide insight into the mechanism of compound binding. In our study of peptide-MHC binding, (24) for example, the van der Waals interaction was shown to be the dominant component and to manifest a good correlation with the experimental binding free energies in the 3-trajectory ESMACS study. In the current molecular systems, however, there are no significant correlations between any energy component and the experimental data, except the bonded (including bond stretching, angle bending, torsions and improper torsions) and nonbonded (van der Waals, electrostatic and solvation) interactions as shown in Figure 6. The sum of the two interactions improves the correlation further, with a similar correlation coefficient as shown in Figure 4 for the 3-trajectory approach. It can therefore be deduced that the configurational entropy component does not contribute to the quality of the ranking prediction. As for the impact of the configurational entropy on the ranking of calculated binding affinities, different conclusions—improving, (27) worsening, (39) or having no effect (24)—have been drawn for diverse protein–ligand complexes. The differences may indeed reflect the mechanism of protein–ligand binding which can be driven predominantly by enthalpy, by entropy, or by both. (40)

Figure 6

Figure 6. Correlations of free energy components and the experimental data from 3-traj approaches. Both bonded and nonbonded energy terms contribute to the ranking of binding affinities. Their combination (the MMPBSA energy) exhibits a better correlation with experimental data than the components themselves.

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Comparison between TIES Calculations and Experiments

Good agreement is found for the binding free energy differences between the TIES calculations and the experimental measurements. The TIES approach is both accurate and precise, yielding a Spearman ranking coefficient of 0.92 for the means of calculated and experimental binding free energy differences. The bootstrap analyses give a Spearman coefficient of 0.86 ± 0.15, drawn from a non-normal distribution of resampling correlation coefficients (see Figure S4 in the Supporting Information). An average difference of 0.06 ± 0.26 kcal/mol, and an average unsigned difference of 0.75 ± 0.14 kcal/mol, are found between the predictions and experimental measurements (Figure 7). It should be noted that experimental binding affinities may have statistical errors of around 24% from isothermal titration calorimetry (ITC) (37) which is a more reliable method to measure binding affinities than the IC50 measurements used in this study. The variances observed in the study can be partially attributed to these experimental errors. The regression line is close to an ideal 1:1 regression, with a slope of 0.93 ± 0.24 and an intercept of −0.10 ± 0.33 kcal/mol. A similar level of accuracy was recently reported (17) in an absolute binding free energy calculation for a set of drug-like molecules binding to BRD4, albeit little attention was paid to reproducibility in that work.

Figure 7

Figure 7. Correlations of the calculated binding free energy differences from the TIES study and from experimental measurement. The standard error bars from the TIES calculations are all no greater than 0.2 kcal/mol.

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4 Discussion

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To analyze the results it is necessary to consider the differences between the 1-, 2- and 3-trajectory methods. The 1-trajectory simulation calculates the ΔGbinding assuming there is no energetic penalty for the adaptation of the protein or ligand to the binding conformation, the 2-trajectory method takes the change in protein energy into consideration and the 3-trajectory method accounts for the changes in both protein and ligand energy.
The test set for this evaluation was designed to investigate the ability of ESMACS to predict specific SAR trends. The first trend is the loss of potency observed as the hydrophobic part of the acetyl lysine mimetics is grown from methyl (1) to ethyl (8) to isopropyl (9). Figure 8 shows that, in the 1-traj simulation, compound 1 is predicted to be more potent than compounds 8 and 9, but no difference is predicted between 8 and 9. This is in contrast to the experimental results which show a modest loss of potency going from methyl to ethyl, but a substantial loss going from ethyl to isopropyl. On comparing the same three compounds in the 2-traj simulation, the predicted affinity of compound 9 is substantially reduced giving the correct ranking of the three compounds. The predictions for the three compounds are qualitatively the same for the 3-traj calculation. These results indicate that the low activity of compound 9 is the result of the increased bulk of the isopropyl group causing strain in the system, which is manifested in an increased internal energy of the protein. In fact, compound 9 has the highest protein internal energy of the whole data set (Figure 6c). The TIES study gives the same ranking for the binding affinities as those from the 2- and 3-traj ESMACS, but with an enhanced correlation coefficient compared to that of ESMACS. Structurally, this result makes sense because the isopropyl group is rigid and so the strain caused by the increased bulk cannot be accommodated by the ligand and hence is transmitted to the protein.

Figure 8

Figure 8. Calculated vs experimental binding free energies for ligands 1, 8, and 9 which are labeled in the 1-traj subfigure.

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The second SAR trend of interest is the effect of increasing bulk at the R2-position of the tetrahydroquinoline (THQ). Similar to the previous instance, increasing the size of the substituent at this position from methyl (10) to ethyl (11) to n-propyl (12) results in a sequential loss of activity. In this case the 1-traj method inverts the rank order of the three compounds (Figure 9), relative to experiment, predicting the n-propyl to be the tightest binder. The 2-traj calculation predicts a decrease of the potency of compound 12, consequently predicting it to be substantially weaker than compound 11, as observed experimentally. In the 3-traj method the potency of compound 12 drops further, relative to the other compounds. In all three ESMACS methods, the potency of compound 10 is under-predicted relative to the other compounds; the reason for this is unclear. The TIES study also predicts the binding of compound 12 to be the weakest in this subgroup, but could not distinguish the affinities of the compounds 10 and 11. A second pair of compounds also has the ethyl (14) to n-propyl (13) modification at the same position, and qualitatively the results parallel those described above. In this case, the n-propyl compound shows a correctly predicted loss of activity in both the TIES and 2- and 3-traj ESMACS methods, indicating the loss in potency for this bulky group is due to a combination of protein and ligand strain (Figure 6c). Again, this is consistent with the molecular structure of compound 12, because the n-propyl group is more flexible than the isopropyl group in the first example and consequently is more able to adopt a slightly strained ligand conformation.

Figure 9

Figure 9. Calculated vs experimental binding free energies for ligands 10, 11, and 12 which are labeled in the 1-traj subfigure.

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The carbonyl group in all compounds forms a hydrogen bond with a conserved asparagine Asn140 in the BRD4. This is a key interaction observed in bromodomain-ligand complexes as it mimics the interaction made by the carbonyl of the acetyl lysine of the substrate. The occupancies of this hydrogen bond in all of the compounds are very similar, and do not appear to correlate with their binding affinities. Hence, when bulk is increased adjacent to this key binding motif, as described in the previous cases, the loss of potency does not result from the disruption of this hydrogen bond. Conversely, the interaction is maintained at the expense of creating internal strain in the system. This is consistent with the observation that this is a ubiquitous interaction in this protein and a key binding pharmacophore.
For compounds 13, 14, and 15, there is an extra hydrogen bond formed between the carboxylate group of the ligands and the Lys 91 of the protein. The replacement of n-propyl (13) with ethyl (14) and methyl (15) slightly changes the orientations of the compounds, making the carboxylate group better aligned for the formation of hydrogen bonds. The occupancies of this hydrogen bond are 16.6%, 31.7%, and 33.3% for the compounds 13, 14, and 15, respectively (the cutoff values are 3 Å and 120° for the donor–acceptor distance and donor–hydrogen–acceptor angle). The occupancies of the hydrogen bonds for these 3 compounds appear to correlate with their binding affinities (−7.41, −9.20, and −10.51 kcal/mol). However, the energetic contribution of this solvent exposed interaction is difficult to quantify, and the energetic analysis elsewhere in this section suggests that differences in intermolecular interactions in the complex contribute modestly to the differences in binding free energy compared to differences in internal energies. Further evidence for this is seen in the pairs of compounds 11,14 and 12,13, which are identical except for a carboxylic acid to piperidine (base) modification in this region. These pairs of compounds have very similar binding affinities both in terms of experimental and predicted values.
These data suggest that the internal energy of the protein and ligand are major contributors to the relative binding affinities of this series of compounds. The internal energy contributions are exemplified by plotting the difference between the binding free energies predicted using the different ESMACS methods (Figure 10).

Figure 10

Figure 10. Correlations of the internal energy contributions to the calculated binding free energies and experimental measurement. The internal energy changes are calculated as the differences of the binding free energies between those from the 1-traj and 3-traj approaches: ΔΔGcalc = ΔGbinding3-traj – ΔGbinding1-traj.

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Figure 10 plots the difference between the ΔGbinding calculated by the 3-traj method and the 1-traj method against the experimental ΔGbinding. This is a plot of the internal energy of the protein and ligand against the experimental ΔGbinding; it shows a strong correlation (r = 0.87 ± 0.13). If this is contrasted with the 1 trajectory method—which essentially contains the intermolecular contributions to ΔGbinding, Figure 4a (r = 0.29 ± 0.26)—one can conclude that, for this protein and set of ligands, the internal energy of the ligand and the protein differentiate between the ligands to a far greater extent than protein–ligand interaction energies.

5 Conclusions

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The Binding Affinity Calculator (BAC) software environment has been used to run ESMACS and TIES calculations against a series of inhibitors of BRD4 from the THQ chemical series. High performance computing was used in an automated workflow to build models, run multiple replicas of calculations and analyze the output, placing reliable standard error bounds on predicted binding affinities.
Despite the challenging data set used for this evaluation, good agreement is found for the binding free energy differences between the experimental measurements and the theoretical calculations, for both ESMACS and TIES. ESMACS is good as an “absolute” method for ranking an arbitrary set of ligands, which may be very diverse in terms of structures and electronic properties. To produce good rankings it is necessary in this case to use a 3-trajectory version, which has the further benefit of clearly distinguishing between ligands that adhere more closely to the “lock and key” or to the “induced fit” binding hypotheses. TIES performs well in determining relative binding free energies of congeners when there is no change of net charge, even when there are differences in structural features between pairs of compounds which one would not intuitively regard as minor.
Overall, ESMACS provides reliable binding affinity rankings and clear mechanistic insight into what factors drive binding processes in individual ligand–protein systems. TIES offers more quantitative accuracy in its predictions but, owing to its alchemical basis which necessarily keeps two congeneric ligands in play at all times, is less able to provide similar structural and mechanistic insights into binding. The standard errors in ESMACS and TIES are fully controlled through simulation length and number of replicas used in the ensembles chosen. (24, 27)
The results also offer insight into possible design strategies for BRD4 ligands. In particular it has been noted that, within a chemical series, differences in binding affinity do not seem to result from differences in protein–ligand interaction energies. On the contrary, to avoid unfavorable (in this case, mainly steric) interactions, both ligands and protein adopt strained states resulting in large adaptation energies. Hence, during the optimization of a chemical series for BRD4 it would be prudent to carefully consider the shape complementarity of the ligand and the active site cavity. It should be noted, however, that this study did not include molecules in which unfavorable electrostatic protein–ligand interactions were introduced.
The results offer encouragement that BAC, and its underlying approach of running multiple replicas of each simulation to improve predictive power, (5) can accurately rank ligands by their binding free energy. Further evaluations are planned to confirm this potential. As large and secure computing resources become more routinely available, for example through cloud computing, it will become increasingly easy for industrial groups to access approaches like the one outlined in this study. Consequently, the robust prediction of protein–ligand binding affinities in an industrial setting should become more routine and offer a long awaited development in the field of structure-based design.

Supporting Information

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.6b00794.

  • Detailed description of the methods used, additional energetic analyses of the metadynamics, free energy calculation with inclusion of explicit water molecules, alongside the atomic coordinates of the compound-protein complexes and experimental data on compound binding (PDF)

  • Structures of the studied compounds (ZIP)

Terms & Conditions

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

Author Information

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  • Corresponding Author
  • Authors
    • Shunzhou Wan - Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, United Kingdom
    • Agastya P. Bhati - Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, United Kingdom
    • Stefan J. Zasada - Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, United Kingdom
    • Ian Wall - GlaxoSmithKline, Gunnels Wood Road, Stevenage, Hertfordshire, SG1 2NY, United Kingdom
    • Darren Green - GlaxoSmithKline, Gunnels Wood Road, Stevenage, Hertfordshire, SG1 2NY, United Kingdom
    • Paul Bamborough - GlaxoSmithKline, Gunnels Wood Road, Stevenage, Hertfordshire, SG1 2NY, United Kingdom
  • Funding

    The authors would like to acknowledge the support of EPSRC via the 2020 Science programme (http://www.2020science.net/, EP/I017909/1), the Qatar National Research Fund (7-1083-1-191), the MRC Medical Bioinformatics project (MR/L016311/1), the EU H2020 CompBioMed (675451) and ComPat (671564) projects, and funding from the UCL Provost. We acknowledge use of Hartree Centre computer BlueWonder2 in this work and assistance from its scientific support staff. The STFC Hartree Centre is a research collaboratory in association with IBM providing High Performance Computing platforms funded by the UK’s investment in e-Infrastructure. We made use of ARCHER, the UK’s national High Performance Computing Service, funded by the Office of Science and Technology through EPSRC’s High-End Computing Programme. Access to ARCHER was provided through the 2020 Science programme. This research was partially supported by the PLGrid Infrastructure through which access to Prometheus, the fastest Polish supercomputer run by ACK Cyfronet AGH in Krakow, was provided.

  • Notes
    The authors declare no competing financial interest.

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    Automated Molecular Simulation Based Binding Affinity Calculator for Ligand-Bound HIV-1 Proteases
    Sadiq, S. Kashif; Wright, David; Watson, Simon J.; Zasada, Stefan J.; Stoica, Ileana; Coveney, Peter V.
    Journal of Chemical Information and Modeling (2008), 48 (9), 1909-1919CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    The successful application of high throughput mol. simulations to det. biochem. properties would be of great importance to the biomedical community if such simulations could be turned around in a clin. relevant timescale. An important example is the detn. of antiretroviral inhibitor efficacy against varying strains of HIV through calcn. of drug-protein binding affinities. We describe the Binding Affinity Calculator (BAC), a tool for the automated calcn. of HIV-1 protease-ligand binding affinities. The tool employs fully atomistic mol. simulations alongside the well established mol. mechanics Poisson-Boltzmann solvent accessible surface area (MMPBSA) free energy methodol. to enable the calcn. of the binding free energy of several ligand-protease complexes, including all nine FDA approved inhibitors of HIV-1 protease and seven of the natural substrates cleaved by the protease. This enables the efficacy of these inhibitors to be ranked across several mutant strains of the protease relative to the wildtype. BAC is a tool that utilizes the power provided by a computational grid to automate all of the stages required to compute free energies of binding: model prepn., equilibration, simulation, postprocessing, and data-marshaling around the generally widely distributed compute resources utilized. Such automation enables the mol. dynamics methodol. to be used in a high throughput manner not achievable by manual methods. This paper describes the architecture and workflow management of BAC and the function of each of its components. Given adequate compute resources, BAC can yield quant. information regarding drug resistance at the mol. level within 96 h. Such a timescale is of direct clin. relevance and can assist in decision support for the assessment of patient-specific optimal drug treatment and the subsequent response to therapy for any given genotype.
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  14. 14
    Groen, D.; Bhati, A. P.; Suter, J.; Hetherington, J.; Zasada, S. J.; Coveney, P. V. FabSim: Facilitating computational research through automation on large-scale and distributed e-infrastructures Comput. Phys. Commun. 2016, 207, 375– 385 DOI: 10.1016/j.cpc.2016.05.020
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    14
    FabSim: Facilitating computational research through automation on large-scale and distributed e-infrastructures
    Groen, Derek; Bhati, Agastya P.; Suter, James; Hetherington, James; Zasada, Stefan J.; Coveney, Peter V.
    Computer Physics Communications (2016), 207 (), 375-385CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    We present FabSim, a toolkit developed to simplify a range of computational tasks for researchers in diverse disciplines. FabSim is flexible, adaptable, and allows users to perform a wide range of tasks with ease. It also provides a systematic way to automate the use of resources, including HPC and distributed machines, and to make tasks easier to repeat by recording contextual information. To demonstrate this, we present three use cases where FabSim has enhanced our research productivity. These include simulating cerebrovascular bloodflow, modeling clay-polymer nanocomposites across multiple scales, and calcg. ligand-protein binding affinities.
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  15. 15
    Wyce, A.; Ganji, G.; Smitheman, K. N.; Chung, C. W.; Korenchuk, S.; Bai, Y.; Barbash, O.; Le, B.; Craggs, P. D.; McCabe, M. T.; Kennedy-Wilson, K. M.; Sanchez, L. V.; Gosmini, R. L.; Parr, N.; McHugh, C. F.; Dhanak, D.; Prinjha, R. K.; Auger, K. R.; Tummino, P. J. BET inhibition silences expression of MYCN and BCL2 and induces cytotoxicity in neuroblastoma tumor models PLoS One 2013, 8 (8) e72967 DOI: 10.1371/journal.pone.0072967
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  16. 16
    Gosmini, R.; Nguyen, V. L.; Toum, J.; Simon, C.; Brusq, J. M.; Krysa, G.; Mirguet, O.; Riou-Eymard, A. M.; Boursier, E. V.; Trottet, L.; Bamborough, P.; Clark, H.; Chung, C. W.; Cutler, L.; Demont, E. H.; Kaur, R.; Lewis, A. J.; Schilling, M. B.; Soden, P. E.; Taylor, S.; Walker, A. L.; Walker, M. D.; Prinjha, R. K.; Nicodeme, E. The discovery of I-BET726 (GSK1324726A), a potent tetrahydroquinoline ApoA1 up-regulator and selective BET bromodomain inhibitor J. Med. Chem. 2014, 57 (19) 8111– 8131 DOI: 10.1021/jm5010539
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    16
    The Discovery of I-BET726 (GSK1324726A), a Potent Tetrahydroquinoline ApoA1 Up-Regulator and Selective BET Bromodomain Inhibitor
    Gosmini, Romain; Nguyen, Van Loc; Toum, Jerome; Simon, Christophe; Brusq, Jean-Marie G.; Krysa, Gael; Mirguet, Olivier; Riou-Eymard, Alizon M.; Boursier, Eric V.; Trottet, Lionel; Bamborough, Paul; Clark, Hugh; Chung, Chun-wa; Cutler, Leanne; Demont, Emmanuel H.; Kaur, Rejbinder; Lewis, Antonia J.; Schilling, Mark B.; Soden, Peter E.; Taylor, Simon; Walker, Ann L.; Walker, Matthew D.; Prinjha, Rab K.; Nicodeme, Edwige
    Journal of Medicinal Chemistry (2014), 57 (19), 8111-8131CODEN: JMCMAR; ISSN:0022-2623. (American Chemical Society)
    Through their function as epigenetic readers of the histone code, the BET family of bromodomain-contg. proteins regulate expression of multiple genes of therapeutic relevance, including those involved in tumor cell growth and inflammation. BET bromodomain inhibitors have profound antiproliferative and anti-inflammatory effects which translate into efficacy in oncol. and inflammation models, and the first compds. have now progressed into clin. trials. The exciting biol. of the BETs has led to great interest in the discovery of novel inhibitor classes. Here we describe the identification of a novel tetrahydroquinoline series through up-regulation of apolipoprotein A1 and the optimization into potent compds. active in murine models of septic shock and neuroblastoma. At the mol. level, these effects are produced by inhibition of BET bromodomains. X-ray crystallog. reveals the interactions explaining the structure-activity relationships of binding. The resulting lead mol., I-BET726, represents a new, potent, and selective class of tetrahydroquinoline-based BET inhibitors.
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  17. 17
    Aldeghi, M.; Heifetz, A.; Bodkin, M. J.; Knapp, S.; Biggin, P. C. Accurate calculation of the absolute free energy of binding for drug molecules Chem. Sci. 2016, 7 (1) 207– 218 DOI: 10.1039/C5SC02678D
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    17
    Accurate calculation of the absolute free energy of binding for drug molecules
    Aldeghi, Matteo; Heifetz, Alexander; Bodkin, Michael J.; Knapp, Stefan; Biggin, Philip C.
    Chemical Science (2016), 7 (1), 207-218CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    Accurate prediction of binding affinities has been a central goal of computational chem. for decades, yet remains elusive. Despite good progress, the required accuracy for use in a drug-discovery context has not been consistently achieved for drug-like mols. Here, we perform abs. free energy calcns. based on a thermodn. cycle for a set of diverse inhibitors binding to bromodomain-contg. protein 4 (BRD4) and demonstrate that a mean abs. error of 0.6 kcal mol-1 can be achieved. We also show a similar level of accuracy (1.0 kcal mol-1) can be achieved in pseudo prospective approach. Bromodomains are epigenetic mark readers that recognize acetylation motifs and regulate gene transcription, and are currently being investigated as therapeutic targets for cancer and inflammation. The unprecedented accuracy offers the exciting prospect that the binding free energy of drug-like compds. can be predicted for pharmacol. relevant targets.
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  18. 18
    Lindorff-Larsen, K.; Piana, S.; Palmo, K.; Maragakis, P.; Klepeis, J. L.; Dror, R. O.; Shaw, D. E. Improved side-chain torsion potentials for the Amber ff99SB protein force field Proteins: Struct., Funct., Genet. 2010, 78 (8) 1950– 1958 DOI: 10.1002/prot.22711
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    18
    Improved side-chain torsion potentials for the Amber ff99SB protein force field
    Lindorff-Larsen, Kresten; Piana, Stefano; Palmo, Kim; Maragakis, Paul; Klepeis, John L.; Dror, Ron O.; Shaw, David E.
    Proteins: Structure, Function, and Bioinformatics (2010), 78 (8), 1950-1958CODEN: PSFBAF ISSN:. (Wiley-Liss, Inc.)
    Recent advances in hardware and software have enabled increasingly long mol. dynamics (MD) simulations of biomols., exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, the authors further advance simulation accuracy by improving the amino acid side-chain torsion potentials of the Amber ff99SB force field. First, the authors used simulations of model alpha-helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, the authors optimized the side-chain torsion potentials of these residues to match new, high-level quantum-mech. calcns. Finally, the authors used microsecond-timescale MD simulations in explicit solvent to validate the resulting force field against a large set of exptl. NMR measurements that directly probe side-chain conformations. The new force field, which the authors have termed Amber ff99SB-ILDN, exhibits considerably better agreement with the NMR data. Proteins 2010. © 2010 Wiley-Liss, Inc.
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  19. 19
    Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and testing of a general amber force field J. Comput. Chem. 2004, 25 (9) 1157– 1174 DOI: 10.1002/jcc.20035
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    19
    Development and testing of a general Amber force field
    Wang, Junmei; Wolf, Romain M.; Caldwell, James W.; Kollman, Peter A.; Case, David A.
    Journal of Computational Chemistry (2004), 25 (9), 1157-1174CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    We describe here a general Amber force field (GAFF) for org. mols. GAFF is designed to be compatible with existing Amber force fields for proteins and nucleic acids, and has parameters for most org. and pharmaceutical mols. that are composed of H, C, N, O, S, P, and halogens. It uses a simple functional form and a limited no. of atom types, but incorporates both empirical and heuristic models to est. force consts. and partial at. charges. The performance of GAFF in test cases is encouraging. In test I, 74 crystallog. structures were compared to GAFF minimized structures, with a root-mean-square displacement of 0.26 Å, which is comparable to that of the Tripos 5.2 force field (0.25 Å) and better than those of MMFF 94 and CHARMm (0.47 and 0.44 Å, resp.). In test II, gas phase minimizations were performed on 22 nucleic acid base pairs, and the minimized structures and intermol. energies were compared to MP2/6-31G* results. The RMS of displacements and relative energies were 0.25 Å and 1.2 kcal/mol, resp. These data are comparable to results from Parm99/RESP (0.16 Å and 1.18 kcal/mol, resp.), which were parameterized to these base pairs. Test III looked at the relative energies of 71 conformational pairs that were used in development of the Parm99 force field. The RMS error in relative energies (compared to expt.) is about 0.5 kcal/mol. GAFF can be applied to wide range of mols. in an automatic fashion, making it suitable for rational drug design and database searching.
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  20. 20
    Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A., Gaussian 03; Gaussian, Inc.: Wallingford, CT, 2004.
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  21. 21
    Case, D. A.; Cheatham, T. E., 3rd; Darden, T.; Gohlke, H.; Luo, R.; Merz, K. M., Jr.; Onufriev, A.; Simmerling, C.; Wang, B.; Woods, R. J. The Amber biomolecular simulation programs J. Comput. Chem. 2005, 26 (16) 1668– 1688 DOI: 10.1002/jcc.20290
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    21
    The amber biomolecular simulation programs
    Case, David A.; Cheatham, Thomas E., III; Darden, Tom; Gohlke, Holger; Luo, Ray; Merz, Kenneth M., Jr.; Onufriev, Alexey; Simmerling, Carlos; Wang, Bing; Woods, Robert J.
    Journal of Computational Chemistry (2005), 26 (16), 1668-1688CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    The authors describe the development, current features, and some directions for future development of the Amber package of computer programs. This package evolved from a program that was constructed in the late 1970s to do Assisted Model Building with Energy Refinement, and now contains a group of programs embodying a no. of powerful tools of modern computational chem., focused on mol. dynamics and free energy calcns. of proteins, nucleic acids, and carbohydrates.
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  22. 22
    Laio, A.; Gervasio, F. L. Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science Rep. Prog. Phys. 2008, 71 (12) 126601 DOI: 10.1088/0034-4885/71/12/126601
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    22
    Metadynamics: a method to stimulate rare events and reconstruct the free energy in biophysics, chemistry and material science
    Laio, Alessandro; Gervasio, Francesco L.
    Reports on Progress in Physics (2008), 71 (12), 126601/1-126601/22CODEN: RPPHAG; ISSN:0034-4885. (Institute of Physics Publishing)
    A review. Metadynamics is a powerful algorithm that can be used both for reconstructing the free energy and for accelerating rare events in systems described by complex Hamiltonians, at the classical or at the quantum level. In the algorithm the normal evolution of the system is biased by a history-dependent potential constructed as a sum of Gaussians centered along the trajectory followed by a suitably chosen set of collective variables. The sum of Gaussians is exploited for reconstructing iteratively an estimator of the free energy and forcing the system to escape from local min. This review is intended to provide a comprehensive description of the algorithm, with a focus on the practical aspects that need to be addressed when one attempts to apply metadynamics to a new system: (i) the choice of the appropriate set of collective variables; (ii) the optimal choice of the metadynamics parameters and (iii) how to control the error and ensure convergence of the algorithm.
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  23. 23
    Lin, Y. L.; Aleksandrov, A.; Simonson, T.; Roux, B. An overview of electrostatic free energy computations for solutions and proteins J. Chem. Theory Comput. 2014, 10 (7) 2690– 2709 DOI: 10.1021/ct500195p
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    23
    An Overview of Electrostatic Free Energy Computations for Solutions and Proteins
    Lin, Yen-Lin; Aleksandrov, Alexey; Simonson, Thomas; Roux, Benoit
    Journal of Chemical Theory and Computation (2014), 10 (7), 2690-2709CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    A review. Free energy simulations for electrostatic and charging processes in complex mol. systems encounter specific difficulties owing to the long-range, 1/r Coulomb interaction. To calc. the solvation free energy of a simple ion, it is essential to take into account the polarization of nearby solvent but also the electrostatic potential drop across the liq.-gas boundary, however distant. The latter does not exist in a simulation model based on periodic boundary conditions because there is no phys. boundary to the system. An important consequence is that the ref. value of the electrostatic potential is not an ion in a vacuum. Also, in an infinite system, the electrostatic potential felt by a perturbing charge is conditionally convergent and dependent on the choice of computational conventions. Furthermore, with Ewald lattice summation and tinfoil conducting boundary conditions, the charges experience a spurious shift in the potential that depends on the details of the simulation system such as the vol. fraction occupied by the solvent. All these issues can be handled with established computational protocols, as reviewed here and illustrated for several small ions and three solvated proteins.
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  24. 24
    Wan, S.; Knapp, B.; Wright, D. W.; Deane, C. M.; Coveney, P. V. Rapid, precise, and reproducible prediction of peptide-MHC binding affinities from molecular dynamics that correlate well with experiment J. Chem. Theory Comput. 2015, 11 (7) 3346– 3356 DOI: 10.1021/acs.jctc.5b00179
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    24
    Rapid, precise, and reproducible prediction of peptide-MHC binding affinities from molecular dynamics that correlate well with experiment
    Wan, Shunzhou; Knapp, Bernhard; Wright, David W.; Deane, Charlotte M.; Coveney, Peter V.
    Journal of Chemical Theory and Computation (2015), 11 (7), 3346-3356CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The presentation of potentially pathogenic peptides by major histocompatibility complex (MHC) mols. is one of the most important processes in adaptive immune defense. Prediction of peptide-MHC (pMHC) binding affinities is therefore a principal objective of theor. immunol. Machine learning techniques achieve good results if substantial exptl. training data are available. Approaches based on structural information become necessary if sufficiently similar training data are unavailable for a specific MHC allele, although they have often been deemed to lack accuracy. In this study, we use a free energy method to rank the binding affinities of 12 diverse peptides bound by a class I MHC mol. HLA-A*02:01. The method is based on enhanced sampling of mol. dynamics calcns. in combination with a continuum solvent approxn. and includes ests. of the configurational entropy based on either a one or a three trajectory protocol. It produces precise and reproducible free energy ests. which correlate well with exptl. measurements. If the results are combined with an amino acid hydrophobicity scale, then an extremely good ranking of peptide binding affinities emerges. Our approach is rapid, robust, and applicable to a wide range of ligand-receptor interactions without further adjustment.
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  25. 25
    Bhati, A. P.; Wan, S.; Wright, D. W.; Coveney, P. V. Rapid, accurate, precise and reliable relative free energy prediction using ensemble based thermodynamic integration J. Chem. Theory Comput. 2016,  DOI: 10.1021/acs.jctc.6b00979
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  26. 26
    Kollman, P. A.; Massova, I.; Reyes, C.; Kuhn, B.; Huo, S.; Chong, L.; Lee, M.; Lee, T.; Duan, Y.; Wang, W.; Donini, O.; Cieplak, P.; Srinivasan, J.; Case, D. A.; Cheatham, T. E., III Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models Acc. Chem. Res. 2000, 33 (12) 889– 897 DOI: 10.1021/ar000033j
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    26
    Calculating Structures and Free Energies of Complex Molecules: Combining Molecular Mechanics and Continuum Models
    Kollman, Peter A.; Massova, Irina; Reyes, Carolina; Kuhn, Bernd; Huo, Shuanghong; Chong, Lillian; Lee, Matthew; Lee, Taisung; Duan, Yong; Wang, Wei; Donini, Oreola; Cieplak, Piotr; Srinivasan, Jaysharee; Case, David A.; Cheatham, Thomas E., III
    Accounts of Chemical Research (2000), 33 (12), 889-897CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
    A review, with 63 refs. A historical perspective on the application of mol. dynamics (MD) to biol. macromols. is presented. Recent developments combining state-of-the-art force fields with continuum solvation calcns. have allowed us to reach the fourth era of MD applications in which one can often derive both accurate structure and accurate relative free energies from mol. dynamics trajectories. We illustrate such applications on nucleic acid duplexes, RNA hairpins, protein folding trajectories, and protein-ligand, protein-protein, and protein-nucleic acid interactions.
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  27. 27
    Wright, D. W.; Hall, B. A.; Kenway, O. A.; Jha, S.; Coveney, P. V. Computing Clinically Relevant Binding Free Energies of HIV-1 Protease Inhibitors J. Chem. Theory Comput. 2014, 10 (3) 1228– 1241 DOI: 10.1021/ct4007037
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    27
    Computing Clinically Relevant Binding Free Energies of HIV-1 Protease Inhibitors
    Wright, David W.; Hall, Benjamin A.; Kenway, Owain A.; Jha, Shantenu; Coveney, Peter V.
    Journal of Chemical Theory and Computation (2014), 10 (3), 1228-1241CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The use of mol. simulation to est. the strength of macromol. binding free energies is becoming increasingly widespread, with goals ranging from lead optimization and enrichment in drug discovery to personalizing or stratifying treatment regimes. To realize the potential of such approaches to predict new results, not merely to explain previous exptl. findings, it is necessary that the methods used are reliable and accurate, and that their limitations are thoroughly understood. However, the computational cost of atomistic simulation techniques such as mol. dynamics (MD) has meant that until recently little work has focused on validating and verifying the available free energy methodologies, with the consequence that many of the results published in the literature are not reproducible. Here, we present a detailed anal. of two of the most popular approx. methods for calcg. binding free energies from mol. simulations, mol. mechanics Poisson-Boltzmann surface area (MMPBSA) and mol. mechanics generalized Born surface area (MMGBSA), applied to the nine FDA-approved HIV-1 protease inhibitors. Our results show that the values obtained from replica simulations of the same protease-drug complex, differing only in initially assigned atom velocities, can vary by as much as 10 kcal mol-1, which is greater than the difference between the best and worst binding inhibitors under investigation. Despite this, anal. of ensembles of simulations producing 50 trajectories of 4 ns duration leads to well converged free energy ests. For seven inhibitors, we find that with correctly converged normal mode ests. of the configurational entropy, we can correctly distinguish inhibitors in agreement with exptl. data for both the MMPBSA and MMGBSA methods and thus have the ability to rank the efficacy of binding of this selection of drugs to the protease (no account is made for free energy penalties assocd. with protein distortion leading to the over estn. of the binding strength of the two largest inhibitors ritonavir and atazanavir). We obtain improved rankings and ests. of the relative binding strengths of the drugs by using a novel combination of MMPBSA/MMGBSA with normal mode entropy ests. and the free energy of assocn. calcd. directly from simulation trajectories. Our work provides a thorough assessment of what is required to produce converged and hence reliable free energies for protein-ligand binding.
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  28. 28
    Genheden, S.; Ryde, U. The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities Expert Opin. Drug Discovery 2015, 10 (5) 449– 461 DOI: 10.1517/17460441.2015.1032936
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    The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities
    Genheden, Samuel; Ryde, Ulf
    Expert Opinion on Drug Discovery (2015), 10 (5), 449-461CODEN: EODDBX; ISSN:1746-0441. (Informa Healthcare)
    Introduction: The mol. mechanics energies combined with the Poisson-Boltzmann or generalized Born and surface area continuum solvation (MM/PBSA and MM/GBSA) methods are popular approaches to est. the free energy of the binding of small ligands to biol. macromols. They are typically based on mol. dynamics simulations of the receptor-ligand complex and are therefore intermediate in both accuracy and computational effort between empirical scoring and strict alchem. perturbation methods. They have been applied to a large no. of systems with varying success. Areas covered: The authors review the use of MM/PBSA and MM/GBSA methods to calc. ligand-binding affinities, with an emphasis on calibration, testing and validation, as well as attempts to improve the methods, rather than on specific applications. Expert opinion: MM/PBSA and MM/GBSA are attractive approaches owing to their modular nature and that they do not require calcns. on a training set. They have been used successfully to reproduce and rationalize exptl. findings and to improve the results of virtual screening and docking. However, they contain several crude and questionable approxns., for example, the lack of conformational entropy and information about the no. and free energy of water mols. in the binding site. Moreover, there are many variants of the method and their performance varies strongly with the tested system. Likewise, most attempts to ameliorate the methods with more accurate approaches, for example, quantum-mech. calcns., polarizable force fields or improved solvation have deteriorated the results.
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  29. 29
    Swanson, J. M.; Henchman, R. H.; McCammon, J. A. Revisiting free energy calculations: a theoretical connection to MM/PBSA and direct calculation of the association free energy Biophys. J. 2004, 86, 67– 74 DOI: 10.1016/S0006-3495(04)74084-9
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    The prediction of abs. ligand-receptor binding affinities is essential in a wide range of biophys. queries, from the study of protein-protein interactions to structure-based drug design. End-point free energy methods, such as the Mol. Mechanics Poisson-Boltzmann Surface Area (MM/PBSA) model, have received much attention and widespread application in recent literature. These methods benefit from computational efficiency as only the initial and final states of the system are evaluated, yet there remains a need for strengthening their theor. foundation. Here a clear connection between statistical thermodn. and end-point free energy models is presented. The importance of the assocn. free energy, arising from one mol.'s loss of translational and rotational freedom from the std. state concn., is addressed. A novel method for calcg. this quantity directly from a mol. dynamics simulation is described. The challenges of accounting for changes in the protein conformation and its fluctuations from sep. simulations are discussed. A simple first-order approxn. of the configuration integral is presented to lay the groundwork for future efforts. This model has been applied to FKBP12, a small immunophilin that has been widely studied in the drug industry for its potential immunosuppressive and neuroregenerative effects.
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    We report an efficient implementation of the finite-difference Poisson-Boltzmann solvent model based on the Modified Incomplete Cholsky Conjugate Gradient algorithm, which gives rather impressive performance for both static and dynamic systems. This is achieved by implementing the algorithm with Eisenstat's two optimizations, utilizing the electrostatic update in simulations, and applying prudent approxns., including: relaxing the convergence criterion, not updating Poisson-Boltzmann-related forces every step, and using electrostatic focusing. It is also possible to markedly accelerate the supporting routines that are used to set up the calcns. and to obtain energies and forces. The resulting finite difference Poisson-Boltzmann method delivers efficiency comparable to the distance-dependent dielec. model for a system tested, HIV Protease, making it a strong candidate for soln.-phase mol. dynamics simulations. Further, the finite difference method includes all intra-solute electrostatic interactions, whereas the distance dependent dielec. calcns. use a 15-Å cutoff. The speed of our numerical finite difference method is comparable to that of the pair-wise Generalized Born approxn. to the Poisson-Boltzmann method.
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    NAMD is a parallel mol. dynamics code designed for high-performance simulation of large biomol. systems. NAMD scales to hundreds of processors on high-end parallel platforms, as well as tens of processors on low-cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats. This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical mol. dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temp. and pressure controls used. Features for steering the simulation across barriers and for calcg. both alchem. and conformational free energy differences are presented. The motivations for and a roadmap to the internal design of NAMD, implemented in C++ and based on Charm++ parallel objects, are outlined. The factors affecting the serial and parallel performance of a simulation are discussed. Finally, typical NAMD use is illustrated with representative applications to a small, a medium, and a large biomol. system, highlighting particular features of NAMD, for example, the Tcl scripting language. The article also provides a list of the key features of NAMD and discusses the benefits of combining NAMD with the mol. graphics/sequence anal. software VMD and the grid computing/collab. software BioCoRE. NAMD is distributed free of charge with source code at www.ks.uiuc.edu.
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    Accurate calcn. of important thermodn. properties, such as macromol. binding free energies, is one of the principal goals of mol. dynamics simulations. However, single long simulation frequently produces incorrectly converged quant. results due to inadequate sampling of conformational space in a feasible wall-clock time. Multiple short (ensemble) simulations have been shown to explore conformational space more effectively than single long simulations, but the two methods have not yet been thermodynamically compared. Here we show that, for end-state binding free energy detn. methods, ensemble simulations exhibit significantly enhanced thermodn. sampling over single long simulations and result in accurate and converged relative binding free energies that are reproducible to within 0.5 kcal/mol. Completely correct ranking is obtained for six HIV-1 protease variants bound to lopinavir with a correlation coeff. of 0.89 and a mean relative deviation from expt. of 0.9 kcal/mol. Multidrug resistance to lopinavir is enthalpically driven and increases through a decrease in the protein-ligand van der Waals interaction, principally due to the V82A/I84V mutation, and an increase in net electrostatic repulsion due to water-mediated disruption of protein-ligand interactions in the catalytic region. Furthermore, we correctly rank, to within 1 kcal/mol of expt., the substantially increased chem. potency of lopinavir binding to the wild-type protease compared to saquinavir and show that lopinavir takes advantage of a decreased net electrostatic repulsion to confer enhanced binding. Our approach is dependent on the combined use of petascale computing resources and on an automated simulation workflow to attain the required level of sampling and turn around time to obtain the results, which can be as little as three days. This level of performance promotes integration of such methodol. with clin. decision support systems for the optimization of patient-specific therapy.
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    A review. Recent calorimetric studies of interactions between small mols. and biomol. targets have generated renewed interest in the phenomenon of entropy-enthalpy compensation. In these studies, entropic and enthalpic contributions to binding are obsd. to vary substantially and in an opposing manner as the ligand or protein is modified, whereas the binding free energy varies little. In severe examples, engineered enthalpic gains can lead to completely compensating entropic penalties, frustrating ligand design. Here, we examine the evidence for compensation, as well as its potential origins, prevalence, severity, and ramifications for ligand engineering. We find the evidence for severe compensation to be weak in light of the large magnitude of and correlation between errors in exptl. measurements of entropic and enthalpic contributions to binding, though a limited form of compensation may be common. Given the difficulty of predicting or measuring entropic and enthalpic changes to useful precision, or using this information in design, we recommend ligand engineering efforts instead focus on computational and exptl. methodologies to directly assess changes in binding free energy.
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    Zhu, Yong-Liang; Beroza, Paul; Artis, Dean R.
    Journal of Chemical Information and Modeling (2014), 54 (2), 462-469CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    Water is the natural medium of mols. in the cell and plays an important role in protein structure, function and interaction with small mol. ligands. However, the widely used mol. mechanics Poisson-Boltzmann surface area (MM/PBSA) method for binding energy calcn. does not explicitly take account of water mols. that mediate key protein-ligand interactions. We have developed a protocol to include water mols. that mediate ligand-protein interactions as part of the protein structure in calcn. of MM/PBSA binding energies (a method we refer to as water-MM/PBSA) for a series of JNK3 kinase inhibitors. Improved correlation between water-MM/PBSA binding energies and exptl. IC50 values was obtained compared to that obtained from classical MM/PBSA binding energy. This improved correlation was further validated using sets of neuraminidase and avidin inhibitors. The obsd. improvement, however, appears to be limited to systems in which there are water-mediated ligand-protein hydrogen bond interactions. We conclude that the water-MM/PBSA method performs better than classical MM/PBSA in predicting binding affinities when water mols. play a direct role in mediating ligand-protein hydrogen bond interactions.
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    In the drug discovery process, accurate methods of computing the affinity of small mols. with a biol. target are strongly needed. This is particularly true for mol. docking and virtual screening methods, which use approximated scoring functions and struggle in estg. binding energies in correlation with exptl. values. Among the various methods, MM-PBSA (mol. mechanics Poisson-Boltzmann surface area) and MM-GBSA (mol. mechanics-generalized Born surface area) are emerging as useful and effective approaches. Although these methods are typically applied to large collections of equilibrated structures of protein-ligand complexes sampled during mol. dynamics in water, the possibility to reliably est. ligand affinity using a single energy-minimized structure and implicit solvation models has not been explored in sufficient detail. Herein, the authors thoroughly investigate this hypothesis by comparing different methods for the generation of protein-ligand complexes and diverse methods for free energy prediction for their ability to correlate with exptl. values. The methods were tested on a series of structurally diverse inhibitors of Plasmodium falciparum DHFR (dihydrofolate reductase) with known binding mode and measured affinities. The results showed that correlations between MM-PBSA or MM-GBSA binding free energies with exptl. affinities were in most cases excellent. Importantly, the authors found that correlations obtained with the use of a single protein-ligand minimized structure and with implicit solvation models were similar to those obtained after averaging over multiple MD snapshots with explicit water mols., with consequent save of computing time without loss of accuracy. When applied to a virtual screening expt., such an approach proved to discriminate between true binders and decoy mols. and yielded significantly better enrichment curves. © 2009 Wiley Periodicals, Inc. J Comput Chem, 31: 797-810, 2010.
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    Reynolds, Charles H.; Holloway, M. Katharine
    ACS Medicinal Chemistry Letters (2011), 2 (6), 433-437CODEN: AMCLCT; ISSN:1948-5875. (American Chemical Society)
    Anal. of the exptl. binding thermodn. for approx. 100 protein-ligand complexes provides important insights into the factors governing ligand affinity and efficiency. The commonly accepted correlation between enthalpy and -TΔS is clearly obsd. for this relatively diverse data set. It is also clear that affinity (i.e., ΔG) is not generally correlated to either enthalpy or -TΔS. This is a worrisome trend since the vast majority of computational structure-based design is carried out using interaction energies for one, or at most a few, ligand poses. As such, these energies are most closely comparable to enthalpies not free energies. Closer inspection of the data shows that in a few cases the enthalpy (or -TΔS) is correlated with free energy. It is tempting to speculate that this could be an important consideration as to why some targets are readily amenable to modeling and others are not. Addnl., anal. of the enthalpy and -TΔS efficiencies shows that the trends obsd. for ligand efficiencies with respect to mol. size are primarily a consequence of enthalpic, not entropic, effects.
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  2. Agastya P. Bhati, Art Hoti, Andrew Potterton, Mateusz K. Bieniek, Peter V. Coveney. Long Time Scale Ensemble Methods in Molecular Dynamics: Ligand–Protein Interactions and Allostery in SARS-CoV-2 Targets. Journal of Chemical Theory and Computation 2023, 19 (11) , 3359-3378. https://doi.org/10.1021/acs.jctc.3c00020
  3. Margarita Stampelou, Anna Suchankova, Efpraxia Tzortzini, Lakshiv Dhingra, Kerry Barkan, Nikolaos Lougiakis, Panagiotis Marakos, Nicole Pouli, Graham Ladds, Antonios Kolocouris. Dual A1/A3 Adenosine Receptor Antagonists: Binding Kinetics and Structure−Activity Relationship Studies Using Mutagenesis and Alchemical Binding Free Energy Calculations. Journal of Medicinal Chemistry 2022, 65 (19) , 13305-13327. https://doi.org/10.1021/acs.jmedchem.2c01123
  4. Alexander D. Wade, Agastya P. Bhati, Shunzhou Wan, Peter V. Coveney. Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy, Precision, and Reproducibility. Journal of Chemical Theory and Computation 2022, 18 (6) , 3972-3987. https://doi.org/10.1021/acs.jctc.2c00114
  5. Shunzhou Wan, Agastya P. Bhati, David W. Wright, Ian D. Wall, Alan P. Graves, Darren Green, Peter V. Coveney. Ensemble Simulations and Experimental Free Energy Distributions: Evaluation and Characterization of Isoxazole Amides as SMYD3 Inhibitors. Journal of Chemical Information and Modeling 2022, 62 (10) , 2561-2570. https://doi.org/10.1021/acs.jcim.2c00255
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  21. Agastya P. Bhati, Shunzhou Wan, David W. Wright, and Peter V. Coveney . Rapid, Accurate, Precise, and Reliable Relative Free Energy Prediction Using Ensemble Based Thermodynamic Integration. Journal of Chemical Theory and Computation 2017, 13 (1) , 210-222. https://doi.org/10.1021/acs.jctc.6b00979
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  26. Arnaldo F. Silva, Ellen E. Guest, Bruno N. Falcone, Stephen D. Pickett, David M. Rogers, Jonathan D. Hirst. Free energy perturbation calculations of tetrahydroquinolines complexed to the first bromodomain of BRD4. Molecular Physics 2023, 121 (9-10) https://doi.org/10.1080/00268976.2022.2124201
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  28. Shunzhou Wan, Agastya P. Bhati, David W. Wright, Alexander D. Wade, Gary Tresadern, Herman van Vlijmen, Peter V. Coveney. The performance of ensemble-based free energy protocols in computing binding affinities to ROS1 kinase. Scientific Reports 2022, 12 (1) https://doi.org/10.1038/s41598-022-13319-6
  29. Manas Bandyopadhyay, Utsav Sengupta, Muthaimanoj Periyasamy, Sudipta Mukhopadhyay, Avantika Hasija, Deepak Chopra, Namık Özdemir, Musa A. Said, Mrinal K. Bera. Cu(II)(PhOMe-Salophen) Complex: Greener Pasture Biological Study, XRD/HAS Interactions, and MEP. Russian Journal of Inorganic Chemistry 2022, 67 (S2) , S114-S127. https://doi.org/10.1134/S0036023623700274
  30. Shunzhou Wan, Agastya P. Bhati, Alexander D. Wade, Dario Alfè, Peter V. Coveney. Thermodynamic and structural insights into the repurposing of drugs that bind to SARS-CoV-2 main protease. Molecular Systems Design & Engineering 2022, 7 (2) , 123-131. https://doi.org/10.1039/D1ME00124H
  31. Agastya P. Bhati, Shunzhou Wan, Dario Alfè, Austin R. Clyde, Mathis Bode, Li Tan, Mikhail Titov, Andre Merzky, Matteo Turilli, Shantenu Jha, Roger R. Highfield, Walter Rocchia, Nicola Scafuri, Sauro Succi, Dieter Kranzlmüller, Gerald Mathias, David Wifling, Yann Donon, Alberto Di Meglio, Sofia Vallecorsa, Heng Ma, Anda Trifan, Arvind Ramanathan, Tom Brettin, Alexander Partin, Fangfang Xia, Xiaotan Duan, Rick Stevens, Peter V. Coveney. Pandemic drugs at pandemic speed: infrastructure for accelerating COVID-19 drug discovery with hybrid machine learning- and physics-based simulations on high-performance computers. Interface Focus 2021, 11 (6) https://doi.org/10.1098/rsfs.2021.0018
  32. Shunzhou Wan, Deepak Kumar, Valentin Ilyin, Ussama Al Homsi, Gulab Sher, Alexander Knuth, Peter V. Coveney. The effect of protein mutations on drug binding suggests ensuing personalised drug selection. Scientific Reports 2021, 11 (1) https://doi.org/10.1038/s41598-021-92785-w
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  • Abstract

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    Figure 1

    Figure 1. Bromodomain inhibitor I-BET726 and its binding mode in BRD4-BD1. Two views are displayed for the binding mode (PDB ID: 4BJX (15)), in which I-BET726 (16) is represented as stick in cyan/blue/red/green, the protein is shown as cartoon in silver, the crystallographic water molecules are shown as red balls, and clipped protein surfaces are shown in orange.

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    Figure 2

    Figure 2. Correlation and standard errors of the calculated binding free energies from two independent studies of the BRD4-ligand models performed on BlueWonder2 and ARCHER. (a) Correlation of the predictions, including all rotamers, from 1-traj calculations performed on BlueWonder2 (BW2, horizontal axis) and ARCHER (vertical axis). Solid line, regression of the data using means of the calculated free energies; dotted line, 1:1 ideal regression. (b) the averages and their standard errors from the two separate calculations. One rotamer is used for each ligand.

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    Figure 3

    Figure 3. Calculated binding free energies from simulations on BlueWonder2 and ARCHER. The ligands are numbered as per Table 1. Circles with red/blue colors are the results based on studies with different rotamers. The circles with crosses are the final results with selected rotamers which are chosen on the basis of the sum of energies Gligand and ΔGbinding (see eq 1). All of the calculated binding free energies are associated with standard errors of less than 1.7 kcal/mol, and are not shown in the figures for reasons of clarity.

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    Figure 4

    Figure 4. Spearman ranking correlations of the calculated binding free energies and the experimental data from 1-traj (left panel), 2-traj (center), and 3-traj (right panel) ESMACS approaches. The equations on the subfigures indicate the calculations used in each case. The subscripts (com/rec/lig) and the superscripts (com/lig) in the equations indicate the components (complexes, receptor, and ligands) and the simulations (complexes and free ligands), respectively. The ligands with modifications at the R2-position of the tetrahydroquinoline are marked with crosses; they are all significantly improved in the 2- and 3-trajectory version. The standard errors, which are 0.19–0.34 kcal/mol for the 1-traj and 1.02–1.71 kcal/mol for the 2- and 3-traj approaches, are not shown for reasons of clarity. They are calculated using a bootstrapping method (see Supporting Information). The 2- and 3-traj approaches have similar errors because the energy of the receptor is treated as a constant and hence the uncertainties are dominated by the energies of the complexes.

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    Figure 5

    Figure 5. Improvement of the predictions by inclusion of the adaptation free energies of the receptor and the ligands: (a) the binding free energy changes between the 1-traj (black circles) and 2-traj (magenta circles) indicate the relative adaptation energies of the receptor; those between the 2-traj (magenta circles) and 3-traj (orange circles) show the adaptation energies of the ligands. The adaptation energies can be seen more clearly in panels b as a function of binding affinities, and in panels c for each ligand.

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    Figure 6

    Figure 6. Correlations of free energy components and the experimental data from 3-traj approaches. Both bonded and nonbonded energy terms contribute to the ranking of binding affinities. Their combination (the MMPBSA energy) exhibits a better correlation with experimental data than the components themselves.

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    Figure 7

    Figure 7. Correlations of the calculated binding free energy differences from the TIES study and from experimental measurement. The standard error bars from the TIES calculations are all no greater than 0.2 kcal/mol.

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    Figure 8

    Figure 8. Calculated vs experimental binding free energies for ligands 1, 8, and 9 which are labeled in the 1-traj subfigure.

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    Figure 9

    Figure 9. Calculated vs experimental binding free energies for ligands 10, 11, and 12 which are labeled in the 1-traj subfigure.

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    Figure 10

    Figure 10. Correlations of the internal energy contributions to the calculated binding free energies and experimental measurement. The internal energy changes are calculated as the differences of the binding free energies between those from the 1-traj and 3-traj approaches: ΔΔGcalc = ΔGbinding3-traj – ΔGbinding1-traj.

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  • References

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      Automated Molecular Simulation Based Binding Affinity Calculator for Ligand-Bound HIV-1 Proteases
      Sadiq, S. Kashif; Wright, David; Watson, Simon J.; Zasada, Stefan J.; Stoica, Ileana; Coveney, Peter V.
      Journal of Chemical Information and Modeling (2008), 48 (9), 1909-1919CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      The successful application of high throughput mol. simulations to det. biochem. properties would be of great importance to the biomedical community if such simulations could be turned around in a clin. relevant timescale. An important example is the detn. of antiretroviral inhibitor efficacy against varying strains of HIV through calcn. of drug-protein binding affinities. We describe the Binding Affinity Calculator (BAC), a tool for the automated calcn. of HIV-1 protease-ligand binding affinities. The tool employs fully atomistic mol. simulations alongside the well established mol. mechanics Poisson-Boltzmann solvent accessible surface area (MMPBSA) free energy methodol. to enable the calcn. of the binding free energy of several ligand-protease complexes, including all nine FDA approved inhibitors of HIV-1 protease and seven of the natural substrates cleaved by the protease. This enables the efficacy of these inhibitors to be ranked across several mutant strains of the protease relative to the wildtype. BAC is a tool that utilizes the power provided by a computational grid to automate all of the stages required to compute free energies of binding: model prepn., equilibration, simulation, postprocessing, and data-marshaling around the generally widely distributed compute resources utilized. Such automation enables the mol. dynamics methodol. to be used in a high throughput manner not achievable by manual methods. This paper describes the architecture and workflow management of BAC and the function of each of its components. Given adequate compute resources, BAC can yield quant. information regarding drug resistance at the mol. level within 96 h. Such a timescale is of direct clin. relevance and can assist in decision support for the assessment of patient-specific optimal drug treatment and the subsequent response to therapy for any given genotype.
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    14. 14
      Groen, D.; Bhati, A. P.; Suter, J.; Hetherington, J.; Zasada, S. J.; Coveney, P. V. FabSim: Facilitating computational research through automation on large-scale and distributed e-infrastructures Comput. Phys. Commun. 2016, 207, 375– 385 DOI: 10.1016/j.cpc.2016.05.020
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      14
      FabSim: Facilitating computational research through automation on large-scale and distributed e-infrastructures
      Groen, Derek; Bhati, Agastya P.; Suter, James; Hetherington, James; Zasada, Stefan J.; Coveney, Peter V.
      Computer Physics Communications (2016), 207 (), 375-385CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      We present FabSim, a toolkit developed to simplify a range of computational tasks for researchers in diverse disciplines. FabSim is flexible, adaptable, and allows users to perform a wide range of tasks with ease. It also provides a systematic way to automate the use of resources, including HPC and distributed machines, and to make tasks easier to repeat by recording contextual information. To demonstrate this, we present three use cases where FabSim has enhanced our research productivity. These include simulating cerebrovascular bloodflow, modeling clay-polymer nanocomposites across multiple scales, and calcg. ligand-protein binding affinities.
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    15. 15
      Wyce, A.; Ganji, G.; Smitheman, K. N.; Chung, C. W.; Korenchuk, S.; Bai, Y.; Barbash, O.; Le, B.; Craggs, P. D.; McCabe, M. T.; Kennedy-Wilson, K. M.; Sanchez, L. V.; Gosmini, R. L.; Parr, N.; McHugh, C. F.; Dhanak, D.; Prinjha, R. K.; Auger, K. R.; Tummino, P. J. BET inhibition silences expression of MYCN and BCL2 and induces cytotoxicity in neuroblastoma tumor models PLoS One 2013, 8 (8) e72967 DOI: 10.1371/journal.pone.0072967
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    16. 16
      Gosmini, R.; Nguyen, V. L.; Toum, J.; Simon, C.; Brusq, J. M.; Krysa, G.; Mirguet, O.; Riou-Eymard, A. M.; Boursier, E. V.; Trottet, L.; Bamborough, P.; Clark, H.; Chung, C. W.; Cutler, L.; Demont, E. H.; Kaur, R.; Lewis, A. J.; Schilling, M. B.; Soden, P. E.; Taylor, S.; Walker, A. L.; Walker, M. D.; Prinjha, R. K.; Nicodeme, E. The discovery of I-BET726 (GSK1324726A), a potent tetrahydroquinoline ApoA1 up-regulator and selective BET bromodomain inhibitor J. Med. Chem. 2014, 57 (19) 8111– 8131 DOI: 10.1021/jm5010539
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      16
      The Discovery of I-BET726 (GSK1324726A), a Potent Tetrahydroquinoline ApoA1 Up-Regulator and Selective BET Bromodomain Inhibitor
      Gosmini, Romain; Nguyen, Van Loc; Toum, Jerome; Simon, Christophe; Brusq, Jean-Marie G.; Krysa, Gael; Mirguet, Olivier; Riou-Eymard, Alizon M.; Boursier, Eric V.; Trottet, Lionel; Bamborough, Paul; Clark, Hugh; Chung, Chun-wa; Cutler, Leanne; Demont, Emmanuel H.; Kaur, Rejbinder; Lewis, Antonia J.; Schilling, Mark B.; Soden, Peter E.; Taylor, Simon; Walker, Ann L.; Walker, Matthew D.; Prinjha, Rab K.; Nicodeme, Edwige
      Journal of Medicinal Chemistry (2014), 57 (19), 8111-8131CODEN: JMCMAR; ISSN:0022-2623. (American Chemical Society)
      Through their function as epigenetic readers of the histone code, the BET family of bromodomain-contg. proteins regulate expression of multiple genes of therapeutic relevance, including those involved in tumor cell growth and inflammation. BET bromodomain inhibitors have profound antiproliferative and anti-inflammatory effects which translate into efficacy in oncol. and inflammation models, and the first compds. have now progressed into clin. trials. The exciting biol. of the BETs has led to great interest in the discovery of novel inhibitor classes. Here we describe the identification of a novel tetrahydroquinoline series through up-regulation of apolipoprotein A1 and the optimization into potent compds. active in murine models of septic shock and neuroblastoma. At the mol. level, these effects are produced by inhibition of BET bromodomains. X-ray crystallog. reveals the interactions explaining the structure-activity relationships of binding. The resulting lead mol., I-BET726, represents a new, potent, and selective class of tetrahydroquinoline-based BET inhibitors.
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    17. 17
      Aldeghi, M.; Heifetz, A.; Bodkin, M. J.; Knapp, S.; Biggin, P. C. Accurate calculation of the absolute free energy of binding for drug molecules Chem. Sci. 2016, 7 (1) 207– 218 DOI: 10.1039/C5SC02678D
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      17
      Accurate calculation of the absolute free energy of binding for drug molecules
      Aldeghi, Matteo; Heifetz, Alexander; Bodkin, Michael J.; Knapp, Stefan; Biggin, Philip C.
      Chemical Science (2016), 7 (1), 207-218CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      Accurate prediction of binding affinities has been a central goal of computational chem. for decades, yet remains elusive. Despite good progress, the required accuracy for use in a drug-discovery context has not been consistently achieved for drug-like mols. Here, we perform abs. free energy calcns. based on a thermodn. cycle for a set of diverse inhibitors binding to bromodomain-contg. protein 4 (BRD4) and demonstrate that a mean abs. error of 0.6 kcal mol-1 can be achieved. We also show a similar level of accuracy (1.0 kcal mol-1) can be achieved in pseudo prospective approach. Bromodomains are epigenetic mark readers that recognize acetylation motifs and regulate gene transcription, and are currently being investigated as therapeutic targets for cancer and inflammation. The unprecedented accuracy offers the exciting prospect that the binding free energy of drug-like compds. can be predicted for pharmacol. relevant targets.
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    18. 18
      Lindorff-Larsen, K.; Piana, S.; Palmo, K.; Maragakis, P.; Klepeis, J. L.; Dror, R. O.; Shaw, D. E. Improved side-chain torsion potentials for the Amber ff99SB protein force field Proteins: Struct., Funct., Genet. 2010, 78 (8) 1950– 1958 DOI: 10.1002/prot.22711
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      18
      Improved side-chain torsion potentials for the Amber ff99SB protein force field
      Lindorff-Larsen, Kresten; Piana, Stefano; Palmo, Kim; Maragakis, Paul; Klepeis, John L.; Dror, Ron O.; Shaw, David E.
      Proteins: Structure, Function, and Bioinformatics (2010), 78 (8), 1950-1958CODEN: PSFBAF ISSN:. (Wiley-Liss, Inc.)
      Recent advances in hardware and software have enabled increasingly long mol. dynamics (MD) simulations of biomols., exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, the authors further advance simulation accuracy by improving the amino acid side-chain torsion potentials of the Amber ff99SB force field. First, the authors used simulations of model alpha-helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, the authors optimized the side-chain torsion potentials of these residues to match new, high-level quantum-mech. calcns. Finally, the authors used microsecond-timescale MD simulations in explicit solvent to validate the resulting force field against a large set of exptl. NMR measurements that directly probe side-chain conformations. The new force field, which the authors have termed Amber ff99SB-ILDN, exhibits considerably better agreement with the NMR data. Proteins 2010. © 2010 Wiley-Liss, Inc.
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    19. 19
      Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and testing of a general amber force field J. Comput. Chem. 2004, 25 (9) 1157– 1174 DOI: 10.1002/jcc.20035
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      19
      Development and testing of a general Amber force field
      Wang, Junmei; Wolf, Romain M.; Caldwell, James W.; Kollman, Peter A.; Case, David A.
      Journal of Computational Chemistry (2004), 25 (9), 1157-1174CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      We describe here a general Amber force field (GAFF) for org. mols. GAFF is designed to be compatible with existing Amber force fields for proteins and nucleic acids, and has parameters for most org. and pharmaceutical mols. that are composed of H, C, N, O, S, P, and halogens. It uses a simple functional form and a limited no. of atom types, but incorporates both empirical and heuristic models to est. force consts. and partial at. charges. The performance of GAFF in test cases is encouraging. In test I, 74 crystallog. structures were compared to GAFF minimized structures, with a root-mean-square displacement of 0.26 Å, which is comparable to that of the Tripos 5.2 force field (0.25 Å) and better than those of MMFF 94 and CHARMm (0.47 and 0.44 Å, resp.). In test II, gas phase minimizations were performed on 22 nucleic acid base pairs, and the minimized structures and intermol. energies were compared to MP2/6-31G* results. The RMS of displacements and relative energies were 0.25 Å and 1.2 kcal/mol, resp. These data are comparable to results from Parm99/RESP (0.16 Å and 1.18 kcal/mol, resp.), which were parameterized to these base pairs. Test III looked at the relative energies of 71 conformational pairs that were used in development of the Parm99 force field. The RMS error in relative energies (compared to expt.) is about 0.5 kcal/mol. GAFF can be applied to wide range of mols. in an automatic fashion, making it suitable for rational drug design and database searching.
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    20. 20
      Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A., Gaussian 03; Gaussian, Inc.: Wallingford, CT, 2004.
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    21. 21
      Case, D. A.; Cheatham, T. E., 3rd; Darden, T.; Gohlke, H.; Luo, R.; Merz, K. M., Jr.; Onufriev, A.; Simmerling, C.; Wang, B.; Woods, R. J. The Amber biomolecular simulation programs J. Comput. Chem. 2005, 26 (16) 1668– 1688 DOI: 10.1002/jcc.20290
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      21
      The amber biomolecular simulation programs
      Case, David A.; Cheatham, Thomas E., III; Darden, Tom; Gohlke, Holger; Luo, Ray; Merz, Kenneth M., Jr.; Onufriev, Alexey; Simmerling, Carlos; Wang, Bing; Woods, Robert J.
      Journal of Computational Chemistry (2005), 26 (16), 1668-1688CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      The authors describe the development, current features, and some directions for future development of the Amber package of computer programs. This package evolved from a program that was constructed in the late 1970s to do Assisted Model Building with Energy Refinement, and now contains a group of programs embodying a no. of powerful tools of modern computational chem., focused on mol. dynamics and free energy calcns. of proteins, nucleic acids, and carbohydrates.
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    22. 22
      Laio, A.; Gervasio, F. L. Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science Rep. Prog. Phys. 2008, 71 (12) 126601 DOI: 10.1088/0034-4885/71/12/126601
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      22
      Metadynamics: a method to stimulate rare events and reconstruct the free energy in biophysics, chemistry and material science
      Laio, Alessandro; Gervasio, Francesco L.
      Reports on Progress in Physics (2008), 71 (12), 126601/1-126601/22CODEN: RPPHAG; ISSN:0034-4885. (Institute of Physics Publishing)
      A review. Metadynamics is a powerful algorithm that can be used both for reconstructing the free energy and for accelerating rare events in systems described by complex Hamiltonians, at the classical or at the quantum level. In the algorithm the normal evolution of the system is biased by a history-dependent potential constructed as a sum of Gaussians centered along the trajectory followed by a suitably chosen set of collective variables. The sum of Gaussians is exploited for reconstructing iteratively an estimator of the free energy and forcing the system to escape from local min. This review is intended to provide a comprehensive description of the algorithm, with a focus on the practical aspects that need to be addressed when one attempts to apply metadynamics to a new system: (i) the choice of the appropriate set of collective variables; (ii) the optimal choice of the metadynamics parameters and (iii) how to control the error and ensure convergence of the algorithm.
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    23. 23
      Lin, Y. L.; Aleksandrov, A.; Simonson, T.; Roux, B. An overview of electrostatic free energy computations for solutions and proteins J. Chem. Theory Comput. 2014, 10 (7) 2690– 2709 DOI: 10.1021/ct500195p
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      23
      An Overview of Electrostatic Free Energy Computations for Solutions and Proteins
      Lin, Yen-Lin; Aleksandrov, Alexey; Simonson, Thomas; Roux, Benoit
      Journal of Chemical Theory and Computation (2014), 10 (7), 2690-2709CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      A review. Free energy simulations for electrostatic and charging processes in complex mol. systems encounter specific difficulties owing to the long-range, 1/r Coulomb interaction. To calc. the solvation free energy of a simple ion, it is essential to take into account the polarization of nearby solvent but also the electrostatic potential drop across the liq.-gas boundary, however distant. The latter does not exist in a simulation model based on periodic boundary conditions because there is no phys. boundary to the system. An important consequence is that the ref. value of the electrostatic potential is not an ion in a vacuum. Also, in an infinite system, the electrostatic potential felt by a perturbing charge is conditionally convergent and dependent on the choice of computational conventions. Furthermore, with Ewald lattice summation and tinfoil conducting boundary conditions, the charges experience a spurious shift in the potential that depends on the details of the simulation system such as the vol. fraction occupied by the solvent. All these issues can be handled with established computational protocols, as reviewed here and illustrated for several small ions and three solvated proteins.
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    24. 24
      Wan, S.; Knapp, B.; Wright, D. W.; Deane, C. M.; Coveney, P. V. Rapid, precise, and reproducible prediction of peptide-MHC binding affinities from molecular dynamics that correlate well with experiment J. Chem. Theory Comput. 2015, 11 (7) 3346– 3356 DOI: 10.1021/acs.jctc.5b00179
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      Rapid, precise, and reproducible prediction of peptide-MHC binding affinities from molecular dynamics that correlate well with experiment
      Wan, Shunzhou; Knapp, Bernhard; Wright, David W.; Deane, Charlotte M.; Coveney, Peter V.
      Journal of Chemical Theory and Computation (2015), 11 (7), 3346-3356CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The presentation of potentially pathogenic peptides by major histocompatibility complex (MHC) mols. is one of the most important processes in adaptive immune defense. Prediction of peptide-MHC (pMHC) binding affinities is therefore a principal objective of theor. immunol. Machine learning techniques achieve good results if substantial exptl. training data are available. Approaches based on structural information become necessary if sufficiently similar training data are unavailable for a specific MHC allele, although they have often been deemed to lack accuracy. In this study, we use a free energy method to rank the binding affinities of 12 diverse peptides bound by a class I MHC mol. HLA-A*02:01. The method is based on enhanced sampling of mol. dynamics calcns. in combination with a continuum solvent approxn. and includes ests. of the configurational entropy based on either a one or a three trajectory protocol. It produces precise and reproducible free energy ests. which correlate well with exptl. measurements. If the results are combined with an amino acid hydrophobicity scale, then an extremely good ranking of peptide binding affinities emerges. Our approach is rapid, robust, and applicable to a wide range of ligand-receptor interactions without further adjustment.
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    25. 25
      Bhati, A. P.; Wan, S.; Wright, D. W.; Coveney, P. V. Rapid, accurate, precise and reliable relative free energy prediction using ensemble based thermodynamic integration J. Chem. Theory Comput. 2016,  DOI: 10.1021/acs.jctc.6b00979
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    26. 26
      Kollman, P. A.; Massova, I.; Reyes, C.; Kuhn, B.; Huo, S.; Chong, L.; Lee, M.; Lee, T.; Duan, Y.; Wang, W.; Donini, O.; Cieplak, P.; Srinivasan, J.; Case, D. A.; Cheatham, T. E., III Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models Acc. Chem. Res. 2000, 33 (12) 889– 897 DOI: 10.1021/ar000033j
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      26
      Calculating Structures and Free Energies of Complex Molecules: Combining Molecular Mechanics and Continuum Models
      Kollman, Peter A.; Massova, Irina; Reyes, Carolina; Kuhn, Bernd; Huo, Shuanghong; Chong, Lillian; Lee, Matthew; Lee, Taisung; Duan, Yong; Wang, Wei; Donini, Oreola; Cieplak, Piotr; Srinivasan, Jaysharee; Case, David A.; Cheatham, Thomas E., III
      Accounts of Chemical Research (2000), 33 (12), 889-897CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
      A review, with 63 refs. A historical perspective on the application of mol. dynamics (MD) to biol. macromols. is presented. Recent developments combining state-of-the-art force fields with continuum solvation calcns. have allowed us to reach the fourth era of MD applications in which one can often derive both accurate structure and accurate relative free energies from mol. dynamics trajectories. We illustrate such applications on nucleic acid duplexes, RNA hairpins, protein folding trajectories, and protein-ligand, protein-protein, and protein-nucleic acid interactions.
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    27. 27
      Wright, D. W.; Hall, B. A.; Kenway, O. A.; Jha, S.; Coveney, P. V. Computing Clinically Relevant Binding Free Energies of HIV-1 Protease Inhibitors J. Chem. Theory Comput. 2014, 10 (3) 1228– 1241 DOI: 10.1021/ct4007037
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      27
      Computing Clinically Relevant Binding Free Energies of HIV-1 Protease Inhibitors
      Wright, David W.; Hall, Benjamin A.; Kenway, Owain A.; Jha, Shantenu; Coveney, Peter V.
      Journal of Chemical Theory and Computation (2014), 10 (3), 1228-1241CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The use of mol. simulation to est. the strength of macromol. binding free energies is becoming increasingly widespread, with goals ranging from lead optimization and enrichment in drug discovery to personalizing or stratifying treatment regimes. To realize the potential of such approaches to predict new results, not merely to explain previous exptl. findings, it is necessary that the methods used are reliable and accurate, and that their limitations are thoroughly understood. However, the computational cost of atomistic simulation techniques such as mol. dynamics (MD) has meant that until recently little work has focused on validating and verifying the available free energy methodologies, with the consequence that many of the results published in the literature are not reproducible. Here, we present a detailed anal. of two of the most popular approx. methods for calcg. binding free energies from mol. simulations, mol. mechanics Poisson-Boltzmann surface area (MMPBSA) and mol. mechanics generalized Born surface area (MMGBSA), applied to the nine FDA-approved HIV-1 protease inhibitors. Our results show that the values obtained from replica simulations of the same protease-drug complex, differing only in initially assigned atom velocities, can vary by as much as 10 kcal mol-1, which is greater than the difference between the best and worst binding inhibitors under investigation. Despite this, anal. of ensembles of simulations producing 50 trajectories of 4 ns duration leads to well converged free energy ests. For seven inhibitors, we find that with correctly converged normal mode ests. of the configurational entropy, we can correctly distinguish inhibitors in agreement with exptl. data for both the MMPBSA and MMGBSA methods and thus have the ability to rank the efficacy of binding of this selection of drugs to the protease (no account is made for free energy penalties assocd. with protein distortion leading to the over estn. of the binding strength of the two largest inhibitors ritonavir and atazanavir). We obtain improved rankings and ests. of the relative binding strengths of the drugs by using a novel combination of MMPBSA/MMGBSA with normal mode entropy ests. and the free energy of assocn. calcd. directly from simulation trajectories. Our work provides a thorough assessment of what is required to produce converged and hence reliable free energies for protein-ligand binding.
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    28. 28
      Genheden, S.; Ryde, U. The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities Expert Opin. Drug Discovery 2015, 10 (5) 449– 461 DOI: 10.1517/17460441.2015.1032936
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      The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities
      Genheden, Samuel; Ryde, Ulf
      Expert Opinion on Drug Discovery (2015), 10 (5), 449-461CODEN: EODDBX; ISSN:1746-0441. (Informa Healthcare)
      Introduction: The mol. mechanics energies combined with the Poisson-Boltzmann or generalized Born and surface area continuum solvation (MM/PBSA and MM/GBSA) methods are popular approaches to est. the free energy of the binding of small ligands to biol. macromols. They are typically based on mol. dynamics simulations of the receptor-ligand complex and are therefore intermediate in both accuracy and computational effort between empirical scoring and strict alchem. perturbation methods. They have been applied to a large no. of systems with varying success. Areas covered: The authors review the use of MM/PBSA and MM/GBSA methods to calc. ligand-binding affinities, with an emphasis on calibration, testing and validation, as well as attempts to improve the methods, rather than on specific applications. Expert opinion: MM/PBSA and MM/GBSA are attractive approaches owing to their modular nature and that they do not require calcns. on a training set. They have been used successfully to reproduce and rationalize exptl. findings and to improve the results of virtual screening and docking. However, they contain several crude and questionable approxns., for example, the lack of conformational entropy and information about the no. and free energy of water mols. in the binding site. Moreover, there are many variants of the method and their performance varies strongly with the tested system. Likewise, most attempts to ameliorate the methods with more accurate approaches, for example, quantum-mech. calcns., polarizable force fields or improved solvation have deteriorated the results.
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    29. 29
      Swanson, J. M.; Henchman, R. H.; McCammon, J. A. Revisiting free energy calculations: a theoretical connection to MM/PBSA and direct calculation of the association free energy Biophys. J. 2004, 86, 67– 74 DOI: 10.1016/S0006-3495(04)74084-9
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      29
      Revisiting free energy calculations: A theoretical connection to MM/PBSA and direct calculation of the association free energy
      Swanson, Jessica M. J.; Henchman, Richard H.; McCammon, J. Andrew
      Biophysical Journal (2004), 86 (1, Pt. 1), 67-74CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
      The prediction of abs. ligand-receptor binding affinities is essential in a wide range of biophys. queries, from the study of protein-protein interactions to structure-based drug design. End-point free energy methods, such as the Mol. Mechanics Poisson-Boltzmann Surface Area (MM/PBSA) model, have received much attention and widespread application in recent literature. These methods benefit from computational efficiency as only the initial and final states of the system are evaluated, yet there remains a need for strengthening their theor. foundation. Here a clear connection between statistical thermodn. and end-point free energy models is presented. The importance of the assocn. free energy, arising from one mol.'s loss of translational and rotational freedom from the std. state concn., is addressed. A novel method for calcg. this quantity directly from a mol. dynamics simulation is described. The challenges of accounting for changes in the protein conformation and its fluctuations from sep. simulations are discussed. A simple first-order approxn. of the configuration integral is presented to lay the groundwork for future efforts. This model has been applied to FKBP12, a small immunophilin that has been widely studied in the drug industry for its potential immunosuppressive and neuroregenerative effects.
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    30. 30
      Genheden, S.; Ryde, U. How to obtain statistically converged MM/GBSA results J. Comput. Chem. 2010, 31 (4) 837– 846 DOI: 10.1002/jcc.21366
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      Luo, R.; David, L.; Gilson, M. K. Accelerated Poisson-Boltzmann calculations for static and dynamic systems J. Comput. Chem. 2002, 23 (13) 1244– 1253 DOI: 10.1002/jcc.10120
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      Accelerated Poisson-Boltzmann calculations for static and dynamic systems
      Luo, Ray; David, Laurent; Gilson, Michael K.
      Journal of Computational Chemistry (2002), 23 (13), 1244-1253CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      We report an efficient implementation of the finite-difference Poisson-Boltzmann solvent model based on the Modified Incomplete Cholsky Conjugate Gradient algorithm, which gives rather impressive performance for both static and dynamic systems. This is achieved by implementing the algorithm with Eisenstat's two optimizations, utilizing the electrostatic update in simulations, and applying prudent approxns., including: relaxing the convergence criterion, not updating Poisson-Boltzmann-related forces every step, and using electrostatic focusing. It is also possible to markedly accelerate the supporting routines that are used to set up the calcns. and to obtain energies and forces. The resulting finite difference Poisson-Boltzmann method delivers efficiency comparable to the distance-dependent dielec. model for a system tested, HIV Protease, making it a strong candidate for soln.-phase mol. dynamics simulations. Further, the finite difference method includes all intra-solute electrostatic interactions, whereas the distance dependent dielec. calcns. use a 15-Å cutoff. The speed of our numerical finite difference method is comparable to that of the pair-wise Generalized Born approxn. to the Poisson-Boltzmann method.
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    32. 32
      Beveridge, D. L.; Dicapua, F. M. Free-energy via molecular simulation - applications to chemical and biomolecular systems Annu. Rev. Biophys. Biophys. Chem. 1989, 18, 431– 492 DOI: 10.1146/annurev.bb.18.060189.002243
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      Bunney, T. D.; Wan, S.; Thiyagarajan, N.; Sutto, L.; Williams, S. V.; Ashford, P.; Koss, H.; Knowles, M. A.; Gervasio, F. L.; Coveney, P. V.; Katan, M. The effect of mutations on drug sensitivity and kinase activity of fibroblast growth factor receptors: A combined experimental and theoretical study EBioMedicine 2015, 2 (3) 194– 204 DOI: 10.1016/j.ebiom.2015.02.009
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      Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kale, L.; Schulten, K. Scalable molecular dynamics with NAMD J. Comput. Chem. 2005, 26 (16) 1781– 1802 DOI: 10.1002/jcc.20289
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      Scalable molecular dynamics with NAMD
      Phillips, James C.; Braun, Rosemary; Wang, Wei; Gumbart, James; Tajkhorshid, Emad; Villa, Elizabeth; Chipot, Christophe; Skeel, Robert D.; Kale, Laxmikant; Schulten, Klaus
      Journal of Computational Chemistry (2005), 26 (16), 1781-1802CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      NAMD is a parallel mol. dynamics code designed for high-performance simulation of large biomol. systems. NAMD scales to hundreds of processors on high-end parallel platforms, as well as tens of processors on low-cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats. This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical mol. dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temp. and pressure controls used. Features for steering the simulation across barriers and for calcg. both alchem. and conformational free energy differences are presented. The motivations for and a roadmap to the internal design of NAMD, implemented in C++ and based on Charm++ parallel objects, are outlined. The factors affecting the serial and parallel performance of a simulation are discussed. Finally, typical NAMD use is illustrated with representative applications to a small, a medium, and a large biomol. system, highlighting particular features of NAMD, for example, the Tcl scripting language. The article also provides a list of the key features of NAMD and discusses the benefits of combining NAMD with the mol. graphics/sequence anal. software VMD and the grid computing/collab. software BioCoRE. NAMD is distributed free of charge with source code at www.ks.uiuc.edu.
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      Sadiq, S. K.; Wright, D. W.; Kenway, O. A.; Coveney, P. V. Accurate ensemble molecular dynamics binding free energy ranking of multidrug-resistant HIV-1 proteases J. Chem. Inf. Model. 2010, 50 (5) 890– 905 DOI: 10.1021/ci100007w
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      Accurate Ensemble Molecular Dynamics Binding Free Energy Ranking of Multidrug-Resistant HIV-1 Proteases
      Sadiq, S. Kashif; Wright, David W.; Kenway, Owain A.; Coveney, Peter V.
      Journal of Chemical Information and Modeling (2010), 50 (5), 890-905CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      Accurate calcn. of important thermodn. properties, such as macromol. binding free energies, is one of the principal goals of mol. dynamics simulations. However, single long simulation frequently produces incorrectly converged quant. results due to inadequate sampling of conformational space in a feasible wall-clock time. Multiple short (ensemble) simulations have been shown to explore conformational space more effectively than single long simulations, but the two methods have not yet been thermodynamically compared. Here we show that, for end-state binding free energy detn. methods, ensemble simulations exhibit significantly enhanced thermodn. sampling over single long simulations and result in accurate and converged relative binding free energies that are reproducible to within 0.5 kcal/mol. Completely correct ranking is obtained for six HIV-1 protease variants bound to lopinavir with a correlation coeff. of 0.89 and a mean relative deviation from expt. of 0.9 kcal/mol. Multidrug resistance to lopinavir is enthalpically driven and increases through a decrease in the protein-ligand van der Waals interaction, principally due to the V82A/I84V mutation, and an increase in net electrostatic repulsion due to water-mediated disruption of protein-ligand interactions in the catalytic region. Furthermore, we correctly rank, to within 1 kcal/mol of expt., the substantially increased chem. potency of lopinavir binding to the wild-type protease compared to saquinavir and show that lopinavir takes advantage of a decreased net electrostatic repulsion to confer enhanced binding. Our approach is dependent on the combined use of petascale computing resources and on an automated simulation workflow to attain the required level of sampling and turn around time to obtain the results, which can be as little as three days. This level of performance promotes integration of such methodol. with clin. decision support systems for the optimization of patient-specific therapy.
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    36. 36
      Norman, G. E.; Stegailov, V. V. Stochastic theory of the classical molecular dynamics method Math. Models Comput. Simul. 2013, 5 (4) 305– 333 DOI: 10.1134/S2070048213040108
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      Chodera, J. D.; Mobley, D. L. Entropy-enthalpy compensation: role and ramifications in biomolecular ligand recognition and design Annu. Rev. Biophys. 2013, 42, 121– 142 DOI: 10.1146/annurev-biophys-083012-130318
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      Entropy-enthalpy compensation: role and ramifications in biomolecular ligand recognition and design
      Chodera, John D.; Mobley, David L.
      Annual Review of Biophysics (2013), 42 (), 121-142CODEN: ARBNCV; ISSN:1936-122X. (Annual Reviews)
      A review. Recent calorimetric studies of interactions between small mols. and biomol. targets have generated renewed interest in the phenomenon of entropy-enthalpy compensation. In these studies, entropic and enthalpic contributions to binding are obsd. to vary substantially and in an opposing manner as the ligand or protein is modified, whereas the binding free energy varies little. In severe examples, engineered enthalpic gains can lead to completely compensating entropic penalties, frustrating ligand design. Here, we examine the evidence for compensation, as well as its potential origins, prevalence, severity, and ramifications for ligand engineering. We find the evidence for severe compensation to be weak in light of the large magnitude of and correlation between errors in exptl. measurements of entropic and enthalpic contributions to binding, though a limited form of compensation may be common. Given the difficulty of predicting or measuring entropic and enthalpic changes to useful precision, or using this information in design, we recommend ligand engineering efforts instead focus on computational and exptl. methodologies to directly assess changes in binding free energy.
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    38. 38
      Zhu, Y. L.; Beroza, P.; Artis, D. R. Including explicit water molecules as part of the protein structure in MM/PBSA calculations J. Chem. Inf. Model. 2014, 54 (2) 462– 469 DOI: 10.1021/ci4001794
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      Including Explicit Water Molecules as Part of the Protein Structure in MM/PBSA Calculations
      Zhu, Yong-Liang; Beroza, Paul; Artis, Dean R.
      Journal of Chemical Information and Modeling (2014), 54 (2), 462-469CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      Water is the natural medium of mols. in the cell and plays an important role in protein structure, function and interaction with small mol. ligands. However, the widely used mol. mechanics Poisson-Boltzmann surface area (MM/PBSA) method for binding energy calcn. does not explicitly take account of water mols. that mediate key protein-ligand interactions. We have developed a protocol to include water mols. that mediate ligand-protein interactions as part of the protein structure in calcn. of MM/PBSA binding energies (a method we refer to as water-MM/PBSA) for a series of JNK3 kinase inhibitors. Improved correlation between water-MM/PBSA binding energies and exptl. IC50 values was obtained compared to that obtained from classical MM/PBSA binding energy. This improved correlation was further validated using sets of neuraminidase and avidin inhibitors. The obsd. improvement, however, appears to be limited to systems in which there are water-mediated ligand-protein hydrogen bond interactions. We conclude that the water-MM/PBSA method performs better than classical MM/PBSA in predicting binding affinities when water mols. play a direct role in mediating ligand-protein hydrogen bond interactions.
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      Rastelli, G.; Del Rio, A.; Degliesposti, G.; Sgobba, M. Fast and accurate predictions of binding free energies using MM-PBSA and MM-GBSA J. Comput. Chem. 2010, 31 (4) 797– 810 DOI: 10.1002/jcc.21372
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      Fast and accurate predictions of binding free energies using MM-PBSA and MM-GBSA
      Rastelli, Giulio; Del Rio, Alberto; Degliesposti, Gianluca; Sgobba, Miriam
      Journal of Computational Chemistry (2010), 31 (4), 797-810CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      In the drug discovery process, accurate methods of computing the affinity of small mols. with a biol. target are strongly needed. This is particularly true for mol. docking and virtual screening methods, which use approximated scoring functions and struggle in estg. binding energies in correlation with exptl. values. Among the various methods, MM-PBSA (mol. mechanics Poisson-Boltzmann surface area) and MM-GBSA (mol. mechanics-generalized Born surface area) are emerging as useful and effective approaches. Although these methods are typically applied to large collections of equilibrated structures of protein-ligand complexes sampled during mol. dynamics in water, the possibility to reliably est. ligand affinity using a single energy-minimized structure and implicit solvation models has not been explored in sufficient detail. Herein, the authors thoroughly investigate this hypothesis by comparing different methods for the generation of protein-ligand complexes and diverse methods for free energy prediction for their ability to correlate with exptl. values. The methods were tested on a series of structurally diverse inhibitors of Plasmodium falciparum DHFR (dihydrofolate reductase) with known binding mode and measured affinities. The results showed that correlations between MM-PBSA or MM-GBSA binding free energies with exptl. affinities were in most cases excellent. Importantly, the authors found that correlations obtained with the use of a single protein-ligand minimized structure and with implicit solvation models were similar to those obtained after averaging over multiple MD snapshots with explicit water mols., with consequent save of computing time without loss of accuracy. When applied to a virtual screening expt., such an approach proved to discriminate between true binders and decoy mols. and yielded significantly better enrichment curves. © 2009 Wiley Periodicals, Inc. J Comput Chem, 31: 797-810, 2010.
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      Reynolds, C. H.; Holloway, M. K. Thermodynamics of ligand binding and efficiency ACS Med. Chem. Lett. 2011, 2 (6) 433– 437 DOI: 10.1021/ml200010k
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      Thermodynamics of Ligand Binding and Efficiency
      Reynolds, Charles H.; Holloway, M. Katharine
      ACS Medicinal Chemistry Letters (2011), 2 (6), 433-437CODEN: AMCLCT; ISSN:1948-5875. (American Chemical Society)
      Anal. of the exptl. binding thermodn. for approx. 100 protein-ligand complexes provides important insights into the factors governing ligand affinity and efficiency. The commonly accepted correlation between enthalpy and -TΔS is clearly obsd. for this relatively diverse data set. It is also clear that affinity (i.e., ΔG) is not generally correlated to either enthalpy or -TΔS. This is a worrisome trend since the vast majority of computational structure-based design is carried out using interaction energies for one, or at most a few, ligand poses. As such, these energies are most closely comparable to enthalpies not free energies. Closer inspection of the data shows that in a few cases the enthalpy (or -TΔS) is correlated with free energy. It is tempting to speculate that this could be an important consideration as to why some targets are readily amenable to modeling and others are not. Addnl., anal. of the enthalpy and -TΔS efficiencies shows that the trends obsd. for ligand efficiencies with respect to mol. size are primarily a consequence of enthalpic, not entropic, effects.
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