Absolute Protein Binding Free Energy Simulations for Ligands with Multiple Poses,a Thermodynamic Path That Avoids Exhaustive Enumeration of the Poses

We propose a free energy calculation method for receptor–ligand binding, which have multiple binding poses that avoids exhaustive enumeration of the poses. For systems with multiple binding poses, the standard procedure is to enumerate orientations of the binding poses, restrain the ligand to each orientation, and then, calculate the binding free energies for each binding pose. In this study, we modify a part of the thermodynamic cycle in order to sample a broader conformational space of the ligand in the binding site. This modification leads to more accurate free energy calculation without performing separate free energy simulations for each binding pose. We applied our modification to simple model host–guest systems as a test, which have only two binding poses, by using a single decoupling method (SDM) in implicit solvent. The results showed that the binding free energies obtained from our method without knowing the two binding poses were in good agreement with the benchmark results obtained by explicit enumeration of the binding poses. Our method is applicable to other alchemical binding free energy calculation methods such as the double decoupling method (DDM) in explicit solvent. We performed a calculation for a protein–ligand system with explicit solvent using our modified thermodynamic path. The results of the free energy simulation along our modified path were in good agreement with the results of conventional DDM, which requires a separate binding free energy calculation for each of the binding poses of the example of phenol binding to T4 lysozyme in explicit solvent. © 2019 Wiley Periodicals, Inc.     

Assessment of programs for ligand binding affinity prediction

The prediction of the binding free energy between a ligand and a protein is an important component in the virtual screening and lead optimization of ligands for drug discovery. To determine the quality of current binding free energy estimation programs, we examined FlexX, X-Score, AutoDock, and BLEEP for their performance in binding free energy prediction in various situations including cocrystallized complex structures, cross docking of ligands to their non-cocrystallized receptors, docking of thermally unfolded receptor decoys to their ligands, and complex structures with "randomized" ligand decoys. In no case was there a satisfactory correlation between the experimental and estimated binding free energies over all the datasets tested. Meanwhile, a strong correlation between ligand molecular weight-binding affinity correlation and experimental predicted binding affinity correlation was found. Sometimes the programs also correctly ranked ligands' binding affinities even though native interactions between the ligands and their receptors were essentially lost because of receptor deformation or ligand randomization, and the programs could not decisively discriminate randomized ligand decoys from their native ligands; this suggested that the tested programs miss important components for the accurate capture of specific ligand binding interactions.     

Fast and accurate predictions of binding free energies using MM‐PBSA and MM‐GBSA

In the drug discovery process, accurate methods of computing the affinity of small molecules with a biological target are strongly needed. This is particularly true for molecular docking and virtual screening methods, which use approximated scoring functions and struggle in estimating binding energies in correlation with experimental values. Among the various methods, MM‐PBSA and MM‐GBSA 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 molecular dynamics in water, the possibility to reliably estimate ligand affinity using a single energy‐minimized structure and implicit solvation models has not been explored in sufficient detail. Herein, we 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 experimental values. The methods were tested on a series of structurally diverse inhibitors of Plasmodium falciparum DHFR with known binding mode and measured affinities. The results showed that correlations between MM‐PBSA or MM‐GBSA binding free energies with experimental affinities were in most cases excellent. Importantly, we 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 molecules, with consequent save of computing time without loss of accuracy. When applied to a virtual screening experiment, such an approach proved to discriminate between true binders and decoy molecules and yielded significantly better enrichment curves. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

The F130L mutation in streptavidin reduces its binding affinity to biotin through electronic polarization effect

Recently, Baugh et al. discovered that a distal point mutation (F130L) in streptavidin causes no distinct variation to the structure of the binding pocket but a 1000‐fold reduction in biotin binding affinity. In this work, we carry out molecular dynamics simulations and apply an end‐state free energy method to calculate the binding free energies of biotin to wild type streptavidin and its F130L mutant. The absolute binding affinities based on AMBER charge are repulsive, and the mutation induced binding loss is underestimated. When using the polarized protein‐specific charge, the absolute binding affinities are significantly enhanced. In particular, both the absolute and relative binding affinities are in line with the experimental measurements. Further investigation indicates that polarization effect is indispensable in both the generation of structural ensembles and the calculation of interaction energies. This work verifies Baugh's conjecture that electrostatic polarization effect plays an essential role in modulating the binding affinity of biotin to the streptavidin through F130L mutation. © 2013 Wiley Periodicals, Inc.     

Large scale free energy calculations for blind predictions of protein–ligand binding: the D3R Grand Challenge 2015

We describe binding free energy calculations in the D3R Grand Challenge 2015 for blind prediction of the binding affinities of 180 ligands to Hsp90. The present D3R challenge was built around experimental datasets involving Heat shock protein (Hsp) 90, an ATP-dependent molecular chaperone which is an important anticancer drug target. The Hsp90 ATP binding site is known to be a challenging target for accurate calculations of ligand binding affinities because of the ligand-dependent conformational changes in the binding site, the presence of ordered waters and the broad chemical diversity of ligands that can bind at this site. Our primary focus here is to distinguish binders from nonbinders. Large scale absolute binding free energy calculations that cover over 3000 protein–ligand complexes were performed using the BEDAM method starting from docked structures generated by Glide docking. Although the ligand dataset in this study resembles an intermediate to late stage lead optimization project while the BEDAM method is mainly developed for early stage virtual screening of hit molecules, the BEDAM binding free energy scoring has resulted in a moderate enrichment of ligand screening against this challenging drug target. Results show that, using a statistical mechanics based free energy method like BEDAM starting from docked poses offers better enrichment than classical docking scoring functions and rescoring methods like Prime MM-GBSA for the Hsp90 data set in this blind challenge. Importantly, among the three methods tested here, only the mean value of the BEDAM binding free energy scores is able to separate the large group of binders from the small group of nonbinders with a gap of 2.4 kcal/mol. None of the three methods that we have tested provided accurate ranking of the affinities of the 147 active compounds. We discuss the possible sources of errors in the binding free energy calculations. The study suggests that BEDAM can be used strategically to discriminate binders from nonbinders in virtual screening and to more accurately predict the ligand binding modes prior to the more computationally expensive FEP calculations of binding affinity.     

Tinker‐OpenMM: Absolute and relative alchemical free energies using AMOEBA on GPUs

The capabilities of the polarizable force fields for alchemical free energy calculations have been limited by the high computational cost and complexity of the underlying potential energy functions. In this work, we present a GPU‐based general alchemical free energy simulation platform for polarizable potential AMOEBA. Tinker‐OpenMM, the OpenMM implementation of the AMOEBA simulation engine has been modified to enable both absolute and relative alchemical simulations on GPUs, which leads to a ∼200‐fold improvement in simulation speed over a single CPU core. We show that free energy values calculated using this platform agree with the results of Tinker simulations for the hydration of organic compounds and binding of host–guest systems within the statistical errors. In addition to absolute binding, we designed a relative alchemical approach for computing relative binding affinities of ligands to the same host, where a special path was applied to avoid numerical instability due to polarization between the different ligands that bind to the same site. This scheme is general and does not require ligands to have similar scaffolds. We show that relative hydration and binding free energy calculated using this approach match those computed from the absolute free energy approach. © 2017 Wiley Periodicals, Inc.     

Efficient estimation of binding free energies between peptides and an MHC class II molecule using coarse‐grained molecular dynamics simulations with a weighted histogram analysis method

We estimate the binding free energy between peptides and an MHC class II molecule using molecular dynamics (MD) simulations with the weighted histogram analysis method (WHAM). We show that, owing to its more thorough sampling in the available computational time, the binding free energy obtained by pulling the whole peptide using a coarse‐grained (CG) force field (MARTINI) is less prone to significant error induced by inadequate‐sampling than using an atomistic force field (AMBER). We further demonstrate that using CG MD to pull 3–4 residue peptide segments while leaving the remaining peptide segments in the binding groove and adding up the binding free energies of all peptide segments gives robust binding free energy estimations, which are in good agreement with the experimentally measured binding affinities for the peptide sequences studied. Our approach thus provides a promising and computationally efficient way to rapidly and reliably estimate the binding free energy between an arbitrary peptide and an MHC class II molecule. © 2017 Wiley Periodicals, Inc.     

X‐Ray Crystallography and Free Energy Calculations Reveal the Binding Mechanism of A2A Adenosine Receptor Antagonists

We present a robust protocol based on iterations of free energy perturbation (FEP) calculations, chemical synthesis, biophysical mapping and X‐ray crystallography to reveal the binding mode of an antagonist series to the A_2A adenosine receptor (AR). Eight A_2AAR binding site mutations from biophysical mapping experiments were initially analyzed with sidechain FEP simulations, performed on alternate binding modes. The results distinctively supported one binding mode, which was subsequently used to design new chromone derivatives. Their affinities for the A_2AAR were experimentally determined and investigated through a cycle of ligand‐FEP calculations, validating the binding orientation of the different chemical substituents proposed. Subsequent X‐ray crystallography of the A_2AAR with a low and a high affinity chromone derivative confirmed the predicted binding orientation. The new molecules and structures here reported were driven by free energy calculations, and provide new insights on antagonist binding to the A_2AAR, an emerging target in immuno‐oncology.     

X-Ray Crystallography and Free Energy Calculations Reveal the Binding Mechanism of A2A Adenosine Receptor Antagonists

We present a robust protocol based on iterations of free energy perturbation (FEP) calculations, chemical synthesis, biophysical mapping and X-ray crystallography to reveal the binding mode of an antagonist series to the A_2A adenosine receptor (AR). Eight A_2AAR binding site mutations from biophysical mapping experiments were initially analyzed with sidechain FEP simulations, performed on alternate binding modes. The results distinctively supported one binding mode, which was subsequently used to design new chromone derivatives. Their affinities for the A_2AAR were experimentally determined and investigated through a cycle of ligand-FEP calculations, validating the binding orientation of the different chemical substituents proposed. Subsequent X-ray crystallography of the A_2AAR with a low and a high affinity chromone derivative confirmed the predicted binding orientation. The new molecules and structures here reported were driven by free energy calculations, and provide new insights on antagonist binding to the A_2AAR, an emerging target in immuno-oncology.     

Fragment‐based quantum mechanical calculation of protein–protein binding affinities

The electrostatically embedded generalized molecular fractionation with conjugate caps (EE‐GMFCC) method has been successfully utilized for efficient linear‐scaling quantum mechanical (QM) calculation of protein energies. In this work, we applied the EE‐GMFCC method for calculation of binding affinity of Endonuclease colicin–immunity protein complex. The binding free energy changes between the wild‐type and mutants of the complex calculated by EE‐GMFCC are in good agreement with experimental results. The correlation coefficient (R) between the predicted binding energy changes and experimental values is 0.906 at the B3LYP/6‐31G*‐D level, based on the snapshot whose binding affinity is closest to the average result from the molecular mechanics/Poisson–Boltzmann surface area (MM/PBSA) calculation. The inclusion of the QM effects is important for accurate prediction of protein–protein binding affinities. Moreover, the self‐consistent calculation of PB solvation energy is required for accurate calculations of protein–protein binding free energies. This study demonstrates that the EE‐GMFCC method is capable of providing reliable prediction of relative binding affinities for protein–protein complexes. © 2018 Wiley Periodicals, Inc.     

Calculation of affinities of peptides for proteins

Several methodologies were employed to calculate the Gibbs standard free energy of binding for a collection of protein-ligand complexes, where the ligand is a peptide and the protein is representative for various protein families. Almost 40 protein-ligand complexes were employed for a continuum approach, which considers the protein and the peptide at the atomic level, but includes solvent as a polarizable continuum. Five protein-ligand complexes were employed for an all-atom approach that relies on a combination of the double decoupling method with thermodynamic integration and molecular dynamics. These affinities were also computed by means of the linear interaction energy method. Although it generally proved rather difficult to predict the absolute free energies correctly, for some protein families the experimental ranking order was correctly reproduced by the continuum and all-atom approach. Considerable attention has also been given to correctly analyze the affinities of charged peptides, where it is required to judge the effect of one or more ions that are being decoupled in an all-atom approach to preserve electroneutrality. The various methods are further judged upon their merits.     

Prediction and analysis of binding affinities for chemically diverse HIV-1 PR inhibitors by the modified SAFE_p approach

One of the biggest challenges in the "in silico" screening of enzyme ligands is to have a protocol that could predict the ligand binding free energies. In our group we have developed a very simple screening function (referred to as solvent accessibility free energy of binding predictor, SAFE_p) which we have applied previously to the study of peptidic HIV-1 protease (HIV-1 PR) inhibitors and later to cyclic urea type HIV-1 PR inhibitors. In this work, we have extended the SAFE_p protocol to a chemically diverse set of HIV-1 PR inhibitors with binding constants that differ by several orders of magnitude. The resulting function is able to reproduce the ranking and in many cases the value of the inhibitor binding affinities for the HIV-1 PR, with accuracy comparable with that of costlier protocols. We also demonstrate that the binding pocket SAFE_p analysis can contribute to the understanding of the physical forces that participate in ligand binding. The analysis tools afforded by our protocol have allowed us to identify an induced fit phenomena mediated by the inhibitor and have demonstrated that larger fragments do not necessarily contribute the most to the binding free energy, an outcome partially brought about by the substantial role the desolvation penalty plays in the energetics of binding. Finally, we have revisited the effect of the Asp dyad protonation state on the predicted binding affinities.     

Predicting relative binding affinities of non-peptide HIV protease inhibitors with free energy perturbation calculations

The relative binding free energies in HIV protease of haloperidol thioketal (THK) and three of its derivatives were examined with free energy calculations. THK is a weak inhibitor (IC50 = 15 M) for which two cocrystal structures with HIV type 1 proteases have been solved [Rutenber, E. et al., J. Biol. Chem., 268 (1993) 15343]. A THK derivative with a phenyl group on C2 of the piperidine ring was expected to be a poor inhibitor based on experiments with haloperidol ketal and its 2- phenyl derivative (Caldera, P., personal communication). Our calculations predict that a 5-phenyl THK derivative, suggested based on examination of the crystal structure, will bind significantly better than THK. Although there are large error bars as estimated from hysteresis, the calculations predict that the 5-phenyl substituent is clearly favored over the 2-phenyl derivative as well as the parent compound. The unfavorable free energies of solvation of both phenyl THK derivatives relative to the parent compound contributed to their predicted binding free energies. In a third simulation, the change in binding free energy for 5-benzyl THK relative to THK was calculated. Although this derivative has a lower free energy in the protein, its decreased free energy of solvation increases the predicted G(bind) to the same range as that of the 2-phenyl derivative.     

Calculation of ligand binding free energies from molecular dynamics simulations

A recently developed method for predicting binding affinities in ligand–receptor complexes, based on interaction energy averaging and conformational sampling by molecular dynamics simulation, is presented. Polar and nonpolar contributions to the binding free energy are approximated by a linear scaling of the corresponding terms in the average intermolecular interaction energy for the bound and free states of the ligand. While the method originally assumed the validity of electrostatic linear response, we show that incorporation of systematic deviations from linear response derived from free energy perturbation calculations enhances the accuracy of the approach. The method is applied to complexes of wild-type and mutant human dihydrofolate reductases with 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors. It is shown that a binding energy accuracy of about 1 kcal/mol is attainable even for multiply ionized compounds, such as methotrexate, for which electrostatic interactions energies are very large. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 77–88, 1998     

Exhaustive search of the configurational space of heat-shock protein 90 with its inhibitor by multicanonical molecular dynamics based dynamic docking

Multicanonical molecular dynamics based dynamic docking was used to exhaustively search the configurational space of an inhibitor binding to the N-terminal domain of heat-shock protein 90 (Hsp90). The obtained structures at 300 K cover a wide structural ensemble, with the top two clusters ranked by their free energy coinciding with the native binding site. The representative structure of the most stable cluster reproduced the experimental binding configuration, but an interesting conformational change in Hsp90 could be observed. The combined effects of solvation and ligand binding shift the equilibrium from a preferred loop-in conformation in the unbound state to an α-helical one in the bound state for the flexible lid region of Hsp90. Thus, our dynamic docking method is effective at predicting the native binding site while exhaustively sampling a wide configurational space, modulating the protein structure upon binding.     

Calculation of relative binding affinities of fructose 1,6-bisphosphatase mutants with adenosine monophosphate using free energy perturbation method

The free energy perturbation (FEP) methodology is the most accurate means of estimating relative binding affinities between inhibitors and protein variants. In this article, the importance of hydrophobic and hydrophilic residues to the binding of adenosine monophosphate (AMP) to the fructose 1,6-bisphosphatase (FBPase), a target enzyme for type-II diabetes, was examined by FEP method. Five mutations were made to the FBPase enzyme with AMP inhibitor bound: 113Tyr --> 113Phe, 31Thr --> 31Ala, 31Thr --> 31Ser, 177Met --> 177Ala, and 30Leu --> 30Phe. These mutations test the strength of hydrogen bonds and van der Waals interactions between the ligand and enzyme. The calculated relative free energies indicated that: 113Tyr and 31Thr play an important role, each via two hydrogen bonds affecting the binding affinity of inhibitor AMP to FBPase, and any changes in these hydrogen bonds due to mutations on the protein will have significant effect on the binding affinity of AMP to FBPase, consistent to experimental results. Also, the free energy calculations clearly show that the hydrophilic interactions are more important than the hydrophobic interactions of the binding pocket of FBPase.     

Simulating GTP:Mg and GDP:Mg with a simple force field: A structural and thermodynamic analysis

Di‐ and tri‐phosphate nucleotides are essential cofactors for many proteins, usually in an Mg²⁺‐bound form. Proteins like GTPases often detect the difference between NDP and NTP and respond by changing conformations. To study such complexes, simple, fixed charge force fields have been used, which allow long simulations and precise free energy calculations. The preference for NTP or NDP binding depends on many factors, including ligand structure and Mg²⁺ coordination and the changes they undergo upon binding. Here, we use a simple force field to examine two Mg²⁺ coordination modes for the unbound GDP and GTP: direct, or “Inner Sphere” (IS) coordination by one or more phosphate oxygens and indirect, “Outer Sphere” (OS) coordination involving one or more bridging waters. We compare GTP: and GDP:Mg binding with OS and IS coordination; combining the results with experimental data then indicates that GTP prefers the latter. We also examine different kinds of IS coordination and their sensitivity to a key force field parameter: the optimal Mg:oxygen van der Waals distance R_min. Increasing R_min improves the Mg:oxygen distances, the GTP: and GDP:Mg binding affinities, and the fraction of GTP:Mg with β + γ phosphate coordination, but does not improve or change the GTP/GDP affinity difference, which remains much larger than experiment. It has no effect on the free energy of GDP binding to a GTPase. © 2012 Wiley Periodicals, Inc.     

AADS--an automated active site identification, docking, and scoring protocol for protein targets based on physicochemical descriptors

We report here a robust automated active site detection, docking, and scoring (AADS) protocol for proteins with known structures. The active site finder identifies all cavities in a protein and scores them based on the physicochemical properties of functional groups lining the cavities in the protein. The accuracy realized on 620 proteins with sizes ranging from 100 to 600 amino acids with known drug active sites is 100% when the top ten cavity points are considered. These top ten cavity points identified are then submitted for an automated docking of an input ligand/candidate molecule. The docking protocol uses an all atom energy based Monte Carlo method. Eight low energy docked structures corresponding to different locations and orientations of the candidate molecule are stored at each cavity point giving 80 docked structures overall which are then ranked using an effective free energy function and top five structures are selected. The predicted structure and energetics of the complexes agree quite well with experiment when tested on a data set of 170 protein-ligand complexes with known structures and binding affinities. The AADS methodology is implemented on an 80 processor cluster and presented as a freely accessible, easy to use tool at http://www.scfbio-iitd.res.in/dock/ActiveSite_new.jsp .     

Electrostatic component of binding energy: Interpreting predictions from poisson–boltzmann equation and modeling protocols

Macromolecular interactions are essential for understanding numerous biological processes and are typically characterized by the binding free energy. Important component of the binding free energy is the electrostatics, which is frequently modeled via the solutions of the Poisson–Boltzmann Equations (PBE). However, numerous works have shown that the electrostatic component (ΔΔG_elec) of binding free energy is very sensitive to the parameters used and modeling protocol. This prompted some researchers to question the robustness of PBE in predicting ΔΔG_elec. We argue that the sensitivity of the absolute ΔΔG_elec calculated with PBE using different input parameters and definitions does not indicate PBE deficiency, rather this is what should be expected. We show how the apparent sensitivity should be interpreted in terms of the underlying changes in several numerous and physical parameters. We demonstrate that PBE approach is robust within each considered force field (CHARMM‐27, AMBER‐94, and OPLS‐AA) once the corresponding structures are energy minimized. This observation holds despite of using two different molecular surface definitions, pointing again that PBE delivers consistent results within particular force field. The fact that PBE delivered ΔΔG_elec values may differ if calculated with different modeling protocols is not a deficiency of PBE, but natural results of the differences of the force field parameters and potential functions for energy minimization. In addition, while the absolute ΔΔG_elec values calculated with different force field differ, their ordering remains practically the same allowing for consistent ranking despite of the force field used. © 2016 Wiley Periodicals, Inc.     

A Gibbs free energy correlation for automated docking of carbohydrates

Thermodynamic information can be inferred from static atomic configurations. To model the thermodynamics of carbohydrate binding to proteins accurately, a large binding data set has been assembled from the literature. The data set contains information from 262 unique protein-carbohydrate crystal structures for which experimental binding information is known. Hydrogen atoms were added to the structures and training conformations were generated with the automated docking program AutoDock 3.06, resulting in a training set of 225,920 all-atom conformations. In all, 288 formulations of the AutoDock 3.0 free energy model were trained against the data set, testing each of four alternate methods of computing the van der Waals, solvation, and hydrogen-bonding energetic components. The van der Waals parameters from AutoDock 1 produced the lowest errors, and an entropic model derived from statistical mechanics produced the only models with five physically and statistically significant coefficients. Eight models predict the Gibbs free energy of binding with an error of less than 40% of the error of any similar models previously published.