Net charge changes in the calculation of relative ligand-binding free energies via classical atomistic molecular dynamics simulation

Multistate Method to Efficiently Account for Tautomerism and Protonation in Alchemical Free-Energy Calculations

The majority of drug-like molecules contain at least one ionizable group, and many common drug scaffolds are subject to tautomeric equilibria. Thus, these compounds are found in a mixture of protonation and/or tautomeric states at physiological pH. Intrinsically, standard classical molecular dynamics (MD) simulations cannot describe such equilibria between states, which negatively impacts the prediction of key molecular properties in silico. Following the formalism described by de Oliveira and co-workers (J. Chem. Theory Comput. 2019, 15, 424-435) to consider the influence of all states on the binding process based on alchemical free-energy calculations, we demonstrate in this work that the multistate method replica-exchange enveloping distribution sampling (RE-EDS) is well suited to describe molecules with multiple protonation and/or tautomeric states in a single simulation. We apply our methodology to a series of eight inhibitors of factor Xa with two protonation states and a series of eight inhibitors of glycogen synthase kinase 3β (GSK3β) with two tautomeric states. In particular, we show that given a sufficient phase-space overlap between the states, RE-EDS is computationally more efficient than standard pairwise free-energy methods.

Guidelines for Free-Energy Calculations Involving Charge Changes

The Coulomb interactions in molecular simulations are inherently approximated due to the finite size of the molecular box sizes amenable to current-day compute power. Several methods exist for treating long-range electrostatic interactions, yet these approaches are subject to various finite-size-related artifacts. Lattice-sum methods are frequently used to approximate long-range interactions; however, these approaches also suffer from artifacts which become particularly pronounced for free-energy calculations that involve charge changes. The artifacts, however, also affect the sampling when plain simulations are performed, leading to a biased ensemble. Here, we investigate two previously described model systems to determine if artifacts continue to play a role when overall neutral boxes are considered, in the context of both free-energy calculations and sampling. We find that ensuring that no net-charge changes take place, while maintaining a neutral simulation box, may be sufficient provided that the simulation boxes are large enough. Addition of salt to the solution (when appropriate) can further alleviate the remaining artifacts in the sampling or the calculated free-energy differences. We provide practical guidelines to avoid finite-size artifacts.

Scaffold Hopping and Optimization of Small Molecule Soluble Adenyl Cyclase Inhibitors Led by Free Energy Perturbation

Free energy perturbation is a computational technique that can be used to predict how small changes to an inhibitor structure will affect the binding free energy to its target. In this paper, we describe the utility of free energy perturbation with FEP+ in the hit-to-lead stage of a drug discovery project targeting soluble adenyl cyclase. The project was structurally enabled by X-ray crystallography throughout. We employed free energy perturbation to first scaffold hop to a preferable chemotype and then optimize the binding affinity to sub-nanomolar levels while retaining druglike properties. The results illustrate that effective use of free energy perturbation can enable a drug discovery campaign to progress rapidly from hit to lead, facilitating proof-of-concept studies that enable target validation.

Targeting UNC-51-like kinase 1 and 2 by lignans to modulate autophagy: possible implications in metastatic colorectal cancer

Colorectal cancer (CRC), especially metastatic (mCRC) form, becomes a major reason behind cancer morbidity worldwide, whereas the treatment strategy is not optimum. Several novel targets are under investigation for mCRC including the autophagy pathway. Natural compounds including dietary lignans are sparsely reported as autophagy modulators. Nonetheless, the interaction between dietary lignans and core autophagy complexes are yet to be characterised. We aimed to describe the interaction between the dietary lignans from flaxseed (Linum usitatissimum) and sesame seeds (Sesamum indicum) along with the enterolignans (enterodiol and enterolactone) and the UNC-51-like kinase 1 and 2 (ULK1/2), important kinases required for the autophagy. A range of in-silico technologies viz. molecular docking, drug likeness, and ADME/T was employed to select the best fit modulator and/or inhibitor of the target kinases from the list of selected lignans. Drug likeness and ADME/T studied further selected the best-suited lignans as potential autophagy inhibitor. Molecular dynamic simulation (MDS) analyses were used to validate the molecular docking results. Binding free energies of the protein-ligand interactions by MM-PBSA method further confirmed best-selected lignans as ULK1 and/or ULK2 inhibitor. In conclusion, three dietary lignans pinoresinol, medioresinol, and lariciresinol successfully identified as dual ULK1/2 inhibitor/modifier, whereas enterodiol emerged as a selective ULK2 inhibitor/modifier.

Non-Ewald methods for evaluating the electrostatic interactions of charge systems: similarity and difference

In molecular simulations, it is essential to properly calculate the electrostatic interactions of particles in the physical system of interest. Here we consider a method called the non-Ewald method, which does not rely on the standard Ewald method with periodic boundary conditions, but instead relies on the cutoff-based techniques. We focus on the physicochemical and mathematical conceptual aspects of the method in order to gain a deeper understanding of the simulation methodology. In particular, we take into account the reaction field (RF) method, the isotropic periodic sum (IPS) method, and the zero-multipole summation method (ZMM). These cutoff-based methods are based on different physical ideas and are completely distinguishable in their underlying concepts. The RF and IPS methods are "additive" methods that incorporate information outside the cutoff region, via dielectric medium and isotropic boundary condition, respectively. In contrast, the ZMM is a "subtraction" method that tries to remove the artificial effects, generated near the boundary, from the cutoff sphere. Nonetheless, we find physical and/or mathematical similarities between these methods. In particular, the modified RF method can be derived by the principle of neutralization utilized in the ZMM, and we also found a direct relationship between IPS and ZMM.

Leveraging the Sampling Efficiency of RE-EDS in OpenMM Using a Shifted Reaction-Field With an Atom-Based Cutoff

Replica-exchange enveloping distribution sampling (RE-EDS) is a pathway-independent multistate free-energy method, currently implemented in the GROMOS software package for molecular dynamics (MD) simulations. It has a high intrinsic sampling efficiency as the interactions between the unperturbed particles have to be calculated only once for multiple end-states. As a result, RE-EDS is an attractive method for the calculation of relative solvation and binding free energies. An essential requirement for reaching this high efficiency is the separability of the nonbonded interactions into solute-solute, solute-environment, and environment-environment contributions. Such a partitioning is trivial when using a Coulomb term with a reaction-field (RF) correction to model the electrostatic interactions, but not when using lattice- sum schemes. To avoid cutoff artifacts, the RF correction is typically used in combination with a charge-group based cutoff, which is not supported by most small-molecule force fields and other MD engines. To address this issue, we investigate the combination of RE-EDS simulations with a recently introduced RF scheme including a shifting function that enables the rigorous calculation of RF electrostatics with atom-based cutoffs. The resulting approach is validated by calculating solvation free energies with the generalized AMBER force field (GAFF) in water and chloroform using both the GROMOS software package and a proof-of-concept implementation in OpenMM.

Improving the Potential of Mean Force and Nonequilibrium Pulling Simulations by Simultaneous Alchemical Modifications

We present an approach combining alchemical modifications and physical-pathway methods to calculate absolute binding free energies. The employed physical-pathway method is either a stratified umbrella sampling to calculate a potential of mean force or nonequilibrium pulling. We devised two basic approaches: the simultaneous approach (S-approach), where, along the physical unbinding pathway, an alchemical transformation of ligand-protein interactions is installed and deinstalled, and the prior-plus-simultaneous approach (PPS-approach), where, prior to the physical-pathway simulation, an alchemical transformation of ligand-protein interactions is installed in the binding site and deinstalled during the physical-pathway simulation. Using a mutant of T4 lysozyme with a benzene ligand as an example, we show that installation and deinstallation of soft-core interactions concurrent with physical ligand unbinding (S-approach) allow successful potential of mean force calculations and nonequilibrium pulling simulations despite the problems posed by the occluded nature of the lysozyme binding pocket. Good agreement between the potential of the mean-force-based S-approach and double decoupling simulations as well as a remarkable efficiency and accuracy of the nonequilibrium-pulling-based S-approach is found. The latter turned out to be more compute-efficient than the potential of mean force calculation by approximately 70%. Furthermore, we illustrate the merits of reducing ligand-protein interactions prior to potential of mean force calculations using the murine double minute homologue protein MDM2 with a p53-derived peptide ligand (PPS-approach). Here, the problem of breaking strong interactions in the binding pocket is transferred to a prior alchemical transformation that reduces the free-energy barrier between the bound and unbound state in the potential of mean force. Besides, disentangling physical ligand displacement from the deinstallation of ligand-protein interactions was seen to allow a more uniform sampling of distance histograms in the umbrella sampling. In the future, physical ligand unbinding combined with simultaneous alchemical modifications may prove useful in the calculation of protein-protein binding free energies, where sampling problems posed by multiple, possibly sticky interactions and potential steric clashes can thus be reduced.

Designing of disruptor molecules to restrain the protein-protein interaction network of VANG1/SCRIB/NOS1AP using fragment-based drug discovery techniques

Governing protein-protein interaction networks are the cynosure of cell signaling and oncogenic networks. Multifarious processes when aligned with one another can result in a dysregulated output which can result in cancer progression. In the current research, one such network of proteins comprising VANG1/SCRIB/NOS1AP, which is responsible for cell migration, is targeted. The proteins are modeled using in-silico approaches, and the interaction is visualized utilizing protein-protein docking. Designing drugs for the convoluted protein network can serve as a challenging task that can be overcome by fragment-based drug designing, a recent game-changer in the computational drug discovery strategy for protein interaction networks. The model is exposed to the extraction of hotspots, also known as the restrained regions for small molecular hits. The hotspot regions are subjected to a library of generated fragments, which are then recombined and rejoined to develop small molecular disruptors of the macromolecular assemblage. Rapid screening methods using pharmacokinetic tools and 2D interaction studies resulted in four molecules that could serve the purpose of a disruptor. The final validation is executed by long-range simulations of 100 ns and exploring the stability of the complex using several parameters leading to the emergence of two novel molecules VNS003 and VNS005 that could be used as the disruptors of the protein assembly VANG1/SCRIB/NOS1AP. Also, the molecules were explored as single protein targets approbated via molecular docking and 100 ns molecular dynamics simulation. This concluded VNS003 as the most suitable inhibitor module capable of acting as a disruptor of a macromolecular assembly as well as acting on individual protein chains, thus leading to the primary hindrance in the formation of the protein interaction complex.

How Peptides Bind to PSD-95/Discs-Large/ZO-1 Domains

PSD-95/discs-large/ZO-1 (PDZ) domains form a large family of adaptor proteins that bind to the C-terminal tails of their binding partner proteins. Via extensive molecular dynamics simulations and alchemical free energy calculations, we characterized the binding modi of phosphorylated and unphosphorylated EQVSAV peptides and of a EQVEAV phosphate mimic to the hPTP1E PDZ2 and MAGI1 PDZ1 domains. The simulations reproduced the well-known binding characteristics such as tight coordination of the peptidic carboxyl tail and pronounced hydrogen bonding between the peptide backbone and the backbone atoms of a β-sheet in PDZ. Overall, coordination by hPTP1E PDZ2 appeared tighter than by MAGI1 PDZ1. Simulations of wild-type PDZ and arginine mutants suggest that contacts with Arg79/85 in hPTP1E/MAGI1 are more important for the EQVEAV peptide than for EQVSAV. Alchemical free energy calculations and PaCS-MD simulations could well reproduce the difference in binding free energy between unphosphorylated EQVSAV and EQVEAV peptides and the absolute binding free energy of EQVSAV. However, likely due to small force field inaccuracies, the simulations erroneously favored binding of the phosphorylated peptide instead of its unphosphorylated counterpart, which is in contrast to the experiment.

The Use of Molecular Dynamics Simulation Method to Quantitatively Evaluate the Affinity between HBV Antigen T Cell Epitope Peptides and HLA-A Molecules

Chronic hepatitis B virus (HBV), a potentially life-threatening liver disease, makes people vulnerable to serious diseases such as cancer. T lymphocytes play a crucial role in clearing HBV virus, while the pathway depends on the strong binding of T cell epitope peptide and HLA. However, the experimental identification of HLA-restricted HBV antigenic peptides is extremely time-consuming. In this study, we provide a novel prediction strategy based on structure to assess the affinity between the HBV antigenic peptide and HLA molecule. We used residue scanning, peptide docking and molecular dynamics methods to obtain the molecular docking model of HBV peptide and HLA, and then adopted the MM-GBSA method to calculate the binding affinity of the HBV peptide–HLA complex. Overall, we collected 59 structures of HLA-A from Protein Data Bank, and finally obtained 352 numerical affinity results to figure out the optimal bind choice between the HLA-A molecules and 45 HBV T cell epitope peptides. The results were highly consistent with the qualitative affinity level determined by the competitive peptide binding assay, which confirmed that our affinity prediction process based on an HLA structure is accurate and also proved that the homologous modeling strategy for HLA-A molecules in this study was reliable. Hence, our work highlights an effective way by which to predict and screen for HLA-peptide binding that would improve the treatment of HBV infection.

Explicit solvation thermodynamics in ionic solution: extending grid inhomogeneous solvation theory to solvation free energy of salt-water mixtures

Hydration thermodynamics play a fundamental role in fields ranging from the pharmaceutical industry to environmental research. Numerous methods exist to predict solvation thermodynamics of compounds ranging from small molecules to large biomolecules. Arguably the most precise methods are those based on molecular dynamics (MD) simulations in explicit solvent. One theory that has seen increased use is inhomogeneous solvation theory (IST). However, while many applications require accurate description of salt-water mixtures, no implementation of IST is currently able to estimate solvation properties involving more than one solvent species. Here, we present an extension to grid inhomogeneous solvation theory (GIST) that can take salt contributions into account. At the example of carbazole in 1 M NaCl solution, we compute the solvation energy as well as first and second order entropies. While the effect of the first order ion entropy is small, both the water-water and water-ion entropies contribute strongly. We show that the water-ion entropies are efficiently approximated using the Kirkwood superposition approximation. However, this approach cannot be applied to the water-water entropy. Furthermore, we test the quantitative validity of our method by computing salting-out coefficients and comparing them to experimental data. We find a good correlation to experimental salting-out constants, while the absolute values are overpredicted due to the approximate second order entropy. Since ions are frequently used in MD, either to neutralize the system or as a part of the investigated process, our method greatly extends the applicability of GIST. The use-cases range from biopharmaceuticals, where many assays require high salt concentrations, to environmental research, where solubility in sea water is important to model the fate of organic substances.

Computational Tools for Accurate Binding Free-Energy Prediction

A quantitative thermodynamic understanding of the noncovalent association of (bio)molecules is of central importance in molecular life sciences. An important quantity characterizing (bio)molecular association is the binding affinity or absolute binding free energy. In recent years, the computational prediction of absolute binding free energies has evolved considerably in terms of accuracy, computational speed, and user-friendliness. In this chapter, we first give an overview of how absolute free energies are defined and how they can be determined with computational means. We proceed with an outline of the theoretical basis of the two most reliable methods, potential of mean force, and double decoupling calculations. In particular, we describe how the sampling problem can be alleviated by application of restraints. Finally, we provide step-by-step instructions of how to set up corresponding molecular simulations with a commonly employed molecular dynamics simulation engine.

Building intuition for binding free energy calculations: Bound state definition, restraints, and symmetry

The theory behind computation of absolute binding free energies using explicit-solvent molecular simulations is well-established, yet somewhat complex, with counter-intuitive aspects. This leads to frequent frustration, common misconceptions, and sometimes erroneous numerical treatment. To improve this, we present the main practically relevant segments of the theory with constant reference to physical intuition. We pinpoint the role of the implicit or explicit definition of the bound state (or the binding site) to make a robust link between an experimental measurement and a computational result. We clarify the role of symmetry and discuss cases where symmetry number corrections have been misinterpreted. In particular, we argue that symmetry corrections as classically presented are a source of confusion and could be advantageously replaced by restraint free energy contributions. We establish that contrary to a common intuition, partial or missing sampling of some modes of symmetric bound states does not affect the calculated decoupling free energies. Finally, we review these questions and pitfalls in the context of a few common practical situations: binding to a symmetric receptor (equivalent binding sites), binding of a symmetric ligand (equivalent poses), and formation of a symmetric complex, in the case of homodimerization.

Generalizing the Discrete Gibbs Sampler-Based λ-Dynamics Approach for Multisite Sampling of Many Ligands

In this work, the discrete λ variant of the Gibbs sampler-based λ-dynamics (d-GSλD) method is developed to enable multiple functional group perturbations to be investigated at one or more sites of substitution off a common ligand core. The theoretical framework and special considerations for constructing discrete λ states for multisite d-GSλD are presented. The precision and accuracy of the d-GSλD method is evaluated with three test cases of increasing complexity. Specifically, methyl → methyl symmetric perturbations in water, 1,4-benzene hydration free energies and protein-ligand binding affinities for an example HIV-1 reverse transcriptase inhibitor series are computed with d-GSλD. Complementary MSλD calculations were also performed to compare with d-GSλD's performance. Excellent agreement between d-GSλD and MSλD is observed, with mean unsigned errors of 0.12 and 0.22 kcal/mol for computed hydration and binding free energy test cases, respectively. Good agreement with experiment is also observed, with errors of 0.5-0.7 kcal/mol. These findings support the applicability of the d-GSλD free energy method for a variety of molecular design problems, including structure-based drug design. Finally, a discussion of d-GSλD versus MSλD approaches is presented to compare and contrast features of both methods.

Efficient In Silico Saturation Mutagenesis of a Member of the Caspase Protease Family

Rational-design methods have proven to be a valuable toolkit in the field of protein design. Numerical approaches such as free-energy calculations or QM/MM methods are fit to widen the understanding of a protein-sequence space but require large amounts of computational time and power. Here, we apply an efficient method for free-energy calculations that combines the one-step perturbation (OSP) with the third-power-fitting (TPF) approach. It is fit to calculate full free energies of binding from three different end states only. The nonpolar contribution to the free energies are calculated for a set of chosen amino acids from a single simulation of a judiciously chosen reference state. The electrostatic contributions, on the other hand, are predicted from simulations of the neutral and charged end states of the individual amino acids. We used this method to perform in silico saturation mutagenesis of two sites in human Caspase-2. We calculated relative binding free energies toward two different substrates that differ in their P1' site and in their affinity toward the unmutated protease. Although being approximate, our approach showed very good agreement upon validation against experimental data. 76% of the predicted relative free energies of amino acid mutations was found to be true positives or true negatives. We observed that this method is fit to discriminate amino acid mutations because the rate of false negatives is very low (<1.5%). The approach works better for a substrate with medium/low affinity with a Matthews correlation coefficient (MCC) of 0.63, whereas for a substrate with very low affinity, the MCC was 0.38. In all cases, the combined TPF + OSP approach outperformed the linear interaction energy method.

A Benchmark of Electrostatic Method Performance in Relative Binding Free Energy Calculations

Relative free energy calculations are fast becoming a critical part of early stage pharmaceutical design, making it important to know how to obtain the best performance with these calculations in applications that could span hundreds of calculations and molecules. In this work, we compared two different treatments of long-range electrostatics, Particle Mesh Ewald (PME) and Reaction Field (RF), in relative binding free energy calculations using a nonequilibrium switching protocol. We found simulations using RF achieve comparable results to those using PME but gain more efficiency when using CPU and similar performance using GPU. The results from this work encourage more use of RF in molecular simulations.

The effect of different cutoff schemes in molecular simulations of proteins

Molecular simulations of nanoscale systems invariably involve assumptions and approximations to describe the electrostatic interactions, which are long-ranged in nature. One approach is the use of cutoff schemes with a reaction-field contribution to account for the medium outside the cutoff scheme. Recent reports show that macroscopic properties may depend on the exact choice of cutoff schemes in modern day simulations. In this work, a systematic analysis of the effects of different cutoff schemes was performed using a set of 52 proteins. We find no statistically significant differences between using a twin-range or a single-range cutoff scheme. Applying the cutoff based on charge groups or based on atomic positions, does lead to significant differences, which is traced to the cutoff noise for energies and forces. While group-based cutoff schemes show increased cutoff noise in the potential energy, applying an atomistic cutoff leads to artificial structure in the solvent at the cutoff distance. Carefully setting the temperature control, or using an atomistic cutoff for the solute and a group-based cutoff for the solvent significantly reduces the effects of the cutoff noise, without introducing structure in the solvent. This study aims to deepen the understanding of the implications different cutoffs have on molecular dynamics simulations.

Charge-Changing Perturbations and Path Sampling via Classical Molecular Dynamic Simulations of Simple Guest-Host Systems

Currently, two different methods dominate the field of biomolecular free-energy calculations for the prediction of binding affinities. Pathway methods are frequently used for large ligands that bind on the surface of a host, such as protein-protein complexes. Alchemical methods, on the other hand, are preferably applied for small ligands that bind to deeply buried binding sites. The latter methods are also widely known to be heavily artifacted by the representation of electrostatic energies in periodic simulation boxes, in particular, when net-charge changes are involved. Different methods have been described to deal with these artifacts, including postsimulation correction schemes and instantaneous correction schemes (e.g., co-alchemical perturbation of ions). Here, we use very simple test systems to show that instantaneous correction schemes with no change in the system net charge lower the artifacts but do not eliminate them. Furthermore, we show that free energies from pathway methods suffer from the same artifacts.

Improved GROMOS 54A7 Charge Sets for Phosphorylated Tyr, Ser, and Thr to Deal with pH-Dependent Binding Phenomena

Phosphorylation is a ubiquitous post-translational modification in proteins, and the phosphate group is present constitutively or transiently in most biological building blocks. These phosphorylated biomolecules are involved in many high-affinity binding/unbinding events that rely predominantly on electrostatic interactions. To build accurate models of these molecules, we need an improved description of the atomic partial charges for all relevant protonation states. In this work, we showed that the commonly used protocols to derive atomic partial charges using well-solvated molecules are inadequate to model the protonation equilibria in binding events. We introduced a protocol based on PB/MC calculations with a single representative conformation (of both protonation states) and used the resulting pK_a estimations to help manually curate the atomic partial charges. The final charge set, which is fully compatible with the GROMOS 54A7 force field, proved to be very effective in modeling the protonation equilibrium in different phosphorylated peptides in the free (tetrapeptides, pentapeptides, and pY1021) and protein-complexed forms (pY1021/PLC-γ1 complex). This was particularly important in the case of the pY1021 bound to the SH2 domain of PLC-γ1, where only our curated charge set captured the correct protonation equilibrium at the neutral to slightly acidic pH range. The binding/unbinding phenomena in that pH range are biologically relevant, and to improve our models, we need to go beyond the commonly used protocols and obtain revised force field parameters for these molecules.

Enhancing the promiscuity of a member of the Caspase protease family by rational design

The N-terminal cleavage of fusion tags to restore the native N-terminus of recombinant proteins is a challenging task and up to today, protocols need to be optimized for different proteins individually. Within this work, we present a novel protease that was designed in-silico to yield enhanced promiscuity toward different N-terminal amino acids. Two mutations in the active-site amino acids of human Caspase-2 were determined to increase the recognition of branched amino-acids, which show only poor binding capabilities in the unmutated protease. These mutations were determined by sequential and structural comparisons of Caspase-2 and Caspase-3 and their effect was additionally predicted using free-energy calculations. The two mutants proposed in the in-silico studies were expressed and in-vitro experiments confirmed the simulation results. Both mutants showed not only enhanced activities toward branched amino acids, but also smaller, unbranched amino acids. We believe that the created mutants constitute an important step toward generalized procedures to restore original N-termini of recombinant fusion proteins.

On the importance of statistics in molecular simulations for thermodynamics, kinetics and simulation box size

Computational simulations, akin to wetlab experimentation, are subject to statistical fluctuations. Assessing the magnitude of these fluctuations, that is, assigning uncertainties to the computed results, is of critical importance to drawing statistically reliable conclusions. Here, we use a simulation box size as an independent variable, to demonstrate how crucial it is to gather sufficient amounts of data before drawing any conclusions about the potential thermodynamic and kinetic effects. In various systems, ranging from solvation free energies to protein conformational transition rates, we showcase how the proposed simulation box size effect disappears with increased sampling. This indicates that, if at all, the simulation box size only minimally affects both the thermodynamics and kinetics of the type of biomolecular systems presented in this work.

Advances in the calculation of binding free energies

In recent years, calculations of binding affinities from molecular simulations seem to have matured significantly. While the number of applications of such methods in drug design and biotechnology increases, the number of truly new methodological developments decreases. This review provides an overview of the current status of the field as reflected in recent publications. The focus is on the challenges that remain when using endstate, alchemical and pathway methods. For endstate methods this is the calculation of entropic contributions. For alchemical methods there are unsolved problems associated with the solvation of the active site, sampling slow degrees of freedom and when modifying the net charge. For pathway methods achieving sufficient sampling remains challenging. New trends are also highlighted, including the use of pathway methods for the quantification of protein-protein interactions.

Correcting electrostatic artifacts due to net-charge changes in the calculation of ligand binding free energies

Alchemically derived free energies are artifacted when the perturbed moiety has a nonzero net charge. The source of the artifacts lies in the effective treatment of the electrostatic interactions within and between the perturbed atoms and remaining (partial) charges in the simulated system. To treat the electrostatic interactions effectively, lattice-summation (LS) methods or cutoff schemes in combination with a reaction-field contribution are usually employed. Both methods render the charging component of the calculated free energies sensitive to essential parameters of the system like the cutoff radius or the box side lengths. Here, we discuss the results of three previously published studies of ligand binding. These studies presented estimates of binding free energies that were artifacted due to the charged nature of the ligands. We show that the size of the artifacts can be efficiently calculated and raw simulation data can be corrected. We compare the corrected results with experimental estimates and nonartifacted estimates from path-sampling methods. Although the employed correction scheme involves computationally demanding continuum-electrostatics calculations, we show that the correction estimate can be deduced from a small sample of configurations rather than from the entire ensemble. This observation makes the calculations of correction terms feasible for complex biological systems. To show the general applicability of the proposed procedure, we also present results where the correction scheme was used to correct independent free energies obtained from simulations employing a cutoff scheme or LS electrostatics. In this work, we give practical guidelines on how to apply the appropriate corrections easily.

DPP1 Inhibitors: Exploring the Role of Water in the S2 Pocket of DPP1 with Substituted Pyrrolidines

A series of pyrrolidine amino nitrile DPP1 inhibitors have been developed and characterized. The S2 pocket structure-activity relationship for these compounds shows significant gains in potency for DPP1 from interacting further with target residues and a network of water molecules in the binding pocket. Herein we describe the X-ray crystal structures of several of these compounds alongside an analysis of factors influencing the inhibitory potency toward DPP1 of which stabilization of the water network, demonstrated using Grand Canonical Monte Carlo simulations and free energy calculations, is attributed as a main factor.

Relative Binding Affinity Prediction of Charge-Changing Sequence Mutations with FEP in Protein-Protein Interfaces

Building on the substantial progress that has been made in using free energy perturbation (FEP) methods to predict the relative binding affinities of small molecule ligands to proteins, we have previously shown that results of similar quality can be obtained in predicting the effect of mutations on the binding affinity of protein–protein complexes. However, these results were restricted to mutations which did not change the net charge of the side chains due to known difficulties with modeling perturbations involving a change in charge in FEP. Various methods have been proposed to address this problem. Here we apply the co-alchemical water approach to study the efficacy of FEP calculations of charge changing mutations at the protein–protein interface for the antibody–gp120 system investigated previously and three additional complexes. We achieve an overall root mean square error of 1.2 kcal/mol on a set of 106 cases involving a change in net charge selected by a simple suitability filter using side-chain predictions and solvent accessible surface area to be relevant to a biologic optimization project. Reasonable, although less precise, results are also obtained for the 44 more challenging mutations that involve buried residues, which may in some cases require substantial reorganization of the local protein structure, which can extend beyond the scope of a typical FEP simulation. We believe that the proposed prediction protocol will be of sufficient efficiency and accuracy to guide protein engineering projects for which optimization and/or maintenance of a high degree of binding affinity is a key objective.

Blinded predictions of standard binding free energies: lessons learned from the SAMPL6 challenge

In the context of the SAMPL6 challenges, series of blinded predictions of standard binding free energies were made with the SOMD software for a dataset of 27 host-guest systems featuring two octa-acids hosts (OA and TEMOA) and a cucurbituril ring (CB8) host. Three different models were used, ModelA computes the free energy of binding based on a double annihilation technique; ModelB additionally takes into account long-range dispersion and standard state corrections; ModelC additionally introduces an empirical correction term derived from a regression analysis of SAMPL5 predictions previously made with SOMD. The performance of each model was evaluated with two different setups; buffer explicitly matches the ionic strength from the binding assays, whereas no-buffer merely neutralizes the host-guest net charge with counter-ions. ModelC/no-buffer shows the lowest mean-unsigned error for the overall dataset (MUE 1.29 < 1.39 < 1.50 kcal mol^-1, 95% CI), while explicit modelling of the buffer improves significantly results for the CB8 host only. Correlation with experimental data ranges from excellent for the host TEMOA (R² 0.91 < 0.94 < 0.96), to poor for CB8 (R² 0.04 < 0.12 < 0.23). Further investigations indicate a pronounced dependence of the binding free energies on the modelled ionic strength, and variable reproducibility of the binding free energies between different simulation packages.

Comparing alchemical and physical pathway methods for computing the absolute binding free energy of charged ligands

Accurately predicting absolute binding free energies of protein-ligand complexes is important as a fundamental problem in both computational biophysics and pharmaceutical discovery. Calculating binding free energies for charged ligands is generally considered to be challenging because of the strong electrostatic interactions between the ligand and its environment in aqueous solution. In this work, we compare the performance of the potential of mean force (PMF) method and the double decoupling method (DDM) for computing absolute binding free energies for charged ligands. We first clarify an unresolved issue concerning the explicit use of the binding site volume to define the complexed state in DDM together with the use of harmonic restraints. We also provide an alternative derivation for the formula for absolute binding free energy using the PMF approach. We use these formulas to compute the binding free energy of charged ligands at an allosteric site of HIV-1 integrase, which has emerged in recent years as a promising target for developing antiviral therapy. As compared with the experimental results, the absolute binding free energies obtained by using the PMF approach show unsigned errors of 1.5-3.4 kcal mol-1, which are somewhat better than the results from DDM (unsigned errors of 1.6-4.3 kcal mol-1) using the same amount of CPU time. According to the DDM decomposition of the binding free energy, the ligand binding appears to be dominated by nonpolar interactions despite the presence of very large and favorable intermolecular ligand-receptor electrostatic interactions, which are almost completely cancelled out by the equally large free energy cost of desolvation of the charged moiety of the ligands in solution. We discuss the relative strengths of computing absolute binding free energies using the alchemical and physical pathway methods.

Multiple binding modes of ibuprofen in human serum albumin identified by absolute binding free energy calculations

Human serum albumin possesses multiple binding sites and transports a wide range of ligands that include the anti-inflammatory drug ibuprofen. A complete map of the binding sites of ibuprofen in albumin is difficult to obtain in traditional experiments, because of the structural adaptability of this protein in accommodating small ligands. In this work, we provide a set of predictions covering the geometry, affinity of binding and protonation state for the pharmaceutically most active form (S-isomer) of ibuprofen to albumin, by using absolute binding free energy calculations in combination with classical molecular dynamics (MD) simulations and molecular docking. The most favorable binding modes correctly reproduce several experimentally identified binding locations, which include the two Sudlow's drug sites (DS2 and DS1) and the fatty acid binding sites 6 and 2 (FA6 and FA2). Previously unknown details of the binding conformations were revealed for some of them, and formerly undetected binding modes were found in other protein sites. The calculated binding affinities exhibit trends which seem to agree with the available experimental data, and drastically degrade when the ligand is modeled in a protonated (neutral) state, indicating that ibuprofen associates with albumin preferentially in its charged form. These findings provide a detailed description of the binding of ibuprofen, help to explain a wide range of results reported in the literature in the last decades, and demonstrate the possibility of using simulation methods to predict ligand binding to albumin.

Binding affinities of the farnesoid X receptor in the D3R Grand Challenge 2 estimated by free-energy perturbation and docking

We have studied the binding of 102 ligands to the farnesoid X receptor within the D3R Grand Challenge 2016 blind-prediction competition. First, we employed docking with five different docking software and scoring functions. The selected docked poses gave an average root-mean-squared deviation of 4.2 Å. Consensus scoring gave decent results with a Kendall's τ of 0.26 ± 0.06 and a Spearman's ρ of 0.41 ± 0.08. For a subset of 33 ligands, we calculated relative binding free energies with free-energy perturbation. Five transformations between the ligands involved a change of the net charge and we implemented and benchmarked a semi-analytic correction (Rocklin et al., J Chem Phys 139:184103, 2013) for artifacts caused by the periodic boundary conditions and Ewald summation. The results gave a mean absolute deviation of 7.5 kJ/mol compared to the experimental estimates and a correlation coefficient of R 2 = 0.1. These results were among the four best in this competition out of 22 submissions. The charge corrections were significant (7-8 kJ/mol) and always improved the results. By employing 23 intermediate states in the free-energy perturbation, there was a proper overlap between all states and the precision was 0.1-0.7 kJ/mol. However, thermodynamic cycles indicate that the sampling was insufficient in some of the perturbations.

Free energy calculations on the stability of the 14-3-3ζ protein

Mutations of cysteine are often introduced to e.g. avoid formation of non-physiological inter-molecular disulfide bridges in in-vitro experiments, or to maintain specificity in labeling experiments. Alanine or serine is typically preferred, which usually do not alter the overall protein stability, when the original cysteine was surface exposed. However, selecting the optimal mutation for cysteines in the hydrophobic core of the protein is more challenging. In this work, the stability of selected Cys mutants of 14-3-3ζ was predicted by free-energy calculations and the obtained data were compared with experimentally determined stabilities. Both the computational predictions as well as the experimental validation point at a significant destabilization of mutants C94A and C94S. This destabilization could be attributed to the formation of hydrophobic cavities and a polar solvation of a hydrophilic side chain. A L12E, M78K double mutant was further studied in terms of its reduced dimerization propensity. In contrast to naïve expectations, this double mutant did not lead to the formation of strong salt bridges, which was rationalized in terms of a preferred solvation of the ionic species. Again, experiments agreed with the calculations by confirming the monomerization of the double mutants. Overall, the simulation data is in good agreement with experiments and offers additional insight into the stability and dimerization of this important family of regulatory proteins.

Transition state-based ST6Gal I inhibitors: Mimicking the phosphodiester linkage with a triazole or carbamate through an enthalpy-entropy compensation

Human β-galactoside α-2,6-sialyltransferase I (ST6Gal I) catalyses the synthesis of sialylated glycoconjugates. Overexpression of ST6Gal I is observed in many cancers, where it promotes metastasis through altered cell surface sialylation. A wide range of sialyltransferase inhibitors have been developed, with analogues structurally similar to the transition state exhibiting the highest inhibitory activity. To improve synthetic accessibility and pharmacokinetics of previously reported inhibitors, the replacement of the charged phosphodiester linker with a potential neutral isostere such as a carbamate or a 1,2,3-triazole has been investigated. Extensive molecular dynamics simulations have demonstrated that compounds with the alternate linkers could maintain key interactions with the human ST6Gal I active site, demonstrating the potential of a carbamate or a 1,2,3-triazole as a phosphodiester isostere. Free energy perturbation calculations provided energetic evidence suggesting that the carbamate and 1,2,3-triazole were slightly more favourable than the phosphodiester. Further exploration with free energy component, quasi-harmonic and cluster analysis suggested that there is an enthalpy-entropy compensation accounting for the replacement of the flexible charged phosphodiester with a neutral and rigid isostere. Overall, these simulations provide a strong rationale for the use of a carbamate or 1,2,3-triazole as a phosphodiester isostere in the development of novel inhibitors of human ST6Gal I.

Attach-Pull-Release Calculations of Ligand Binding and Conformational Changes on the First BRD4 Bromodomain

Bromodomains, protein domains involved in epigenetic regulation, are able to bind small molecules with high affinity. In the present study, we report free energy calculations for the binding of seven ligands to the first BRD4 bromodomain, using the attach-pull-release (APR) method to compute the reversible work of removing the ligands from the binding site and then allowing the protein to relax conformationally. We test three different water models, TIP3P, TIP4PEw, and SPC/E, as well as the GAFF and GAFF2 parameter sets for the ligands. Our simulations show that the apo crystal structure of BRD4 is only metastable, with a structural transition happening in the absence of the ligand typically after 20 ns of simulation. We compute the free energy change for this transition with a separate APR calculation on the free protein and include its contribution to the ligand binding free energies, which generally causes an underestimation of the affinities. By testing different water models and ligand parameters, we are also able to assess their influence in our results and determine which one produces the best agreement with the experimental data. Both free energies associated with the conformational change and ligand binding are affected by the choice of water model, with the two sets of ligand parameters affecting their binding free energies to a lesser degree. Across all six combinations of water model and ligand potential function, the Pearson correlation coefficients between calculated and experimental binding free energies range from 0.55 to 0.83, and the root-mean-square errors range from 1.4-3.2 kcal/mol. The current protocol also yields encouraging preliminary results when used to assess the relative stability of ligand poses generated by docking or other methods, as illustrated for two different ligands. Our method takes advantage of the high performance provided by graphics processing units and can readily be applied to other ligands as well as other protein systems.

Predicting Binding Free Energies: Frontiers and Benchmarks

Binding free energy calculations based on molecular simulations provide predicted affinities for biomolecular complexes. These calculations begin with a detailed description of a system, including its chemical composition and the interactions among its components. Simulations of the system are then used to compute thermodynamic information, such as binding affinities. Because of their promise for guiding molecular design, these calculations have recently begun to see widespread applications in early-stage drug discovery. However, many hurdles remain in making them a robust and reliable tool. In this review, we highlight key challenges of these calculations, discuss some examples of these challenges, and call for the designation of standard community benchmark test systems that will help the research community generate and evaluate progress. In our view, progress will require careful assessment and evaluation of new methods, force fields, and modeling innovations on well-characterized benchmark systems, and we lay out our vision for how this can be achieved.

Free Energy Perturbation Calculation of Relative Binding Free Energy between Broadly Neutralizing Antibodies and the gp120 Glycoprotein of HIV-1

Direct calculation of relative binding affinities between antibodies and antigens is a long-sought goal. However, despite substantial efforts, no generally applicable computational method has been described. Here, we describe a systematic free energy perturbation (FEP) protocol and calculate the binding affinities between the gp120 envelope glycoprotein of HIV-1 and three broadly neutralizing antibodies (bNAbs) of the VRC01 class. The protocol has been adapted from successful studies of small molecules to address the challenges associated with modeling protein-protein interactions. Specifically, we built homology models of the three antibody-gp120 complexes, extended the sampling times for large bulky residues, incorporated the modeling of glycans on the surface of gp120, and utilized continuum solvent-based loop prediction protocols to improve sampling. We present three experimental surface plasmon resonance data sets, in which antibody residues in the antibody/gp120 interface were systematically mutated to alanine. The RMS error in the large set (55 total cases) of FEP tests as compared to these experiments, 0.68kcal/mol, is near experimental accuracy, and it compares favorably with the results obtained from a simpler, empirical methodology. The correlation coefficient for the combined data set including residues with glycan contacts, R2=0.49, should be sufficient to guide the choice of residues for antibody optimization projects, assuming that this level of accuracy can be realized in prospective prediction. More generally, these results are encouraging with regard to the possibility of using an FEP approach to calculate the magnitude of protein-protein binding affinities.

Blinded predictions of distribution coefficients in the SAMPL5 challenge

In the context of the SAMPL5 challenge water-cyclohexane distribution coefficients for 53 drug-like molecules were predicted. Four different models based on molecular dynamics free energy calculations were tested. All models initially assumed only one chemical state present in aqueous or organic phases. Model A is based on results from an alchemical annihilation scheme; model B adds a long range correction for the Lennard Jones potentials to model A; model C adds charging free energy corrections; model D applies the charging correction from model C to ionizable species only. Model A and B perform better in terms of mean-unsigned error ([Formula: see text] D units - 95 % confidence interval) and determination coefficient [Formula: see text], while charging corrections lead to poorer results with model D ([Formula: see text] and [Formula: see text]). Because overall errors were large, a retrospective analysis that allowed co-existence of ionisable and neutral species of a molecule in aqueous phase was investigated. This considerably reduced systematic errors ([Formula: see text] and [Formula: see text]). Overall accurate [Formula: see text] predictions for drug-like molecules that may adopt multiple tautomers and charge states proved difficult, indicating a need for methodological advances to enable satisfactory treatment by explicit-solvent molecular simulations.

All-Atom Continuous Constant pH Molecular Dynamics With Particle Mesh Ewald and Titratable Water

Development of a pH stat to properly control solution pH in biomolecular simulations has been a long-standing goal in the community. Toward this goal recent years have witnessed the emergence of the so-called constant pH molecular dynamics methods. However, the accuracy and generality of these methods have been hampered by the use of implicit-solvent models or truncation-based electrostatic schemes. Here we report the implementation of the particle mesh Ewald (PME) scheme into the all-atom continuous constant pH molecular dynamics (CpHMD) method, enabling CpHMD to be performed with a standard MD engine at a fractional added computational cost. We demonstrate the performance using pH replica-exchange CpHMD simulations with titratable water for a stringent test set of proteins, HP36, BBL, HEWL, and SNase. With the sampling time of 10 ns per replica, most pK_a's are converged, yielding the average absolute and root-mean-square deviations of 0.61 and 0.77, respectively, from experiment. Linear regression of the calculated vs experimental pK_a shifts gives a correlation coefficient of 0.79, a slope of 1, and an intercept near 0. Analysis reveals inadequate sampling of structure relaxation accompanying a protonation-state switch as a major source of the remaining errors, which are reduced as simulation prolongs. These data suggest PME-based CpHMD can be used as a general tool for pH-controlled simulations of macromolecular systems in various environments, enabling atomic insights into pH-dependent phenomena involving not only soluble proteins but also transmembrane proteins, nucleic acids, surfactants, and polysaccharides.

Blinded predictions of host-guest standard free energies of binding in the SAMPL5 challenge

In the context of the SAMPL5 blinded challenge standard free energies of binding were predicted for a dataset of 22 small guest molecules and three different host molecules octa-acids (OAH and OAMe) and a cucurbituril (CBC). Three sets of predictions were submitted, each based on different variations of classical molecular dynamics alchemical free energy calculation protocols based on the double annihilation method. The first model (model A) yields a free energy of binding based on computed free energy changes in solvated and host-guest complex phases; the second (model B) adds long range dispersion corrections to the previous result; the third (model C) uses an additional standard state correction term to account for the use of distance restraints during the molecular dynamics simulations. Model C performs the best in terms of mean unsigned error for all guests (MUE [Formula: see text]-95 % confidence interval) for the whole data set and in particular for the octa-acid systems (MUE [Formula: see text]). The overall correlation with experimental data for all models is encouraging ([Formula: see text]). The correlation between experimental and computational free energy of binding ranks as one of the highest with respect to other entries in the challenge. Nonetheless the large MUE for the best performing model highlights systematic errors, and submissions from other groups fared better with respect to this metric.

Multistate λ-local-elevation umbrella-sampling (MS-λ-LEUS): method and application to the complexation of cations by crown ethers

An extension of the λ-local-elevation umbrella-sampling (λ-LEUS) scheme [ Bieler et al. J. Chem. Theory Comput. 2014 , 10 , 3006 ] is proposed to handle the multistate (MS) situation, i.e. the calculation of the relative free energies of multiple physical states based on a single simulation. The key element of the MS-λ-LEUS approach is to use a single coupling variable Λ controlling successive pairwise mutations between the states of interest in a cyclic fashion. The Λ variable is propagated dynamically as an extended-system variable, using a coordinate transformation with plateaus and a memory-based biasing potential as in λ-LEUS. Compared to other available MS schemes (one-step perturbation, enveloping distribution sampling and conventional λ-dynamics) the proposed method presents a number of important advantages, namely: (i) the physical states are visited explicitly and over finite time periods; (ii) the extent of unphysical space required to ensure transitions is kept minimal and, in particular, one-dimensional; (iii) the setup protocol solely requires the topologies of the physical states; and (iv) the method only requires limited modifications in a simulation code capable of handling two-state mutations. As an initial application, the absolute binding free energies of five alkali cations to three crown ethers in three different solvents are calculated. The results are found to reproduce qualitatively the main experimental trends and, in particular, the experimental selectivity of 18C6 for K(+) in water and methanol, which is interpreted in terms of opposing trends along the cation series between the solvation free energy of the cation and the direct electrostatic interactions within the complex.

Origin of Asymmetric Solvation Effects for Ions in Water and Organic Solvents Investigated Using Molecular Dynamics Simulations: The Swain Acity-Basity Scale Revisited

The asymmetric solvation of ions can be defined as the tendency of a solvent to preferentially solvate anions over cations or cations over anions, at identical ionic charge magnitudes and effective sizes. Taking water as a reference, these effects are quantified experimentally for many solvents by the relative acity (A) and basity (B) parameters of the Swain scale. The goal of the present study is to investigate the asymmetric solvation of ions using molecular dynamics simulations, and to connect the results to this empirical scale. To this purpose, the charging free energies of alkali and halide ions, and of their hypothetical oppositely charged counterparts, are calculated in a variety of solvents. In a first set of calculations, artificial solvent models are considered that present either a charge or a shape asymmetry at the molecular level. The solvation asymmetry, probed by the difference in charging free energy between the two oppositely charged ions, is found to encompass a term quadratic in the ion charge, related to the different solvation structures around the anion and cation, and a term linear in the ion charge, related to the solvation structure around the uncharged ion-sized cavity. For these simple solvent models, the two terms are systematically counteracting each other, and it is argued that only the quadratic term should be retained when comparing the results of simulations involving physical solvents to experimental data. In a second set of calculations, 16 physical solvents are considered. The theoretical estimates for the acity A are found to correlate very well with the Swain parameters, whereas the correlation for B is very poor. Based on this observation, the Swain scale is reformulated into a new scale involving an asymmetry parameter Σ, positive for acitic solvents and negative for basitic ones, and a polarity parameter Π. This revised scale has the same predictive power as the original scale, but it characterizes asymmetry in an absolute sense, the atomistic simulations playing the role of an extra-thermodynamic assumption, and is optimally compatible with the simulation results. Considering the 55 solvents in the Swain set, it is observed that a moderate basity (Σ between -0.9 and -0.3, related to electronic polarization) represents the baseline for most solvents, while a highly variable acity (Σ between 0.0 and 3.0, related to hydrogen-bond donor capacity modulated by inductive effects) represents a landmark of protic solvents.

Effect of Oxidative Damage on the Stability and Dimerization of Superoxide Dismutase 1

During their life cycle, proteins are subject to different modifications involving reactive oxygen species. Such oxidative damage to proteins may lead to the formation of insoluble aggregates and cytotoxicity and is associated with age-related disorders including neurodegenerative diseases, cancer, and diabetes. Superoxide dismutase 1 (SOD1), a key antioxidant enzyme in human cells, is particularly susceptible to such modifications. Moreover, this homodimeric metalloenzyme has been directly linked to both familial and sporadic amyotrophic lateral sclerosis (ALS), a devastating, late-onset motor neuronal disease, with more than 150 ALS-related mutations in the SOD1 gene. Importantly, oxidatively damaged SOD1 aggregates have been observed in both familial and sporadic forms of the disease. However, the molecular mechanisms as well as potential implications of oxidative stress in SOD1-induced cytotoxicity remain elusive. In this study, we examine the effects of oxidative modification on SOD1 monomer and homodimer stability, the key molecular properties related to SOD1 aggregation. We use molecular dynamics simulations in combination with thermodynamic integration to study microscopic-level site-specific effects of oxidative "mutations" at the dimer interface, including lysine, arginine, proline and threonine carbonylation, and cysteine oxidation. Our results show that oxidative damage of even single residues at the interface may drastically destabilize the SOD1 homodimer, with several modifications exhibiting a comparable effect to that of the most drastic ALS-causing mutations known. Additionally, we show that the SOD1 monomer stability decreases upon oxidative stress, which may lead to partial local unfolding and consequently to increased aggregation propensity. Importantly, these results suggest that oxidative stress may play a key role in development of ALS, with the mutations in the SOD1 gene being an additional factor.

Selective binding modes and allosteric inhibitory effects of lupane triterpenes on protein tyrosine phosphatase 1B

Protein Tyrosine Phosphatase 1B (PTP1B) has been recognized as a promising therapeutic target for treating obesity, diabetes, and certain cancers for over a decade. Previous drug design has focused on inhibitors targeting the active site of PTP1B. However, this has not been successful because the active site is positively charged and conserved among the protein tyrosine phosphatases. Therefore, it is important to develop PTP1B inhibitors with alternative inhibitory strategies. Using computational studies including molecular docking, molecular dynamics simulations, and binding free energy calculations, we found that lupane triterpenes selectively inhibited PTP1B by targeting its more hydrophobic and less conserved allosteric site. These findings were verified using two enzymatic assays. Furthermore, the cell culture studies showed that lupeol and betulinic acid inhibited the PTP1B activity stimulated by TNFα in neurons. Our study indicates that lupane triterpenes are selective PTP1B allosteric inhibitors with significant potential for treating those diseases with elevated PTP1B activity.

Prediction of Ligand Binding Affinity by the Combination of Replica-Exchange Method and Double-Decoupling Method

A prediction method for ligand binding affinities to proteins is proposed. We first predict the structures of protein-ligand complex by the replica-exchange umbrella sampling or its extension. We then calculate ligand binding affinities based on these predicted ligand-protein bound structures by the double-decoupling method. As a test of the effectiveness of the proposed method, we applied it to the system of the oncoprotein MDM2 and a ligand. The value of the predicted binding affinity turned out to be in good agreement with that from experiments.

Parameterization of an effective potential for protein-ligand binding from host-guest affinity data

Force field accuracy is still one of the "stalemates" in biomolecular modeling. Model systems with high quality experimental data are valuable instruments for the validation and improvement of effective potentials. With respect to protein-ligand binding, organic host-guest complexes have long served as models for both experimental and computational studies because of the abundance of binding affinity data available for such systems. Binding affinity data collected for cyclodextrin (CD) inclusion complexes, a popular model for molecular recognition, is potentially a more reliable resource for tuning energy parameters than hydration free energy measurements. Convergence of binding free energy calculations on CD host-guest systems can also be obtained rapidly, thus offering the opportunity to assess the robustness of these parameters. In this work, we demonstrate how implicit solvent parameters can be developed using binding affinity experimental data and the binding energy distribution analysis method (BEDAM) and validated using the Grid Inhomogeneous Solvation Theory analysis. These new solvation parameters were used to study protein-ligand binding in two drug targets against the HIV-1 virus and improved the agreement between the calculated and the experimental binding affinities. This work illustrates how benchmark sets of high quality experimental binding affinity data and physics-based binding free energy models can be used to evaluate and optimize force fields for protein-ligand systems. Copyright © 2015 John Wiley & Sons, Ltd.

Toward the correction of effective electrostatic forces in explicit-solvent molecular dynamics simulations: restraints on solvent-generated electrostatic potential and solvent polarization

Despite considerable advances in computing power, atomistic simulations under nonperiodic boundary conditions, with Coulombic electrostatic interactions and in systems large enough to reduce finite-size associated errors in thermodynamic quantities to within the thermal energy, are still not affordable. As a result, periodic boundary conditions, systems of microscopic size and effective electrostatic interaction functions are frequently resorted to. Ensuing artifacts in thermodynamic quantities are nowadays routinely corrected a posteriori, but the underlying configurational sampling still descends from spurious forces. The present study addresses this problem through the introduction of on-the-fly corrections to the physical forces during an atomistic molecular dynamics simulation. Two different approaches are suggested, where the force corrections are derived from special potential energy terms. In the first approach, the solvent-generated electrostatic potential sampled at a given atom site is restrained to a target value involving corrections for electrostatic artifacts. In the second approach, the long-range regime of the solvent polarization around a given atom site is restrained to the Born polarization, i.e., the solvent polarization corresponding to the ideal situation of a macroscopic system under nonperiodic boundary conditions and governed by Coulombic electrostatic interactions. The restraints are applied to the explicit-water simulation of a hydrated sodium ion, and the effect of the restraints on the structural and energetic properties of the solvent is illustrated. Furthermore, by means of the calculation of the charging free energy of a hydrated sodium ion, it is shown how the electrostatic potential restraint translates into the on-the-fly consideration of the corresponding free-energy correction terms. It is discussed how the restraints can be generalized to situations involving several solute particles. Although the present study considers a very simple system only, it is an important step toward the on-the-fly elimination of finite-size and approximate-electrostatic artifacts during atomistic molecular dynamics simulations.