Prediction of protein-ligand binding affinity by free energy simulations: assumptions, pitfalls and expectations

Absolute Binding Free Energies with OneOPES

The calculation of absolute binding free energies (ABFEs) for protein-ligand systems has long been a challenge. Recently, refined force fields and algorithms have improved the quality of the ABFE calculations. However, achieving the level of accuracy required to inform drug discovery efforts remains difficult. Here, we present a transferable enhanced sampling strategy to accurately calculate absolute binding free energies using OneOPES with simple geometric collective variables. We tested the strategy on two protein targets, BRD4 and Hsp90, complexed with a total of 17 chemically diverse ligands, including both molecular fragments and drug-like molecules. Our results show that OneOPES accurately predicts protein-ligand binding affinities with a mean unsigned error within 1 kcal mol-1 of experimentally determined free energies, without the need to tailor the collective variables to each system. Furthermore, our strategy effectively samples different ligand binding modes and consistently matches the experimentally determined structures regardless of the initial protein-ligand configuration. Our results suggest that the proposed OneOPES strategy can be used to inform lead optimization campaigns in drug discovery and to study protein-ligand binding and unbinding mechanisms.

Insights into the Role of Side-Chain Team Work in nDsbDOx/Red Proteins: Mechanism of Substrate Binding

N-terminal disulfide bond oxidoreductase (nDsbDOx/Red) proteins display divergent substrate binding mechanisms depending on the conformational changes to the Phe70 cap, which is also dependent on the disulfide redox state. In nDsbDOx, the cap dynamics is complex (shows both open/closed Phe70 cap conformations), resulting in an active site that is highly flexible. So the system's active site is conformationally selective (the active site adapts before substrate binding) toward its substrate. In nDsbDRed, the cap is generally closed, resulting in induced fit-type binding (adapts after substrate approach). Recent studies predict Tyr40 and Tyr42 residues to act as internal nucleophiles (Tyr40/42O-) for disulfide association/dissociation in nDsbDOx/Red, supplementing the electron transfer channel. From this perspective, we investigate the cap dynamics and the subsequent substrate binding modes in these proteins. Our molecular dynamics simulations show that the cap opening eliminates Tyr42O- electrostatic interactions irrespective of the disulfide redox state. The active site becomes highly flexible, and the conformational selection mechanism governs. However, Tyr40O- formation does not alter the chemical environment; the cap remains mostly closed and plausibly follows the induced fit mechanism. Thus, it is apparent that mostly Tyr42O- facilitates the internal nucleophile-mediated self-preparation of nDsbDOx/Red proteins for binding.

Automated Absolute Binding Free Energy Calculation Workflow for Drug Discovery

Absolute binding free energies play a crucial role in drug development, particularly as part of the lead discovery process. In recent work, we showed how in silico predictions directly could support drug development by ranking and recommending favorable ideas over unfavorable ones. Here, we demonstrate a Python workflow that enables the calculation of ABFEs with minimal manual input effort, such as the receptor PDB and ligand SDF files, and outputs a .tsv file containing the ranked ligands and their corresponding binding free energies. The implementation uses Snakemake to structure and control the execution of tasks, allowing for dynamic control of parameters and execution patterns. We provide an example of a benchmark system that demonstrates the effectiveness of the automated workflow.

Alchemical Free Energy Workflows for the Computation of Protein-Ligand Binding Affinities

Alchemical free energy methods can be used for the efficient computation of relative binding free energies during preclinical drug discovery stages. In recent years, this has been facilitated further by the implementation of workflows that enable non-experts to quickly and consistently set up the required simulations. Given the correct input structures, workflows handle the difficult aspects of setting up perturbations, including consistently defining the perturbable molecule, its atom mapping and topology generation, perturbation network generation, running of the simulations via different sampling methods, and analysis of the results. Different academic and commercial workflows are discussed, including FEW, FESetup, FEPrepare, CHARMM-GUI, Transformato, PMX, QLigFEP, TIES, ProFESSA, PyAutoFEP, BioSimSpace, FEP+, Flare, and Orion. These workflows differ in various aspects, such as mapping algorithms or enhanced sampling methods. Some workflows can accommodate more than one molecular dynamics (MD) engine and use external libraries for tasks. Differences between workflows can present advantages for different use cases, however a lack of interoperability of the workflows' components hinders systematic comparisons.

Attempting Well-Tempered Funnel Metadynamics Simulations for the Evaluation of the Binding Kinetics of Methionine Aminopeptidase-II Inhibitors

Understanding the unbinding kinetics of protein-ligand complexes is considered a significant approach for the design of ligands with desired specificity and safety. In recent years, enhanced sampling methods have emerged as effective tools for studying the unbinding kinetics of protein-ligand complexes at the atomistic level. MetAP-II is a target for the treatment of cancer for which not a single effective drug is available yet. The identification of the dissociation rate of ligands from the complexes often serves as a better predictor for in vivo efficacy than the ligands' binding affinity. Here, funnel-based restraint well-tempered metadynamics simulations were applied to predict the residence time of two ligands bound to MetAP-II, along with the ligand association and dissociation mechanism involving the identification of the binding hotspot during ligand egress. The ligand-egressing route revealed by metadynamics simulations also correlated with the identified pathways from the CAVER analysis and by the enhanced sampling simulation using PLUMED. Ligand 1 formed a strong H-bond interaction with GLU364 estimating a higher residence time of 28.22 ± 5.29 ns in contrast to ligand 2 with a residence time of 19.05 ± 3.58 ns, which easily dissociated from the binding pocket of MetAP-II. The results obtained from the simulations were consistent to reveal ligand 1 being superior to ligand 2; however, the experimental data related to residence time were close for both ligands, and no kinetic data were available for ligand 2. The current study could be considered the first attempt to apply an enhanced sampling method for the evaluation of the binding kinetics and thermodynamics of two different classes of ligands to a binuclear metalloprotein.

Exploring the Binding Pathway of Novel Nonpeptidomimetic Plasmepsin V Inhibitors

Predicting the interaction modes and binding affinities of virtual compound libraries is of great interest in drug development. It reduces the cost and time of lead compound identification and selection. Here we apply path-based metadynamics simulations to characterize the binding of potential inhibitors to the Plasmodium falciparum aspartic protease plasmepsin V (plm V), a validated antimalarial drug target that has a highly mobile binding site. The potential plm V binders were identified in a high-throughput virtual screening (HTVS) campaign and were experimentally verified in a fluorescence resonance energy transfer (FRET) assay. Our simulations allowed us to estimate compound binding energies and revealed relevant states along binding/unbinding pathways in atomistic resolution. We believe that the method described allows the prioritization of compounds for synthesis and enables rational structure-based drug design for targets that undergo considerable conformational changes upon inhibitor binding.

On the Path to Optimal Alchemistry

Alchemical free energy calculations have become a standard and widely used tool, in particular for calculating and comparing binding affinities of drugs. Although methods to compute such free energies have improved significantly over the last decades, the choice of path between the end states of interest is usually still the same as two decades ago. We will show that there is a fundamentally arbitrary, implicit choice of parametrization of this path. To address this, the notion of the length of a path or a metric is required. A metric recently introduced in the context of the accelerated weight histogram method also proves to be very useful here. We demonstrate that this metric can not only improve the efficiency of sampling along a given path, but that it can also be used to improve the actual choice of path. For a set of relevant use cases, the combination of these improvements can increase the efficiency of alchemical free energy calculations by up to a factor 16.

ACES: Optimized Alchemically Enhanced Sampling

We present an alchemical enhanced sampling (ACES) method implemented in the GPU-accelerated AMBER free energy MD engine. The methods hinges on the creation of an "enhanced sampling state" by reducing or eliminating selected potential energy terms and interactions that lead to kinetic traps and conformational barriers while maintaining those terms that curtail the need to otherwise sample large volumes of phase space. For example, the enhanced sampling state might involve transforming regions of a ligand and/or protein side chain into a noninteracting "dummy state" with internal electrostatics and torsion angle terms turned off. The enhanced sampling state is connected to a real-state end point through a Hamiltonian replica exchange (HREMD) framework that is facilitated by newly developed alchemical transformation pathways and smoothstep softcore potentials. This creates a counterdiffusion of real and enhanced-sampling states along the HREMD network. The effect of a differential response of the environment to the real and enhanced-sampling states is minimized by leveraging the dual topology framework in AMBER to construct a counterbalancing HREMD network in the opposite alchemical direction with the same (or similar) real and enhanced sampling states at inverted end points. The method has been demonstrated in a series of test cases of increasing complexity where traditional MD, and in several cases alternative REST2-like enhanced sampling methods, are shown to fail. The hydration free energy for acetic acid was shown to be independent of the starting conformation, and the values for four additional edge case molecules from the FreeSolv database were shown to have a significantly closer agreement with experiment using ACES. The method was further able to handle different rotamer states in a Cdk2 ligand identified as fractionally occupied in crystal structures. Finally, ACES was applied to T4-lysozyme and demonstrated that the side chain distribution of V111χ1 could be reliably reproduced for the apo state, bound to p-xylene, and in p-xylene→ benzene transformations. In these cases, the ACES method is shown to be highly robust and superior to a REST2-like enhanced sampling implementation alone.

Accelerated Enveloping Distribution Sampling (AEDS) Allows for Efficient Sampling of Orthogonal Degrees of Freedom

One of the most challenging aspects in the molecular simulation of proteins is the study of slowly relaxing processes, such as loop rearrangements or ligands that adopt different conformations in the binding site. State-of-the-art methods used to calculate binding free energies rely on performing several short simulations (lambda steps), in which the ligand is slowly transformed into the endstates of interest. This makes capturing the slowly relaxing processes even more difficult, as they would need to be observed in all of the lambda steps. One attractive alternative is the use of a reference state capable of sampling all of the endstates of interest in a single simulation. However, the energy barriers between the states can be too high to overcome, thus hindering the sampling of all of the relevant conformations. Accelerated enveloping distribution sampling (AEDS) is a recently developed reference state technique that circumvents the high-energy-barrier challenge by adding a boosting potential that flattens the energy landscape without distorting the energy minima. In the present work, we apply AEDS to the well-studied benchmark system T4 lysozyme L99A. The T4 lysozyme L99A mutant contains a hydrophobic pocket in which there is a valine (valine 111), whose conformation influences the binding efficiencies of the different ligands. Incorrectly sampling the dihedral angle can lead to errors in predicted binding free energies of up to 16 kJ mol^-1. This protein constitutes an ideal scenario to showcase the advantages and challenges when using AEDS in the presence of slow relaxing processes. We show that AEDS is able to successfully sample the relevant degrees of freedom, providing accurate binding free energies, without the need of previous information of the system in the form of collective variables. Additionally, we showcase the capabilities of AEDS to efficiently screen a set of ligands. These results represent a promising first step toward the development of free-energy methods that can respond to more intricate molecular events.

Shedding light on the binding mechanism of kinase inhibitors BI-2536, Volasetib and Ro-3280 with their pharmacological target PLK1

In the present work, the interactions of the novel kinase inhibitors BI-2536, Volasetib (BI-6727) and Ro-3280 with the pharmacological target PLK1 have been studied by fluorescence spectroscopy and molecular dynamics calculations. High Stern-Volmer constants were found in fluorescence experiments suggesting the formation of stable protein-ligand complexes. In addition, it was observed that the binding constant between BI-2536 and PLK1 increases about 100-fold in presence of the phosphopeptide Cdc25C-p that docks to the polo box domain of the protein and releases the kinase domain. All the determined binding constants are higher for the kinase inhibitors than for their competitor for the active center (ATP) being BI-2536 and Volasertib the inhibitors that showed more affinity for PLK1. Calculated binding free energies confirmed the higher affinity of PLK1 for BI-2536 and Volasertib than for ATP. The higher affinity of the inhibitors to PLK1 compared to ATP was mainly attributed to stronger van der Waals interactions. Results may help with the challenge of designing and developing new kinase inhibitors more effective in clinical cancer therapy.

A lesson for the maestro of the replication fork: Targeting the protein-binding interface of proliferating cell nuclear antigen for anticancer therapy

The proliferating cell nuclear antigen (PCNA) has emerged as a promising candidate for the development of novel cancer therapeutics. PCNA is a nononcogenic mediator of DNA replication that regulates a diverse range of cellular functions and pathways through a comprehensive list of protein-protein interactions. The hydrophobic binding pocket on PCNA offers an opportunity for the development of inhibitors to target various types of cancers and modulate protein-protein interactions. In the present study, we explored the binding modes and affinity of molecule I1 (standard molecule) with the previously suggested dimer interface pocket and the hydrophobic pocket present on the frontal side of the PCNA monomer. We also identified potential lead molecules from the library of in-house synthesized 3-methylenisoindolin-1-one based molecules to inhibit the protein-protein interactions of PCNA. Our results were based on robust computational methods, including molecular docking, conventional, steered, and umbrella sampling molecular dynamics simulations. Our results suggested that the standard inhibitor I1 interacts with the hydrophobic pocket of PCNA with a higher affinity than the previously suggested binding site. Also, the proposed molecules showed better or comparable binding free energies as calculated by the Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) approach and further validated by enhanced umbrella sampling simulations. In vitro and in vivo methods could test the computationally suggested molecules for advancement in the drug discovery pipeline.

RestraintMaker: a graph-based approach to select distance restraints in free-energy calculations with dual topology

The calculation of relative binding free energies (RBFE) involves the choice of the end-state/system representation, of a sampling approach, and of a free-energy estimator. System representations are usually termed "single topology" or "dual topology". As the terminology is often used ambiguously in the literature, a systematic categorization of the system representations is proposed here. In the dual-topology approach, the molecules are simulated as separate molecules. Such an approach is relatively easy to automate for high-throughput RBFE calculations compared to the single-topology approach. Distance restraints are commonly applied to prevent the molecules from drifting apart, thereby improving the sampling efficiency. In this study, we introduce the program RestraintMaker, which relies on a greedy algorithm to find (locally) optimal distance restraints between pairs of atoms based on geometric measures. The algorithm is further extended for multi-state methods such as enveloping distribution sampling (EDS) or multi-site [Formula: see text]-dynamics. The performance of RestraintMaker is demonstrated for toy models and for the calculation of relative hydration free energies. The Python program can be used in script form or through an interactive GUI within PyMol. The selected distance restraints can be written out in GROMOS or GROMACS file formats. Additionally, the program provides a human-readable JSON format that can easily be parsed and processed further. The code of RestraintMaker is freely available on GitHub https://github.com/rinikerlab/restraintmaker.

Substrate Access Mechanism in a Novel Membrane-Bound Phospholipase A of Pseudomonas aeruginosa Concordant with Specificity and Regioselectivity

PlaF is a cytoplasmic membrane-bound phospholipase A₁ from Pseudomonas aeruginosa that alters the membrane glycerophospholipid (GPL) composition and fosters the virulence of this human pathogen. PlaF activity is regulated by a dimer-to-monomer transition followed by tilting of the monomer in the membrane. However, how substrates reach the active site and how the characteristics of the active site tunnels determine the activity, specificity, and regioselectivity of PlaF for natural GPL substrates have remained elusive. Here, we combined unbiased and biased all-atom molecular dynamics (MD) simulations and configurational free-energy computations to identify access pathways of GPL substrates to the catalytic center of PlaF. Our results map out a distinct tunnel through which substrates access the catalytic center. PlaF variants with bulky tryptophan residues in this tunnel revealed decreased catalysis rates due to tunnel blockage. The MD simulations suggest that GPLs preferably enter the active site with the sn-1 acyl chain first, which agrees with the experimentally demonstrated PLA₁ activity of PlaF. We propose that the acyl chain-length specificity of PlaF is determined by the structural features of the access tunnel, which results in favorable free energy of binding of medium-chain GPLs. The suggested egress route conveys fatty acid (FA) products to the dimerization interface and, thus, contributes to understanding the product feedback regulation of PlaF by FA-triggered dimerization. These findings open up opportunities for developing potential PlaF inhibitors, which may act as antibiotics against P. aeruginosa.

The automated optimisation of a coarse-grained force field using free energy data

Atomistic models provide a detailed representation of molecular systems, but are sometimes inadequate for simulations of large systems over long timescales. Coarse-grained models enable accelerated simulations by reducing the number of degrees of freedom, at the cost of reduced accuracy. New optimisation processes to parameterise these models could improve their quality and range of applicability. We present an automated approach for the optimisation of coarse-grained force fields, by reproducing free energy data derived from atomistic molecular simulations. To illustrate the approach, we implemented hydration free energy gradients as a new target for force field optimisation in ForceBalance and applied it successfully to optimise the un-charged side-chains and the protein backbone in the SIRAH protein coarse-grain force field. The optimised parameters closely reproduced hydration free energies of atomistic models and gave improved agreement with experiment.

OnionNet-2: A Convolutional Neural Network Model for Predicting Protein-Ligand Binding Affinity Based on Residue-Atom Contacting Shells

One key task in virtual screening is to accurately predict the binding affinity (△G) of protein-ligand complexes. Recently, deep learning (DL) has significantly increased the predicting accuracy of scoring functions due to the extraordinary ability of DL to extract useful features from raw data. Nevertheless, more efforts still need to be paid in many aspects, for the aim of increasing prediction accuracy and decreasing computational cost. In this study, we proposed a simple scoring function (called OnionNet-2) based on convolutional neural network to predict △G. The protein-ligand interactions are characterized by the number of contacts between protein residues and ligand atoms in multiple distance shells. Compared to published models, the efficacy of OnionNet-2 is demonstrated to be the best for two widely used datasets CASF-2016 and CASF-2013 benchmarks. The OnionNet-2 model was further verified by non-experimental decoy structures from docking program and the CSAR NRC-HiQ data set (a high-quality data set provided by CSAR), which showed great success. Thus, our study provides a simple but efficient scoring function for predicting protein-ligand binding free energy.

Perturbation Free-Energy Toolkit: An Automated Alchemical Topology Builder

Free-energy calculations play an important role in the application of computational chemistry to a range of fields, including protein biochemistry, rational drug design, or materials science. Importantly, the free-energy difference is directly related to experimentally measurable quantities such as partition and adsorption coefficients, water activity, and binding affinities. Among several techniques aimed at predicting free-energy differences, perturbation approaches, involving the alchemical transformation of one molecule into another through intermediate states, stand out as rigorous methods based on statistical mechanics. However, despite the importance of free-energy calculations, the applicability of the perturbation approaches is still largely impeded by a number of challenges, including the definition of the perturbation path, i.e., alchemical changes leading to the transformation of one molecule to the other. To address this, an automatic perturbation topology builder based on a graph-matching algorithm is developed, which can identify the maximum common substructure (MCS) of two or multiple molecules and provide the perturbation topologies suitable for free-energy calculations using the GROMOS and the GROMACS simulation packages. Various MCS search options are presented leading to alternative definitions of the perturbation pathway. Moreover, perturbation topologies generated using the default multistate MCS search are used to calculate the changes in free energy between lysine and its two post-translational modifications, 3-methyllysine and acetyllysine. The pairwise free-energy calculations performed on this test system led to a cycle closure of 0.5 ± 0.3 and 0.2 ± 0.2 kJ mol-1, with GROMOS and GROMACS simulation packages, respectively. The same relative free energies between the three states are obtained by employing the enveloping distribution sampling (EDS) approach when compared to the pairwise perturbations. Importantly, this toolkit is made available online as an open-source Python package (https://github.com/drazen-petrov/SMArt).

New perspectives in cancer drug development: computational advances with an eye to design

Computational chemistry has come of age in drug discovery. Indeed, most pharmaceutical development programs rely on computer-based data and results at some point. Herein, we discuss recent applications of advanced simulation techniques to difficult challenges in drug discovery. These entail the characterization of allosteric mechanisms and the identification of allosteric sites or cryptic pockets determined by protein motions, which are not immediately evident in the experimental structure of the target; the study of ligand binding mechanisms and their kinetic profiles; and the evaluation of drug-target affinities. We analyze different approaches to tackle challenging and emerging biological targets. Finally, we discuss the possible perspectives of future application of computation in drug discovery.

Docking-generated multiple ligand poses for bootstrapping bioactivity classifying Machine Learning: Repurposing covalent inhibitors for COVID-19-related TMPRSS2 as case study

In the present work we introduce the use of multiple docked poses for bootstrapping machine learning-based QSAR modelling. Ligand-receptor contact fingerprints are implemented as descriptor variables. We implemented this method for the discovery of potential inhibitors of the serine protease enzyme TMPRSS2 involved the infectivity of coronaviruses. Several machine learners were scanned, however, Xgboost, support vector machines (SVM) and random forests (RF) were the best with testing set accuracies reaching 90%. Three potential hits were identified upon using the method to scan known untested FDA approved drugs against TMPRSS2. Subsequent molecular dynamics simulation and covalent docking supported the results of the new computational approach.

Machine Learning and Enhanced Sampling Simulations for Computing the Potential of Mean Force and Standard Binding Free Energy

Computational capabilities are rapidly increasing, primarily because of the availability of GPU-based architectures. This creates unprecedented simulative possibilities for the systematic and robust computation of thermodynamic observables, including the free energy of a drug binding to a target. In contrast to calculations of relative binding free energy, which are nowadays widely exploited for drug discovery, we here push the boundary of computing the binding free energy and the potential of mean force. We introduce a novel protocol that leverages enhanced sampling, machine learning, and ad hoc algorithms to limit human intervention, computing time, and free parameters in free energy calculations. We first validate the method on a host-guest system, and then we apply the protocol to glycogen synthase kinase 3 beta, a protein kinase of pharmacological interest. Overall, we obtain a good correlation with experimental values in relative and absolute terms. While we focus on protein-ligand binding, the strategy is of broad applicability to any complex event that can be described with a path collective variable. We systematically discuss key details that influence the final result. The parameters and simulation settings are available at PLUMED-NEST to allow full reproducibility.

Conformational Shifts of Stacked Heteroaromatics: Vacuum vs. Water Studied by Machine Learning

Stacking interactions play a crucial role in drug design, as we can find aromatic cores or scaffolds in almost any available small molecule drug. To predict optimal binding geometries and enhance stacking interactions, usually high-level quantum mechanical calculations are performed. These calculations have two major drawbacks: they are very time consuming, and solvation can only be considered using implicit solvation. Therefore, most calculations are performed in vacuum. However, recent studies have revealed a direct correlation between the desolvation penalty, vacuum stacking interactions and binding affinity, making predictions even more difficult. To overcome the drawbacks of quantum mechanical calculations, in this study we use neural networks to perform fast geometry optimizations and molecular dynamics simulations of heteroaromatics stacked with toluene in vacuum and in explicit solvation. We show that the resulting energies in vacuum are in good agreement with high-level quantum mechanical calculations. Furthermore, we show that using explicit solvation substantially influences the favored orientations of heteroaromatic rings thereby emphasizing the necessity to include solvation properties starting from the earliest phases of drug design.

The critical role of QM/MM X-ray refinement and accurate tautomer/protomer determination in structure-based drug design

Conventional protein:ligand crystallographic refinement uses stereochemistry restraints coupled with a rudimentary energy functional to ensure the correct geometry of the model of the macromolecule-along with any bound ligand(s)-within the context of the experimental, X-ray density. These methods generally lack explicit terms for electrostatics, polarization, dispersion, hydrogen bonds, and other key interactions, and instead they use pre-determined parameters (e.g. bond lengths, angles, and torsions) to drive structural refinement. In order to address this deficiency and obtain a more complete and ultimately more accurate structure, we have developed an automated approach for macromolecular refinement based on a two layer, QM/MM (ONIOM) scheme as implemented within our DivCon Discovery Suite and "plugged in" to two mainstream crystallographic packages: PHENIX and BUSTER. This implementation is able to use one or more region layer(s), which is(are) characterized using linear-scaling, semi-empirical quantum mechanics, followed by a system layer which includes the balance of the model and which is described using a molecular mechanics functional. In this work, we applied our Phenix/DivCon refinement method-coupled with our XModeScore method for experimental tautomer/protomer state determination-to the characterization of structure sets relevant to structure-based drug design (SBDD). We then use these newly refined structures to show the impact of QM/MM X-ray refined structure on our understanding of function by exploring the influence of these improved structures on protein:ligand binding affinity prediction (and we likewise show how we use post-refinement scoring outliers to inform subsequent X-ray crystallographic efforts). Through this endeavor, we demonstrate a computational chemistry ↔ structural biology (X-ray crystallography) "feedback loop" which has utility in industrial and academic pharmaceutical research as well as other allied fields.

Sensitivity of Binding Free Energy Calculations to Initial Protein Crystal Structure

Binding free energy calculations using alchemical free energy (AFE) methods are widely considered to be the most rigorous tool in the computational drug discovery arsenal. Despite this, the calculations suffer from accuracy, precision, and reproducibility issues. In this publication, we perform a high-throughput study of more than a thousand AFE calculations, utilizing over 220 μs of total sampling time, on three different protein systems to investigate the impact of the initial crystal structure on the resulting binding free energy values. We also consider the influence of equilibration time and discover that the initial crystal structure can have a significant effect on free energy values obtained at short timescales that can manifest itself as a free energy difference of more than 1 kcal/mol. At longer timescales, these differences are largely overtaken by important rare events, such as torsional ligand motions, typically resulting in a much higher uncertainty in the obtained values. This work emphasizes the importance of rare event sampling and long-timescale dynamics in free energy calculations even for routinely performed alchemical perturbations. We conclude that an optimal protocol should not only concentrate computational resources on achieving convergence in the alchemical coupling parameter (λ) space but also on longer simulations and multiple repeats.

Reversibly Sampling Conformations and Binding Modes Using Molecular Darting

Sampling multiple binding modes of a ligand in a single molecular dynamics simulation is difficult. A given ligand may have many internal degrees of freedom, along with many different ways it might orient itself in a binding site or across several binding sites, all of which might be separated by large energy barriers. We have developed a novel Monte Carlo move called molecular darting (MolDarting) to reversibly sample between predefined binding modes of a ligand. Here, we couple this with nonequilibrium candidate Monte Carlo (NCMC) to improve acceptance of moves. We apply this technique to a simple dipeptide system, a ligand binding to T4 lysozyme L99A, and ligand binding to HIV integrase to test this new method. We observe significant increases in acceptance compared to uniformly sampling the internal and rotational/translational degrees of freedom in these systems.

The role of water in host-guest interaction

One of the main applications of atomistic computer simulations is the calculation of ligand binding free energies. The accuracy of these calculations depends on the force field quality and on the thoroughness of configuration sampling. Sampling is an obstacle in simulations due to the frequent appearance of kinetic bottlenecks in the free energy landscape. Very often this difficulty is circumvented by enhanced sampling techniques. Typically, these techniques depend on the introduction of appropriate collective variables that are meant to capture the system's degrees of freedom. In ligand binding, water has long been known to play a key role, but its complex behaviour has proven difficult to fully capture. In this paper we combine machine learning with physical intuition to build a non-local and highly efficient water-describing collective variable. We use it to study a set of host-guest systems from the SAMPL5 challenge. We obtain highly accurate binding free energies and good agreement with experiments. The role of water during the binding process is then analysed in some detail.

Free Energy Calculations for Protein-Ligand Binding Prediction

Computational prediction of protein-ligand binding involves initial determination of the binding mode and subsequent evaluation of the strength of the protein-ligand interactions, which directly correlates with ligand binding affinities. As a consequence of increasing computer power, rigorous approaches to calculate protein-ligand binding affinities, such as free energy perturbation (FEP) methods, are becoming an essential part of the toolbox of computer-aided drug design. In this chapter, we provide a general overview of these methods and introduce the QFEP modules, which are open-source API workflows based on our molecular dynamics (MD) package Q. The module QligFEP allows estimation of relative binding affinities along ligand series, while QresFEP is a module to estimate binding affinity shifts caused by single-point mutations of the protein. We herein provide guidelines for the use of each of these modules based on data extracted from ligand-design projects. While these modules are stand-alone, the combined use of the two workflows in a drug-design project yields complementary perspectives of the ligand binding problem, providing two sides of the same coin. The selected case studies illustrate how to use QFEP to approach the two key questions associated with ligand binding prediction: identifying the most favorable binding mode from different alternatives and establishing structure-affinity relationships that allow the rational optimization of hit compounds.

Mechanistic Understanding From Molecular Dynamics Simulation in Pharmaceutical Research 1: Drug Delivery

In this review, we outline the growing role that molecular dynamics simulation is able to play as a design tool in drug delivery. We cover both the pharmaceutical and computational backgrounds, in a pedagogical fashion, as this review is designed to be equally accessible to pharmaceutical researchers interested in what this new computational tool is capable of and experts in molecular modeling who wish to pursue pharmaceutical applications as a context for their research. The field has become too broad for us to concisely describe all work that has been carried out; many comprehensive reviews on subtopics of this area are cited. We discuss the insight molecular dynamics modeling has provided in dissolution and solubility, however, the majority of the discussion is focused on nanomedicine: the development of nanoscale drug delivery vehicles. Here we focus on three areas where molecular dynamics modeling has had a particularly strong impact: (1) behavior in the bloodstream and protective polymer corona, (2) Drug loading and controlled release, and (3) Nanoparticle interaction with both model and biological membranes. We conclude with some thoughts on the role that molecular dynamics simulation can grow to play in the development of new drug delivery systems.

Rigorous Computational Study Reveals What Docking Overlooks: Double Trouble from Membrane Association in Protein Kinase C Modulators

Increasing protein kinase C (PKC) activity is of potential therapeutic value. Its activation involves an interaction between the C1 domain and diacylglycerol (DAG) at intracellular membrane surfaces; DAG mimetics hold promise as new drugs. We previously developed the isophthalate derivative HMI-1a3, an effective but highly lipophilic (clogP = 6.46) DAG mimetic. Although a less lipophilic pyrimidine analog, PYR-1gP (clogP = 3.30), gave positive results in computational docking, it unexpectedly presented greatly diminished binding to PKC in vitro. Through more rigorous computational molecular modeling, we reveal that, unlike HMI-1a3, PYR-1gP forms an intramolecular hydrogen bond, which both obstructs binding and reorients PYR-1gP in the membrane in a fashion that prevents it from correctly accessing the PKC C1 domain. Our results highlight the great value of molecular dynamics simulations as a key component for the drug design process of ligands targeting weakly membrane-associated proteins, where simulation in the relevant membrane environment is crucial for obtaining biologically applicable results.

Molecular Simulation of αvβ6 Integrin Inhibitors

The urgent need for new treatments for the chronic lung disease idiopathic pulmonary fibrosis (IPF) motivates research into antagonists of the RGD binding integrin αvβ6, a protein linked to the initiation and progression of the disease. Molecular dynamics (MD) simulations of αvβ6 in complex with its natural ligand, pro-TGF-β1, show the persistence over time of a bidentate Arg-Asp ligand-receptor interaction and a metal chelate interaction between an aspartate on the ligand and an Mg²⁺ ion in the active site. This is typical of RGD binding ligands. Additional binding site interactions, which are not observed in the static crystal structure, are also identified. We investigate an RGD mimetic, which serves as a framework for a series of potential αvβ6 antagonists. The scaffold includes a derivative of the widely utilized 1,8-naphthyridine moiety, for which we present force field parameters, to enable MD and relative free energy perturbation (FEP) simulations. The MD simulations highlight the importance of hydrogen bonding and cation-π interactions. The FEP calculations predict relative binding affinities, within 1.5 kcal mol^-1, on average, of experiments.

Cell Type-Dependent Escape of Capsid Inhibitors by Simian Immunodeficiency Virus SIVcpz

Pandemic human immunodeficiency virus type 1 (HIV-1) is the result of the zoonotic transmission of simian immunodeficiency virus (SIV) from the chimpanzee subspecies Pan troglodytes troglodytes (SIVcpzPtt). The related subspecies Pan troglodytes schweinfurthii is the host of a similar virus, SIVcpzPts, which did not spread to humans. We tested these viruses with small-molecule capsid inhibitors (PF57, PF74, and GS-CA1) that interact with a binding groove in the capsid that is also used by CPSF6. While HIV-1 was sensitive to capsid inhibitors in cell lines, human macrophages, and peripheral blood mononuclear cells (PBMCs), SIVcpzPtt was resistant in rhesus FRhL-2 cells and human PBMCs but was sensitive to PF74 in human HOS and HeLa cells. SIVcpzPts was insensitive to PF74 in FRhL-2 cells, HeLa cells, PBMCs, and macrophages but was inhibited by PF74 in HOS cells. A truncated version of CPSF6 (CPSF6-358) inhibited SIVcpzPtt and HIV-1, while in contrast, SIVcpzPts was resistant to CPSF6-358. Homology modeling of HIV-1, SIVcpzPtt, and SIVcpzPts capsids and binding energy estimates suggest that these three viruses bind similarly to the host proteins cyclophilin A (CYPA) and CPSF6 as well as the capsid inhibitor PF74. Cyclosporine treatment, mutation of the CYPA-binding loop in the capsid, or CYPA knockout eliminated the resistance of SIVcpzPts to PF74 in HeLa cells. These experiments revealed that the antiviral capacity of PF74 is controlled by CYPA in a virus- and cell type-specific manner. Our data indicate that SIVcpz viruses can use infection pathways that escape the antiviral activity of PF74. We further suggest that the antiviral activity of PF74 capsid inhibitors depends on cellular cofactors.IMPORTANCE HIV-1 originated from SIVcpzPtt but not from the related virus SIVcpzPts, and thus, it is important to describe molecular infection by SIVcpzPts in human cells to understand the zoonosis of SIVs. Pharmacological HIV-1 capsid inhibitors (e.g., PF74) bind a capsid groove that is also a binding site for the cellular protein CPSF6. SIVcpzPts was resistant to PF74 in HeLa cells but sensitive in HOS cells, thus indicating cell line-specific resistance. Both SIVcpz viruses showed resistance to PF74 in human PBMCs. Modulating the presence of cyclophilin A or its binding to capsid in HeLa cells overcame SIVcpzPts resistance to PF74. These results indicate that early cytoplasmic infection events of SIVcpzPts may differ between cell types and affect, in an unknown manner, the antiviral activity of capsid inhibitors. Thus, capsid inhibitors depend on the activity or interaction of currently uncharacterized cellular factors.

Implicit ligand theory for relative binding free energies: II. An estimator based on control variates

Implicit ligand theory describes the relationship between the noncovalent binding free energy and the binding free energy between a ligand and multiple rigid receptor conformations. We have previously shown that if the receptor conformations are sampled from or reweighed to a holo ensemble, the binding free energy relative to the ligand that defines the ensemble can be calculated. Here, we apply a variance reduction technique known as control variates to derive a new statistical estimator for the relative binding free energy. In applications to a data set of 6 reference ligands and 18 test ligands, statistically significant differences between the estimators are not observed for most systems. However, in cases where such differences are observed, the new estimator is more accurate, precise, and converges more quickly. Performance improvements are most consistent where there is a clear correlation, with a correlation coefficient greater than 0.3, between the control variate and the statistic being averaged.

Targeting thermoTRP ion channels: in silico preclinical approaches and opportunities

INTRODUCTION

A myriad of cellular pathophysiological responses are mediated by polymodal ion channels that respond to chemical and physical stimuli such as thermoTRP channels. Intriguingly, these channels are pivotal therapeutic targets with limited clinical pharmacology. In silico methods offer an unprecedented opportunity for discovering new lead compounds targeting thermoTRP channels with improved pharmacological activity and therapeutic index.

AREAS COVERED

This article reviews the progress on thermoTRP channel pharmacology because of (i) advances in solving their atomic structure using cryo-electron microscopy and, (ii) progress on computational techniques including homology modeling, molecular docking, virtual screening, molecular dynamics, ADME/Tox and artificial intelligence. Together, they have increased the number of lead compounds with clinical potential to treat a variety of pathologies. We used original and review articles from Pubmed (1997-2020), as well as the clinicaltrials.gov database, containing the terms thermoTRP, artificial intelligence, docking, and molecular dynamics.

EXPERT OPINION

The atomic structure of thermoTRP channels along with computational methods constitute a realistic first line strategy for designing drug candidates with improved pharmacology and clinical translation. In silico approaches can also help predict potential side-effects that can limit clinical development of drug candidates. Together, they should provide drug candidates with upgraded therapeutic properties.

MovableType Software for Fast Free Energy-Based Virtual Screening: Protocol Development, Deployment, Validation, and Assessment

For decades, the complicated energy surfaces found in macromolecular protein:ligand structures, which require large amounts of computational time and resources for energy state sampling, have been an inherent obstacle to fast, routine free energy estimation in industrial drug discovery efforts. Beginning in 2013, the Merz research group addressed this cost with the introduction of a novel sampling methodology termed “Movable Type” (MT). Using numerical integration methods, the MT method reduces the computational expense for energy state sampling by independently calculating each atomic partition function from an initial molecular conformation in order to estimate the molecular free energy using ensembles of the atomic partition functions. In this work, we report a software package, the DivCon Discovery Suite with the MovableType module from QuantumBio Inc., that performs this MT free energy estimation protocol in a fast, fully encapsulated manner. We discuss the computational procedures and improvements to the original work, and we detail the corresponding settings for this software package. Finally, we introduce two validation benchmarks to evaluate the overall robustness of the method against a broad range of protein:ligand structural cases. With these publicly available benchmarks, we show that the method can use a variety of input types and parameters and exhibits comparable predictability whether the method is presented with “expensive” X-ray structures or “inexpensively docked” theoretical models. We also explore some next steps for the method. The MovableType software is available at http://www.quantumbioinc.com/

Improved Alchemical Free Energy Calculations with Optimized Smoothstep Softcore Potentials

Progress in the development of GPU-accelerated free energy simulation software has enabled practical applications on complex biological systems and fueled efforts to develop more accurate and robust predictive methods. In particular, this work re-examines concerted (a.k.a., one-step or unified) alchemical transformations commonly used in the prediction of hydration and relative binding free energies (RBFEs). We first classify several known challenges in these calculations into three categories: endpoint catastrophes, particle collapse, and large gradient-jumps. While endpoint catastrophes have long been addressed using softcore potentials, the remaining two problems occur much more sporadically and can result in either numerical instability (i.e., complete failure of a simulation) or inconsistent estimation (i.e., stochastic convergence to an incorrect result). The particle collapse problem stems from an imbalance in short-range electrostatic and repulsive interactions and can, in principle, be solved by appropriately balancing the respective softcore parameters. However, the large gradient-jump problem itself arises from the sensitivity of the free energy to large values of the softcore parameters, as might be used in trying to solve the particle collapse issue. Often, no satisfactory compromise exists with the existing softcore potential form. As a framework for solving these problems, we developed a new family of smoothstep softcore (SSC) potentials motivated by an analysis of the derivatives along the alchemical path. The smoothstep polynomials generalize the monomial functions that are used in most implementations and provide an additional path-dependent smoothing parameter. The effectiveness of this approach is demonstrated on simple yet pathological cases that illustrate the three problems outlined. With appropriate parameter selection, we find that a second-order SSC(2) potential does at least as well as the conventional approach and provides vast improvement in terms of consistency across all cases. Last, we compare the concerted SSC(2) approach against the gold-standard stepwise (a.k.a., decoupled or multistep) scheme over a large set of RBFE calculations as might be encountered in drug discovery.

BRIDGE: An Open Platform for Reproducible High-Throughput Free Energy Simulations

Biomolecular Reaction and Interaction Dynamics Global Environment (BRIDGE) is an open-source web platform developed with the aim to provide an environment for the design of reliable methods to conduct reproducible biomolecular simulations. It is built on the well-known Galaxy bioinformatics platform. Through this, BRIDGE hosts computational chemistry tools on public web servers for internet use and provides machine- and operating-system-independent portability using the Docker container platform for local use. This construction improves the accessibility, shareability, and reproducibility of computational methods for molecular simulations. Here we present integrated free energy tools (or apps) to calculate absolute binding free energies (ABFEs) and relative binding free energies (RBFEs), as illustrated through use cases. We present free energy perturbation (FEP) methods contained in various software packages such as GROMACS and YANK that are independent of hardware configuration, software libraries, or operating systems when ported in the Galaxy-BRIDGE Docker container platform. By performing cyclin-dependent kinase 2 (CDK2) FEP calculations on geographically dispersed web servers (in Africa and Europe), we illustrate that large-scale computations can be performed using the exact same codes and methodology by collaborating groups through publicly shared protocols and workflows. The ease of public sharing and independent reproduction of simulations via BRIDGE makes possible an open review of methods and complete simulation protocols. This makes the discovery of inhibitors for drug targets accessible to nonexperts and the computer experiments that are used to arrive at leads verifiable by experts and reviewers. We illustrate this on β-galactoside α-2,3-sialyltransferase I (ST3Gal-I), a breast cancer drug target, where a combination of RBFE and ABFE methods are used to compute the binding free energies of three inhibitors.

Pharmacoinformatics approaches to identify potential hits against tetraacyldisaccharide 4'-kinase (LpxK) of Pseudomonas aeruginosa

Pseudomonas aeruginosa infection can cause pneumonia and urinary tract infection and the management of Pseudomonas aeruginosa infection is critical in multidrug resistance, hospital-acquired bacteremia and ventilator-associated pneumonia. The key enzymes of lipid A biosynthesis in Pseudomonas aeruginosa are promising drug targets. However, the enzyme tetraacyldisaccharide 4'-kinase (LpxK) has not been explored as a drug target so far. Several pharmacoinformatics tools such as comparative metabolic pathway analysis (Metacyc), data mining from a database of essential genes (DEG), homology modeling, molecular docking, pharmacophore based virtual screening, ADMET prediction and molecular dynamics simulation were used in identifying novel lead compounds against this target. The top virtual hits STOCK6S-33288, 43621, 39892, 37164 and 35740 may serve as the templates for the design and synthesis of potent LpxK inhibitors in the management of serious Pseudomonas aeruginosa infection.

Repulsive Soft-Core Potentials for Efficient Alchemical Free Energy Calculations

In alchemical free energy (FE) simulations, annihilation and creation of atoms are generally achieved with the soft-core potential that shifts the interparticle separations. While this soft-core potential eliminates the numerical instability occurring near the two end states of the transformation, it makes the hybrid Hamiltonian vary nonlinearly with respect to the parameter λ, which interpolates between the Hamiltonians representing the two end states. This complicates FE estimation by Bennett acceptance ratio (BAR), free energy perturbation (FEP), and thermodynamic integration (TI) methods, thus reducing their calculation efficiency. In this work, we develop a new type of repulsive soft-core potential, called Gaussian soft-core (GSC) potential, with two parameters controlling its maximum and width. The main advantage of this potential is the linearity of the hybrid Hamiltonian with respect to λ, thus permitting the direct application of BAR, FEP, TI, and other variant FE methods. The accuracy and efficiency of the GSC potential are demonstrated by comparing the free energies of annihilation determined for 13 small molecules and an alchemical mutation of a protein side chain. In addition, in combination with a TI integrand (∂H/∂λ) estimation strategy, we show that GSC can considerably reduce the number of λ simulations compared to the commonly used separation-shifted soft-core potential.

Absolute Binding Free Energy Calculations for Highly Flexible Protein MDM2 and Its Inhibitors

Reliable prediction of binding affinities for ligand-receptor complex has been the primary goal of a structure-based drug design process. In this respect, alchemical methods are evolving as a popular choice to predict the binding affinities for biomolecular complexes. However, the highly flexible protein-ligand systems pose a challenge to the accuracy of binding free energy calculations mostly due to insufficient sampling. Herein, integrated computational protocol combining free energy perturbation based absolute binding free energy calculation with free energy landscape method was proposed for improved prediction of binding free energy for flexible protein-ligand complexes. The proposed method is applied to the dataset of various classes of p53-MDM2 (murine double minute 2) inhibitors. The absolute binding free energy calculations for MDMX (murine double minute X) resulted in a mean absolute error value of 0.816 kcal/mol while it is 3.08 kcal/mol for MDM2, a highly flexible protein compared to MDMX. With the integration of the free energy landscape method, the mean absolute error for MDM2 is improved to 1.95 kcal/mol.

Mechanism of Fully Reversible, pH-Sensitive Inhibition of Human Glutamine Synthetase by Tyrosine Nitration

Glutamine synthetase (GS) catalyzes an ATP-dependent condensation of glutamate and ammonia to form glutamine. This reaction-and therefore GS-are indispensable for the hepatic nitrogen metabolism. Nitration of tyrosine 336 (Y336) inhibits human GS activity. GS nitration and the consequent loss of GS function are associated with a broad range of neurological diseases. The mechanism by which Y336 nitration inhibits GS, however, is not understood. Here, we show by means of unbiased MD simulations, binding, and configurational free energy computations that Y336 nitration hampers ATP binding but only in the deprotonated and negatively charged state of residue 336. By contrast, for the protonated and neutral state, our computations indicate an increased binding affinity for ATP. pK_a computations of nitrated Y336 within GS predict a pK_a of ∼5.3. Thus, at physiological pH, nitrated Y336 exists almost exclusively in the deprotonated and negatively charged state. In vitro experiments confirm these predictions, in that, the catalytic activity of nitrated GS is decreased at pH 7 and 6 but not at pH 4. These results indicate a novel, fully reversible, pH-sensitive mechanism for the regulation of GS activity by tyrosine nitration.

Combining Machine Learning and Enhanced Sampling Techniques for Efficient and Accurate Calculation of Absolute Binding Free Energies

Calculating absolute binding free energies is challenging and important. In this paper, we test some recently developed metadynamics-based methods and develop a new combination with a Hamiltonian replica-exchange approach. The methods were tested on 18 chemically diverse ligands with a wide range of different binding affinities to a complex target; namely, human soluble epoxide hydrolase. The results suggest that metadynamics with a funnel-shaped restraint can be used to calculate, in a computationally affordable and relatively accurate way, the absolute binding free energy for small fragments. When used in combination with an optimal pathlike variable obtained using machine learning or with the Hamiltonian replica-exchange algorithm SWISH, this method can achieve reasonably accurate results for increasingly complex ligands, with a good balance of computational cost and speed. An additional benefit of using the combination of metadynamics and SWISH is that it also provides useful information about the role of water in the binding mechanism.

Gibbs Free Energy Calculation of Mutation in PncA and RpsA Associated With Pyrazinamide Resistance

A central approach for better understanding the forces involved in maintaining protein structures is to investigate the protein folding and thermodynamic properties. The effect of the folding process is often disturbed in mutated states. To explore the dynamic properties behind mutations, molecular dynamic (MD) simulations have been widely performed, especially in unveiling the mechanism of drug failure behind mutation. When comparing wild type (WT) and mutants (MTs), the structural changes along with solvation free energy (SFE), and Gibbs free energy (GFE) are calculated after the MD simulation, to measure the effect of mutations on protein structure. Pyrazinamide (PZA) is one of the first-line drugs, effective against latent Mycobacterium tuberculosis isolates, affecting the global TB control program 2030. Resistance to this drug emerges due to mutations in pncA and rpsA genes, encoding pyrazinamidase (PZase) and ribosomal protein S1 (RpsA) respectively. The question of how the GFE may be a measure of PZase and RpsA stabilities, has been addressed in the current review. The GFE and SFE of MTs have been compared with WT, which were already found to be PZA-resistant. WT structures attained a more stable state in comparison with MTs. The physiological effect of a mutation in PZase and RpsA may be due to the difference in energies. This difference between WT and MTs, depicted through GFE plots, might be useful in predicting the stability and PZA-resistance behind mutation. This study provides useful information for better management of drug resistance, to control the global TB problem.

Alchemical Grid Dock (AlGDock): Binding Free Energy Calculations between Flexible Ligands and Rigid Receptors

Alchemical Grid Dock (AlGDock) is open-source software designed to compute the binding potential of mean force-the binding free energy between a flexible ligand and a rigid receptor-for a small organic ligand and a biological macromolecule. Multiple BPMFs can be used to rigorously compute binding affinities between flexible partners. AlGDock uses replica exchange between thermodynamic states at different temperatures and receptor-ligand interaction strengths. Receptor-ligand interaction energies are represented by interpolating precomputed grids. Thermodynamic states are adaptively initialized and adjusted on-the-fly to maintain adequate replica exchange rates. In demonstrative calculations, when the bound ligand is treated as fully solvated, AlGDock estimates BPMFs with a precision within 4 kT in 65% and within 8 kT for 91% of systems. It correctly identifies the native binding pose in 83% of simulations. Performance is sometimes limited by subtle differences in the important configuration space of sampled and targeted thermodynamic states. © 2019 Wiley Periodicals, Inc.

Sampling Conformational Changes of Bound Ligands Using Nonequilibrium Candidate Monte Carlo and Molecular Dynamics

Flexible ligands often have multiple binding modes or bound conformations that differ by rotation of a portion of the molecule around internal rotatable bonds. Knowledge of these binding modes is important for understanding the interactions stabilizing the ligand in the binding pocket, and other studies indicate it is important for calculating accurate binding affinities. In this work, we use a hybrid molecular dynamics (MD)/nonequilibrium candidate Monte Carlo (NCMC) method to sample the different binding modes of several flexible ligands and also to estimate the population distribution of the modes. The NCMC move proposal is divided into three parts. The flexible part of the ligand is alchemically turned off by decreasing the electrostatics and steric interactions gradually, followed by rotating the rotatable bond by a random angle and then slowly turning the ligand back on to its fully interacting state. The alchemical steps prior to and after the move proposal help the surrounding protein and water atoms in the binding pocket relax around the proposed ligand conformation and increase move acceptance rates. The protein-ligand system is propagated using classical MD in between the NCMC proposals. Using this MD/NCMC method, we were able to correctly reproduce the different binding modes of inhibitors binding to two kinase targets-c-Jun N-terminal kinase-1 and cyclin-dependent kinase 2-at a much lower computational cost compared to conventional MD and umbrella sampling. This method is available as a part of the BLUES software package.

Best Practices for Alchemical Free Energy Calculations [Article v1.0]

Alchemical free energy calculations are a useful tool for predicting free energy differences associated with the transfer of molecules from one environment to another. The hallmark of these methods is the use of "bridging" potential energy functions representing alchemical intermediate states that cannot exist as real chemical species. The data collected from these bridging alchemical thermodynamic states allows the efficient computation of transfer free energies (or differences in transfer free energies) with orders of magnitude less simulation time than simulating the transfer process directly. While these methods are highly flexible, care must be taken in avoiding common pitfalls to ensure that computed free energy differences can be robust and reproducible for the chosen force field, and that appropriate corrections are included to permit direct comparison with experimental data. In this paper, we review current best practices for several popular application domains of alchemical free energy calculations performed with equilibrium simulations, in particular relative and absolute small molecule binding free energy calculations to biomolecular targets.

Ligand Binding Thermodynamic Cycles: Hysteresis, the Locally Weighted Histogram Analysis Method, and the Overlapping States Matrix

Free energy perturbation (FEP) simulations have been widely applied to obtain predictions of the relative binding free energy for a series of congeneric ligands binding to the same receptor, which is an essential component for the lead optimization process in computer-aided drug discovery. In the case of several congeneric ligands forming a perturbation map involving a closed thermodynamic cycle, the summation of the estimated free energy change along each edge in the cycle using Bennett acceptance ratio (BAR) usually will deviate from zero due to systematic and random errors, which is the hysteresis of cycle closure. In this work, the advanced reweighting techniques binless weighted histogram analysis method (UWHAM) and locally weighted histogram analysis method (LWHAM) are applied to provide statistical estimators of the free energy change along each edge in order to eliminate the hysteresis effect. As an example, we analyze a closed thermodynamic cycle involving four congeneric ligands which bind to HIV-1 integrase, a promising target which has emerged for antiviral therapy. We demonstrate that, compared with FEP and BAR, more accurate and hysteresis-free estimates of free energy differences can be achieved by using UWHAM to find a single estimate of the density of states based on all of the data in the cycle. Furthermore, by comparison of LWHAM results obtained from the inclusion of different numbers of neighboring states with UWHAM estimation involving all the states, we show how to determine the optimal neighborhood size in the LWHAM analysis to balance the trade-offs between computational cost and accuracy of the free energy prediction. Even with the smallest neighborhood, LWHAM can improve the BAR free energy estimates using the same input data as BAR. We introduce an overlapping states matrix that is constructed by using the global jump formula of LWHAM and plot its heat map. The heat map provides a quantitative measure of the overlap between pairs of alchemical/thermodynamic states. We explain how to identify and improve the FEP calculations along the edges that most likely cause large systematic errors by using the heat map of the overlapping states matrix and by comparing the BAR and UWHAM estimates of the free energy change.

Application of the Movable Type Free Energy Method to the Caspase-Inhibitor BindingAffinity Study

Many studies have provided evidence suggesting that caspases not only contribute to the neurodegeneration associated with Alzheimer’s disease (AD) but also play essential roles in promoting the underlying pathology of this disease. Studies regarding the caspase inhibition draw researchers’ attention through time due to its therapeutic value in the treatment of AD. In this work, we apply the “Movable Type” (MT) free energy method, a Monte Carlo sampling method extrapolating the binding free energy by simulating the partition functions for both free-state and bound-state protein and ligand configurations, to the caspase-inhibitor binding affinity study. Two test benchmarks are introduced to examine the robustness and sensitivity of the MT method concerning the caspase inhibition complexing. The first benchmark employs a large-scale test set including more than a hundred active inhibitors binding to caspase-3. The second benchmark includes several smaller test sets studying the relative binding free energy differences for minor structural changes at the caspase-inhibitor interaction interfaces. Calculation results show that the RMS errors for all test sets are below 1.5 kcal/mol compared to the experimental binding affinity values, demonstrating good performance in simulating the caspase-inhibitor complexing. For better understanding the protein-ligand interaction mechanism, we then take a closer look at the global minimum binding modes and free-state ligand conformations to study two pairs of caspase-inhibitor complexes with (1) different caspase targets binding to the same inhibitor, and (2) different polypeptide inhibitors targeting the same caspase target. By comparing the contact maps at the binding site of different complexes, we revealed how small structural changes affect the caspase-inhibitor interaction energies. Overall, this work provides a new free energy approach for studying the caspase inhibition, with structural insight revealed for both free-state and bound-state molecular configurations.