Modeling Local Structural Rearrangements Using FEP/REST: Application to Relative Binding Affinity Predictions of CDK2 Inhibitors

Automated Adaptive Absolute Binding Free Energy Calculations

Alchemical absolute binding free energy (ABFE) calculations have substantial potential in drug discovery, but are often prohibitively computationally expensive. To unlock their potential, efficient automated ABFE workflows are required to reduce both computational cost and human intervention. We present a fully automated ABFE workflow based on the automated selection of λ windows, the ensemble-based detection of equilibration, and the adaptive allocation of sampling time based on inter-replicate statistics. We find that the automated selection of intermediate states with consistent overlap is rapid, robust, and simple to implement. Robust detection of equilibration is achieved with a paired t-test between the free energy estimates at initial and final portions of a an ensemble of runs. We determine reasonable default parameters for all algorithms and show that the full workflow produces equivalent results to a nonadaptive scheme over a variety of test systems, while often accelerating equilibration. Our complete workflow is implemented in the open-source package A3FE (https://github.com/michellab/a3fe).

Robust Prediction of Relative Binding Energies for Protein-Protein Complex Mutations Using Free Energy Perturbation Calculations

Computational free energy-based methods have the potential to significantly improve throughput and decrease costs of protein design efforts. Such methods must reach a high level of reliability, accuracy, and automation to be effectively deployed in practical industrial settings in a way that impacts protein design projects. Here, we present a benchmark study for the calculation of relative changes in protein-protein binding affinity for single point mutations across a variety of systems from the literature, using free energy perturbation (FEP+) calculations. We describe a method for robust treatment of alternate protonation states for titratable amino acids, which yields improved correlation with and reduced error compared to experimental binding free energies. Following careful analysis of the largest outlier cases in our dataset, we assess limitations of the default FEP+ protocols and introduce an automated script which identifies probable outlier cases that may require additional scrutiny and calculates an empirical correction for a subset of charge-related outliers. Through a series of three additional case study systems, we discuss how Protein FEP+ can be applied to real-world protein design projects, and suggest areas of further study.

Current State of Open Source Force Fields in Protein-Ligand Binding Affinity Predictions

In drug discovery, the in silico prediction of binding affinity is one of the major means to prioritize compounds for synthesis. Alchemical relative binding free energy (RBFE) calculations based on molecular dynamics (MD) simulations are nowadays a popular approach for the accurate affinity ranking of compounds. MD simulations rely on empirical force field parameters, which strongly influence the accuracy of the predicted affinities. Here, we evaluate the ability of six different small-molecule force fields to predict experimental protein-ligand binding affinities in RBFE calculations on a set of 598 ligands and 22 protein targets. The public force fields OpenFF Parsley and Sage, GAFF, and CGenFF show comparable accuracy, while OPLS3e is significantly more accurate. However, a consensus approach using Sage, GAFF, and CGenFF leads to accuracy comparable to OPLS3e. While Parsley and Sage are performing comparably based on aggregated statistics across the whole dataset, there are differences in terms of outliers. Analysis of the force field reveals that improved parameters lead to significant improvement in the accuracy of affinity predictions on subsets of the dataset involving those parameters. Lower accuracy can not only be attributed to the force field parameters but is also dependent on input preparation and sampling convergence of the calculations. Especially large perturbations and nonconverged simulations lead to less accurate predictions. The input structures, Gromacs force field files, as well as the analysis Python notebooks are available on GitHub.

Structures of synaptic vesicle protein 2A and 2B bound to anticonvulsants

Epilepsy is a common neurological disorder characterized by abnormal activity of neuronal networks, leading to seizures. The racetam class of anti-seizure medications bind specifically to a membrane protein found in the synaptic vesicles of neurons called synaptic vesicle protein 2 (SV2) A (SV2A). SV2A belongs to an orphan subfamily of the solute carrier 22 organic ion transporter family that also includes SV2B and SV2C. The molecular basis for how anti-seizure medications act on SV2s remains unknown. Here we report cryo-electron microscopy structures of SV2A and SV2B captured in a luminal-occluded conformation complexed with anticonvulsant ligands. The conformation bound by anticonvulsants resembles an inhibited transporter with closed luminal and intracellular gates. Anticonvulsants bind to a highly conserved central site in SV2s. These structures provide blueprints for future drug design and will facilitate future investigations into the biological function of SV2s.

Adaptive lambda schemes for efficient relative binding free energy calculation

The relative free energy perturbation (RFEP) calculation is one of the most theoretically sound computational chemistry approaches for the binding affinity prediction. However, its application is often hindered by the complexity of the calculation choices and the requirement of expertise in the field. Improper lambda scheme of RFEP may result in deviations from an accurate description of the perturbation process and is prone to erroneous affinity predictions. To address such challenges, an automated adaptive lambda method is proposed where the adaptive lambda schemes are obtained through a split-and-merge algorithm based on the pilot runs. The newly established workflow along with a series of improvements to the perturbation settings increases the consistency of the RFEP calculation results. Comparing the pilot and adaptive lambda schemes, the latter demonstrated improvements in convergence and reproducibility and lowered the mean unsigned error and the root-mean-square error. Overall, the adaptive lambda method is a reliable and robust choice to predict small molecule relative binding free energy and can be capitalized to benefit routine RFEP calculations for drug discovery projects.

Robust prediction of relative binding energies for protein-protein complex mutations using free energy perturbation calculations

Computational free energy-based methods have the potential to significantly improve throughput and decrease costs of protein design efforts. Such methods must reach a high level of reliability, accuracy, and automation to be effectively deployed in practical industrial settings in a way that impacts protein design projects. Here, we present a benchmark study for the calculation of relative changes in protein-protein binding affinity for single point mutations across a variety of systems from the literature, using free energy perturbation (FEP+) calculations. We describe a method for robust treatment of alternate protonation states for titratable amino acids, which yields improved correlation with and reduced error compared to experimental binding free energies. Following careful analysis of the largest outlier cases in our dataset, we assess limitations of the default FEP+ protocols and introduce an automated script which identifies probable outlier cases that may require additional scrutiny and calculates an empirical correction for a subset of charge-related outliers. Through a series of three additional case study systems, we discuss how protein FEP+ can be applied to real-world protein design projects, and suggest areas of further study.

Potts Hamiltonian Models and Molecular Dynamics Free Energy Simulations for Predicting the Impact of Mutations on Protein Kinase Stability

Single-point mutations in kinase proteins can affect their stability and fitness, and computational analysis of these effects can provide insights into the relationships among protein sequence, structure, and function for this enzyme family. To assess the impact of mutations on protein stability, we used a sequence-based Potts Hamiltonian model trained on a kinase family multiple-sequence alignment (MSA) to calculate the statistical energy (fitness) effects of mutations and compared these against relative folding free energies (ΔΔGs) calculated from all-atom molecular dynamics free energy perturbation (FEP) simulations in explicit solvent. The fitness effects of mutations in the Potts model (ΔEs) showed good agreement with experimental thermostability data (Pearson r = 0.68), similar to the correlation we observed with ΔΔGs predicted from structure-based relative FEP simulations. Recognizing the possible advantages of using Potts models to rapidly estimate protein stability effects of kinase mutations seen in cancer genomics data, we used the Potts statistical energy model to estimate the stability effects of 65 conservative and nonconservative mutations across three distinct kinases (Wee1, Abl1, and Cdc7) with somatic mutations reported in the Genomic Data Commons (GDC) database. The ΔEs of these mutations calculated from the Potts model are consistent with the corresponding ΔΔGs from FEP simulations (Pearson ratio of 0.72). The agreement between these methods suggests that the Potts model may be used as a sequence-based tool for high-throughput screening of mutational effects as part of a computational pipeline for predicting the stability effects of mutations. We also demonstrate how the scalability of the fitness-based Potts model calculations permits analyses that are not easily accessed using FEP simulations. To this end, we employed site-saturation mutagenesis in the Potts model in order to investigate the relative stability effects of mutations seen in different cancer evolutionary scenarios. We used this approach to analyze the effects of drug pressure in Abl kinase by contrasting the relative fitness penalties of somatic mutations seen in miscellaneous cancer types with those calculated for mutations associated with cancer drug resistance. We observed that, in contrast to somatic mutations of Abl seen in various tumors that appear to have evolved neutrally, cancer mutations that evolved under drug pressure in Abl-targeted therapies tend to preserve enzyme stability.

What to Make of Zero: Resolving the Statistical Noise from Conformational Reorganization in Alchemical Binding Free Energy Estimates with Metadynamics Sampling

We introduce the self-relative binding free energy (self-RBFE) approach to evaluate the intrinsic statistical variance of dual-topology alchemical binding free energy estimators. The self-RBFE is the relative binding free energy between a ligand and a copy of the same ligand, and its true value is zero. Nevertheless, because the two copies of the ligand move independently, the self-RBFE value produced by a finite-length simulation fluctuates and can be used to measure the variance of the model. The results of this validation provide evidence that a significant fraction of the errors observed in benchmark studies reflect the statistical fluctuations of unconverged estimates rather than the models' accuracy. Furthermore, we find that ligand reorganization is a significant contributing factor to the statistical variance of binding free energy estimates and that metadynamics-accelerated conformational sampling of the torsional degrees of freedom of the ligand can drastically reduce the time to convergence.

Development and Comprehensive Benchmark of a High-Quality AMBER-Consistent Small Molecule Force Field with Broad Chemical Space Coverage for Molecular Modeling and Free Energy Calculation

Biomolecular simulations have become an essential tool in contemporary drug discovery, and molecular mechanics force fields (FFs) constitute its cornerstone. Developing a high quality and broad coverage general FF is a significant undertaking that requires substantial expert knowledge and computing resources, which is beyond the scope of general practitioners. Existing FFs originate from only a limited number of groups and organizations, and they either suffer from limited numbers of training sets, lower than desired quality because of oversimplified representations, or are costly for the molecular modeling community to access. To address these issues, in this work, we developed an AMBER-consistent small molecule FF with extensive chemical space coverage, and we provide Open Access parameters for the entire modeling community. To validate our FF, we carried out benchmarks of quantum mechanics (QM)/molecular mechanics conformer comparison and free energy perturbation calculations on several benchmark data sets. Our FF achieves a higher level of performance at reproducing QM energies and geometries than two popular open-source FFs, OpenFF2 and GAFF2. In relative binding free energy calculations for 31 protein-ligand data sets, comprising 1079 pairs of ligands, the new FF achieves an overall root-mean-square error of 1.19 kcal/mol for ΔΔG and 0.92 kcal/mol for ΔG on a subset of 463 ligands without bespoke fitting to the data sets. The results are on par with those of the leading commercial series of OPLS FFs.

Molecular Mechanism of Labelling Functional Cysteines by Heterocyclic Thiones

Heterocyclic thiones have recently been identified as reversible covalent warheads, consistent with their mild electrophilic nature. Little is known so far about their mechanism of action in labelling nucleophilic sidechains, especially cysteines. The vast number of tractable cysteines promotes a wide range of target proteins to examine; however, our focus was put on functional cysteines. We chose the main protease of SARS-CoV-2 harboring Cys145 at the active site that is a structurally characterized and clinically validated target of covalent inhibitors. We screened an in-house, cysteine-targeting covalent inhibitor library which resulted in several covalent fragment hits with benzoxazole, benzothiazole and benzimidazole cores. Thione derivatives and Michael acceptors were selected for further investigations with the objective of exploring the mechanism of inhibition of the thiones and using the thoroughly characterized Michael acceptors for benchmarking our studies. Classical and hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations were carried out that revealed a new mechanism of covalent cysteine labelling by thione derivatives, which was supported by QM and free energy calculations and by a wide range of experimental results. Our study shows that the molecular recognition step plays a crucial role in the overall binding of both sets of molecules.

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.

Fast free energy estimates from λ-dynamics with bias-updated Gibbs sampling

Relative binding free energy calculations have become an integral computational tool for lead optimization in structure-based drug design. Classical alchemical methods, including free energy perturbation or thermodynamic integration, compute relative free energy differences by transforming one molecule into another. However, these methods have high operational costs due to the need to perform many pairwise perturbations independently. To reduce costs and accelerate molecular design workflows, we present a method called λ-dynamics with bias-updated Gibbs sampling. This method uses dynamic biases to continuously sample between multiple ligand analogues collectively within a single simulation. We show that many relative binding free energies can be determined quickly with this approach without compromising accuracy. For five benchmark systems, agreement to experiment is high, with root mean square errors near or below 1.0 kcal mol-1. Free energy results are consistent with other computational approaches and within statistical noise of both methods (0.4 kcal mol-1 or less). Notably, large efficiency gains over thermodynamic integration of 18-66-fold for small perturbations and 100-200-fold for whole aromatic ring substitutions are observed. The rapid determination of relative binding free energies will enable larger chemical spaces to be more readily explored and structure-based drug design to be accelerated.

Dealing with Induced Fit, Conformational Selection, and Secondary Poses in Molecular Dynamics Simulations for Reliable Free Energy Predictions

In this study, we have tested the performance of standard molecular dynamics (MD) simulations, replicates of shorter standard MD simulations, and Hamiltonian Replica Exchange (HREM) simulations for the sampling of two macrocyclic hosts for guest delivery, characterized by induced fit (phenyl-based host) and conformation selection (naphthyl-based host) and of the ODR-BRD4(I) drug-receptor system where the ligand can assume two main poses. For the optimization of the HREM simulation, we have proposed and tested an on-the-fly iterative scheme for equalizing the acceptance ratio along the replica progression at a constant replica number resulting in a moderate impact of the sampling efficiency. Concerning standard MD, we have found that, while splitting the total allocated simulation time in short MD replicates can reproduce the sampling efficiency of HREM in the phenyl-based host and in the ODR-BRD4(I) complex, in the naphthyl-based macrocycle, characterized by long-lived metastable states, enhanced sampling techniques are the only viable alternative for a reliable canonical sampling of the rugged conformational landscape.

Synthesis and evaluation of highly potent HBV capsid assembly modulators (CAMs)

Chronic hepatitis B virus (HBV) infection remains a major global health burden. It affects more than 290 million individuals worldwide and is responsible for approximately 900,000 deaths annually. Anti-HBV treatment with a nucleoside analog in combination with pegylated interferon are considered first-line therapy for patients with chronic HBV infection and liver inflammation. However, because cure rates are low, most patients will require lifetime treatment. HBV Capsid Assembly Modulators (CAMs) have emerged as a promising new class of compounds as they can affect levels of HBV covalently closed-circular DNA (cccDNA) associated with viral persistence. SAR studies around the core structure of lead HBV CAM GLP-26 (Fig. 1B) was performed and led to the discovery of non-toxic compound 10a displaying sub-nanomolar anti-HBV activity. Advanced toxicity and cellular pharmacology profiles of compounds 10a were also established and the results are discussed herein.

Landscape of In Silico Tools for Modeling Covalent Modification of Proteins: A Review on Computational Covalent Drug Discovery

Covalent drug discovery has been a challenging research area given the struggle of finding a sweet balance between selectivity and reactivity for these drugs, the lack of which often leads to off-target activities and hence undesirable side effects. However, there has been a resurgence in covalent drug design following the success of several covalent drugs such as boceprevir (2011), ibrutinib (2013), neratinib (2017), dacomitinib (2018), zanubrutinib (2019), and many others. Design of covalent drugs includes many crucial factors, where "evaluation of the binding affinity" and "a detailed mechanistic understanding on covalent inhibition" are at the top of the list. Well-defined experimental techniques are available to elucidate these factors; however, often they are expensive and/or time-consuming and hence not suitable for high throughput screens. Recent developments in in silico methods provide promise in this direction. In this report, we review a set of recent publications that focused on developing and/or implementing novel in silico techniques in "Computational Covalent Drug Discovery (CCDD)". We also discuss the advantages and disadvantages of these approaches along with what improvements are required to make it a great tool in medicinal chemistry in the near future.

The maximal and current accuracy of rigorous protein-ligand binding free energy calculations

Computational techniques can speed up the identification of hits and accelerate the development of candidate molecules for drug discovery. Among techniques for predicting relative binding affinities, the most consistently accurate is free energy perturbation (FEP), a class of rigorous physics-based methods. However, uncertainty remains about how accurate FEP is and can ever be. Here, we present what we believe to be the largest publicly available dataset of proteins and congeneric series of small molecules, and assess the accuracy of the leading FEP workflow. To ascertain the limit of achievable accuracy, we also survey the reproducibility of experimental relative affinity measurements. We find a wide variability in experimental accuracy and a correspondence between binding and functional assays. When careful preparation of protein and ligand structures is undertaken, FEP can achieve accuracy comparable to experimental reproducibility. Throughout, we highlight reliable protocols that can help maximize the accuracy of FEP in prospective studies.

Dynamic extracellular vestibule of human SERT: Unveiling druggable potential with high-affinity allosteric inhibitors

The serotonin transporter (SERT) tightly regulates synaptic serotonin levels and has been the primary target of antidepressants. Binding of inhibitors to the allosteric site of human SERT (hSERT) impedes the dissociation of antidepressants bound at the central site and may enhance the efficacy of such antidepressants to potentially reduce their dosage and side effects. Here, we report the identification of a series of high-affinity allosteric inhibitors of hSERT in a unique scaffold, with the lead compound, Lu AF88273 (3-(1-(2-(1H-indol-3-yl)ethyl)piperidin-4-yl)-6-chloro-1H-indole), having 2.1 nM allosteric potency in inhibiting imipramine dissociation. In addition, we find that Lu AF88273 also inhibits serotonin transport in a noncompetitive manner. The binding pose of Lu AF88273 in the allosteric site of hSERT is determined with extensive molecular dynamics simulations and rigorous absolute binding free energy perturbation (FEP) calculations, which show that a part of the compound occupies a dynamically formed small cavity. The predicted binding location and pose are validated by site-directed mutagenesis and can explain much of the structure-activity relationship of these inhibitors using the relative binding FEP calculations. Together, our findings provide a promising lead compound and the structural basis for the development of allosteric drugs targeting hSERT. Further, they demonstrate that the divergent allosteric sites of neurotransmitter transporters can be selectively targeted.

Replica Exchange with Hybrid Tempering Efficiently Samples PGLa Peptide Binding to Anionic Bilayer

We evaluated the utility of a variant of the replica exchange method, a replica exchange with hybrid tempering (REHT), for all-atom explicit water biomolecular simulations and compared it with a more traditional replica exchange with the solute tempering (REST) algorithm. As a test system, we selected a 21-mer antimicrobial peptide PGLa binding to an anionic DMPC/DMPG lipid bilayer. Application of REHT revealed the following binding mechanism. Due to the strong hydrophobic moment, the bound PGLa adopts an extensive helical structure. The binding free energy landscape identifies two major bound states, a metastable surface bound state and a dominant inserted state. In both states, positively charged PGLa amino acids maintain electrostatic interactions with anionic phosphate groups by rotating the PGLa helix around its axis. PGLa binding causes an influx of anionic DMPG and an efflux of zwitterionic DMPC lipids from the peptide proximity. PGLa thins the bilayer and disorders the adjacent fatty acid tails. Deep invasion of water wires into the bilayer hydrophobic core is detected in the inserted peptide state. The analysis of charge density distributions indicated that peptide positive charges are nearly compensated for by lipid negative charges and water dipole ordering, whereas ions play no role in peptide binding. Thus, electrostatic interactions are the key energetic factor in binding cationic PGLa to an anionic DMPC/DMPG bilayer. Comparison of REHT and REST shows that due to exclusion of lipids from tempered partition, REST lags behind REHT in peptide equilibration, particularly, with respect to peptide insertion and helix acquisition. As a result, REST struggles to provide accurate details of PGLa binding, although it still qualitatively maps the bimodal binding mechanism. Importantly, REHT not only equilibrates PGLa in the bilayer faster than REST, but also with less computational effort. We conclude that REHT is a preferable choice for studying interfacial biomolecular systems.

Thermodynamically consistent determination of free energies and rates in kinetic cycle models

Kinetic and thermodynamic models of biological systems are commonly used to connect microscopic features to system function in a bottom-up multiscale approach. The parameters of such models-free energy differences for equilibrium properties and in general rates for equilibrium and out-of-equilibrium observables-have to be measured by different experiments or calculated from multiple computer simulations. All such parameters necessarily come with uncertainties so that when they are naively combined in a full model of the process of interest, they will generally violate fundamental statistical mechanical equalities, namely detailed balance and an equality of forward/backward rate products in cycles due to Hill. If left uncorrected, such models can produce arbitrary outputs that are physically inconsistent. Here, we develop a maximum likelihood approach (named multibind) based on the so-called potential graph to combine kinetic or thermodynamic measurements to yield state-resolved models that are thermodynamically consistent while being most consistent with the provided data and their uncertainties. We demonstrate the approach with two theoretical models, a generic two-proton binding site and a simplified model of a sodium/proton antiporter. We also describe an algorithm to use the multibind approach to solve the inverse problem of determining microscopic quantities from macroscopic measurements and, as an example, we predict the microscopic p K a values and protonation states of a small organic molecule from 1D NMR data. The multibind approach is applicable to any thermodynamic or kinetic model that describes a system as transitions between well-defined states with associated free energy differences or rates between these states. A Python package multibind, which implements the approach described here, is made publicly available under the MIT Open Source license.

FEP Protocol Builder: Optimization of Free Energy Perturbation Protocols Using Active Learning

Significant improvements have been made in the past decade to methods that rapidly and accurately predict binding affinity through free energy perturbation (FEP) calculations. This has been driven by recent advances in small-molecule force fields and sampling algorithms combined with the availability of low-cost parallel computing. Predictive accuracies of ∼1 kcal mol-1 have been regularly achieved, which are sufficient to drive potency optimization in modern drug discovery campaigns. Despite the robustness of these FEP approaches across multiple target classes, there are invariably target systems that do not display expected performance with default FEP settings. Traditionally, these systems required labor-intensive manual protocol development to arrive at parameter settings that produce a predictive FEP model. Due to the (a) relatively large parameter space to be explored, (b) significant compute requirements, and (c) limited understanding of how combinations of parameters can affect FEP performance, manual FEP protocol optimization can take weeks to months to complete, and often does not involve rigorous train-test set splits, resulting in potential overfitting. These manual FEP protocol development timelines do not coincide with tight drug discovery project timelines, essentially preventing the use of FEP calculations for these target systems. Here, we describe an automated workflow termed FEP Protocol Builder (FEP-PB) to rapidly generate accurate FEP protocols for systems that do not perform well with default settings. FEP-PB uses an active-learning workflow to iteratively search the protocol parameter space to develop accurate FEP protocols. To validate this approach, we applied it to pharmaceutically relevant systems where default FEP settings could not produce predictive models. We demonstrate that FEP-PB can rapidly generate accurate FEP protocols for the previously challenging MCL1 system with limited human intervention. We also apply FEP-PB in a real-world drug discovery setting to generate an accurate FEP protocol for the p97 system. FEP-PB is able to generate a more accurate protocol than the expert user, rapidly validating p97 as amenable to free energy calculations. Additionally, through the active-learning workflow, we are able to gain insight into which parameters are most important for a given system. These results suggest that FEP-PB is a robust tool that can aid in rapidly developing accurate FEP protocols and increasing the number of targets that are amenable to the technology.

Identifying and Overcoming the Sampling Challenges in Relative Binding Free Energy Calculations of a Model Protein:Protein Complex

Relative alchemical binding free energy calculations are routinely used in drug discovery projects to optimize the affinity of small molecules for their drug targets. Alchemical methods can also be used to estimate the impact of amino acid mutations on protein:protein binding affinities, but these calculations can involve sampling challenges due to the complex networks of protein and water interactions frequently present in protein:protein interfaces. We investigate these challenges by extending a graphics processing unit (GPU)-accelerated open-source relative free energy calculation package (Perses) to predict the impact of amino acid mutations on protein:protein binding. Using the well-characterized model system barnase:barstar, we describe analyses for identifying and characterizing sampling problems in protein:protein relative free energy calculations. We find that mutations with sampling problems often involve charge-changes, and inadequate sampling can be attributed to slow degrees of freedom that are mutation-specific. We also explore the accuracy and efficiency of current state-of-the-art approaches─alchemical replica exchange and alchemical replica exchange with solute tempering─for overcoming relevant sampling problems. By employing sufficiently long simulations, we achieve accurate predictions (RMSE 1.61, 95% CI: [1.12, 2.11] kcal/mol), with 86% of estimates within 1 kcal/mol of the experimentally determined relative binding free energies and 100% of predictions correctly classifying the sign of the changes in binding free energies. Ultimately, we provide a model workflow for applying protein mutation free energy calculations to protein:protein complexes, and importantly, catalog the sampling challenges associated with these types of alchemical transformations. Our free open-source package (Perses) is based on OpenMM and is available at https://github.com/choderalab/perses.

Thermodynamically consistent determination of free energies and rates in kinetic cycle models

Kinetic and thermodynamic models of biological systems are commonly used to connect microscopic features to system function in a bottom-up multiscale approach. The parameters of such models-free energy differences for equilibrium properties and in general rates for equilibrium and out-of-equilibrium observables-have to be measured by different experiments or calculated from multiple computer simulations. All such parameters necessarily come with uncertainties so that when they are naively combined in a full model of the process of interest, they will generally violate fundamental statistical mechanical equalities, namely detailed balance and an equality of forward/backward rate products in cycles due to T. Hill. If left uncorrected, such models can produce arbitrary outputs that are physically inconsistent. Here we develop a maximum likelihood approach (named multibind ) based on the so-called potential graph to combine kinetic or thermodynamic measurements to yield state resolved models that are thermodynamically consistent while being most consistent with the provided data and their uncertainties. We demonstrate the approach with two theoretical models, a generic two-proton binding site and a simplified model of a sodium/proton antiporter. We also describe an algorithm to use the multibind approach to solve the inverse problem of determining microscopic quantities from macroscopic measurements and as an example we predict the microscopic p K a s and protonation states of a small organic molecule from 1D NMR data. The multibind approach is applicable to any thermodynamic or kinetic model that describes a system as transitions between well-defined states with associated free energy differences or rates between these states. A Python package multibind , which implements the approach described here, is made publicly available under the MIT Open Source license.

WHY IT MATTERS

The increase in computational efficiency and rapid advances in methodology for quantitative free energy and rate calculations has allowed for the construction of increasingly complex thermodynamic or kinetic "bottom-up" models of chemical and biological processes. These multi-scale models serve as a framework for analyzing aspects of cellular function in terms of microscopic, molecular properties and provide an opportunity to connect molecular mechanisms to cellular function. The underlying model parameters-free energy differences or rates-are constrained by thermodynamic identities over cycles of states but these identities are not necessarily obeyed during model construction, thus potentially leading to inconsistent models. We address these inconsistencies through the use of a maximum likelihood approach for free energies and rates to adjust the model parameters in such a way that they are maximally consistent with the input parameters and exactly fulfill the thermodynamic cycle constraints. This approach enables formulation of thermodynamically consistent multi-scale models from simulated or experimental measurements.

Enhancing Hit Discovery in Virtual Screening through Absolute Protein-Ligand Binding Free-Energy Calculations

In the hit identification stage of drug discovery, a diverse chemical space needs to be explored to identify initial hits. Contrary to empirical scoring functions, absolute protein-ligand binding free-energy perturbation (ABFEP) provides a theoretically more rigorous and accurate description of protein-ligand binding thermodynamics and could, in principle, greatly improve the hit rates in virtual screening. In this work, we describe an implementation of an accurate and reliable ABFEP method in FEP+. We validated the ABFEP method on eight congeneric compound series binding to eight protein receptors including both neutral and charged ligands. For ligands with net charges, the alchemical ion approach is adopted to avoid artifacts in electrostatic potential energy calculations. The calculated binding free energies correlate with experimental results with a weighted average of R² = 0.55 for the entire dataset. We also observe an overall root-mean-square error (RMSE) of 1.1 kcal/mol after shifting the zero-point of the simulation data to match the average experimental values. Through ABFEP calculations using apo versus holo protein structures, we demonstrated that the protein conformational and protonation state changes between the apo and holo proteins are the main physical factors contributing to the protein reorganization free energy manifested by the overestimation of raw ABFEP calculated binding free energies using the holo structures of the proteins. Furthermore, we performed ABFEP calculations in three virtual screening applications for hit enrichment. ABFEP greatly improves the hit rates as compared to docking scores or other methods like metadynamics. The good performance of ABFEP in rank ordering compounds demonstrated in this work confirms it as a useful tool to improve the hit rates in virtual screening, thus facilitating hit discovery.

Automated relative binding free energy calculations from SMILES to ΔΔG

In drug discovery, computational methods are a key part of making informed design decisions and prioritising experiments. In particular, optimizing compound affinity is a central concern during the early stages of development. In the last 10 years, alchemical free energy (FE) calculations have transformed our ability to incorporate accurate in silico potency predictions in design decisions, and represent the 'gold standard' for augmenting experiment-driven drug discovery. However, relative FE calculations are complex to set up, require significant expert intervention to prepare the calculation and analyse the results or are provided only as closed-source software, not allowing for fine-grained control over the underlying settings. In this work, we introduce an end-to-end relative FE workflow based on the non-equilibrium switching approach that facilitates calculation of binding free energies starting from SMILES strings. The workflow is implemented using fully modular steps, allowing various components to be exchanged depending on licence availability. We further investigate the dependence of the calculated free energy accuracy on the initial ligand pose generated by various docking algorithms. We show that both commercial and open-source docking engines can be used to generate poses that lead to good correlation of free energies with experimental reference data.

To Design Scalable Free Energy Perturbation Networks, Optimal Is Not Enough

Drug discovery is accelerated with computational methods such as alchemical simulations to estimate ligand affinities. In particular, relative binding free energy (RBFE) simulations are beneficial for lead optimization. To use RBFE simulations to compare prospective ligands in silico, researchers first plan the simulation experiment, using graphs where nodes represent ligands and graph edges represent alchemical transformations between ligands. Recent work demonstrated that optimizing the statistical architecture of these perturbation graphs improves the accuracy of the predicted changes in the free energy of ligand binding. Therefore, to improve the success rate of computational drug discovery, we present the open-source software package High Information Mapper (HiMap)─a new take on its predecessor, Lead Optimization Mapper (LOMAP). HiMap removes heuristics decisions from design selection and instead finds statistically optimal graphs over ligands clustered with machine learning. Beyond optimal design generation, we present theoretical insights for designing alchemical perturbation maps. Some of these results include that for n number of nodes, the precision of perturbation maps is stable at n·ln(n) edges. This result indicates that even an "optimal" graph can result in unexpectedly high errors if a plan includes too few alchemical transformations for the given number of ligands and edges. And, as a study compares more ligands, the performance of even optimal graphs will deteriorate with linear scaling of the edge count. In this sense, ensuring an A- or D-optimal topology is not enough to produce robust errors. We additionally find that optimal designs will converge more rapidly than radial and LOMAP designs. Moreover, we derive bounds for how clustering reduces cost for designs with a constant expected relative error per cluster, invariant of the size of the design. These results inform how to best design perturbation maps for computational drug discovery and have broader implications for experimental design.

Identifying and overcoming the sampling challenges in relative binding free energy calculations of a model protein:protein complex

Relative alchemical binding free energy calculations are routinely used in drug discovery projects to optimize the affinity of small molecules for their drug targets. Alchemical methods can also be used to estimate the impact of amino acid mutations on protein:protein binding affinities, but these calculations can involve sampling challenges due to the complex networks of protein and water interactions frequently present in protein:protein interfaces. We investigate these challenges by extending a GPU-accelerated opensource relative free energy calculation package (Perses) to predict the impact of amino acid mutations on protein:protein binding. Using the well-characterized model system barnase:barstar, we describe analyses for identifying and characterizing sampling problems in protein:protein relative free energy calculations. We find that mutations with sampling problems often involve charge-changes, and inadequate sampling can be attributed to slow degrees of freedom that are mutation-specific. We also explore the accuracy and efficiency of current state-of-the-art approaches-alchemical replica exchange and alchemical replica exchange with solute tempering-for overcoming relevant sampling problems. By employing sufficiently long simulations, we achieve accurate predictions (RMSE 1.61, 95% CI: [1.12, 2.11] kcal/mol), with 86% of estimates within 1 kcal/mol of the experimentally-determined relative binding free energies and 100% of predictions correctly classifying the sign of the changes in binding free energies. Ultimately, we provide a model workflow for applying protein mutation free energy calculations to protein:protein complexes, and importantly, catalog the sampling challenges associated with these types of alchemical transformations. Our free open-source package (Perses) is based on OpenMM and available at https://github.com/choderalab/perses .

The slow but steady rise of binding free energy calculations in drug discovery

Binding free energy calculations are increasingly used in drug discovery research to predict protein-ligand binding affinities and to prioritize candidate drug molecules accordingly. It has taken decades of collective effort to transform this academic concept into a technology adopted by the pharmaceutical and biotech industry. Having personally witnessed and taken part in this transformation, here I recount the (incomplete) list of problems that had to be solved to make this computational tool practical and suggest areas of future development.

Target-template relationships in protein structure prediction and their effect on the accuracy of thermostability calculations

Improving protein thermostability has been a labor- and time-consuming process in industrial applications of protein engineering. Advances in computational approaches have facilitated the development of more efficient strategies to allow the prioritization of stabilizing mutants. Among these is FEP+, a free energy perturbation implementation that uses a thoroughly tested physics-based method to achieve unparalleled accuracy in predicting changes in protein thermostability. To gauge the applicability of FEP+ to situations where crystal structures are unavailable, here we have applied the FEP+ approach to homology models of 12 different proteins covering 316 mutations. By comparing predictions obtained with homology models to those obtained using crystal structures, we have identified that local rather than global sequence conservation between target and template sequence is a determining factor in the accuracy of predictions. By excluding mutation sites with low local sequence identity (<40%) to a template structure, we have obtained predictions with comparable performance to crystal structures (R2 of 0.67 and 0.63 and an RMSE of 1.20 and 1.16 kcal/mol for crystal structure and homology model predictions, respectively) for identifying stabilizing mutations when incorporating residue scanning into a cascade screening strategy. Additionally, we identify and discuss inherent limitations in sequence alignments and homology modeling protocols that translate into the poor FEP+ performance of a few select examples. Overall, our retrospective study provides detailed guidelines for the application of the FEP+ approach using homology models for protein thermostability predictions, which will greatly extend this approach to studies that were previously limited by structure availability.

An Open Source Graph-Based Weighted Cycle Closure Method for Relative Binding Free Energy Calculations

Free energy perturbation-relative binding free energy (FEP-RBFE) prediction has shown its reliability and accuracy in the prediction of protein-ligand binding affinities, which plays a fundamental role in structure-based drug design. In FEP-RBFE predictions, the calculation of each mutation path is associated with a statistical error, and cycle closure (cc) has proven to be an effective method in improving the calculation accuracy by correcting the hysteresis (summation of errors) of each closed cycle to the theoretical value 0. However, a primary hypothesis was made in the current cycle closure method that the hysteresis is evenly distributed to all paths, which is unlikely to be true in practice and may limit the further improvement of the calculation accuracy when better error estimation methods are available. Moreover, being a closed source software makes the current cycle closure method unachievable in many studies. In this paper, a newly implemented open source graph-based weighted cycle closure (wcc) algorithm was developed and introduced, not only including functions from the original cc method but also containing a new wcc method which can consider different error contributions from different paths and further improve the calculation accuracy. The wcc program also provides a new path-independent molecular error calculation method, which can be quite useful in many studies (like structure-activity relationship (SAR)) compared with the path-dependent method of the original cc program.

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.

Exploring the Effect of Halogenation in a Series of Potent and Selective A2B Adenosine Receptor Antagonists

The modulation of the A_2B adenosine receptor is a promising strategy in cancer (immuno) therapy, with A_2BAR antagonists emerging as immune checkpoint inhibitors. Herein, we report a systematic assessment of the impact of (di- and mono-)halogenation at positions 7 and/or 8 on both A_2BAR affinity and pharmacokinetic properties of a collection of A_2BAR antagonists and its study with structure-based free energy perturbation simulations. Monohalogenation at position 8 produced potent A_2BAR ligands irrespective of the nature of the halogen. In contrast, halogenation at position 7 and dihalogenation produced a halogen-size-dependent decay in affinity. Eight novel A_2BAR ligands exhibited remarkable affinity (K_i < 10 nM), exquisite subtype selectivity, and enantioselective recognition, with some eutomers eliciting sub-nanomolar affinity. The pharmacokinetic profile of representative derivatives showed enhanced solubility and microsomal stability. Finally, two compounds showed the capacity of reversing the antiproliferative effect of adenosine in activated primary human peripheral blood mononuclear cells.

Pathfinder-Driven Chemical Space Exploration and Multiparameter Optimization in Tandem with Glide/IFD and QSAR-Based Active Learning Approach to Prioritize Design Ideas for FEP+ Calculations of SARS-CoV-2 PLpro Inhibitors

A global pandemic caused by the SARS-CoV-2 virus that started in 2020 and has wreaked havoc on humanity still ravages up until now. As a result, the negative impact of travel restrictions and lockdowns has underscored the importance of our preparedness for future pandemics. The main thrust of this work was based on addressing this need by traversing chemical space to design inhibitors that target the SARS-CoV-2 papain-like protease (PLpro). Pathfinder-based retrosynthesis analysis was used to generate analogs of GRL-0617 using commercially available building blocks by replacing the naphthalene moiety. A total of 10 models were built using active learning QSAR, which achieved good statistical results such as an R2 > 0.70, Q2 > 0.64, STD Dev < 0.30, and RMSE < 0.31, on average for all models. A total of 35 ideas were further prioritized for FEP+ calculations. The FEP+ results revealed that compound 45 was the most active compound in this series with a ΔG of −7.28 ± 0.96 kcal/mol. Compound 5 exhibited a ΔG of −6.78 ± 1.30 kcal/mol. The inactive compounds in this series were compound 91 and compound 23 with a ΔG of −5.74 ± 1.06 and −3.11 ± 1.45 kcal/mol. The combined strategy employed here is envisaged to be of great utility in multiparameter lead optimization efforts, to traverse chemical space, maintaining and/or improving the potency as well as the property space of synthetically aware design ideas.

In Silico Positional Analogue Scanning with Amber GPU-TI

Positional analogue scanning (PAS) is an accepted strategy for multiparameter lead optimization (MPO) in drug discovery. Small structural changes as introduced by PAS can lead to 10-fold changes in binding potency in ∼10-20% of cases, a significant parameter shift irrespective of other MPO objectives. Sometimes performing a complete PAS is challenging due to resource and time constraints, building block availability, or difficulty in synthesis. Calculating relative binding free energies (RBFEs) for all positions can contribute to prioritizing the most promising analogues for synthesis. We tested a well-established RBFE calculation method, Amber GPU-TI, for 20 positional analogue scans in 14 test systems (cyclin-dependent kinase 8 (CDK8), hepatitis C virus nonstructural protein 5B (HCV NS5B), tankyrase, RAC-α serine/threonine-protein kinase (Akt), phosphodiesterase 1B (PDE1B), orexin/hypocretin receptor type 1 (OX1R), orexin/hypocretin receptor type 2 (OX2R), histone acetyltransferase K (lysine) acetyltransferase 6A (KAT6A), peroxisome proliferator-activated receptor γ (PPARγ), extracellular signal-regulated kinases (ERK1/2), coactivator-associated arginine methyltransferase 1 (PRMT4), α_vβ₆, bromodomain 1 (BD1), human immunodeficiency virus-1 (HIV-1) entry) involving nitrogen, methyl, halogen, methoxy, and hydroxyl scans with at least four analogues per set. Among the 66 analogue positions explored, we found that in 18 cases Amber GPU-TI calculations predicted a more than 10-fold change in potency. In all of these cases, the experimentally observed direction of potency changes agreed with the predictions. In 16 cases, more than 10-fold changes in experimental potency were observed. Again, in all of these cases, Amber GPU-TI predicted the direction of the potency changes correctly. In none of these cases would a decision made for or against synthesis based on a 10-fold change in potency have resulted in missing an important analogue. Therefore, in silico RBFE calculations using Amber GPU-TI can meaningfully contribute to the prioritization of positional analogues before synthesis.

Large-scale application of free energy perturbation calculations for antibody design

Alchemical free energy perturbation (FEP) is a rigorous and powerful technique to calculate the free energy difference between distinct chemical systems. Here we report our implementation of automated large-scale FEP calculations, using the Amber software package, to facilitate antibody design and evaluation. In combination with Hamiltonian replica exchange, our FEP simulations aim to predict the effect of mutations on both the binding affinity and the structural stability. Importantly, we incorporate multiple strategies to faithfully estimate the statistical uncertainties in the FEP results. As a case study, we apply our protocols to systematically evaluate variants of the m396 antibody for their conformational stability and their binding affinity to the spike proteins of SARS-CoV-1 and SARS-CoV-2. By properly adjusting relevant parameters, the particle collapse problems in the FEP simulations are avoided. Furthermore, large statistical errors in a small fraction of the FEP calculations are effectively reduced by extending the sampling, such that acceptable statistical uncertainties are achieved for the vast majority of the cases with a modest total computational cost. Finally, our predicted conformational stability for the m396 variants is qualitatively consistent with the experimentally measured melting temperatures. Our work thus demonstrates the applicability of FEP in computational antibody design.

Does Hamiltonian Replica Exchange via Lambda-Hopping Enhance the Sampling in Alchemical Free Energy Calculations?

In the context of computational drug design, we examine the effectiveness of the enhanced sampling techniques in state-of-the-art free energy calculations based on alchemical molecular dynamics simulations. In a paradigmatic molecule with competition between conformationally restrained E and Z isomers whose probability ratio is strongly affected by the coupling with the environment, we compare the so-called λ-hopping technique to the Hamiltonian replica exchange methods assessing their convergence behavior as a function of the enhanced sampling protocols (number of replicas, scaling factors, simulation times). We found that the pure λ-hopping, commonly used in solvation and binding free energy calculations via alchemical free energy perturbation techniques, is ineffective in enhancing the sampling of the isomeric states, exhibiting a pathological dependence on the initial conditions. Correct sampling can be restored in λ-hopping simulation by the addition of a "hot-zone" scaling factor to the λ-stratification (FEP+ approach), provided that the additive hot-zone scaling factors are tuned and optimized using preliminary ordinary replica-exchange simulation of the end-states.

Relative Binding Free Energy between Chemically Distant Compounds Using a Bidirectional Nonequilibrium Approach

In the context of advanced hit-to-lead drug design based on atomistic molecular dynamics simulations, we propose a dual topology alchemical approach for calculating the relative binding free energy (RBFE) between two chemically distant compounds. The method (termed NE-RBFE) relies on the enhanced sampling of the end-states in bulk and in the bound state via Hamiltonian Replica Exchange, alchemically connected by a series of independent and fast nonequilibrium (NE) simulations. The technique has been implemented in a bidirectional fashion, applying the Crooks theorem to the NE work distributions for RBFE predictions. The dissipation of the NE process, negatively affecting accuracy, has been minimized by introducing a smooth regularization based on shifted electrostatic and Lennard-Jones non bonded potentials. As a challenging testbed, we have applied our method to the calculation of the RBFEs in the recent host-guest SAMPL international contest, featuring a macrocyclic host with guests varying in the net charge, volume, and chemical fingerprints. Closure validation has been successfully verified in cycles involving compounds with disparate Tanimoto coefficients, volume, and net charge. NE-RBFE is specifically tailored for massively parallel facilities and can be used with little or no code modification on most of the popular software packages supporting nonequilibrium alchemical simulations, such as Gromacs, Amber, NAMD, or OpenMM. The proposed methodology bypasses most of the entanglements and limitations of the standard single topology RBFE approach for strictly congeneric series based on free-energy perturbation, such as slowly relaxing cavity water, sampling issues along the alchemical stratification, and the need for highly overlapping molecular fingerprints.

In silico design of a novel nucleotide antiviral agent by free energy perturbation

Nucleoside analogs are the backbone of antiviral therapies. Drugs from this class undergo processing by host or viral kinases to form the active nucleoside triphosphate species that selectively inhibits the viral polymerase. It is the central hypothesis that the nucleoside triphosphate analog must be a favorable substrate for the viral polymerase and the nucleoside precursor must be a satisfactory substrate for the host kinases to inhibit viral replication. Herein, free energy perturbation (FEP) was used to predict substrate affinity for both host and viral enzymes. Several uridine 5'-monophosphate prodrug analogs known to inhibit hepatitis C virus (HCV) were utilized in this study to validate the use of FEP. Binding free energies to the host monophosphate kinase and viral RNA-dependent RNA polymerase (RdRp) were calculated for methyl-substituted uridine analogs. The 2'-C-methyl-uridine and 4'-C-methyl-uridine scaffolds delivered favorable substrate binding to the host kinase and HCV RdRp that were consistent with results from cellular antiviral activity in support of our new approach. In a prospective evaluation, FEP results suggest that 2'-C-dimethyl-uridine scaffold delivered favorable monophosphate and triphosphate substrates for both host kinase and HCV RdRp, respectively. Novel 2'-C-dimethyl-uridine monophosphate prodrug was synthesized and exhibited sub-micromolar inhibition of HCV replication. Using this novel approach, we demonstrated for the first time that nucleoside analogs can be rationally designed that meet the multi-target requirements for antiviral activity.

Improving ΔΔG Predictions with a Multitask Convolutional Siamese Network

The lead optimization phase of drug discovery refines an initial hit molecule for desired properties, especially potency. Synthesis and experimental testing of the small perturbations during this refinement can be quite costly and time-consuming. Relative binding free energy (RBFE, also referred to as ΔΔG) methods allow the estimation of binding free energy changes after small changes to a ligand scaffold. Here, we propose and evaluate a Siamese convolutional neural network (CNN) for the prediction of RBFE between two bound ligands. We show that our multitask loss is able to improve on a previous state-of-the-art Siamese network for RBFE prediction via increased regularization of the latent space. The Siamese network architecture is well suited to the prediction of RBFE in comparison to a standard CNN trained on the same data (Pearson's R of 0.553 and 0.5, respectively). When evaluated on a left-out protein family, our Siamese CNN shows variability in its RBFE predictive performance depending on the protein family being evaluated (Pearson's R ranging from -0.44 to 0.97). RBFE prediction performance can be improved during generalization by injecting only a few examples (few-shot learning) from the evaluation data set during model training.

Exploring the Effect of Enhanced Sampling on Protein Stability Prediction

Changes in protein stability due to side-chain mutations are evaluated by alchemical free-energy calculations based on classical molecular dynamics (MD) simulations in explicit solvent using the GROMOS force field. Three proteins of different complexity with a total number of 93 single-point mutations are analyzed, and the relative free-energy differences are discussed with respect to configurational sampling and (dis)agreement with experimental data. For the smallest protein studied, a 34-residue WW domain, the starting structure dependence of the alchemical free-energy changes, is discussed in detail. Deviations from previous simulations for the two other proteins are shown to result from insufficient sampling in the earlier studies. Hamiltonian replica exchange in combination with multiple starting structures and sufficient sampling time of more than 100 ns per intermediate alchemical state is required in some cases to reach convergence.

Machine Learning Applied to the Modeling of Pharmacological and ADMET Endpoints

The well-known concept of quantitative structure-activity relationships (QSAR) has been gaining significant interest in the recent years. Data, descriptors, and algorithms are the main pillars to build useful models that support more efficient drug discovery processes with in silico methods. Significant advances in all three areas are the reason for the regained interest in these models. In this book chapter we review various machine learning (ML) approaches that make use of measured in vitro/in vivo data of many compounds. We put these in context with other digital drug discovery methods and present some application examples.

CHARMM-GUI Free Energy Calculator for Practical Ligand Binding Free Energy Simulations with AMBER

Alchemical free energy methods, such as free energy perturbation (FEP) and thermodynamic integration (TI), become increasingly popular and crucial for drug design and discovery. However, the system preparation of alchemical free energy simulation is an error-prone, time-consuming, and tedious process for a large number of ligands. To address this issue, we have recently presented CHARMM-GUI Free Energy Calculator that can provide input and postprocessing scripts for NAMD and GENESIS FEP molecular dynamics systems. In this work, we extended three submodules of Free Energy Calculator to work with the full suite of GPU-accelerated alchemical free energy methods and tools in AMBER, including input and postprocessing scripts. The BACE1 (β-secretase 1) benchmark set was used to validate the AMBER-TI simulation systems and scripts generated by Free Energy Calculator. The overall results of relatively large and diverse systems are almost equivalent with different protocols (unified and split) and with different timesteps (1, 2, and 4 fs), with R² > 0.9. More importantly, the average free energy differences between two protocols are small and reliable with four independent runs, with a mean unsigned error (MUE) below 0.4 kcal/mol. Running at least four independent runs for each pair with AMBER20 (and FF19SB/GAFF2.1/OPC force fields), we obtained a MUE of 0.99 kcal/mol and root-mean-square error of 1.31 kcal/mol for 58 alchemical transformations in comparison with experimental data. In addition, a set of ligands for T4-lysozyme was used to further validate our free energy calculation protocol whose results are close to experimental data (within 1 kcal/mol). In summary, Free Energy Calculator provides a user-friendly web-based tool to generate the AMBER-TI system and input files for high-throughput binding free energy calculations with access to the full set of GPU-accelerated alchemical free energy, enhanced sampling, and analysis methods in AMBER.

PyAutoFEP: An Automated Free Energy Perturbation Workflow for GROMACS Integrating Enhanced Sampling Methods

Free energy perturbation (FEP) calculations are now routinely used in drug discovery to estimate the relative FEB (RFEB) of small molecules to a biomolecular target of interest. Using enhanced sampling can improve the correlation between predictions and experimental data, especially in systems with conformational changes. Due to the large number of perturbations required in drug discovery campaigns, the manual setup of FEP calculations is no longer viable. Here, we introduce PyAutoFEP, a flexible and open-source tool to aid the setup of RFEB FEP. PyAutoFEP is written in Python3, and automates the generation of perturbation maps, dual topologies, system building and molecular dynamics (MD), and analysis. PyAutoFEP supports multiple force fields, incorporates replica exchange with solute tempering (REST) and replica exchange with solute scaling (REST2) enhanced sampling methods, and allows flexible λ values along perturbation windows. To validate PyAutoFEP, it was applied to a set of 14 Farnesoid X receptor ligands, a system included in the drug design data resource grand challenge 2. An 88% mean correct sign prediction was achieved, and 75% of the predictions had an error below 1.5 kcal/mol. Results using Amber03/GAFF, CHARMM36m/CGenFF, and OPLS-AA/M/LigParGen had Pearson's r values of 0.71 ± 0.13, 0.30 ± 0.27, and 0.66 ± 0.20, respectively. The Amber03/GAFF and OPLS-AA/M/LigParGen results were on par with the top grand challenge 2 submissions. Applying REST2 improved the results using CHARMM36m/CGenFF (Pearson's r = 0.43 ± 0.21) but had little impact on the other force fields. CHARMM36-YF and CHARMM36-WYF modifications did not yield improved predictions compared to CHARMM36m. Finally, we estimated the probability of finding a molecule 1 pK_i better than a lead when using PyAutoFEP to screen 10 or 100 analogues. The probabilities, when compared to random sampling, increased up to sevenfold when 100 molecules were to be screened, suggesting that PyAutoFEP would likely be useful for lead optimization. PyAutoFEP is available on GitHub at https://github.com/lmmpf/PyAutoFEP.

Rapid and accurate estimation of protein-ligand relative binding affinities using site-identification by ligand competitive saturation

Predicting relative protein-ligand binding affinities is a central pillar of lead optimization efforts in structure-based drug design. The site identification by ligand competitive saturation (SILCS) methodology is based on functional group affinity patterns in the form of free energy maps that may be used to compute protein-ligand binding poses and affinities. Presented are results obtained from the SILCS methodology for a set of eight target proteins as reported originally in Wang et al. (J. Am. Chem. Soc., 2015, 137, 2695-2703) using free energy perturbation (FEP) methods in conjunction with enhanced sampling and cycle closure corrections. These eight targets have been subsequently studied by many other authors to compare the efficacy of their method while comparing with the outcomes of Wang et al. In this work, we present results for a total of 407 ligands on the eight targets and include specific analysis on the subset of 199 ligands considered previously. Using the SILCS methodology we can achieve an average accuracy of up to 77% and 74% when considering the eight targets with their 199 and 407 ligands, respectively, for rank-ordering ligand affinities as calculated by the percent correct metric. This accuracy increases to 82% and 80%, respectively, when the SILCS atomic free energy contributions are optimized using a Bayesian Markov-chain Monte Carlo approach. We also report other metrics including Pearson's correlation coefficient, Pearlman's predictive index, mean unsigned error, and root mean square error for both sets of ligands. The results obtained for the 199 ligands are compared with the outcomes of Wang et al. and other published works. Overall, the SILCS methodology yields similar or better-quality predictions without a priori need for known ligand orientations in terms of the different metrics when compared to current FEP approaches with significant computational savings while additionally offering quantitative estimates of individual atomic contributions to binding free energies. These results further validate the SILCS methodology as an accurate, computationally efficient tool to support lead optimization and drug discovery.

Performance of Relative Binding Free Energy Calculations on an Automatically Generated Dataset of Halogen-Deshalogen Matched Molecular Pairs

In this study, we generated a matched molecular pair dataset of halogen/deshalogen compounds with reliable binding affinity data and structural binding mode information from public databases. The workflow includes automated system preparation and setup of free energy perturbation relative binding free energy calculations. We demonstrate the suitability of these datasets to investigate the performance of molecular mechanics force fields and molecular simulation algorithms for the purpose of in silico affinity predictions in lead optimization. Our datasets of a total of 115 matched molecular pairs show highly accurate binding free energy predictions with an average error of <1 kcal/mol despite the semi-automated calculation scheme. We quantify the accuracy of the optimized potential for liquid simulations (OPLS) force field to predict the effect of halogen addition to compounds, a commonly employed chemical modification in the design of drug-like molecules.

Molecular mechanism concerning conformational changes of CDK2 mediated by binding of inhibitors using molecular dynamics simulations and principal component analysis

Cyclin-dependent kinase 2 (CDK2) has been regarded as a promising drug target for anti-tumour agents. In this study, molecular dynamics (MD) simulations and principal component (PC) analysis were used to explore binding mechanism of three inhibitors 1PU, CDK, 50Z to CDK2 and influences of their bindings on conformational changes of CDK2. The results show that bindings of inhibitors yield obvious impacts on internal dynamics, movement patterns and conformational changes of CDK2. In addition, molecular mechanics generalized Born surface area (MM-GBSA) was applied to calculate binding free energies between three inhibitors and CDK2 and evaluate their binding ability to CDK2. The results show that CDK has the strongest binding to CDK2 among the current three inhibitors. Residue-based free energy decomposition method was further utilized to decode the contributions of a single residue to binding of inhibitors, and it was found that three inhibitors not only produce hydrogen bonding interactions and hydrophobic interactions with key residues of CDK2, which promotes binding of three inhibitors to CDK2, but also share similar binding modes. This work is expected to be helpful for design of efficient drugs targeting CDK2.

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.

Protein Loop Conformational Free Energy Changes via an Alchemical Path without Reaction Coordinates

We introduce a method called restrain-free energy perturbation-release 2.0 (R-FEP-R 2.0) to estimate conformational free energy changes of protein loops via an alchemical path. R-FEP-R 2.0 is a generalization of the method called restrain-free energy perturbation-release (R-FEP-R) that can only estimate conformational free energy changes of protein side chains but not loops. The reorganization of protein loops is a central feature of many biological processes. Unlike other advanced sampling algorithms such as umbrella sampling and metadynamics, R-FEP-R and R-FEP-R 2.0 do not require predetermined collective coordinates and transition pathways that connect the two endpoint conformational states. The R-FEP-R 2.0 method was applied to estimate the conformational free energy change of a β-turn flip in the protein ubiquitin. The result obtained by R-FEP-R 2.0 agrees with the benchmarks very well. We also comment on problems commonly encountered when applying umbrella sampling to calculate protein conformational free energy changes.

Variational Method for Networkwide Analysis of Relative Ligand Binding Free Energies with Loop Closure and Experimental Constraints

We describe an efficient method for the simultaneous solution of all free energies within a relative binding free-energy (RBFE) network with cycle closure and experimental/reference constraint conditions using Bennett Acceptance Ratio (BAR) and Multistate BAR (MBAR) analysis. Rather than solving the BAR or MBAR equations for each transformation independently, the simultaneous solution of all transformations are obtained by performing a constrained minimization of a global objective function. The nonlinear optimization of the objective function is subjected to affine linear constraints that couple the free energies between the network edges. The constraints are used to enforce the closure of thermodynamic cycles within the RBFE network, and to enforce an additional set of linear constraint conditions demonstrated here to be subsets of (1 or 2) experimental values. We describe details of the practical implementation of the network BAR/MBAR procedure, including use of generalized coordinates in the minimization of the free-energy objective function, propagation of bootstrap errors from those coordinates, and performance and memory optimization. In some cases it is found that use of restraints in the optimization is more practical than use of generalized coordinates for enforcing constraint conditions. The fast BARnet and MBARnet methods are used to analyze the RBFEs of six prototypical protein-ligand systems, and it is shown that enforcement of cycle closure conditions reduces the error in the predictions only modestly, and further reduction in errors can be achieved when one or two experimental RBFEs are included in the optimization procedure. These methods have been implemented into FE-ToolKit, a new free-energy analysis toolkit. The BARnet/MBARnet framework presented here opens the door to new, more efficient and robust free-energy analysis with enhanced predictive capability for drug discovery applications.