Predicting Binding Free Energies in a Large Combinatorial Chemical Space Using Multisite λ Dynamics

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

How to Sample Dozens of Substitutions per Site with λ Dynamics

Alchemical free energy methods are useful in computer-aided drug design and computational protein design because they provide rigorous statistical mechanics-based estimates of free energy differences from molecular dynamics simulations. λ dynamics is a free energy method with the ability to characterize combinatorial chemical spaces spanning thousands of related systems within a single simulation, which gives it a distinct advantage over other alchemical free energy methods that are mostly limited to pairwise comparisons. Recently developed methods have improved the scalability of λ dynamics to perturbations at many sites; however, the size of chemical space that can be explored at each individual site has previously been limited to fewer than ten substituents. As the number of substituents increases, the volume of alchemical space corresponding to nonphysical alchemical intermediates grows exponentially relative to the size corresponding to the physical states of interest. Beyond nine substituents, λ dynamics simulations become lost in an alchemical morass of intermediate states. In this work, we introduce new biasing potentials that circumvent excessive sampling of intermediate states by favoring sampling of physical end points relative to alchemical intermediates. Additionally, we present a more scalable adaptive landscape flattening algorithm for these larger alchemical spaces. Finally, we show that this potential enables more efficient sampling in both protein and drug design test systems with up to 24 substituents per site, enabling, for the first time, simultaneous simulation of all 20 amino acids.

A λ-Dynamics Investigation of Insulin Wakayama and Other A3 Variant Binding Affinities to the Insulin Receptor

Insulin Wakayama is a clinical insulin variant where a conserved valine at the third residue on insulin's A chain (ValA3) is replaced with a leucine (LeuA3), weakening insulin receptor (IR) binding by 140-500-fold. This severe impact on binding from a subtle modification has posed an intriguing problem for decades. Although experimental investigations of natural and unnatural A3 mutations have highlighted the sensitivity of insulin-IR binding at this site, atomistic explanations of these binding trends have remained elusive. We investigate this problem computationally using λ-dynamics free energy calculations to model structural changes in response to perturbations of the ValA3 side chain and to calculate associated relative changes in binding free energy (ΔΔGbind). The Wakayama LeuA3 mutation and seven other A3 substitutions were studied in this work. The calculated ΔΔGbind results showed high agreement compared to experimental binding potencies with a Pearson correlation of 0.88 and a mean unsigned error of 0.68 kcal/mol. Extensive structural analyses of λ-dynamics trajectories revealed that critical interactions were disrupted between insulin and the insulin receptor as a result of the A3 mutations. This investigation also quantifies the effect that adding an A3 Cδ atom or losing an A3 Cγ atom has on insulin's binding affinity to the IR. Thus, λ-dynamics was able to successfully model the effects of mutations to insulin's A3 side chain on its protein-protein interactions with the IR and shed new light on a decades-old mystery: the exquisite sensitivity of hormone-receptor binding to a subtle modification of an invariant insulin residue.

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

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

A λ-dynamics investigation of insulin Wakayama and other A3 variant binding affinities to the insulin receptor

Insulin Wakayama is a clinical insulin variant where a conserved valine at the third residue on insulin's A chain (ValA3) is replaced with a leucine (LeuA3), impairing insulin receptor (IR) binding by 140-500 fold. This severe impact on binding from such a subtle modification has posed an intriguing problem for decades. Although experimental investigations of natural and unnatural A3 mutations have highlighted the sensitivity of insulin-IR binding to minor changes at this site, an atomistic explanation of these binding trends has remained elusive. We investigate this problem computationally using λ-dynamics free energy calculations to model structural changes in response to perturbations of the ValA3 side chain and to calculate associated relative changes in binding free energy (ΔΔGbind). The Wakayama LeuA3 mutation and seven other A3 substitutions were studied in this work. The calculated ΔΔGbind results showed high agreement compared to experimental binding potencies with a Pearson correlation of 0.88 and a mean unsigned error of 0.68 kcal/mol. Extensive structural analyses of λ-dynamics trajectories revealed that critical interactions were disrupted between insulin and the insulin receptor as a result of the A3 mutations. This investigation also quantifies the effect that adding an A3 Cδ atom or losing an A3 Cγ atom has on insulin's binding affinity to the IR. Thus, λ-dynamics was able to successfully model the effects of subtle modifications to insulin's A3 side chain on its protein-protein interactions with the IR and shed new light on a decades-old mystery: the exquisite sensitivity of hormone-receptor binding to a subtle modification of an invariant insulin residue.

Biomolecular dynamics in the 21st century

The relevance of motions in biological macromolecules has been clear since the early structural analyses of proteins by X-ray crystallography. Computer simulations have been applied to provide a deeper understanding of the dynamics of biological macromolecules since 1976, and are now a standard tool in many labs working on the structure and function of biomolecules. In this mini-review we highlight some areas of current interest and active development for simulations, in particular all-atom molecular dynamics simulations.

In silico λ-dynamics predicts protein binding specificities to modified RNAs

RNA modifications shape gene expression through a smorgasbord of chemical changes to canonical RNA bases. Although numbering in the hundreds, only a few RNA modifications are well characterized, in part due to the absence of methods to identify modification sites. Antibodies remain a common tool to identify modified RNA and infer modification sites through straightforward applications. However, specificity issues can result in off-target binding and confound conclusions. This work utilizes in silico λ-dynamics to efficiently estimate binding free energy differences of modification-targeting antibodies between a variety of naturally occurring RNA modifications. Crystal structures of inosine and N6-methyladenosine (m6A) targeting antibodies bound to their modified ribonucleosides were determined and served as structural starting points. λ-Dynamics was utilized to predict RNA modifications that permit or inhibit binding to these antibodies. In vitro RNA-antibody binding assays supported the accuracy of these in silico results. High agreement between experimental and computed binding propensities demonstrated that λ-dynamics can serve as a predictive screen for antibody specificity against libraries of RNA modifications. More importantly, this strategy is an innovative way to elucidate how hundreds of known RNA modifications interact with biological molecules without the limitations imposed by in vitro or in vivo methodologies.

Selection pressures on evolution of ribonuclease H explored with rigorous free-energy-based design

Understanding natural protein evolution and designing novel proteins are motivating interest in development of high-throughput methods to explore large sequence spaces. In this work, we demonstrate the application of multisite λ dynamics (MSλD), a rigorous free energy simulation method, and chemical denaturation experiments to quantify evolutionary selection pressure from sequence-stability relationships and to address questions of design. This study examines a mesophilic phylogenetic clade of ribonuclease H (RNase H), furthering its extensive characterization in earlier studies, focusing on E. coli RNase H (ecRNH) and a more stable consensus sequence (AncCcons) differing at 15 positions. The stabilities of 32,768 chimeras between these two sequences were computed using the MSλD framework. The most stable and least stable chimeras were predicted and tested along with several other sequences, revealing a designed chimera with approximately the same stability increase as AncCcons, but requiring only half the mutations. Comparing the computed stabilities with experiment for 12 sequences reveals a Pearson correlation of 0.86 and root mean squared error of 1.18 kcal/mol, an unprecedented level of accuracy well beyond less rigorous computational design methods. We then quantified selection pressure using a simple evolutionary model in which sequences are selected according to the Boltzmann factor of their stability. Selection temperatures from 110 to 168 K are estimated in three ways by comparing experimental and computational results to evolutionary models. These estimates indicate selection pressure is high, which has implications for evolutionary dynamics and for the accuracy required for design, and suggests accurate high-throughput computational methods like MSλD may enable more effective protein design.

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.

Accelerating Alchemical Free Energy Prediction Using a Multistate Method: Application to Multiple Kinases

Alchemical free-energy methods based on molecular dynamics (MD) simulations have become important tools to identify modifications of small organic molecules that improve their protein binding affinity during lead optimization. The routine application of pairwise free-energy methods to rank potential binders from best to worst is impacted by the combinatorial increase in calculations to perform when the number of molecules to assess grows. To address this fundamental limitation, our group has developed replica-exchange enveloping distribution sampling (RE-EDS), a pathway-independent multistate method, enabling the calculation of alchemical free-energy differences between multiple ligands (N > 2) from a single MD simulation. In this work, we apply the method to a set of four kinases with diverse binding pockets and their corresponding inhibitors (42 in total), chosen to showcase the general applicability of RE-EDS in prospective drug design campaigns. We show that for the targets studied, RE-EDS is able to model up to 13 ligands simultaneously with high sampling efficiency, leading to a substantial decrease in computational cost when compared to pairwise methods.

QSAR via Multisite λ-Dynamics in the Orphaned TSSK1B Kinase

Multisite λ-dynamics (MSλD) is a novel method for the calculation of relative free energies of binding for ligands to their targeted receptors. It can be readily used to examine a large number of molecules with multiple functional groups at multiple sites around a common core. This makes MSλD a powerful tool in structure-based drug design. In the present study, MSλD is applied to calculate the relative binding free energies of 1296 inhibitors to the testis specific serine kinase 1B (TSSK1B), a validated target for male contraception. For this system, MSλD requires significantly fewer computational resources compared to traditional free energy methods like free energy perturbation or thermodynamic integration. From MSλD simulations, we examined whether modifications of a ligand at two different sites are coupled or not. Based on our calculations, we established a quantitative structure-activity relationship (QSAR) for this set of molecules and identified a site in the ligand where further modification, such as adding more polar groups, may lead to increased binding affinity. This article is protected by copyright. All rights reserved.

An Empirical Quantitative Structure-Activity Relationship Equation Assists the Discovery of High-Affinity Phosphodiesterase 4D Inhibitors as Leads to PET Radioligands

A positron emission tomography (PET) radioligand for imaging phosphodiesterase 4D (PDE4D) would benefit drug discovery and the investigation of neuropsychiatric disorders. The most promising radioligand to date, namely, [11C]T1650, has shown unstable quantification in humans. Structural elaboration of [11C]T1650 was therefore deemed necessary. High target affinity in the low nM range is usually required for successful PET radioligands. In our PDE4D PET radioligand development, we formulated and optimized an empirical equation (log[IC50 (nM)] = P1 + P2 + P3 + P4) that well described the relationship between binding affinity and empirically derived values (P1-P4) for the individual fragments in four subregions commonly composing each inhibitor (R2 = 0.988, n = 62). This equation was used to predict compounds that would have high inhibitory potency. Fourteen new compounds were obtained with IC50 of 0.3-10 nM. Finally, eight compounds were judged to be worthy of future radiolabeling and evaluation as PDE4D PET radioligands.

Best practices for constructing, preparing, and evaluating protein-ligand binding affinity benchmarks [Article v0.1]

Free energy calculations are rapidly becoming indispensable in structure-enabled drug discovery programs. As new methods, force fields, and implementations are developed, assessing their expected accuracy on real-world systems (benchmarking) becomes critical to provide users with an assessment of the accuracy expected when these methods are applied within their domain of applicability, and developers with a way to assess the expected impact of new methodologies. These assessments require construction of a benchmark-a set of well-prepared, high quality systems with corresponding experimental measurements designed to ensure the resulting calculations provide a realistic assessment of expected performance when these methods are deployed within their domains of applicability. To date, the community has not yet adopted a common standardized benchmark, and existing benchmark reports suffer from a myriad of issues, including poor data quality, limited statistical power, and statistically deficient analyses, all of which can conspire to produce benchmarks that are poorly predictive of real-world performance. Here, we address these issues by presenting guidelines for (1) curating experimental data to develop meaningful benchmark sets, (2) preparing benchmark inputs according to best practices to facilitate widespread adoption, and (3) analysis of the resulting predictions to enable statistically meaningful comparisons among methods and force fields. We highlight challenges and open questions that remain to be solved in these areas, as well as recommendations for the collection of new datasets that might optimally serve to measure progress as methods become systematically more reliable. Finally, we provide a curated, versioned, open, standardized benchmark set adherent to these standards (PLBenchmarks) and an open source toolkit for implementing standardized best practices assessments (arsenic) for the community to use as a standardized assessment tool. While our main focus is free energy methods based on molecular simulations, these guidelines should prove useful for assessment of the rapidly growing field of machine learning methods for affinity prediction as well.

On the Rapid Calculation of Binding Affinities for Antigen and Antibody Design and Affinity Maturation Simulations

The accurate and efficient calculation of protein-protein binding affinities is an essential component in antibody and antigen design and optimization, and in computer modeling of antibody affinity maturation. Such calculations remain challenging despite advances in computer hardware and algorithms, primarily because proteins are flexible molecules, and thus, require explicit or implicit incorporation of multiple conformational states into the computational procedure. The astronomical size of the amino acid sequence space further compounds the challenge by requiring predictions to be computed within a short time so that many sequence variants can be tested. In this study, we compare three classes of methods for antibody/antigen (Ab/Ag) binding affinity calculations: (i) a method that relies on the physical separation of the Ab/Ag complex in equilibrium molecular dynamics (MD) simulations, (ii) a collection of 18 scoring functions that act on an ensemble of structures created using homology modeling software, and (iii) methods based on the molecular mechanics-generalized Born surface area (MM-GBSA) energy decomposition, in which the individual contributions of the energy terms are scaled to optimize agreement with the experiment. When applied to a set of 49 antibody mutations in two Ab/HIV gp120 complexes, all of the methods are found to have modest accuracy, with the highest Pearson correlations reaching about 0.6. In particular, the most computationally intensive method, i.e., MD simulation, did not outperform several scoring functions. The optimized energy decomposition methods provided marginally higher accuracy, but at the expense of requiring experimental data for parametrization. Within each method class, we examined the effect of the number of independent computational replicates, i.e., modeled structures or reinitialized MD simulations, on the prediction accuracy. We suggest using about ten modeled structures for scoring methods, and about five simulation replicates for MD simulations as a rule of thumb for obtaining reasonable convergence. We anticipate that our study will be a useful resource for practitioners working to incorporate binding affinity calculations within their protein design and optimization process.

Addressing Intersite Coupling Unlocks Large Combinatorial Chemical Spaces for Alchemical Free Energy Methods

Alchemical free energy methods are playing a growing role in molecular design, both for computer-aided drug design of small molecules and for computational protein design. Multisite λ dynamics (MSλD) is a uniquely scalable alchemical free energy method that enables more efficient exploration of combinatorial alchemical spaces encountered in molecular design, but simulations have typically been limited to a few hundred ligands or sequences. Here, we focus on coupling between sites to enable scaling to larger alchemical spaces. We first discuss updates to the biasing potentials that facilitate MSλD sampling to include coupling terms and show that this can provide more thorough sampling of alchemical states. We then harness coupling between sites by developing a new free energy estimator based on the Potts models underlying direct coupling analysis, a method for predicting contacts from sequence coevolution, and find it yields more accurate free energies than previous estimators. The sampling requirements of the Potts model estimator scale with the square of the number of sites, a substantial improvement over the exponential scaling of the standard estimator. This opens up exploration of much larger alchemical spaces with MSλD for molecular design.

Optimizing Multisite λ-Dynamics Throughput with Charge Renormalization

With the ability to sample combinations of alchemical perturbations at multiple sites off a small molecule core, multisite λ-dynamics (MSλD) has become an attractive alternative to conventional alchemical free energy methods for exploring large combinatorial chemical spaces. However, current software implementations dictate that combinatorial sampling with MSλD must be performed with a multiple topology model (MTM), which is nontrivial to create by hand, especially for a series of ligand analogues which may have diverse functional groups attached. This work introduces an automated workflow, referred to as msld_py_prep, to assist in the creation of a MTM for use with MSλD. One approach for partitioning partial atomic charges between ligands to create a MTM, called charge renormalization, is also presented and rigorously evaluated. We find that msld_py_prep greatly accelerates the preparation of MSλD ready-to-use files and that charge renormalization can provide a successful approach for MTM generation, as long as bookending calculations are applied to correct small differences introduced by charge renormalization. Charge renormalization also facilitates the use of many different force field parameters with MSλD, broadening the applicability of MSλD for computer-aided drug design.

Application of Site-Identification by Ligand Competitive Saturation in Computer-Aided Drug Design

Site Identification by Ligand Competitive Saturation (SILCS) is a molecular simulation approach that uses diverse small solutes in aqueous solution to obtain functional group affinity patterns of a protein or other macromolecule. This involves employing a combined Grand Canonical Monte Carlo (GCMC)-molecular dynamics (MD) method to sample the full 3D space of the protein, including deep binding pockets and interior cavities from which functional group free energy maps (FragMaps) are obtained. The information content in the maps, which include contributions from protein flexibilty and both protein and functional group desolvation contributions, can be used in many aspects of the drug discovery process. These include identification of novel ligand binding pockets, including allosteric sites, pharmacophore modeling, prediction of relative protein-ligand binding affinities for database screening and lead optimization efforts, evaluation of protein-protein interactions as well as in the formulation of biologics-based drugs including monoclonal antibodies. The present article summarizes the various tools developed in the context of the SILCS methodology and their utility in computer-aided drug design (CADD) applications, showing how the SILCS toolset can improve the drug-development process on a number of fronts with respect to both accuracy and throughput representing a new avenue of CADD applications.

BLaDE: A Basic Lambda Dynamics Engine for GPU-Accelerated Molecular Dynamics Free Energy Calculations

There is an accelerating interest in practical applications of alchemical free energy methods to problems in protein design, constant pH simulations, and especially computer-aided drug design. In the present paper, we describe a basic lambda dynamics engine (BLaDE) that enables alchemical free energy simulations, including multisite λ dynamics (MSλD) simulations, on graphical processor units (GPUs). We find that BLaDE is 5 to 8 times faster than the current GPU implementation of MSλD-based free energy calculations in CHARMM. We also demonstrate that BLaDE running standard molecular dynamics attains a performance competitive with and sometimes exceeding that of the highly optimized OpenMM GPU code. BLaDE is available as a standalone program and through an API in CHARMM.

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.

Implementation of the QUBE Force Field in SOMD for High-Throughput Alchemical Free-Energy Calculations

The quantum mechanical bespoke (QUBE) force-field approach has been developed to facilitate the automated derivation of potential energy function parameters for modeling protein-ligand binding. To date, the approach has been validated in the context of Monte Carlo simulations of protein-ligand complexes. We describe here the implementation of the QUBE force field in the alchemical free-energy calculation molecular dynamics simulation package SOMD. The implementation is validated by demonstrating the reproducibility of absolute hydration free energies computed with the QUBE force field across the SOMD and GROMACS software packages. We further demonstrate, by way of a case study involving two series of non-nucleoside inhibitors of HIV-1 reverse transcriptase, that the availability of QUBE in a modern simulation package that makes efficient use of graphics processing unit acceleration will facilitate high-throughput alchemical free-energy calculations.

Mutant thermal proteome profiling for characterization of missense protein variants and their associated phenotypes within the proteome

Temperature-sensitive (TS) missense mutants have been foundational for characterization of essential gene function. However, an unbiased approach for analysis of biochemical and biophysical changes in TS missense mutants within the context of their functional proteomes is lacking. We applied MS-based thermal proteome profiling (TPP) to investigate the proteome-wide effects of missense mutations in an application that we refer to as mutant thermal proteome profiling (mTPP). This study characterized global impacts of temperature sensitivity-inducing missense mutations in two different subunits of the 26S proteasome. The majority of alterations identified by RNA-Seq and global proteomics were similar between the mutants, which could suggest that a similar functional disruption is occurring in both missense variants. Results from mTPP, however, provide unique insights into the mechanisms that contribute to the TS phenotype in each mutant, revealing distinct changes that were not obtained using only steady-state transcriptome and proteome analyses. Computationally, multisite λ-dynamics simulations add clear support for mTPP experimental findings. This work shows that mTPP is a precise approach to measure changes in missense mutant-containing proteomes without the requirement for large amounts of starting material, specific antibodies against proteins of interest, and/or genetic manipulation of the biological system. Although experiments were performed under permissive conditions, mTPP provided insights into the underlying protein stability changes that cause dramatic cellular phenotypes observed at nonpermissive temperatures. Overall, mTPP provides unique mechanistic insights into missense mutation dysfunction and connection of genotype to phenotype in a rapid, nonbiased fashion.

Identification of Optimal Ligand Growth Vectors Using an Alchemical Free-Energy Method

In this work, a novel method to rationally design inhibitors with improved steric contacts and enhanced binding free energies is presented. This new method uses alchemical single step perturbation calculations to rapidly optimize the van der Waals interactions of a small molecule in a protein-ligand complex in order to maximize its binding affinity. The results of the optimizer are used to predict beneficial growth vectors on the ligand, and good agreement is found between the predictions from the optimizer and a more rigorous free energy calculation, with a Spearman's rank order correlation of 0.59. The advantage of the method presented here is the significant speed up of over 10-fold compared to traditional free energy calculations and sublinear scaling with the number of growth vectors assessed. Where experimental data were available, mutations from hydrogen to a methyl group at sites highlighted by the optimizer were calculated with MBAR, and the mean unsigned error between experimental and calculated values of the binding free energy was 0.83 kcal/mol.

Automated, Accurate, and Scalable Relative Protein-Ligand Binding Free-Energy Calculations Using Lambda Dynamics

Accurate predictions of changes to protein-ligand binding affinity in response to chemical modifications are of utility in small-molecule lead optimization. Relative free-energy perturbation (FEP) approaches are one of the most widely utilized for this goal but involve significant computational cost, thus limiting their application to small sets of compounds. Lambda dynamics, also rigorously based on the principles of statistical mechanics, provides a more efficient alternative. In this paper, we describe the development of a workflow to set up, execute, and analyze multisite lambda dynamics (MSLD) calculations run on GPUs with CHARMM implemented in BIOVIA Discovery Studio and Pipeline Pilot. The workflow establishes a framework for setting up simulation systems for exploratory screening of modifications to a lead compound, enabling the calculation of relative binding affinities of combinatorial libraries. To validate the workflow, a diverse data set of congeneric ligands for seven proteins with experimental binding affinity data is examined. A protocol to automatically tailor fit biasing potentials iteratively to flatten the free-energy landscape of any MSLD system is developed, which enhances sampling and allows for efficient estimation of free-energy differences. The protocol is first validated on a large number of ligand subsets that model diverse substituents, which shows accurate and reliable performance. The scalability of the workflow is also tested to screen more than 100 ligands modeled in a single system, which also resulted in accurate predictions. With a cumulative sampling time of 150 ns or less, the method results in average unsigned errors of under 1 kcal/mol in most cases for both small and large combinatorial libraries. For the multisite systems examined, the method is estimated to be more than an order of magnitude more efficient than contemporary FEP applications. The results thus demonstrate the utility of the presented MSLD workflow to efficiently screen combinatorial libraries and explore the chemical space around a lead compound and thus are of utility in lead optimization.

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.

Large scale relative protein ligand binding affinities using non-equilibrium alchemy

Ligand binding affinity calculations based on molecular dynamics (MD) simulations and non-physical (alchemical) thermodynamic cycles have shown great promise for structure-based drug design. However, their broad uptake and impact is held back by the notoriously complex setup of the calculations. Only a few tools other than the free energy perturbation approach by Schrödinger Inc. (referred to as FEP+) currently enable end-to-end application. Here, we present for the first time an approach based on the open-source software pmx that allows to easily set up and run alchemical calculations for diverse sets of small molecules using the GROMACS MD engine. The method relies on theoretically rigorous non-equilibrium thermodynamic integration (TI) foundations, and its flexibility allows calculations with multiple force fields. In this study, results from the Amber and Charmm force fields were combined to yield a consensus outcome performing on par with the commercial FEP+ approach. A large dataset of 482 perturbations from 13 different protein-ligand datasets led to an average unsigned error (AUE) of 3.64 ± 0.14 kJ mol-1, equivalent to Schrödinger's FEP+ AUE of 3.66 ± 0.14 kJ mol-1. For the first time, a setup is presented for overall high precision and high accuracy relative protein-ligand alchemical free energy calculations based on open-source software.

Approaching protein design with multisite λ dynamics: Accurate and scalable mutational folding free energies in T4 lysozyme

The estimation of changes in free energy upon mutation is central to the problem of protein design. Modern protein design methods have had remarkable success over a wide range of design targets, but are reaching their limits in ligand binding and enzyme design due to insufficient accuracy in mutational free energies. Alchemical free energy calculations have the potential to supplement modern design methods through more accurate molecular dynamics based prediction of free energy changes, but suffer from high computational cost. Multisite λ dynamics (MSλD) is a particularly efficient and scalable free energy method with potential to explore combinatorially large sequence spaces inaccessible with other free energy methods. This work aims to quantify the accuracy of MSλD and demonstrate its scalability. We apply MSλD to the classic problem of calculating folding free energies in T4 lysozyme, a system with a wealth of experimental measurements. Single site mutants considering 32 mutations show remarkable agreement with experiment with a Pearson correlation of 0.914 and mean unsigned error of 1.19 kcal/mol. Multisite mutants in systems with up to five concurrent mutations spanning 240 different sequences show comparable agreement with experiment. These results demonstrate the promise of MSλD in exploring large sequence spaces for protein design.

Overcoming Challenging Substituent Perturbations with Multisite λ-Dynamics: A Case Study Targeting β-Secretase 1

Alchemical free energy calculations have made a dramatic impact upon the field of structure-based drug design by allowing functional group modifications to be explored computationally prior to experimental synthesis and assay evaluation, thereby informing and directing synthetic strategies. In furthering the advancement of this area, a series of 21 β-secretase 1 (BACE1) inhibitors developed by Janssen Pharmaceuticals were examined to evaluate the ability to explore large substituent perturbations, some of which contain scaffold modifications, with multisite λ-dynamics (MSλD), an innovative alchemical free energy framework. Our findings indicate that MSλD is able to efficiently explore all structurally diverse ligand end-states simultaneously within a single MD simulation with a high degree of precision and with reduced computational costs compared to the widely used approach TI/MBAR. Furthermore, computational predictions were shown to be accurate to within 0.5-0.8 kcal/mol when CM1A partial atomic charges were combined with CHARMM or OPLS-AA-based force fields, demonstrating that MSλD is force field independent and a viable alternative to FEP or TI approaches for drug design.

Reaction-Based Enumeration, Active Learning, and Free Energy Calculations To Rapidly Explore Synthetically Tractable Chemical Space and Optimize Potency of Cyclin-Dependent Kinase 2 Inhibitors

The hit-to-lead and lead optimization processes usually involve the design, synthesis, and profiling of thousands of analogs prior to clinical candidate nomination. A hit finding campaign may begin with a virtual screen that explores millions of compounds, if not more. However, this scale of computational profiling is not frequently performed in the hit-to-lead or lead optimization phases of drug discovery. This is likely due to the lack of appropriate computational tools to generate synthetically tractable lead-like compounds in silico, and a lack of computational methods to accurately profile compounds prospectively on a large scale. Recent advances in computational power and methods provide the ability to profile much larger libraries of ligands than previously possible. Herein, we report a new computational technique, referred to as "PathFinder", that uses retrosynthetic analysis followed by combinatorial synthesis to generate novel compounds in synthetically accessible chemical space. In this work, the integration of PathFinder-driven compound generation, cloud-based FEP simulations, and active learning are used to rapidly optimize R-groups, and generate new cores for inhibitors of cyclin-dependent kinase 2 (CDK2). Using this approach, we explored >300 000 ideas, performed >5000 FEP simulations, and identified >100 ligands with a predicted IC₅₀ < 100 nM, including four unique cores. To our knowledge, this is the largest set of FEP calculations disclosed in the literature to date. The rapid turnaround time, and scale of chemical exploration, suggests that this is a useful approach to accelerate the discovery of novel chemical matter in drug discovery campaigns.

Alchemical Free-Energy Calculations by Multiple-Replica λ-Dynamics: The Conveyor Belt Thermodynamic Integration Scheme

A new method is proposed to calculate alchemical free-energy differences based on molecular dynamics (MD) simulations, called the conveyor belt thermodynamic integration (CBTI) scheme. As in thermodynamic integration (TI), K replicas of the system are simulated at different values of the alchemical coupling parameter λ. The number K is taken to be even, and the replicas are equally spaced on a forward-turn-backward-turn path, akin to a conveyor belt (CB) between the two physical end-states; and as in λ-dynamics (λD), the λ-values associated with the individual systems evolve in time along the simulation. However, they do so in a concerted fashion, determined by the evolution of a single dynamical variable Λ of period 2π controlling the advance of the entire CB. Thus, a change of Λ is always associated with K/2 equispaced replicas moving forward and K/2 equispaced replicas moving backward along λ. As a result, the effective free-energy profile of the replica system along Λ is periodic of period 2 πK^-1, and the magnitude of its variations decreases rapidly upon increasing K, at least as K^-1 in the limit of large K. When a sufficient number of replicas is used, these variations become small, which enables a complete and quasi-homogeneous coverage of the λ-range by the replica system, without application of any biasing potential. If desired, a memory-based biasing potential can still be added to further homogenize the sampling, the preoptimization of which is computationally inexpensive. The final free-energy profile along λ is calculated similarly to TI, by binning of the Hamiltonian λ-derivative as a function of λ considering all replicas simultaneously, followed by quadrature integration. The associated quadrature error can be kept very low owing to the continuous and quasi-homogeneous λ-sampling. The CBTI scheme can be viewed as a continuous/deterministic/dynamical analog of the Hamiltonian replica-exchange/permutation (HRE/HRP) schemes or as a correlated multiple-replica analog of the λD or λ-local elevation umbrella sampling (λ-LEUS) schemes. Compared to TI, it shares the advantage of the latter schemes in terms of enhanced orthogonal sampling, i.e. the availability of variable-λ paths to circumvent conformational barriers present at specific λ-values. Compared to HRE/HRP, it permits a deterministic and continuous sampling of the λ-range, is expected to be less sensitive to possible artifacts of the thermo- and barostating schemes, and bypasses the need to carefully preselect a λ-ladder and a swapping-attempt frequency. Compared to λ-LEUS, it eliminates (or drastically reduces) the dead time associated with the preoptimization of a biasing potential. The goal of this article is to provide the mathematical/physical formulation of the proposed CBTI scheme, along with an initial application of the method to the calculation of the hydration free energy of methanol.