Reduced Free Energy Perturbation/Hamiltonian Replica Exchange Molecular Dynamics Method with Unbiased Alchemical Thermodynamic Axis

Broad-spectrum coronavirus inhibitors discovered by modeling viral fusion dynamics

Development of oral, broad-spectrum therapeutics targeting SARS-CoV-2, its variants, and related coronaviruses could curb the spread of COVID-19 and avert future pandemics. We created a novel computational discovery pipeline that employed molecular dynamics simulation (MDS), artificial intelligence (AI)-based docking predictions, and medicinal chemistry to design viral entry inhibitors that target a conserved region in the SARS-CoV-2 spike (S) protein that mediates membrane fusion. DrugBank library screening identified the orally available, FDA-approved AXL kinase inhibitor bemcentinib as binding this site and we demonstrated that it inhibits viral entry in a kinase-independent manner. Novel analogs predicted to bind to the same region and disrupt S protein conformational changes were designed using MDS and medicinal chemistry. These compounds significantly suppressed SARS-CoV-2 infection and blocked the entry of S protein-bearing pseudotyped α,β,γ,δ,ο variants as well as SARS CoV and MERS-CoV in human ACE2-expressing or DPP4-expressing cells more effectively than bemcentinib. When administered orally, the optimized lead compound also significantly inhibited SARS-CoV2 infection in mice. This computational design strategy may accelerate drug discovery for a broad range of applications.

Leveraging Cryptic Ligand Envelopes through Enhanced Molecular Simulations

Protein-bound ligands can adopt a range of different conformations, collectively defining a ligand envelope that has proven to be crucial for the design of potent and selective drugs. Yet, the cryptic nature of this ligand envelope makes it difficult to visualize, characterize, and ultimately exploit for drug design. Using enhanced molecular dynamics simulations, here, we provide a general framework to reconstruct the cryptic ligand envelope that is dynamically accessible by protein-bound small molecules in solution. We apply this approach to quantify hidden conformational heterogeneity in structurally complex ligands including the marine natural product plitidepsin. The computed conformational heterogeneity expands the small-molecule footprint beyond that typically observed in experiments, also revealing key thermodynamic and kinetic properties of single ligand-target interactions. The model agrees quantitatively with solution NMR, X-ray crystallography, and biochemical measurements, showcasing a versatile strategy to integrate receptor-bound ligand conformational ensembles in molecular design.

Multiple Topology Replica Exchange of Expanded Ensembles for Multidimensional Alchemical Calculations

Relative free energy (RFE) calculations are now widely used in academia and the industry, but their accuracy is often limited by poor sampling of the complexes' conformational ensemble. To help address conformational sampling problems when simulating many relative binding free energies, we developed a novel method termed multiple topology replica exchange of expanded ensembles (MT-REXEE). This method enables parallel expanded ensemble calculations, facilitating iterative RFE computations while allowing conformational exchange between parallel transformations. These iterative transformations can be adaptable to any set of systems with a common backbone or central substructure. We demonstrate that the MT-REXEE method maintains thermodynamic cycle closure to the same extent as standard expanded ensemble calculations for both solvation free energy and relative binding free energy calculations. The transformations tested involve systems that incorporate diverse heavy atoms and multisite perturbations of a small molecule core resembling multisite λ dynamics, without necessitating modifications to the MD code. Our initial implementation is in GROMACS. We outline a systematic approach for the topology setup and provide instructions on how to perform inter-replica coordinate modifications. This work shows that MT-REXEE can be used to perform accurate and reproducible free energy estimates and prompts expansion to more complex test systems and other molecular dynamics simulation infrastructures.

A Method for Treating Significant Conformational Changes in Alchemical Free Energy Simulations of Protein-Ligand Binding

Relative binding free energy (RBFE) simulation is a rigorous approach to the calculation of quantitatively accurate binding free energy values for protein-ligand binding in which a reference binder is gradually converted to a target binder through alchemical transformation during the simulation. The success of such simulations relies on being able to accurately sample the correct conformational phase space for each alchemical state; however, this becomes a challenge when a significant conformation change occurs between the reference and target binder-receptor complexes. Increasing the simulation time and using enhanced sampling methods can be helpful, but effects can be limited, especially when the free energy barrier between conformations is high or when the correct target complex conformation is difficult to find and maintain. Current RBFE protocols seed the reference complex structure into every alchemical window of the simulation. In our study, we describe an improved protocol in which the reference structure is seeded into the first half of the alchemical windows, and the target structure is seeded into the second half of the alchemical windows. By applying information about the relevant correct end point conformations to different simulation windows from the beginning, the need for large barrier crossings or simulation prediction of the correct structures during an alchemical simulation is in many cases obviated. In the diverse cases we examine below, the simulations yielded free energy predictions that are satisfactory as compared to experiment and superior to running the simulations utilizing the conventional protocol. The method is straightforward to implement for publicly available FEP workflows.

A Comprehensive Study of Factors Affecting the Prediction of the pKa Shift of Asp26 in Thioredoxin Protein

The stable protonation state of ionizable amino acids in a protein can be predicted by computing the pKa shift of that residue within the protein environment. Thermodynamic Integration (TI) is an ideal molecular dynamics-based approach for predicting the pKa shift of ionizable protein residues. Here, we probe TI-based simulation protocols for their ability to accurately predict the pKa shift of Asp26 in thioredoxin. While implicit solvent models can predict the pKa shift accurately, explicit solvent models result in substantial errors. To understand the underlying reason for this surprising discrepancy, we investigate the role of various factors such as solvent models, conformational sampling, background charges, and polarization.

Ligand Binding Affinity Prediction for Membrane Proteins with Alchemical Free Energy Calculation Methods

Alchemical relative binding free energy (ΔΔG) calculations have shown high accuracy in predicting ligand binding affinity and have been used as important tools in computer-aided drug discovery and design. However, there has been limited research on the application of ΔΔG methods to membrane proteins despite the fact that these proteins represent a significant proportion of drug targets, play crucial roles in biological processes, and are implicated in numerous diseases. In this study, to predict the binding affinity of ligands to G protein-coupled receptors (GPCRs), we employed two ΔΔG calculation methods: thermodynamic integration (TI) with AMBER and the alchemical transfer method (AToM) with OpenMM. We calculated ΔΔG values for 53 transformations involving four class A GPCRs and evaluated the performance of AMBER-TI and AToM-OpenMM. In addition, we conducted tests using different numbers of windows and varying simulation times to achieve reliable ΔΔG results and to optimize resource utilization. Overall, both AMBER-TI and AToM-OpenMM show good agreement with the experimental data. Our results validate the applicability of AMBER-TI and AToM-OpenMM for optimization of lead compounds targeting membrane proteins.

MedChemExpress compounds prevent neuraminidase N1 via physics- and knowledge-based methods

Influenza A viruses spread out worldwide, causing several global concerns. Hence, discovering neuraminidase inhibitors to prevent the influenza A virus is of great interest. In this work, a machine learning model was employed to evaluate the ligand-binding affinity of ca. 10 000 compounds from the MedChemExpress (MCE) database for inhibiting neuraminidase. Atomistic simulations, including molecular docking and molecular dynamics simulations, then confirmed the ligand-binding affinity. Furthermore, we clarified the physical insights into the binding process of ligands to neuraminidase. It was found that five compounds, including micronomicin, didesmethyl cariprazine, argatroban, Kgp-IN-1, and AY 9944, are able to inhibit neuraminidase N1 of the influenza A virus. Ten residues, including Glu119, Asp151, Arg152, Trp179, Gln228, Glu277, Glu278, Arg293, Asn295, and Tyr402, may be very important in controlling the ligand-binding process to N1.

Studying the Collective Functional Response of a Receptor in Alchemical Ligand Binding Free Energy Simulations with Accelerated Solvation Layer Dynamics

Ligand binding free energy simulations (LB-FES) that involve sampling of protein functional conformations have been longstanding challenges in research on molecular recognition. Particularly, modeling of the conformational transition pathway and design of the heuristic biasing mechanism are severe bottlenecks for the existing enhanced configurational sampling (ECS) methods. Inspired by the key role of hydration in regulating conformational dynamics of macromolecules, this report proposes a novel ECS approach that facilitates binding-associated structural dynamics by accelerated hydration transitions in combination with the λ-exchange of free energy perturbation (FEP). Two challenging protein-ligand binding processes involving large configurational transitions of the receptor are studied, with hydration transitions at binding sites accelerated by Hamiltonian-simulated annealing of the hydration layer. Without the need for pathway analysis or ad hoc barrier flattening potential, LB-FES were performed with FEP/λ-exchange molecular dynamics simulation at a minor overhead for annealing of the hydration layer. The LB-FES studies showed that the accelerated rehydration significantly enhances the collective conformational transitions of the receptor, and convergence of binding affinity calculations is obtained at a sweet-spot simulation time scale. Alchemical LB-FES with the proposed ECS strategy is free from the effort of trial and error for the setup and realizes efficient on-the-fly sampling for the collective functional response of the receptor and bound water and therefore presents a practical approach to high-throughput screening in drug discovery.

Enhancing torsional sampling using fully adaptive simulated tempering

Enhanced sampling algorithms are indispensable when working with highly disconnected multimodal distributions. An important application of these is the conformational exploration of particular internal degrees of freedom of molecular systems. However, despite the existence of many commonly used enhanced sampling algorithms to explore these internal motions, they often rely on system-dependent parameters, which negatively impact efficiency and reproducibility. Here, we present fully adaptive simulated tempering (FAST), a variation of the irreversible simulated tempering algorithm, which continuously optimizes the number, parameters, and weights of intermediate distributions to achieve maximally fast traversal over a space defined by the change in a predefined thermodynamic control variable such as temperature or an alchemical smoothing parameter. This work builds on a number of previously published methods, such as sequential Monte Carlo, and introduces a novel parameter optimization procedure that can, in principle, be used in any expanded ensemble algorithms. This method is validated by being applied on a number of different molecular systems with high torsional kinetic barriers. We also consider two different soft-core potentials during the interpolation procedure and compare their performance. We conclude that FAST is a highly efficient algorithm, which improves simulation reproducibility and can be successfully used in a variety of settings with the same initial hyperparameters.

Standard Binding Free-Energy Calculations: How Far Are We from Automation?

Recent success stories suggest that in silico protein-ligand binding free-energy calculations are approaching chemical accuracy. However, their widespread application remains limited by the extensive human intervention required, posing challenges for the neophyte. As such, it is critical to develop automated workflows for estimating protein-ligand binding affinities with minimum personal involvement. Key human efforts include setting up and tuning enhanced-sampling or alchemical-transformation algorithms as a preamble to computational binding free-energy estimations. Additionally, preparing input files, bookkeeping, and postprocessing represent nontrivial tasks. In this Perspective, we discuss recent progress in automating standard binding free-energy calculations, featuring the development of adaptive or parameter-free algorithms, standardization of binding free-energy calculation workflows, and the implementation of user-friendly software. We also assess the current state of automated standard binding free-energy calculations and evaluate the limitations of existing methods. Last, we outline the requirements for future algorithms and workflows to facilitate automated free-energy calculations for diverse protein-ligand complexes.

Enhanced Configurational Sampling Approaches to Alchemical Ligand Binding Free Energy Simulations: Current Status and Challenges

Ligand binding free energy simulations (LB-FES) have been routine tasks in modern drug discovery campaign. A long-standing challenge for LB-FES is the difficulty in adequately sampling nontrivial environmental reorganizations in response to ligand binding. Therefore, various enhanced configurational sampling (ECS) approaches were devised to speed up fluctuations of relevant slow degrees of freedom (SDOF) and ensure simulation convergence. However, in contrast to the achievements in parametrization, software performance, and workflow automation, efficient ECS methodology suitable for high throughput screening remains in an early stage of development. Here, a review of ECS developments with LB-FES is presented, revisiting current approaches and underlining the major technical pitfalls and challenges. This Perspective focuses on alchemical LB-FES on account of their predominant role in high throughput drug screening as well as the established partnership with ECS. The critical aspects of designing ECS approaches, from both theoretical and applied perspectives, are described. This work is intended to provide a contemporary review of the scientific, technical, and practical issues associated with the accelerating convergence of alchemical LB-FES.

Counteraction of stability-activity trade-off of Nattokinase through flexible region shifting

The widespread trade-off between stability and activity severely limits enzyme evolution. Although some progresses have been made to overcome this limitation, the counteraction mechanism for enzyme stability-activity trade-off remains obscure. Here, we clarified the counteraction mechanism of the Nattokinase stability-activity trade-off. A combinatorial mutant M4 was obtained by multi-strategy engineering, exhibiting a 20.7-fold improved half-life; meanwhile, the catalytic efficiency was doubled. Molecular dynamics simulation revealed that an obvious flexible region shifting in the structure of mutant M4 was occurred. The flexible region shifting which contributed to maintain the global structural flexibility, was considered to be the key factor for counteracting the stability-activity trade-off. Further analysis illustrated that the flexible region shifting was driven by region dynamical networks reshaping. This work provided deep insight into the counteraction mechanism of enzyme stability-activity trade-off, suggesting that flexible region shifting would be an effective strategy for enzyme evolution through computational protein engineering.

ACES: Optimized Alchemically Enhanced Sampling

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

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

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

Searching for potential inhibitors of SARS-COV-2 main protease using supervised learning and perturbation calculations

Inhibiting the biological activity of SARS-CoV-2 Mpro can prevent viral replication. In this context, a hybrid approach using knowledge- and physics-based methods was proposed to characterize potential inhibitors for SARS-CoV-2 Mpro. Initially, supervised machine learning (ML) models were trained to predict a ligand-binding affinity of ca. 2 million compounds with the correlation on a test set of R = 0.748 ± 0.044 . Atomistic simulations were then used to refine the outcome of the ML model. Using LIE/FEP calculations, nine compounds from the top 100 ML inhibitors were suggested to bind well to the protease with the domination of van der Waals interactions. Furthermore, the binding affinity of these compounds is also higher than that of nirmatrelvir, which was recently approved by the US FDA to treat COVID-19. In addition, the ligands altered the catalytic triad Cys145 - His41 - Asp187, possibly disturbing the biological activity of SARS-CoV-2.

Elucidating the enhanced binding affinity of a double mutant SP-D with trimannose on the influenza A virus using molecular dynamics

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The Asp325Ala mutation in SP-D promotes a trimannose conformational change to a more stable state.

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The Arg343Val mutation in SP-D reduces its interaction with Glu333 to increase the binding affinity with trimannose.

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The Arg343Val mutation contributes more to the increase of SP-D’s binding affinity with trimannose than Asp325Ala.

Surfactant protein D (SP-D) is an essential component of the human pulmonary surfactant system, which is crucial in the innate immune response against glycan-containing pathogens, including Influenza A viruses (IAV) and SARS-CoV-2. Previous studies have shown that wild-type (WT) SP-D can bind IAV but exhibits poor antiviral activities. However, a double mutant (DM) SP-D consisting of two point mutations (Asp325Ala and Arg343Val) inhibits IAV more potently. Presently, the structural mechanisms behind the point mutations’ effects on SP-D’s binding affinity with viral surface glycans are not fully understood. Here we use microsecond-scale, full-atomistic molecular dynamics (MD) simulations to understand the molecular mechanism of mutation-induced SP-D’s higher antiviral activity. We find that the Asp325Ala mutation promotes a trimannose conformational change to a more stable state. Arg343Val increases the binding with trimannose by increasing the hydrogen bonding interaction with Glu333. Free energy perturbation (FEP) binding free energy calculations indicate that the Arg343Val mutation contributes more to the increase of SP-D’s binding affinity with trimannose than Asp325Ala. This study provides a molecular-level exploration of how the two mutations increase SP-D binding affinity with trimannose, which is vital for further developing preventative strategies for related diseases.

Construction and Application of a High-Throughput In Vivo Screening Platform for the Evolution of Nitrile Metabolism-Related Enzymes Based on a Desensitized Repressive Biosensor

Transcription factor (TF)-based biosensors are expected to serve as powerful tools for the high-throughput screening of biocatalytic systems; however, most of them respond to ligands in a narrow concentration range, which limits their application. In this study, we constructed a heterogenous niacin biosensor using the repressive TF BsNadR and its target promoters from Bacillus subtilis. The fine-tunable output of the niacin biosensor was expanded to a wide range of niacin concentrations (0-50 mM) through desensitization engineering, which was suitable for the accurate identification of differences in enzyme activity. Structural mechanism analysis indicated that weakening the affinity of BsNadR with the ligand niacin and with DNA alters its regulatory properties. Based on the desensitized niacin biosensor, a high-throughput in vivo screening platform was developed for evolving nitrile metabolism-related enzymes. The evolved nitrilase, amidase, and nitrile hydratase with 6.6-, 2.1-, and 21.3-fold improvements in activity were achieved, respectively. In addition, these mutants also exhibited elevated activity toward other cognate substrates, indicating the broad applicability of the screening platform. This study not only provided a universal high-throughput screening platform for different nitrile metabolism-related enzymes but also demonstrated the advantages of repressive biosensors and the vital role of desensitization engineering of the TF in the development of high-throughput screening platforms for enzymes.

Binding Analysis Using Accelerated Molecular Dynamics Simulations and Future Perspectives

Biomolecular recognition such as binding of small molecules, nucleic acids, peptides and proteins to their target receptors plays key roles in cellular function and has been targeted for therapeutic drug design. Molecular dynamics (MD) is a computational approach to analyze these binding processes at an atomistic level, which provides valuable understandings of the mechanisms of biomolecular recognition. However, the rather slow biomolecular binding events often present challenges for conventional MD (cMD), due to limited simulation timescales (typically over hundreds of nanoseconds to tens of microseconds). In this regard, enhanced sampling methods, particularly accelerated MD (aMD), have proven useful to bridge the gap and enable all-atom simulations of biomolecular binding events. Here, we will review the recent method developments of Gaussian aMD (GaMD), ligand GaMD (LiGaMD) and peptide GaMD (Pep-GaMD), which have greatly expanded our capabilities to simulate biomolecular binding processes. Spontaneous binding of various biomolecules to their receptors has been successfully simulated by GaMD. Microsecond LiGaMD and Pep-GaMD simulations have captured repetitive binding and dissociation of small-molecule ligands and highly flexible peptides, and thus enabled ligand/peptide binding thermodynamics and kinetics calculations. We will also present relevant application studies in simulations of important drug targets and future perspectives for rational computer-aided drug design.

Improving ligand-ranking of AutoDock Vina by changing the empirical parameters

AutoDock Vina (Vina) achieved a very high docking-success rate, p ^ , but give a rather low correlation coefficient, R , for binding affinity with respect to experiments. This low correlation can be an obstacle for ranking of ligand-binding affinity, which is the main objective of docking simulations. In this context, we evaluated the dependence of Vina R coefficient upon its empirical parameters. R is affected more by changing the gauss2 and rotation than other terms. The docking-success rate p ^ is sensitive to the alterations of the gauss1, gauss2, repulsion, and hydrogen bond parameters. Based on our benchmarks, the parameter set1 has been suggested to be the most optimal. The testing study over 800 complexes indicated that the modified Vina provided higher correlation with experiment R set 1 = 0.556 ± 0.025 compared with R Default = 0.493 ± 0.028 obtained by the original Vina and R Vina 1.2 = 0.503 ± 0.029 by Vina version 1.2. Besides, the modified Vina can be also applied more widely, giving R ≥ 0.500 for 32/48 targets, compared with the default package, giving R ≥ 0.500 for 31/48 targets. In addition, validation calculations for 1036 complexes obtained from version 2019 of PDBbind refined structures showed that the set1 of parameters gave higher correlation coefficient ( R set 1 = 0.617 ± 0.017 ) than the default package ( R Default = 0.543 ± 0.020 ) and Vina version 1.2 ( R Vina 1.2 = 0.540 ± 0.020 ). The version of Vina with set1 of parameters can be downloaded at https://github.com/sontungngo/mvina. The outcomes would enhance the ranking of ligand-binding affinity using Autodock Vina.

Recent developments in multiscale free energy simulations

Physics-based free energy simulations enable the rigorous calculation of properties, such as conformational equilibria, solvation or binding free energies. While historically most applications have occurred at the atomistic level of resolution, a range of advances in the past years make it possible now to reliably cross the temporal, spatial and theory scales for the modeling of complex systems or the efficient prediction of results at the accuracy level of expensive quantum-mechanical calculations. In this mini-review, we discuss recent methodological advances as well as opportunities opened up by the introduction of machine learning approaches, which tackle the diverse challenges across the different scales, improve the accuracy and feasibility, and push the boundaries of multiscale free energy simulations.

Gaussian accelerated molecular dynamics (GaMD): principles and applications

Gaussian accelerated molecular dynamics (GaMD) is a robust computational method for simultaneous unconstrained enhanced sampling and free energy calculations of biomolecules. It works by adding a harmonic boost potential to smooth biomolecular potential energy surface and reduce energy barriers. GaMD greatly accelerates biomolecular simulations by orders of magnitude. Without the need to set predefined reaction coordinates or collective variables, GaMD provides unconstrained enhanced sampling and is advantageous for simulating complex biological processes. The GaMD boost potential exhibits a Gaussian distribution, thereby allowing for energetic reweighting via cumulant expansion to the second order (i.e., "Gaussian approximation"). This leads to accurate reconstruction of free energy landscapes of biomolecules. Hybrid schemes with other enhanced sampling methods, such as the replica exchange GaMD (rex-GaMD) and replica exchange umbrella sampling GaMD (GaREUS), have also been introduced, further improving sampling and free energy calculations. Recently, new "selective GaMD" algorithms including the ligand GaMD (LiGaMD) and peptide GaMD (Pep-GaMD) enabled microsecond simulations to capture repetitive dissociation and binding of small-molecule ligands and highly flexible peptides. The simulations then allowed highly efficient quantitative characterization of the ligand/peptide binding thermodynamics and kinetics. Taken together, GaMD and its innovative variants are applicable to simulate a wide variety of biomolecular dynamics, including protein folding, conformational changes and allostery, ligand binding, peptide binding, protein-protein/nucleic acid/carbohydrate interactions, and carbohydrate/nucleic acid interactions. In this review, we present principles of the GaMD algorithms and recent applications in biomolecular simulations and drug design.

Recent Developments in Free Energy Calculations for Drug Discovery

The grand challenge in structure-based drug design is achieving accurate prediction of binding free energies. Molecular dynamics (MD) simulations enable modeling of conformational changes critical to the binding process, leading to calculation of thermodynamic quantities involved in estimation of binding affinities. With recent advancements in computing capability and predictive accuracy, MD based virtual screening has progressed from the domain of theoretical attempts to real application in drug development. Approaches including the Molecular Mechanics Poisson Boltzmann Surface Area (MM-PBSA), Linear Interaction Energy (LIE), and alchemical methods have been broadly applied to model molecular recognition for drug discovery and lead optimization. Here we review the varied methodology of these approaches, developments enhancing simulation efficiency and reliability, remaining challenges hindering predictive performance, and applications to problems in the fields of medicine and biochemistry.

Challenges Encountered Applying Equilibrium and Nonequilibrium Binding Free Energy Calculations

Binding free energy calculations have become increasingly valuable to drive decision making in drug discovery projects. However, among other issues, inadequate sampling can reduce accuracy, limiting the value of the technique. In this paper, we apply absolute binding free energy calculations to ligands binding to T4 lysozyme L99A and HSP90 using equilibrium and nonequilibrium approaches. We highlight sampling problems encountered in these systems, such as slow side chain rearrangements and slow changes of water placement upon ligand binding. These same types of challenges are also likely to show up in other protein-ligand systems, and we propose some strategies to diagnose and test for such problems in alchemical free energy calculations. We also explore similarities and differences in how the equilibrium and the nonequilibrium approaches handle these problems. Our results show the large amount of work still to be done to make free energy calculations robust and reliable and provide insight for future research in this area.

Computational Determination of Potential Inhibitors of SARS-CoV-2 Main Protease

The novel coronavirus (SARS-CoV-2) has infected several million people and caused thousands of deaths worldwide since December 2019. As the disease is spreading rapidly all over the world, it is urgent to find effective drugs to treat the virus. The main protease (Mpro) of SARS-CoV-2 is one of the potential drug targets. Therefore, in this context, we used rigorous computational methods, including molecular docking, fast pulling of ligand (FPL), and free energy perturbation (FEP), to investigate potential inhibitors of SARS-CoV-2 Mpro. We first tested our approach with three reported inhibitors of SARS-CoV-2 Mpro, and our computational results are in good agreement with the respective experimental data. Subsequently, we applied our approach on a database of ∼4600 natural compounds, as well as 8 available HIV-1 protease (PR) inhibitors and an aza-peptide epoxide. Molecular docking resulted in a short list of 35 natural compounds, which was subsequently refined using the FPL scheme. FPL simulations resulted in five potential inhibitors, including three natural compounds and two available HIV-1 PR inhibitors. Finally, FEP, the most accurate and precise method, was used to determine the absolute binding free energy of these five compounds. FEP results indicate that two natural compounds, cannabisin A and isoacteoside, and an HIV-1 PR inhibitor, darunavir, exhibit a large binding free energy to SARS-CoV-2 Mpro, which is larger than that of 13b, the most reliable SARS-CoV-2 Mpro inhibitor recently reported. The binding free energy largely arises from van der Waals interaction. We also found that Glu166 forms H-bonds to all of the inhibitors. Replacing Glu166 by an alanine residue leads to ∼2.0 kcal/mol decreases in the affinity of darunavir to SARS-CoV-2 Mpro. Our results could contribute to the development of potential drugs inhibiting SARS-CoV-2.

CHARMM-GUI Free Energy Calculator for Absolute and Relative Ligand Solvation and Binding Free Energy Simulations

Alchemical free energy simulations have long been utilized to predict free energy changes for binding affinity and solubility of small molecules. However, while the theoretical foundation of these methods is well established, seamlessly handling many of the practical aspects regarding the preparation of the different thermodynamic end states of complex molecular systems and the numerous processing scripts often remains a burden for successful applications. In this work, we present CHARMM-GUI Free Energy Calculator (http://www.charmm-gui.org/input/fec) that provides various alchemical free energy perturbation molecular dynamics (FEP/MD) systems with input and post-processing scripts for NAMD and GENESIS. Four submodules are available: Absolute Ligand Binder (for absolute ligand binding FEP/MD), Relative Ligand Binder (for relative ligand binding FEP/MD), Absolute Ligand Solvator (for absolute ligand solvation FEP/MD), and Relative Ligand Solvator (for relative ligand solvation FEP/MD). Each module is designed to build multiple systems of a set of selected ligands at once for high-throughput FEP/MD simulations. The capability of Free Energy Calculator is illustrated by absolute and relative solvation FEP/MD of a set of ligands and absolute and relative binding FEP/MD of a set of ligands for T4-lysozyme in solution and the adenosine A_2A receptor in a membrane. The calculated free energy values are overall consistent with the experimental and published free energy results (within ∼1 kcal/mol). We hope that Free Energy Calculator is useful to carry out high-throughput FEP/MD simulations in the field of biomolecular sciences and drug discovery.

Large-Scale Assessment of Binding Free Energy Calculations in Active Drug Discovery Projects

Accurate ranking of compounds with regards to their binding affinity to a protein using computational methods is of great interest to pharmaceutical research. Physics-based free energy calculations are regarded as the most rigorous way to estimate binding affinity. In recent years, many retrospective studies carried out both in academia and industry have demonstrated its potential. Here, we present the results of large-scale prospective application of the FEP+ method in active drug discovery projects in an industry setting at Merck KGaA, Darmstadt, Germany. We compare these prospective data to results obtained on a new diverse, public benchmark of eight pharmaceutically relevant targets. Our results offer insights into the challenges faced when using free energy calculations in real-life drug discovery projects and identify limitations that could be tackled by future method development. The new public data set we provide to the community can support further method development and comparative benchmarking of free energy calculations.

Insights on small molecule binding to the Hv1 proton channel from free energy calculations with molecular dynamics simulations

Hv1 is a voltage-gated proton channel whose main function is to facilitate extrusion of protons from the cell. The development of effective channel blockers for Hv1 can lead to new therapeutics for the treatment of maladies related to Hv1 dysfunction. Although the mechanism of proton permeation in Hv1 remains to be elucidated, a series of small molecules have been discovered to inhibit Hv1. Here, we computed relative binding free energies of a prototypical Hv1 blocker on a model of human Hv1 in an open state. We used alchemical free energy perturbation techniques based on atomistic molecular dynamics simulations. The results support our proposed open state model and shed light on the preferred tautomeric state of the channel blocker. This work lays the groundwork for future studies on adapting the blocker molecule for more effective inhibition of Hv1.

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.

Molecular Dynamics Simulations with NAMD2

X-ray diffraction crystallography is the primary technique to determine the three-dimensional structures of biomolecules. Although a robust method, X-ray crystallography is not able to access the dynamical behavior of macromolecules. To do so, we have to carry out molecular dynamics simulations taking as an initial system the three-dimensional structure obtained from experimental techniques or generated using homology modeling. In this chapter, we describe in detail a tutorial to carry out molecular dynamics simulations using the program NAMD2. We chose as a molecular system to simulate the structure of human cyclin-dependent kinase 2.

On Restraints in End-Point Protein-Ligand Binding Free Energy Calculations

The impact of harmonic restraints on protein heavy atoms and ligand atoms on end-point free energy calculations is systematically characterized for 54 protein-ligand complexes. We observe that stronger restraints reduce the equilibration time and statistical inefficiency, suppress conformational sampling, influence correlation with experiment, and monotonically decrease the estimated loss of entropy upon binding, leading to stronger estimated binding free energies in most systems. A statistical estimator that reweights for the biasing potential and includes data prior to the estimated equilibration time has the highest correlation with experiment. A spring constant of 20 cal mol-1 Å-2 maintains a near-native energy landscape and suppresses artifactual energy minima while minimally limiting thermal fluctuations about the crystal structure. © 2019 Wiley Periodicals, Inc.

Conformational flexibility correlates with glucose tolerance for point mutations in β-glucosidases - a computational study

β-glucosidases (EC 3.2.1.21) have been described as essential to second-generation biofuel production. They act in the last step of the lignocellulosic saccharification, cleaving the β - 1,4 glycosidic bonds in cellobiose to produce two molecules of glucose. However, β-glucosidases have been described as strongly inhibited by glucose, causing an increment of cellobiose concentration. Also, cellobiose is an inhibitor of other enzymes used in this process, such as exoglucanases and endoglucanases. Hence, the engineering of thermostable and glucose-tolerant β-glucosidases has been targeted by many studies. In this study, we performed high sampling accelerated molecular dynamics for a wild glucose-tolerant GH1 β-glucosidase (Bgl1A), a wild non-tolerant (Bgl1B), and a set of glucose-tolerant Bgl1B's mutants: V302F, N301Q/V302F, F172I, V227M, G246S, T299S, and H228T. Our results suggest that point mutations promissory to induce glucose tolerance trend to enhance the mobility of the flexible loops around the active site. Mutations affected B and C loops regions, and an αβ-hairpin motif between them. Conformational clusters and free energy landscape profiles suggest that the mobility acquired by mutants allows a higher closure of the substrate channel. This closure is compatible with a higher impedance for glucose entrance and stimulus of its withdrawal. Based on mutants' structural analyses, we inferred that both the direct stereochemical effect on the glucose path and the changes in the mobility affect glucose tolerance. We hope these results be useful for the rational design of glucose-tolerant and industrially promising enzymes.Communicated by Ramaswamy H. Sarma.

Advances in the calculation of binding free energies

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

Enhanced sampling and free energy calculations for protein simulations

Molecular dynamics simulation is a powerful computational technique to study biomolecular systems, which complements experiments by providing insights into the structural dynamics relevant to biological functions at atomic scale. It can also be used to calculate the free energy landscapes of the conformational transitions to better understand the functions of the biomolecules. However, the sampling of biomolecular configurations is limited by the free energy barriers that need to be overcome, leading to considerable gaps between the timescales reached by MD simulation and those governing biological processes. To address this issue, many enhanced sampling methodologies have been developed to increase the sampling efficiency of molecular dynamics simulations and free energy calculations. Usually, enhanced sampling algorithms can be classified into methods based on collective variables (CV-based) and approaches which do not require predefined CVs (CV-free). In this chapter, the theoretical basis of free energy estimation is briefly reviewed first, followed by the reviews of the most common CV-based and CV-free methods including the presentation of some examples and recent developments. Finally, the combination of different enhanced sampling methods is discussed.

Effective estimation of the inhibitor affinity of HIV-1 protease via a modified LIE approach

The inhibition of the Human Immunodeficiency Virus Type 1 Protease (HIV-1 PR) can prevent the synthesis of new viruses. Computer-aided drug design (CADD) would enhance the discovery of new therapies, through which the estimation of ligand-binding affinity is critical to predict the most efficient inhibitor. A time-consuming binding free energy method would reduce the usefulness of CADD. The modified linear interaction energy (LIE) approach emerges as an appropriate protocol that performs this task. In particular, the polar interaction free energy, which is obtained via numerically resolving the linear Poisson-Boltzmann equation, plays as an important role in driving the binding mechanism of the HIV-1 PR + inhibitor complex. The electrostatic interaction energy contributes to the attraction between two molecules, but the vdW interaction acts as a repulsive factor between the ligand and the HIV-1 PR. Moreover, the ligands were found to adopt a very strong hydrophobic interaction with the HIV-1 PR. Furthermore, the results obtained corroborate the high accuracy and precision of computational studies with a large correlation coefficient value R = 0.83 and a small RMSE δ RMSE = 1.25 kcal mol-1. This method is less time-consuming than the other end-point methods, such as the molecular mechanics Poisson-Boltzmann surface area (MM/PBSA) and free energy perturbation (FEP) approaches. Overall, the modified LIE approach would provide ligand-binding affinity with HIV-1 PR accurately, precisely, and rapidly, resulting in a more efficient design of new inhibitors.

Allosteric Motions of the CRISPR-Cas9 HNH Nuclease Probed by NMR and Molecular Dynamics

CRISPR-Cas9 is a widely employed genome-editing tool with functionality reliant on the ability of the Cas9 endonuclease to introduce site-specific breaks in double-stranded DNA. In this system, an intriguing allosteric communication has been suggested to control its DNA cleavage activity through flexibility of the catalytic HNH domain. Here, solution NMR experiments and a novel Gaussian-accelerated molecular dynamics (GaMD) simulation method are used to capture the structural and dynamic determinants of allosteric signaling within the HNH domain. We reveal the existence of a millisecond time scale dynamic pathway that spans HNH from the region interfacing the adjacent RuvC nuclease and propagates up to the DNA recognition lobe in full-length CRISPR-Cas9. These findings reveal a potential route of signal transduction within the CRISPR-Cas9 HNH nuclease, advancing our understanding of the allosteric pathway of activation. Further, considering the role of allosteric signaling in the specificity of CRISPR-Cas9, this work poses the mechanistic basis for novel engineering efforts aimed at improving its genome-editing capability.

Computing Relative Binding Affinity of Ligands to Receptor: An Effective Hybrid Single-Dual-Topology Free-Energy Perturbation Approach in NAMD

An effective hybrid single-dual-topology protocol is designed for the calculation of relative binding affinities of small ligands to a receptor. The protocol was developed as an extension of the NAMD molecular dynamics program, which exclusively supports a dual-topology framework for relative alchemical free-energy perturbation (FEP) calculations. In this protocol, the alchemical end states are represented as two separate molecules sharing a common substructure identified through maximum structural mapping. Within the substructure, an atom-to-atom correspondence is established, and each pair of corresponding atoms is holonomically constrained to share identical coordinates at all time throughout the simulation. The forces are projected and combined at each step for propagation. Following this formulation, a set of illustrative calculations of reliable experiment/simulation data, including relative solvation free energies of small molecules and relative binding affinities of drug compounds to proteins, are presented. To enhance sampling of the dual-topology region, the FEP calculations were carried out within a replica-exchange MD scheme supported by the multiple-copy algorithm module of NAMD, with periodically attempted swapping of the thermodynamic coupling parameter λ between neighboring states. The results are consistent with experiments and benchmarks reported in the literature, lending support to the validity of the current protocol. In summary, this hybrid single-dual-topology approach combines the conceptual simplicity of the dual-topology paradigm with the advantageous sampling efficiency of the single-topology approach, making it an ideal strategy for high-throughput in silico drug design.