λ‐dynamics: A new approach to free energy calculations

Constant pH Simulation with FMM Electrostatics in GROMACS. (A) Design and Applications

The structural dynamics of biological macromolecules, such as proteins, DNA/RNA, or complexes thereof, are strongly influenced by protonation changes of their typically many titratable groups, which explains their sensitivity to pH changes. Conversely, conformational and environmental changes of the biomolecule affect the protonation state of these groups. With few exceptions, conventional force field-based molecular dynamics (MD) simulations neither account for these effects nor do they allow for coupling to a pH buffer. Here, we present design decisions and applications of a rigorous Hamiltonian interpolation λ-dynamics constant pH method in GROMACS, which rests on GPU-accelerated Fast Multipole Method (FMM) electrostatics. Our implementation supports both CHARMM36m and Amber99sb*-ILDN force fields and is largely automated to enable seamless switching from regular MD to constant pH MD, involving minimal changes to the input files. Here, the first of two companion papers describes the underlying constant pH protocol and sample applications to several prototypical benchmark systems such as cardiotoxin V, lysozyme, and staphylococcal nuclease. Enhanced convergence is achieved through a new dynamic barrier height optimization method, and high pKa accuracy is demonstrated. We use Functional Mode Analysis (FMA) and Mutual Information (MI) to explore the complex intra- and intermolecular couplings between the protonation states of titratable groups as well as those between protonation states and conformational dynamics. We identify striking conformation-dependent pKa variations and unexpected inter-residue couplings. Conformation-protonation coupling is identified as a primary cause of the slow protonation convergence notorious to constant pH simulations involving multiple titratable groups, suggesting enhanced sampling methods to accelerate convergence.

Constant pH Simulation with FMM Electrostatics in GROMACS. (B) GPU Accelerated Hamiltonian Interpolation

The structural dynamics of biological macromolecules, such as proteins, DNA/RNA, or their complexes, are strongly influenced by protonation changes of their typically many titratable groups, which explains their pH sensitivity. Conversely, conformational and environmental changes in the biomolecule affect the protonation state of these groups. With a few exceptions, conventional force field-based molecular dynamics (MD) simulations do not account for these effects, nor do they allow for coupling to a pH buffer. The λ-dynamics method implements this coupling and thus allows for MD simulations at constant pH. It uses separate Hamiltonians for the protonated and deprotonated states of each titratable group, with a dynamic λ variable that continuously interpolates between them. However, rigorous implementations of Hamiltonian Interpolation (HI) λ-dynamics are prohibitively slow for typical numbers of sites when used with particle mesh Ewald (PME). To circumvent this problem, it has recently been proposed to interpolate the charges (QI) instead of the Hamiltonians. Here, in the second of two companion papers, we propose a rigorous yet efficient Multipole-Accelerated Hamiltonian Interpolation (MAHI) method to perform λ-dynamics in GROMACS. Starting from a charge-scaled Hamiltonian, precomputed with the Fast Multipole Method (FMM), the correct HI forces are calculated with negligible computational overhead. However, other electrostatic solvers, such as PME, can also be used for the precomputation. We compare Hamiltonian interpolation with charge interpolation and show that HI leads to more frequent transitions between protonation states, resulting in better sampling and accuracy. Our accuracy and performance benchmarks show that introducing, e.g., 512 titratable sites to a one million atom MD system increases runtime by less than 20% compared to a regular FMM-based simulation. We have integrated the scheme into our GPU-accelerated FMM code for the simulation software GROMACS, allowing easy and effortless transitions from standard force field simulations to constant pH simulations.

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.

Superimposing Ligands with a Ligand Overlay as an Alternate Topology Model for λ-Dynamics-Based Calculations

Alchemical free energy (AFE) calculations can predict binding affinity changes as a function of structural modifications and have become powerful tools for lead optimization and drug discovery. Central to the setup and performance of AFE calculations is the manner of mapping alchemical transformations, known as the topology model. Single, dual, and hybrid topology models have been used with various AFE methods in the field. In recent works, λ-dynamics (λD) free energy calculations, specifically, have preferred the use of a hybrid multiple topology (HMT) for sampling multiple ligand perturbations. In this work, we evaluate a new topology method called ligand overlay (LO) for use with λD-based calculations, including the recently introduced λ-dynamics with a bias-updated Gibbs sampling (LaDyBUGS) approach. LO is a full multiple topology model that allows entire ligands to be sampled and restrained within a λ-dynamics framework. Relative binding free energies were computed with HMT or LO topology models with LaDyBUGS for 45 ligands across five protein benchmark systems. An overall Pearson R correlation of 0.98 and mean unsigned error of 0.32 kcal/mol were observed, suggesting that LO is a viable alternative topology model for λD-based calculations. We discuss the merits of using an HMT or LO model for future ligand studies with λD or LaDyBUGS calculations.

Expanded Functionality and Portability for the Colvars Library

Colvars is an open-source C++ library that provides a modular toolkit for collective-variable-based molecular simulations. It allows practitioners to easily create and implement descriptors that best fit a process of interest and to apply a wide range of biasing algorithms in collective variable space. This paper reviews several features and improvements to Colvars that were added since its original introduction. Special attention is given to contributions that significantly expanded the capabilities of this software or its distribution with major MD simulation packages. Collective variables can now be optimized either manually or by machine-learning methods, and the space of descriptors can be explored interactively using the graphical interface included in VMD. Beyond the spatial coordinates of individual molecules, Colvars can now apply biasing forces to mesoscale structures and alchemical degrees of freedom and perform simulations guided by experimental data within ensemble averages or probability distributions. It also features advanced computational schemes to boost the accuracy, robustness, and general applicability of simulation methods, including extended-system and multiple-walker adaptive biasing force, boundary conditions for metadynamics, replica exchange with biasing potentials, and adiabatic bias molecular dynamics. The library is made available directly within the main distributions of the academic software GROMACS, LAMMPS, NAMD, Tinker-HP, and VMD. The robustness of the software and the reliability of the results are ensured through the use of continuous integration with a test suite within the source repository.

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.

Alchemical Transformations and Beyond: Recent Advances and Real-World Applications of Free Energy Calculations in Drug Discovery

Computational methods constitute efficient strategies for screening and optimizing potential drug molecules. A critical factor in this process is the binding affinity between candidate molecules and targets, quantified as binding free energy. Among various estimation methods, alchemical transformation methods stand out for their theoretical rigor. Despite challenges in force field accuracy and sampling efficiency, advancements in algorithms, software, and hardware have increased the application of free energy perturbation (FEP) calculations in the pharmaceutical industry. Here, we review the practical applications of FEP in drug discovery projects since 2018, covering both ligand-centric and residue-centric transformations. We show that relative binding free energy calculations have steadily achieved chemical accuracy in real-world applications. In addition, we discuss alternative physics-based simulation methods and the incorporation of deep learning into free energy calculations.

Automated Adaptive Absolute Binding Free Energy Calculations

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

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.

Resolving coupled pH titrations using alchemical free energy calculations

In a protein, nearby titratable sites can be coupled: the (de)protonation of one may affect the other. The degree of this interaction depends on several factors and can influence the measured p K a . Here, we derive a formalism based on double free energy differences ( Δ Δ G ) for quantifying the individual site p K a values of coupled residues. As Δ Δ G values can be obtained by means of alchemical free energy calculations, the presented approach allows for a convenient estimation of coupled residue p K a s in practice. We demonstrate that our approach and a previously proposed microscopic p K a formalism, can be combined with alchemical free energy calculations to resolve pH-dependent protein p K a values. Toy models and both, regular and constant-pH molecular dynamics simulations, alongside experimental data, are used to validate this approach. Our results highlight the insights gleaned when coupling and microstate probabilities are analyzed and suggest extensions to more complex enzymatic contexts. Furthermore, we find that naïvely computed p K a values that ignore coupling, can be significantly improved when coupling is accounted for, in some cases reducing the error by half. In short, alchemical free energy methods can resolve the p K a values of both uncoupled and coupled residues.

Lambda-ABF: Simplified, Portable, Accurate, and Cost-Effective Alchemical Free-Energy Computation

We introduce the lambda-Adaptive Biasing Force (lambda-ABF) method for the computation of alchemical free-energy differences. We propose a software implementation and showcase it on biomolecular systems. The method arises from coupling multiple-walker adaptive biasing force with λ-dynamics. The sampling of the alchemical variable is continuous and converges toward a uniform distribution, making manual optimization of the λ schedule unnecessary. Contrary to most other approaches, alchemical free-energy estimates are obtained immediately without any postprocessing. Free diffusion of λ improves orthogonal relaxation compared to fixed-λ thermodynamic integration or free-energy perturbation. Furthermore, multiple walkers provide generic orthogonal space coverage with minimal user input and negligible computational overhead. We show that our high-performance implementations coupling the Colvars library with NAMD and Tinker-HP can address real-world cases including ligand-receptor binding with both fixed-charge and polarizable models, with a demonstrably richer sampling than fixed-λ methods. The implementation is fully open-source, publicly available, and readily usable by practitioners of current alchemical methods. Thanks to the portable Colvars library, lambda-ABF presents a unified user interface regardless of the back-end (NAMD, Tinker-HP, or any software to be interfaced in the future), sparing users the effort of learning multiple interfaces. Finally, the Colvars Dashboard extension of the visual molecular dynamics (VMD) software provides an interactive monitoring and diagnostic tool for lambda-ABF simulations.

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.

Surface-Accelerated String Method for Locating Minimum Free Energy Paths

We present a surface-accelerated string method (SASM) to efficiently optimize low-dimensional reaction pathways from the sampling performed with expensive quantum mechanical/molecular mechanical (QM/MM) Hamiltonians. The SASM accelerates the convergence of the path using the aggregate sampling obtained from the current and previous string iterations, whereas approaches like the string method in collective variables (SMCV) or the modified string method in collective variables (MSMCV) update the path only from the sampling obtained from the current iteration. Furthermore, the SASM decouples the number of images used to perform sampling from the number of synthetic images used to represent the path. The path is optimized on the current best estimate of the free energy surface obtained from all available sampling, and the proposed set of new simulations is not restricted to being located along the optimized path. Instead, the umbrella potential placement is chosen to extend the range of the free energy surface and improve the quality of the free energy estimates near the path. In this manner, the SASM is shown to improve the exploration for a minimum free energy pathway in regions where the free energy surface is relatively flat. Furthermore, it improves the quality of the free energy profile when the string is discretized with too few images. We compare the SASM, SMCV, and MSMCV using 3 QM/MM applications: a ribozyme methyltransferase reaction using 2 reaction coordinates, the 2'-O-transphosphorylation reaction of Hammerhead ribozyme using 3 reaction coordinates, and a tautomeric reaction in B-DNA using 5 reaction coordinates. We show that SASM converges the paths using roughly 3 times less sampling than the SMCV and MSMCV methods. All three algorithms have been implemented in the FE-ToolKit package made freely available.

Comprehensive, Open-Source, and Automated Workflow for Multisite λ-Dynamics in Lead Optimization

Multisite λ-dynamics (MSLD) is a highly efficient binding free energy calculation method that samples multiple ligands in a single round by assigning different λ values to the alchemical part of each ligand. This method holds great promise for lead optimization (LO) in drug discovery. However, the complex data preparation and simulation process limits its widespread application in diverse protein-ligand systems. To address this challenge, we developed a comprehensive, open-source, and automated workflow for MSLD calculations based on the BLaDE dynamics engine. This workflow incorporates the Ligand Internal and Cartesian coordinate reconstruction-based alignment algorithm (LIC-align) and an optimized maximum common substructure (MCS) search algorithm to accurately generate MSLD multiple topologies with ideal perturbation patterns. Furthermore, our workflow is highly modularized, allowing straightforward integration and extension of various simulation techniques, and is highly accessible to nonexperts. This workflow was validated by calculating the relative binding free energies of large-scale congeneric ligands, many of which have large perturbing groups. The agreement between the calculations and experiments was excellent, with an average unsigned error of 1.08 ± 0.47 kcal/mol. More than 57.1% of the ligands had an error of less than 1.0 kcal/mol, and the perturbations of 6 targets were fully connected via the calculations, while those of 2 targets were connected via both calculations and experimental data. The Pearson correlation coefficient reached 0.88, indicating that the MSLD workflow provides accurate predictions that can guide lead optimization in drug discovery. We also examined the impact of single-site versus multisite perturbations, ligand grouping by perturbing group size, and the position of the anchor atom on the MSLD performance. By integrating our proposed LIC-align and optimized MCS search algorithm along with the coping strategies to handle challenging molecular substructures, our workflow can handle many realistic scenarios more reasonably than all previously published methods. Moreover, we observed that our MSLD workflow achieved similar accuracy to free energy perturbation (FEP) while improving computational efficiency by over 1 order of magnitude in speedup. These findings provide valuable insights and strategies for further MSLD development, making MSLD a competitive tool for lead optimization.

Enhanced Sampling of Buried Charges in Free Energy Calculations Using Replica Exchange with Charge Tempering

Buried ionizable groups in proteins often play important structural and functional roles. However, it is generally challenging to study the detailed molecular mechanisms solely based on experimental measurements. Free energy calculations using atomistic simulations, on the other hand, complement experimental studies and can provide high temporal and spatial resolution information that can lead to mechanistic insights. Nevertheless, it is also well recognized that sufficient sampling of such atomistic simulations can be challenging, considering that structural changes related to the buried charges may be very slow. In the present study, we describe a simple but effective enhanced sampling technique called replica exchange with charge tempering (REChgT) with a novel free energy method, multisite λ dynamics (MSλD), to study two systems containing buried charges, pKa prediction of a small molecule, orotate, in complex with the dihydroorotate dehydrogenase, and relative stability of a Glu-Lys pair buried in the hydrophobic core of two variants of Staphylococcal nuclease. Compared to the original MSλD simulations, the usage of REChgT dramatically increases sampling in both conformational and alchemical spaces, which directly translates into a significant reduction of wall time to converge the free energy calculations. This study highlights the importance of sufficient sampling toward developing improved free energy methods.

Investigating Polypharmacology through Targeting Known Human Neutrophil Elastase Inhibitors to Proteinase 3

Using a combination of multisite λ-dynamics (MSλD) together with in vitro IC50 assays, we evaluated the polypharmacological potential of a scaffold currently in clinical trials for inhibition of human neutrophil elastase (HNE), targeting cardiopulmonary disease, for efficacious inhibition of Proteinase 3 (PR3), a related neutrophil serine proteinase. The affinities we observe suggest that the dihydropyrimidinone scaffold can serve as a suitable starting point for the establishment of polypharmacologically targeting both enzymes and enhancing the potential for treatments addressing diseases like chronic obstructive pulmonary disease.

phbuilder: A Tool for Efficiently Setting up Constant pH Molecular Dynamics Simulations in GROMACS

Constant pH molecular dynamics (MD) is a powerful technique that allows the protonation state of residues to change dynamically, thereby enabling the study of pH dependence in a manner that has not been possible before. Recently, a constant pH implementation was incorporated into the GROMACS MD package. Although this implementation provides good accuracy and performance, manual modification and the preparation of simulation input files are required, which can be complicated, tedious, and prone to errors. To simplify and automate the setup process, we present phbuilder, a tool that automatically prepares constant pH MD simulations for GROMACS by modifying the input structure and topology as well as generating the necessary parameter files. phbuilder can prepare constant pH simulations from both initial structures and existing simulation systems, and it also provides functionality for performing titrations and single-site parametrizations of new titratable group types. The tool is freely available at www.gitlab.com/gromacs-constantph. We anticipate that phbuilder will make constant pH simulations easier to set up, thereby making them more accessible to the GROMACS user community.

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.

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.

Expanded ensemble predictions of absolute binding free energies in the SAMPL9 host-guest challenge

As part of the SAMPL9 community-wide blind host-guest challenge, we implemented an expanded ensemble workflow to predict absolute binding free energies for 13 small molecules against pillar[6]arene. Notable features of our protocol include consideration of a variety of protonation and enantiomeric states for both host and guests, optimization of alchemical intermediates, and analysis of free energy estimates and their uncertainty using large numbers of simulation replicates performed using distributed computing. Our predictions of absolute binding free energies resulted in a mean absolute error of 2.29 kcal mol-1 and an R2 of 0.54. Overall, results show that expanded ensemble calculations using all-atom molecular dynamics simulations are a valuable and efficient computational tool in predicting absolute binding free energies.

Modern Alchemical Free Energy Methods for Drug Discovery Explained

This Perspective provides a contextual explanation of the current state-of-the-art alchemical free energy methods and their role in drug discovery as well as highlights select emerging technologies. The narrative attempts to answer basic questions about what goes on "under the hood" in free energy simulations and provide general guidelines for how to run simulations and analyze the results. It is the hope that this work will provide a valuable introduction to students and scientists in the field.

Accurately Predicting Protein pKa Values Using Nonequilibrium Alchemy

The stability, solubility, and function of a protein depend on both its net charge and the protonation states of its individual residues. pKa is a measure of the tendency for a given residue to (de)protonate at a specific pH. Although pKa values can be resolved experimentally, theory and computation provide a compelling alternative. To this end, we assess the applicability of a nonequilibrium (NEQ) alchemical free energy method to the problem of pKa prediction. On a data set of 144 residues that span 13 proteins, we report an average unsigned error of 0.77 ± 0.09, 0.69 ± 0.09, and 0.52 ± 0.04 pK for aspartate, glutamate, and lysine, respectively. This is comparable to current state-of-the-art predictors and the accuracy recently reached using free energy perturbation methods (e.g., FEP+). Moreover, we demonstrate that our open-source, pmx-based approach can accurately resolve the pKa values of coupled residues and observe a substantial performance disparity associated with the lysine partial charges in Amber14SB/Amber99SB*-ILDN, for which an underused fix already exists.

Anions and Cations Affect Amino Acid Dissociation Equilibria via Distinct Mechanisms

Salts reduce the pKa of weak acids by a mechanism sensitive to ion identity and concentration via charge screening of the deprotonated state. In this study, we utilize constant pH molecular dynamics simulations to understand the molecular mechanism behind the salt-dependent dissociation of aspartic acid (Asp). We calculate the pKa of Asp in the presence of a monovalent salt and investigate Hofmeister ion effects by systematically varying the ionic radii. We observe that increasing the anion size leads to a monotonic decrease in Asp pKa. Conversely, the cation size affects the pKa nonmonotonically, interpretable in the context of the law of matching water affinity. The net effect of salt on Asp acidity is governed by an interplay of solvation and competing ion interactions. The proposed mechanism is rather general and can be applicable to several problems in Hofmeister ion chemistry, such as pH effects on protein stability and soft matter interfaces.

Flexible Topology: A Dynamic Model of a Continuous Chemical Space

Ligand design problems involve searching chemical space for a molecule with a set of desired properties. As chemical space is discrete, this search must be conducted in a pointwise manner, separately investigating one molecule at a time, which can be inefficient. We propose a method called "Flexible Topology", where a ligand is composed of a set of shapeshifting "ghost" atoms, whose atomic identities and connectivity can dynamically change over the course of a simulation. Ghost atoms are guided toward their target positions using a translation-, rotation-, and index-invariant restraint potential. This is the first step toward a continuous model of chemical space, where a dynamic simulation can move from one molecule to another by following gradients of a potential energy function. This builds on a substantial history of alchemy in the field of molecular dynamics simulation, including the Lambda dynamics method developed by Brooks and co-workers [X. Kong and C.L. Brooks III, J. Chem. Phys. 105, 2414 (1996)], but takes it to an extreme by associating a set of four dynamical attributes with each shapeshifting ghost atom that control not only its presence but also its atomic identity. Here, we outline the theoretical details of this method, its implementation using the OpenMM simulation package, and some preliminary studies of ghost particle assembly simulations in vacuum. We examine a set of 10 small molecules, ranging in size from 6 to 50 atoms, and show that Flexible Topology is able to consistently assemble all of these molecules to high accuracy, beginning from randomly initialized positions and attributes.

Fighting Celiac Disease: Improvement of pH Stability of Cathepsin L In Vitro by Computational Design

Roughly 1% of the global population is susceptible to celiac disease (CD)-inheritable autoimmune inflammation of the small intestine caused by intolerance to gliadin proteins present in wheat, rye, and barley grains, and called gluten in wheat. Classical treatment is a life-long gluten-free diet, which is constraining and costly. An alternative approach is based upon the development and oral reception of effective peptidases that degrade in the stomach immunogenic proline- and glutamine-rich gliadin peptides, which are the cause of the severe reaction in the intestine. In previous research, we have established that the major digestive peptidase of an insect Tribolium castaneum-cathepsin L-hydrolyzes immunogenic prolamins after Gln residues but is unstable in the extremely acidic environment (pH 2-4) of the human stomach and cannot be used as a digestive aid. In this work, using molecular dynamics simulations, we discover the probable cause of the pH instability of cathepsin L-loss of the catalytically competent rotameric state of one of the active site residues, His 275. To "fix" the correct orientation of this residue, we designed a V277A mutant variant, which extends the range of stability of the peptidase in the acidic environment while retaining most of its activity. We suggest this protein as a lead glutenase for the development of oral medical preparation that fights CD and gluten intolerance in susceptible people.

Distinct chemical factors in hydrolytic reactions catalyzed by metalloenzymes and metal complexes

The selective hydrolysis of the extremely stable phosphoester, peptide and ester bonds of molecules by bio-inspired metal-based catalysts (metallohydrolases) is required in a wide range of biological, biotechnological and industrial applications. Despite the impressive advances made in the field, the ultimate goal of designing efficient enzyme mimics for these reactions is still elusive. Its realization will require a deeper understanding of the diverse chemical factors that influence the activities of both natural and synthetic catalysts. They include catalyst-substrate complexation, non-covalent interactions and the electronic nature of the metal ion, ligand environment and nucleophile. Based on our computational studies, their roles are discussed for several mono- and binuclear metallohydrolases and their synthetic analogues. Hydrolysis by natural metallohydrolases is found to be promoted by a ligand environment with low basicity, a metal bound water and a heterobinuclear metal center (in binuclear enzymes). Additionally, peptide and phosphoester hydrolysis is dominated by two competing effects, i.e. nucleophilicity and Lewis acid activation, respectively. In synthetic analogues, hydrolysis is facilitated by the inclusion of a second metal center, hydrophobic effects, a biological metal (Zn, Cu and Co) and a terminal hydroxyl nucleophile. Due to the absence of the protein environment, hydrolysis by these small molecules is exclusively influenced by nucleophile activation. The results gleaned from these studies will enhance the understanding of fundamental principles of multiple hydrolytic reactions. They will also advance the development of computational methods as a predictive tool to design more efficient catalysts for hydrolysis, Diels-Alder reaction, Michael addition, epoxide opening and aldol condensation.

Identification of non-histone substrates of the lysine methyltransferase PRDM9

Lysine methylation is a dynamic, post-translational mark that regulates the function of histone and non-histone proteins. Many of the enzymes that mediate lysine methylation, known as lysine methyltransferases (KMTs), were originally identified to modify histone proteins but have also been discovered to methylate non-histone proteins. In this work, we investigate the substrate selectivity of the lysine methyltransferase PRDM9 to identify both potential histone and non-histone substrates. Though normally expressed in germ cells, PRDM9 is significantly upregulated across many cancer types. The methyltransferase activity of PRDM9 is essential for double-strand break formation during meiotic recombination. PRDM9 has been reported to methylate histone H3 at lysine residues 4 and 36; however, PRDM9 KMT activity had not previously been evaluated on non-histone proteins. Using lysine-oriented peptide (K-OPL) libraries to screen potential substrates of PRDM9, we determined that PRDM9 preferentially methylates peptide sequences not found in any histone protein. We confirmed PRDM9 selectivity through in vitro KMT reactions using peptides with substitutions at critical positions. A multisite λ-dynamics computational analysis provided a structural rationale for the observed PRDM9 selectivity. The substrate selectivity profile was then used to identify putative non-histone substrates, which were tested by peptide spot array, and a subset were further validated at the protein level by in vitro KMT assays on recombinant proteins. Finally, one of the non-histone substrates, CTNNBL1, was found to be methylated by PRDM9 in cells.

The role of conformational change and key glutamic acid residues in the ClC-ec1 antiporter

The triple glutamine (Q) mutant (QQQ) structure of a Cl-/H+ antiporter from Escherichia coli (ClC-ec1) displaying a novel backbone arrangement has been used to challenge the long-held notion that Cl-/H+ antiporters do not operate through large conformational motions. The QQQ mutant substitutes the glutamine residue for an external glutamate E148, an internal glutamate E203, and a third glutamate E113 that hydrogen-bonds with E203. However, it is unknown if QQQ represents a physiologically relevant state, as well as how the protonation of the wild-type glutamates relates to the global dynamics. We herein apply continuous constant-pH molecular dynamics to investigate the H+-coupled dynamics of ClC-ec1. Although any large-scale conformational rearrangement upon acidification would be due to the accumulation of excess charge within the protein, protonation of the glutamates significantly impacts mainly the local structure and dynamics. Despite the fact that the extracellular pore enlarges at acidic pHs, an occluded ClC-ec1 within the active pH range of 3.5-7.5 requires a protonated E148 to facilitate extracellular Cl- release. E203 is also involved in the intracellular H+ transfer as an H+ acceptor. The water wire connection of E148 with the intracellular solution is regulated by the charge states of the E113/E203 dyad with coupled proton titration. However, the dynamics extracted from our simulations are not QQQ-like, indicating that the QQQ mutant does not represent the behavior of the wild-type ClC-ec1. These findings reinforce the necessity of having a protonatable residue at the E203 position in ClC-ec1 and suggest that a higher level of complexity exists for the intracellular H+ transfer in Cl-/H+ antiporters.

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.

Assessing transition rates as functions of environmental variables

We present a method to estimate the transition rates of molecular systems under different environmental conditions that cause the formation or the breaking of bonds and require the sampling of the Grand Canonical Ensemble. For this purpose, we model the molecular system in terms of probable "scenarios," governed by different potential energy functions, which are separately sampled by classical MD simulations. Reweighting the canonical distribution of each scenario according to specific environmental variables, we estimate the grand canonical distribution, then use the Square Root Approximation method to discretize the Fokker-Planck operator into a rate matrix and the robust Perron Cluster Cluster Analysis method to coarse-grain the kinetic model. This permits efficiently estimating the transition rates of conformational states as functions of environmental variables, for example, the local pH at a cell membrane. In this work, we formalize the theoretical framework of the procedure, and we present a numerical experiment comparing the results with those provided by a constant-pH method based on non-equilibrium Molecular Dynamics Monte Carlo simulations. The method is relevant for the development of new drug design strategies that take into account how the cellular environment influences biochemical processes.

GPU-Accelerated All-Atom Particle-Mesh Ewald Continuous Constant pH Molecular Dynamics in Amber

Constant pH molecular dynamics (MD) simulations sample protonation states on the fly according to the conformational environment and user specified pH conditions; however, the current accuracy is limited due to the use of implicit-solvent models or a hybrid solvent scheme. Here, we report the first GPU-accelerated implementation, parametrization, and validation of the all-atom continuous constant pH MD (CpHMD) method with particle-mesh Ewald (PME) electrostatics in the Amber22 pmemd.cuda engine. The titration parameters for Asp, Glu, His, Cys, and Lys were derived for the CHARMM c22 and Amber ff14sb and ff19sb force fields. We then evaluated the PME-CpHMD method using the asynchronous pH replica-exchange titration simulations with the c22 force field for six benchmark proteins, including BBL, hen egg white lysozyme (HEWL), staphylococcal nuclease (SNase), thioredoxin, ribonuclease A (RNaseA), and human muscle creatine kinase (HMCK). The root-mean-square deviation from the experimental pK_a's of Asp, Glu, His, and Cys is 0.76 pH units, and the Pearson's correlation coefficient for the pK_a shifts with respect to model values is 0.80. We demonstrated that a finite-size correction or much enlarged simulation box size can remove a systematic error of the calculated pK_a's and improve agreement with experiment. Importantly, the simulations captured the relevant biology in several challenging cases, e.g., the titration order of the catalytic dyad Glu35/Asp52 in HEWL and the coupled residues Asp19/Asp21 in SNase, the large pK_a upshift of the deeply buried catalytic Asp26 in thioredoxin, and the large pK_a downshift of the deeply buried catalytic Cys283 in HMCK. We anticipate that PME-CpHMD will offer proper pH control to improve the accuracies of MD simulations and enable mechanistic studies of proton-coupled dynamical processes that are ubiquitous in biology but remain poorly understood due to the lack of experimental tools and limitation of current MD simulations.

Multireference Generalization of the Weighted Thermodynamic Perturbation Method

We describe the generalized weighted thermodynamic perturbation (gwTP) method for estimating the free energy surface of an expensive "high-level" potential energy function from the umbrella sampling performed with multiple inexpensive "low-level" reference potentials. The gwTP method is a generalization of the weighted thermodynamic perturbation (wTP) method developed by Li and co-workers [J. Chem. Theory Comput. 2018, 14, 5583-5596] that uses a single "low-level" reference potential. The gwTP method offers new possibilities in model design whereby the sampling generated from several low-level potentials may be combined (e.g., specific reaction parameter models that might have variable accuracy at different stages of a multistep reaction). The gwTP method is especially well suited for use with machine learning potentials (MLPs) that are trained against computationally expensive ab initio quantum mechanical/molecular mechanical (QM/MM) energies and forces using active learning procedures that naturally produce multiple distinct neural network potentials. Simulations can be performed with greater sampling using the fast MLPs and then corrected to the ab initio level using gwTP. The capabilities of the gwTP method are demonstrated by creating reference potentials based on the MNDO/d and DFTB2/MIO semiempirical models supplemented with the "range-corrected deep potential" (DPRc). The DPRc parameters are trained to ab initio QM/MM data, and the potentials are used to calculate the free energy surface of stepwise mechanisms for nonenzymatic RNA 2'-O-transesterification model reactions. The extended sampling made possible by the reference potentials allows one to identify unequilibrated portions of the simulations that are not always evident from the short time scale commonly used with ab initio QM/MM potentials. We show that the reference potential approach can yield more accurate ab initio free energy predictions than the wTP method or what can be reasonably afforded from explicit ab initio QM/MM sampling.

A New Formulation for the Concerted Alchemical Calculation of van der Waals and Coulomb Components of Solvation Free Energies

Alchemical free energy calculations via molecular dynamics have been widely used to obtain thermodynamic properties related to protein-ligand binding and solute-solvent interactions. Although soft-core modeling is the most common approach, the linear basis function (LBF) methodology [Naden, L. N.; et al. J. Chem. Theory Comput.2014, 10 (3), 1128; 2015, 11 (6), 2536] has emerged as a suitable alternative. It overcomes the end-point singularity of the scaling method while maintaining essential advantages such as ease of implementation and high flexibility for postprocessing analysis. In the present work, we propose a simple LBF variant and formulate an efficient protocol for evaluating van der Waals and Coulomb components of an alchemical transformation in tandem, in contrast to the prevalent sequential evaluation mode. To validate our proposal, which results from a careful optimization study, we performed solvation free energy calculations and obtained octanol-water partition coefficients of small organic molecules. Comparisons with results obtained via the sequential mode using either another LBF approach or the soft-core model attest to the effectiveness and correctness of our method. In addition, we show that a reaction field model with an infinite dielectric constant can provide very accurate hydration free energies when used instead of a lattice-sum method to model solute-solvent electrostatics.

Best Practices in Constant pH MD Simulations: Accuracy and Sampling

Various approaches have been proposed to include the effect of pH in molecular dynamics (MD) simulations. Among these, the λ-dynamics approach proposed by Brooks and co-workers [Kong, X.; Brooks III, C. L. J. Chem. Phys.1996, 105, 2414−2423] can be performed with little computational overhead and hfor each typeence be used to routinely perform MD simulations at microsecond time scales, as shown in the accompanying paper [Aho, N. et al. J. Chem. Theory Comput.2022, DOI: 10.1021/acs.jctc.2c00516]. At such time scales, however, the accuracy of the molecular mechanics force field and the parametrization becomes critical. Here, we address these issues and provide the community with guidelines on how to set up and perform long time scale constant pH MD simulations. We found that barriers associated with the torsions of side chains in the CHARMM36m force field are too high for reaching convergence in constant pH MD simulations on microsecond time scales. To avoid the high computational cost of extending the sampling, we propose small modifications to the force field to selectively reduce the torsional barriers. We demonstrate that with such modifications we obtain converged distributions of both protonation and torsional degrees of freedom and hence consistent pK_a estimates, while the sampling of the overall configurational space accessible to proteins is unaffected as compared to normal MD simulations. We also show that the results of constant pH MD depend on the accuracy of the correction potentials. While these potentials are typically obtained by fitting a low-order polynomial to calculated free energy profiles, we find that higher order fits are essential to provide accurate and consistent results. By resolving problems in accuracy and sampling, the work described in this and the accompanying paper paves the way to the widespread application of constant pH MD beyond pK_a prediction.

Drug Discovery by Automated Adaptation of Chemical Structure and Identity

Computer-aided drug design offers the potential to dramatically reduce the cost and effort required for drug discovery. While screening-based methods are valuable in the early stages of hit identification, they are frequently succeeded by iterative, hypothesis-driven computations that require recurrent investment of human time and intuition. To increase automation, we introduce a computational method for lead refinement that combines concerted dynamics of the ligand/protein complex via molecular dynamics simulations with integrated Monte Carlo-based changes in the chemical formula of the ligand. This approach, which we refer to as ligand-exchange Monte Carlo molecular dynamics, accounts for solvent- and entropy-based contributions to competitive binding free energies by coupling the energetics of bound and unbound states during the ligand-exchange attempt. Quantitative comparison of relative binding free energies to reference values from free energy perturbation, conducted in vacuum, indicates that ligand-exchange Monte Carlo molecular dynamics simulations sample relevant conformational ensembles and are capable of identifying strongly binding compounds. Additional simulations demonstrate the use of an implicit solvent model. We speculate that the use of chemical graphs in which exchanges are only permitted between ligands with sufficient similarity may enable an automated search to capture some of the benefits provided by human intuition during hypothesis-guided lead refinement.

A Rigorous Method for Identifying a One-Dimensional Reaction Coordinate in Complex Molecules

Understanding the mechanism of functional protein dynamics is critical to understanding protein functions. Reaction coordinate (RC) is a central topic in protein dynamics, and the grail is to find the one-dimensional RC (1D-RC) that can fully determine the value of a committor (i.e., the reaction probability in configuration space) for any protein configuration. We present a new method that, for the first time, uses a fundamental mechanical operator, the generalized work functional, to identify the rigorous 1D-RC in complex molecules. For a prototypical biomolecular isomerization reaction, the 1D-RC identified by the current method can determine the committor with an accuracy far exceeding what was achieved by previous methods. This method only requires modest computational cost and can be readily applied to large molecules. Most importantly, the generalized work functional is the physical determinant of the collectivity in functional protein dynamics and provides a tentative roadmap that connects the structure of a protein to its function.

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.

Alchemical Free Energy Methods Applied to Complexes of the First Bromodomain of BRD4

Accurate and rapid predictions of the binding affinity of a compound to a target are one of the ultimate goals of computer aided drug design. Alchemical approaches to free energy estimations follow the path from an initial state of the system to the final state through alchemical changes of the energy function during a molecular dynamics simulation. Herein, we explore the accuracy and efficiency of two such techniques: relative free energy perturbation (FEP) and multisite lambda dynamics (MSλD). These are applied to a series of inhibitors for the bromodomain-containing protein 4 (BRD4). We demonstrate a procedure for obtaining accurate relative binding free energies using MSλD when dealing with a change in the net charge of the ligand. This resulted in an impressive comparison with experiment, with an average difference of 0.4 ± 0.4 kcal mol-1. In a benchmarking study for the relative FEP calculations, we found that using 20 lambda windows with 0.5 ns of equilibration and 1 ns of data collection for each window gave the optimal compromise between accuracy and speed. Overall, relative FEP and MSλD predicted binding free energies with comparable accuracy, an average of 0.6 kcal mol-1 for each method. However, MSλD makes predictions for a larger molecular space over a much shorter time scale than relative FEP, with MSλD requiring a factor of 18 times less simulation time for the entire molecule space.

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.

Improved Cell-Potent and Selective Peptidomimetic Inhibitors of Protein N-Terminal Methyltransferase 1

Protein N-terminal methyltransferase 1 (NTMT1) recognizes a unique N-terminal X-P-K/R motif (X represents any amino acid other than D/E) and transfers 1–3 methyl groups to the N-terminal region of its substrates. Guided by the co-crystal structures of NTMT1 in complex with the previously reported peptidomimetic inhibitor DC113, we designed and synthesized a series of new peptidomimetic inhibitors. Through a focused optimization of DC113, we discovered a new cell-potent peptidomimetic inhibitor GD562 (IC50 = 0.93 ± 0.04 µM). GD562 exhibited improved inhibition of the cellular N-terminal methylation levels of both the regulator of chromosome condensation 1 and the oncoprotein SET with an IC50 value of ~50 µM in human colorectal cancer HCT116 cells. Notably, the inhibitory activity of GD562 for the SET protein increased over 6-fold compared with the previously reported cell-potent inhibitor DC541. Furthermore, GD562 also exhibited over 100-fold selectivity for NTMT1 against several other methyltransferases. Thus, this study provides a valuable probe to investigate the biological functions of NTMT1.

Interactions of Urea-Based Inhibitors with Prostate-Specific Membrane Antigen for Boron Neutron Capture Therapy

In this study, molecular interactions of prostate-specific membrane antigen (PSMA) with five chemically distinct urea-based boron-containing inhibitors have been investigated at the atomic level using molecular docking and molecular dynamics simulations. The PSMA-inhibitor complexations have been analyzed by comparing their binding modes, secondary structures, root-mean-square deviations, noncovalent interactions, principal components, and binding free energies. PSMA is a cell surface glycoprotein upregulated in cancerous cells and can be targeted by boron-labeled inhibitors for boron neutron capture therapy (BNCT). The effective BNCT requires the selective boron delivery to the tumor area and highly specific PSMA-mediated cellular uptake by tumor. Thus, a potent inhibitor must exhibit both high binding affinity and high boron density. The computational results suggest that the chemical nature of inhibitors affects the binding mode and their association with PSMA is primarily dominated by hydrogen bonding, salt bridge, electrostatic, and π-π interactions. The binding free energies (-28.0, -15.2, -43.9, -23.2, and -38.2 kcal/mol) calculated using λ-dynamics for all inhibitors (In1-5) predict preferential binding that is in accordance with experimental data. Among all inhibitors, In5 was found to be the best candidate for BNCT. The binding of this inhibitor to PSMA preserved its overall secondary structure. These results provide computational insights into the coordination flexibility of PSMA and its interaction with various inhibitors. They can be used for the design and synthesis of efficient BNCT agents with improved drug selectivity and high boron percentage.

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.

CORE-MD II: A fast, adaptive, and accurate enhanced sampling method

In this paper, we present a fast and adaptive correlation guided enhanced sampling method (CORE-MD II). The CORE-MD II technique relies, in part, on partitioning of the entire pathway into short trajectories that we refer to as instances. The sampling within each instance is accelerated by adaptive path-dependent metadynamics simulations. The second part of this approach involves kinetic Monte Carlo (kMC) sampling between the different states that have been accessed during each instance. Through the combination of the partition of the total simulation into short non-equilibrium simulations and the kMC sampling, the CORE-MD II method is capable of sampling protein folding without any a priori definitions of reaction pathways and additional parameters. In the validation simulations, we applied the CORE-MD II on the dialanine peptide and the folding of two peptides: TrpCage and TrpZip2. In a comparison with long time equilibrium Molecular Dynamics (MD), 1 µs replica exchange MD (REMD), and CORE-MD I simulations, we find that the level of convergence of the CORE-MD II method is improved by a factor of 8.8, while the CORE-MD II method reaches acceleration factors of ∼120. In the CORE-MD II simulation of TrpZip2, we observe the formation of the native state in contrast to the REMD and the CORE-MD I simulations. The method is broadly applicable for MD simulations and is not restricted to simulations of protein folding or even biomolecules but also applicable to simulations of protein aggregation, protein signaling, or even materials science simulations.

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.

A strategy for proline and glycine mutations to proteins with alchemical free energy calculations

Computation of the thermodynamic consequences of protein mutations holds great promise in protein biophysics and design. Alchemical free energy methods can give improved estimates of mutational free energies, and are already widely used in calculations of relative and absolute binding free energies in small molecule design problems. In principle, alchemical methods can address any amino acid mutation with an appropriate alchemical pathway, but identifying a strategy that produces such a path for proline and glycine mutations is an ongoing challenge. Most current strategies perturb only side chain atoms, while proline and glycine mutations also alter the backbone parameters and backbone ring topology. Some strategies also perturb backbone parameters and enable glycine mutations. This work presents a strategy that enables both proline and glycine mutations and comprises two key elements: a dual backbone with restraints and scaling of bonded terms, facilitating backbone parameter changes, and a soft bond in the proline ring, enabling ring topology changes in proline mutations. These elements also have utility for core hopping and macrocycle studies in computer-aided drug design. This new strategy shows slight improvements over an alternative side chain perturbation strategy for a set T4 lysozyme mutations lacking proline and glycine, and yields good agreement with experiment for a set of T4 lysozyme proline and glycine mutations not previously studied. To our knowledge this is the first report comparing alchemical predictions of proline mutations with experiment. With this strategy in hand, alchemical methods now have access to the full palette of amino acid mutations.