Can Absolute Free Energies of Association Be Estimated from Molecular Mechanical Simulations? The Biotin−Streptavidin System Revisited

Equilibrium and Nonequilibrium Ensemble Methods for Accurate, Precise and Reproducible Absolute Binding Free Energy Calculations

Free energy calculations for protein-ligand complexes have become widespread in recent years owing to several conceptual, methodological and technological advances. Central among these is the use of ensemble methods which permits accurate, precise and reproducible predictions and is necessary for uncertainty quantification. Absolute binding free energies (ABFEs) are challenging to predict using alchemical methods and their routine application in drug discovery has remained out of reach until now. Here, we apply ensemble alchemical ABFE methods to a large data set comprising 219 ligand-protein complexes and obtain statistically robust results with high accuracy (<1 kcal/mol). We compare equilibrium and nonequilibrium methods for ABFE predictions at large scale and provide a systematic critical assessment of each method. The equilibrium method is more accurate, precise, faster, computationally more cost-effective and requires a much simpler protocol, making it preferable for large scale and blind applications. We find that the calculated free energy distributions are non-normal and discuss the consequences. We recommend a definitive protocol to perform ABFE calculations optimally. Using this protocol, it is possible to perform thousands of ABFE calculations within a few hours on modern exascale machines.

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.

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

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

On Analytical Corrections for Restraints in Absolute Binding Free Energy Calculations

Double decoupling absolute binding free energy simulations require an intermediate state at which the ligand is held solely by restraints in a position and orientation resembling the bound state. One possible choice consists of one distance, two angle, and three dihedral angle restraints. Here, I demonstrate that in practically all cases the analytical correction derived under the rigid rotator harmonic oscillator approximation is sufficient to account for the free energy of the restraints.

Performance and Analysis of the Alchemical Transfer Method for Binding-Free-Energy Predictions of Diverse Ligands

The Alchemical Transfer Method (ATM) is herein validated against the relative binding-free energies (RBFEs) of a diverse set of protein-ligand complexes. We employed a streamlined setup workflow, a bespoke force field, and AToM-OpenMM software to compute the RBFEs of the benchmark set prepared by Schindler and collaborators at Merck KGaA. This benchmark set includes examples of standard small R-group ligand modifications as well as more challenging scenarios, such as large R-group changes, scaffold hopping, formal charge changes, and charge-shifting transformations. The novel coordinate perturbation scheme and a dual-topology approach of ATM address some of the challenges of single-topology alchemical RBFE methods. Specifically, ATM eliminates the need for splitting electrostatic and Lennard-Jones interactions, atom mapping, defining ligand regions, and postcorrections for charge-changing perturbations. Thus, ATM is simpler and more broadly applicable than conventional alchemical methods, especially for scaffold-hopping and charge-changing transformations. Here, we performed well over 500 RBFE calculations for eight protein targets and found that ATM achieves accuracy comparable to that of existing state-of-the-art methods, albeit with larger statistical fluctuations. We discuss insights into the specific strengths and weaknesses of the ATM method that will inform future deployments. This study confirms that ATM can be applied as a production tool for RBFE predictions across a wide range of perturbation types within a unified, open-source framework.

Alchemical Calculation of Relative Free Energies for Charge-Changing Mutations at Protein-Protein Interfaces Considering Fixed and Variable Protonation States

The calculation of relative free energies (ΔΔG) for charge-changing mutations at protein-protein interfaces through alchemical methods remains challenging due to variations in the system's net charge during charging steps, the possibility of mutated and contacting ionizable residues occurring in various protonation states, and undersampling issues. In this study, we present a set of strategies, collectively termed TIRST/TIRST-H+, to address some of these challenges. Our approaches combine thermodynamic integration (TI) with the prediction of pKa shifts to calculate ΔΔG values. Moreover, special sets of restraints are employed to keep the alchemically transformed molecules separated. The accuracy of the devised approaches was assessed on a large and diverse data set comprising 164 point mutations of charged residues (Asp, Glu, Lys, and Arg) to Ala at the protein-protein interfaces of complexes with known three-dimensional structures. Mean absolute and root-mean-square errors ranging from 1.38 to 1.66 and 1.89 to 2.44 kcal/mol, respectively, and Pearson correlation coefficients of ∼0.6 were obtained when testing the approaches on the selected data set using the GPU-TI module of Amber18 suite and the ff14SB force field. Furthermore, the inclusion of variable protonation states for the mutated acid residues improved the accuracy of the predicted ΔΔG values. Therefore, our results validate the use of TIRST/TIRST-H+ in prospective studies aimed at evaluating the impact of charge-changing mutations to Ala on the stability of protein-protein complexes.

Integrative Approach to Dissect the Drug Resistance Mechanism of the H172Y Mutation of SARS-CoV-2 Main Protease

Nirmatrelvir is an orally available inhibitor of SARS-CoV-2 main protease (Mpro) and the main ingredient of Paxlovid, a drug approved by the U.S. Food and Drug Administration for high-risk COVID-19 patients. Recently, a rare natural mutation, H172Y, was found to significantly reduce nirmatrelvir's inhibitory activity. As the COVID-19 cases skyrocket in China and the selective pressure of antiviral therapy builds in the US, there is an urgent need to characterize and understand how the H172Y mutation confers drug resistance. Here, we investigated the H172Y Mpro's conformational dynamics, folding stability, catalytic efficiency, and inhibitory activity using all-atom constant pH and fixed-charge molecular dynamics simulations, alchemical and empirical free energy calculations, artificial neural networks, and biochemical experiments. Our data suggest that the mutation significantly weakens the S1 pocket interactions with the N-terminus and perturbs the conformation of the oxyanion loop, leading to a decrease in the thermal stability and catalytic efficiency. Importantly, the perturbed S1 pocket dynamics weaken the nirmatrelvir binding in the P1 position, which explains the decreased inhibitory activity of nirmatrelvir. Our work demonstrates the predictive power of the combined simulation and artificial intelligence approaches, and together with biochemical experiments, they can be used to actively surveil continually emerging mutations of SARS-CoV-2 Mpro and assist the optimization of antiviral drugs. The presented approach, in general, can be applied to characterize mutation effects on any protein drug targets.

Field-Induced Hydration Shell Reorganization Enables Electro-osmotic Flow in Nanochannels

Electro-osmotic flow is the motion of fluid driven by an applied electric field, for which an electric double layer near a charged surface is deemed essential. Here, we find that electro-osmotic flow can occur in electrically neutral nanochannels in the absence of definable electric double layers through extensive molecular dynamics simulations. An applied electric field is shown to cause an intrinsic channel selectivity between cations and anions, by reorienting the hydration shells of these confined ions. The ion selectivity then results in a net charge density in the channel that induces the unconventional electro-osmotic flow. The flow direction is amenable to manipulation by the field strength and the channel size, which will inform ongoing efforts to develop highly integrated nanofluidic systems capable of complex flow control.

Binding affinity estimation from restrained umbrella sampling simulations

The protein-ligand binding affinity quantifies the binding strength between a protein and its ligand. Computer modeling and simulations can be used to estimate the binding affinity or binding free energy using data- or physics-driven methods or a combination thereof. Here we discuss a purely physics-based sampling approach based on biased molecular dynamics simulations. Our proposed method generalizes and simplifies previously suggested stratification strategies that use umbrella sampling or other enhanced sampling simulations with additional collective-variable-based restraints. The approach presented here uses a flexible scheme that can be easily tailored for any system of interest. We estimate the binding affinity of human fibroblast growth factor 1 to heparin hexasaccharide based on the available crystal structure of the complex as the initial model and four different variations of the proposed method to compare against the experimentally determined binding affinity obtained from isothermal titration calorimetry experiments.

Hazardous Shortcuts in Standard Binding Free Energy Calculations

Calculating the standard binding free energies of protein-protein and protein-ligand complexes from atomistic molecular dynamics simulations in explicit solvent is a problem of central importance in computational biophysics. A rigorous strategy for carrying out such calculations is the so-called "geometrical route". In this method, two molecular objects are progressively separated from one another in the presence of orientational and conformational restraints serving to control the change in configurational entropy that accompanies the dissociation process, thereby allowing the computations to converge within simulations of affordable length. Although the geometrical route provides a rigorous theoretical framework, a tantalizing computational shortcut consists of simply leaving out such orientational and conformational degrees of freedom during the separation process. Here the accuracy and convergence of the two approaches are critically compared in the case of two protein-ligand complexes (Abl kinase-SH3:p41 and MDM2-p53:NVP-CGM097) and three protein-protein complexes (pig insulin dimer, SARS-CoV-2 spike RBD:ACE2, and CheA kinase-P2:CheY). The results of the simulations that strictly follow the geometrical route match the experimental standard binding free energies within chemical accuracy. In contrast, simulations bereft of geometrical restraints converge more poorly, yielding inconsistent results that are at variance with the experimental measurements. Furthermore, the orientational and positional time correlation functions of the protein in the unrestrained simulations decay over several microseconds, a time scale that is far longer than the typical simulation times of the geometrical route, which explains why those simulations fail to sample the relevant degrees of freedom during the separation process of the complexes.

Exploring the Effect of Enhanced Sampling on Protein Stability Prediction

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

Relative Binding Free Energy Calculations for Ligands with Diverse Scaffolds with the Alchemical Transfer Method

We present an extension of the alchemical transfer method (ATM) for the estimation of relative binding free energies of molecular complexes applicable to conventional, as well as scaffold-hopping, alchemical transformations. Named ATM-RBFE, the method is implemented in the free and open-source OpenMM molecular simulation package and aims to provide a simpler and more generally applicable route to the calculation of relative binding free energies than what is currently available. ATM-RBFE is based on sound statistical mechanics theory and a novel coordinate perturbation scheme designed to swap the positions of a pair of ligands such that one is transferred from the bulk solvent to the receptor binding site while the other moves simultaneously in the opposite direction. The calculation is conducted directly in a single solvent box with a system prepared with conventional setup tools, without splitting of electrostatic and nonelectrostatic transformations, and without pairwise soft-core potentials. ATM-RBFE is validated here against the absolute binding free energies of the SAMPL8 GDCC host-guest benchmark set and against protein-ligand benchmark sets that include complexes of the estrogen receptor ERα and those of the methyltransferase EZH2. In each case the method yields self-consistent and converged relative binding free energy estimates in agreement with absolute binding free energies and reference literature values, as well as experimental measurements.

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.

Modeling the Energy Landscape of Side Reactions in the Cytochrome bc1 Complex

Much of the metabolic molecular machinery responsible for energy transduction processes in living organisms revolves around a series of electron and proton transfer processes. The highly redox active enzymes can, however, also pose a risk of unwanted side reactions leading to reactive oxygen species, which are harmful to cells and are a factor in aging and age-related diseases. Using extensive quantum and classical computational modeling, we here show evidence of a particular superoxide production mechanism through stray reactions between molecular oxygen and a semiquinone reaction intermediate bound in the mitochondrial complex III of the electron transport chain, also known as the cytochrome b c 1 complex. Free energy calculations indicate a favorable electron transfer from semiquinone occurring at low rates under normal circumstances. Furthermore, simulations of the product state reveal that superoxide formed at the Q _o -site exclusively leaves the b c 1 complex at the positive side of the membrane and escapes into the intermembrane space of mitochondria, providing a critical clue in further studies of the harmful effects of mitochondrial superoxide production.

BFEE2: Automated, Streamlined, and Accurate Absolute Binding Free-Energy Calculations

Accurate absolute binding free-energy estimation in silico, following either an alchemical or a geometrical route, involves several subprocesses and requires the introduction of geometric restraints. Human intervention, for instance, to define the necessary collective variables, prepare the input files, monitor the simulation, and perform post-treatments is, however, tedious, cumbersome, and prone to errors. With the aim of automating and streamlining free-energy calculations, especially for nonexperts, version 2.0 of the binding free energy estimator (BFEE2) provides both standardized alchemical and geometrical workflows and obviates the need for extensive human intervention to guarantee complete reproducibility of the results. To achieve the largest gamut of protein-ligand and, more generally, of host-guest complexes, BFEE2 supports most academic force fields, such as CHARMM, Amber, OPLS, and GROMOS. Configurational files are generated in the NAMD and Gromacs formats, and all the post-treatments are performed in an automated fashion. Moreover, convergence of the free-energy calculation can be monitored from the intermediate files generated during the simulation. All in all, BFEE2 is a foolproof, versatile tool for accurate absolute binding free-energy calculations, assisting the end-user over a broad range of applications.

Inhibition Mechanism of Antimalarial Drugs Targeting the Cytochrome bc1 Complex

Plasmodium falciparum (P. falciparum) is the main parasite known to cause malaria in humans. The antimalarial drug atovaquone is known to inhibit the Q_o-site of the cytochrome bc₁ complex of P. falciparum, which ultimately blocks ATP synthesis, leading to cell death. Through the years, mutations of the P. falciparum cytochrome bc₁ complex, causing resistance to atovaquone, have emerged. The present investigation applies molecular dynamics (MD) simulations to study how the specific mutations Y279S and L282V, known to cause atovaquone resistance in malarial parasites, affect the inhibition mechanism of two known inhibitors. Binding free energy estimates were obtained through free energy perturbation calculations but were unable to confidently resolve the effects of mutations due to the great complexity of the binding environment. Meanwhile, basic mechanistic considerations from the MD simulations provide a detailed characterization of inhibitor binding modes and indicate that the Y279S mutation weakens the natural binding of the inhibitors, while no conclusive effect of the L282V mutation could be observed.

N-Terminus of the Third PDZ Domain of PSD-95 Orchestrates Allosteric Communication for Selective Ligand Binding

PDZ domains constitute common models to study single-domain allostery without significant structural changes. The third PDZ domain of PSD-95 (PDZ3) is known to have selective structural features that confer unique modulatory roles to this unit. In this model system, two residues, H372 directly connected to the binding site and G330 holding an off-binding-site position, were designated to assess the effect of mutations on binding selectivity. It has been observed that the H372A and G330T-H372A mutations change ligand preferences from class I (T/S amino acid at position -2 of the ligand) to class II (hydrophobic amino acid at the same position). Alternatively, the G330T single mutation leads to the recognition of both ligand classes. We have performed a series of molecular dynamics (MD) simulations for wild-type, H372A, and G330T single mutants and a double mutant of PDZ3 in the absence and presence of both types of ligands. With the combination of free-energy difference calculations and a detailed analysis of MD trajectories, "class switching" and "class bridging" behavior of PDZ3 mutants, as well as their effects on ligand selection and binding affinities are explained. We show that the dynamics of the charged N-terminus plays a fundamental role in determining the binding preferences in PDZ3 by altering the electrostatic energy. These findings are corroborated by simulations on N-terminus-truncated versions of these systems. The dynamical allostery orchestrated by the N-terminus offers a fresh perspective to the study of communication pathways in proteins.

Charge-Changing Perturbations and Path Sampling via Classical Molecular Dynamic Simulations of Simple Guest-Host Systems

Currently, two different methods dominate the field of biomolecular free-energy calculations for the prediction of binding affinities. Pathway methods are frequently used for large ligands that bind on the surface of a host, such as protein-protein complexes. Alchemical methods, on the other hand, are preferably applied for small ligands that bind to deeply buried binding sites. The latter methods are also widely known to be heavily artifacted by the representation of electrostatic energies in periodic simulation boxes, in particular, when net-charge changes are involved. Different methods have been described to deal with these artifacts, including postsimulation correction schemes and instantaneous correction schemes (e.g., co-alchemical perturbation of ions). Here, we use very simple test systems to show that instantaneous correction schemes with no change in the system net charge lower the artifacts but do not eliminate them. Furthermore, we show that free energies from pathway methods suffer from the same artifacts.

Sila-Ibuprofen

The synthesis, characterization, biological activity, and toxicology of sila-ibuprofen, a silicon derivative of the most common nonsteroidal anti-inflammatory drug, is reported. The key improvements compared with ibuprofen are a four times higher solubility in physiological media and a lower melting enthalpy, which are attributed to the carbon-silicon switch. The improved solubility is of interest for postsurgical intravenous administration. A potential for pain relief is rationalized via inhibition experiments of cyclooxygenases I and II (COX-I and COX-II) as well as via a set of newly developed methods that combine molecular dynamics, quantum chemistry, and quantum crystallography. The binding affinity of sila-ibuprofen to COX-I and COX-II is quantified in terms of London dispersion and electrostatic interactions in the active receptor site. This study not only shows the potential of sila-ibuprofen for medicinal application but also improves our understanding of the mechanism of action of the inhibition process.

Boosting Free-Energy Perturbation Calculations with GPU-Accelerated NAMD

Harnessing the power of graphics processing units (GPUs) to accelerate molecular dynamics (MD) simulations in the context of free-energy calculations has been a longstanding effort toward the development of versatile, high-performance MD engines. We report a new GPU-based implementation in NAMD of free-energy perturbation (FEP), one of the oldest, most popular importance-sampling approaches for the determination of free-energy differences that underlie alchemical transformations. Compared to the CPU implementation available since 2001 in NAMD, our benchmarks indicate that the new implementation of FEP in traditional GPU code is about four times faster, without any noticeable loss of accuracy, thereby paving the way toward more affordable free-energy calculations on large biological objects. Moreover, we have extended this new FEP implementation to a code path highly optimized for a single-GPU node, which proves to be up to nearly 30 times faster than the CPU implementation. Through optimized GPU performance, the present developments provide the community with a cost-effective solution for conducting FEP calculations. The new FEP-enabled code has been released with NAMD 3.0.

Scalable molecular dynamics on CPU and GPU architectures with NAMD

NAMDis a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

Introducing VIKING: A Novel Online Platform for Multiscale Modeling

Various biochemical and biophysical processes, occurring on multiple time and length scales, can nowadays be studied using specialized software packages on supercomputer clusters. The complexity of such simulations often requires application of different methods in a single study and strong computational expertise. We have developed VIKING, a convenient web platform for carrying out multiscale computations on supercomputers. VIKING allows combining methods in standardized workflows, making complex simulations accessible to a broader biochemical and biophysical society.

Correcting electrostatic artifacts due to net-charge changes in the calculation of ligand binding free energies

Alchemically derived free energies are artifacted when the perturbed moiety has a nonzero net charge. The source of the artifacts lies in the effective treatment of the electrostatic interactions within and between the perturbed atoms and remaining (partial) charges in the simulated system. To treat the electrostatic interactions effectively, lattice-summation (LS) methods or cutoff schemes in combination with a reaction-field contribution are usually employed. Both methods render the charging component of the calculated free energies sensitive to essential parameters of the system like the cutoff radius or the box side lengths. Here, we discuss the results of three previously published studies of ligand binding. These studies presented estimates of binding free energies that were artifacted due to the charged nature of the ligands. We show that the size of the artifacts can be efficiently calculated and raw simulation data can be corrected. We compare the corrected results with experimental estimates and nonartifacted estimates from path-sampling methods. Although the employed correction scheme involves computationally demanding continuum-electrostatics calculations, we show that the correction estimate can be deduced from a small sample of configurations rather than from the entire ensemble. This observation makes the calculations of correction terms feasible for complex biological systems. To show the general applicability of the proposed procedure, we also present results where the correction scheme was used to correct independent free energies obtained from simulations employing a cutoff scheme or LS electrostatics. In this work, we give practical guidelines on how to apply the appropriate corrections easily.

Strong Adverse Contribution of Conformational Dynamics to Streptavidin-Biotin Binding

Molecular dynamics plays an important role for the biological function of proteins. For protein ligand interactions, changes of conformational entropy of protein and hydration layer are relevant for the binding process. Quasielastic neutron scattering (QENS) was used to investigate differences in protein dynamics and conformational entropy of ligand-bound and ligand-free streptavidin. Protein dynamics were probed both on the fast picosecond time scale using neutron time-of-flight spectroscopy and on the slower nanosecond time scale using high-resolution neutron backscattering spectroscopy. We found the internal equilibrium motions of streptavidin and the corresponding mean square displacements (MSDs) to be greatly reduced upon biotin binding. On the basis of the observed MSDs, we calculated the difference of conformational entropy ΔS_conf of the protein component between ligand-bound and ligand-free streptavidin. The rather large negative ΔS_conf value (-2 kJ mol^-1 K^-1 on the nanosecond time scale) obtained for the streptavidin tetramer seems to be counterintuitive, given the exceptionally high affinity of streptavidin-biotin binding. Literature data on the total entropy change ΔS observed upon biotin binding to streptavidin, which includes contributions from both the protein and the hydration water, suggest partial compensation of the unfavorable ΔS_conf by a large positive entropy gain of the surrounding hydration layer and water molecules that are displaced during ligand binding.

String Method for Protein-Protein Binding Free-Energy Calculations

A powerful computational strategy to determine the equilibrium association constant of two macromolecules with explicit-solvent molecular dynamics (MD) simulations is the "geometric route", which considers the reversible physical separation of the bound complex in solution. Nonetheless, multiple challenges remain to render this type of methodology reliable and computationally efficient in practice. In particular, in one, formulation of the geometric route relies on the potential of mean force (PMF) for physically separating the two binding partners restrained along a straight axis, which must be selected prior to the calculation. However, practical applications indicate that the calculation of the separation PMF along the predefined rectilinear pathway may be suboptimal and slowly convergent. Recognizing that a rectilinear straight separation pathway is generally not representative of how the protein complex physically separates in solution, we put forth a novel theoretical framework for binding free-energy calculations, leaning on the optimal curvilinear minimum free-energy path (MFEP) determined from the string method. The proposed formalism is validated by comparing the results obtained using both rectilinear and curvilinear pathways for a prototypical host-guest complex formed by cucurbit[7]uril (CB[7]) binding benzene, and for the barnase-barstar protein complex. On the basis of multi-microsecond MD calculations, we find that the calculations following the traditional rectilinear pathway and the string-based curvilinear pathway agree quantitatively, but convergence is faster with the latter.

Accurate Estimation of the Standard Binding Free Energy of Netropsin with DNA

DNA is the target of chemical compounds (drugs, pollutants, photosensitizers, etc.), which bind through non-covalent interactions. Depending on their structure and their chemical properties, DNA binders can associate to the minor or to the major groove of double-stranded DNA. They can also intercalate between two adjacent base pairs, or even replace one or two base pairs within the DNA double helix. The subsequent biological effects are strongly dependent on the architecture of the binding motif. Discriminating between the different binding patterns is of paramount importance to predict and rationalize the effect of a given compound on DNA. The structural characterization of DNA complexes remains, however, cumbersome at the experimental level. In this contribution, we employed all-atom molecular dynamics simulations to determine the standard binding free energy of DNA with netropsin, a well-characterized antiviral and antimicrobial drug, which associates to the minor groove of double-stranded DNA. To overcome the sampling limitations of classical molecular dynamics simulations, which cannot capture the large change in configurational entropy that accompanies binding, we resort to a series of potentials of mean force calculations involving a set of geometrical restraints acting on collective variables.

Insights into functions of the H channel of cytochrome c oxidase from atomistic molecular dynamics simulations

Proton pumping A-type cytochrome c oxidase (CcO) terminates the respiratory chains of mitochondria and many bacteria. Three possible proton transfer pathways (D, K, and H channels) have been identified based on structural, functional, and mutational data. Whereas the D channel provides the route for all pumped protons in bacterial A-type CcOs, studies of bovine mitochondrial CcO have led to suggestions that its H channel instead provides this route. Here, we have studied H-channel function by performing atomistic molecular dynamics simulations on the entire, as well as core, structure of bovine CcO in a lipid-solvent environment. The majority of residues in the H channel do not undergo large conformational fluctuations. Its upper and middle regions have adequate hydration and H-bonding residues to form potential proton-conducting channels, and Asp51 exhibits conformational fluctuations that have been observed crystallographically. In contrast, throughout the simulations, we do not observe transient water networks that could support proton transfer from the N phase toward heme a via neutral His413, regardless of a labile H bond between Ser382 and the hydroxyethylfarnesyl group of heme a In fact, the region around His413 only became sufficiently hydrated when His413 was fixed in its protonated imidazolium state, but its calculated pK_a is too low for this to provide the means to create a proton transfer pathway. Our simulations show that the electric dipole moment of residues around heme a changes with the redox state, hence suggesting that the H channel could play a more general role as a dielectric well.

New insights into human farnesyl pyrophosphate synthase inhibition by second-generation bisphosphonate drugs

Pamidronate, alendronate, APHBP and neridronate are a group of drugs, known as second-generation bisphosphonates (2G-BPs), commonly used in the treatment of bone-resorption disorders, and recently their use has been related to some collateral side effects. The therapeutic activity of 2G-BPs is related to the inhibition of the human Farnesyl Pyrophosphate Synthase (hFPPS). Available inhibitory activity values show that 2G-BPs act time-dependently, showing big differences in their initial inhibitory activities but similar final IC₅₀ values. However, there is a lack of information explaining this similar final inhibitory potency. Although different residues have been identified in the stabilization of the R₂ side chain of 2G-BPs into the active site, similar free binding energies were obtained that highlighted a similar stability of the ternary complexes, which in turns justified the similar IC₅₀ values reported. Free binding energy calculations also demonstrated that the union of 2G-BPs to the active site were 38 to 54 kcal mol^-1 energetically more favourable than the union of the natural substrate, which is the basis of the inhibition potency of the hFPPS activity.

Accurate Three States Model for Amino Acids with Two Chemically Coupled Titrating Sites in Explicit Solvent Atomistic Constant pH Simulations and pK(a) Calculations

Correct protonation of titratable groups in biomolecules is crucial for their accurate description by molecular dynamics simulations. In the context of constant pH simulations, an additional protonation degree of freedom is introduced for each titratable site, allowing the protonation state to change dynamically with changing structure or electrostatics. Here, we extend previous approaches for an accurate description of chemically coupled titrating sites. A second reaction coordinate is used to switch between two tautomeric states of an amino acid with chemically coupled titratable sites, such as aspartate (Asp), glutamate (Glu), and histidine (His). To this aim, we test a scheme involving three protonation states. To facilitate charge neutrality as required for periodic boundary conditions and Particle Mesh Ewald (PME) electrostatics, titration of each respective amino acid is coupled to a "water" molecule that is charged in the opposite direction. Additionally, a force field modification for Amber99sb is introduced and tested for the description of carboxyl group protonation. Our three states model is tested by titration simulations of Asp, Glu, and His, yielding a good agreement, reproducing the correct geometry of the groups in their different protonation forms. We further show that the ion concentration change due to the neutralizing "water" molecules does not significantly affect the protonation free energies of the titratable groups, suggesting that the three states model provides a good description of biomolecular dynamics at constant pH.

Constant-pH Hybrid Nonequilibrium Molecular Dynamics-Monte Carlo Simulation Method

A computational method is developed to carry out explicit solvent simulations of complex molecular systems under conditions of constant pH. In constant-pH simulations, preidentified ionizable sites are allowed to spontaneously protonate and deprotonate as a function of time in response to the environment and the imposed pH. The method, based on a hybrid scheme originally proposed by H. A. Stern (J. Chem. Phys. 2007, 126, 164112), consists of carrying out short nonequilibrium molecular dynamics (neMD) switching trajectories to generate physically plausible configurations with changed protonation states that are subsequently accepted or rejected according to a Metropolis Monte Carlo (MC) criterion. To ensure microscopic detailed balance arising from such nonequilibrium switches, the atomic momenta are altered according to the symmetric two-ends momentum reversal prescription. To achieve higher efficiency, the original neMD-MC scheme is separated into two steps, reducing the need for generating a large number of unproductive and costly nonequilibrium trajectories. In the first step, the protonation state of a site is randomly attributed via a Metropolis MC process on the basis of an intrinsic pKa; an attempted nonequilibrium switch is generated only if this change in protonation state is accepted. This hybrid two-step inherent pKa neMD-MC simulation method is tested with single amino acids in solution (Asp, Glu, and His) and then applied to turkey ovomucoid third domain and hen egg-white lysozyme. Because of the simple linear increase in the computational cost relative to the number of titratable sites, the present method is naturally able to treat extremely large systems.

Charge-Neutral Constant pH Molecular Dynamics Simulations Using a Parsimonious Proton Buffer

In constant pH molecular dynamics simulations, the protonation states of titratable sites can respond to changes of the pH and of their electrostatic environment. Consequently, the number of protons bound to the biomolecule, and therefore the overall charge of the system, fluctuates during the simulation. To avoid artifacts associated with a non-neutral simulation system, we introduce an approach to maintain neutrality of the simulation box in constant pH molecular dynamics simulations, while maintaining an accurate description of all protonation fluctuations. Specifically, we introduce a proton buffer that, like a buffer in experiment, can exchange protons with the biomolecule enabling its charge to fluctuate. To keep the total charge of the system constant, the uptake and release of protons by the buffer are coupled to the titration of the biomolecule with a constraint. We find that, because the fluctuation of the total charge (number of protons) of a typical biomolecule is much smaller than the number of titratable sites of the biomolecule, the number of buffer sites required to maintain overall charge neutrality without compromising the charge fluctuations of the biomolecule, is typically much smaller than the number of titratable sites, implying markedly enhanced simulation and sampling efficiency.

Accurate calculation of the absolute free energy of binding for drug molecules

Accurate prediction of binding affinities has been a central goal of computational chemistry for decades, yet remains elusive. Despite good progress, the required accuracy for use in a drug-discovery context has not been consistently achieved for drug-like molecules. Here, we perform absolute free energy calculations based on a thermodynamic cycle for a set of diverse inhibitors binding to bromodomain-containing protein 4 (BRD4) and demonstrate that a mean absolute error of 0.6 kcal mol-1 can be achieved. We also show a similar level of accuracy (1.0 kcal mol-1) can be achieved in pseudo prospective approach. Bromodomains are epigenetic mark readers that recognize acetylation motifs and regulate gene transcription, and are currently being investigated as therapeutic targets for cancer and inflammation. The unprecedented accuracy offers the exciting prospect that the binding free energy of drug-like compounds can be predicted for pharmacologically relevant targets.

The effect of solvent heterogeneity on the solvation and complexation of alkali cations by 18-crown-6: a simulation study in the 90 : 10 chloroform/methanol mixture

Although chloroform is in excess over methanol in the mixture, the predicted ion binding affinities and selectivities are more “methanol-like” than “chloroform-like”.

Thermodynamics of DNA: sensitizer recognition. Characterizing binding motifs with all-atom simulations

We report the investigation of the thermochemical properties of benzophenone interacting with B-DNA studied by all-atom molecular dynamic simulations.

Liquid–liquid extraction of alkali cations by 18-crown-6: complexation and interface crossing studied by MD and PMF simulations

The 18C6/M⁺Pic⁻complexes form and adsorb “right at the nano-interface” where 18C6 prefers the K⁺guest.

Fast Switching Alchemical Transformations in Molecular Dynamics Simulations

We present an efficient and rigorous implementation of the fast switching alchemical transformation for systems where electrostatic interactions are treated using the smooth particle mesh Ewald method. Free energies are computed using bidirectional nonequilibrium alchemical trajectories by applying the Crooks fluctuation theorem and the Bennett acceptance ratio to the collection of the final alchemical works. The technique is used for the evaluation of the 1-octanol/water partition coefficients for some selected organic molecules. Fast switching alchemical tranformations appear to be competitive, both in accuracy and in efficiency, with respect to the traditional methods based on independent equilibrium simulations of intermediate states.

Milestones in the Activation of a G Protein-Coupled Receptor. Insights from Molecular-Dynamics Simulations into the Human Cholecystokinin Receptor-1

Activation of G protein-coupled receptors (GPCRs) obeys an allosteric mechanism triggered by ligand binding. To understand how the signal is transduced in the cell, identification of the milestones paving the pathway between the active and the inactive states of the receptor is necessary. A model of the human cholecystokinin receptor-1 (CCK1R) has been proposed recently. The complex formed by CCK1R and an agonist ligand will serve as a paradigm of an active conformation to capture milestones in GPCR activation. To reach this goal, assuming microreversibility, the initial step toward the inactivation of CCK1R was modeled using free energy calculations, whereby the ligand is removed from the binding pocket. However accurate the reproduction of the experimental affinity constant, this simulation only represents an embryonic stage of the inactivation process. Starting from the apo receptor, an unprecedented 0.1-μs molecular dynamics trajectory was generated, bereft of experimental biases, bringing into the light key events in the inactivation of CCK1R, chief among which the hydration of its internal cavity, concomitant with the spatial rearrangement of the transmembrane helical segments. Hydration is intimately related to the isomerization of the highly conserved residue W326 of helix VI, acting as a two-state toggle switch, and of residue M121 of helix III. In the active state, the former residue obstructs the crevice, thereby preventing water leakage, which would otherwise trigger the disruption of an ionic lock between helices II and III involving the signature E/DRY motif ubiquitous to GPCRs.

Accurate Estimates of Free Energy Changes in Charge Mutations

The ability to determine the effect of charge changes on the free energy is necessary for fundamental studies of the electrostatic contribution to protein binding and stability. Currently, calculations of differences in free energy for charge mutations carried out in systems with periodic boundary conditions must include an approximate self-energy correction that can be on the same order of magnitude as the calculated free energy change. Here, a new method for accurately calculating the free energy change associated with any alchemical mutation, regardless of charge, is presented. In this method, paired mutations of opposite charge exactly cancel the self-energy term because of its quadratic charge dependence. Since the self-energy term implicitly cancels within the method, a correction never needs to be applied, and the statistical uncertainty associated is thereby removed. An implementation procedure is described and applied to the free energy of ionic hydration and a charged amino acid mutation.

Calculation of free energy changes due to mutations from alchemical free energy simulations

How a mutation affects the binding free energy of a ligand is a fundamental problem in molecular biology/biochemistry with many applications in pharmacology and biotechnology, e.g. design of drugs and enzymes. Free energy change due to a mutation can be determined most accurately by performing alchemical free energy calculations in molecular dynamics (MD) simulations. Here we discuss the necessary conditions for success of free energy calculations using toxin peptides that bind to ion channels as examples. We show that preservation of the binding mode is an essential requirement but this condition is not always satisfied, especially when the mutation involves a charged residue. Otherwise problems with accuracy of results encountered in mutation of charged residues can be overcome by performing the mutation on the ligand in the binding site and bulk simultaneously and in the same system. The proposed method will be useful in improving the affinity and selectivity profiles of drug leads and enzymes via computational design and protein engineering.

Effects of system net charge and electrostatic truncation on all-atom constant pH molecular dynamics

Constant pH molecular dynamics offers a means to rigorously study the effects of solution pH on dynamical processes. Here, we address two critical questions arising from the most recent developments of the all-atom continuous constant pH molecular dynamics (CpHMD) method: (1) What is the effect of spatial electrostatic truncation on the sampling of protonation states? (2) Is the enforcement of electrical neutrality necessary for constant pH simulations? We first examined how the generalized reaction field and force-shifting schemes modify the electrostatic forces on the titration coordinates. Free energy simulations of model compounds were then carried out to delineate the errors in the deprotonation free energy and salt-bridge stability due to electrostatic truncation and system net charge. Finally, CpHMD titration of a mini-protein HP36 was used to understand the manifestation of the two types of errors in the calculated pK(a) values. The major finding is that enforcing charge neutrality under all pH conditions and at all time via cotitrating ions significantly improves the accuracy of protonation-state sampling. We suggest that such finding is also relevant for simulations with particle mesh Ewald, considering the known artifacts due to charge-compensating background plasma.

Practical Aspects of Free-Energy Calculations: A Review

Free-energy calculations in the framework of classical molecular dynamics simulations are nowadays used in a wide range of research areas including solvation thermodynamics, molecular recognition, and protein folding. The basic components of a free-energy calculation, that is, a suitable model Hamiltonian, a sampling protocol, and an estimator for the free energy, are independent of the specific application. However, the attention that one has to pay to these components depends considerably on the specific application. Here, we review six different areas of application and discuss the relative importance of the three main components to provide the reader with an organigram and to make nonexperts aware of the many pitfalls present in free energy calculations.

Analyzing machupo virus-receptor binding by molecular dynamics simulations

In many biological applications, we would like to be able to computationally predict mutational effects on affinity in protein-protein interactions. However, many commonly used methods to predict these effects perform poorly in important test cases. In particular, the effects of multiple mutations, non alanine substitutions, and flexible loops are difficult to predict with available tools and protocols. We present here an existing method applied in a novel way to a new test case; we interrogate affinity differences resulting from mutations in a host-virus protein-protein interface. We use steered molecular dynamics (SMD) to computationally pull the machupo virus (MACV) spike glycoprotein (GP1) away from the human transferrin receptor (hTfR1). We then approximate affinity using the maximum applied force of separation and the area under the force-versus-distance curve. We find, even without the rigor and planning required for free energy calculations, that these quantities can provide novel biophysical insight into the GP1/hTfR1 interaction. First, with no prior knowledge of the system we can differentiate among wild type and mutant complexes. Moreover, we show that this simple SMD scheme correlates well with relative free energy differences computed via free energy perturbation. Second, although the static co-crystal structure shows two large hydrogen-bonding networks in the GP1/hTfR1 interface, our simulations indicate that one of them may not be important for tight binding. Third, one viral site known to be critical for infection may mark an important evolutionary suppressor site for infection-resistant hTfR1 mutants. Finally, our approach provides a framework to compare the effects of multiple mutations, individually and jointly, on protein-protein interactions.

Computation of standard binding free energies of polar and charged ligands to the glutamate receptor GluA2

Accurate calculation of the binding affinity of small molecules to proteins has the potential to become an important tool in rational drug design. In this study, we use the free energy perturbation (FEP) method with restraints to calculate the standard binding free energy of five ligands (ACPA, AMPA, CNQX, DNQX, and glutamate) to the glutamate receptor GluA2, which plays an essential role in synaptic transmission. To deal with the convergence problem in FEP calculations with charged ligands, we use a protocol where the ligand is coupled in the binding site while it is decoupled in bulk solution simultaneously. The contributions from the conformational, rotational, and translational entropies to the standard binding free energy are determined by applying/releasing respective restraints to the ligand in bulk/binding site. We also employ the confine-and-release approach, which helps to resolve convergence problems in FEP calculations. Our results are in good agreement with the experimental values for all five ligands, including the charged ones which are often problematic in FEP calculations. We also analyze the different contributions to the binding free energy of each ligand to GluA2 and discuss the nature of these interactions.

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: an accurate correction scheme for electrostatic finite-size effects

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol(-1)). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.