Ligand-receptor interactions

Rapid, Accurate, Ranking of Protein-Ligand Binding Affinities with VM2, the Second-Generation Mining Minima Method

The structure-based technologies most widely used to rank the affinities of candidate small molecule drugs for proteins range from faster but less reliable docking methods to slower but more accurate explicit solvent free energy methods. In recent years, we have advanced another technology, which is called mining minima because it "mines" out the main contributions to the chemical potentials of the free and bound molecular species by identifying and characterizing their main local energy minima. The present study provides systematic benchmarks of the accuracy and computational speed of mining minima, as implemented in the VeraChem Mining Minima Generation 2 (VM2) code, across two well-regarded protein-ligand benchmark data sets, for which there are already benchmark data for docking, free energy, and other computational methods. A core result is that VM2's accuracy approaches that of explicit solvent free energy methods at a far lower computational cost. In finer-grained analyses, we also examine the influence of various run settings, such as the treatment of crystallographic water molecules, on the accuracy, and define the costs in time and dollars of representative runs on Amazon Web Services (AWS) compute instances with various CPU and GPU combinations. We also use the benchmark data to determine the importance of VM2's correction from generalized Born to finite-difference Poisson-Boltzmann results for each energy well and find that this correction affords a remarkably consistent improvement in accuracy at a modest computational cost. The present results establish VM2 as a distinctive technology for early-stage drug discovery, which provides a strong combination of efficiency and predictivity.

DeltaGzip: Computing Biopolymer-Ligand Binding Affinity via Kolmogorov Complexity and Lossless Compression

The design of biosequences for biosensing and therapeutics is a challenging multistep search and optimization task. In principle, computational modeling may speed up the design process by virtual screening of sequences based on their binding affinities to target molecules. However, in practice, existing machine-learned models trained to predict binding affinities lack the flexibility with respect to reaction conditions, and molecular dynamics simulations that can incorporate reaction conditions suffer from high computational costs. Here, we describe a computational approach called DeltaGzip that evaluates the free energy of binding in biopolymer-ligand complexes from ultrashort equilibrium molecular dynamics simulations. The entropy of binding is evaluated using the Kolmogorov complexity definition of entropy and approximated using a lossless compression algorithm, Gzip. We benchmark the method on a well-studied data set of protein-ligand complexes comparing the predictions of DeltaGzip to the free energies of binding obtained using Jarzynski equality and experimental measurements.

GENESIS 2.1: High-Performance Molecular Dynamics Software for Enhanced Sampling and Free-Energy Calculations for Atomistic, Coarse-Grained, and Quantum Mechanics/Molecular Mechanics Models

GENeralized-Ensemble SImulation System (GENESIS) is a molecular dynamics (MD) software developed to simulate the conformational dynamics of a single biomolecule, as well as molecular interactions in large biomolecular assemblies and between multiple biomolecules in cellular environments. To achieve the latter purpose, the earlier versions of GENESIS emphasized high performance in atomistic MD simulations on massively parallel supercomputers, with or without graphics processing units (GPUs). Here, we implemented multiscale MD simulations that include atomistic, coarse-grained, and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations. They demonstrate high performance and are integrated with enhanced conformational sampling algorithms and free-energy calculations without using external programs except for the QM programs. In this article, we review new functions, molecular models, and other essential features in GENESIS version 2.1 and discuss ongoing developments for future releases.

Interplay of halogen bonding and solvation in protein-ligand binding

Halogen bonding is increasingly utilized in efforts to achieve high affinity and selectivity of molecules designed to bind proteins, making it paramount to understand the relationship between structure, dynamics, and thermodynamic driving forces. We present a detailed analysis addressing this problem using a series of protein-ligand complexes involving single halogen substitutions - F, Cl, Br, and I - and nearly identical structures. Isothermal titration calorimetry reveals an increasingly favorable binding enthalpy from F to I that correlates with the halogen size and σ-hole electropositive character, but is partially counteracted by unfavorable entropy, which is constant from F to Cl and Br, but worse for I. Consequently, the binding free energy is roughly equal for Cl, Br, and I. QM and solvation-free-energy calculations reflect an intricate balance between halogen bonding, hydrogen bonds, and solvation. These advances have the potential to aid future drug design initiatives involving halogenated compounds.

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.

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.

Understanding the sources of error in MBAR through asymptotic analysis

Many sampling strategies commonly used in molecular dynamics, such as umbrella sampling and alchemical free energy methods, involve sampling from multiple states. The Multistate Bennett Acceptance Ratio (MBAR) formalism is a widely used way of recombining the resulting data. However, the error of the MBAR estimator is not well-understood: previous error analyses of MBAR assumed independent samples. In this work, we derive a central limit theorem for MBAR estimates in the presence of correlated data, further justifying the use of MBAR in practical applications. Moreover, our central limit theorem yields an estimate of the error that can be decomposed into contributions from the individual Markov chains used to sample the states. This gives additional insight into how sampling in each state affects the overall error. We demonstrate our error estimator on an umbrella sampling calculation of the free energy of isomerization of the alanine dipeptide and an alchemical calculation of the hydration free energy of methane. Our numerical results demonstrate that the time required for the Markov chain to decorrelate in individual states can contribute considerably to the total MBAR error, highlighting the importance of accurately addressing the effect of sample correlation.

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

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

Effect of alanine versus serine at position 88 of human transthyretin mutants on the protein stability

Human transthyretin (TTR) is a homo-tetrameric plasma protein associated with a high percentage of β-sheet forming amyloid fibrils. It accumulates in tissues or extracellular matrices to cause amyloid diseases. Free energy simulations with thermodynamic integration based on all-atom molecular dynamics simulations have been carried out to analyze the effects of the His88 → Ala and Ser mutations on the stability of human TTR. The calculated free energy change differences (ΔΔG) caused by the His88 → Ala and His88 → Ser mutations are -1.84 ± 0.86 and 7.56 ± 0.55 kcal/mol, respectively, which are in excellent agreement with prior reported experimental values. The simulation results show that the H88A mutant is more stable than the wild type, whereas the H88S mutant is less stable than the wild type. The free energy component analysis shows that the contribution to the free energy change difference (ΔΔG) for the His88 → Ala and His88 → Ser mutations mainly arise from electrostatic and van der Waals interactions, respectively. The electrostatic term stabilizes the H88A mutant more than the wild type, but the van der Waals interaction destabilizes the H88S mutant relative to the wild type. Individual residue contributions to the free energy change show neighboring residues exert stabilizing and destabilizing influence on the mutants. The implications of the simulation results for understanding the stabilizing and destabilizing effect and its contribution to protein stability are discussed.

AMBER Free Energy Tools: A New Framework for the Design of Optimized Alchemical Transformation Pathways

We develop a framework for the design of optimized alchemical transformation pathways in free energy simulations using nonlinear mixing and a new functional form for so-called "softcore" potentials. We describe the implementation and testing of this framework in the GPU-accelerated AMBER software suite. The new optimized alchemical transformation pathways integrate a number of important features, including (1) the use of smoothstep functions to stabilize behavior near the transformation end points, (2) consistent power scaling of Coulomb and Lennard-Jones (LJ) interactions with unitless control parameters to maintain balance of electrostatic attractions and exchange repulsions, (3) pairwise form based on the LJ contact radius for the effective interaction distance with separation-shifted scaling, and (4) rigorous smoothing of the potential at the nonbonded cutoff boundary. The new softcore potential form is combined with smoothly transforming nonlinear λ weights for mixing specific potential energy terms, along with flexible λ-scheduling features, to enable robust and stable alchemical transformation pathways. The resulting pathways are demonstrated and tested, and shown to be superior to the traditional methods in terms of numerical stability and minimal variance of the free energy estimates for all cases considered. The framework presented here can be used to design new alchemical enhanced sampling methods, and leveraged in robust free energy workflows for large ligand data sets.

Predictive Molecular Models for Charged Materials Systems: From Energy Materials to Biomacromolecules

Electrostatic interactions play a dominant role in charged materials systems. Understanding the complex correlation between macroscopic properties with microscopic structures is of critical importance to develop rational design strategies for advanced materials. But the complexity of this challenging task is augmented by interfaces present in the charged materials systems, such as electrode-electrolyte interfaces or biological membranes. Over the last decades, predictive molecular simulations that are founded in fundamental physics and optimized for charged interfacial systems have proven their value in providing molecular understanding of physicochemical properties and functional mechanisms for diverse materials. Novel design strategies utilizing predictive models have been suggested as promising route for the rational design of materials with tailored properties. Here, an overview of recent advances in the understanding of charged interfacial systems aided by predictive molecular simulations is presented. Focusing on three types of charged interfaces found in energy materials and biomacromolecules, how the molecular models characterize ion structure, charge transport, morphology relation to the environment, and the thermodynamics/kinetics of molecular binding at the interfaces is discussed. The critical analysis brings two prominent field of energy materials and biological science under common perspective, to stimulate crossover in both research field that have been largely separated.

Use of multistate Bennett acceptance ratio method for free-energy calculations from enhanced sampling and free-energy perturbation

Multistate Bennett acceptance ratio (MBAR) works as a method to analyze molecular dynamics (MD) simulation data after the simulations have been finished. It is widely used to estimate free-energy changes between different states and averaged properties at the states of interest. MBAR allows us to treat a wide range of states from those at different temperature/pressure to those with different model parameters. Due to the broad applicability, the MBAR equations are rather difficult to apply for free-energy calculations using different types of MD simulations including enhanced conformational sampling methods and free-energy perturbation. In this review, we first summarize the basic theory of the MBAR equations and categorize the representative usages into the following four: (i) perturbation, (ii) scaling, (iii) accumulation, and (iv) full potential energy. For each, we explain how to prepare input data using MD simulation trajectories for solving the MBAR equations. MBAR is also useful to estimate reliable free-energy differences using MD trajectories based on a semi-empirical quantum mechanics/molecular mechanics (QM/MM) model and ab initio QM/MM energy calculations on the MD snapshots. We also explain how to use the MBAR software in the GENESIS package, which we call mbar_analysis, for the four representative cases. The proposed estimations of free-energy changes and thermodynamic averages are effective and useful for various biomolecular systems.

Relative binding free energy calculations with transformato: A molecular dynamics engine-independent tool

We present the software package transformato for the setup of large-scale relative binding free energy calculations. Transformato is written in Python as an open source project (https://github.com/wiederm/transformato); in contrast to comparable tools, it is not closely tied to a particular molecular dynamics engine to carry out the underlying simulations. Instead of alchemically transforming a ligand L₁ directly into another L₂, the two ligands are mutated to a common core. Thus, while dummy atoms are required at intermediate states, in particular at the common core state, none are present at the physical endstates. To validate the method, we calculated 76 relative binding free energy differences ΔΔGL1→L2bind for five protein–ligand systems. The overall root mean squared error to experimental binding free energies is 1.17 kcal/mol with a Pearson correlation coefficient of 0.73. For selected cases, we checked that the relative binding free energy differences between pairs of ligands do not depend on the choice of the intermediate common core structure. Additionally, we report results with and without hydrogen mass reweighting. The code currently supports OpenMM, CHARMM, and CHARMM/OpenMM directly. Since the program logic to choose and construct alchemical transformation paths is separated from the generation of input and topology/parameter files, extending transformato to support additional molecular dynamics engines is straightforward.

Free energy simulations to study mutational effect of a conserved residue, Trp24, on stability of human serum retinol-binding protein

Human serum retinol-binding protein (RBP) is a plasma transport protein for vitamin A. RBP is a prime subclass of lipocalins, which bind nonpolar ligands within a β-barrel. To understand the role of Trp 24, one of the highly conserved residues in RBP, free energy simulations have been carried out to understand the effects of the mutations from Trp at position 24 to Leu, Phe, and Tyr in the apo-RBP on its thermal stability. We examine various unfolded systems to study the dependence of the free energy differences on the denatured structure. Our calculated free energy difference values for the three mutations are in excellent agreement with the experimental values when the initial coordinates of the seven-residue peptide segments truncated from the crystal structure are used for the denatured systems. Our free energy change differences for the Trp→Leu, Trp→Phe, and Trp→Tyr mutations are 2.50 ± 0.69, 2.58 ± 0.50, and 2.49 ± 0.48 kcal/mol, respectively, when the native-like seven-residue peptides are used as models for the denatured systems. The main contributions to the free energy change differences for the Trp24→Leu and Trp24→Phe mutations are mainly from van der Waals and covalent interactions, respectively. Electrostatic, van der Waals and covalent terms equally contribute to the free energy change difference for the Trp24→Tyr mutation. The free energy simulation helps understand the detailed microscopic mechanism of the stability of the RBP mutants relative to the wild type and the role of the highly conserved residue, Trp24, of the human RBP.Communicated by Ramaswamy H. Sarma.

Simulation analysis of selective alanine mutation effect on stability of human prion protein

Prion diseases are neurodegenerative disorders caused by spongiform degeneration of the brain. Understanding the fundamental mechanism of prion protein aggregation caused by mutations is very crucial to resolve the pathology of prion diseases. To help understand the roles of individual residues on the stability of the human prion protein, the computational method of free energy simulations based on atomistic molecular dynamics trajectories is applied to Phe175 → Ala, Val180 → Ala, and Val209 → Ala mutations of the human prion protein. The simulations show that all three alanine mutations destabilize the human prion protein. The calculated free energy change differences, ΔΔG, for the Phe175 → Ala, Val180 → Ala, and Val209 → Ala mutations are in good agreement with the experimental values. The significant destabilizing effects on the mutants relative to the wild-type protein arise from van der Waals terms. Furthermore, our free energy decomposition analysis shows that the major contribution to destabilizing the V180A and V209A mutants relative to the wild-type protein is originated from van der Waals interactions from residues near the mutation sites. In contrast, the contribution to destabilizing the F175A mutant is mainly caused by van der Waals interactions from residues near and far away from the mutation site. Our results show that the free energy simulation with a thermodynamic integration approach for selected alanine scanning mutations is beneficial for understanding the detailed mechanism of human prion protein destabilization, specific residues' role, and the hydrophobic effect on protein stability.Communicated by Ramaswamy H. Sarma.

Relative Binding Free-Energy Calculations at Lipid-Exposed Sites: Deciphering Hot Spots

Relative binding free-energy (RBFE) calculations are experiencing resurgence in the computer-aided drug design of novel small molecules due to performance gains allowed by cutting-edge molecular mechanic force fields and computer hardware. Application of RBFE to soluble proteins is becoming a routine, while recent studies outline necessary steps to successfully apply RBFE at the orthosteric site of membrane-embedded G-protein-coupled receptors (GPCRs). In this work, we apply RBFE to a congeneric series of antagonists that bind to a lipid-exposed, extra-helical site of the P2Y1 receptor. We find promising performance of RBFE, such that it may be applied in a predictive manner on drug discovery programs targeting lipid-exposed sites. Further, by the application of the microkinetic model, binding at a lipid-exposed site can be split into (1) membrane partitioning of the drug molecule followed by (2) binding at the extra-helical site. We find that RBFE can be applied to calculate the free energy of each step, allowing the uncoupling of observed binding free energy from the influence of membrane affinity. This protocol may be used to identify binding hot spots at extra-helical sites and guide drug discovery programs toward optimizing intrinsic activity at the target.

Fast Equilibration of Water between Buried Sites and the Bulk by Molecular Dynamics with Parallel Monte Carlo Water Moves on Graphical Processing Units

Molecular dynamics (MD) simulations of proteins are commonly used to sample from the Boltzmann distribution of conformational states, with wide-ranging applications spanning chemistry, biophysics, and drug discovery. However, MD can be inefficient at equilibrating water occupancy for buried cavities in proteins that are inaccessible to the surrounding solvent. Indeed, the time needed for water molecules to equilibrate between the bulk solvent and the binding site can be well beyond what is practical with standard MD, which typically ranges from hundreds of nanoseconds to a few microseconds. We recently introduced a hybrid Monte Carlo/MD (MC/MD) method, which speeds up the equilibration of water between buried cavities and the surrounding solvent, while sampling from the thermodynamically correct distribution of states. While the initial implementation of the MC functionality led to considerable slowing of the overall simulations, here we address this problem with a parallel MC algorithm implemented on graphical processing units. This results in speed-ups of 10-fold to 1000-fold over the original MC/MD algorithm, depending on the system and simulation parameters. The present method is available for use in the AMBER simulation software.

Rimantadine Binds to and Inhibits the Influenza A M2 Proton Channel without Enantiomeric Specificity

The influenza A M2 wild-type (WT) proton channel is the target of the anti-influenza drug rimantadine. Rimantadine has two enantiomers, though most investigations into drug binding and inhibition have used a racemic mixture. Solid-state NMR experiments using the full length-M2 WT have shown significant spectral differences that were interpreted to indicate tighter binding for (R)- vs (S)-rimantadine. However, it was unclear if this correlates with a functional difference in drug binding and inhibition. Using X-ray crystallography, we have determined that both (R)- and (S)-rimantadine bind to the M2 WT pore with slight differences in the hydration of each enantiomer. However, this does not result in a difference in potency or binding kinetics, as shown by similar values for kon, koff, and Kd in electrophysiological assays and for EC50 values in cellular assays. We concluded that the slight differences in hydration for the (R)- and (S)-rimantadine enantiomers are not relevant to drug binding or channel inhibition. To further explore the effect of the hydration of the M2 pore on binding affinity, the water structure was evaluated by grand canonical ensemble molecular dynamics simulations as a function of the chemical potential of the water. Initially, the two layers of ordered water molecules between the bound drug and the channel's gating His37 residues mask the drug's chirality. As the chemical potential becomes more unfavorable, the drug translocates down to the lower water layer, and the interaction becomes more sensitive to chirality. These studies suggest the feasibility of displacing the upper water layer and specifically recognizing the lower water layers in novel drugs.

Energy-entropy method using multiscale cell correlation to calculate binding free energies in the SAMPL8 host-guest challenge

Free energy drives a wide range of molecular processes such as solvation, binding, chemical reactions and conformational change. Given the central importance of binding, a wide range of methods exist to calculate it, whether based on scoring functions, machine-learning, classical or electronic structure methods, alchemy, or explicit evaluation of energy and entropy. Here we present a new energy-entropy (EE) method to calculate the host-guest binding free energy directly from molecular dynamics (MD) simulation. Entropy is evaluated using Multiscale Cell Correlation (MCC) which uses force and torque covariance and contacts at two different length scales. The method is tested on a series of seven host-guest complexes in the SAMPL8 (Statistical Assessment of the Modeling of Proteins and Ligands) "Drugs of Abuse" Blind Challenge. The EE-MCC binding free energies are found to agree with experiment with an average error of 0.9 kcal mol-1. MCC makes clear the origin of the entropy changes, showing that the large loss of positional, orientational, and to a lesser extent conformational entropy of each binding guest is compensated for by a gain in orientational entropy of water released to bulk, combined with smaller decreases in vibrational entropy of the host, guest and contacting water.

Dummy Atoms in Alchemical Free Energy Calculations

In calculations of relative free energy differences, the number of atoms of the initial and final states is rarely the same. This necessitates the introduction of dummy atoms. These placeholders interact with the physical system only by bonded energy terms. We investigate the conditions necessary so that the presence of dummy atoms does not influence the result of a relative free energy calculation. On the one hand, one has to ensure that dummy atoms only give a multiplicative contribution to the partition function so that their contribution cancels from double-free energy differences. On the other hand, the bonded terms used to attach a dummy atom (or group of dummy atoms) to the physical system have to maintain it in a well-defined position and orientation relative to the physical system. A detailed theoretical analysis of both aspects is provided, illustrated by 24 calculations of relative solvation free energy differences, for which all four legs of the underlying thermodynamic cycle were computed. Cycle closure (or lack thereof) was used as a sensitive indicator to probing the effects of dummy atom treatment on the resulting free energy differences. We find that a naive (but often practiced) treatment of dummy atoms results in errors of up to kBT when calculating the relative solvation free energy difference between two small solutes, such as methane and ammonia. While our analysis focuses on the so-called single topology approach to set up alchemical transformations, similar considerations apply to dual topology, at least many widely used variants thereof.

Free energy simulations to understand the effect of Met → Ala mutations at positions 205, 206 and 213 on stability of human prion protein

Prion diseases are a family of infectious amyloid diseases affecting human and animals. Prion propagation in transmissible spongiform encephalopathies is associated with the unfolding and conversion of normal cellular prion protein into its pathogenic scrapie form. Understanding the fundamentals of prion protein aggregation caused by mutations is crucial to unravel the pathology of prion diseases. To help understand the contributions of individual residues to the stability of the human prion protein, we have carried out free energy simulations based on atomistic molecular dynamics trajectories. We focus on Met → Ala mutations at positions 205, 206 and 213, which are mostly buried residues located on helix 3 of the protein. The simulations predicted that all three mutations destabilize the prion protein. Changes in unfolding free energy upon mutation, ∆∆G, are 3.10 ± 0.79, 2.00 ± 0.26 and 3.06 ± 0.66 kcal/mol for M205A, M206A and M213A, respectively, in excellent agreement with the corresponding experimental values of 3.09 ± 0.28, 1.50 ± 0.34 and 3.12 ± 0.27 kcal/mol [T. Hart et al. (2009) PNAS 106, 5651-5656]. Component analysis indicates that the major contributions to the loss of protein stability arise from van der Waals interactions for the M205A and M206A mutations, and from van der Waals and covalent energy terms for M213A. Interestingly, while free energy contributions from a majority of residues neighboring the mutation sites tend to stabilize the wild type, there are a few residues stabilizing the mutant side chains. Our results show that this approach to free energy calculation can be very useful for understanding the detailed mechanism of human prion protein stability.

Exploring the Minimum-Energy Pathways and Free-Energy Profiles of Enzymatic Reactions with QM/MM Calculations

Understanding molecular mechanisms of enzymatic reactions is of vital importance in biochemistry and biophysics. Here, we introduce new functions of hybrid quantum mechanical/molecular mechanical (QM/MM) calculations in the GENESIS program to compute the minimum-energy pathways (MEPs) and free-energy profiles of enzymatic reactions. For this purpose, an interface in GENESIS is developed to utilize a highly parallel electronic structure program, QSimulate-QM (https://qsimulate.com), calling it as a shared library from GENESIS. Second, algorithms to search the MEP are implemented, combining the string method (E et al. J. Chem. Phys. 2007, 126, 164103) with the energy minimization of the buffer MM region. The method implemented in GENESIS is applied to an enzyme, triosephosphate isomerase, which converts dihyroxyacetone phosphate to glyceraldehyde 3-phosphate in four proton-transfer processes. QM/MM-molecular dynamics simulations show performances of greater than 1 ns/day with the density functional tight binding (DFTB), and 10-30 ps/day with the hybrid density functional theory, B3LYP-D3. These performances allow us to compute not only MEP but also the potential of mean force (PMF) of the enzymatic reactions using the QM/MM calculations. The barrier height obtained as 13 kcal mol-1 with B3LYP-D3 in the QM/MM calculation is in agreement with the experimental results. The impact of conformational sampling in PMF calculations and the level of electronic structure calculations (DFTB vs B3LYP-D3) suggests reliable computational protocols for enzymatic reactions without high computational costs.

Molecular mechanism of secreted amyloid-β precursor protein in binding and modulating GABABR1a

A recent phenomenal study discovered that the extension domain of secreted amyloid-β precursor protein (sAPP) can bind to the intrinsically disordered sushi 1 domain of the γ-aminobutyric acid type B receptor subunit 1a (GABA_BR1a) and modulate its synaptic transmission. The work provided an important structural foundation for the modulation of GABA_BR1a; however, the detailed molecular interaction mechanism, crucial for future drug design, remains elusive. Here, we further investigated the dynamical interactions between sAPP peptides and the natively unstructured sushi 1 domain using all-atom molecular dynamics simulations, for both the 17-residue sAPP peptide (APP 17-mer) and its minimally active 9 residue segment (APP 9-mer). We then explored mutations of the APP 9-mer with rigorous free energy perturbation (FEP) calculations. Our in silico mutagenesis studies revealed key residues (D4, W6, and W7) responsible for the binding with the sushi 1 domain. More importantly, one double mutation based on different vertebrate APP sequences from evolution exhibited a stronger binding (ΔΔG = −1.91 ± 0.66 kcal mol⁻¹), indicating a potentially enhanced GABA_BR1a modulator. These large-scale simulations may provide new insights into the binding mechanism between sAPP and the sushi 1 domain, which could open new avenues in the development of future GABA_BR1a-specific therapeutics.

A recent phenomenal study discovered that the extension domain of secreted amyloid-β precursor protein (sAPP) can bind to the intrinsically disordered sushi 1 domain of the γ-aminobutyric acid type B receptor subunit 1a (GABA_BR1a) and modulate its synaptic transmission.

Automation of absolute protein-ligand binding free energy calculations for docking refinement and compound evaluation

Absolute binding free energy calculations with explicit solvent molecular simulations can provide estimates of protein-ligand affinities, and thus reduce the time and costs needed to find new drug candidates. However, these calculations can be complex to implement and perform. Here, we introduce the software BAT.py, a Python tool that invokes the AMBER simulation package to automate the calculation of binding free energies for a protein with a series of ligands. The software supports the attach-pull-release (APR) and double decoupling (DD) binding free energy methods, as well as the simultaneous decoupling-recoupling (SDR) method, a variant of double decoupling that avoids numerical artifacts associated with charged ligands. We report encouraging initial test applications of this software both to re-rank docked poses and to estimate overall binding free energies. We also show that it is practical to carry out these calculations cheaply by using graphical processing units in common machines that can be built for this purpose. The combination of automation and low cost positions this procedure to be applied in a relatively high-throughput mode and thus stands to enable new applications in early-stage drug discovery.

Free Energy Calculations for Protein-Ligand Binding Prediction

Computational prediction of protein-ligand binding involves initial determination of the binding mode and subsequent evaluation of the strength of the protein-ligand interactions, which directly correlates with ligand binding affinities. As a consequence of increasing computer power, rigorous approaches to calculate protein-ligand binding affinities, such as free energy perturbation (FEP) methods, are becoming an essential part of the toolbox of computer-aided drug design. In this chapter, we provide a general overview of these methods and introduce the QFEP modules, which are open-source API workflows based on our molecular dynamics (MD) package Q. The module QligFEP allows estimation of relative binding affinities along ligand series, while QresFEP is a module to estimate binding affinity shifts caused by single-point mutations of the protein. We herein provide guidelines for the use of each of these modules based on data extracted from ligand-design projects. While these modules are stand-alone, the combined use of the two workflows in a drug-design project yields complementary perspectives of the ligand binding problem, providing two sides of the same coin. The selected case studies illustrate how to use QFEP to approach the two key questions associated with ligand binding prediction: identifying the most favorable binding mode from different alternatives and establishing structure-affinity relationships that allow the rational optimization of hit compounds.

Accounting for the Central Role of Interfacial Water in Protein-Ligand Binding Free Energy Calculations

Rigorous binding free energy methods in drug discovery are growing in popularity because of a combination of methodological advances, improvements in computer hardware, and workflow automation. These calculations typically use molecular dynamics (MD) to sample from the Boltzmann distribution of conformational states. However, when part or all of the binding sites is inaccessible to the bulk solvent, the time needed for water molecules to equilibrate between bulk solvent and the binding site can be well beyond what is practical with standard MD. This sampling limitation is problematic in relative binding free energy calculations, which compute the reversible work of converting ligand 1 to ligand 2 within the binding site. Thus, if ligand 1 is smaller and/or more polar than ligand 2, the perturbation may allow additional water molecules to occupy a region of the binding site. However, this change in hydration may not be captured by standard MD simulations and may therefore lead to errors in the computed free energy. We recently developed a hybrid Monte Carlo/MD (MC/MD) method, which speeds up the equilibration of water between bulk solvent and buried cavities, while sampling from the intended distribution of states. Here, we report on the use of this approach in the context of alchemical binding free energy calculations. We find that using MC/MD markedly improves the accuracy of the calculations and also reduces hysteresis between the forward and reverse perturbations, relative to matched calculations using only MD with or without the crystallographic water molecules. The present method is available for use in AMBER simulation software.

Alchemical Binding Free Energy Calculations in AMBER20: Advances and Best Practices for Drug Discovery

Predicting protein-ligand binding affinities and the associated thermodynamics of biomolecular recognition is a primary objective of structure-based drug design. Alchemical free energy simulations offer a highly accurate and computationally efficient route to achieving this goal. While the AMBER molecular dynamics package has successfully been used for alchemical free energy simulations in academic research groups for decades, widespread impact in industrial drug discovery settings has been minimal because of the previous limitations within the AMBER alchemical code, coupled with challenges in system setup and postprocessing workflows. Through a close academia-industry collaboration we have addressed many of the previous limitations with an aim to improve accuracy, efficiency, and robustness of alchemical binding free energy simulations in industrial drug discovery applications. Here, we highlight some of the recent advances in AMBER20 with a focus on alchemical binding free energy (BFE) calculations, which are less computationally intensive than alternative binding free energy methods where full binding/unbinding paths are explored. In addition to scientific and technical advances in AMBER20, we also describe the essential practical aspects associated with running relative alchemical BFE calculations, along with recommendations for best practices, highlighting the importance not only of the alchemical simulation code but also the auxiliary functionalities and expertise required to obtain accurate and reliable results. This work is intended to provide a contemporary overview of the scientific, technical, and practical issues associated with running relative BFE simulations in AMBER20, with a focus on real-world drug discovery applications.

Toward Automated Free Energy Calculation with Accelerated Enveloping Distribution Sampling (A-EDS)

Free-energy perturbation (FEP) methods are commonly used in drug design to calculate relative binding free energies of different ligands to a common host protein. Alchemical ligand transformations are usually performed in multiple steps which need to be chosen carefully to ensure sufficient phase-space overlap between neighboring states. With one-step or single-step FEP techniques, a single reference state is designed that samples phase-space not only representative of a full transformation but also ideally resembles multiple ligand end states and hence allows for efficient multistate perturbations. Enveloping distribution sampling (EDS) is one example for such a method in which the reference state is created by a mathematical combination of the different ligand end states based on solid statistical mechanics. We have recently proposed a novel approach to EDS which enables efficient barrier crossing between the different end states, termed accelerated EDS (A-EDS). In this work, we further simplify the parametrization of the A-EDS reference state and demonstrate the automated calculation of multiple free-energy differences between different ligands from a single simulation in three different well-described drug design model systems.

Hydration properties of a protein at low and high pressures: Physics of pressure denaturation

Using experimentally determined structures of ubiquitin at 1 and 3000 bar, we generate sufficiently large ensembles of model structures in the native and pressure-induced (denatured) states by means of molecular dynamics simulations with explicit water. We calculate the values of a free-energy function (FEF), which comprises the hydration free energy (HFE) and the intramolecular (conformational) energy and entropy, for the two states at 1 and 3000 bar. The HFE and the conformational entropy, respectively, are calculated using our statistical-mechanical method, which has recently been shown to be accurate, and the Boltzmann-quasi-harmonic method. The HFE is decomposed into a variety of physically insightful components. We show that the FEF of the native state is lower than that of the denatured state at 1 bar, whereas the opposite is true at 3000 bar, thus being successful in reproducing the pressure denaturation. We argue that the following two quantities of hydration play essential roles in the denaturation: the WASA-dependent term in the water-entropy loss upon cavity creation for accommodating the protein (WASA is the water-accessible surface area of the cavity) and the protein-water Lennard-Jones interaction energy. At a high pressure, the mitigation of the serious water crowding in the system is the most important, and the WASA needs to be sufficiently enlarged with the increase in the excluded-volume being kept as small as possible. The denatured structure thus induced is characterized by the water penetration into the protein interior. The pressure denaturation is accompanied by a significantly large gain of water entropy.

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.

GRAM: A True Null Model for Relative Binding Affinity Predictions

Relative binding affinity prediction is a critical component in computer aided drug design. A significant amount of effort has been dedicated to developing rapid and reliable in silico methods. However, robust assessment of their performance is still a complicated issue, as it requires a performance measure applicable in the prospective setting and more importantly a true null model that defines the expected performance of being random in an objective manner. Although many performance metrics, such as the Pearson correlation coefficient (r), mean unsigned error (MUE), and root-mean-square error (RMSE), are frequently used in the literature, a true and nontrivial null model has yet been identified. To address this problem, here we introduce an interval estimate as an additional measure, namely, the prediction interval (PI), which can be estimated from the error distribution of the predictions. The benefits of using the interval estimate are (1) it provides the uncertainty range in the predicted activities, which is important in prospective applications, and (2) a true null model with well-defined PI can be established. We provide one such example termed the Gaussian Random Affinity Model (GRAM), which is based on the empirical observation that the affinity change in a typical lead optimization effort has the tendency to distribute normally N (0, σ). Having an analytically defined PI that only depends on the variation in the activities, GRAM should, in principle, allow us to compare the performance of relative binding affinity prediction methods in a standard way, ultimately critical to measuring the progress made in algorithm development.

Optimal Measurement Network of Pairwise Differences

When both the difference between two quantities and their individual values can be measured or computationally predicted, multiple quantities can be determined from the measurements or predictions of select individual quantities and select pairwise differences. These measurements and predictions form a network connecting the quantities through their differences. Here, I analyze the optimization of such networks, where the trace (A-optimal), the largest eigenvalue (E-optimal), or the determinant (D-optimal) of the covariance matrix associated with the estimated quantities are minimized with respect to the allocation of the measurement (or computational) cost to different measurements (or predictions). My statistical analysis of the performance of such optimal measurement networks-based on large sets of simulated data-suggests that they substantially accelerate the determination of the quantities and that they may be useful in applications such as the computational prediction of binding free energies of candidate drug molecules.

Receptor-Ligand Rebinding Kinetics in Confinement

Rebinding kinetics of molecular ligands plays a key role in the operation of biomachinery, from regulatory networks to protein transcription, and is also a key factor in design of drugs and high-precision biosensors. In this study, we investigate initial release and rebinding of ligands to their binding sites grafted on a planar surface, a situation commonly observed in single-molecule experiments and that occurs in vivo, e.g., during exocytosis. Via scaling arguments and molecular dynamic simulations, we analyze the dependence of nonequilibrium rebinding kinetics on two intrinsic length scales: the average separation distance between the binding sites and the total diffusible volume (i.e., height of the experimental reservoir in which diffusion takes place or average distance between receptor-bearing surfaces). We obtain time-dependent scaling laws for on rates and for the cumulative number of rebinding events. For diffusion-limited binding, the (rebinding) on rate decreases with time via multiple power-law regimes before the terminal steady-state (constant on-rate) regime. At intermediate times, when particle density has not yet become uniform throughout the diffusible volume, the cumulative number of rebindings exhibits a novel, to our knowledge, plateau behavior because of the three-dimensional escape process of ligands from binding sites. The duration of the plateau regime depends on the average separation distance between binding sites. After the three-dimensional diffusive escape process, a one-dimensional diffusive regime describes on rates. In the reaction-limited scenario, ligands with higher affinity to their binding sites (e.g., longer residence times) delay entry to the power-law regimes. Our results will be useful for extracting hidden timescales in experiments such as kinetic rate measurements for ligand-receptor interactions in microchannels, as well as for cell signaling via diffusing molecules.

QligFEP: an automated workflow for small molecule free energy calculations in Q

The process of ligand binding to a biological target can be represented as the equilibrium between the relevant solvated and bound states of the ligand. This which is the basis of structure-based, rigorous methods such as the estimation of relative binding affinities by free energy perturbation (FEP). Despite the growing capacity of computing power and the development of more accurate force fields, a high throughput application of FEP is currently hampered due to the need, in the current schemes, of an expert user definition of the "alchemical" transformations between molecules in the series explored. Here, we present QligFEP, a solution to this problem using an automated workflow for FEP calculations based on a dual topology approach. In this scheme, the starting poses of each of the two ligands, for which the relative affinity is to be calculated, are explicitly present in the MD simulations associated with the (dual topology) FEP transformation, making the perturbation pathway between the two ligands univocal. We show that this generalized method can be applied to accurately estimate solvation free energies for amino acid sidechain mimics, as well as the binding affinity shifts due to the chemical changes typical of lead optimization processes. This is illustrated in a number of protein systems extracted from other FEP studies in the literature: inhibitors of CDK2 kinase and a series of A2A adenosine G protein-coupled receptor antagonists, where the results obtained with QligFEP are in excellent agreement with experimental data. In addition, our protocol allows for scaffold hopping perturbations to identify the binding affinities between different core scaffolds, which we illustrate with a series of Chk1 kinase inhibitors. QligFEP is implemented in the open-source MD package Q, and works with the most common family of force fields: OPLS, CHARMM and AMBER.

Host-Guest Relative Binding Affinities at Density-Functional Theory Level from Semiempirical Molecular Dynamics Simulations

Relative free energies for the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host were calculated at the combined density-functional theory and molecular mechanics (DFT/MM) level of theory. The DFT calculations employed the BLYP functional and the 6-31G* basis set for the ligand. We employed free-energy perturbations (FEP) with the reference-potential approach and used molecular dynamics (MD) simulations with the semiempirical quantum mechanical (SQM) PM6-DH+ method for the ligand as an intermediate level between MM and DFT/MM to improve the convergence. Thus, the relative binding free energy of two ligands was first calculated at the MM level by an alchemical transformation from one ligand to another in both the bound and unbound states. Then, for each ligand the free-energy correction for going from the MM to the SQM/MM potentials was calculated using explicit SQM/MM MD simulations. Finally, the free-energy correction for going from the SQM/MM to the DFT/MM potentials was estimated with FEP without running any DFT/MM simulations. Instead, the free energy was calculated by single-step exponential averaging (ssEA) or employing the cumulant approximation to the second order (CA). The results show that CA converges much better than ssEA, and with 500-4500 DFT/MM single-point energy calculations, converged free energies with a precision of 0.3 kJ/mol can be obtained. These free energies reproduce the experimental binding free energy differences with a mean absolute deviation of 3.4 kJ/mol, a correlation ( R²) of 0.97, and correct signs for all of the eight free-energy differences. This is appreciably better than the results obtained at the SQM/MM level of theory and also slightly better than those obtained with MM. We show that the convergence of the SQM/MM → DFT/MM perturbations can be monitored by the use of Wu and Kofke's bias metric Π and by the standard deviation of the difference between the SQM/MM and DFT/MM energies. Finally, we show that the use of the intermediate SQM/MM MD simulations improves the convergence of the free energies by a factor of at least two, compared to doing direct MM → DFT/MM perturbations.

Simulating Water Exchange to Buried Binding Sites

Traditional molecular dynamics (MD) simulations of proteins, which relies on integration of Newton's equations of motion, cannot efficiently equilibrate water occupancy for buried cavities in proteins. This leads to slow convergence of thermodynamic averages for such systems. We have addressed this challenge by efficiently integrating standard Metropolis Monte Carlo (MC) translational water moves with MD in the AMBER simulation package. The translational moves allow water to easily enter or exit buried sites in a thermodynamically correct way during a simulation. To maximize efficiency, the algorithm avoids moves that only interchange waters within the bulk around the protein instead focusing on moves that can transfer water between bulk and the protein interior. In addition, a steric grid allows avoidance of moves that would lead to obvious steric clashes, and a fast grid-based energy evaluation is used to reduce the number of expensive full energy calculations. The potential energy distribution produced using MC/MD was found to be statistically indistinguishable from that of control simulations using only MD, and the algorithm effectively equilibrated water across steric barriers and into binding pockets that are not accessible with pure MD. The MC/MD method introduced here should be of increasing utility for applications spanning protein folding, the elucidation of protein mechanisms, and free energy calculations for computer-aided drug design. It is available in version 18 release of the widely disseminated AMBER simulation package.

Exploration of HIV-1 fusion peptide–antibody VRC34.01 binding reveals fundamental neutralization sites

VRC34.01 antibody binding to a vulnerable site of HIV envelope glycoprotein (Env), the gp41 fusion peptide, renders robust HIV neutralization, but several critical mutations decrease binding affinity and result in unbinding.

Reproducibility of Free Energy Calculations across Different Molecular Simulation Software Packages

Alchemical free energy calculations are an increasingly important modern simulation technique to calculate free energy changes on binding or solvation. Contemporary molecular simulation software such as AMBER, CHARMM, GROMACS, and SOMD include support for the method. Implementation details vary among those codes, but users expect reliability and reproducibility, i.e., for a given molecular model and set of force field parameters, comparable free energy differences should be obtained within statistical bounds regardless of the code used. Relative alchemical free energy (RAFE) simulation is increasingly used to support molecule discovery projects, yet the reproducibility of the methodology has been less well tested than its absolute counterpart. Here we present RAFE calculations of hydration free energies for a set of small organic molecules and demonstrate that free energies can be reproduced to within about 0.2 kcal/mol with the aforementioned codes. Absolute alchemical free energy simulations have been carried out as a reference. Achieving this level of reproducibility requires considerable attention to detail and package-specific simulation protocols, and no universally applicable protocol emerges. The benchmarks and protocols reported here should be useful for the community to validate new and future versions of software for free energy calculations.

Layered nested Markov chain Monte Carlo

A configurational sampling algorithm based on nested layerings of Markov chains (Layered Nested Markov Chain Monte Carlo or L-NMCMC) is presented for simulations of systems characterized by rugged free energy landscapes. The layerings are generated using a set of auxiliary potential energy surfaces. The implementation of the method is demonstrated in the context of a rugged, two-dimensional potential energy surface. The versatility of the algorithm is next demonstrated on a simple, many-body system, namely, a canonical Lennard-Jones fluid in the liquid state. In that example, different layering schemes and auxiliary potentials are used, including variable cutoff distances and excluded-volume tempering. In addition to calculating a variety of properties of the system, it is also shown that L-NMCMC, when combined with a free-energy perturbation formalism, provides a straightforward means to construct approximate free-energy surfaces at no additional computational cost using the sampling distributions of each auxiliary Markov chain. The proposed L-NMCMC scheme is general in that it could be complementary to any number of methods that rely on sampling from a target distribution or methods that exploit a hierarchy of time scales and/or length scales through decomposition of the potential energy.

SAR-Guided Scoring Function and Mutational Validation Reveal the Binding Mode of CGS-8216 at the α1+/γ2- Benzodiazepine Site

The structural resolution of a bound ligand-receptor complex is a key asset to efficiently drive lead optimization in drug design. However, structural resolution of many drug targets still remains a challenging endeavor. In the absence of structural knowledge, scientists resort to structure-activity relationships (SARs) to promote compound development. In this study, we incorporated ligand-based knowledge to formulate a docking scoring function that evaluates binding poses for their agreement with a known SAR. We showcased this protocol by identifying the binding mode of the pyrazoloquinolinone (PQ) CGS-8216 at the benzodiazepine binding site of the GABA_A receptor. Further evaluation of the final pose by molecular dynamics and free energy simulations revealed a close proximity between the pendent phenyl ring of the PQ and γ2D56, congruent with the low potency of carboxyphenyl analogues. Ultimately, we introduced the γ2D56A mutation and in fact observed a 10-fold potency increase in the carboxyphenyl analogue, providing experimental evidence in favor of our binding hypothesis.