This tutorial examines the application of constant-pH molecular dynamics simulations, a method that addresses the critical problem of modeling systems that can adopt multiple protonation states. While conventional molecular dynamics simulations generally assume fixed protonation states, using a constant-pH technique actively explores dynamic shifts in protonation as the simulation progresses. Once completed, constant-pH simulations can be analyzed to yield titration curves that can be readily compared to experiment.

Alchemical binding free energy (BFE) calculations offer an efficient and thermodynamically rigorous approach to in silico binding affinity predictions. As a result of decades of methodological improvements and recent advances in computer technology, alchemical BFE calculations are now widely used in drug discovery research. They help guide the prioritization of candidate drug molecules by predicting their binding affinities for a biomolecular target of interest (and potentially selectivity against undesirable antitargets). Statistical variance associated with such calculations, however, may undermine the reliability of their predictions, introducing uncertainty both in ranking candidate molecules and in benchmarking their predictive accuracy. Here, we present a computational method that substantially improves the statistical precision in BFE calculations for a set of ligands binding to a common receptor by dynamically allocating computational resources to different BFE calculations according to an optimality objective established in a previous work from our group and extended in this work. Our method, termed Network Binding Free Energy (NetBFE), performs adaptive BFE calculations in iterations, re-optimizing the allocations in each iteration based on the statistical variances estimated from previous iterations. Using examples of NetBFE calculations for protein binding of congeneric ligand series, we demonstrate that NetBFE approaches the optimal allocation in a small number (≤5) of iterations and that NetBFE reduces the statistical variance in the BFE estimates by approximately a factor of 2 when compared to a previously published and widely used allocation method at the same total computational cost.

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 bulk solvent and the binding site can be well beyond what is practical with standard MD, which typically ranges to hundreds of nanoseconds to low 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 (GPUs). This results in speedups 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.

Virtual high throughput screening (vHTS) in drug discovery is a powerful approach to identify hits: when applied successfully, it can be much faster and cheaper than experimental high-throughput screening approaches. However, mainstream vHTS tools have significant limitations: ligand-based methods depend on knowledge of existing chemical matter, while structure-based tools such as docking involve significant approximations that limit their accuracy. Recent advances in scientific methods coupled with dramatic speedups in computational processing with GPUs make this an opportune time to consider the role of more rigorous methods that could improve the predictive power of vHTS workflows. In this Perspective, we assert that alchemical binding free energy methods using all-atom molecular dynamics simulations have matured to the point where they can be applied in virtual screening campaigns as a final scoring stage to prioritize the top molecules for experimental testing. Specifically, we propose that alchemical absolute binding free energy (ABFE) calculations offer the most direct and computationally efficient approach within a rigorous statistical thermodynamic framework for computing binding energies of diverse molecules, as is required for virtual screening. ABFE calculations are particularly attractive for drug discovery at this point in time, where the confluence of large-scale genomics data and insights from chemical biology have unveiled a large number of promising disease targets for which no small molecule binders are known, precluding ligand-based approaches, and where traditional docking approaches have foundered to find progressible chemical matter.

Rigorous binding free energy methods in drug discovery are growing in popularity due to 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 the binding site is inaccessible to 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 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 the AMBER simulation software.

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.

Progress in the development of GPU-accelerated free energy simulation software has enabled practical applications on complex biological systems and fueled efforts to develop more accurate and robust predictive methods. In particular, this work re-examines concerted (a.k.a., one-step or unified) alchemical transformations commonly used in the prediction of hydration and relative binding free energies (RBFEs). We first classify several known challenges in these calculations into three categories: endpoint catastrophes, particle collapse, and large gradient-jumps. While endpoint catastrophes have long been addressed using softcore potentials, the remaining two problems occur much more sporadically and can result in either numerical instability (i.e., complete failure of a simulation) or inconsistent estimation (i.e., stochastic convergence to an incorrect result). The particle collapse problem stems from an imbalance in short-range electrostatic and repulsive interactions and can, in principle, be solved by appropriately balancing the respective softcore parameters. However, the large gradient-jump problem itself arises from the sensitivity of the free energy to large values of the softcore parameters, as might be used in trying to solve the particle collapse issue. Often, no satisfactory compromise exists with the existing softcore potential form. As a framework for solving these problems, we developed a new family of smoothstep softcore (SSC) potentials motivated by an analysis of the derivatives along the alchemical path. The smoothstep polynomials generalize the monomial functions that are used in most implementations and provide an additional path-dependent smoothing parameter. The effectiveness of this approach is demonstrated on simple yet pathological cases that illustrate the three problems outlined. With appropriate parameter selection, we find that a second-order SSC(2) potential does at least as well as the conventional approach and provides vast improvement in terms of consistency across all cases. Last, we compare the concerted SSC(2) approach against the gold-standard stepwise (a.k.a., decoupled or multistep) scheme over a large set of RBFE calculations as might be encountered in 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.

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.

In practical free energy estimation, the bias is often neglected once it has been shown to vanish in the large-sample limit. Yet finite-sample bias always exists and ought to be considered in any rigorous study. This work develops a metric for bias in a broad class of free energy “bridge estimators” (e.g., Bennett’s method). The framework complements existing variance estimation methods and provides a means for comparing systematic and statistical errors. Examples show that, contrary to what is often assumed, the bias can be quite substantial when the sample size is modest.

Phosphoinositide phosphates (PIPs) are ubiquitous components in numerous cell signaling pathways. However, there is currently a considerable lack of detailed atomistic models for how PIPs interact with their environment, especially with kinase and phosphatase proteins. While it is well-documented that molecular recognition of PIPs depends on the specific number of phosphorylated sites (one to three), the protonation state of each phosphate is also a critical component. Indeed, this clearly has an effect on the specific protein-lipid binding pose. Nonetheless, there have been very few studies of how these protonation states change between bound/unbound states or even when a PIP is in a membrane versus free in solution. Here we present constant-pH molecular dynamics simulations of various PIP-related compounds in order to analyze correlations between their pKa values, structure, and environment.

Molecular dynamics (MD) trajectories based on classical equations of motion can be used to sample the configurational space of complex molecular systems. However, brute-force MD often converges slowly due to the ruggedness of the underlying potential energy surface. Several schemes have been proposed to address this problem by effectively smoothing the potential energy surface. However, in order to recover the proper Boltzmann equilibrium probability distribution, these approaches must then rely on statistical reweighting techniques or generate the simulations within a Hamiltonian tempering replica-exchange scheme. The present work puts forth a novel hybrid sampling propagator combining Metropolis-Hastings Monte Carlo (MC) with proposed moves generated by non-equilibrium MD (neMD). This hybrid neMD-MC propagator comprises three elementary elements: (i) an atomic system is dynamically propagated for some period of time using standard equilibrium MD on the correct potential energy surface; (ii) the system is then propagated for a brief period of time during what is referred to as a "boosting phase," via a time-dependent Hamiltonian that is evolved toward the perturbed potential energy surface and then back to the correct potential energy surface; (iii) the resulting configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-end momentum reversal prescription is used at the end of the neMD trajectories to guarantee that the hybrid neMD-MC sampling propagator obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The hybrid neMD-MC sampling propagator is designed and implemented to enhance the sampling by relying on the accelerated MD and solute tempering schemes. It is also combined with the adaptive biased force sampling algorithm to examine. Illustrative tests with specific biomolecular systems indicate that the method can yield a significant speedup.

Expanded ensemble simulation is a powerful technique for enhancing sampling over a range of thermodynamic parameters. However, although the premise is relatively simple, running successful simulations in practice still presents something of an ad hoc challenge. Three main difficulties exist: (1) the selection of the thermodynamic states, (2) the selection of the sampling weights, and (3) efficient sampling of the expanded parameter space. Here we consider these problems in the context of a pairwise linear response approach to the work fluctuation theorem. The approach offers comprehensive tactics for addressing the three difficulties and can be used as either an alternative or a complement to replica exchange simulations. Importantly, the results are trivially implemented for multi-dimensional parameter spaces and they recover results from the literature aimed at the special cases of simulated/parallel tempering and replica exchange umbrella sampling. Illustrative examples are shown using the NAMD simulation engine.

Molecular dynamics (MD) is now a widespread tool for investigating biochemical and biomolecular systems, its prevalence, in no small part, being due to significant advances in computational hardware over the last few decades. Even non-experts can now routinely use MD for protein and nucleic acid structure refinement, studying conformational switching events, and investigating solvation effects due to ligand/drug binding. Nonetheless, the vast majority of simulations being done today utilize only rudimentary algorithmic approaches – so-called “brute force” MD – which only permit access to a small fraction of what the approach has to offer. This is largely because the core algorithm is simple, while advanced techniques can require everything from more sophisticated models and data structures to complicated on-the-fly analysis. A core goal of this early science project is to bring one such advanced MD approach into the broader arena of high-performance computing.In particular, the powerful method of constant-pH MD has long been a relegated to experienced users and specialized model systems. In this work we develop and implement a constant-pH MD algorithm in the NAMD simulation engine making it suitable for deployment on large-scale, next-generation supercomputers as well as ambitious, cutting-edge biological applications. We report,for the first time, constant-pH simulations of a membrane transport protein and use the results to analyze its free energy landscape for ion-selectivity.

An increasingly important endeavor is to develop computational strategies that enable molecular dynamics (MD) simulations of biomolecular systems with spontaneous changes in protonation states under conditions of constant pH. The present work describes our efforts to implement the powerful constant-pH MD simulation method, based on a hybrid nonequilibrium MD/Monte Carlo (neMD/MC) technique within the highly scalable program NAMD. The constant-pH hybrid neMD/MC method has several appealing features; it samples the correct semigrand canonical ensemble rigorously, the computational cost increases linearly with the number of titratable sites, and it is applicable to explicit solvent simulations. The present implementation of the constant-pH hybrid neMD/MC in NAMD is designed to handle a wide range of biomolecular systems with no constraints on the choice of force field. Furthermore, the sampling efficiency can be adaptively improved on-the-fly by adjusting algorithmic parameters during the simulation. Illustrative examples emphasizing medium- and large-scale applications on next-generation supercomputing architectures are provided.