OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials.

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features in simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations with only a modest increase in cost.

OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials.

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features on simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein (GFP) chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations at only a modest increase in cost.

Revisiting the pseudo-supercritical path method: An improved formulation for the alchemical calculation of solid-liquid coexistence.

Alchemical free energy calculations via molecular dynamics have been applied to obtain thermodynamic properties related to solid-liquid equilibrium conditions, such as melting points. In recent years, the pseudo-supercritical path (PSCP) method has proved to be an important approach to melting point prediction due to its flexibility and applicability. In the present work, we propose improvements to the PSCP alchemical cycle to make it more compact and efficient through a concerted evaluation of different potential energies. The multistate Bennett acceptance ratio (MBAR) estimator was applied at all stages of the new cycle to provide greater accuracy and uniformity, which is essential concerning uncertainty calculations. In particular, for the multistate expansion stage from solid to liquid, we employed the MBAR estimator with a reduced energy function that allows affine transformations of coordinates. Free energy and mean derivative profiles were calculated at different cycle stages for argon, triazole, propenal, and the ionic liquid 1-ethyl-3-methyl-imidazolium hexafluorophosphate. Comparisons showed a better performance of the proposed method than the original PSCP cycle for systems with higher complexity, especially the ionic liquid. A detailed study of the expansion stage revealed that remapping the centers of mass of the molecules or ions is preferable to remapping the coordinates of each atom, yielding better overlap between adjacent states and improving the accuracy of the methodology.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package.

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

An exploration of machine learning models for the determination of reaction coordinates associated with conformational transitions.

Determining collective variables (CVs) for conformational transitions is crucial to understanding their dynamics and targeting them in enhanced sampling simulations. Often, CVs are proposed based on intuition or prior knowledge of a system. However, the problem of systematically determining a proper reaction coordinate (RC) for a specific process in terms of a set of putative CVs can be achieved using committor analysis (CA). Identifying essential degrees of freedom that govern such transitions using CA remains elusive because of the high dimensionality of the conformational space. Various schemes exist to leverage the power of machine learning (ML) to extract an RC from CA. Here, we extend these studies and compare the ability of 17 different ML schemes to identify accurate RCs associated with conformational transitions. We tested these methods on an alanine dipeptide in vacuum and on a sarcosine dipeptoid in an implicit solvent. Our comparison revealed that the light gradient boosting machine method outperforms other methods. In order to extract key features from the models, we employed Shapley Additive exPlanations analysis and compared its interpretation with the "feature importance" approach. For the alanine dipeptide, our methodology identifies ϕ and θ dihedrals as essential degrees of freedom in the C7ax to C7eq transition. For the sarcosine dipeptoid system, the dihedrals ψ and ω are the most important for the cisαD to transαD transition. We further argue that analysis of the full dynamical pathway, and not just endpoint states, is essential for identifying key degrees of freedom governing transitions.

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

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

Molecular Dynamics with Very Large Time Steps for the Calculation of Solvation Free Energies.

In multiple time scale molecular dynamics, the use of isokinetic constraints along with massive thermostatting has enabled the adoption of very large integration steps, well beyond the limits imposed by resonance artifacts in standard algorithms. In this work, we present two new contributions to this topic. First, we investigate the velocity distribution and the temperature-kinetic energy relationship associated with the isokinetic Nosé-Hoover family of methods, showing how they depend on the number of thermostats attached to each atomic degree of freedom. Second, we investigate the performance of these methods in the calculation of solvation free energies, the determination of which is often key for understanding the partition of a chemical species among distinct environments. We show how one can extract this property from canonical (constant-NVT) simulations and compare the result to experimental data obtained at a specific pressure. Finally, we demonstrate that large time steps can, in fact, be used to improve the efficiency of these calculations and that attaching multiple thermostats per degree of freedom is beneficial for effectively exploring the configurational space of a molecular system.

Refinement of thermostated molecular dynamics using backward error analysis.

Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical integration may lead to deviations from equipartition. Fortunately, backward error analysis allows us to obtain a higher-order estimate of the quantity that is actually subject to equipartition. This is related to a shadow Hamiltonian, which converges to the specified Hamiltonian only when the time-step size approaches zero. This paper deals with discretization effects in a straightforward way. With a small computational overhead, we obtain refined versions of the kinetic and potential energies, whose sum is a suitable estimator of the shadow Hamiltonian. Then, we tune the thermostatting procedure by employing the refined kinetic energy instead of the conventional one. This procedure is shown to reproduce a canonical ensemble compatible with the refined system, as opposed to the original one, but canonical averages regarding the latter can easily be recovered by reweighting. Water, modeled as a rigid body, is an excellent test case for our proposal because its numerical stability extends up to time steps large enough to yield pronounced discretization errors in Verlet-type integrators. By applying our new approach, we were able to mitigate discretization effects in equilibrium properties of liquid water for time-step sizes up to 5 fs.

Solvent effects on the decarboxylation of trichloroacetic acid: insights from ab initio molecular dynamics simulations.

The kinetics of trichloroacetic acid (TCA) decarboxylation strongly depends on the solvent in which it occurs, proceeding faster in polar aprotic solvents compared to protic solvents. In particular, the reaction is known to be fast in DMSO even at room temperature and is rather slow in water even at higher temperatures. In order to understand the role of the solvent in the kinetics of TCA decarboxylation, the present study investigates this reaction using both ab initio molecular dynamics (AIMD) simulations in explicit solvents and static electronic structure calculations with the SMD polarizable continuum model, considering DMSO and water as solvents. Both methodologies yield activation free energies in good agreement with experimental data, however they differ with respect to the reaction profile for the process occurring in water. The simulations suggest that DMSO does not participate chemically in the reaction and that the high reaction rate in DMSO can be explained by differential solvation of the reactant and transition state. In water, a protonation step was observed along the simulation trajectory, indicating chemical participation of the solvent in this case. Moreover, the continuum model has shown to be useful to predict the reaction rates in other solvents, suggesting that reaction rates increase upon decreasing solvent polarity up to the point where the apolar solvents are not able to efficiently screen the strong electrostatic interactions to form the required isolated ionic species.

Molecular dynamics with rigid bodies: Alternative formulation and assessment of its limitations when employed to simulate liquid water.

Sets of atoms collectively behaving as rigid bodies are often used in molecular dynamics to model entire molecules or parts thereof. This is a coarse-graining strategy that eliminates degrees of freedom and supposedly admits larger time steps without abandoning the atomistic character of a model. In this paper, we rely on a particular factorization of the rotation matrix to simplify the mechanical formulation of systems containing rigid bodies. We then propose a new derivation for the exact solution of torque-free rotations, which are employed as part of a symplectic numerical integration scheme for rigid-body dynamics. We also review methods for calculating pressure in systems of rigid bodies with pairwise-additive potentials and periodic boundary conditions. Finally, simulations of liquid phases, with special focus on water, are employed to analyze the numerical aspects of the proposed methodology. Our results show that energy drift is avoided for time step sizes up to 5 fs, but only if a proper smoothing is applied to the interatomic potentials. Despite this, the effects of discretization errors are relevant, even for smaller time steps. These errors induce, for instance, a systematic failure of the expected equipartition of kinetic energy between translational and rotational degrees of freedom.

Isochronal sampling in non-Boltzmann Monte Carlo methods.

Non-Boltzmann sampling (NBS) methods are usually able to overcome ergodicity issues which conventional Monte Carlo methods often undergo. In short, NBS methods are meant to broaden the sampling range of some suitable order parameter (e.g., energy). For many years, a standard for their development has been the choice of sampling weights that yield uniform sampling of a predefined parameter range. However, Trebst et al. [Phys. Rev. E 70, 046701 (2004)] demonstrated that better results are obtained by choosing weights that reduce as much as possible the average number of steps needed to complete a roundtrip in that range. In the present work, we prove that the method they developed to minimize roundtrip times also equalizes downtrip and uptrip times. Then, we propose a discrete-parameter extension using such isochronal character as our main goal. To assess the features of the new method, we carry out simulations of a spin system and of lattice chains designed to exhibit folding transition, thus being suitable models for proteins. Our results show that the new method performs on a par with the original method when the latter is applicable. However, there are cases in which the method of Trebst et al. becomes inapplicable, depending on the chosen order parameter and on the employed Monte Carlo moves. With a practical example, we demonstrate that our method can naturally handle these cases, thus being more robust than the original one. Finally, we find an interesting correspondence between the kind of approach dealt with here and the committor analysis of reaction coordinates, which is another topic of rising interest in the field of molecular simulation.

On the use of transition matrix methods with extended ensembles.

Different extended ensemble schemes for non-Boltzmann sampling (NBS) of a selected reaction coordinate lambda were formulated so that they employ (i) "variable" sampling window schemes (that include the "successive umbrella sampling" method) to comprehensibly explore the lambda domain and (ii) transition matrix methods to iteratively obtain the underlying free-energy eta landscape (or "importance" weights) associated with lambda. The connection between "acceptance ratio" and transition matrix methods was first established to form the basis of the approach for estimating eta(lambda). The validity and performance of the different NBS schemes were then assessed using as lambda coordinate the configurational energy of the Lennard-Jones fluid. For the cases studied, it was found that the convergence rate in the estimation of eta is little affected by the use of data from high-order transitions, while it is noticeably improved by the use of a broader window of sampling in the variable window methods. Finally, it is shown how an "elastic" window of sampling can be used to effectively enact (nonuniform) preferential sampling over the lambda domain, and how to stitch the weights from separate one-dimensional NBS runs to produce a eta surface over a two-dimensional domain.

A general framework for non-Boltzmann Monte Carlo sampling.

Non-Boltzmann sampling (NBS) methods have been extensively employed in recent years, mainly due to their ability to enhance ergodicity in simulations of complex systems. In addition, they make possible reliable computation of equilibrium properties (ensemble averages, free-energy differences, and potentials of mean force) over continuous ranges of thermodynamic conditions. In this work, we put forward a general and systematic framework for NBS methods that allows a single set of equations and procedures to be applied to diverse systems. Moreover, we show how to exploit simulation data most effectively by obtaining continuous profiles of any mechanical properties, including structural quantities not directly related to the ensemble parameters. Finally, we demonstrate the usefulness of the developed formulation by applying it to spin systems, Lennard-Jones fluids, and a model protein molecule (both in isolation and in the proximity of a flat wall).