Path probability ratios for Langevin dynamics-Exact and approximate

Implementation of Girsanov Reweighting in OpenMM and Deeptime

Classical molecular dynamics (MD) simulations provide invaluable insights into complex molecular systems but face limitations in capturing phenomena occurring on time scales beyond their reach. To bridge this gap, various enhanced sampling techniques have been developed, which are complemented by reweighting techniques to recover the unbiased dynamics. Girsanov reweighting is a reweighting technique that reweights simulation paths, generated by a stochastic MD integrator, without evoking an effective model of the dynamics. Instead, it calculates the relative path probability density at the time resolution of the MD integrator. Efficient implementation of Girsanov reweighting requires that the reweighting factors are calculated on-the-fly during the simulations and thus needs to be implemented within the MD integrator. Here, we present a comprehensive guide for implementing Girsanov reweighting into MD simulations. We demonstrate the implementation in the MD simulation package OpenMM by extending the library openmmtools. Additionally, we implemented a reweighted Markov state model estimator within the time series analysis package Deeptime.

Dynamical Reweighting for Biased Rare Event Simulations

Dynamical reweighting techniques aim to recover the correct molecular dynamics from a simulation at a modified potential energy surface. They are important for unbiasing enhanced sampling simulations of molecular rare events. Here, we review the theoretical frameworks of dynamical reweighting for modified potentials. Based on an overview of kinetic models with increasing level of detail, we discuss techniques to reweight two-state dynamics, multistate dynamics, and path integrals. We explore the natural link to transition path sampling and how the effect of nonequilibrium forces can be reweighted. We end by providing an outlook on how dynamical reweighting integrates with techniques for optimizing collective variables and with modern potential energy surfaces.

Optimizing molecular potential models by imposing kinetic constraints with path reweighting

Empirical force fields employed in molecular dynamics simulations of complex systems are often optimized to reproduce experimentally determined structural and thermodynamic properties. In contrast, experimental knowledge about the interconversion rates between metastable states in such systems is hardly ever incorporated in a force field due to a lack of an efficient approach. Here, we introduce such a framework based on the relationship between dynamical observables, such as rate constants, and the underlying molecular model parameters using the statistical mechanics of trajectories. Given a prior ensemble of molecular dynamics trajectories produced with imperfect force field parameters, the approach allows for the optimal adaption of these parameters such that the imposed constraint of equally predicted and experimental rate constant is obeyed. To do so, the method combines the continuum path ensemble maximum caliber approach with path reweighting methods for stochastic dynamics. When multiple solutions are found, the method selects automatically the combination that corresponds to the smallest perturbation of the entire path ensemble, as required by the maximum entropy principle. To show the validity of the approach, we illustrate the method on simple test systems undergoing rare event dynamics. Next to simple 2D potentials, we explore particle models representing molecular isomerization reactions and protein-ligand unbinding. Besides optimal interaction parameters, the methodology gives physical insights into what parts of the model are most sensitive to the kinetics. We discuss the generality and broad implications of the methodology.

Girsanov Reweighting Enhanced Sampling Technique (GREST): On-the-Fly Data-Driven Discovery of and Enhanced Sampling in Slow Collective Variables

Molecular dynamics simulations of microscopic phenomena are limited by the short integration time steps which are required for numerical stability but which limit the practically achievable simulation time scales. Collective variable (CV) enhanced sampling techniques apply biases to predefined collective coordinates to promote barrier crossing, phase space exploration, and sampling of rare events. The efficacy of these techniques is contingent on the selection of good CVs correlated with the molecular motions governing the long-time dynamical evolution of the system. In this work, we introduce Girsanov Reweighting Enhanced Sampling Technique (GREST) as an adaptive sampling scheme that interleaves rounds of data-driven slow CV discovery and enhanced sampling along these coordinates. Since slow CVs are inherently dynamical quantities, a key ingredient in our approach is the use of both thermodynamic and dynamical Girsanov reweighting corrections for rigorous estimation of slow CVs from biased simulation data. We demonstrate our approach on a toy 1D 4-well potential, a simple biomolecular system alanine dipeptide, and the Trp-Leu-Ala-Leu-Leu (WLALL) pentapeptide. In each case GREST learns appropriate slow CVs and drives sampling of all thermally accessible metastable states starting from zero prior knowledge of the system. We make GREST accessible to the community via a publicly available open source Python package.

Hierarchical Materials from High Information Content Macromolecular Building Blocks: Construction, Dynamic Interventions, and Prediction

Hierarchical materials that exhibit order over multiple length scales are ubiquitous in nature. Because hierarchy gives rise to unique properties and functions, many have sought inspiration from nature when designing and fabricating hierarchical matter. More and more, however, nature's own high-information content building blocks, proteins, peptides, and peptidomimetics, are being coopted to build hierarchy because the information that determines structure, function, and interfacial interactions can be readily encoded in these versatile macromolecules. Here, we take stock of recent progress in the rational design and characterization of hierarchical materials produced from high-information content blocks with a focus on stimuli-responsive and "smart" architectures. We also review advances in the use of computational simulations and data-driven predictions to shed light on how the side chain chemistry and conformational flexibility of macromolecular blocks drive the emergence of order and the acquisition of hierarchy and also on how ionic, solvent, and surface effects influence the outcomes of assembly. Continued progress in the above areas will ultimately usher in an era where an understanding of designed interactions, surface effects, and solution conditions can be harnessed to achieve predictive materials synthesis across scale and drive emergent phenomena in the self-assembly and reconfiguration of high-information content building blocks.

Assessing transition rates as functions of environmental variables

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

Enhanced-Sampling Simulations for the Estimation of Ligand Binding Kinetics: Current Status and Perspective

The dissociation rate (k off) associated with ligand unbinding events from proteins is a parameter of fundamental importance in drug design. Here we review recent major advancements in molecular simulation methodologies for the prediction of k off. Next, we discuss the impact of the potential energy function models on the accuracy of calculated k off values. Finally, we provide a perspective from high-performance computing and machine learning which might help improve such predictions.

Collective variable-based enhanced sampling and machine learning

ABSTRACT

Collective variable-based enhanced sampling methods have been widely used to study thermodynamic properties of complex systems. Efficiency and accuracy of these enhanced sampling methods are affected by two factors: constructing appropriate collective variables for enhanced sampling and generating accurate free energy surfaces. Recently, many machine learning techniques have been developed to improve the quality of collective variables and the accuracy of free energy surfaces. Although machine learning has achieved great successes in improving enhanced sampling methods, there are still many challenges and open questions. In this perspective, we shall review recent developments on integrating machine learning techniques and collective variable-based enhanced sampling approaches. We also discuss challenges and future research directions including generating kinetic information, exploring high-dimensional free energy surfaces, and efficiently sampling all-atom configurations.

GRAPHIC ABSTRACT