Position-Dependent Diffusion from Biased Simulations and Markov State Model Analysis

Abstract

A variety of enhanced statistical and numerical methods are now routinely used to extract important thermodynamic and kinetic information from the vast amount of complex, high-dimensional data obtained from molecular simulations. For the characterization of kinetic properties, Markov state models, in which the long-time statistical dynamics of a system is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. However, obtaining kinetic properties for molecular systems with high energy barriers remains challenging as often enhanced sampling techniques are required with biased simulations to observe the relevant rare events. Particularly, the calculation of diffusion coefficients remains elusive from biased molecular simulation data. Here, we propose a novel method that can calculate multidimensional position-dependent diffusion coefficients equally from either biased or unbiased simulations using the same formalism. Our method builds on Markov state model analysis and the Kramers−Moyal expansion. We demonstrate the validity of our formalism using one-and two-dimensional analytic potentials and also apply it to data from explicit solvent molecular dynamics simulations, including the water-mediated conformations of alanine dipeptide and umbrella sampling simulations of drug transport across a lipid bilayer. Importantly, the developed algorithm presents significant improvement compared to standard methods when the transport of solute across threedimensional heterogeneous porous media is studied, for example, the prediction of membrane permeation of drug molecules.

Role of structural rigidity and collective behaviour in the molecular design of gas hydrate anti-agglomerants

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Proton Coupling and the Multiscale Kinetic Mechanism of a Peptide Transporter

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Momentum removal to obtain the position‐dependent diffusion constant in constrained molecular dynamics simulation

“…The position‐dependent diffusion coefficient, along with the free energy profile, is an important physical quantity utilized in studies of the mass transport phenomena of heterogeneous systems using molecular dynamics (MD) calculations. Because of its importance, many methods 10–19 have been proposed to obtain the position‐dependent diffusion coefficient. Two of us and other coworkers have also previously proposed a method for obtaining the position‐dependent diffusion coefficient with high accuracy in any heterogeneous system 20 …”