MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations

Abstract

Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long-timescale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large lengthscales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time- and lengthscales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B <--> C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.

References in corpus (16)

• Identification of slow molecular order parameters for Markov model construction
• VAMPnets: Deep learning of molecular kinetics
• Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions
• Spatio-temporal correlations can drastically change the response of a MAPK pathway
• Data-driven model reduction and transfer operator approximation
• Projected and Hidden Markov Models for calculating kinetics and metastable states of complex molecules
• A First-Passage Kinetic Monte Carlo Algorithm for Complex Diffusion-Reaction Systems
• Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states
• An O(N^2) Approximation for Hydrodynamic Interactions in Brownian Dynamics Simulations
• Dynamics of protein-protein encounter: a Langevin equation approach with reaction patches
• Efficient Reactive Brownian Dynamics
• Multiscale simulations of anisotropic particles combining Brownian Dynamics and Green's Function Reaction Dynamics
• xTRAM: Estimating equilibrium expectations from time-correlated simulation data at multiple thermodynamic states
• Dimensional Reduction of Markov State Models from Renormalization Group Theory
• An efficient multi-scale Green's Functions Reaction Dynamics scheme
• A Discrete Stochastic Formulation for Reversible Bimolecular Reactions via Diffusion Encounter

Cited by in corpus (11)

• A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations
• Diffusion-influenced reaction rates in the presence of pair interactions
• Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics
• Grand canonical diffusion-influenced reactions: a stochastic theory with applications to multiscale reaction-diffusion simulations
• Data-driven construction of stochastic reduced dynamics encoded with non-Markovian features
• Chemical diffusion master equation: formulations of reaction--diffusion processes on the molecular level
• Hydrodynamic coupling for particle-based solvent-free membrane models
• Data-driven dynamical coarse-graining for condensed matter systems
• Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs
• Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems
• Open reaction-diffusion systems: bridging probabilistic theory and simulations across scales