TY - JOUR A1 - Koltai, Péter A1 - Schütte, Christof T1 - A multiscale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics JF - SIAM J. Multiscale Model. Simul. N2 - We investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one. Y1 - 2018 U6 - https://doi.org/10.1137/17M1146403 VL - 16 IS - 4 SP - 1455 EP - 1485 PB - SIAM ER - TY - JOUR A1 - Dibak, Manuel A1 - J. del Razo, Mauricio A1 - De Sancho, David A1 - Schütte, Christof A1 - Noé, Frank T1 - MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations JF - Journal of Chemical Physics N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1063/1.5020294 VL - 148 IS - 214107 ER -