**Dynamic force matching: A method for constructing dynamical coarse-
grained models with realistic time dependence**

A Davtyan and JF Dama and GA Voth and HC Andersen, JOURNAL OF CHEMICAL PHYSICS, 142, 154104 (2015).

DOI: 10.1063/1.4917454

Coarse-grained (CG) models of molecular systems, with fewer mechanical
degrees of freedom than an all-atom model, are used extensively in
chemical physics. It is generally accepted that a coarse-grained model
that accurately describes equilibrium structural properties (as a result
of having a well constructed CG potential energy function) does not
necessarily exhibit appropriate dynamical behavior when simulated using
conservative Hamiltonian dynamics for the CG degrees of freedom on the
CG potential energy surface. Attempts to develop accurate CG dynamic
models usually focus on replacing Hamiltonian motion by stochastic but
Markovian dynamics on that surface, such as Langevin or Brownian
dynamics. However, depending on the nature of the system and the extent
of the coarse-graining, a Markovian dynamics for the CG degrees of
freedom may not be appropriate. In this paper, we consider the problem
of constructing dynamic CG models within the context of the Multi-Scale
Coarse-graining (MS-CG) method of Voth and coworkers. We propose a
method of converting a MS-CG model into a dynamic CG model by adding
degrees of freedom to it in the form of a small number of fictitious
particles that interact with the CG degrees of freedom in simple ways
and that are subject to Langevin forces. The dynamic models are members
of a class of nonlinear systems interacting with special heat baths that
were studied by Zwanzig **J. Stat. Phys. 9, 215 (1973)**. The properties
of the fictitious particles can be inferred from analysis of the
dynamics of all-atom simulations of the system of interest. This is
analogous to the fact that the MS-CG method generates the CG potential
from analysis of equilibrium structures observed in all-atom simulation
data. The dynamic models generate a non-Markovian dynamics for the CG
degrees of freedom, but they can be easily simulated using standard
molecular dynamics programs. We present tests of this method on a series
of simple examples that demonstrate that the method provides realistic
dynamical CG models that have non-Markovian or close to Markovian
behavior that is consistent with the actual dynamical behavior of the
all-atom system used to construct the CG model. Both the construction
and the simulation of such a dynamic CG model have computational
requirements that are similar to those of the corresponding MS-CG model
and are good candidates for CG modeling of very large systems. (C) 2015
AIP Publishing LLC.

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