The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models.
Coarse-grained (CG) models provide a computationally efficient method for rapidly investigating the long time- and length-scale processes that play a critical role in many important biological and soft matter processes. Recently, Izvekov and Voth introduced a new multiscale coarse-graining (MS-CG) method [J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] for determining the effective interactions between CG sites using information from simulations of atomically detailed models. The present work develops a formal statistical mechanical framework for the MS-CG method and demonstrates that the variational principle underlying the method may, in principle, be employed to determine the many-body potential of mean force (PMF) that governs the equilibrium distribution of positions of the CG sites for the MS-CG models. A CG model that employs such a PMF as a "potential energy function" will generate an equilibrium probability distribution of CG sites that is consistent with the atomically detailed model from which the PMF is derived. Consequently, the MS-CG method provides a formal multiscale bridge rigorously connecting the equilibrium ensembles generated with atomistic and CG models. The variational principle also suggests a class of practical algorithms for calculating approximations to this many-body PMF that are optimal. These algorithms use computer simulation data from the atomically detailed model. Finally, important generalizations of the MS-CG method are introduced for treating systems with rigid intramolecular constraints and for developing CG models whose equilibrium momentum distribution is consistent with that of an atomically detailed model.
Noid
W G
WG
Center for Biophysical Modeling and Simulation and Department of Chemistry, University of Utah, Salt Lake City, Utah 84112-0850, USA.
Chu
Jhih-Wei
JW
Ayton
Gary S
GS
Krishna
Vinod
V
Izvekov
Sergei
S
Voth
Gregory A
GA
Das
Avisek
A
Andersen
Hans C
HC
D003198:Computer Simulation; D008956:Models, Chemical; D015233:Models, Statistical; D016008:Statistical Distributions