The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models

Abstract

Coarse-grained ͑CG͒ 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-CG͒ method ͓J. Phys. Chem. B 109, 2469 ͑2005͒; J. Chem. Phys. 123, 134105 ͑2005͔͒ 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 ͑PMF͒ 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.

Hybrid simulations: combining atomistic and coarse-grained force fields using virtual sites

“…The pressure correction was applied at every cycle and the convergence was measured as the root mean square deviation (RMSD) Force matching. Force matching 40,41 is another technique to construct CG potentials. It also uses information from reference atomistic simulations to construct the effective CG interaction.…”

“…Thus it aims at reproducing the multibody potential of mean force with a set of CG interaction functions, in the present case with effective pair interaction functions. 41 In order to evaluate FM CG potentials, first reference forces on CG beads are calculated as a sum of atomistic forces f g…”

Multiscale modeling of emergent materials: biological and soft matter

“…94 To compare the methods more closely, it is useful to define exactly what we would like to achieve with systematic coarse graining. The logical definition is the reproduction of the equilibrium probability distribution functions of the coarse-grained coordinates 95 (for this discussion, we neglect the momentum part of the Hamiltonian). Following the presentation by Noid et al, 95 let R N be the coarse-grained degrees of freedom and r n the detailed degrees of freedom, and define a mapping operator M N that maps the detailed model to the coarse-grained model: R N = M N (r n ).…”

How Short Is Too Short for the Interactions of a Water Potential? Exploring the Parameter Space of a Coarse-Grained Water Model Using Uncertainty Quantification

“…Boltzmann inversion and reverse Monte Carlo have been used to develop isotropic pairwise water−water interaction potentials directly from the radial distribution functions calculated from atomistic simulations. 9,10 Coarse-graining methods such as force matching (FM) 11,12 and relative entropy minimization (REM) 4 are gaining use and have been employed for the development of water models. 2, 3,13,14 The primary limitation of REM and FM methods is that although they are grounded in well-established statistical mechanical formalisms, they are not trivial to implement in practice and do not necessarily produce properties in good agreement with the target finer-grained model from which they are derived.…”