Coarse-graining molecular dynamics: stochastic models with non-Gaussian force distributions.
J Math Biol 2019;
80:457-479. [PMID:
31541299 PMCID:
PMC7012987 DOI:
10.1007/s00285-019-01433-5]
[Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2019] [Revised: 08/28/2019] [Indexed: 12/28/2022]
Abstract
Incorporating atomistic and molecular information into models of cellular behaviour is challenging because of a vast separation of spatial and temporal scales between processes happening at the atomic and cellular levels. Multiscale or multi-resolution methodologies address this difficulty by using molecular dynamics (MD) and coarse-grained models in different parts of the cell. Their applicability depends on the accuracy and properties of the coarse-grained model which approximates the detailed MD description. A family of stochastic coarse-grained (SCG) models, written as relatively low-dimensional systems of nonlinear stochastic differential equations, is presented. The nonlinear SCG model incorporates the non-Gaussian force distribution which is observed in MD simulations and which cannot be described by linear models. It is shown that the nonlinearities can be chosen in such a way that they do not complicate parametrization of the SCG description by detailed MD simulations. The solution of the SCG model is found in terms of gamma functions.
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