Coarse-graining molecular dynamics: stochastic models with non-Gaussian force distributions

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...

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Bibliographic Details
Published in:Journal of mathematical biology 2020-01, Vol.80 (1-2), p.457-479
Main Author: Erban, Radek
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computer simulation
Differential equations
Force distribution
Gamma function
Granulation
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Model accuracy
Molecular dynamics
Molecular Dynamics Simulation
Molecular modelling
Multiscale analysis
Nonlinear Dynamics
Nonlinear equations
Nonlinear systems
Normal distribution
Parameterization
Statistical Distributions
Stochastic models
Stochastic Processes
Stress concentration
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Summary: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.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-019-01433-5