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
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.