Comparison of Stochastic Simulation Methods in Mechanobiology

Abstract

Stochastic simulations in mechanobiology generally use rate constants from an effective one-dimensional Kramers problem in the high friction regime. This assumes that the dynamics along one coordinate (generally the mechanical coordinate) are much faster compared to the dynamics along the other coordinate. Here, we investigate systems with comparable dynamics along the mechanical and chemical coordinates, in search of a better mechanochemical simulation method for a system governed by a potential in more than one dimension. We simulate test systems to compare our method and the existing simulation methods to a numerically exact solution of the multidimensional Fokker-Planck equation with bi-stable potential. We also study effects of introducing an external force and changing the friction anisotropy in the system on the rate constants.