Coarse-grained computational stability analysis and acceleration of the collective dynamics of a Monte Carlo simulation of bacterial locomotion

Over the past few years it has been demonstrated that the so called equation-free framework establishes a link between traditional computational analysis and microscopic/stochastic simulation of complex systems. The underlying assumption is that macroscopic models can be in principle written in terms of a few statistical moments of the evolving distributions, but they are unavailable in closed form. Here it is shown how this multiscale framework can be used to find the level at which closures should be sought for a Monte Carlo simulation of bacterial locomotion with flagellar motility. For illustration purposes, a simple biologically inspired one-dimensional in space Monte Carlo model of Escherichia coli locomotion was used. The coarse-grained stability analysis of the emergent dynamics revealed that the collective behavior for the particular model can be parametrized by just a few moments of the distribution of the cells positions indicating that higher-order moments as well as other “internal” variables of the model become relatively fast in time, functionals of these few coarse-grained observables. Acceleration of the Monte Carlo simulations in time based on these “slow” macroscopic variables is also demonstrated.