Effects of Velocity Fluctuation on Active Matter Diffusion

Abstract

Systematic motion exhibited by biological cells is fluctuated by various random external forces and unknown, complex internal biological mechanisms. To simulate the fluctuation of this systematic motion and its effect on cell diffusion, we develop a theoretical model, where we treat fluctuation from external forces as a simple diffusion process and fluctuation from internal biological mechanisms as an Ornstein-Uhlenbeck (OU) process. Our exactly solvable theoretical model with various initial conditions yields the analytic results for mean-square displacement of cell diffusion, which are confirmed by comparing with stochastic simulation results. This study demonstrates that the velocity fluctuation systematically increases the diffusion coefficient. In particular, our model with pulse initial conditions shows a time-dependent transient diffusion pattern that changes from superdiffusion to subdiffusion.