Derivation of persistent time for anisotropic migration of cells

Cell migration plays an essential role in a wide variety of physiological and pathological processes. In this paper we numerically discuss the properties of an anisotropic persistent random walk (APRW) model, in which two different and independent persistent times are assumed for cell migrations in the x-and y-axis directions. An intrinsic orthogonal coordinates with the primary and non-primary directions can be defined for each migration trajectory based on the singular vector decomposition method. Our simulation results show that the decay time of single exponential distribution of velocity auto-correlation function (VACF) in the primary direction is actually the large persistent time of the APRW model, and the small decay time of double exponential VACF in the non-primary direction equals the small persistent time of the APRW model. Thus, we propose that the two persistent times of anisotropic migration of cells can be properly estimated by discussing the VACFs of trajectory projected to the primary and non-primary directions.