Nonmotile Single-Cell Migration as a Random Walk in Nonuniformity: the "extreme Dumping Limit" for Cell-To-Cell Communications

In the present work, we model single-cell movement as a random walk in an external potential observed within the extreme dumping limit, which we define herein as the extreme nonuniform behavior observed for cell responses and cell-To-cell communications. Starting from the Newton-Langevin equation of motion, we solve the corresponding Fokker-Planck equation to compute higher moments of the displacement of the cell, and then we build certain quantities that can be measurable experimentally. We show that, each time, the dynamics depend on the external force applied, leading to predictions distinct from the standard results of a free Brownian particle. Our findings demonstrate that cell migration viewed as a stochastic process is still compatible with biological and experimental observations without the need to rely on more complicated or sophisticated models proposed previously in the literature.