Crawling migration under chemical signalling: A stochastic model

Abstract

Cell migration is an essential and complex mechanism involved in many physiological processes such as tissue formation or tumor invasion. External and internal cues are known to guide cell motion by regulating cytoskeleton dynamics. Here, we approach cell‐crawling migration under a large‐scale assumption so that it reduces to a particle in motion. However, we describe the cell displacement as the result of its internal activity: the cell velocity is a function of the (discrete) protrusive forces exerted by filopodia on the substrate. Cell polarization ability is modeled in the feedback that the cell motion exerts on the protrusion rates: faster cells form preferentially protrusions in the direction of motion. In addition, we incorporate a gradient in attractive chemical signal, which may vary in time. We perform numerical simulations on this model, showing that the balance between cells self‐polarized internal machinery and signal sensing leads to nontrivial behaviors. Finally, by using the mathematical framework of structured population processes previously developed to study population dynamics, we study rigorously the mathematical model, and we derive some of its fundamental properties.