A stochastic model for protrusion activity

TL;DR

This paper introduces a stochastic model of cell migration where internal protrusive forces and feedback mechanisms influence cell movement, capturing various migration behaviors through mathematical analysis and simulations.

Contribution

It develops a novel stochastic framework for cell migration that incorporates protrusive forces and feedback, providing rigorous analysis and diverse trajectory simulations.

Findings

The model reproduces Brownian-like, persistent, and intermittent trajectories.

Simulations align with observed cell migration behaviors.

Mathematical properties of the model are rigorously derived.

Abstract

In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a function of the (discrete) protrusive forces exerted by filopodia on the substrate. Cell polarisation 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. By using the mathematical framework of structured population processes previously developed to study population dynamics [Fournier and M{\'e}l{\'e}ard, 2004], we introduce rigorously the mathematical model and we derive some of its fundamental properties. We perform numerical simulations on this model showing that different types of trajectories may be obtained: Brownian-like, persistent, or intermittent when the cell switches between both previous regimes. We find back the trajectories usually described in the literature for cell migration.