Modelling non-local cell-cell adhesion: a multiscale approach

TL;DR

This paper introduces a multiscale model for cell-cell adhesion that combines microscopic and mesoscopic descriptions, leading to new non-local kinetic equations and insights into cell migration dynamics.

Contribution

It develops a novel multiscale framework integrating microscopic adhesion mechanisms with mesoscopic stochastic processes, resulting in new non-local kinetic models.

Findings

Simulations demonstrate combined effects of adhesion and stochastic motion.

The model captures microscopic adhesion molecule binding.

Derived equations include a new non-linear integral component.

Abstract

Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a versatile multiscale approach to modelling a moving self-adhesive cell population that combines a careful microscopic description of a deterministic adhesion-driven motion component with an efficient mesoscopic representation of a stochastic velocity-jump process. This approach gives rise to mesoscopic models in the form of kinetic transport equations featuring multiple non-localities. Subsequent parabolic and hyperbolic scalings produce general classes of equations with non-local adhesion and myopic diffusion, a special case being the classical macroscopic model proposed in [4]. Our simulations show how the combination of the two motion effects can unfold. Cell-cell adhesion relies on the subcellular cell adhesion molecule binding. Our approach lends itself conveniently to capturing this microscopic effect. On the macroscale, this results in an additional non-linear integral equation of a novel type that is coupled to the cell density equation.