A particle system approach to cell-cell adhesion models

TL;DR

This paper rigorously derives macroscopic PDE models for cell-cell adhesion from stochastic particle systems, bridging microscopic interactions and large-scale biological behavior.

Contribution

It provides a rigorous derivation of two PDE models, including non-local and local forms, from stochastic particle systems with moderate interactions.

Findings

Derivation of PDE models from particle systems

Establishment of law of large numbers for cell adhesion

Connection between microscopic interactions and macroscopic behavior

Abstract

We investigate micro-to-macroscopic derivations in two models of living cells, in presence to cell-cell adhesive interactions. We rigorously address two PDE-based models, one featuring non-local terms and another purely local, as a a result of a law of large numbers for stochastic particle systems, with moderate interactions in the sense of K. Oelshchlaeger (1985).