# Modelling the Impact of Phenotypic Heterogeneity on Cell Migration: A Continuum Framework Derived from Individual-Based Principles

## TL;DR

This paper introduces a mathematical model to study how different cell types affect collective migration, useful for understanding processes like tumor growth and wound healing.

## Contribution

A new continuum framework is derived from individual-based principles to model phenotypic heterogeneity in cell migration.

## Key findings

- The model demonstrates how phenotypic transitions and environmental pressures influence migration patterns.
- The framework is shown to be effective in scenarios like range expansion and T cell exhaustion.
- The model provides a computationally efficient alternative to individual-based simulations for large phenotype populations.

## Abstract

Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This study derives a general mathematical framework for modelling cell migration in the local environment, which is coarse-grained from an underlying individual-based model that captures the dynamics of cell migration that are influenced by the phenotype of the cell, such as random movement, proliferation, phenotypic transitions, and interactions with the local environment. The resulting, flexible, and general model provides a continuum, macroscopic description of cell invasion, which represents the phenotype of the cell as a continuous variable and is much more amenable to simulation and analysis than its individual-based counterpart when considering a large number of phenotypes. We showcase the utility of the generalised framework in three biological scenarios: range expansion; cell invasion into the extracellular matrix; and T cell exhaustion. The results highlight how phenotypic structuring impacts the spatial and temporal dynamics of cell populations, demonstrating that different environmental pressures and phenotypic transition mechanisms significantly influence migration patterns, a phenomenon that would be computationally very expensive to explore using an individual-based model alone. This framework provides a versatile and robust tool for understanding the role of phenotypic heterogeneity in collective cell migration, with potential applications in optimising therapeutic strategies for diseases involving cell migration.

The online version contains supplementary material available at 10.1007/s11538-025-01502-5.