Continuum models of collective cell migration

Collective cell motility is crucial in biology, especially in development and medicine. Current models, from individual-based approaches to partial differential equations (PDEs), often overlook key factors such as population heterogeneity and cell signalling, which are known to significantly influence motility. This project aims to enhance current mathematical frameworks by incorporating multiple signalling cues, cell heterogeneity, and phenotypic switching.
The research begins by reviewing existing literature on collective motion across biology, medicine, and ecology, which mainly examines densely packed individuals and short-range interactions. A key innovation in this project is adapting these models to account for excluded volume effects.
This project focuses on phenomenological models for collective cell migration, essential for normal development and tumour invasion. Evidence indicates that cells respond to multiple different signals and exhibit phenotypic switching, yet existing models lack a comprehensive approach.
To address this, we develop a suite of models simulating cell invasion into the microenvironment, which is systematically coarse-grained to derive new PDE models. This links individual cell behaviours to tissue-level dynamics, while clarifying assumptions in traditional PDEs. We extend these models to include multiple cell types and investigate the role of phenotypic switching and signalling mechanisms.
We use analytical and numerical methods to assess these models' robustness to parameter changes and compare findings with evaluate data to guide validations.
This interdisciplinary project, within the EPSRC Mathematical Biology research area, aims to enhance the understanding of biological processes such as crowding, tumour growth, and developmental biology using advanced mathematical modelling.