The role of phenotypic heterogeneity in collective cell migration

Thesis

Understanding collective cell migration requires robust mathematical models that effectively bridge the gap between individual cell behaviours and population-level dynamics. This thesis develops and analyses a suite of mathematical models for cell invasion into extracellular matrix (ECM), that are systematically derived from individual-based frameworks to ensure consistency in the inclusion of key biological mechanisms. Beginning with a single cell type, a volume-filling framework is introduced that accounts for spatial constraints imposed by both cells and ECM. These effects are incorporated coherently across all migration and proliferation processes to investigate their influence on invasion speed and wave structure by comparison to existing models in the literature. To further these insights, a variational principle approach is developed through the lens of optimal control theory, that characterises a new and improved lower bound on the speed of cell invasion in multi-species systems.

Building on the homogeneous foundation, the volume-filling model developed initially is then extended to incorporate phenotypic heterogeneity. Firstly, by introducing two distinct sub-populations: one specialising in movement and ECM degradation, and the other in proliferation. Secondly, by replacing discrete phenotypes with a continuum of states, allowing for a more flexible representation of phenotypic variation across diverse biological contexts, including tumour invasion and immune cell exhaustion. By exploring different environmentally-dependent phenotypic switching mechanisms, it is demonstrated that phenotypic switching fundamentally alters both the cell invasion dynamics and the structure of the travelling fronts. Overall, this work demonstrates the importance of systematically deriving population-level models from their individual-based counterparts and reveals that phenotypic heterogeneity plays a crucial role in shaping migration patterns. These insights highlight key features for consideration when modelling collective migration and help improve our understanding of cell invasion and its broader biological implications.

Authors: Crossley, R

• DOI: 10.5287/ora-j1obmp9vg
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: mathematical biology; extracellular matrix; travelling wave; phenotype; variational principle; heterogeneity
• Subjects: Differential equations, Partial--Numerical solutions; Applied mathematics; Population biology--Mathematical models; Mathematical models; Biology--Mathematical models; Developmental biology--Mathematical models