Modelling Collective Cell Migration

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Collective cell migration, in which individual cells move in a coherent manner, is commonly observed in many areas of biology and medicine, for example, developmental biology, wound healing, cancer growth. The goal of this project is to begin to develop a unified mathematical modelling framework in which to study this phenomenon. This mathematical framework should account for multicellular, multi-population interactions whilst possessing as many of the key relevant biological characteristics that accompany the dynamics of such systems as possible, while maintaining mathematical/computational tractability. Specific examples will include (i) neural crest cell migration, a phenomenon that occurs during embryogenesis, which is essential for the normal development of the embryo, and (ii) angiogenesis, the process by which new vasculature forms, either in response to wounding, or to cues released by cancer cells requiring more nutrient. These two examples are chosen because they span a broad range of application areas, while sharing many common processes. For example: in both cases there is cell phenotype heterogeneity, and cell phenotype can change in response to environment cues; key "leader" cells perform a biased random walk in response to a gradient in chemoattractant; cues (mechanical and chemical) are created by leader cells that influence and align "follower" cells. To date, these two processes have been modelled via a range of approaches - for example, agent-based models in which cells are considered as discrete entities responding to (and modifying) tissue-level cues represented by partial differential equations (PDEs), through to fully continuum descriptions in which non-local interactions are modelled via an integral kernel.In this project, we will aim to develop a single mathematical framework that can incorporate these two biological examples (and others) as special cases. We will investigate the vast literature that has been developed for flocking behaviour of animals in ecology, and exploit many of the similarities that exist between collective animal migration and collective cell migration, but also account for some of the very important differences. We will compare and contrast a number of different methodologies (for example, phenomenological PDE descriptions, kinetic theory and hydrodynamical model approaches) to investigate how different microscale (cell-level) properties scale up to the population, tissue-level macroscale. This unified mathematical framework would then allow us to compare and contrast these models in a systematic fashion and begin to identify and elucidate the hallmarks of collective cell migration. For example, we will use the model to develop insights on what is the range of non-local signalling required for robustly leading to successful cell invasion, and what different environmental cues ensure that cells adopt the correct phenotypic behaviours. We will then see how such behaviours are realised biologically through consulting the literature and in discussions with our experimental collaborators.This project falls within the EPSRC Mathematical Biology research area as it will advance mathematical modelling and interdisciplinary research in the biological sciences.