A mathematical exploration of principles of collective cell migration and self-organisation

This thesis explores the role of collective cell migration and self-organisation in the development of the embryo and in vitro tissue formation through mathematical and computational approaches. We consider how population heterogeneity, microenvironmental signals and cell-cell interactions facilitate cells to collectively organise and navigate, with the aim to work towards uncovering general rules and principles, rather than delving into the microscopic molecular details. To ensure the biological relevance of our results, we collaborate closely with experimental biologists working on two model systems. First, to understand how neural crest cells obtain directionality, maintain persistence and specialise during their migration, we use computational simulations in parallel with imaging of chick embryos under genetic and surgical perturbations. We show how only a few cells adopting a leader state that enables them to read out chemical signals can lead a population of cells in a follower state over long distances in the embryo. Furthermore, we devise and test an improved mechanism of how cells dynamically switch between leader and follower states in the presence of a chemoattractant gradient. Our computational work guides the choice of new experiments, aids in their interpretation and probes hypotheses in ways the experiments can not. Secondly, to study the self-organisation of mouse skin cells in vitro, we draw on aggregation processes and scaling theory. Dermal and epidermal cells, after being dissociated and mixed, can reconstitute functional (transplantable and hair-growing) skin in culture. Using kinetic aggregation models and scaling analysis we show that the initial clustering of epidermal cells can be described by Smoluchowski coagulation, consistent with the dynamics of the "clustering clusters" universality class. Then, we investigate a potential mechanism for the size-regulation of cell aggregates during the later stages of the skin reconstitution process. Our analysis shows the extent to which this tissue formation follows a single physical process and when the transition to different dynamics occurs, which may be triggered by cellular biochemical changes.