Modelling Collective Cell Migration

Collective cell motility is a widely observed phenomenon in many areas of biology, particularly in developmental biology and medicine. There have been a number of modelling approaches developed for studying the different modes of collective cell migration, ranging from partial differential equation models to individual-based models. However, such models generally do not take into account biological details such as population heterogeneity and the role of cell signalling, despite increasing evidence for their relevance in driving collective cell motility. As such, the aim of this project is to extend existing mathematical frameworks to include the presence of multiple different signalling cues, as well as cell heterogeneity and phenotypic switching.

This research will begin by considering the vast range of literature already available to draw upon the techniques used to study collective motion (not only in biology and medicine, but also in ecology). Much of this existing work concerns the movement of closely packed individuals (considered as point particles), with a focus on understanding how short-range interactions impact collective motility. The novel aspect of this research will be both to develop an understanding of how more loosely packed populations can move as a coherent unit, and to extend the models of high-density situations to take account of excluded volume effects.

The specific application will be to cranial neural crest cell migration. Proper migration of the neural crest is vital for normal development, but this system also serves as a paradigm for cell migration more generally (for example, tumour cell invasion). It has already been observed experimentally (driven by previous modelling studies by the Oxford group) that cells in the neural crest respond to multiple signalling cues and also switch phenotype. However, a systematic approach to modelling these phenomena has yet to be developed. To make progress on this challenging problem, I will first build a hybrid cellular automaton model in which I will encode phenotypic switching and multiple signalling cues (specifically chemotaxis and haptotaxis). I will then systematically coarse-grain this model to generate a new partial differential equation (PDE) model. Not only will this allow us to determine how parameters scale between microscopic (individual cell) and macroscopic (tissue or population) levels, it will also make explicit the model assumptions that are used to derive phenomenological PDE models.

We will use the hybrid cellular automaton framework to determine, in the context of the cranial neural crest, the appropriate implementation of a leader/follower description of cell migration, where 'leader' cells respond to a cell-induced gradient of chemoattractant, and influence the movement of 'followers' via haptotaxis. We will then coarse-grain this system to derive a PDE model which we envisage as being a fully nonlinear coupled system with novel nonlinear transport (diffusion and advection) and reaction terms that account for cell-environment feedback. Analysis of this model (analytical and numerical) will then allow us to determine how robust the behaviour of the model is to changes in parameter values and this, in turn, will suggest experiments for our collaborators to perform to validate the model.

This project falls within the EPSRC Mathematical Biology research area, as an interdisciplinary project aiming to improve the understanding of biological situations, including crowding, tumour growth and developmental biology through the use of mathematical modelling.