Stochastic multiscale models of cell behaviour

Abstract

Cells are the fundamental units of life and, as such, the most simple entities for which we can meaningfully talk about behaviour. All living creatures, including humans, can be considered the result of the behaviour of a group of cells and their interactions. Some cellular behaviours play more central roles than others. For example, cell migration and cell division constitute the main driving forces of many homeostatic and pathological processes in human body. Elucidating the role of a specific cell behaviour on the emergence of a biological phenomenon is a fundamental step for many medical interventions. Despite the great experimental advances of the past century, we are still lacking a full understanding of how complex biological processes, such as the development of a multicellular organism, arise from the interactions of significantly simpler entities - cells. In this context, multiscale mathematical modelling represents a powerful assistive tool which, by employing a combination of discrete and continuum approaches, provides a theoretical framework to bridge between the microscopic and macroscopic dynamics of the cell population.
The goal of this thesis is to elucidate some complex dynamics driven by cell migration and proliferation. Throughout the work we will make systematic use of multiscale modelling. We will introduce a series of stochastic and deterministic models describing cell migration and proliferation with increasing levels of realism. By exploiting the mutual benefits offered by these different paradigms, we will develop an equivalence framework which allows the connection of microscopic cellular properties with the dynamics of the total population. In particular, the first part of this study will focus on the interaction between the phenomena of directional persistence with excluding properties and on the spatial correlation that emerges from their interplay. In the second part, we will explore the role of stochastic cell proliferation in the context of an invading cellular front and its importance when interpreting experimental observations.

Date of Award	13 May 2020
Original language	English
Awarding Institution	University of Bath
Supervisor	Kit Yates (Supervisor) & Tim Rogers (Supervisor)