Mathematical Modelling of Collective Cell Migration

This project falls within the EPSRC Mathematical Biology research area.

Background
Collective cell migration is an integrated biological process, essential for the function of numerous organisms throughout their life span. For example, it plays a vital role in embryonic growth and tissue development, as well as in wound healing and cancer metastasis. In my doctoral project supervised by Prof. Ruth Baker and Prof. Sarah Waters, we will develop new mathematical frameworks of collective cell migration, focusing on the interplay between cells and the extracellular matrix (ECM, a network of proteins and molecules which provide biochemical and structural support for individual cells). In this context, a key unanswered question is
how do properties of the extracellular matrix enhance or decrease the ability of cells to invade a particular tissue.
We will adopt a multiscale modelling approach (see Methodology below) to probe this question. We will collaborate with the group of Prof. Paul Riley to apply our models to cardiac wound healing. By integrating our mathematical framework with experiments, our project will provide a novel interdisciplinary approach to understanding mechanisms driving cardiac fibrosis.
Objectives
Ob1). Build cell-only models of various complexities to incorporate different mechanisms of cell movements.
Ob2). Develop multiscale models that couple cell motility with ECM dynamics.
Ob3). Estimate model parameters using quantitative experimental data. Validate and refine the models to provide new biological insights.

Methodology
M1). We will apply agent-based modelling techniques to develop in-silico models of cell motility. Depending on different hypotheses and cell movement mechanisms, the in-silico models can range from on-lattice ones, such as cellular automata, to off-lattice ones, such as overlapping spheres. Numerical methods will be developed to simulate the model, where necessary harnessing techniques to improve efficiency, such as variance reduction and multigrid methods, to ensure it is possible to conduct widespread parameter sensitivity analysis (see M3 below).
M2). By coupling the ECM dynamics to the cell-only models in M1, we will construct multiscale models where cells are treated as individual entities and the ECM dynamics are modelled using systems of partial differential equations. The bi-directional linkages between cells and ECM (such as through contact guidance and matrix remodelling) will be considered. In addition, via coarse-graining methods, simplified, differential-equation-based models that are amenable to analytic exploration using approaches such as linear stability and travelling wave analysis will be developed.
M3). Based on experimental data from Prof. Riley's group, we will use a Bayesian framework to estimate model parameters and quantify their uncertainties. For instance, we will first use profile likelihood analysis to provide a preliminary assessment of practical identifiability before sampling from the posterior parameter distribution using a Metropolis-Hastings Markov Chain Monte Carlo algorithm. We will then perform model calibration, selection, and refinement using methods such as leave-one-out cross validation and identifiability analysis.
Impact
Equipped with data from Prof. Riley's group, we will develop the first fully validated model of cell migration through the ECM. This model will be used to explore the two-way coupling between cell movements and ECM dynamics. In a biological context, this model will enable us to better understand the mechanisms driving cardiac wound healing, and how to modulate the tipping point between optimal cardiac repair and excess inflammation and fibrosis.