*EPSRC* Developing realistic mathematical models of cell movement and interaction

Cell movement and cell-cell interactions play key roles in determining correlations in the relative cell positions and velocities in cell populations. Mathematical models of such systems have typically been deterministic, i.e., consisting of a set of coupled partial differential equations describing the temporal and spatial evolution of the local cell number density. However it is well known that such models are only accurate in the limit of large population densities. It is often the case that the number density of cells is low in some regions of space; in such a scenario, random fluctuations in the cell numbers become important and cannot be neglected. Stochastic models hence constitute a more general framework for modelling cell populations but their analysis is substantially more difficult than that of deterministic models. In this project, the aim is to develop novel methods to extract biologically relevant information from stochastic models of cell populations, as well as to develop new computationally efficient means of simulating such models.

This project is ideal for a student with a Bachelors or Masters in Applied Mathematics, Physics or Engineering. Previous familiarity with mathematical modelling in biology is useful but not a necessity.

The student will be given extensive interdisciplinary training in deterministic and stochastic modelling in biology in their first year to ensure a solid foundation. The student will be co-supervised by Dr. Ramon Grima (http://grimagroup.bio.ed.ac.uk/index.html) and Dr. Nikola Popovic (http://www.maths.ed.ac.uk/school-of-mathematics/people?person=148) and will be part of the Centre for Synthetic and Systems Biology (SynthSys) at the University of Edinburgh.