The goal of this project is to develop mathematical and computational models to help understand how the immune system maintains its diversity of millions of lymphocyte populations, able to protect against pathogens while avoiding auto-immune diseases. The processes of positive and negative selection in the thymus will be studied with stochastic modelling techniques, including computational modelling and analysis of experimental data.
The student will make use of the theory of multi-variate stochastic processes to develop mathematical models of positive and negative selection in the thymus. The first models to be developed will only involve modelling the population of thymocytes as a function of time, and it is to be expected that the student will develop four-dimensional models (in space and time) of the cellular interactions that take place in the thymus before T cells are exported to peripheral tissues, such as the lymph nodes. The student will benefit from the immunological expertise of our collaborators (Prof. Palmer, Switzerland, Prof. Anderson, Birmingham and Prof. Garside, Glasgow).
Key words: Stochastic processes, T cell development, birth-and-death Markov processes, parameter estimation, model selection, mathematical biology, applied mathematics
Modelling biological systems is one of the most challenging and fastest growing research areas in Applied Mathematics. Mathematics and physics are used to describe biology at different levels: genes, proteins, cells and populations.
The description can be simple, such as the time evolution of the number of cells, or more complex, such as the description, both in space and time, of the molecules inside a cell. In this group, the five permanent members of staff work with four postdocs and postgraduate students.
Mathematical Biology and Medicine Group
In the Leeds Mathematical Biology and Medicine group, research is being carried out in theoretical immunology, gene regulatory networks, and synchronisation in neuronal networks. The immune system is one of the most complicated multiscale systems imaginable. The adaptive immune system of a vertebrate is a vast army of cells and molecules that cooperate to seek out, mark, bind to and destroy pathogens. Stochastic modelling is ideally suited to immunology at many scales. For example, cells live in a Brownian world, where motion is partly directed and partly random, so the battle between invading pathogens and the immune system is best described statistically.
Similarly, gene expression is influenced by noise and fluctuations: small numbers of molecules as well as the intrinsically stochastic nature of biochemical reactions mean that fluctuations must be taken into account in order to understand cellular function.