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| Stochastic models of receptor and co-receptor binding (MBM) | |||||||||||||
Most existing models of receptor clustering and cross-linking and multivalent ligands are based on ordinary differential equations (ODEs). If the number of receptors and/or ligands is small, ODEs are not the appropriate mathematical tool to describe these chemical reactions and one needs to make use of stochastic methods. We have recently developed a new model of how T cell receptors (TCRs) bind with multivalent ligands (pMHC dimers, tetramers or pentamers), including the role of co-receptors. Preliminary results from the new model qualitatively reproduce existing gold-immuno-labelling experiments and predict appropriate distributions and sizes of clusters of TCRs, both in naive and memory T cells of mice. The student will learn state-of-the-art models of initiation of TCR signalling, stoichiometry and assembly of the TCR/CD3 complex, and TCR/CD3 conformational changes as a mechanism contributing to T cell activation. Laboratory data (from Madrid, Basel and Heidelberg) will be used to test and refine stochastic models of multivalent TCR-pMHC interactions and the role of the co-receptor in the binding. Mathematical Biology and Medicine 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. 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 inlfuenced 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. |
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