Mathematical models of centromere associating proteins
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This thesis describes the development and analysis of new mathematical models of Centromere Protein A (CENP-A) incorporation in mammalian centromeres, intermolecular autophosphorylation and Aurora B kinase activity in prophase and metaphase. The models are all developed using a dynamical systems approach. CENP-A is incorporated as part of nucleosomes at centromeres and is required for correct chromosome segregation in mitosis. A first mathematical model of CENP-A incorporation is developed in Chapter 3. The results of simulations of this model are presented in Chapter 4. The model correctly produces the behaviour of the system and helps explain apparently conflicting experimental results. In Chapter 5, a generic model of intermolecular autophosphorylation is developed. The model includes dephosphorylation by a phosphatase of constant concentration, and predicts a threshold concentration for the phosphorylation of enzyme and the possible existence of a bistable switch. Aurora B is a mitotic kinase that localises to centromeres in prophase and metaphase and is vital in ensuring correct attachment of kinetochores to microtubules. A first model of Aurora B binding and activation is developed in Chapter 6 based on the autophosphorylation model of Chapter 5. The model supports the hypothesis that it is possible for soluble Aurora B in the cytoplasm to activate due to binding at centromeres. Both CENP-A and Aurora B play important roles in cellular regulation and have been identified as targets of cancer therapies due to their roles in cell division. The mathematical models developed in this thesis help to shed light on key mechanisms in the functioning of the cell.
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