# Mathematical model of the role and temporal dynamics of protein p53 after drug-induced DNA damage

2 MAMBA - Modelling and Analysis for Medical and Biological Applications
LJLL - Laboratoire Jacques-Louis Lions, Inria de Paris
Abstract : Various molecular pharmacokinetic–pharmacodynamic models have been proposed in the last decades to represent and predict drug effects in anticancer therapies. Most of these models are cell population based models since clearly measurable effects of drugs can be seen on populations of (healthy and tumour) cells much more easily than in individual cells.The actual targets of drugs are, however, cells themselves. The drugs in use either disrupt genome integrity by causing DNA strand breaks and consequently initiate programmed cell death or block cell proliferation mainly by inhibiting proteins (cdks) that enable cells to proceed from one cell cycle phase to another. DNA damage caused by cytotoxic drugs or $\gamma$-irradiation activates, among others, the p53 protein-modulated signalling pathways that directly or indirectly force the cell to make a decision between survival and death.The thesis aims to explore closely intracellular pathways involving p53, the guardian of the genome", initiated by DNA damage and thus to provide oncologists with a rationale to predict and optimise the effects of anticancer drugs in the clinic. It describes p53 activation and regulation in single cells following their exposure to DNA damaging agents. We show that dynamical patterns that have been observed in individual cells can be reconstructed and predicted by compartmentalisation of cellular events occurring either in the nucleus or in the cytoplasm, and by describing protein interactions, using both ordinary and partial differential equations, among several key antagonists including ATM, p53, Mdm2 and Wip1, in each compartment and in between them. Recently observed positive role of Mdm2 in the synthesis of p53 is explored and a novel mechanism triggering oscillations is proposed. For example, new model can explain experimental observations that previous (not only our) models could not, e.g., excitability of p53.Using mathematical methods we look closely on how a stimulus (e.g., $\gamma$-radiation or drugs used in chemotherapy) is converted to a specific (spatio-temporal) pattern of p53 whereas such specific p53 dynamics as a transmitter of cellular information can modulate cellular outcomes, e.g., cell cycle arrest or apoptosis. Mathematical ODE and reaction-diffusion PDE models are thus used to see how the (spatio-temporal) behaviour of p53 is shaped and what possible applications in cancer treatment this behaviour might have. Protein-protein interactions are considered as enzyme reactions. We present some mathematical results for enzyme reactions, among them the large-time behaviour of the reaction-diffusion system for the reversible enzyme reaction treated by an entropy approach. To our best knowledge this is published for the first time.
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• HAL Id : tel-01237604, version 1

### Citation

Jan Elias. Mathematical model of the role and temporal dynamics of protein p53 after drug-induced DNA damage. Number Theory [math.NT]. Université Pierre et Marie Curie - Paris VI, 2015. English. ⟨NNT : 2015PA066253⟩. ⟨tel-01237604⟩

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