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Modeling the dynamics of the P53 regulation network with the negative feedback regulator Wip1 and P53 protein form expansion


In response to cellular stress, such as DNA damage, the tumor suppressor p53 is activated to regulate hundreds of genes involved in DNA damage repair, cell cycle arrest, apoptosis, and senescence. The regulation of p53 activation by Hdm2, HdmX, and kinases such as ATM, results in different dynamics in cancerous cells and normally proliferating cells. Multiple models have been published to quantitatively capture the dynamics of this regulation and have included between 2 and 20 compartments. We developed 5 and 6-compartment mathematical models of P53 regulation using ordinary differential equations (ODEs) by incorporating Wip1 mRNA and protein, a molecular gatekeeper of the p53 autoregulatory loop. We performed parameter estimation formulated as an optimization problem on noncancerous cell data to determine the values of 23 parameters and achieved a best fit for the 5-state variable model using a combination of global and local search algorithms and maximizing a log likelihood cost function. A couple of measured data points were not fitted within a 20% confidence interval and multiple parameters sets showed correlation through a covariance matrix analysis. We therefore explored the expansion of the P53 protein into its unphosphorylated and phosphorylated form as another method of capturing the complexity of the model and achieved a best fit using the Simplex search algorithm and a nonlinear least squares cost function where all measured data points were fitted within a 20% confidence interval. We tested this model on additional cancerous data yet only achieved an adequate fit with relatively large residuals and we propose additional tools such as parameter regularization and fitting on simulated data to achieve a more robust and accurate model.

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