Modelling the p53 gene regulatory network
p53 is the central protein in the DNA damage response and is part of a complex and extensive gene regulatory network. This network integrates a variety of stress signals to produce the up-regulation of active p53 and a range of effects including apoptosis, growth arrest and DNA damage repair. The p53 system has typically been studied qualitatively as a linear pathway, however this approach is insufficient to gain a full functional under standing of the dynamic nature of the network. In this work a better description of the DNA damage response will be constructed through the use of mathematical techniques. Ordinary differential equations models of the p53 network between DNA damage and p53 up-regulation are proposed, including a model that takes into account various localisation mechanisms. Parameter estimation is required to validate these models with biological data. A number of established techniques axe examined along with a novel method based on linear algebra, collocation and B-splines. To examine the network downstream of p53 and the global response to DNA damage, a "G" time profile (Gg(t)) quantifying the activity driving the formation of each gene is constructed. This is derived from a model of gene transcription, microarray data and mRNA degradation rates. The new parameter estimation technique developed works significantly better than the other techniques examined. Also, it was found that the mechanisms that control the location of p53 significantly contribute to the rapid DNA damage response. The G time profiles suggest that there are four principal transcription activities in the DNA damage response: p53, an early peaking response (possibly AP-1), stopping and restarting the cell cycle, and a double peaked response. The G time profile in combination with a training set of genes can be used to successfully find confirmed p53 targets.