From structure to dynamics: frequency tuning in the p53-Mdm2 network I. Logical approach.

We investigate the dynamical properties of a simple four-variable model describing the interactions between the tumour suppressor protein p53, its main negative regulator Mdm2 and DNA damage, a model inspired by the work of Ciliberto et al. [2005. Steady states and oscillations in the p53/Mdm2 network. Cell Cycle 4(3), 488-493]. Its core consists of an antagonist circuit between p53 and nuclear Mdm2 embedded in a three-element negative circuit involving p53, cytoplasmic and nuclear Mdm2. A major concern has been to develop an integrated approach in which various types of descriptions complement each other. Here we present the logical analysis of our network and briefly discuss the corresponding differential model. Introducing the new notion of "logical bifurcation diagrams", we show that the essential qualitative dynamical properties of our network can be summarized by a small number of bifurcation scenarios, which can be understood in terms of the balance between the positive and negative circuits of the core network. The model displays a wide variety of behaviours depending on the level of damage, the efficiency of damage repair and, importantly, the DNA-binding affinity and transcriptional activity of p53, which are both stress- and cell-type specific. Our results qualitatively account for several experimental observations such as p53 pulses after irradiation, failure to respond to irradiation, shifts in the frequency of the oscillations, or rapid dampening of the oscillations in a cell population. They also suggest a great variability of behaviour from cell to cell and between different cell-types on the basis of different post-translational modifications and transactivation properties of p53. Finally, our differential analysis provides an interpretation of the high and low frequency oscillations observed by Geva-Zatorsky et al. [2006. Oscillations and variability in the p53 system. Mol. Syst. Biol. 2, 2006.0033] depending on the irradiation dose. A more detailed analysis of our differential model as well as its stochastic analysis will be developed in a next paper.