From structure to dynamics: frequency tuning in the p53-Mdm2 network. II Differential and stochastic approaches.

In Part I of this work, we carried out a logical analysis of a simple model describing the interplay between protein p53, its main negative regulator Mdm2 and DNA damage, and briefly discussed the corresponding differential model (Abou-Jaoudé et al., 2009). This analysis allowed us to reproduce several qualitative features of the kinetics of the p53 response to damage and provided an interpretation of the short and long characteristic periods of oscillation reported by Geva-Zatorsky et al. (2006) depending on the irradiation dose. Starting from this analysis, we focus here on more quantitative aspects of the dynamics of our network and combine the differential description of our system with stochastic simulations which take molecular fluctuations into account. We find that the amplitude of the p53 and Mdm2 oscillations is highly variable (to a degree that depends, however, on the bifurcation properties of the system). In contrast, peak width and timing remain more regular, consistent with the experimental data. Our simulations also show that noise can induce repeated pulses of p53 and Mdm2 that, at low damage, resemble the slow irregular fluctuations observed experimentally. Adding the stochastic dimension in our modeling further allowed us to account for an increase of the fraction of cells oscillating with a high frequency when the irradiation dose increases, as observed by Geva-Zatorsky et al. (2006).