Exploring mechanisms of oscillations in p53 and nuclear factor-κb systems

A number of regulatory networks have the potential to generate sustained oscillations of irregular amplitude, but well conserved period. Single-cell experiments revealed that in p53 and nuclear factor (NF)-kappaB systems the oscillation period is homogenous in cell populations, insensitive to the strength of the stimulation, and is not influenced by the overexpression of p53 or NF-kappaB transcription factors. We propose a novel computational method of validation of molecular pathways models, based on the analysis of sensitivity of the oscillation period to the particular gene(s) copy number and the level of stimulation. Using this method, the authors demonstrate that existing p53 models, in which oscillations are borne at a saddle-node-on-invariant-circle or subcritical Hopf bifurcations (characteristic for systems with interlinked positive and negative feedbacks), are highly sensitive to gene copy number. Hence, these models cannot explain existing experiments. Analysing NF-kappaB system, the authors show the importance of saturation in transcription of the NF-kappaB inhibitor IkappaBkappa. Models without saturation predict that the oscillation period is a rapidly growing function of total NF-kappaB level, which is in disagreement with experiments. The study supports the hypothesis that oscillations of robust period are based on supercritical Hopf bifurcation, characteristic for dynamical systems involving negative feedback and time delay. We hypothesise that in the p53 system, the role of positive feedback is not sustaining oscillations, but terminating them in severely damaged cells in which the apoptotic programme should be initiated.