Decoding the Mechanism of Oscillations in Feedback-Connected Biological Networks

p53 is a transcription factor involved in cellular stress response, and plays a role in directing the programs of cell cycle arrest, DNA damage repair, and apoptosis. p53 protein levels are seen to undergo a series of pulses after ionizing radiation induced DNA damage. The signaling network associated with this response is complex, consisting of a number of feedback loops that both positively and negatively regulate p53 levels. We are interested in identifying the combination of feedback loops that drive p53's dynamics, and finding biochemical parameters that can specifically tune the period or amplitude of oscillation. In order to make such predictions based on system topology, we are developing methods analyze the function of feedback-connected biochemical networks.

We are conducting a combined experimental and theoretical study of the p53 oscillatory network. By introducing p53 driven by an inducible promoter and increasing p53 production from this promoter, we are able to elicit p53 upregulation without causing its phosphorylation and activation. This stimulus experimentally isolates the p53 network's core negative feedback loop. In this loop, p53 activates the ubiquitin ligase Mdm2, which subsequently signals p53 for degradation. This allows us to investigate a system in which the observed dynamics are linked to a known network topology. Here, we report that increasing p53's transcription rate leads to damped oscillation in p53 and Mdm2 concentration in individual cells, and the behavior of a typical cell can be fit to models of this negative feedback loop.

To understand this response, we constructed multiple models of the p53-Mdm2 negative feedback loop ranging in detail from a minimal 3-equation abstract model to a detailed, 25-equation mass-action model. These models vary both in their representations of the species, as well as their reactions with one another. In order to compare their mechanisms of operation, we are challenged to identify lumped parameters that can be computationally measured from each model. With such metrics in hand, it would be possible to compare their relationship to features of output trajectories across multiple models.

We have developed a small-signal technique to obtain two such metrics, and can compute the gain and transit time around feedback loops consisting of cascades of nonlinear chemical reactions. This method reduces to the lifetime of species in a reaction cascade under hypothesis that allow this lifetime to be computed. These particular metrics are motivated by the fact that many biological systems are connected in multiple non-interacting feedback loops, such as those regulating p53, and that these parameters are a first approximation to the effects of these feedback connections.

Applying this method to each model elucidates striking similarities in their responses. In particular, we find that the transit time around the negative feedback loop is linearly related to the timing between pulses, and that the strength of feedback modulates the slope of this line. These results stand in stark contrast to those obtained by standard sensitivity analyses performed on each model, which indicate that individual biochemical rates have complex and ambiguous relationships to model outputs. This work suggests that common principles may underlie the basic operation of feedback-connected network models.

In future work, we plan to extend this analysis to candidate models of the full p53 network after DNA damage. The larger p53 network consists of a large number of feedback loops. To make predictions about the relative importance of these loops, we will build and fit models of subsets of these loops. Application of the techniques to compare the operation of these models should allow us to make predictions about the relative importance of each feedback loop in governing the system's dynamical response.