Bifurcation Analysis for Intracellular Regulation Networks Based on Their Circuit Structure

In earlier work we have developed the circuit-breaking algorithm. This algorithm uses the topology of a dynamic model for a regulatory network to construct a one-dimensional circuit-characteristic. Zeros of this characteristic correspond to the fixed points of the system. Here we use the circuit-breaking algorithm as a tool to identify feedback circuits that are responsible for fixed point bifurcations, which are a main source of complex dynamic behavior. The methods are applied to and evaluated with two biological network models, a simplified regulatory network for a switch with three interconnected positive circuits, and a more complex network for cell cycle control in Xenopus frog eggs.