A feedback approach to bifurcation analysis in biochemical networks with many parameters

Abstract

Feedback circuits in biochemical networks which underly cellular signaling pathways are important elements in creating complex behavior. A specific aspect thereof is how stability of equilibrium points depends on model parameters. For biochemical networks, which are modelled using many parameters, it is typically very difficult to estimate the influence of parameters on stability. Finding parameters which result in a change in stability is a key step for a meaningful bifurcation analysis. We describe a method based on well known approaches from control theory, which can locate parameters leading to a change in stability. The method considers a feedback circuit in the biochemical network and relates stability properties to the control system obtained by loop--breaking. The method is applied to a model of a MAPK cascade as an illustrative example