Description and analysis of switchlike regulatory networks exemplified by a model of cellular iron homeostasis

The post-transcriptional regulation of factors involved in the maintenance of cellular iron homeostasis is exerted by iron regulatory proteins (IRPs), which bind to mRNA structures known as iron regulatory elements (IREs). The IRP-IRE interactions are regulated by the intracellular iron level by affecting the binding affinity, synthesis and stability of the IRPs. A model of this homeostasis phenomenon is described and analysed within a methodological framework specifically designed for handling complex systems with steep sigmoidal input/output relationships between the state variables. According to the analysis there is only one threshold regulated homeostatic point. Approximate values for its coordinates, and the conditions ensuring its existence, may be given in terms of parameters. The analysis also provides some tentative insight into the evolution of the regulatory system. A comparison between analytical and numerical estimates of the position of the stationary point as a function of the steepness of the sigmoidal interactions show that the analytical approximations agree quite well with the numerical ones. The results show that we are able to obtain a deeper analytical insight by this methodological framework than what is achievable by most alternative approaches. We find this type of insight to be of considerable heuristic value in connection with the numerical simulation work which normally must be done to unfold the predictive potential of a complex model.