Modeling signal transduction in enzyme cascades with the concept of elementary flux modes

Concepts such as elementary flux modes (EFMs) and extreme pathways are useful tools in the detection of non-decomposable routes (metabolic pathways) in biochemical networks. These methods are based on the fact that metabolic networks obey a mass balance condition. In signal transduction networks, that condition is of minor importance because it is the flow of information that matters. Nevertheless, it would be interesting to apply pathway detection methods to signaling systems. Here, we present a formalism by which this can be achieved in the case of enzyme cascades operating, for example, by phosphorylation and dephosphorylation. It is based on the ideas that the signal is not diminished along each route and that the system has to return to its original state after each signaling event. We illustrate the method by several simple prototypic single-phosphorylation and double-phosphorylation cascades, including convergent and divergent branching. Moreover, it is applied to a specific example from insulin signaling. (See online Supplementary Material at www.liebertonline.com.).