Due to the difference between mass and signal flow, current modeling of metabolic and signaling networks has major discrepancies. Metabolic networks are typically represented as bipartite reaction graphs, where one node type symbolizes metabolites and another one reactions, in which metabolites participate. Metabolic network analysis mainly focuses on investigating mass fluxes through these graphs via flux balance analysis or via extraction of elementary sub-reaction systems (e.g. elementary flux modes). Signaling networks, on the other hand, are typically represented as protein-protein interaction graphs, where edges symbolize either activations (e.g. phosphorylation) or inhibitions (e.g. de-phosphorylation). Mathematical modeling of these networks includes ODEs, Boolean Networks as well as probabilistic approaches (e.g. Dynamic Bayesian Networks).

In this work we modeled and mathematically analyzed the well-known muscarinic M2 receptor-dependent signaling pathway combined with relevant secondary messenger molecules (Ca2+, cAMP) using mass action. Our developed model consists of about 180 reactions and 90 species double-checked and verified by literature review. In our joint signaling and metabolic model all binding and phosphorylation events are explicitly taken into account in order to enable subsequent stochiometric matrix analysis.

In particular, we adapted analysis of elementary flux modes, extreme pathways and flux sampling to investigate the principal behavior of the network. This way we could identify biologically important sub-networks which have been described in literature. Moreover, our model could reproduce the experimentally observable increase of cAMP production after receptor stimulation, which has an influence on the cytoskeleton structure (marked by aktin and tubulin) and in consequence changes the optical density of cells. Taken together our analysis suggests that mathematical tools developed for metabolic network analysis can also be applied to mixed metabolic and signaling models. This could be very helpful to perform a priori model analyses with little effort, and to generate hypotheses for further research.