Petri net siphon analysis and graph theoretic measures for identifying combination therapies in cancer.

Epidermal Growth Factor Receptor (EGFR) signaling to the Ras-MAPK pathway is implicated in the development and progression of cancer and is a major focus of targeted combination therapies. Physiochemical models have been used for identifying and testing the signal-inhibiting potential of targeted therapies, however, their application to larger multi-pathway networks is limited by the availability of experimentally-determined rate and concentration parameters. An alternate strategy for identifying and evaluating drug-targetable nodes is proposed. A physiochemical model of EGFR-Ras-MAPK signaling is implemented and calibrated to experimental data. Essential topological features of the model are converted into a Petri net and nodes that behave as siphons-a structural property of Petri nets-are identified. Siphons represent potential drug-targets since they are unrecoverable if their values fall below a threshold. Centrality measures are then used to prioritize siphons identified as candidate drug-targets. Single and multiple drug-target combinations are identified which correspond to clinically relevant drug targets and exhibit inhibition synergy in physiochemical simulations of EGF-induced EGFR-Ras-MAPK signaling. Taken together, these studies suggest that siphons and centrality analyses are a promising computational strategy to identify and rank drug-targetable nodes in larger networks as they do not require knowledge of the dynamics of the system, but rely solely on topology.