Dependent shrink for Petri net models of signaling pathways

Retention-free Petri net has been used in modeling of signaling pathways, which is a timed Petri net such that total input and total output token flows are equivalent at any place. Previously we have investigated the dependency of transitions in retention-free Petri net. In this paper, we introduce a modeling method for signaling pathway by using Petri net, giving properties of retention-freeness by considering arc weight. Based on the obtained properties, we propose an algorithm to find shrinkable transitions and to shrink them into a single transition. This algorithm eventually provides a set of transitions whose firing frequencies are dependent. As an example, we apply the algorithm to IL-3 signaling pathway Petri net model to show the usefulness of our proposed algorithm.