Incorporation of Cycles and Inhibitory Arcs into the Timed Petri Net Model of Signaling Pathway

Yuki MURAKAMI  Qi-Wei GE  Hiroshi MATSUNO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.2   pp.514-524
Publication Date: 2013/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.514
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Mathematical Systems Science and its Applications)
Category: Concurrent Systems
signaling pathway,  timed Petri net,  retention-free Petri net,  self-loop,  cycle,  inhibitory arc,  

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In our privious paper, we proposed an algorithm that determines delay times of a timed Petri net from the structural information of a signaling pathway, but Petri net structures containing cycles and inhibitory arcs were not considered. This paper provides conditions for cycle-contained Petri nets to have reasonable delay times. Furthermore, handling of inhibitory arcs are discussed in terms of the reaction rate of inhibitory interaction in signaling pathway, especially the conversion process of Petri net with inhibitory arc to the one without inhibitory arc is given.