The purpose of this paper is to discuss how to model and analyze signaling pathways by using Petri net. Firstly, we propose a modeling method based on Petri net by paying attention to the molecular interactions and mechanisms. Then, we introduce a new notion "activation transduction component" in order to describe an enzymic activation process of reactions in signaling pathways and shows its correspondence to a so-called elementary T-invariant in the Petri net models. Further, we design an algorithm to effectively find basic enzymic activation processes by obtaining a series of elementary T-invariants in the Petri net models. Finally, we demonstrate how our method is practically used in modeling and analyzing signaling pathway mediated by thrombopoietin as an example.
This paper first presents basic Petri net components representing molecular interactions and mechanisms of signaling pathways, and introduces a method to construct a Petri net model of a signaling pathway with these components. Then a simulation method of determining the delay time of transitions of Petri net model, i.e. the time taken in firing of each transition, is proposed based on some simple principles that the number of tokens flowed into a place is equivalent to the number of tokens flowed out. Finally, the availability of proposed method is confirmed by observing signaling transductions in biological pathways through simulation experiments of the apoptosis signaling pathways as an example.
This paper deals with WF-net based modeling and verification of interorganizational workflows (interworkflows for short) based on the protocol of WfMC. In the protocol, there are three patterns of interoperability: Chained, Nested, and Parallel synchronized; and an interworkflow is constructed by using those interoperability patterns. We first give a WF-net based modeling method. In this modeling method, the three interoperability patterns are respectively expressed in terms of WF-nets. They enable us to model a given interworkflow as a WF-net by connecting WFnets representing its constituent workflows. We also indicate that if free choice WF-nets are connected by means of any combination of the three patterns then the resultant WF-net is asymmetric choice. Next we discuss verification of WF-nets obtained through the modeling method. Intuitively, a WF-net is said to be sound if, for any case, the initial state is always transformed to the final state. Unfortunately, even if every constituent WF-net is sound FC, the resultant WF-net is not always sound. We give a sufficient condition of non-soundness checkable in polynomial time. We also show that if they are connected by only the Nested pattern then the resultant WF-net is sound.
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