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Algorithms 2017, 10(1), 4; doi:10.3390/a10010004

Dependent Shrink of Transitions for Calculating Firing Frequencies in Signaling Pathway Petri Net Model

1
Graduate School of Science and Engineering, Yamaguchi University, Yamaguchi 7538512, Japan
2
Faculty of Education, Yamaguchi University, Yamaguchi 7538513, Japan
3
Graduate School of Science and Technology for Innovation, Yamaguchi University, Yamaguchi 7538512, Japan
*
Author to whom correspondence should be addressed.
Academic Editors: Henning Fernau and Takeyuki Tamura
Received: 13 August 2016 / Revised: 5 December 2016 / Accepted: 26 December 2016 / Published: 31 December 2016
(This article belongs to the Special Issue Biological Networks)
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Abstract

Despite the recent rapid progress in high throughput measurements of biological data, it is still difficult to gather all of the reaction speed data in biological pathways. This paper presents a Petri net-based algorithm that can derive estimated values for non-valid reaction speeds in a signaling pathway from biologically-valid data. In fact, these reaction speeds are reflected based on the delay times in the timed Petri net model of the signaling pathway. We introduce the concept of a “dependency relation” over a transition set of a Petri net and derive the properties of the dependency relation through a structural analysis. Based on the theoretical results, the proposed algorithm can efficiently shrink the transitions with two elementary structures into a single transition repeatedly to reduce the Petri net size in order to eventually discover all transition sets with a dependency relation. Finally, to show the usefulness of our algorithm, we apply our algorithm to the IL-3 Petri net model. View Full-Text
Keywords: signaling pathway; Petri net; retention-free Petri net; dependent shrink; dependency relation signaling pathway; Petri net; retention-free Petri net; dependent shrink; dependency relation
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Mizuta, A.; Ge, Q.-W.; Matsuno, H. Dependent Shrink of Transitions for Calculating Firing Frequencies in Signaling Pathway Petri Net Model. Algorithms 2017, 10, 4.

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