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

• Main Authors: Atsushi Mizuta, Qi-Wei Ge, Hiroshi Matsuno
• Format: Article
• Language: English
• Published: MDPI AG 2016-12-01
• Series: Algorithms
• Subjects: signaling pathway; Petri net; retention-free Petri net; dependent shrink; dependency relation
• Online Access: http://www.mdpi.com/1999-4893/10/1/4

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.