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Biological Petri Nets
On Determining Firing Delay Time of
Transitions for Petri Net Based Signaling
Pathways by Introducing Stochastic Decision
Rules
Yoshimasa Miwa
a
,
1
, Chen Li
b
,
1
, Qi-Wei Ge
c
, Hiroshi Matsuno
a
,∗
and Satoru Miyano
b
a
Graduate School of Science and Engineering, Yamaguchi University, Yamaguchi, Japan
b
Human Genome Center, Institute of Medical Science, University of Tokyo, Minato-ku, Tokyo, Japan
c
Faculty of Education, Yamaguchi University, Yamaguchi, Japan
ABSTRACT:
Parameter determination is important in modeling and simulating biological pathways including signaling path-
ways. Parameters are determined according to biological facts obtained from biological experiments and scientific publications.
However, such reliable data describing detailed reactions are not reported in most cases. This prompted us to develop a general
methodology of determining the parameters of a model in the case of that no information of the underlying biological facts is
provided. In this study, we use the Petri net approach for modeling signaling pathways, and propose a method to determine
firing delay times of transitions for Petri net models of signaling pathways by introducing stochastic decision rules. Petri
net technology provides a powerful approach to modeling and simulating various concurrent systems, and recently have been
widely accepted as a description method for biological pathways. Our method enables to determine the range of firing delay
time which realizes smooth token flows in the Petri net model of a signaling pathway. The availability of this method has been
confirmed by the results of an application to the interleukin-1 induced signaling pathway.
KEYWORDS:
Petri net, interleukin-1 (IL-1) signaling pathway, firing delay time, stochastic decision rule, conflict resolution
INTRODUCTION
Petri net is a formal description for modeling concurrent systems [1]. Petri nets have recently been
widely accepted as a description method for biological pathways such as gene regulation networks,
metabolic pathways and signaling pathways by researchers in computer science as well as those in
biochemistry [2]. Various types of Petri nets (e.g. stochastic Petri nets [3,4], hybrid Petri nets [5,6],
colored Petri nets [7]) have been applied to study biological pathways in both quantitative and qualitative
1
These authors equally contributed to this work.
∗
Corresponding author: Hiroshi Matsuno, Graduate School of Science and Engineering, Yamaguchi University, Yoshida
1677-1, Yamaguchi, 753-8512, Japan. E-mail:
matsuno@sci.yamaguchi-u.ac.jp
.
