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Biological Petri Nets
Constructing Biological Pathway Models
with Hybrid Functional Petri Nets
Atsushi Doi a , Sachie Fujita a , Hiroshi Matsuno a ,∗ , Masao Nagasaki b and Satoru Miyano b
a Faculty of Science, Yamaguchi University, Japan
E-mail: matsuno@sci.yamaguchi-u.ac.jp
b Human Genome Center, Institute of Medical Science, University of Tokyo, Japan
ABSTRACT: In many research projects on modeling and analyzing biological pathways, the Petri net has been recognized as
a promising method for representing biological pathways. From the pioneering works by Reddy et al., 1993, and Hofestadt,
1994, that model metabolic pathways by traditional Petri net, several enhanced Petri nets such as colored Petri net, stochastic
Petri net, and hybrid Petri net have been used for modeling biological phenomena. Recently, Matsuno et al., 2003b, introduced
the hybrid functional Petri net (HFPN) in order to give a more intuitive and natural modeling method for biological pathways
than these existing Petri nets. Although the paper demonstrates the effectiveness of HFPN with two examples of gene regulation
mechanism for circadian rhythms and apoptosis signaling pathway, there has been no detailed explanation about the method of
HFPN construction for these examples. The purpose of this paper is to describe method to construct biological pathways with
the HFPN step-by-step. The method is demonstrated by the well-known glycolytic pathway controlled by the lac operon gene
regulatory mechanism.
KEYWORDS: Hybrid functional Petri net, lac operon, biological pathway, simulation, Genomic Object Net
INTRODUCTION
A Petri net [Reisig, 1985] is method to describe and model concurrent systems. It has been mainly
used so far to model artificial systems such as manufacturing systems [Proth, 1997] and communication
protocols [Wheeler, 1999]. The first attempt to use Petri nets for modeling biological pathways was
made by Reddy et al., 1993, giving a method to represent metabolic pathways. Hofest adt expanded this
method to model metabolic networks [Hofest adt, 1994]. Subsequently, several enhanced Petri nets have
been used to model biological phenomena. Genrich et al., 2001, modeled metabolic pathways with a
colored Petri net by assigning enzymatic reaction speeds to the transitions, and simulated a chain of these
reactions quantitatively. Voss et al., 2003, used the colored Petri net in a different way, accomplishing
a qualitative analysis of steady state in metabolic pathways [Voss et al., 2003]. The stochastic Petri
net has been applied to model a variety of biological pathways; the ColE1 plasmid replication [Goss
and Peccoud, 1998], the response of the σ 32 transcription factor to a heat shock [Srivastava et al.,
2001], and the interaction kinetics of a viral invasion [Srivastava et al., 2002]. On the other hand, we
have shown that the gene regulatory network of λ phage can be more naturally modeled as a hybrid
Corresponding author.
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