Abstract
Hybrid Petri net (HPN) is an extension of the Petri net formalism, which enables us to handle continuous information in addition to discrete information. Firstly, this paper demonstrates how biological pathways can be modeled by the integration of discrete and continuous elements, with an example of the λ phage genetic switch system including induction and retroregulation mechanisms. Although HPN allows intuitive modeling of biological pathways, some fundamental biological processes such as complex formation cannot be represented with HPN. Thus, this paper next provides the formal definition of hybrid functional Petri net with extension (HFPNe), which has high potential for modeling various kinds of biological processes. Cell Illustrator is a software tool developed on the basis of the definition of HFPNe. Hypothesis creation by Cell Illustrator is demonstrated with the example of the cyanobacterial circadian gene clock system. Finally, our ongoing tasks, which include the development of a computational platform for systems biology, are presented.
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Notes
The HPN model in (Matsuno et al. 2000) employs the firing rule “the firing rate of a continuous transition can be expressed as a function of the input places of the continuous transition,” which was defined in the notion of hybrid dynamic net in (Drath et al. 1999). The incorporation of this firing rule in the HPN allows us to represent the rate of a reaction in a biological pathway as a function of the substances of the reaction. This representation has been commonly used in the dynamic modeling of biological pathways [see e.g. Gilbert and Heiner (2006)].
For example, discrete places P L and P R in Fig. 5 are used to represent the promoter status of operons starting from N and Cro genes, respectively. The status of the promoter, i.e., the presence of a token in the place P L or P R in this case, is determined by the token provision from its adjacent transition which is further controlled by the content(s) of its upstream place(s).
Figure 5 involves two operons starting from discrete places P L and P R , which are comprised of the sequences of N-CIII-Xis-Int B and Cro-CII-O-P-Q, respectively.
For the actual values of thresholds in Fig. 5 including this th 1, refer to the CSML file of Cell Illustrator (see subsection 5.2) that can be download from the website (http://www.genome.ib.sci.yamaguchi-u.ac.jp/~matsuno/lambda_CI.zip).
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Acknowledgements
Hiroshi Matsuno, one of the authors of this paper, would like to express his gratitude to Dr. Atsushi Doi at Cell Innovator Inc., and Ms. Mao Yamaji at CORE Corporation who contributed to the constructions of the hybrid functional Petri net models of λ phage genetic switch and cyanobacteria circadian rhythm, respectively. This work is partially supported by Grant-in-Aid for Scientific Research on Priority Areas “Systems Genomics”and Grant-in-Aid for Scientific Research (B) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.
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Matsuno, H., Nagasaki, M. & Miyano, S. Hybrid Petri net based modeling for biological pathway simulation. Nat Comput 10, 1099–1120 (2011). https://doi.org/10.1007/s11047-009-9164-6
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DOI: https://doi.org/10.1007/s11047-009-9164-6