Hybrid Petri net representation of gene regulatory network.

It is important to provide a representation method of gene regulatory networks which realizes the intuitions of biologists while keeping the universality in its computational ability. In this paper, we propose a method to exploit hybrid Petri net (HPN) for representing gene regulatory networks. The HPN is an extension of Petri nets which have been used to represent many kinds of systems including stochastic ones in the field of computer sciences and engineerings. Since the HPN has continuous and discrete elements, it can easily handle biological factors such as protein and mRNA concentrations. We demonstrate that, by using HPNs, it is possible to translate biological facts into HPNs in a natural manner. It should be also emphasized that a hierarchical approach is taken for our construction of the genetic switch mechanism of lambda phage which is realized by using HPNs. This hierarchical approach with HPNs makes easier the arrangement of the components in the gene regulatory network based on the biological facts and provides us a prospective view of the network. We also show some computational results of the protein dynamics of the lambda phage mechanism that is simulated and observed by implementing the HPN on a currently available tool.