We apply hybrid functional Petri net technique for representing and simulating the well known genetic switch mechanism of l phage to choose between lysis and lysogeny growth pathways. Which a phage selects lysis or lysogeny is basically decided depending on the concentration of CII protein which is affected by the condition of E. coli cell. Lysis and lysogeny pathways are kept by feedback loops of Cro and CI proteins, respectively (Figure 1). We translate the objects appearing in this network into the terms of HFPN as follows:

• Continuous places (doubled circles) contain real numbers which represent the concentrations of mRNA and proteins.
• Discrete places (single circles) correspond to the promoter or operator sites for expressing the binding situation of transcription factors, and also used for representing whether RNA polymerase is located between genes.
• Continuous transitions (white rectangles) are used for expressing the production/degradation speed of mRNA or proteins.
• Discrete transitions (black rectangles) are used for expressing the required time for RNA polymerase which moves between two genes, and also used for representing CI (Cro) binding condition on the three operator sites depending on the concentration of itself.
• Inhibitory arc (arc with small circle) is used for representing the biological process which relates to repression functions of gene products.

Figure 1: Transcription of the genes cro, cII and genes followed by cII gene from the promoter PR begin, when neither CI protein nor Cro protein does not bind to the operator sites OR3, OR2, and OR1. The genes cro, cII and the genes followed by cII will be transcripted from the promoter PR, when neither CI protein nor Cro protein does not bind to the operator sites OR3, OR2, and OR1. The condition of E. coli gives an effect to the concentration of CII protein. If the concentration of CII protein is low, the transcription from PR continues and keeps the concentration of Cro protein at some level by the feedback control of the Cro protein itself. On the other hand, if the concentration of CII protein is high, the CII protein binds to the promoter PRE as a positive transcription factor, then the transcription from PRE begins. Then, anti-sense RNA of the gene cro is produced, which helps to degrade the concentration of Cro protein more rapidly. Transcription of cI gene is followed and concentration of CI protein keeps at some level by the feedback control of the CI protein itself.

Figure 2: The central part of the switching mechanism of l phage and its hybrid functional Petri net (HFPN) description.