Modeling of Genetic Regulatory Network in Stochastic π-Calculus

In this paper, we address the problem of modeling biological regulatory networks thanks to the stochastic pi-calculus. We propose a method which extends a logical method, that is the approach of Rene Thomas. By introducing temporal and stochastic aspects there, we make our formalism closer to biological reality. We then use the SPiM stochastic simulator to illustrate the practical interests of this description. The application example concerns the behaviors of four interacting genes involved in the A-phage. Interesting results are emerging from the simulations. First, it confirms knowledge of the regulation phenomena. In addition, experiments with different values of the delay parameters give some precious hints of a tendency either for the lytic phase or to the lysogenic phase.