Stochastic CLS for the Modeling and Simulation of Biological Systems

The paper presents the Stochastic Calculus of Looping Sequences (Stochastic CLS) suitable to describe microbiological systems and their evolution. The terms of the calculus are constructed by basic constituent elements and operators of sequencing, looping, containment and parallel composition. The looping operator allows tying up the ends of a sequence, thus creating a circular sequence which can represent a membrane. The evolution of a term is modeled by a set of rewrite rules enriched with stochastic rates representing the speeds of the activities described by the rules. The evolution of terms described by using the Stochastic CLS can be simulated automatically. As an application, we give a Stochastic CLS representation of the regulation process of the lactose operon in Escherichia coli and we perform some simulations.