Stochastic Calculus of Looping Sequences for the Modelling and Simulation of Cellular Pathways

The paper presents the Stochastic Calculus of Looping Sequences (SCLS) suitable to describe microbiological systems, such as cellular pathways, and their evolution. Systems are represented by terms. 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 modelled by a set of rewrite rules enriched with stochastic rates representing the speed of the activities described by the rules, and can be simulated automatically. As applications, we give SCLS representations of the regulation process of the lactose operon in Escherichia coli and of the quorum sensing in Pseudomonas aeruginosa. A prototype simulator (SCLSm) has been implemented in F# and used to run the experiments. A public version of the tool is available at the url: http://www.di.unipi.it/~milazzo/biosims/.