Stochastic Simulation of Biological Systems with Dynamical Compartment Structure

The Gillespie stochastic simulation algorithm represents one of the main physical abstractions exploited for the simulation of biological systems modeled by means of concurrent calculi. While the faithful modelling of bio-systems often requires multi-compartment semantics, the original Gillespie algorithm considers only one fixed-size volume. In this paper we introduce an extended formalisation of the above algorithm which preserves the original model but allows the stochastic simulation in presence of multiple compartments with dynamical structure and variable sizes. The presented algorithm can be then used as basis for simulating systems expressed in an extended version of the stochastic π-Calculus, the Sπ@ language, obtained by means of polyadic synchronisation. Despite of its conservativeness, Sπ@ is showed to allow flexible modelling of multiple compartments with dynamical structure and to provide increased biological faithfulness.