Stochastic biological modelling in the presence of multiple compartments

The application of concurrent calculi to the formalisation of biological systems constitutes a promising approach to the analysis of biological phenomena in silico. The peculiar nature of such systems inspired the introduction of specific features in biologically-oriented calculi, such as compartments to model more faithfully their highly organised structure.In this paper we present Sπ@, a conservative extension of the stochastic π-calculus which allows an intuitive and concise formalisation of multi-compartment systems with dynamic structure, despite retaining the simplicity of the original π-calculus. The possibility to encode into Sπ@ several bio-inspired, compartmentalised languages demonstrates its expressive power and flexibility.The calculus is accompanied by an extended version of Gillespie’s stochastic simulation algorithm, able to handle multiple compartments with varying volumes. An enhanced formalisation of the algorithm is also presented, in order to provide efficient simulation in the presence of a high number of compartments and reactions.