Efficient Stochastic Simulation of Biological Systems with Multiple Variable Volumes

The application of concurrent calculi to the formalisation of biological systems constitutes a promising approach to the analysis in silico of biological phenomena. The Gillespie algorithm is one of the main models exploited for their stochastic simulation. While the original algorithm considers only one fixed-volume compartment, the simulation of biological systems often requires multi-compartment semantics. In this paper we present an enhanced formulation of an extended version of the algorithm which handles multiple compartments with varying volumes. The presented algorithm is used as basis for the implementation of an extension of the stochastic π-Calculus, called Sπ@, which allows an intuitive and concise formalisation of such systems. The algorithm is also efficient in presence of a high number of compartments and reactions, therefore Sπ@ represents the starting point for the development of an effective tool for the simulation of biological systems with dynamical structure even in presence of computationally expensive phenomena like diffusion.