Stochastic modelling of cellular growth and division by means of the pi@ calculus

The application of Concurrency Theory to Systems Biology is in its earliest stage of progress. The metaphor of cells as computing systems by Regev and Shapiro opened the employment of concurrent languages for the modelling of biological systems. Their peculiar characteristics led to the design of many bio-inspired formalisms which achieve higher faithfulness and specificity. In this paper we discuss the application to the biological modelling of pi@, a core calculus for the representation of biological systems. The pi@ language represents a keystone in this respect, thanks to its expressiveness capabilities which allow the modelling of a wide variety of phenomena (e.g. simple chemical reactions, but also formation of molecular or protein complexes, organisation of complex system in dynamical compartment hierarchies) despite of its simplicity and conservativeness. Here we analyse a biological case study involving cellular growth and division, modelled in the stochastic variant of pi@: the case study is formalised and stochastically simulated according to a multi-compartment extension of Gillespie's stochastic simulation algorithm. The results underline the usefulness of the modelling approach adopted in pi@ for the correct handling of systems with variable volume.