A core calculus for the analysis and implementation of biologically inspired languages

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 [85] 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 thesis we present π@, an extremely simple and conservative extension of the π-calculus representing a keystone in this respect, thanks to its expressiveness capabilities. The π@ calculus is obtained by the addition of polyadic synchronisation and priority to the π-calculus, in order to achieve compartment semantics and atomicity of complex operations respectively. In its direct application to biological modelling, the stochastic variant of the calculus, Sπ@, is shown able to model consistently several phenomena such as formation of molecular complexes, hierarchical subdivision of the system into compartments, inter-compartment reactions, dynamic reorganisation of compartment structure consistent with volume variation. The pivotal role of π@ is evidenced by its capability of encoding in a compositional way several bio-inspired formalisms, so that it represents the optimal core of a framework for the analysis and implementation of bio-inspired languages. In this respect, the encodings of BioAmbients [88], Brane Calculi [22] and a variant of P Systems [78] into π@ are formalised. The conciseness of their translation into π@ allows their indirect comparison by means of their encodings. Furthermore it pro-