Continuous and spatial extension of stochastic π - calculus Final Year Project

In this project, we work towards a continuous and spatial extension of stochastic π calculus. The continuous semantics is a useful alternative to the discrete semantics and has been recently provided for other process algebras. Ability to express spatial properties of the models is an important practical extension, specially in Systems Biology. Inspired by previous work [7][20], after showing results on process aggregation in stochastic π calculus (Sπ) in form of multisets, we formulate and informally justify the continuous semantics. We show that this is tractable (in the sense that the set of resulting ordinary differential equations (ODEs) is finite) for the case of a subset of stochastic π calculus called Chemical Ground Form (CGF) defined in [7]. We attempt to tackle the problem of potentially infinite set of ODEs. We define two notions of finiteness, one allowing a direct analysis and another allowing further investigation of convergence results. We also provide an algorithm translating models in stochastic Sπ into CGF in case the finiteness is satisfied. We give a syntactical restriction of Sπ which guarantees finiteness. We intuitively and informally describe another condition on Sπ models guaranteeing finiteness. We explore the relationship between the continuous and discrete semantics. We experimentally look at the effect of scaling populations of processes in various existing models. We define a simple spatial extension of Sπ. We bring the aggregation results to this extension and define an extended continuous semantics. We give an original example demonstrating advantages of this extension. As an essential co-product, we develop an efficient, user friendly and portable tool implementing the above formalisms, with comparable simulation performance with the state of the art Stochastic Pi Machine (SPiM) simulator[32]. We also collect some of the available models in stochastic π calculus from Systems Biology, whose analysis can be enriched by the additional continuous semantics.