EPTCS Proceedings of the Fourth Workshop on Membrane Computing and Biologically Inspired Process Calculi 2010

Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. Numerous programming languages have been developed for modelling such systems, many of which are based on process calculi. Most of these calculi, particularly those involving membrane interactions, are expressive enough to generate potentially unbounded numbers of species and reactions. As a result, they cannot rely on standard reaction-based simulation algorithms or tools, since these require a fixed number of species and reactions. Therefore, most calculi generally require a custom algorithm to be developed. To help address this issue, we propose a generic abstract machine that can be instantiated to a broad range of process calculi and a range of reaction-based simulation algorithms. This is achieved by means of a just-in-time compiler, which dynamically updates the set of possible reactions and chooses the next reaction in an iterative cycle. The abstract machine is instantiated to a particular calculus by defining two functions: one for transforming a process of the calculus to a set of species, and another for computing the set of possible reactions between species. As a proof of concept, the generic abstract machine is instantiated to the stochastic pi-calculus, and the instantiation is implemented as part of the SPiM stochastic simulator. The implementation is used to simulate a stochastic pi-calculus model of plasmid co-transfection, where plasmids can form aggregates of arbitrary size and where rates of mRNA degradation are non-exponential. The example illustrates the flexibility of our framework, which allows an appropriate high-level language to be paired with the required simulation algorithm, based on the biological system under consideration. To illustrate the broader applicability of the approach, we outline how the generic abstract machine can be instantiated to a variant of the stochastic bioambient calculus for simulating mobile compartments, and to a variant of the DNA strand displacement calculus for simulating computation in DNA.