A generic abstract machine for stochastic process calculi

Abstract

International audienceThis paper presents a generic abstract machine for simulating a broad range of process calculi with an arbitrary reaction-based simulation algorithm. 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. Unlike existing simulation algorithms for chemical reactions, the abstract machine can simulate process calculi that generate potentially unbounded numbers of species and reactions. 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. As a proof of concept, the generic abstract machine is instantiated for the stochastic pi-calculus, and the instantiation is implemented as part of the SPiM stochastic simulator. The structure of the abstract machine facilitates a significant optimisation by allowing channel restrictions to be stored as species complexes. We also present a novel algorithm for simulating chemical reactions with general distributions, based on the Next Reaction Method of Gibson and Bruck. We use our generic framework 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

Stochastic Simulation of Process Calculi for Biology

“…Finally, the function next(T ) chooses a reaction from T with probability proportional to the reaction propensity, and computes the corresponding duration of the reaction according to [6]. We have also instantiated the abstract machine to the Next Reaction Method of [5] and to the NonMarkovian Next Reaction Method of [8], by defining corresponding init, next and updates functions, as described in [8]. We have used the abstract machine to implement the DNA Strand Displacement (DSD) calculus for modelling DNA circuits [12], the Genetic Engineering of Cells (GEC) calculus for modelling of genetic devices [9], and the Stochastic Pi Machine (SPiM) calculus for general modelling of biological systems [17], by defining appropriate species and reactions functions for each calculus.…”

“…Simulators for these three calculi are available online at http://research.microsoft.com/dna, http://research.microsoft.com/gec and http://research.microsoft.com/spim, respectively. Technical details of the instantiation of the generic abstract machine with the stochastic pi-calculus and the bioambient calculus are outlined in [8]. We are currently developing an instantiation of the generic abstract machine to the kappa calculus of [2].…”

“…Instead, a custom simulation algorithm is typically developed for each calculus. The choice of algorithm depends on the nature of the underlying biological system, such as whether exact simulation is required [6,5], whether certain reactions operate at different timescales [7,16], or whether non-Markovian reaction rates are needed [1,8].…”

“…In this short paper we give a brief summary of the generic abstract machine of [8], and show how it can be instantiated with the stochastic simulation algorithm of [6]. We also discuss the wider implications of such an abstract machine, and outline how it can be used to simulate multiple calculi simultaneously within a common framework.…”

Modelling, Simulating and Verifying Turing-Powerful Strand Displacement Systems

“…Section 2 presents an extension of the DSD language syntax and semantics [5] to model the formation of linear DNA heteropolymers, while Section 3 presents a stochastic simulation algorithm, based on [6], for DNA strand displacement systems involving polymers. Section 4 presents an encoding of a stack machine design in the DSD language which is optimised for mechanical verification.…”