Stochastic Simulation of Process Calculi for Biology

TL;DR

This paper introduces a generic abstract machine for stochastic simulation of biological process calculi, enabling flexible, on-the-fly reaction updates and supporting multiple calculi within a unified framework.

Contribution

It presents a novel abstract machine that can be instantiated with various process calculi and simulation algorithms, simplifying stochastic modeling of complex biological systems.

Findings

The abstract machine can be instantiated with Gillespie's Direct Method.

It allows dynamic updating of reactions during simulation.

Supports simultaneous simulation of multiple process calculi.

Abstract

Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. To model this complexity, numerous programming languages based on process calculi have been developed, many of which are expressive enough to generate unbounded numbers of molecular species and reactions. As a result of this expressiveness, such calculi cannot rely on standard reaction-based simulation methods, which require fixed numbers of species and reactions. Rather than implementing custom stochastic simulation algorithms for each process calculus, we propose to use a generic abstract machine that can be instantiated to a range of process calculi and a range of reaction-based simulation algorithms. The abstract machine functions as a just-in-time compiler, which dynamically updates the set of possible reactions and chooses the next reaction in an iterative cycle. In this short paper we give a brief summary of the generic abstract machine, and show how it can be instantiated with the stochastic simulation algorithm known as Gillespie's Direct Method. 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.