Hybrid Calculus of Wrapped Compartments

TL;DR

This paper introduces a hybrid simulation method combining stochastic and ODE approaches for biological systems modeled in the calculus of wrapped compartments, enabling efficient analysis of systems with varying molecular counts and dynamic compartmentalization.

Contribution

It presents a novel hybrid simulation technique that integrates stochastic and deterministic models within the CWC calculus framework for biological systems.

Findings

Enables efficient simulation of compartmentalized biological systems.

Balances stochastic and deterministic modeling for different molecular regimes.

Provides a flexible approach for dynamic compartmentalization analysis.

Abstract

The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of ordinary differential equations (ODEs). Alternative approaches based on formal calculi, often derived from process algebras or term rewriting systems, provide a quite complementary way to analyze the behaviour of biological systems. These calculi allow to cope in a natural way with notions like compartments and membranes, which are not easy (sometimes impossible) to handle with purely numerical approaches, and are often based on stochastic simulation methods. Recently, it has also become evident that stochastic effects in regulatory networks play a crucial role in the analysis of such systems. Actually, in many situations it is necessary to use stochastic models. For example when the system to be described is based on the interaction of few molecules, when we are at the presence of a chemical instability, or when we want to simulate the functioning of a pool of entities whose compartmentalised structure evolves dynamically. In contrast, stable metabolic networks, involving a large number of reagents, for which the computational cost of a stochastic simulation becomes an insurmountable obstacle, are efficiently modelled with ODEs. In this paper we define a hybrid simulation method, combining the stochastic approach with ODEs, for systems described in CWC, a calculus on which we can express the compartmentalisation of a biological system whose evolution is defined by a set of rewrite rules.