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.

Hybrid Calculus of Wrapped Compartments

COPPO, Mario;DAMIANI, Ferruccio;DROCCO, MAURIZIO;GRASSI, ELENA;SCIACCA, EVA;SPINELLA, SALVATORE;TROINA, ANGELO
2010

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.
Fourth Workshop on Membrane Computing and Biologically Inspired Process Calculi 2010 (MeCBIC 2010)
Jena, Germany
23 August 2010
40
102
120
http://arxiv.org/abs/1011.0051
http://rvg.web.cse.unsw.edu.au/eptcs/content.cgi?MeCBIC2010
Stochastic rewrite systems; Ordinary differential equations
Mario Coppo; Ferruccio Damiani; Maurizio Drocco; Elena Grassi; Eva Sciacca; Salvatore Spinella; Angelo Troina
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/81896
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