Geodesic
Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems
Aurélien Alfonsi1 ; Eric Cancès2 ; Gabriel Turinici3 ; Barbara Di Ventura4 ; Wilhelm Huisinga5
1 CERMICS, ENPC, 6-8 Avenue Blaise Pascal, Cité Descartes - Champs sur Marne, 77455 Marne la Vallée Cedex 2, France
2 CERMICS, ENPC, 6-8 Avenue Blaise Pascal, Cité Descartes, 77455 Marne la Vallée Cedex 2, France, and INRIA Rocquencourt, Domaine de Voluceau, 78153 Le Chesnay Cedex, France
3 INRIA Rocquencourt, Domaine de Voluceau, 78153 Le Chesnay Cedex, France and CERMICS, ENPC, 6-8 Avenue Blaise Pascal, Cité Descartes, 77455 Marne la Vallée Cedex 2, France
4 Structural Biology and Biocomputing program, EMBL, Meyerhofstrasse 1, 69117 Heidelberg, Germany
5 Corresponding author: Free University Berlin, Department of Mathematics and Computer Science, Arnimallee 2-6, D-14195 Berlin/Germany, and DFG Research Center , Berlin,
ESAIM. Proceedings, Tome 14 (2005), pp. 1-13.

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In the past years it has become evident that stochastic effects in regulatory networks play an important role, leading to an increasing in stochastic modelling attempts. In contrast, metabolic networks involving large numbers of molecules are most often modelled deterministically. Going towards the integration of different model systems, gen-regulatory networks become part of a larger model system including signalling pathways and metabolic networks. Thus, the question arises of how to efficiently and accurately simulation such coupled or hybrid systems. We present an algorithmic approach for the simulation of hybrid stochastic and deterministic reaction models that allows for adaptive step-size integration of the deterministic equations while at the same time accurately tracing the stochastic reaction events. We present a mathematical derivation of the hybrid system on the stochastic process level, and present numerical examples that outline the power of hybrid simulations.
DOI : 10.1051/proc:2005001

Aurélien Alfonsi 1 ; Eric Cancès 2 ; Gabriel Turinici 3 ; Barbara Di Ventura 4 ; Wilhelm Huisinga 5

1 CERMICS, ENPC, 6-8 Avenue Blaise Pascal, Cité Descartes - Champs sur Marne, 77455 Marne la Vallée Cedex 2, France
2 CERMICS, ENPC, 6-8 Avenue Blaise Pascal, Cité Descartes, 77455 Marne la Vallée Cedex 2, France, and INRIA Rocquencourt, Domaine de Voluceau, 78153 Le Chesnay Cedex, France
3 INRIA Rocquencourt, Domaine de Voluceau, 78153 Le Chesnay Cedex, France and CERMICS, ENPC, 6-8 Avenue Blaise Pascal, Cité Descartes, 77455 Marne la Vallée Cedex 2, France
4 Structural Biology and Biocomputing program, EMBL, Meyerhofstrasse 1, 69117 Heidelberg, Germany
5 Corresponding author: Free University Berlin, Department of Mathematics and Computer Science, Arnimallee 2-6, D-14195 Berlin/Germany, and DFG Research Center , Berlin, 
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Aurélien Alfonsi; Eric Cancès; Gabriel Turinici; Barbara Di Ventura; Wilhelm Huisinga. Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems. ESAIM. Proceedings, Tome 14 (2005), pp. 1-13. doi : 10.1051/proc:2005001. http://geodesic.mathdoc.fr/articles/10.1051/proc:2005001/

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