Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems
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.
Affiliations des auteurs :
Aurélien Alfonsi 1 ; Eric Cancès 2 ; Gabriel Turinici 3 ; Barbara Di Ventura 4 ; Wilhelm Huisinga 5
@article{EP_2005_14_a1,
author = {Aur\'elien Alfonsi and Eric Canc\`es and Gabriel Turinici and Barbara Di Ventura and Wilhelm Huisinga},
title = {Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems},
journal = {ESAIM. Proceedings},
pages = {1--13},
year = {2005},
volume = {14},
doi = {10.1051/proc:2005001},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:2005001/}
}
TY - JOUR AU - Aurélien Alfonsi AU - Eric Cancès AU - Gabriel Turinici AU - Barbara Di Ventura AU - Wilhelm Huisinga TI - Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems JO - ESAIM. Proceedings PY - 2005 SP - 1 EP - 13 VL - 14 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc:2005001/ DO - 10.1051/proc:2005001 LA - en ID - EP_2005_14_a1 ER -
%0 Journal Article %A Aurélien Alfonsi %A Eric Cancès %A Gabriel Turinici %A Barbara Di Ventura %A Wilhelm Huisinga %T Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems %J ESAIM. Proceedings %D 2005 %P 1-13 %V 14 %U http://geodesic.mathdoc.fr/articles/10.1051/proc:2005001/ %R 10.1051/proc:2005001 %G en %F EP_2005_14_a1
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
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