Geodesic
Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems
Aurélien Alfonsi1 ; Eric Cancès2 ; Gabriel Turinici3 ; Barbara Di Ventura4 ; Wilhelm Huisinga5
1CERMICS, ENPC, 6-8 Avenue Blaise Pascal, Cité Descartes - Champs sur Marne, 77455 Marne la Vallée Cedex 2, France
2CERMICS, 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
3INRIA 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
4Structural Biology and Biocomputing program, EMBL, Meyerhofstrasse 1, 69117 Heidelberg, Germany
5Corresponding 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
Cet article a éte moissonné depuis la source EDP Sciences

Voir la notice de l'article

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, 
@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

Cité par Sources :