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Entropy 2015, 17(4), 1896-1915; doi:10.3390/e17041896

Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions

1
GeM , Ecole Centrale de Nantes, 1 rue de la Noe, 44300 Nantes, France
2
IRCCyN, Ecole Centrale de Nantes, 1 rue de la Noe, 44300 Nantes, France
3
LAMPA, ENSAM Angers, 2 Boulevard du Ronceray, BP 93525, 49035 Angers Cedex 01, France
4
Universidad de Zaragoza. Maria de Luna, s.n., E-50018 Zaragoza, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Deniz Gencaga
Received: 31 December 2014 / Revised: 25 March 2015 / Accepted: 30 March 2015 / Published: 1 April 2015
View Full-Text   |   Download PDF [830 KB, uploaded 1 April 2015]   |  

Abstract

In this work, we begin by considering the qualitative modeling of biological regulatory systems using process hitting, from which we define its probabilistic counterpart by considering the chemical master equation within a kinetic theory framework. The last equation is efficiently solved by considering a separated representation within the proper generalized decomposition framework that allows circumventing the so-called curse of dimensionality. Finally, model parameters can be added as extra-coordinates in order to obtain a parametric solution of the model. View Full-Text
Keywords: 02.60.-x; 02.50.Ga; 87.18.-h 02.60.-x; 02.50.Ga; 87.18.-h
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Chinesta, F.; Magnin, M.; Roux, O.; Ammar, A.; Cueto, E. Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions. Entropy 2015, 17, 1896-1915.

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