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

Entropy

Francisco Chinesta¹  Morgan Magnin²  Olivier Roux²  Amine Ammar³  Elias Cueto⁴ 

[1] GeM, Ecole Centrale de Nantes, 1 rue de la Noe, 44300 Nantes, France;IRCCyN, Ecole Centrale de Nantes, 1 rue de la Noe, 44300 Nantes, France; E-Mail:;LAMPA, ENSAM Angers, 2 Boulevard du Ronceray, BP 93525, 49035 Angers Cedex 01, France; E-Mail:;I3A, Universidad de Zaragoza. Maria de Luna, s.n., E-50018 Zaragoza, Spain; E-Mail:

关键词: chemical master equation;    proper generalized decomposition (PGD);    qualitative modeling;    process hitting;    biological regulatory networks;    statistical mechanics;    kinetic theory;   

DOI  :  10.3390/e17041896

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland