[Robustesse dans les réseaux de régulation biologique III : Applications biologiques aux réseaux génétiques contrôlant la morphogénèse]
Cette Note utilise les notions mathématiques existant entre entropie et vitesse de retour à lʼéquilibre dans les graphes dʼinteraction des réseaux génétiques de manière générale, appliquées ici au cas particulier des réseaux de régulation génétique booléens probabilistes à seuil (appelés getBrens). Il est prouvé que, dans certaines circonstances de connectivité particulière, lʼentropie de la mesure invariante du système dynamique peut être considérée à la fois comme un indice de complexité et de stabilité, en montrant explicitement le lien existant entre ces deux notions fondamentales, afin de mieux caractériser la résistance dʼun système biologique à des perturbations endogènes ou exogènes, comme dans le cas des n-switches. Des exemples de réseaux sont ensuite traités, montrant lʼintérêt pratique des notions de complexité et stabilité introduites dans cet article. Ils concernent le contrôle de la morphogénèse.
This Note deals with the mathematical notions of entropy and stability rate in interaction graphs of genetic networks, in the particular context of the genetic threshold Boolean random regulatory networks (getBrens). It is proved that in certain circumstances of particular connectance, the entropy of the invariant measure of the dynamical system can be considered both as a complexity and a stability index, by exploiting the link between these two notions, fundamental to characterize the resistance of a biological system against endogenous or exogenous perturbations, as in the case of the n-switches. Examples of biological networks are then given showing the practical interest of the mathematical notions of complexity and stability in the case of the control of the morphogenesis.
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@article{CRMATH_2012__350_5-6_289_0,
author = {Demongeot, Jacques and Waku, Jules},
title = {Robustness in biological regulatory network {III:} {Application} to genetic networks controlling the morphogenesis},
journal = {Comptes Rendus. Math\'ematique},
pages = {289--292},
publisher = {Elsevier},
volume = {350},
number = {5-6},
year = {2012},
doi = {10.1016/j.crma.2012.01.002},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.01.002/}
}
TY - JOUR AU - Demongeot, Jacques AU - Waku, Jules TI - Robustness in biological regulatory network III: Application to genetic networks controlling the morphogenesis JO - Comptes Rendus. Mathématique PY - 2012 SP - 289 EP - 292 VL - 350 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.01.002/ DO - 10.1016/j.crma.2012.01.002 LA - en ID - CRMATH_2012__350_5-6_289_0 ER -
%0 Journal Article %A Demongeot, Jacques %A Waku, Jules %T Robustness in biological regulatory network III: Application to genetic networks controlling the morphogenesis %J Comptes Rendus. Mathématique %D 2012 %P 289-292 %V 350 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.01.002/ %R 10.1016/j.crma.2012.01.002 %G en %F CRMATH_2012__350_5-6_289_0
Demongeot, Jacques; Waku, Jules. Robustness in biological regulatory network III: Application to genetic networks controlling the morphogenesis. Comptes Rendus. Mathématique, Tome 350 (2012) no. 5-6, pp. 289-292. doi : 10.1016/j.crma.2012.01.002. http://www.numdam.org/articles/10.1016/j.crma.2012.01.002/
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