Robustness in biological regulatory networks IV: Application to genetic networks controlling the cell cycle

Jacques Demongeot; Jules Waku

doi:10.1016/j.crma.2012.02.005

Dynamical Systems

Robustness in biological regulatory networks IV: Application to genetic networks controlling the cell cycle

Presented by: the Editorial Board

Jacques Demongeot ¹; Jules Waku ^1,²

¹ AGIM CNRS/UJF 3405, Université J. Fourier Grenoble I, Faculté de Médecine, 38700 La Tronche, France
² LIRIMA-UMMISCO, Université de Yaoundé, Faculté des Sciences, BP 812, Yaoundé, Cameroon

Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 293-298.

Abstract
Résumé

Various indices of complexity are used in biological regulatory networks like the number n of their components and I of the interactions between these components, their connectance (or connectivity) equal to the ratio $I / n$ , or the number of the strong connected components of their interaction graph. The stability of a biological network corresponds to its ability to recover from dynamical or parametric disturbance. Complexity is here quantified by the evolutionary entropy, which describes the way the asymptotic presence distribution or equilibrium distribution of the corresponding dynamical system is spread over the state space and the stability (or robustness) is characterized by the rate at which the system returns to its equilibrium distribution after a perturbation. This article applies these notions in the case of genetic networks having a getBren structure (i.e., being threshold Boolean random networks) and notably those controlling the cell cycle.

De nombres indices ont été proposés pour quantifier la complexité des réseaux biologiques de régulation, comme le nombre de leurs composants, leur connectivité, ou le nombre des composantes fortement connexes de leur graphe dʼinteraction. Quant à la stabilité de ces réseaux biologiques, elle correspond à leur capacité à absorber les changements dynamiques ou paramétriques. La complexité est ici mesurée par lʼentropie évolutionnaire, qui décrit la manière dont la probabilité de présence asymptotique du système dynamique correspondant est distribuée dans lʼespace dʼétat, et la stabilité est caractérisée par la vitesse de retour à lʼéquilibre de cette distribution, après perturbation. Cet article utilise ces notions dans le cadre de réseaux génétiques ayant une structure aléatoire booléenne à seuil, et plus particulièrement ceux contrôlant le cycle cellulaire.

Received: 2011-11-18
Accepted: 2012-01-04
Published online: 2012-03-01

DOI: 10.1016/j.crma.2012.02.005

Author's affiliations:

Jacques Demongeot ¹; Jules Waku ^{1, 2}

¹ AGIM CNRS/UJF 3405, Université J. Fourier Grenoble I, Faculté de Médecine, 38700 La Tronche, France
² LIRIMA-UMMISCO, Université de Yaoundé, Faculté des Sciences, BP 812, Yaoundé, Cameroon

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     author = {Jacques Demongeot and Jules Waku},
     title = {Robustness in biological regulatory networks {IV:} {Application} to genetic networks controlling the cell cycle},
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     language = {en},
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Jacques Demongeot; Jules Waku. Robustness in biological regulatory networks IV: Application to genetic networks controlling the cell cycle. Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 293-298. doi : 10.1016/j.crma.2012.02.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.02.005/

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