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Theses Year : 2015

Modelling, analysis and control of biological networks

Modélisation, analyse et commande des réseaux biologiques


The purpose of this thesis is the modeling, reduction, analysis and control of biological systems. Modeling of biological networks is done by differential equations; the systems are typically nonlinear, of large dimensions, with different time scales, and complex to analyze. First, using techniques of monotone and compartmental systems, we study the global stability of the equilibrium of Michaelis-Menten enzymatic model without any approximation, when the system is closed or opened; we also study the general case of a chain of enzymatic reactions. Biological networks are generally composed of two parts in interaction (genetic and metabolic), we therefore investigate different types of models coupling metabolic reactions chains with a genetic system; we reduce the full system based on the difference in time scales (Tikhonov theorem). In the second part, we apply the same techniques of monotone systems to study a general model of gene expression. Then we consider a model of a loop where the polymerase allows the transcription of the gene of polymerase. This model is not monotone, but based on the parameter values provided by biologists, we have reduced it to a simple and monotone model. The study of the reduced system shows that the full system can have either a single equilibrium point at the origin which is globally stable or there is another one stable strictly positive equilibrium and the origin is locally unstable. The alternative between these two cases depends on the total amount of the concentration of ribosomes. We then study a general model of the genetic machinery, taking the model studied previously for the polymerase and coupling it with a model for the synthesis of ribosomes. We finally apply different types of qualitative controls on models of small nonlinear gene networks to stabilize for example an unstable equilibrium point or to generate a limit cycle instead of a stable equilibrium.
Le but de cette thèse est la modélisation, la réduction, l’analyse et la commande de systèmes biologiques.
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Dates and versions

tel-01243874 , version 1 (17-12-2015)




  • HAL Id : tel-01243874 , version 1


Ismail Belgacem. Modelling, analysis and control of biological networks. Automatic Control Engineering. Université Nice Sophia-Antipolis, 2015. English. ⟨NNT : ⟩. ⟨tel-01243874⟩
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