BELGACEM , Ismail

The purpose of this thesis is the modeling, reduction, analysis and control of biologicalsystems. Modeling of biological networks is done by differential equations; the systemsare typically nonlinear, of large dimensions, with different time scales, and complex toanalyze. First, using techniques of monotone and compartmental systems, we study...

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We describe in this paper the global dynamical behavior of a mathematical model of expression of polymerase in bacteria. This model is given by a differential system and algebraic equations. We use some tools from monotone systems theory with concavity of nonlinearities to obtain a global qualitative result: either the trivial equilibrium is...

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The aim of this paper is to analyze the dynamical behaviour of models of gene transcription in a cell, developed in Kremling (2007), which are a detailed representation of transcription process from DNA to RNA with action of polymerase. Using monotone system theory and compartmental systems theory, we study several versions of these models. We...

We consider the full closed and open Michaelis-Menten enzymatic reactions. We study the corresponding dynamical system and show its global stability if the equilibrium exists. If the system is open, the equilibrium may not exist. Then we consider an open chain of reversible metabolic reactions and also prove global stability. Our mathematical...

We consider a chain of metabolic reactions catalyzed by enzymes, of reversible Michaelis-Menten type with full dynamics, i.e. not reduced with any quasi- steady state approximations. We study the corresponding dynamical system and show its global stability if the equilibrium exists. If the system is open, the equilibrium may not exist. The main...

In the context of gene regulatory networks, a negative feedback loop is modeled by N-coupled ordinary differential equations. The resulting system is highly non-linear due to the use of smooth Hill functions. This classical dynamical system properly captures the two main biological behaviors arising from this type of recurrent network motif:...

The oscillator made of a negative loop of two genes is one of the most classical motifs of genetic networks. We give solutions to control such an oscillator by modifying the synthesis rates. Our models are given by piecewise affine systems, and the control is qualitative, taking only two values. Thus, the necessary measurements for implementing...

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The aim of this paper is to analyse the dynamicalbehaviour of models of gene transcription-translation for thesynthesis of RNA polymerase in a cell, with a closed loopfrom the produced RNA polymerase (end-product) to thetranscription step (RNA polymerase is needed to transcribe itsown gene). Using monotone system theory we study a...

The aim of this paper is to analyze the dynamical behavior of biological models of gene transcription and translation. We focus on a particular positive feedback loop governing the synthesis of RNA polymerase, needed for transcribing its own gene. We write a high-dimension model based on mass-action laws and reduce it to a two-variable model...