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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March 20, 2015 (v1)PublicationUploaded on: March 25, 2023
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December 14, 2020 (v1)Conference paper
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...
Uploaded on: December 4, 2022 -
February 2020 (v1)Journal article
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:...
Uploaded on: December 4, 2022 -
2018 (v1)Journal article
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...
Uploaded on: February 28, 2023