1. Insights from a qualitative analysis of a gene expression model with delays
- Author
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Marc R. Roussel, Hakkı Ulaş Ünal, Islam Boussaada, Silviu-Iulian Niculescu, Eskişehir Technical University, University of Lethbridge, Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Dynamical Interconnected Systems in COmplex Environments (DISCO), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and organisée par I. BOUSSAADA, G. MAZANTI, S.-I. NICULESCU, J. CHEN
- Subjects
Work (thermodynamics) ,Stability (learning theory) ,Expression (computer science) ,[SPI.AUTO]Engineering Sciences [physics]/Automatic ,biochemical systems ,chemistry.chemical_compound ,gene-regulatory systems ,Qualitative analysis ,chemistry ,Control and Systems Engineering ,Control system ,RNA polymerase ,Binding site ,Biological system ,Gene ,Delay systems ,Mathematics - Abstract
International audience; Delays appear in the dynamics of many systems due to non-vanishing reaction times of control systems. In biochemical systems, long sequences of repeated steps, especially in biopolymerization processes, can be modeled by delays. However, modelling systems with delays is often complicated by physical constraints, such as the requirement that solutions representing concentrations of chemical species remain positive. In this work, we consider a model for a detoxifying enzyme whose synthesis is controlled by its substrate. The model includes bindingsite clearance delays, caused by the time required for an RNA polymerase or ribosome to clear its binding site before another such machine can bind. The existence of a positive equilibrium and the positivity and boundedness of solutions of the corresponding delay-differential equations are proven. In addition, the stability of the model is studied using the "small-gain" theorem.
- Published
- 2021
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