Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.13087/2256
Title: Insights from a qualitative analysis of a gene expression model with delays
Authors: Ünal, Hakkı Ulaş
Roussel, Marc R.
Boussaada, Islam
Niculescu, Silviu-Iulian
Keywords: Delay systems
biochemical systems
gene-regulatory systems
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Differential Equations
Stochastic Simulation
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Responses
Systems
Issue Date: 2021
Publisher: Elsevier
Abstract: 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 binding-site 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. Copyright (C) 2021 The Authors.
Description: 24th International Symposium on Mathematical Theory of Networks and Systems (MTNS) -- 2020 -- Cambridge, ENGLAND
URI: http://doi.org/10.1016/j.ifacol.2021.06.174
https://hdl.handle.net/20.500.13087/2256
ISSN: 2405-8963
Appears in Collections:Elektrik-Elektronik Mühendisliği Bölümü Koleksiyonu
WoS İndeksli Yayınlar Koleksiyonu

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