Reduction and stability analysis of a transcription-translation model of RNA polymerase

Autor: Stefano Casagranda, Edith Grac, Delphine Ropers, Jean-Luc Gouzé, Ismail Belgacem
Přispěvatelé: Biological control of artificial ecosystems (BIOCORE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de la Recherche Agronomique (INRA)-Laboratoire d'océanographie de Villefranche (LOV), Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de la Mer de Villefranche (IMEV), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de la Mer de Villefranche (IMEV), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Modeling, simulation, measurement, and control of bacterial regulatory networks (IBIS), Laboratoire Adaptation et pathogénie des micro-organismes [Grenoble] (LAPM), Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Jean Roget, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA), Conseil Regional PACA, Investissements d'Avenir Bio-informatique programme under Project RESET [ANR-11-BINF-0005], Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Inria Grenoble - Rhône-Alpes, Université Côte d'Azur (UCA)
Jazyk: angličtina
Rok vydání: 2018
Předmět:
0301 basic medicine
Monotone systems
Transcription
Genetic
General Mathematics
[SDV]Life Sciences [q-bio]
Immunology
Systems Theory
Computational biology
medicine.disease_cause
Models
Biological
General Biochemistry
Genetics and Molecular Biology
Quantitative Biology::Subcellular Processes
03 medical and health sciences
chemistry.chemical_compound
[SPI]Engineering Sciences [physics]
Transcription (biology)
RNA polymerase
[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering
Escherichia coli
medicine
Computer Simulation
[MATH]Mathematics [math]
Gene
General Environmental Science
Positive feedback
Reduction
Pharmacology
Physics
Messenger RNA
General Neuroscience
Quantitative Biology::Molecular Networks
Trivial equilibrium
Biochemical models
DNA-Directed RNA Polymerases
Mathematical Concepts
Quantitative Biology::Genomics
030104 developmental biology
Monotone polygon
Computational Theory and Mathematics
chemistry
Protein Biosynthesis
Transcription-translation model
General Agricultural and Biological Sciences
Stability
Zdroj: Bulletin of Mathematical Biology
Bulletin of Mathematical Biology, 2018, 80 (2), pp.294-318. ⟨10.1007/s11538-017-0372-4⟩
Bulletin of Mathematical Biology, Springer Verlag, 2018, 80 (2), pp.294-318. ⟨10.1007/s11538-017-0372-4⟩
ISSN: 0092-8240
1522-9602
DOI: 10.1007/s11538-017-0372-4⟩
Popis: International audience; 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 (RNA polymerase and its mRNA) by means of monotone system theory and timescale arguments. We show that the reduced model has either a single globally stable trivial equilibrium in (0, 0), or an unstable zero equilibrium and a globally stable positive one. We give generalizations of this model, notably with a variable growth rate. The dynamical behavior of this system can be related to biological observations on the bacterium Escherichia coli.
Databáze: OpenAIRE
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