Format

Send to

Choose Destination
Bull Math Biol. 2018 Feb;80(2):294-318. doi: 10.1007/s11538-017-0372-4. Epub 2017 Dec 6.

Reduction and Stability Analysis of a Transcription-Translation Model of RNA Polymerase.

Author information

1
Université Côte d'Azur, Inria, INRA, CNRS, UPMC Univ Paris 06, Biocore team, Sophia Antipolis, France.
2
Université Côte d'Azur, Inria, INRA, CNRS, UPMC Univ Paris 06, Biocore team, Sophia Antipolis, France. stefano.casagranda@inria.fr.
3
Univ. Grenoble - Alpes, Inria, Grenoble, France.

Abstract

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.

KEYWORDS:

Biochemical models; Monotone systems; Reduction; Stability; Transcription–translation model

PMID:
29214429
DOI:
10.1007/s11538-017-0372-4
[Indexed for MEDLINE]

Supplemental Content

Full text links

Icon for Springer
Loading ...
Support Center