Oscillations and multiple steady states in a cyclic gene model with repression

Research output: Contribution to journalArticle

70 Citations (Scopus)

Abstract

In this paper we study the cyclic gene model with repression considered by H. T. Banks and J. M. Mahaffy. Roughly, the model describes a biochemical feedback loop consisting of an integer number G of single gene reaction sequences in series. The model leads to a system of functional differential equations. We show that there is a qualitative difference in the dynamics between even and odd G if the feedback repression is sufficiently large. For even G, multiple stable steady states can coexist while for odd G, periodic orbits exist.

Original languageEnglish (US)
Pages (from-to)169-190
Number of pages22
JournalJournal of Mathematical Biology
Volume25
Issue number2
DOIs
StatePublished - Jun 1987
Externally publishedYes

Fingerprint

oscillation
Physiological Feedback
Genes
Oscillation
Gene
Orbit
Odd
Feedback
genes
orbits
Feedback Loop
Functional Differential Equations
Periodic Orbits
Orbits
Differential equations
Model
Integer
Series

Keywords

  • Biochemical feedback
  • Cyclic gene model
  • Functional differential equations
  • Repression

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Agricultural and Biological Sciences (miscellaneous)

Cite this

Oscillations and multiple steady states in a cyclic gene model with repression. / Smith, Hal.

In: Journal of Mathematical Biology, Vol. 25, No. 2, 06.1987, p. 169-190.

Research output: Contribution to journalArticle

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