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

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70 Scopus citations

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 1 1987
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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