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 language | English (US) |
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Pages (from-to) | 169-190 |
Number of pages | 22 |
Journal | Journal Of Mathematical Biology |
Volume | 25 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1987 |
Keywords
- Biochemical feedback
- Cyclic gene model
- Functional differential equations
- Repression
ASJC Scopus subject areas
- Modeling and Simulation
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics