TBI-Preprint 06-05-002
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Titel:
A Generalized Model of the Repressilator
Author(s):
Stefan Müller,
Josef Hofbauer,
Lukas Endler,
Christoph Flamm,
Stefanie Widder,
Peter Schuster
Submitted to:
Journal of Nonlinear Science 2006
Abstract:
The repressilator is a regulatory cycle of n genes where each gene
represses its successor in the cycle: 1 -| 2 -| . . . -| n -|
1
. The system is modelled by ODEs for an arbitrary number of
identical genes and arbitrarily strong repressor binding. A detailed
mathematical analysis of the dynamical behavior is provided for two
model systems: (i) a repressilator with leaky transcription and
single-step cooperative repressor binding, and (ii) a repressilator
with auto-activation and cooperative regulator binding. Genes are
assumed to be present in constant amounts, transcription and
translation are modelled by single-step kinetics, and mRNAs as well as
proteins are assumed to be degraded by first order reactions. Several
dynamical patterns are observed: Multiple steady states, periodic and
aperiodic oscillations corresponding to limit cycles and heteroclinic
cycles, respectively. The results of computer simulations are
complemented by a detailed and complete stability analysis of all
equilibria and of the heteroclinic cycle.
Keywords:
Gene regulatory network,
negative feedback loop,
repressilator,
stability analysis,
Hopf bifurcation,
heteroclinic cycle
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Last modified: 2006-05-12 09:32:35 xtof