A generalized model of the repressilator.
The repressilator is a regulatory cycle of n genes where each gene represses its successor in the cycle: [see text]. 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.
Müller
Stefan
S
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040 Linz, Austria. stefan.mueller@oeaw.ac.at
Hofbauer
Josef
J
Endler
Lukas
L
Flamm
Christoph
C
Widder
Stefanie
S
Schuster
Peter
P
D001665:Binding Sites; D005246:Feedback; D005786:Gene Expression Regulation; D008433:Mathematics; D008957:Models, Genetic; D012333:RNA, Messenger / Q000235:genetics / Q000378:metabolism
D012333:RNA, Messenger