The regulation of gene expression in eukaryotes: bistability and oscillations in repressilator models.
To model the regulation of gene expression in eukaryotes by transcriptional activators and repressors, we introduce delays in conjugation with the mass action law. Delays are associated with the time gap between the mRNA transcription in the nucleoplasm and the protein synthesis in the cytoplasm. After re-parameterisation of the m-repressilator model with the Hill cooperative parameter n, for n=1, the m-repressilator is deducible from the mass action law and, in the limit n→∞, it is a Boolean type model. With this embedding and with delays, if m is odd and n>1, we show that there is always a choice of parameters for which the m-repressilator model has sustained oscillations (limit cycles), implying that the 1-repressilator is the simplest genetic mechanism leading to sustained oscillations in eukaryotes. If m is even and n>1, there is always a choice of parameters for which the m-repressilator model has bistability.
Nonlinear Dynamics Group, Instituto Superior Técnico Av. Rovisco Pais, 1049-001 Lisbon, Portugal; Institut des Hautes Études Scientifiques, 35, route de Chartres, 91440 Bures-sur-Yvette, France. Electronic address: rui@sd.ist.utl.pt.
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D000465:Algorithms; D003198:Computer Simulation; D003593:Cytoplasm / Q000378:metabolism; D056890:Eukaryota / Q000235:genetics* / Q000378:metabolism*; D015870:Gene Expression; D005786:Gene Expression Regulation; D016014:Linear Models; D008957:Models, Genetic; D009991:Oscillometry; D011485:Protein Binding; D014176:Protein Biosynthesis; D014158:Transcription, Genetic
Bistability; Delays; Limit cycles; Regulation of gene expression in eukaryotes; m-repressilator