2018/08/01 by Jonathan Tyler, Tyler, Jonathan, Anne Shiu +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Molecular Networks (q-bio.MN) #Receptor Mechanisms and Signaling
paper · pdf · doi:10.48550/arxiv.1808.00595
openalex publication_date 2018/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2000, Elowitz and Leibler introduced the repressilator--a synthetic gene\ncircuit with three genes that cyclically repress transcription of the next\ngene--as well as a corresponding mathematical model. Experimental data and\nmodel simulations exhibited oscillations in the protein concentrations across\ngenerations. In 2006, M "uller \et al. generalized the model to an\narbitrary number of genes and analyzed the resulting dynamics. Their new model\narose from five key assumptions, two of which are restrictive given current\nbiological knowledge. Accordingly, we propose a new repressilator system that\nallows for general functions to model transcription, degradation, and\ntranslation. We prove that, with an odd number of genes, the new model has a\nunique steady state and the system converges to this steady state or to a\nperiodic orbit. We also give a necessary and sufficient condition for stability\nof steady states when the number of genes is even and conjecture a condition\nfor stability for an odd number. Finally, we derive a new rate function\ndescribing transcription that arises under more reasonable biological\nassumptions than the widely used single-step binding assumption. With this new\ntranscription-rate function, we compare the model's amplitude and period with\nthat of a model with the conventional transcription-rate function. Taken\ntogether, our results enhance our understanding of genetic regulation by\nrepression.\n