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Degradation rate uniformity determines success of oscillations in repressive feedback regulatory networks

Page, KM; Perez-Carrasco, R; (2018) Degradation rate uniformity determines success of oscillations in repressive feedback regulatory networks. Journal of the Royal Society Interface , 15 (142) , Article 20180157. 10.1098/rsif.2018.0157. Green open access

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Abstract

Ring oscillators are biochemical circuits consisting of a ring of interactions capable of sustained oscillations. The nonlinear interactions between genes hinder the analytical insight into their function, usually requiring computational exploration. Here, we show that, despite the apparent complexity, the stability of the unique steady state in an incoherent feedback ring depends only on the degradation rates and a single parameter summarizing the feedback of the circuit. Concretely, we show that the range of regulatory parameters that yield oscillatory behaviour is maximized when the degradation rates are equal. Strikingly, this result holds independently of the regulatory functions used or number of genes. We also derive properties of the oscillations as a function of the degradation rates and number of nodes forming the ring. Finally, we explore the role of mRNA dynamics by applying the generic results to the specific case with two naturally different degradation timescales.

Type: Article
Title: Degradation rate uniformity determines success of oscillations in repressive feedback regulatory networks
Open access status: An open access version is available from UCL Discovery
DOI: 10.1098/rsif.2018.0157
Publisher version: https://doi.org/10.1098/rsif.2018.0157
Language: English
Additional information: © 2018 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/).
Keywords: oscillations, repressilator, degradation rates, dynamical systems, gene regulatory networks
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10049664
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