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

TL;DR

This paper demonstrates that the stability and oscillatory behavior of biochemical ring oscillators are primarily determined by degradation rates, with equal degradation rates maximizing oscillation range regardless of regulatory functions or network size.

Contribution

It reveals that degradation rate uniformity is crucial for oscillation success in repressive feedback networks, providing analytical insights into their stability and dynamics.

Findings

Equal degradation rates maximize oscillation range.

Stability depends only on degradation rates and a single feedback parameter.

Results hold across different regulatory functions and network sizes.

Abstract

Ring oscillators are biochemical circuits consisting of a ring of interactions capable of sustained oscillations. The non-linear 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 results 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 time scales