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Ring oscillators are biochemical circuits consisting of a ring ofinteractions capable of sustained oscillations. The non-linear interactionsbetween genes hinder the analytical insight into their function, usuallyrequiring computational exploration. Here we show that, despite the apparentcomplexity, the stability of the unique steady state in an incoherent feedbackring depends only on the degradation rates and a single parameter summarizingthe feedback of the circuit. Concretely, we show that the range of regulatoryparameters that yield oscillatory behaviour, is maximized when the degradationrates are equal. Strikingly, this results holds independently of the regulatoryfunctions used or number of genes. We also derive properties of theoscillations as a function of the degradation rates and number of nodes formingthe ring. Finally, we explore the role of mRNA dynamics by applying the genericresults to the specific case with two naturally different degradation timescales

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