  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
