Precision of genetic oscillators and clocks.

We develop a stochastic description of feedback oscillators in which functional molecules are produced by an assembly line consisting of many identical steps. The initiation rate of this assembly is regulated by its products via a negative feedback. This model is motivated by genetic oscillators such as circadian clocks. We show that precise oscillations of high quality are possible even when the number of product molecules is low and the fluctuations of amplitude are large. We discuss parameter values which can account for high quality oscillations as observed in single cells. Furthermore, we discuss effects of stochastic amplification steps on precision to account for translational bursting.