Autoinhibition with transcriptional delay: A simple mechanism for the zebrafish somitogenesis oscillator

Background: The pattern of somites is traced out by a mechanism involving oscillating gene expression at the tail end of the embryo. In zebrafish, two linked oscillating genes, her1 and her7, coding for inhibitory gene regulatory proteins, are especially implicated in genesis of the oscillations, while Notch signaling appears necessary for synchronization of adjacent cells. Results: I show by mathematical simulation that direct autorepression of her1 and her7 by their own protein products provides a mechanism for the intracellular oscillator. This mechanism operates robustly even when one allows for the fact that gene regulation is an essentially noisy (stochastic) process. The predicted period is close to the observed period (30 min) and is dictated primarily by the transcriptional delay, the time taken to make an mRNA molecule. Through its coupling to her1/her7 expression, Notch signaling can keep the rapid oscillations in adjacent cells synchronized. When the coupling parameters are varied, however, the model system can switch to oscillations of a much longer period, resembling that of the mouse or chick somitogenesis oscillator and governed by the delays in the Notch pathway. Such Notch-mediated synchronous oscillations are predicted even in the absence of direct her1/her7 autoregulation, through operation of the standard Notch signaling pathway that is usually assumed simply to give lateral inhibition. Conclusions: Direct autorepression of a gene by its own product can generate oscillations, with a period determined by the transcriptional and translational delays. Simple as they are, such systems show surprising behaviors. To understand them, unaided intuition is not enough: we need mathematics.