An analysis of overall network architecture reveals an infinite-period bifurcation underlying oscillation arrest in the segmentation clock

Abstract: Unveiling the mechanisms through which the somitogenesis regulatory network exerts spatiotemporal control of the somitic patterning has required a combination of experimental and mathematical modeling strategies. Significant progress has been made for the zebrafish clockwork. However, due to its complexity, the clockwork of the amniote segmentation regulatory network has not been fully elucidated. Here, we address the question of how oscillations are arrested in the amniote segmentation clock. We do this by constructing a minimal model of the regulatory network, which privileges architectural information over molecular details. With a suitable choice of parameters, our model is able to reproduce the oscillatory behavior of the Wnt, Notch and FGF signaling pathways in presomitic mesoderm (PSM) cells. By introducing positional information via a single Wnt3a gradient, we show that oscillations are arrested following an infinite-period bifurcation. Notably: the oscillations increase their amplitude as cells approach the anterior PSM and remain in an upregulated state when arrested; the transition from the oscillatory regime to the upregulated state exhibits hysteresis; and an opposing distribution of the Fgf8 and RA gradients in the PSM arises naturally in our simulations. We hypothesize that the interaction between a limit cycle (originated by the Notch delayed-negative feedback loop) and a bistable switch (originated by the Wnt-Notch positive cross-regulation) is responsible for the observed segmentation patterning. Our results agree with previously unexplained experimental observations and suggest a simple plausible mechanism for spatiotemporal control of somitogenesis in amniotes.