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 opposing Fgf8 and RA gradients along the
PSM naturally arise 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.