  The biological processes that execute complex multiple functions, such as
cell cycle, must ensure the order of sequential events and keep the dynamic
robustness against various fluctuations. Here, we examine the dynamic mechanism
and the fundamental structure to achieve these properties in the cell-cycle
process of budding yeast Saccharomyces cerevisiae. We show that the budding
yeast cell-cycle process behaves like an excitable system containing three
well-coupled saddle-node bifurcations to execute DNA replication and mitosis
events. The yeast cell-cycle regulatory network can be separated into G1/S
phase module, early M module and late M phase module, where the positive
feedbacks in each module and the interactions among the modules play important
role. If the cell-cycle process operates near the critical points of the
saddle-node bifurcations, there is a critical slowing down or ghost effect.
This can provide the cell-cycle process with a sufficient duration for each
event and an attractive manifold for the state checking of the completion of
DNA replication and mitosis; moreover, the fluctuation in the early
module/event is forbidden to transmit to the latter module/event. Our results
suggest both a fundamental structure of cell-cycle regulatory network and a
hint for the evolution of eukaryotic cell-cycle processes, from the dynamic
checking mechanism to the molecule checkpoint pathway.
