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

Critical slowing down and attractive manifold: a mechanism for dynamic robustness in yeast cell-cycle process