THE MITOTIC OSCILLATOR - TEMPORAL SELF-ORGANIZATION IN A PHOSPHORYLATION-DEPHOSPHORYLATION ENZYMATIC CASCADE

The conditions for temporal self-organization in the form of sustained oscillations are determined in a minimal cascade model previously pro posed (A. Goldbeter, Proc. Natl. Acad. Sci. USA 88, 9107-9111 (1991)) for the mitotic oscillator driving the embryonic cell division cycle. The model is based on a phosphorylation-dephosphorylation cascade invo lving cyclin and cdc2 kinase. In the first cycle of the cascade, cdc2 kinase is activated through dephosphorylation triggered by the accumul ation of cyclin, while in a second cycle the activation of a cyclin pr otease is brought about through phosphorylation by cdc2 kinase. The fa ct that cyclin promotes the activation of cdc2 kinase while the latter enzyme triggers cyclin degradation introduces a negative feedback loo p which is at the core of the, periodic operation of the cascade. We a nalyze the mechanism of oscillatory behavior by constructing stability diagrams as a function of some of the main parameters of the model. I nvestigated in turn are the roles of negative feedback and of phosphor ylation-dephosphorylation thresholds. Such thresholds arise from the p henomenon of zero-order ultrasensitivity associated with the kinetics of covalent modification cycles. An extension of the minimal model all ows one to address the effect of additional phosphorylation-dephosphor ylation cycles and the possible role of autocatalysis by cdc2 kinase i n the generation of periodic behavior. The analysis shows that the exi stence of thresholds as well as an increase in the number of cycles in the cascade favor the occurrence of sustained oscillations. The resul ts further indicate that negative and positive feedback may both contr ibute to the repetitive activation of cdc2 kinase.