Dynamics of the cell cycle engine: Cdk2-kinase and the transition into mitosis.

The autonomous cell divisions during the early development of Xenopus laevis believed to comprise a universal cell cycle engine. Recent experimental data indicates that the Cdk2-cyclin E kinase is required for the rapid divisions during Xenopus embryogenesis and that the complex is crucial for the transition into mitosis. In the present paper, the activity of Cdk2-cyclin E is incorporated into an existing comprehensive model of the cell cycle engine as an activity operating in parallel with the mitosis promotion factor (MPF) on the phosphatase Cdc25. This introduces interesting regulatory and dynamic properties for the transition into mitosis that reveals new insight into the mechanisms of the cell division process. It is shown that the Cdk2-cyclin E complex can act as an effective modulator of the threshold MPF activity needed to initiate mitosis. When the Cdk2-cyclin E activity is below a critical value, the cell cycle arrests in a well-defined state of low MPF activity corresponding to G2 arrest. In agreement with experiments a single mitotic event occurs following injection of free cyclin B. Above a critical activity, the presence of Cdk2-cyclin E allows for sustained oscillations corresponding to repeated cell divisions and the Cdk2-cyclin E may be the cause for the suppressed G2 checkpoint in the early embryonic cell cycles. A detailed bifurcation analysis reveals that the transition from steady to oscillatory behavior involves a homoclinic orbit of infinite period through an omega explosion. The general properties of the omega explosion explain the bifurcation as a dynamic mechanism well-suited for the G2 checkpoint and suggest a plausible explanation for the elongation of the cell cycle as observed at the mid-blastula transition. The proposed mechanism also suggests a plausible explanation of G2 checkpoint failure following DNA damage in human cells overexpressing Cdk2 and we suggest that the onset of mitosis in the mammalian cell occurs as the result of a slow passage through a critical point.