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Mathematical models of the early embryonic cell cycle: The role of MPF activation and cyclin degradation. (English) Zbl 0823.92004
Summary: Recent advances in cell biology indicate that the interactions between two proteins, cdc2 and cyclin, together with the activity of the cdc2/cyclin complex called MPF in the cytoplasm form the basis of a universal biochemical control mechanism for the cell division cycle in eukaryotes. Based on experimental facts that total cdc2 level is constant throughout the cell cycle and that onset of mitosis is subsequent to activation of MPF, we propose and analyze two different but related models – an ordinary differential equations model and a delay differential equations model – for the control of the early embryonic cell division cycle. Assuming very general reaction terms in the model equations, it is shown that MPF activation and rapid cyclin degradation triggered by active MPF drive cells to alternate between interphase and mitosis, the two phases of the cell cycle.

MSC:
92C15 Developmental biology, pattern formation
92C40 Biochemistry, molecular biology
34K35 Control problems for functional-differential equations
34H05 Control problems involving ordinary differential equations
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