MATHEMATICAL-MODELS OF THE EARLY EMBRYONIC-CELL CYCLE - THE ROLE OF MPF ACTIVATION AND CYCLIN DEGRADATION

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 univer sal biochemical control mechanism for the cell division cycle in eukar yotes. Based on experimental facts that total cdc2 level is constant t hroughout the cell cycle and that onset of mitosis is subsequent to ac tivation of MPF, we propose and analyze two different but related mode ls - an ordinary differential equations model and a delay differential equations model - for the control of the early embryonic cell divisio n 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.