Modeling the fission yeast cell cycle: Quantized cycle times in wee1 cdc25 mutant cells

A detailed mathematical model for the fission yeast mitotic cycle is developed based on positive and negative feedback loops by which Cdc13/Cdc2 kinase activates and inactivates itself. Positive feedbacks are created by Cdc13/Cdc2-dependent phosphorylation of specific substrates: inactivating its negative regulators (Rum1, Ste9 and Wee1/Mik1) and activating its positive regulator (Cdc25). A slow negative feedback loop is turned on during mitosis by activation of Slp1/anaphase-promoting complex (APC), which indirectly re-activates the negative regulators, leading to a drop in Cdc13/Cdc2 activity and exit from mitosis. The model explains how fission yeast cells can exit mitosis in the absence of Ste9 (Cdc13 degradation) and Rum1 (an inhibitor of Cdc13/Cdc2). We also show that, if the positive feedback loops accelerating the G₂/M transition (through Wee1 and Cdc25) are weak, then cells can reset back to G₂ from early stages of mitosis by premature activation of the negative feedback loop. This resetting can happen more than once, resulting in a quantized distribution of cycle times, as observed experimentally in wee1^- cdc25<IMG SRC="/math/12pt/normal/Delta.gif" ALIGN=BASELINE ALT="Delta "> mutant cells. Our quantitative description of these quantized cycles demonstrates the utility of mathematical modeling, because these cycles cannot be understood by intuitive arguments alone.