Modeling the fission yeast cell cycle: quantized cycle times in wee1- cdc25Delta mutant cells

Abstract

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 G(2)/M transition (through Wee1 and Cdc25) are weak, then cells can reset back to G(2) 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(-) cdc25Delta 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.

Figure 1

A molecular mechanism for the regulation of Cdc13-associated kinase activity in fission yeast. All of the events of the fission yeast cell cycle can be orchestrated by fluctuations of the activity of a single cyclin-dependent kinase, Cdc13/Cdc2. Cdc13 is synthesized from amino acids (AA) and combines readily with catalytic subunits, Cdc2, which are assumed to be always present in excess. The activity of Cdc13/Cdc2 is modulated by Rum1 inhibition, by Tyr-15 phosphorylation (via Wee1 and Mik1, which is reversed by Cdc25 and Pyp3; the last molecule is not shown on figure), and by Ste9-dependent cyclin degradation. Other cyclins (Puc1, Cig1, and Cig2, which are represented by X on the figure) in complex with Cdc2 can assist these processes.

Figure 2

Numerical simulation of WT cell cycles.

Figure 3

Numerical simulation of ste9Δ rum1Δ double mutant cells.

Figure 4

Numerical simulation of wee1^ts cdc25Δ double mutant cells.

Figure 5

CT vs. BL relationship for simulated wee1^ts cdc25Δ cells. This graph should be compared with the experimental data in figure 6A from ref. .

Figure 6

Effects of Wee1 and Cdc25 activities on BL and phenotype of fission yeast. Curves represent cells of constant BL (BL = 1.0 for WT cells). The shaded regions represent different phenotypes. Both enzyme activities are expressed as percentage of WT. For Wee1 (ordinate), we varied only the large turnover number (V_Wee), leaving the small one (V_wee′  ) unchanged. For Cdc25, we varied both (V₂₅′  and V₂₅), keeping their ratio the same as in WT.