Integrative analysis of cell cycle control in budding yeast

Abstract

The adaptive responses of a living cell to internal and external signals are controlled by networks of proteins whose interactions are so complex that the functional integration of the network cannot be comprehended by intuitive reasoning alone. Mathematical modeling, based on biochemical rate equations, provides a rigorous and reliable tool for unraveling the complexities of molecular regulatory networks. The budding yeast cell cycle is a challenging test case for this approach, because the control system is known in exquisite detail and its function is constrained by the phenotypic properties of >100 genetically engineered strains. We show that a mathematical model built on a consensus picture of this control system is largely successful in explaining the phenotypes of mutants described so far. A few inconsistencies between the model and experiments indicate aspects of the mechanism that require revision. In addition, the model allows one to frame and critique hypotheses about how the division cycle is regulated in wild-type and mutant cells, to predict the phenotypes of new mutant combinations, and to estimate the effective values of biochemical rate constants that are difficult to measure directly in vivo.

Figure 1.

Consensus model of the cell cycle control mechanism in budding yeast. (For a full justification of this diagram, with references to the original literature, see our Web site at http://mpf.biol.vt.edu.) The diagram should be read from bottom left toward top right. (In the diagram, Cln2 stands for Cln1 and 2, Clb5 for Clb5 and 6, and Clb2 for Clb1 and 2; furthermore, the kinase partner of the cyclins, Cdc28, is not shown explicitly. There is an excess of Cdc28 and it combines rapidly with cyclins as soon as they are synthesized.) Newborn daughter cells must grow to a critical size to have enough Cln3 and Bck2 to activate the transcription factors MBF and SBF, which drive synthesis of two classes of cyclins, Cln2 and Clb5. Cln2 is primarily responsible for bud emergence and Clb5 for initiating DNA synthesis. Clb5-dependent kinase activity is not immediately evident because the G1-phase cell is full of cyclin-dependent kinase inhibitors (CKI; namely, Sic1 and Cdc6). After the CKIs are phosphorylated by Cln2/Cdc28, they are rapidly degraded by SCF, releasing Clb5/Cdc28 to do its job. A fourth class of “mitotic cyclins,” denoted Clb2, are out of the picture in G1 because their transcription factor Mcm1 is inactive, their degradation pathway Cdh1/APC is active, and their stoichiometric inhibitors CKI are abundant. Cln2- and Clb5-dependent kinases remove CKI and inactivate Cdh1, allowing Clb2 to accumulate, after some delay, as it activates its own transcription factor, Mcm1. Clb2/Cdc28 turns off SBF and MBF. (Clb5/Cdc28 is probably the other down-regulator of MBF.) As Clb2/Cdc28 drives the cell into mitosis, it also sets the stage for exit from mitosis by stimulating the synthesis of Cdc20 and by phosphorylating components of the APC (see text for details). Meanwhile, Cdc20/APC is kept inactive by the Mad2-dependent checkpoint signal responsive to unattached chromosomes. When the replicated chromosomes are attached, active Cdc20/APC initiates mitotic exit. First, it degrades Pds1, releasing Esp1, a protease involved in sister chromatid separation. It also degrades Clb5 and partially Clb2, lowering their potency on Cdh1 inactivation. In this model, Cdc20/APC promotes degradation of a phosphatase (PPX) that has been keeping Net1 in its unphosphorylated form, which binds with Cdc14. As the attached chromosomes are properly aligned on the metaphase spindle, Tem1 is activated, which in turn activates Cdc15 (the endpoint of the “MEN” signal-transduction pathway in the model). When Net1 gets phosphorylated by Cdc15, it releases its hold on Cdc14. Cdc14 (a phosphatase) then does battle against the cyclin-dependent kinases: activating Cdh1, stabilizing CKIs, and activating Swi5 (the transcription factor for CKIs). In this manner, Cdc14 returns the cell to G1 phase (no cyclins, abundant CKIs, and active Cdh1).

Figure 2.

Wild-type cell cycle. Numerical solution of the differential equations in Table 1, for the parameter values in Table 2. The MDT for an asynchronous culture is 90 min. We show the cycle of a daughter cell (cycle time, 101 min; duration of G1, 36 min). The cycle time for a mother cell (not shown) is 80 min. Division is slightly asymmetric (daughter size at birth = 0.46× mother size at division). During G1 phase, Cdh1 is active and there are abundant CKIs. The G1→S transition is driven by accumulation of Cln2. The M→G1 transition is driven by activation of Cdc20. In panel 4, the left ordinate refers to [Cln2] and the right ordinate to [Cdc20] and [Cdc14].

Figure 3.

Logic of cell cycle transitions in budding yeast. (A) Antagonistic interactions between the G1-stabilizers (Cdh1 and CKI) and the Clb/Cdc28 kinases create two coexisting stable steady states, G1 and S/G2/M. Transitions between these states are called start (G1→S) and finish (M→G1). (B) start is facilitated by Cln/Cdc28 kinases. Cell growth (“mass”) triggers accumulation of Clns. (C) finish is facilitated by Cdc20/APC. Mitotic checkpoint signals restrain the activation of Cdc20.

Figure 4.

Mutations that interfere with the start and finish transitions. (A) Deletion of all three CLN genes arrests cells in G1 because the start-facilitators are missing. (B and C) The triple-cln mutant is rescued by further deletion of SIC1, but not by deletion of CDH1.(D–F) CDC20 mutations (deletion or temperature-sensitive lethal) block cells in metaphase (simulation not shown) can be rescued by deleting both PDS1 and CLB5, but not by deleting either gene alone. (G, H) Deletion of all G1-stabilizers makes inviable cells, and they can be rescued by GALL-CDC20. ^*In reality, the mutant in panel G is not telophase arrested as predicted by the model. See text for a description of its phenotype and possible modifications of the model to account for the discrepancy.

Figure 5.

Robustness assay of the wild-type and six mutant strains, cdh1Δ, ckiΔ, APC-A, cln2Δ, cln3Δ, and clb5Δ. For each strain, simulations were run with systematic variations in each parameter to determine the maximum increase or decrease of that particular parameter the model could still tolerate to give a viable cell according to the criteria described in MATERIALS AND METHODS. Maximum variation tested is 256-fold up and 1/256-fold down. The cumulative distribution of parameters exhibiting a tolerance for a given fold of increase or decrease is plotted for each strain. Wild-type and cln3Δ mutant are most robust to parameter changes, whereas cln2Δ and cdh1Δ are least robust.