Kinetic analysis of a molecular model of the budding yeast cell cycle

Abstract

The molecular machinery of cell cycle control is known in more detail for budding yeast, Saccharomyces cerevisiae, than for any other eukaryotic organism. In recent years, many elegant experiments on budding yeast have dissected the roles of cyclin molecules (Cln1-3 and Clb1-6) in coordinating the events of DNA synthesis, bud emergence, spindle formation, nuclear division, and cell separation. These experimental clues suggest a mechanism for the principal molecular interactions controlling cyclin synthesis and degradation. Using standard techniques of biochemical kinetics, we convert the mechanism into a set of differential equations, which describe the time courses of three major classes of cyclin-dependent kinase activities. Model in hand, we examine the molecular events controlling "Start" (the commitment step to a new round of chromosome replication, bud formation, and mitosis) and "Finish" (the transition from metaphase to anaphase, when sister chromatids are pulled apart and the bud separates from the mother cell) in wild-type cells and 50 mutants. The model accounts for many details of the physiology, biochemistry, and genetics of cell cycle control in budding yeast.

Figure 1

Mother and daughter cycle times (CT) as functions of the mass-doubling time of a culture. Lines, model simulations, calculated from the differential equations and parameter values in Tables 1 and 2. Symbols, experimental results from Lord and Wheals (1980): interdivision times of mothers (▪) and daughters (●) and intervals from bud emergence to division (▴).

Figure 2

Molecular model of the control of CDK activities during the budding yeast cell cycle. We lump together redundant cyclins (Cln1 + Cln2 = “Cln2,” Clb1 + Clb2 = “Clb2,” and Clb5 + Clb6 = “Clb5”) and ignore Clb3 and Clb4. (Notice that we do not draw the kinase subunit, Cdc28, that is associated with each cyclin, because we assume it is in excess.) At the beginning of the cycle, the cell has few cyclin molecules, because the transcription factors (SBF, MBF, and Mcm1) that regulate cyclin synthesis are inactive. Clb-dependent kinases, in addition, are suppressed by a stoichiometric inhibitor (Sic1) and by efficient proteolysis of cyclin subunits. Cln3/Cdc28, which is present at low and nearly constant activity throughout the cycle, triggers a sequence of events leading ultimately to cell division. The sequence can be read from left to right. When the cell grows to a sufficiently large size, Cln3/Cdc28 and Bck2 activate SBF and MBF (by phosphorylation, so we assume), causing Cln2 and Clb5 to begin to accumulate. At first, Clb5 accumulates in inactive trimers, Clb5/Cdc28/Sic1, but Cln2/Cdc28 is not so inhibited. Rising Cln2/Cdc28 activity plays three important roles. First, it initiates bud formation. Second, it phosphorylates Sic1, priming the inhibitor for ubiquitination by SCF and ultimate degradation by the proteasome. Third, it inactivates Hct1, which, in conjunction with APC, was responsible for Clb2 degradation in G1 phase. When Sic1 is destroyed, Clb5/Cdc28 activity rises abruptly and drives the cell into S phase. These are the major physiological events associated with the Start transition. With Sic1 gone and Hct1 inactivated, Clb2-dependent kinase can begin to rise, with some lag, because Clb2/Cdc28 activates its own transcription factor, Mcm1. In addition, Clb2/Cdc28 inactivates SBF, so Cln2-dependent kinase activity begins to fall as Cln2 synthesis shuts off. At about the same time, MBF is inactivated, and the Clb5 level starts to fall. Rising Clb2/Cdc28 activity induces progress through mitosis. The metaphase–anaphase transition is regulated by a pair of proteins, Cdc20 and Hct1, that target substrates to the APC for ubiquitination. At metaphase, they are inactive, but when DNA is fully replicated and all chromosomes are aligned on the metaphase plate, Cdc20 is activated. Indirectly Cdc20 promotes 1) dissociation of sister chromatids (anaphase A), 2) activation of Hct1, which conducts Clb2 to the APC, thereby initiating anaphase B and cell separation, and 3) activation of Swi5, the transcription factor for Sic1. With all CDK activity gone (except for a little associated with Cln3), Sic1 can make a comeback, and the cell returns to G1.

Figure 3

Wild-type cell cycle in daughter cells. Computed from equations and parameter values in Tables 1 and 2.

Figure 4

Length of the unbudded interval of daughter cells depends inversely on birth size. Inset, experimental results from Figure 5 of Johnston et al. (1977), used by permission.

Figure 5

Dependence of cell size on CLN3 dosage. Inset, experimental results compiled from Cross (1988), Dirick et al. (1995), Nash et al. (1988), and Yaglom et al. (1995).

Figure 6

Dissociation of Start events in cln mutants. (A–C) Compare with experiments of Dirick et al. (1995). (A) In wild-type cells, several molecular and physiological events occur together at Start: activation of SBF, inactivation of Hct1, proteolysis of Sic1, initiation of DNA synthesis, and emergence of a bud. (B) In cln1Δ cln2Δ cells, these events are dissociated: SBF is activated at wild-type size, but all other events are delayed until the cell gets much larger. (C) In cln3Δ cells, the events are again concurrent, but they occur at about twice the size of wild-type cells. (D) Under steady-state conditions, cln1Δ cln2Δ cells are much larger than wild type. SBF is activated immediately. However, DNA synthesis is much delayed (to mass = 2.47), beyond the size at which it would occur (at mass = 1.75) in B. This delay is due to the burst of Sic1 synthesis at anaphase. (E) Deletion of SIC1 from cln1Δ cln2Δ suppresses the delay of bud emergence, as observed by Dirick (1995), and pushes DNA synthesis to a size smaller than in wild-type (contrary to their observation). In the absence of inhibitor, the small level of Clb5 early in the cycle is effective in driving DNA synthesis and bud emergence. See text for further discussion. (F) Deletion of SIC1 rescues the inviable cln1Δ cln2Δ cln3Δ mutant. DNA synthesis begins at a small size (smaller than in wild type, as observed by Schneider et al., 1996), but all other events of Start are displaced to large size.

Figure 7

Simulation of MET-CLN2 GAL-CLB2 (no transcriptional control of Cln2 or Clb2 synthesis). In the absence of both methionine and galactose, cells are smaller than wild type, because Cln2 is synthesized constitutively. When galactose is added (arrow), cells get smaller still, eventually dividing at ∼30% of wild-type size. Such small cells may be inviable.

Figure 8

Cells are able to exit from mitosis when any single one of the three Clb2-inhibiting mechanisms is faulty. Top panel, constitutive transcription of CLB2 in G1 phase. Middle panel, no Hct1-mediated degradation of Clb2 at telophase. Bottom panel, no Sic1 to inhibit Clb2/Cdc28 in G1 phase. The arrow on the ordinate indicates mass at division; all three strains have size comparable with wild type.

Figure 9

Bistability and hysteresis (schematic). Steady-state level of total Clb-dependent kinase activity depends on the expression of CLN2 and CDC20. When [Cln2] is large and [Cdc20] is small, the Clb1–6 regulatory system is in a state of high kinase activity (S/M), whereas in the other extreme, Clb-dependent kinase activity is low (G1). When [Cln2] and [Cdc20] are both small, the regulatory system is in neutral (background activity = A/B), and two stable states of Clb activity coexist (bistability). The system is driven around a hysteresis loop (dashed curve) by pulses of Cln2 (stages a and b) and Cdc20 (stages c and d).