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Finishing the Cell Cycle
J. theor. Biol. (1999) 199, 223}233 Article No. jtbi.1999.0956, available online at http://www.idealibrary.com on
Finishing the Cell Cycle BED LA NOVAD K*A, ATTILA TOD TH-, ATTILA CSIKAD SZ-NAGY*, BED LA GYOD D RFFY*, JOHN J. TYSON? AND KIM NASMYTH*Department of Agricultural Chemical ¹echnology, ¹echnical ;niversity of Budapest, GelleH rt teH r 4, Budapest 1521, Hungary, -Institute of Molecular Pathology, Dr Bohr Gasse 7,
The eukaryotic cell division cycle consists of two characteristic states: G1, when replication origins of chromosomes are in a pre-replicative state, and S/G2/M, when they are in a postreplicative state (Nasmyth, 1995). Using straightforward biochemical kinetics, we show that these two states can be created by antagonistic interactions between cyclin-dependent kinases (Cdk) and their foes: the cyclin-degradation machinery (APC) and a stoichiometric inhibitor (CKI). Irreversible transitions between these two self-maintaining steady states drive progress through the cell cycle: at &&Start'' a cell leaves the G1 state and commences chromosome replication, and at &&Finish'' the cell separates the products of replication to the incipient daughter cells and re-enters G1. We propose that a protein-phosphatase, by up-regulating the APC and by stabilizing the CKI, plays an essential role at Finish. The phosphatase acts in parallel pathways; hence, cells can leave mitosis in the absence of cyclin degradation or in the absence of the CKI. 1999 Academic Press
Introduction At Start (the G1/S transition), a eukaryotic cell commits itself to a new round of DNA synthesis, mitosis and division. Before executing Start, the cell surveys its internal state and external milieu to determine if conditions are appropriate for reproduction. At this stage (often called the G1 checkpoint), the cell is sensitive to growth factors, di!erentiation signals, or sex hormones, which can block mitotic cycles and induce a resting state, terminal di!erentiation, or meiosis (see Alberts et al., 1994). At Finish (the meta/
A Author to whom correspondence should be addressed. E-mail: [email protected]. 0022}5193/99/014223#11 $30.00/0
anaphase transition), the cell pulls sister chromatids apart. Before doing so, it checks that the chromosomes are completely replicated and the sister chromatids are all properly attached to opposite poles of the spindle. If these conditions are not satis"ed, the metaphase checkpoint mechanism blocks dissolution of cohesion proteins holding the sister chromatids together. These transitions are triggered by irreversible changes in activities of cyclin-dependent kinases (Cdk). At Start, Cdk activities rise for a combination of reasons: activation of cyclin transcription, inactivation of cyclin degradation, and removal of cyclin-dependent kinase inhibitors (CKIs). At Finish, Cdk activities are extinguished due to activation of cyclin degradation, accumulation of 1999 Academic Press
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CDK inhibitors, and, perhaps, inactivating phosphorylation of CDKs. In this paper, we concentrate on the molecular events that drive exit from mitosis. A Simpli5ed Cell-Cycle Control Network To illustrate how the Finish transition might work we propose a simple mechanism (Fig. 1) largely based on cell-cycle controls in budding yeast (in particular, we ignore inhibitory tyrosine phosphorylation of the Cdk subunit). Consequently, we refer to each protein by its name in budding yeast, although most of them have counterparts in other organisms (some homologues are listed in the "gure legend). The model consists of a single essential Cdk subunit with two important cyclin partners: a CLN-type cyclin (Cln3), which is present at constant concentration, and a single B-type cyclin (representing Clb1-6) which is synthesized and degraded in each cycle. In "ssion yeast, these two cyclins, Puc1 and Cdc13, respectively, are su$cient to drive a complete mitotic cell cycle (Fisher & Nurse, 1996). To keep the model simple, Clb is synthesized at constant rate and it associates rapidly with the Cdk subunit, which is present in excess. The cyclin component of the complex is degraded by ubiquitin-mediated proteolysis (Hershko, 1997). A short sequence near the N-terminus of B-type cyclins is recognized by a speci"c ubiquitin ligase, called the cyclosome (Sudakin et al., 1995) or the Anaphase Promoting Complex (APC; Irniger and Nasmyth, 1997). APC-mediated cyclin ubiquitination requires an ancillary protein, Hct1 (&&homologue of Cdc20'', Cdh1 is a synonym for Hct1; Schwab et al., 1997; Visintin et al., 1997). The activity of the Cdk/cyclin complex is also regulated by Sic1, a stoichiometric inhibitor in budding yeast (Mendenhall, 1993; Schwob et al., 1994). Although Sic1 synthesis varies with the cell-cycle phase in budding yeast (Schwob et al., 1994; Toyn et al., 1997), in this model the inhibitor is synthesized at a constant rate, like the analogous protein (Rum1) in "ssion yeast (Moreno & Nurse, 1994). Like B-type cyclins, Sic1 proteolysis is also ubiquitin-dependent, but it relies on a second ubiquitin-ligase, called SCF (Benito et al., 1998; Feldman et al., 1997; Skowyra
FIG. 1. Skeleton model of the eukaryotic cell cycle. The B-type cyclin (Clb) is targeted to APC by Hct1, which is also called Cdh1 (Schwab et al., 1997; Visintin et al., 1997). Ste9 (also called Srw1) and fzr (&&"zzy related'') are the homologous proteins in "ssion yeast and Drosophila (Kitamura et al., 1998; Sigrist and Lehner, 1997; Yamaguchi et al., 1997). A hypothetical inhibitor is targeted to APC by another auxiliary protein, Cdc20 [the "ssion yeast homolog is Slp1 (Matsumoto, 1997), and in Drosophila it is called ,zzy (Dawson et al., 1995)]. This model is an improved version of our earlier mechanism for cell-cycle control in primitive eukaryotes (Fig. 6 of NovaH k et al., 1998). Here, we use budding yeast-speci"c names for each component in place of the generic names used there: ACT"Cdc20, APC"Hct1, Cyclin"Clb, CKI"Sic1. In the earlier model, Cdc20 directly activated Hct1, while here it acts indirectly by destroying an inhibitor of the Hct1-activating phosphatase, Cdc14. In addition, we now propose that the very same phosphatase rescues phosphorylated Sic1 from degradation. In organisms that regulate Cdk/cyclin activity by tyrosine phosphorylation of the Cdk subunit (not considered in this model, but see Fig. 9 of NovaH k et al., 1998), we propose that the phosphatase also opposes cyclin-dependent phosphorylation of Wee1 and Cdc25.
FINISHING THE CELL CYCLE
et al., 1997). The SCF complex recognizes phosphorylated proteins, and the phosphorylation of Sic1 at Start is Cdk-dependent (Verma et al., 1997). Although CKI phosphorylation in budding and "ssion yeasts is initially carried out by kinases resistant to CKI inhibition, it must be carried on by CKI-sensitive, Clb-dependent kinases. The evidence is two-fold: 1. In budding yeast, Cln-kinases disappear soon after Start, but Sic1 does not make a come back until Finish, when Clb-kinases get destroyed. In fact, in vitro, Clb5/Cdc28 is able to phosphorylate Sic1, which induces its SCF-dependent ubiquitination (Feldman et al., 1997; Skowyra et al., 1997). 2. If "ssion yeast cells in G2 phase (with low Rum1 level) are deprived of mitotic cyclin (Cdc13), they go back to G1 phase (high Rum1 level), suggesting that Cdc13 must play an essential role in keeping Rum1 low in G2 (Hayles et al., 1994). These arguments suggest that active Cdk/Clb can turn o! its negative regulator (Sic1) through phosphorylation. Since Hct1-dependent cyclin ubiquitination follows a similar pro"le to the Sic1 concentration (Amon, 1997; Schwob et al., 1994), we propose that Cdk/Clb complexes also inactivate Hct1 by phosphorylation. Two recent studies provide evidence for this hypothesis (Jaspersen et al., 1999; Zachariae et al., 1998). Since Clb-dependent kinase down-regulates both its enemies (Sic1 and Hct1) at Start, these changes must be reversed at Finish. This could be accomplished by activation of a phosphatase that opposes the action of Cdks on Sic1 and Hct1, as illustrated in Fig. 1. While this work was in progress, two labs reported that the budding yeast phosphatase Cdc14 dephosphorylates both Sic1P and Hct1P at the end of mitosis (Jaspersen et al., 1999; Visintin et al., 1998). Although the phosphatase has been identi"ed, its regulation is largely unknown. We propose that the activity of Cdc14 is regulated by Cdc20 (another ancillary protein of APC) through degradation of an inhibitor of the phosphatase. Evidence suggests that Cdc20-dependent proteolysis is involved in two crucial stages of exit from mitosis. One major substrate of Cdc20 is
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Pds1 (Visintin et al., 1997), which protects the tethers holding sister chromatids together. However, because cdc20 pds1D double-mutant cells initiate sister-chromatid separation but arrest in anaphase with high Cdk activity (Lim et al., 1998; Shirayama et al., 1998), it appears that Cdc20 also plays an essential role in eliminating Clbdependent kinase activity at Finish. Perhaps Cdc20 has a role in budding yeast to conduct Clbs to the APC (cf. early embryos, where ,zzy is the sole conductor; Lorca et al., 1998). However, this e!ect does not give a full explanation of all the experiments. Modest expression of nondegradable Clb2 in wild-type cells does not block budding yeast cells in mitosis (Amon et al., 1994; Schwab et al., 1997; Visintin et al., 1997), hence we suggest that Cdc20 must have another substrate besides Clb and Pds1, whose degradation is required to up-regulate Sic1 and turn on Hct1. This other substrate is the hypothetical inhibitor of Cdc14 phosphatase in Fig. 1. We assume that this inhibitor is synthesized at a constant rate throughout the cell-cycle and is degraded by active Cdc20. The activity of Cdc20 is regulated by the mitotic checkpoint: only when all the chromosomes are aligned on the metaphase plate can Cdc20 be activated to destroy Pds1 and the inhibitor. We also assume that Cdc20 is synthesized in a Cdk-dependent manner (Prinz et al., 1998) and degraded at a constant rate. (Alternatively, the synthesis rate could be constant and degradation be Hct1-dependent.) In either case, it is crucial that the level of Cdc20 be large at Finish and small at Start. It is worth mentioning that the hypothetical phosphatase might also dephosphorylate the Tyr-modifying enzymes (Wee1 and Cdc25) in other organisms, like "ssion yeast, thereby promoting inactivating phosphorylation of Cdk/Clb complexes. Simulation of the Cell Cycle We have converted the cell-cycle regulatory mechanism of Fig. 1 into a set of di!erential equations (DEs) by standard application of the law of mass action (see Table 1). Each component in Fig. 1 is represented by a DE with both positive (one for each arrow pointing to the component) and negative terms (one for each arrow
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pointing away). The actual mechanism is more complicated than what is shown in Fig. 1, because we allow phosphorylated as well as unphosphorylated forms of Sic1 to bind to the Cdk/Clb complexes (see Fig. 2). Our assumption that both Cdk/Clb and Cdk/Cln3 kinases accumulate in the nucleus (Futcher, 1996) gives us a simple way to introduce size control. For this reason we multiply by &&mass'' the rate of Clb
synthesis (k ) and the activity of the starter kinase (SK"Cdk/Cln3). In addition, we assume that the Cdk catalytic subunit is present in excess and does not limit the formation of Cdk/ cyclin dimers. We use Michaelis}Menten kinetics only to describe activation and inactivation of Hct1, which introduces important nonlinearity through zero-order ultrasensitivity (Goldbeter & Koshland, 1981).
TABLE 1 Rate equations based on the mechanism in Figs 1 and 2 d Sic1 "k !k Sic1!k Sic1#k Cdc14 ) Sic1P!k Clb ) Sic1#k Tri#k Tri N NN H HP A dt
(1)
d Sic1P "k Sic1!k Cdc14 ) Sic1P!(k #k )Sic1P!k Clb ) Sic1P#k TriP#k TriP N NN H HP A dt
(2)
d Tri dt
"k Clb ) Sic1!k Tri!k Tri!k Tri!k Tri#k Cdc14 ) TriP H HP A N NN
d TriP dt
"k Tri!k Cdc14 ) TriP#k Clb ) Sic1P!k TriP!k TriP!(k #k )TriP N NN H HP A
(3) (4)
d C1b "k mass!k Clb ) Sic1#k Tri!k Clb ) Sic1P#k TriP H HP H HP dt !k Clb#k Tri#(k #k )TriP d Hct1 k (1!Hct1) k Hct1 " FARP ! FAR dt J #1!Hct1 J #Hct1 FARP FAR d Cdc20 "k Clb!k Cdc20#k Cdc20 !k Cdc20 ?Q ?? ?G ?B dt d Cdc20 "k Cdc20!k Cdc20 !k Cdc20 ?? ?G ?B dt d INH dt
"k !k INH Cdc14#k IC!k Cdc20 INH G GP
(5) (6) (7) (8) (9)
d IC "k INH Cdc14!k IC!k Cdc20 IC G GP dt
(10)
d mass "l mass dt
(11)
where Cdc14"Cdc14 !IC 2 k "k (Clb#SK mass) N N k "< (1!Hct1)#< Hct1 k "< (1!Hct1)#< Hct1 A A A k "k Clb FAR FAR k "k #k Cdc14 FARP FARP FARP
(12) (13) (14) (15) (16) (17)
FINISHING THE CELL CYCLE
FIG. 2. Detailed mechanism of Cdk and Sic1 binding. The phosphorylated form of Sic1 binds and inhibits Cdk/cyclin complexes.
The DEs in Table 1 were solved numerically on a PC with Time0 software, after specifying the rate constants, binding constants, and other parameters. The numerical values of these parameters are listed in Table 2. A representative solution of the full rate equations is illustrated in Fig. 3. Clearly there are two characteristic cell-cycle phases. In G1 phase both Clb level and the kinase activity are low, since the negative regulators (Hct1 and Sic1) win: Clb degradation is active and the CKI level is high, as in budding yeast (Amon et al., 1994; Schwob et al., 1994) and "ssion yeast (Correa-Bordes & Nurse, 1995; Funabiki et al., 1996). In the S/M state the opposite is true: Clb level and its associated kinase activity are high and rising, and the negative regulators (Hct1 and Sic1) are o!. These characteristic states correspond to two alternative stable steady states, which arise from the antagonistic relations between Cdk and its nega-
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tive regulators. Transitions between these two states happen at Start and Finish. The Start transition is driven by cell growth, and it happens when the Sic1- and Hct1-resistant &&starter kinase'' (Cdk/Cln3), which accumulates in the nucleus, reaches a critical concentration there. When its activity exceeds the opposing phosphatase activity, Sic1 gets eliminated. Destruction of the CKI unmasks Clb-dependent kinase activity su$cient to turn o! Hct1. Alternatively Cdk/Cln3 kinase can inactivate Hct1 as well (Amon et al., 1994). &&Start'' is identi"ed by this rise of Cdk/Clb activity, which drives DNA synthesis, spindle formation and chromosome alignment. After Start, Cdc20 also begins to accumulate, but in an inactive form. When the cell's fully replicated chromosomes are all properly aligned on the metaphase plate, the signal keeping Cdc20 inactive is released. Cdc20 activation then leads to rapid degradation of Pds1 and dissolution of protein tethers holding sister chromatids together. In addition, we predict that degradation by Cdc20/APC of a presently unknown inhibitor of Cdc14 is the "rst step toward extinguishing Cdk activity at the end of mitosis (Finish). When the inhibitor is destroyed, active Cdc14 will dephosphorylate both Hct1 (activating it) and Sic1 (stabilizing it). The subsequent rise in Hct1 activity and Sic1 level will squash all B-type cyclindependent kinase activity, because Hct1 conducts B-type cyclins to the APC for ubiquitination, and Sic1 binds to and inhibits any B-type cyclin/Cdk complexes that escape destruction. Our model can also explain how cells ensure that inactivation of Cdks and subsequent cytokinesis never happen before the degradation of Pds1 and sister-chromatid separation. According to the model, both Pds1 degradation and activation of the putative phosphatase depend on Cdc20 activity. Therefore, Pds1 is degraded and sister chromatid cohesion is dissolved before, or no later than, removal of Cdk/Clb activity by Sic1 and/or the APC. The model predicts that, as Cdk activity disappears in G1 phase, Cdc20 also vanishes, and the phosphatase inhibitor makes a comes back. As a consequence, Sic1 protein level drops, but there remains plenty of stoichiometric Cdk-inhibitor in late G1 due to the lack of Cdk activity that could
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TABLE 2 Parameter values* used to simulate wild-type cells Clb synthesis and degradation Sic1 synthesis, phosphorylation and degradation Cdc20 synthesis, degradation, activation and inactivation Inhibitor synthesis, degradation and binding Hct1 activation and inactivation Clb and Sic1 binding and dissociation Starter kinase and growth rate
k "0.05 < "0.05 < "1 < "0.05 < "0.5 ! ! k "0.2 k "0.2 k "10 k "10 k "500 . .. k "0.1 k "0.1 k "1 k "0.25}9?Q ?B ?? ?G k "0.1 k "0.5 k "250 k "0.5 Cdc14 "1 G GP 2 k "3 J "0.01 k "0.025 k "5 J "0.01 FAR FAR FARP FARP FARP k "100 k "0.5 H HP SK"0.023 l"0.00577
* Since all the dynamic variables in the model are dimensionless quantities, all the rate constants (k's) and turn-over numbers (<1s) have a dimension of min\. Accordingly, all the Michaelis constants (J's) are dimensionless. - We assume that the rate constant for inactivation of Cdc20, k "k #k , is determined by both DNA replication (k ) ?G ?GQ ?GK ?GQ and spindle assembly (k ) surveillance mechanisms (Hwang et al., 1998). For k (t), we assume a sawtooth function that ?GK ?GQ increases abruptly to 3, when cells start to replicate their DNA (when Hct1 decreases through 0.2), and then decreases steadily back to its basal level (0.001) within 10 min. The second term, k (t), expresses the inactivatory e!ect of misaligned ?GK chromosomes. It increases abruptly to 6 when cells enter M-phase (10 min after active Cdk/Clb increases above 0.75), and then decreases stepwise (2 in every 3 min) as chromosomes align on the mitotic spindle, stopping at its basal value (0.25). To complete the rules we specify that a cell divides (massPmass/2) when Hct1 increases through 0.2.
destabilize Sic1. Hct1 remains active because, although the phosphatase is inhibited, there is insu$cient kinase activity to inactivate Hct1 in G1. In this model, Cdc20 level #uctuates throughout the cell cycle, being small in G1 and high in S/M. The pattern correlates well with the data about levels of Cdc20 homologues in di!erent organisms (Shirayama et al., 1998; Weinstein, 1997). In G1 phase, there are no signals to keep Cdc20 inactive, so its level must be low. Otherwise, Cdc20 would activate Cdc14 (by destroying its inhibitor) and make it impossible to initiate Start. Antagonism between Cdk and its Negative Regulators The antagonistic relationship between Cdk and its negative regulators can easily be demonstrated by plotting the net rate of increase of cyclin B in all its forms (Clb "Clb#Tri# 2 TriP) as a function of Cdk/Clb activity (see the appendix for details). In Fig. 4, wherever dCIb /dt"0, we have a steady-state cyclin level 2 (synthesis balances degradation). The stability of the steady state is determined by the slope of the
net-rate curve as it crosses the abscissa. If the slope is negative, the steady state is stable; if positive, then unstable. In late G1, before Start, when there is not yet enough starter kinase activity to phosphorylate Sic1, the net-rate curve looks like Fig. 4 (top panel). There are three steady states: two are stable (at Clb+0.002 and 1) and one is unstable (at Clb+0.01). The control system is stuck on the lower stable steady state. As the cell grows, the net-rate curve moves up (because SK) mass increasingly phosphorylates Sic1), until the lower, stable steady state is annihilated by coalescing with the unstable steady state in the middle (Fig. 4, middle panel). When this happens, the system must move over to the only remaining steady state (now at Clb+2). This is the Start transition: Clb-dependent kinase activity increases dramatically as Sic1 is destroyed and Hct1 is inactivated. At the end of mitosis, when Cdc20 is activated, and the phosphatase inhibitor is destroyed, the net-rate curve moves into a new position (Fig. 4, bottom panel), where the only stable steady state has low Clb level. The transition from the upper to the lower steady state is Finish.
FINISHING THE CELL CYCLE
FIG. 3. Numerical simulations of the model. The di!erential equations in Table 1, supplemented by the parameter values in Table 2, are solved numerically, using a fourthorder Runge}Kutta algorithm. In this simulation both Sic1 and Hct1 are present, "ghting against Cdk activity. As a consequence these &&wild-type'' cells have a long G1 phase (83 min, the period when Hct1 is active and Sic1 abundant). These cell cycles are growth-controlled, i.e. interdivision time"mass-doubling time (in this case, 120 min), because the Start transition is a!ected by cell size. When SK) mass [in eqn (13) of Table 1] reaches a critical value, Sic1 phosphorylation and degradation increase abruptly. The unmasked activity of Cdk/Clb feeds back autocatalytically on Sic1 degradation and also inactivates Hct1, forcing the cell to transit from G1 to S/M. In this case, S/M phase lasts 37 min, the time needed to replicate DNA, align chromosomes, activate Cdc20, destroy inhibitor and unmask enough Cdc14 activity to regenerate Hct1 and Sic1. Cell division occurs when Hct1 activity increases through 0.2.
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FIG. 4. The net rate of Clb production as a function of Clb-kinase activity. The right-hand side of Eqn (A.1) is plotted as a function of Cdk/Clb activity as described in the appendix. We use &&mass'' and &&Cdc14'' as parameters in the calculations. The three panels show the rate curve in di!erent cell-cycle phases, depending on mass and Cdc14 values. G1: mass"1.3 and Cdc14"0; S/M: mass"2.0 and Cdc14"0; Meta/anaphase: mass"2.0 and Cdc14"0.6.
Finish in the Absence of either Cyclin Degradation or CKI Accumulation At the end of mitosis, newly activated Cdc20 destroys the inhibitor that is sequestering the Cdc14 phosphatase. The phosphatase then activates Hct1 and stabilizes Sic1. Both of these effects down-regulate Cdk activity and drive the cell out of mitosis. However, it is a redundant mechanism, because either Hct1 alone [Fig. 5(a)] or Sic1 alone [Fig. 5(b)] can eliminate Cdk
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FIG. 5. Cell cycles in the absence of cyclin degradation or CKI accumulation. In the absence of Sic1 (sic1\), Hct1 alone must drive the cell out of mitosis (a), while in the absence of Hct1 (hct1\), Sic1 drives the cells out of mitosis (b). CD " cell division. The cell cycles of these mutants have been simulated by the parameter values used for wildtype cells, except that the rate of Sic1 synthesis (k ) has been set to zero for sic1\ cells, and the large turn-over numbers for cyclin degradation (< and < ) were set equal to the A small turn-over numbers (< and < ) for hct1\ cells. We do A not plot the levels of inhibitor, active Cdc20, and active Cdc14, because they show very similar patterns as in wild type (Fig. 3). The cell cycles of the two mutants are organized by a mitotic size control, which is cryptic in wild-type cells. This mitotic size control derives from our assumption that the spindle cannot form until Cdk/Clb activity exceeds a certain threshold.
activity and push cells from mitosis into G1. These simulations agree well with the existing yeast data. In the absence of Hct1, Clb2 (the major mitotic cyclin in budding yeast) is not degraded at the end of mitosis, but these cells exit mitosis nonetheless (Schwab et al., 1997; Visintin et al., 1997). The same is true for "ssion yeast cells de"cient in ste9, which codes for a protein homologous to Hct1 (Kitamura et al., 1998; Yamaguchi et al., 1997). Both yeasts can also exit from mitosis in the absence of their CKI. The only di!erence between the two yeasts is that
budding yeast hct1 sic1 double mutants are inviable and stuck in mitosis (Schwab et al., 1997), whereas "ssion yeast can exit mitosis in the absence of both cyclin B degradation (ste9\) and CKI activity (rum1\). Since "ssion yeast uses tyrosine kinases (Wee1 and Mik1) extensively to regulate Cdk/cyclin B activity, it could be that exit from mitosis in ste9\ rum1\ mutants is driven by up-regulating these kinase activities by the same phosphatase (the Cdc14 homologue; not yet identi"ed in "ssion yeast). Tyrosine phosphorylation may also play a role in exit from mitosis in budding yeast in a process called adaptation, when cells are blocked in mitosis by nocodazole for a long time (Minshull et al., 1996). Although either Hct1 or Sic1 can drive a cell out of mitosis, both of them are required to stabilize the G1 state. Observe that in wild-type cells (Fig. 3), G1 is long and S/M is short, whereas in the mutants [Fig. 5(a) and (b)] the opposite is true. The phosphatase can drive cells out of mitosis, but after a short G1 phase the inhibitor comes back (because Cdc20 disappears) and the G1 steady state is lost. Yeast mutants con"rm this ephemeral G1 phase. In budding yeast, hct1\ cells, though viable, cannot be blocked in G1 phase by mating factor. Triple-cln mutants cannot execute Start, but triple-cln sic1\ cells are viable (they execute Start because they can no longer stop in G1; Schneider et al., 1996; Tyers, 1996). In "ssion yeast, ste9\ mutants (Kitamura et al., 1998; Yamaguchi et al., 1997) and rum1\ mutants (Moreno and Nurse, 1994) are sterile, because they are defective in arresting in G1 upon starvation. Our research is supported by the National Science Foundation of the U.S.A. (DBI-9724085) and Hungary (T-022182 and FKP-0350), the Howard Hughes Medical Institute (75195-542501).
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MENDENHALL, M. D. (1993). An inhibitor of p34!"! protein kinase activity from Saccharomyces cerevisiae. Science 259, 216}219. MINSHULL, J., STRAIGHT, A., RUDNER, A., DERNBURG, A., BELMONT, A. & MURRAY, A. (1996). Protein phosphatase 2A regulates MPF activity and sister chromatid cohesion in budding yeast. Curr. Biol. 6, 1609}1620. MORENO, S. & NURSE, P. (1994). Regulation of progression through the G1 phase of the cell cycle by the rum1> gene. Nature 367, 236}242. NASMYTH, K. (1995). Evolution of the cell cycle. Phil. ¹rans. R. Soc. ¸ond. B. 349, 271}281. NOVAD K, B., CSIKAD SZ-NAGY, A., GYO RFFY, B., NASMYTH, K. & TYSON, J. (1998). Model scenarios for the evolution of the eukaryotic cell cycle. Phil. ¹rans. R. Soc. ¸ond B. 353, 1063}1076. PRINZ, S., HWANG, E. S., VISINTIN, R. & AMON, A. (1998). The regulation of Cdc20 proteolysis reveals a role for the APC components Cdc23 and Cdc27 during S phase and early mitosis. Curr. Biol. 8, 750}760. SCHNEIDER, B. L., YANG, Q.-H. & FUTCHER, A. B. (1996). Linkage of replication to Start by the Cdk inhibitor Sic1. Science 272, 560}562. SCHWAB, M., LUTUM, A. S. & SEUFERT, W. (1997). Yeast Hct1 is a regulator of Clb2 cyclin proteolysis. Cell 90, 683}693. SCHWOB, E., BOHM, T., MENDENHALL, M. & NASMYTH, K. (1994). The B-type cyclin kinase inhibitor p401'! controls the G1 to S transition in S. cerevisiae. Cell 79, 233}244. SHIRAYAMA, M., ZACHARIAE, W., CIOSK, R. & NASMYTH, K. (1998). The Polo-like kinase Cdc5p and the WD-repeat protein Cdc20p/"zzy are regulators and substrates of the anaphase promoting complex in Saccharomyces cerevisiae. EMBO J. 17, 1336}1349. SIGRIST, S. J. & LEHNER, C. F. (1997). Drosophila "zzy-related down-regulates mitotic cyclins and is required for cell proliferation arrest and entry into endocycles. Cell 90, 671}681. SKOWYRA, D., CRAIG, K. L., TYERS, M., ELLEDGE, S. J. & HARPER, J. W. (1997). F-box proteins are receptors that recruit phosphorylated substrates to the SCF ubiquitinligase complex. Cell 91, 209}219. SUDAKIN, V., GANOTH, D., DAHAN, A., HELLER, H., HERSHKO, J., LUCA, F. C., RUDERMAN, J. V. & HERSHKO, A. (1995). The cyclosome, a large complex containing cyclinselective ubiquitin}ligase activity, targets cyclins for destruction at the end of mitosis. Mol. Biol. Cell 6, 185}197. TOYN, J. H., JOHNSON, A. L., DONOVAN, J. D., TOONE, W. M. & JOHNSTON, L. H. (1997). The Swi5 transcription factor of Saccharomyces cerevisiae has a role in exit from mitosis through induction of the cdk-inhibitor Sic1 in telophase. Genetics 145, 85}96. TYERS, M. (1996). The cyclin-dependent kinase inhibitor p401'! imposes the requirement for Cln G1 cyclin function at Start. Proc. Nat. Acad. Sci. ;.S.A. 93, 7772}7776. VERMA, R., ANNAN, R. S., HUDDLESTON, M. J., CARR, S. A., REYNARD, G. & DESHAIES, R. J. (1997). Phosphorylation of Sic1p by G1 Cdk required for its degradation and entry into S phase. Science 278, 455}460. VISINTIN, R., CRAIG, K., HWANG, E., PRINZ, S., TYERS, M. & AMON, A. (1998). The phosphatase Cdc14 triggers mitotic exit by reversal of Cdk-dependent phosphorylation. Mol. Cell 2, 709}718. VISINTIN, R., PRINZ, S. & AMON, A. (1997). CDC20 and CDH1: a family of substrate-speci"c activators of APCdependent proteolysis. Science 278, 460}463.
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WEINSTEIN, J. (1997). Cell cycle-regulated expression, phosphorylation, and degradation of p55Cdc. A mammalian homolog of CDC20/Fizzy/slp1. J. Biol. Chem. 272, 28 501}28 511. YAMAGUCHI, S., MURAKAMI, H. & OKAYAMA, H (1997). A WD repeat protein controls the cell cycle and di!erentiation by negatively regulating Cdc2/B-type cyclin complexes. Mol. Biol. Cell 8, 2475}2486. ZACHARIAE, W., SCHWAB, M., NASMYTH, K. & SEUFERT, W. (1998). Control of cyclin ubiquitination by Cdk-regulated binding of Hct1 to the Anaphase Promoting Complex. Science 282, 1721}1724.
the components shown in Figs. 1 and 2 are in quasi-steady state. First, we calculate the steady-state level of total Sic1 (Sic1 "Sic1#Sic1P#Tri#TriP) as a 2 function of Clb"[active Cdk/Clb dimers]. To do so, we add together eqns (1)}(4) and eqns (2) and (4) in Table 1: dSic1 2"k !k Sic1 !k (Sic1P#TriP), 2 dt
d(Sic1P#TriP) "k (Clb#SK) mass)(Sic1 !Sic1P!TriP) N 2 dt !(k Cdc14#k #k ) NN
APPENDIX Calculation of the Net Rate of Cyclin Synthesis Curve
(Sic1P#TriP) .
Because Cdk/Clb has antagonistic relationship with Hct1 and Sic1, these enemies tend to exclude each other: either Cdk activity is high, and Hct1 and Sic1 are ine!ectual (S/G2/M), or vice versa (G1). This antagonism can be illustrated by plotting the net rate of increase of cyclin B in all forms (Clb "Clb#Tri#TriP) as a function of 2 Cdk/Clb activity. (In all equations we use the short-hand notation: Clb"[active Cdk/Clb dimers], Tri"[Cdk/Clb/Sic1 trimers], and TriP"[phosphorylated trimers]. It should be clear from the context as to when &&Clb'' is used as the name of a molecule and when it is used as a mathematical variable.) In this section, we describe exactly how dCIb /dt is calculated as 2 a function of Clb. The net rate of increase of cyclin B in all the forms is given by adding together eqns (3)}(5) in Table 1:
Setting the right-hand sides of both equations to zero (quasi-steady-state assumption) and plugging the solution from the second equation into the "rst, we get
dCIb 2"k mass!k Clb dt !k (Tri#TriP). (A.1) A The "rst term represents the rate of cyclin synthesis from amino acids. The second and third terms are the rates of degradation from active Cdk/cyclin dimers and from Cdk/cyclin/CKI trimers, respectively. We calculate the net rate of cyclin synthesis, eqn (A.1), as follows. To begin, we set &&mass'' and protein phosphatase activity (Cdc14) to constant values depending on the phase of the cell cycle. Then we assume that all
Sic1 " 2 k . k (Clb#SK mass) N k #k k (Clb#SK mass)#k Cdc14#k #k N NN (A.2) Second, by assuming fast and reversible binding of Sic1 and Sic1P to Clb kinases, we can calculate the equilibrium concentration of trimers (Tri#TriP) using Sic1 and active Clb 2 values: Tri#Trip Tri#TriP " ¸" (Sic1#Sic1P)Clb (Sic1 !Tri!TriP)C1b 2 simply as Sic1 C1b 2 , Tri#TriP" 1/¸#C1b
(A.3)
where &&¸'' is the binding constant (k /k ). SubH HP stituting eqn (A.2) in (A.3), we can express Tri#TriP in terms of known quantities. The "nal step in calculating the right-hand side of eqn (A.1) is to compute k and k from eqns A (14) and (15) in Table 1. To do this, we must "rst
FINISHING THE CELL CYCLE
solve eqn (6) for active Hct1 in steady state: Hct1(a, b, c, d)" 2ad , b!a#bc#ad#((b!a#bc#ad)!4(b!a)ad
233
where a"k #k Cdc14, b"k Clb, c"J , FARP FARP FAR FARP d"J . FAR This set of calculations, though lengthy, can easily be done by any commercial spreadsheet program.
Finishing the Cell Cycle BED LA NOVAD K*A, ATTILA TOD TH-, ATTILA CSIKAD SZ-NAGY*, BED LA GYOD D RFFY*, JOHN J. TYSON? AND KIM NASMYTH*Department of Agricultural Chemical ¹echnology, ¹echnical ;niversity of Budapest, GelleH rt teH r 4, Budapest 1521, Hungary, -Institute of Molecular Pathology, Dr Bohr Gasse 7,
The eukaryotic cell division cycle consists of two characteristic states: G1, when replication origins of chromosomes are in a pre-replicative state, and S/G2/M, when they are in a postreplicative state (Nasmyth, 1995). Using straightforward biochemical kinetics, we show that these two states can be created by antagonistic interactions between cyclin-dependent kinases (Cdk) and their foes: the cyclin-degradation machinery (APC) and a stoichiometric inhibitor (CKI). Irreversible transitions between these two self-maintaining steady states drive progress through the cell cycle: at &&Start'' a cell leaves the G1 state and commences chromosome replication, and at &&Finish'' the cell separates the products of replication to the incipient daughter cells and re-enters G1. We propose that a protein-phosphatase, by up-regulating the APC and by stabilizing the CKI, plays an essential role at Finish. The phosphatase acts in parallel pathways; hence, cells can leave mitosis in the absence of cyclin degradation or in the absence of the CKI. 1999 Academic Press
Introduction At Start (the G1/S transition), a eukaryotic cell commits itself to a new round of DNA synthesis, mitosis and division. Before executing Start, the cell surveys its internal state and external milieu to determine if conditions are appropriate for reproduction. At this stage (often called the G1 checkpoint), the cell is sensitive to growth factors, di!erentiation signals, or sex hormones, which can block mitotic cycles and induce a resting state, terminal di!erentiation, or meiosis (see Alberts et al., 1994). At Finish (the meta/
A Author to whom correspondence should be addressed. E-mail: [email protected]. 0022}5193/99/014223#11 $30.00/0
anaphase transition), the cell pulls sister chromatids apart. Before doing so, it checks that the chromosomes are completely replicated and the sister chromatids are all properly attached to opposite poles of the spindle. If these conditions are not satis"ed, the metaphase checkpoint mechanism blocks dissolution of cohesion proteins holding the sister chromatids together. These transitions are triggered by irreversible changes in activities of cyclin-dependent kinases (Cdk). At Start, Cdk activities rise for a combination of reasons: activation of cyclin transcription, inactivation of cyclin degradation, and removal of cyclin-dependent kinase inhibitors (CKIs). At Finish, Cdk activities are extinguished due to activation of cyclin degradation, accumulation of 1999 Academic Press
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CDK inhibitors, and, perhaps, inactivating phosphorylation of CDKs. In this paper, we concentrate on the molecular events that drive exit from mitosis. A Simpli5ed Cell-Cycle Control Network To illustrate how the Finish transition might work we propose a simple mechanism (Fig. 1) largely based on cell-cycle controls in budding yeast (in particular, we ignore inhibitory tyrosine phosphorylation of the Cdk subunit). Consequently, we refer to each protein by its name in budding yeast, although most of them have counterparts in other organisms (some homologues are listed in the "gure legend). The model consists of a single essential Cdk subunit with two important cyclin partners: a CLN-type cyclin (Cln3), which is present at constant concentration, and a single B-type cyclin (representing Clb1-6) which is synthesized and degraded in each cycle. In "ssion yeast, these two cyclins, Puc1 and Cdc13, respectively, are su$cient to drive a complete mitotic cell cycle (Fisher & Nurse, 1996). To keep the model simple, Clb is synthesized at constant rate and it associates rapidly with the Cdk subunit, which is present in excess. The cyclin component of the complex is degraded by ubiquitin-mediated proteolysis (Hershko, 1997). A short sequence near the N-terminus of B-type cyclins is recognized by a speci"c ubiquitin ligase, called the cyclosome (Sudakin et al., 1995) or the Anaphase Promoting Complex (APC; Irniger and Nasmyth, 1997). APC-mediated cyclin ubiquitination requires an ancillary protein, Hct1 (&&homologue of Cdc20'', Cdh1 is a synonym for Hct1; Schwab et al., 1997; Visintin et al., 1997). The activity of the Cdk/cyclin complex is also regulated by Sic1, a stoichiometric inhibitor in budding yeast (Mendenhall, 1993; Schwob et al., 1994). Although Sic1 synthesis varies with the cell-cycle phase in budding yeast (Schwob et al., 1994; Toyn et al., 1997), in this model the inhibitor is synthesized at a constant rate, like the analogous protein (Rum1) in "ssion yeast (Moreno & Nurse, 1994). Like B-type cyclins, Sic1 proteolysis is also ubiquitin-dependent, but it relies on a second ubiquitin-ligase, called SCF (Benito et al., 1998; Feldman et al., 1997; Skowyra
FIG. 1. Skeleton model of the eukaryotic cell cycle. The B-type cyclin (Clb) is targeted to APC by Hct1, which is also called Cdh1 (Schwab et al., 1997; Visintin et al., 1997). Ste9 (also called Srw1) and fzr (&&"zzy related'') are the homologous proteins in "ssion yeast and Drosophila (Kitamura et al., 1998; Sigrist and Lehner, 1997; Yamaguchi et al., 1997). A hypothetical inhibitor is targeted to APC by another auxiliary protein, Cdc20 [the "ssion yeast homolog is Slp1 (Matsumoto, 1997), and in Drosophila it is called ,zzy (Dawson et al., 1995)]. This model is an improved version of our earlier mechanism for cell-cycle control in primitive eukaryotes (Fig. 6 of NovaH k et al., 1998). Here, we use budding yeast-speci"c names for each component in place of the generic names used there: ACT"Cdc20, APC"Hct1, Cyclin"Clb, CKI"Sic1. In the earlier model, Cdc20 directly activated Hct1, while here it acts indirectly by destroying an inhibitor of the Hct1-activating phosphatase, Cdc14. In addition, we now propose that the very same phosphatase rescues phosphorylated Sic1 from degradation. In organisms that regulate Cdk/cyclin activity by tyrosine phosphorylation of the Cdk subunit (not considered in this model, but see Fig. 9 of NovaH k et al., 1998), we propose that the phosphatase also opposes cyclin-dependent phosphorylation of Wee1 and Cdc25.
FINISHING THE CELL CYCLE
et al., 1997). The SCF complex recognizes phosphorylated proteins, and the phosphorylation of Sic1 at Start is Cdk-dependent (Verma et al., 1997). Although CKI phosphorylation in budding and "ssion yeasts is initially carried out by kinases resistant to CKI inhibition, it must be carried on by CKI-sensitive, Clb-dependent kinases. The evidence is two-fold: 1. In budding yeast, Cln-kinases disappear soon after Start, but Sic1 does not make a come back until Finish, when Clb-kinases get destroyed. In fact, in vitro, Clb5/Cdc28 is able to phosphorylate Sic1, which induces its SCF-dependent ubiquitination (Feldman et al., 1997; Skowyra et al., 1997). 2. If "ssion yeast cells in G2 phase (with low Rum1 level) are deprived of mitotic cyclin (Cdc13), they go back to G1 phase (high Rum1 level), suggesting that Cdc13 must play an essential role in keeping Rum1 low in G2 (Hayles et al., 1994). These arguments suggest that active Cdk/Clb can turn o! its negative regulator (Sic1) through phosphorylation. Since Hct1-dependent cyclin ubiquitination follows a similar pro"le to the Sic1 concentration (Amon, 1997; Schwob et al., 1994), we propose that Cdk/Clb complexes also inactivate Hct1 by phosphorylation. Two recent studies provide evidence for this hypothesis (Jaspersen et al., 1999; Zachariae et al., 1998). Since Clb-dependent kinase down-regulates both its enemies (Sic1 and Hct1) at Start, these changes must be reversed at Finish. This could be accomplished by activation of a phosphatase that opposes the action of Cdks on Sic1 and Hct1, as illustrated in Fig. 1. While this work was in progress, two labs reported that the budding yeast phosphatase Cdc14 dephosphorylates both Sic1P and Hct1P at the end of mitosis (Jaspersen et al., 1999; Visintin et al., 1998). Although the phosphatase has been identi"ed, its regulation is largely unknown. We propose that the activity of Cdc14 is regulated by Cdc20 (another ancillary protein of APC) through degradation of an inhibitor of the phosphatase. Evidence suggests that Cdc20-dependent proteolysis is involved in two crucial stages of exit from mitosis. One major substrate of Cdc20 is
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Pds1 (Visintin et al., 1997), which protects the tethers holding sister chromatids together. However, because cdc20 pds1D double-mutant cells initiate sister-chromatid separation but arrest in anaphase with high Cdk activity (Lim et al., 1998; Shirayama et al., 1998), it appears that Cdc20 also plays an essential role in eliminating Clbdependent kinase activity at Finish. Perhaps Cdc20 has a role in budding yeast to conduct Clbs to the APC (cf. early embryos, where ,zzy is the sole conductor; Lorca et al., 1998). However, this e!ect does not give a full explanation of all the experiments. Modest expression of nondegradable Clb2 in wild-type cells does not block budding yeast cells in mitosis (Amon et al., 1994; Schwab et al., 1997; Visintin et al., 1997), hence we suggest that Cdc20 must have another substrate besides Clb and Pds1, whose degradation is required to up-regulate Sic1 and turn on Hct1. This other substrate is the hypothetical inhibitor of Cdc14 phosphatase in Fig. 1. We assume that this inhibitor is synthesized at a constant rate throughout the cell-cycle and is degraded by active Cdc20. The activity of Cdc20 is regulated by the mitotic checkpoint: only when all the chromosomes are aligned on the metaphase plate can Cdc20 be activated to destroy Pds1 and the inhibitor. We also assume that Cdc20 is synthesized in a Cdk-dependent manner (Prinz et al., 1998) and degraded at a constant rate. (Alternatively, the synthesis rate could be constant and degradation be Hct1-dependent.) In either case, it is crucial that the level of Cdc20 be large at Finish and small at Start. It is worth mentioning that the hypothetical phosphatase might also dephosphorylate the Tyr-modifying enzymes (Wee1 and Cdc25) in other organisms, like "ssion yeast, thereby promoting inactivating phosphorylation of Cdk/Clb complexes. Simulation of the Cell Cycle We have converted the cell-cycle regulatory mechanism of Fig. 1 into a set of di!erential equations (DEs) by standard application of the law of mass action (see Table 1). Each component in Fig. 1 is represented by a DE with both positive (one for each arrow pointing to the component) and negative terms (one for each arrow
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pointing away). The actual mechanism is more complicated than what is shown in Fig. 1, because we allow phosphorylated as well as unphosphorylated forms of Sic1 to bind to the Cdk/Clb complexes (see Fig. 2). Our assumption that both Cdk/Clb and Cdk/Cln3 kinases accumulate in the nucleus (Futcher, 1996) gives us a simple way to introduce size control. For this reason we multiply by &&mass'' the rate of Clb
synthesis (k ) and the activity of the starter kinase (SK"Cdk/Cln3). In addition, we assume that the Cdk catalytic subunit is present in excess and does not limit the formation of Cdk/ cyclin dimers. We use Michaelis}Menten kinetics only to describe activation and inactivation of Hct1, which introduces important nonlinearity through zero-order ultrasensitivity (Goldbeter & Koshland, 1981).
TABLE 1 Rate equations based on the mechanism in Figs 1 and 2 d Sic1 "k !k Sic1!k Sic1#k Cdc14 ) Sic1P!k Clb ) Sic1#k Tri#k Tri N NN H HP A dt
(1)
d Sic1P "k Sic1!k Cdc14 ) Sic1P!(k #k )Sic1P!k Clb ) Sic1P#k TriP#k TriP N NN H HP A dt
(2)
d Tri dt
"k Clb ) Sic1!k Tri!k Tri!k Tri!k Tri#k Cdc14 ) TriP H HP A N NN
d TriP dt
"k Tri!k Cdc14 ) TriP#k Clb ) Sic1P!k TriP!k TriP!(k #k )TriP N NN H HP A
(3) (4)
d C1b "k mass!k Clb ) Sic1#k Tri!k Clb ) Sic1P#k TriP H HP H HP dt !k Clb#k Tri#(k #k )TriP d Hct1 k (1!Hct1) k Hct1 " FARP ! FAR dt J #1!Hct1 J #Hct1 FARP FAR d Cdc20 "k Clb!k Cdc20#k Cdc20 !k Cdc20 ?Q ?? ?G ?B dt d Cdc20 "k Cdc20!k Cdc20 !k Cdc20 ?? ?G ?B dt d INH dt
"k !k INH Cdc14#k IC!k Cdc20 INH G GP
(5) (6) (7) (8) (9)
d IC "k INH Cdc14!k IC!k Cdc20 IC G GP dt
(10)
d mass "l mass dt
(11)
where Cdc14"Cdc14 !IC 2 k "k (Clb#SK mass) N N k "< (1!Hct1)#< Hct1 k "< (1!Hct1)#< Hct1 A A A k "k Clb FAR FAR k "k #k Cdc14 FARP FARP FARP
(12) (13) (14) (15) (16) (17)
FINISHING THE CELL CYCLE
FIG. 2. Detailed mechanism of Cdk and Sic1 binding. The phosphorylated form of Sic1 binds and inhibits Cdk/cyclin complexes.
The DEs in Table 1 were solved numerically on a PC with Time0 software, after specifying the rate constants, binding constants, and other parameters. The numerical values of these parameters are listed in Table 2. A representative solution of the full rate equations is illustrated in Fig. 3. Clearly there are two characteristic cell-cycle phases. In G1 phase both Clb level and the kinase activity are low, since the negative regulators (Hct1 and Sic1) win: Clb degradation is active and the CKI level is high, as in budding yeast (Amon et al., 1994; Schwob et al., 1994) and "ssion yeast (Correa-Bordes & Nurse, 1995; Funabiki et al., 1996). In the S/M state the opposite is true: Clb level and its associated kinase activity are high and rising, and the negative regulators (Hct1 and Sic1) are o!. These characteristic states correspond to two alternative stable steady states, which arise from the antagonistic relations between Cdk and its nega-
227
tive regulators. Transitions between these two states happen at Start and Finish. The Start transition is driven by cell growth, and it happens when the Sic1- and Hct1-resistant &&starter kinase'' (Cdk/Cln3), which accumulates in the nucleus, reaches a critical concentration there. When its activity exceeds the opposing phosphatase activity, Sic1 gets eliminated. Destruction of the CKI unmasks Clb-dependent kinase activity su$cient to turn o! Hct1. Alternatively Cdk/Cln3 kinase can inactivate Hct1 as well (Amon et al., 1994). &&Start'' is identi"ed by this rise of Cdk/Clb activity, which drives DNA synthesis, spindle formation and chromosome alignment. After Start, Cdc20 also begins to accumulate, but in an inactive form. When the cell's fully replicated chromosomes are all properly aligned on the metaphase plate, the signal keeping Cdc20 inactive is released. Cdc20 activation then leads to rapid degradation of Pds1 and dissolution of protein tethers holding sister chromatids together. In addition, we predict that degradation by Cdc20/APC of a presently unknown inhibitor of Cdc14 is the "rst step toward extinguishing Cdk activity at the end of mitosis (Finish). When the inhibitor is destroyed, active Cdc14 will dephosphorylate both Hct1 (activating it) and Sic1 (stabilizing it). The subsequent rise in Hct1 activity and Sic1 level will squash all B-type cyclindependent kinase activity, because Hct1 conducts B-type cyclins to the APC for ubiquitination, and Sic1 binds to and inhibits any B-type cyclin/Cdk complexes that escape destruction. Our model can also explain how cells ensure that inactivation of Cdks and subsequent cytokinesis never happen before the degradation of Pds1 and sister-chromatid separation. According to the model, both Pds1 degradation and activation of the putative phosphatase depend on Cdc20 activity. Therefore, Pds1 is degraded and sister chromatid cohesion is dissolved before, or no later than, removal of Cdk/Clb activity by Sic1 and/or the APC. The model predicts that, as Cdk activity disappears in G1 phase, Cdc20 also vanishes, and the phosphatase inhibitor makes a comes back. As a consequence, Sic1 protein level drops, but there remains plenty of stoichiometric Cdk-inhibitor in late G1 due to the lack of Cdk activity that could
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TABLE 2 Parameter values* used to simulate wild-type cells Clb synthesis and degradation Sic1 synthesis, phosphorylation and degradation Cdc20 synthesis, degradation, activation and inactivation Inhibitor synthesis, degradation and binding Hct1 activation and inactivation Clb and Sic1 binding and dissociation Starter kinase and growth rate
k "0.05 < "0.05 < "1 < "0.05 < "0.5 ! ! k "0.2 k "0.2 k "10 k "10 k "500 . .. k "0.1 k "0.1 k "1 k "0.25}9?Q ?B ?? ?G k "0.1 k "0.5 k "250 k "0.5 Cdc14 "1 G GP 2 k "3 J "0.01 k "0.025 k "5 J "0.01 FAR FAR FARP FARP FARP k "100 k "0.5 H HP SK"0.023 l"0.00577
* Since all the dynamic variables in the model are dimensionless quantities, all the rate constants (k's) and turn-over numbers (<1s) have a dimension of min\. Accordingly, all the Michaelis constants (J's) are dimensionless. - We assume that the rate constant for inactivation of Cdc20, k "k #k , is determined by both DNA replication (k ) ?G ?GQ ?GK ?GQ and spindle assembly (k ) surveillance mechanisms (Hwang et al., 1998). For k (t), we assume a sawtooth function that ?GK ?GQ increases abruptly to 3, when cells start to replicate their DNA (when Hct1 decreases through 0.2), and then decreases steadily back to its basal level (0.001) within 10 min. The second term, k (t), expresses the inactivatory e!ect of misaligned ?GK chromosomes. It increases abruptly to 6 when cells enter M-phase (10 min after active Cdk/Clb increases above 0.75), and then decreases stepwise (2 in every 3 min) as chromosomes align on the mitotic spindle, stopping at its basal value (0.25). To complete the rules we specify that a cell divides (massPmass/2) when Hct1 increases through 0.2.
destabilize Sic1. Hct1 remains active because, although the phosphatase is inhibited, there is insu$cient kinase activity to inactivate Hct1 in G1. In this model, Cdc20 level #uctuates throughout the cell cycle, being small in G1 and high in S/M. The pattern correlates well with the data about levels of Cdc20 homologues in di!erent organisms (Shirayama et al., 1998; Weinstein, 1997). In G1 phase, there are no signals to keep Cdc20 inactive, so its level must be low. Otherwise, Cdc20 would activate Cdc14 (by destroying its inhibitor) and make it impossible to initiate Start. Antagonism between Cdk and its Negative Regulators The antagonistic relationship between Cdk and its negative regulators can easily be demonstrated by plotting the net rate of increase of cyclin B in all its forms (Clb "Clb#Tri# 2 TriP) as a function of Cdk/Clb activity (see the appendix for details). In Fig. 4, wherever dCIb /dt"0, we have a steady-state cyclin level 2 (synthesis balances degradation). The stability of the steady state is determined by the slope of the
net-rate curve as it crosses the abscissa. If the slope is negative, the steady state is stable; if positive, then unstable. In late G1, before Start, when there is not yet enough starter kinase activity to phosphorylate Sic1, the net-rate curve looks like Fig. 4 (top panel). There are three steady states: two are stable (at Clb+0.002 and 1) and one is unstable (at Clb+0.01). The control system is stuck on the lower stable steady state. As the cell grows, the net-rate curve moves up (because SK) mass increasingly phosphorylates Sic1), until the lower, stable steady state is annihilated by coalescing with the unstable steady state in the middle (Fig. 4, middle panel). When this happens, the system must move over to the only remaining steady state (now at Clb+2). This is the Start transition: Clb-dependent kinase activity increases dramatically as Sic1 is destroyed and Hct1 is inactivated. At the end of mitosis, when Cdc20 is activated, and the phosphatase inhibitor is destroyed, the net-rate curve moves into a new position (Fig. 4, bottom panel), where the only stable steady state has low Clb level. The transition from the upper to the lower steady state is Finish.
FINISHING THE CELL CYCLE
FIG. 3. Numerical simulations of the model. The di!erential equations in Table 1, supplemented by the parameter values in Table 2, are solved numerically, using a fourthorder Runge}Kutta algorithm. In this simulation both Sic1 and Hct1 are present, "ghting against Cdk activity. As a consequence these &&wild-type'' cells have a long G1 phase (83 min, the period when Hct1 is active and Sic1 abundant). These cell cycles are growth-controlled, i.e. interdivision time"mass-doubling time (in this case, 120 min), because the Start transition is a!ected by cell size. When SK) mass [in eqn (13) of Table 1] reaches a critical value, Sic1 phosphorylation and degradation increase abruptly. The unmasked activity of Cdk/Clb feeds back autocatalytically on Sic1 degradation and also inactivates Hct1, forcing the cell to transit from G1 to S/M. In this case, S/M phase lasts 37 min, the time needed to replicate DNA, align chromosomes, activate Cdc20, destroy inhibitor and unmask enough Cdc14 activity to regenerate Hct1 and Sic1. Cell division occurs when Hct1 activity increases through 0.2.
229
FIG. 4. The net rate of Clb production as a function of Clb-kinase activity. The right-hand side of Eqn (A.1) is plotted as a function of Cdk/Clb activity as described in the appendix. We use &&mass'' and &&Cdc14'' as parameters in the calculations. The three panels show the rate curve in di!erent cell-cycle phases, depending on mass and Cdc14 values. G1: mass"1.3 and Cdc14"0; S/M: mass"2.0 and Cdc14"0; Meta/anaphase: mass"2.0 and Cdc14"0.6.
Finish in the Absence of either Cyclin Degradation or CKI Accumulation At the end of mitosis, newly activated Cdc20 destroys the inhibitor that is sequestering the Cdc14 phosphatase. The phosphatase then activates Hct1 and stabilizes Sic1. Both of these effects down-regulate Cdk activity and drive the cell out of mitosis. However, it is a redundant mechanism, because either Hct1 alone [Fig. 5(a)] or Sic1 alone [Fig. 5(b)] can eliminate Cdk
230
B. NOVAD K ET AL.
FIG. 5. Cell cycles in the absence of cyclin degradation or CKI accumulation. In the absence of Sic1 (sic1\), Hct1 alone must drive the cell out of mitosis (a), while in the absence of Hct1 (hct1\), Sic1 drives the cells out of mitosis (b). CD " cell division. The cell cycles of these mutants have been simulated by the parameter values used for wildtype cells, except that the rate of Sic1 synthesis (k ) has been set to zero for sic1\ cells, and the large turn-over numbers for cyclin degradation (< and < ) were set equal to the A small turn-over numbers (< and < ) for hct1\ cells. We do A not plot the levels of inhibitor, active Cdc20, and active Cdc14, because they show very similar patterns as in wild type (Fig. 3). The cell cycles of the two mutants are organized by a mitotic size control, which is cryptic in wild-type cells. This mitotic size control derives from our assumption that the spindle cannot form until Cdk/Clb activity exceeds a certain threshold.
activity and push cells from mitosis into G1. These simulations agree well with the existing yeast data. In the absence of Hct1, Clb2 (the major mitotic cyclin in budding yeast) is not degraded at the end of mitosis, but these cells exit mitosis nonetheless (Schwab et al., 1997; Visintin et al., 1997). The same is true for "ssion yeast cells de"cient in ste9, which codes for a protein homologous to Hct1 (Kitamura et al., 1998; Yamaguchi et al., 1997). Both yeasts can also exit from mitosis in the absence of their CKI. The only di!erence between the two yeasts is that
budding yeast hct1 sic1 double mutants are inviable and stuck in mitosis (Schwab et al., 1997), whereas "ssion yeast can exit mitosis in the absence of both cyclin B degradation (ste9\) and CKI activity (rum1\). Since "ssion yeast uses tyrosine kinases (Wee1 and Mik1) extensively to regulate Cdk/cyclin B activity, it could be that exit from mitosis in ste9\ rum1\ mutants is driven by up-regulating these kinase activities by the same phosphatase (the Cdc14 homologue; not yet identi"ed in "ssion yeast). Tyrosine phosphorylation may also play a role in exit from mitosis in budding yeast in a process called adaptation, when cells are blocked in mitosis by nocodazole for a long time (Minshull et al., 1996). Although either Hct1 or Sic1 can drive a cell out of mitosis, both of them are required to stabilize the G1 state. Observe that in wild-type cells (Fig. 3), G1 is long and S/M is short, whereas in the mutants [Fig. 5(a) and (b)] the opposite is true. The phosphatase can drive cells out of mitosis, but after a short G1 phase the inhibitor comes back (because Cdc20 disappears) and the G1 steady state is lost. Yeast mutants con"rm this ephemeral G1 phase. In budding yeast, hct1\ cells, though viable, cannot be blocked in G1 phase by mating factor. Triple-cln mutants cannot execute Start, but triple-cln sic1\ cells are viable (they execute Start because they can no longer stop in G1; Schneider et al., 1996; Tyers, 1996). In "ssion yeast, ste9\ mutants (Kitamura et al., 1998; Yamaguchi et al., 1997) and rum1\ mutants (Moreno and Nurse, 1994) are sterile, because they are defective in arresting in G1 upon starvation. Our research is supported by the National Science Foundation of the U.S.A. (DBI-9724085) and Hungary (T-022182 and FKP-0350), the Howard Hughes Medical Institute (75195-542501).
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FINISHING THE CELL CYCLE
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MENDENHALL, M. D. (1993). An inhibitor of p34!"! protein kinase activity from Saccharomyces cerevisiae. Science 259, 216}219. MINSHULL, J., STRAIGHT, A., RUDNER, A., DERNBURG, A., BELMONT, A. & MURRAY, A. (1996). Protein phosphatase 2A regulates MPF activity and sister chromatid cohesion in budding yeast. Curr. Biol. 6, 1609}1620. MORENO, S. & NURSE, P. (1994). Regulation of progression through the G1 phase of the cell cycle by the rum1> gene. Nature 367, 236}242. NASMYTH, K. (1995). Evolution of the cell cycle. Phil. ¹rans. R. Soc. ¸ond. B. 349, 271}281. NOVAD K, B., CSIKAD SZ-NAGY, A., GYO RFFY, B., NASMYTH, K. & TYSON, J. (1998). Model scenarios for the evolution of the eukaryotic cell cycle. Phil. ¹rans. R. Soc. ¸ond B. 353, 1063}1076. PRINZ, S., HWANG, E. S., VISINTIN, R. & AMON, A. (1998). The regulation of Cdc20 proteolysis reveals a role for the APC components Cdc23 and Cdc27 during S phase and early mitosis. Curr. Biol. 8, 750}760. SCHNEIDER, B. L., YANG, Q.-H. & FUTCHER, A. B. (1996). Linkage of replication to Start by the Cdk inhibitor Sic1. Science 272, 560}562. SCHWAB, M., LUTUM, A. S. & SEUFERT, W. (1997). Yeast Hct1 is a regulator of Clb2 cyclin proteolysis. Cell 90, 683}693. SCHWOB, E., BOHM, T., MENDENHALL, M. & NASMYTH, K. (1994). The B-type cyclin kinase inhibitor p401'! controls the G1 to S transition in S. cerevisiae. Cell 79, 233}244. SHIRAYAMA, M., ZACHARIAE, W., CIOSK, R. & NASMYTH, K. (1998). The Polo-like kinase Cdc5p and the WD-repeat protein Cdc20p/"zzy are regulators and substrates of the anaphase promoting complex in Saccharomyces cerevisiae. EMBO J. 17, 1336}1349. SIGRIST, S. J. & LEHNER, C. F. (1997). Drosophila "zzy-related down-regulates mitotic cyclins and is required for cell proliferation arrest and entry into endocycles. Cell 90, 671}681. SKOWYRA, D., CRAIG, K. L., TYERS, M., ELLEDGE, S. J. & HARPER, J. W. (1997). F-box proteins are receptors that recruit phosphorylated substrates to the SCF ubiquitinligase complex. Cell 91, 209}219. SUDAKIN, V., GANOTH, D., DAHAN, A., HELLER, H., HERSHKO, J., LUCA, F. C., RUDERMAN, J. V. & HERSHKO, A. (1995). The cyclosome, a large complex containing cyclinselective ubiquitin}ligase activity, targets cyclins for destruction at the end of mitosis. Mol. Biol. Cell 6, 185}197. TOYN, J. H., JOHNSON, A. L., DONOVAN, J. D., TOONE, W. M. & JOHNSTON, L. H. (1997). The Swi5 transcription factor of Saccharomyces cerevisiae has a role in exit from mitosis through induction of the cdk-inhibitor Sic1 in telophase. Genetics 145, 85}96. TYERS, M. (1996). The cyclin-dependent kinase inhibitor p401'! imposes the requirement for Cln G1 cyclin function at Start. Proc. Nat. Acad. Sci. ;.S.A. 93, 7772}7776. VERMA, R., ANNAN, R. S., HUDDLESTON, M. J., CARR, S. A., REYNARD, G. & DESHAIES, R. J. (1997). Phosphorylation of Sic1p by G1 Cdk required for its degradation and entry into S phase. Science 278, 455}460. VISINTIN, R., CRAIG, K., HWANG, E., PRINZ, S., TYERS, M. & AMON, A. (1998). The phosphatase Cdc14 triggers mitotic exit by reversal of Cdk-dependent phosphorylation. Mol. Cell 2, 709}718. VISINTIN, R., PRINZ, S. & AMON, A. (1997). CDC20 and CDH1: a family of substrate-speci"c activators of APCdependent proteolysis. Science 278, 460}463.
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the components shown in Figs. 1 and 2 are in quasi-steady state. First, we calculate the steady-state level of total Sic1 (Sic1 "Sic1#Sic1P#Tri#TriP) as a 2 function of Clb"[active Cdk/Clb dimers]. To do so, we add together eqns (1)}(4) and eqns (2) and (4) in Table 1: dSic1 2"k !k Sic1 !k (Sic1P#TriP), 2 dt
d(Sic1P#TriP) "k (Clb#SK) mass)(Sic1 !Sic1P!TriP) N 2 dt !(k Cdc14#k #k ) NN
APPENDIX Calculation of the Net Rate of Cyclin Synthesis Curve
(Sic1P#TriP) .
Because Cdk/Clb has antagonistic relationship with Hct1 and Sic1, these enemies tend to exclude each other: either Cdk activity is high, and Hct1 and Sic1 are ine!ectual (S/G2/M), or vice versa (G1). This antagonism can be illustrated by plotting the net rate of increase of cyclin B in all forms (Clb "Clb#Tri#TriP) as a function of 2 Cdk/Clb activity. (In all equations we use the short-hand notation: Clb"[active Cdk/Clb dimers], Tri"[Cdk/Clb/Sic1 trimers], and TriP"[phosphorylated trimers]. It should be clear from the context as to when &&Clb'' is used as the name of a molecule and when it is used as a mathematical variable.) In this section, we describe exactly how dCIb /dt is calculated as 2 a function of Clb. The net rate of increase of cyclin B in all the forms is given by adding together eqns (3)}(5) in Table 1:
Setting the right-hand sides of both equations to zero (quasi-steady-state assumption) and plugging the solution from the second equation into the "rst, we get
dCIb 2"k mass!k Clb dt !k (Tri#TriP). (A.1) A The "rst term represents the rate of cyclin synthesis from amino acids. The second and third terms are the rates of degradation from active Cdk/cyclin dimers and from Cdk/cyclin/CKI trimers, respectively. We calculate the net rate of cyclin synthesis, eqn (A.1), as follows. To begin, we set &&mass'' and protein phosphatase activity (Cdc14) to constant values depending on the phase of the cell cycle. Then we assume that all
Sic1 " 2 k . k (Clb#SK mass) N k #k k (Clb#SK mass)#k Cdc14#k #k N NN (A.2) Second, by assuming fast and reversible binding of Sic1 and Sic1P to Clb kinases, we can calculate the equilibrium concentration of trimers (Tri#TriP) using Sic1 and active Clb 2 values: Tri#Trip Tri#TriP " ¸" (Sic1#Sic1P)Clb (Sic1 !Tri!TriP)C1b 2 simply as Sic1 C1b 2 , Tri#TriP" 1/¸#C1b
(A.3)
where &&¸'' is the binding constant (k /k ). SubH HP stituting eqn (A.2) in (A.3), we can express Tri#TriP in terms of known quantities. The "nal step in calculating the right-hand side of eqn (A.1) is to compute k and k from eqns A (14) and (15) in Table 1. To do this, we must "rst
FINISHING THE CELL CYCLE
solve eqn (6) for active Hct1 in steady state: Hct1(a, b, c, d)" 2ad , b!a#bc#ad#((b!a#bc#ad)!4(b!a)ad
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where a"k #k Cdc14, b"k Clb, c"J , FARP FARP FAR FARP d"J . FAR This set of calculations, though lengthy, can easily be done by any commercial spreadsheet program.