Hysteresis: Is the Cell Cycle Characterized by
Bistability?
A central aspect of the model derives from the
bistability concept (
Nasmyth, 1996 
), in which the cell cycle
is considered as an
alternation between two stable self-maintaining states, one
in which Clb kinase is low (G1) and one in which Clb kinase
is high (S/M). The components in the model causing switching
between the two states are the Cln kinases for low-to-high
and Cdc20 for high-to-low. The Cln kinases switch from the
low to the high state by phosphorylating Sic1 and Cdh1,
allowing accumulation of Clb kinases. Clb kinases can
subsequently maintain the high state by continuing Sic1 and
Cdh1 phosphorylation. Cln kinases can reverse the low state
because they are immune to Sic1 and Cdh1 regulation, but
once the Clb kinases are high, Cln kinases are dispensable
(and indeed are predicted to be deleterious; see below).
Conversely, Cdc20 activates the high-to-low transition by
inducing degradation of Clb5 and initial degradation of
Clb2; once Clb kinases have been pushed below a threshold
level, Sic1 and Cdh1 phosphorylation become inefficient, and
they then take over from Cdc20 to push Clb kinase activity
to a very low level. At this point Cdc20 is no longer needed
to maintain the low-Clb kinase state.
The role of Cdc20 in the model is more limited than current
information indicates. Cdc20 not only leads to degradation
of Clb2, but also to degradation of Pds1, and Pds1 is
thought to inhibit release of the
Cdc14 phosphatase from the nucleolus (see INTRODUCTION).
Cdc14 is thought to dephosphorylate and hence activate Cdh1
and Sic1. For purposes of this discussion, because the
available model does not include Cdc14 and its associated
regulatory machinery, we can consider Cdc20 as a component
that somehow encompasses both Cdc20 and Cdc14 activities,
and these jointly drive Clb kinase from the high to the low
state.
The model thus contains initiator activities (Cln kinases,
primarily Cln2 in the model) and terminator activities
(Cdc20, Cdc14,
et al.; Cdc20 in the model).
These initiator and terminator
activities antagonize each other with respect to activation
or inactivation of Cdh1 and Sic1, which are the main final
enforcers of the low-Clb state. Intriguingly, simultaneous
absence of initiator and terminator activities does not
result in a unique predicted final outcome; rather,
hysteresis is predicted. “Hysteresis occurs in systems
with multiple steady states and refers to the fact that the
observed state of the system depends not only on its
parameter values but also on its history (how the system is
prepared)” (
Novak et al., 1998 ). Thus,
if the neutral situation lacking initiator and terminator
is encountered from a prior history of a low-Clb state,
this state will be maintained indefinitely; conversely,
encountering neutral coming from the high-Clb state means
that the high-Clb state will be maintained. This
formulation makes the prediction that a third steady state,
with intermediate values of Clb-dependent kinases, is
mathematically possible but unstable.
To try to experimentally realize the neutral state lacking
both initiator and terminator, we constructed a strain of
the genotype cln1 cln2 cln3 GAL-CLN3 cdc14-1.
The strain is viable on galactose medium at 23°C, because
galactose provides CLN function by keeping
GAL-CLN3 on, and the cdc14-1
temperature-sensitive allele functions at 23°C. The
strain is inviable at 37°C on galactose and is inviable
without galactose at any temperature. Glucose medium at
37°C is the experimental approximation of the neutral
state lacking initiator and terminator simultaneously. What
is the phenotype of this strain in this neutral condition,
and does this phenotype indeed depend on the prior history
of the culture?
We blocked the strain in G1 by
CLN deprivation,
by turning off
GAL-CLN3 by incubation in
raffinose medium at 23°C for 6 h. Under these
conditions ~90% of the cells were unbudded (a
morphological marker of the pre-Start state;
Cross, 1995 ),
and Clb2 protein in the culture was very low (Figure ). We
then induced
GAL-CLN3 transcription with
galactose. At intervals we removed aliquots of the culture,
added glucose to block further
GAL-CLN3
transcription, and shifted to 37°C for 2.5 h to
inactivate
cdc14-1 (
CLN3 RNA and
functional Cln3 protein disappear within minutes of
GAL-CLN3 shutoff;
Cross, 1990 ;
Tyers et
al., 1992 ;
Cross and Blake, 1993 ). The aliquots were
then analyzed for percentage of unbudded cells and Clb2
levels. The results were consistent with the bistability
prediction. Shifting the culture to 37°C + glucose
without prior galactose addition (our unpublished data) or
immediately after galactose addition (time zero) resulted
in stable retention of the low-Clb state, and cells did not
bud in the 2.5-h incubation in 37°C+glucose. In contrast,
incubation in galactose at 23°C for 1 h before shift
to 37°C+glucose resulted in acquisition of a significant
level of Clb2 at the end of the 2.5-h 37°C+glucose
incubation, with most cells arrested in the characteristic
large-budded morphology observed with
cdc14-1
arrest (Figure ). This was so even though before the
shift, Clb2 protein levels were low. These results indicate
that the
cln1,2,3 arrest does not require
CDC14 function for its maintenance, and the
cdc14-1 arrest does not require
CLN
function for its maintenance. The phenotype resulting from
simultaneous absence of
CDC14 and
CLN
function depends on the prior history of the system, and a
relatively short exposure to
CLN function is
sufficient to commit the system to later entrance into the
high-Clb state. In the absence of initiator or terminator,
the system can reside in either of two states (high- or low-
Clb), and which state the system adopts depends on its
prior history.
Thus, Cdc14 activity is not required for maintenance of G1
arrest with low-Clb2 levels. In contrast, Cdh1 and Sic1,
which are activated by Cdc14-dependent dephosphorylation,
are required for maintenance of low-Clb2 G1 blocks due to
cln deprivation (
Tyers, 1996 ) or α-factor
treatment (
Schwab et al., 1997 ). Similarly, we
have observed that
cln-deficient
cdh1
mutants are
inviable but arrest in glucose medium with high Clb2 levels
(our unpublished data). APC activity (presumably Cdh1-
dependent) is also required for maintenance of an α-
factor G1 block (
Irniger and Nasmyth, 1997 ). This
distinction between activities (such as Cdc14) required to
enter a new state and activities (such as Cdh1 and Sic1)
required to maintain the state is expected, based on the
bistability hypothesis (
Nasmyth, 1996 ;
Chen et
al., 2000 ).
Control of Cell Cycle Start by
CLN3
In the model of
Chen et al. (2000) , cell
cycle initiation or “Start” is coupled to cell size by
the following mechanism. The Cln3 G1 cyclin is assumed to
accumulate in total cellular abundance in parallel to total
cell mass. It is assumed to concentrate in the nucleus (or
in principle any cell compartment of constant volume) so
that as its cellular abundance increases, its nuclear
concentration increases. Past a certain threshold level it
triggers G1/S transcription by activating SBF/MBF (
Koch and
Nasmyth, 1994 ), turning on the more downstream-acting G1
cyclins Cln1 and Cln2 along with other genes. Consistent
with this model, we found recently that Cln3 does indeed
accumulate in the nucleus. Also, moving Cln3 from the
nucleus to the cytoplasm significantly reduces its function
(
Miller and Cross, 2000 ; Miller and Cross, submitted).
In the simplest version of the idea that cells read their
size based on Cln3 nuclear abundance, one might expect that
doubling Cln3 levels should result in cells reading their
size as twice the actual size,
thus halving the cell volume at which Start occurs. In
fact, the cell volume response to doubling
CLN3
gene dosage is much more modest (
Nash et al.,
1988 ;
Cross, 1989 ; Figure ). The model primarily accounts
for this using the properties of Bck2, which acts
genetically as a parallel system to Cln3 activating SBF/MBF-
regulated genes (
Epstein and Cross, 1994 ;
Di Como et
al., 1995 ). In the absence of Bck2, Cln3 becomes
essential, and in the absence of both Cln3 and Bck2,
SBF/MBF-regulated genes are expressed at very low levels
(
Epstein and Cross, 1994 ;
Di Como et al., 1995 ).
The presence of the
BCK2 gene provides backup
and blunts the response to
CLN3 gene dosage.
Therefore, according to the model, deleting
BCK2
should result in highly elevated responsiveness of cell
size to
CLN3 gene dosage.
To test this idea, we constructed a series of strains with
or without BCK2, in which the endogenous
CLN3 gene was either present or absent and
additionally containing ectopic copies of the
CLN3 gene inserted at the TRP1 locus.
A 6.2-kb chromosomal segment containing CLN3 was
stably integrated at trp1 in one or multiple
copies (quantitated by Southern hybridization). The size of
the segment makes it likely that expression levels will be
little affected by the site or copy number of integration.
Indeed, we observed a similar cell volume in
cln3::URA3 strains containing a single-
copy CLN3 transgene to the cell volume of wild-
type cells (our unpublished data), whereas CLN3+
strains containing a single-copy transgene or
cln3::URA3 strains containing multiple-
copy transgenes were smaller than wild type (Figure ).
Predictions from the model for approximate modal cell volume were taken
as the midpoint between predicted birth size and division size,
relative to wild type. Modal cell volumes for the constructed strain set
were determined by electronic cell volume measurements, relative to wild
type. A reasonable correspondence between model and experiment was
observed in the BCK2 and bck2 backgrounds (Figure
). A minor difference may be that the model predicts a more extreme
response to CLN3 dosage than was actually observed; thus the
size control system (with or without BCK2) may be more robust
with respect to these genetic perturbations than predicted. (It is also
possible that the effects of CLN3 gene dosage saturate at
higher levels due to limitation of some other factor). It is important
to note that although limited information on the relationship between
CLN3 gene dosage and cell size was used
as input information in formulating the model, these data were all in a
BCK2 background. Therefore, the bck2 results
presented here are independent confirmation of the model.
An interesting feature of
CLN3 expression is that it is
under moderate cell cycle regulation, with RNA expression peaking in
late M/early G1 (
McInerny et al., 1997 ). This feature is not
implemented in the model, and it is unclear how its implementation would
affect these size control predictions.
Predicted Interactions between G1 Cyclin Function and Mitotic
Regulators Sic1 and Cdh1
The model makes critical use of Cln2 as an initiator activity to
drive cells from a low-Clb to a high-Clb state, because Cln2-dependent
phosphorylation is assumed to be able to reverse two independent
controls that reinforce the low-Clb state, Sic1 stability, and Cdh1
function. Cdh1 (Hct1 in the model; see MATERIALS AND METHODS for a note
on nomenclature) is thought to control Clb2 degradation in mitotic exit,
and most specifically in the G1, low-Clb state (
Schwab et
al., 1997 ;
Visintin et al., 1998 ). Cdh1 is dispensable
for viability, presumably because Sic1 is sufficient to control Clb
kinase levels, as evidenced by specific lethality of
cdh1
sic1 double mutants (
Schwab et al., 1997 ;
Visintin
et al., 1998 ).
SIC1 expression is also transcriptionally controlled (
Knapp
et al., 1996 ;
Toyn et al., 1996 ), and this is
implemented in the model. This control is helpful but not essential in
the model: making
SIC1 transcription constitutive at the
level of peak regulated expression is not lethal (Figure A, CONST
SIC1), because first Cln2 and later Clb5 and Clb2 can keep
Sic1 protein levels low. Deleting
CLN2 in the model results
in lethality of constitutive
SIC1 expression (
cln1,2−CONST
SIC1), as has been observed experimentally
(
cln1 cln2 GAL-SIC1 strains are inviable;
Tyers, 1996 ).
CLN2 is turned off transcriptionally by Clb2 (
Amon et
al., 1993 ;
Koch et al., 1996 ). This regulation is
implemented in the model, where it is helpful but not essential:
constitutive
CLN2 expression (at the level of peak regulated
Cln2 expression) is not predicted to be lethal (CONST
CLN2).
Constitutive
CLN2 expression in the
cln1,2
background is predicted to rescue inviability due to constitutive
SIC1 expression (CONST
CLN2, CONST
SIC1).
In contrast, the model predicts that constitutive CLN2
expression should be lethal in the absence of Cdh1, presumably because
then the cell becomes highly sensitive to the ability of even low-level
Cln2 to destabilize Sic1 by phosphorylation (CONST CLN2 cdh1-). Interestingly, at the other extreme, the model predicts that
complete absence of Cln2 should be lethal in the absence of Cdh1
(cln1,2−cdh1-). This lethality is predicted because in the
absence of Cln2, cell cycle Start occurs at abnormally large size.
Therefore, when Clb2 cyclin accumulates, it is driven by the large cell
mass to levels that require the presumed catalytic activity of Cdh1 for
effective Clb2 disposal. Thus, the model makes two predictions: that
Cln2 constitutive expression should be lethal in the absence of Cdh1 and
that simultaneous removal of Cln2 and Cdh1 should also be lethal. In
these simulations, constitutive Cln2 expression from the GAL promoter is
set to be equal to peak expression of the endogenous gene, but the
results are not very sensitive to this level (our unpublished data).
To test these predicted interactions, we constructed a diploid
with the genotype
cdh1::LEU2/CDH1
GAL1::CLN2::TRP1/trp1 GAL1::SIC1::URA3/ura3 cln1/cln1 cln2/cln2. Segregants of this diploid were tested
for
viability on glucose or galactose medium (where the
GAL-controlled cassettes were off or on). As
expected,
GAL-SIC1 expression resulted in
inviability in the
cln1,2 background (
Tyers, 1996 ), and this
inviability was rescued by
GAL-CLN2 expression
(Figure B,
+GAL-SIC1, vs.
+GAL-SIC1 +GAL-
CLN2). These observations meet the expectation
of the model (Figure A,
cln1,2−CONST
SIC1 vs.
cln1,2−CONST
SIC1 CONST
CLN2). In contrast to the
expectations of the model, this
CLN2
overexpression cassette, which effectively rescued
inviability due to
GAL-SIC1, did not cause
lethality in the absence of
CDH1 (Figure A,
cln1,2−cdh1- CONST
CLN2; Figure B,
+GAL-CLN2,
+GAL-
CDH1).
Also, there was no reduction of viability of the
cln1
cln2 segregants (without
GAL1::CLN2 or
GAL1::SIC1 expression) due to
cdh1 deletion, although the model predicts
absolute inviability of
cdh1 cln1 cln2 strains
(Figure A,
cln1,2 cdh1-; Figure B, all
cdh1- strains on glucose medium).
One possible explanation for the viability of
GAL-
CLN2 cdh1 strains, that Cln2 expressed late
in the cell cycle is unable to form an active complex with
Cdc28 kinase, is contradicted by previous experimental
evidence (
Amon et al., 1993 ).
Fiddling with
the parameter set for the model can remedy some of these
incorrect predictions. For example, increasing the rate of
Sic1 expression threefold rescues lethality due to
constitutive Cln2 expression in the absence of Cdh1, but
does not rescue inviability due to lack of Cln2 and Cdh1.
Lowering Clb2 synthesis rates twofold rescues inviability
due to lack of Cln2 and Cdh1, but does not rescue lethality
due to constitutive Cln2 in the absence of Cdh1. These two
changes in the parameter set work essentially by increasing
the Sic1/Clb2 ratio and thus help the model to inactivate
Clb2 kinase even in the absence of Cdh1-mediated Clb2
degradation. Alternatively, increasing the ability of Cdc20
to degrade Clb2 (by increasing kdb2p from 0.05 to 0.5)
rescues inviability due to lack of Cdh1 combined with
either Cln2 overexpression or Cln2 absence. This change
works by reducing the importance of Cdh1 in controlling
Clb2 abundance. A related solution (K. Chen and J. Tyson,
personal communication) is to increase Sic1 expression
twofold and also to increase Cdc20-dependent Clb2
degradation fourfold. Possible empirical justification for
increasing Cdc20-dependent Clb2 degradation are discussed
below (see DISCUSSION), but the case is still unclear.
These findings emphasize a significant problem with the
modeling approach: in the absence of empirical constraints
on parameters, one is free to propose any parameters that
fit the available data. Therefore, it appears likely that
before this or any future model can be forcefully tested,
more of the parameters need to be based on empirical data.
An initial step toward accumulating a suitable data set is
the subject of the remainder of this article.
Quantitative Analysis of Abundance of Cell Cycle
Regulators
There is a large amount of information
available on regulation of abundance of cyclins through the
yeast cell cycle (summarized in
Chen et al.,
2000 ). A nearly universal deficit in this data set is that
one can almost never compare quantities of one cyclin to
another, and absolute abundance of these proteins have
never been determined. The work of Tyers on the G1 cyclins
(
Tyers et al., 1993 ) is an exception to the
first point. Tyers
et al. tagged the three
CLN cyclins identically with the HA epitope tag,
such that after immunoprecipitation and Western analysis,
the abundance of the three tagged cyclins could be compared
with each other. A problem with this analysis was that
detection of Cln3 (clearly the least abundant) was so low
that the exact reduction in its abundance could not be
determined. A related problem was that for some of Tyers'
experiments, immunoprecipitation was required before
Western analysis, with unknown losses in this step.
PrA Tagging
We constructed strains in which endogenous cyclin
genes were C-terminally tagged with protein A, with
expression from the endogenous
promoter and chromosomal location. It is important to
confirm that any epitope tag addition does not significantly
affect function of the tagged protein. To address this, we
performed a range of tests on most of the PrA-tagged genes.
Cdc28-PrA–expressing haploids were viable; because Cdc28
is essential, the PrA tag cannot have inactivated function.
All the PrA-tagged
haploid strains had essentially normal FACS profiles (our
unpublished data). In contrast,
clb5,
clb2, or
sic1 deleted strains have
increased proportions of cells between 1 and 2C DNA content
(
clb5;
Epstein and Cross, 1992 ) or increased
proportions of 2C DNA content cells (
sic1,
clb2;
Surana et al., 1991 ;
Schwob
et al., 1994 ). This indicates approximately
normal function of the tagged Cdc28, Clb5, Clb2, and Sic1.
sic1::HIS3/+ diploids and
sic1::HIS3/SIC1-PrA diploids had FACS
profiles indistinguishable from wild type, in contrast to
the defective profile of
sic1::HIS3
homozygous diploids (with few or no 1C DNA content cells).
This indicates full function of the PrA-tagged Sic1 even
under conditions potentially limiting for Sic1 (our
unpublished data).
clb3 and
clb1 inactivation do not
have an identified phenotype. Therefore, we tested the PrA-
tagged versions by crossing them to a
clb2::LEU2 strain, because
clb1
clb2 and
clb2 clb3 double mutants are
inviable (
Fitch et al., 1992 ). In parallel we
crossed a
clb1::URA3 and a
clb3::TRP1 strain to the
clb2::LEU2 strain. In tetrad analysis
from these diploids, we confirmed inviability of
clb1
clb2 and
clb2 clb3 double mutants. In
contrast,
CLB1-PrA clb2 and
CLB3-PrA
clb2 double mutants were recovered at the expected
frequency and did not have a significant slow-growth
phenotype compared with
clb2 single mutants,
although this was not evaluated quantitatively (our
unpublished data).
clb2 deletion results in a
significant delay in the cell cycle after DNA replication
(
Surana et al., 1991 ), and
CLB1 and
CLB3 are both partially redundant with
CLB2 (
Fitch et al., 1992 ). Therefore,
if PrA-tagged Clb1 or Clb3 were reduced in function, then
clb2 CLB1-PrA or
clb2 CLB3-PrA strains
might be expected to have an exacerbated postreplicative
delay relative to that in
clb2 CLB1 CLB3 strains. We compared the
phenotypes of
clb2 CLB1-PrA and
clb2 CLB3-
PrA strains to
clb2 CLB1 CLB3 strains by
FACS analysis and observed little difference, although the
clb2 CLB3-PrA strains may have had a moderate
decrease in the proportion of 1C cells compared with
clb2 CLB1 CLB3 strains (our unpublished data).
Overall, these data indicate that the tagged Clb1 and Clb3
have a significant degree of biological function.
clb5 CLB6 strains exhibit a lengthened period
of DNA replication and a compensating decrease in the
population of cells with 1C DNA content. Deletion of
clb6 in the
clb5 background results
in a long delay before replication and a large increase in
the population of cells with 1C DNA content (
Epstein and
Cross, 1992 ;
Schwob and Nasmyth, 1993 ). This is due to
activation of early but not late origins of replication by
Clb6 in the absence of Clb5; when both Clb5 and Clb6 are
deleted, neither class of origins is activated until
Clb1,2,3,4 are activated later in the cell cycle (
Donaldson
et al., 1998 ). We therefore tested
CLB6-
PrA in a
clb5 background by FACS analysis,
to test the ability of
CLB6-PrA to promote early
origin activation. We found that
clb5 CLB6-PrA
strains had FACS profiles similar to
clb5 CLB6
strains, lacking the strong accumulation of 1C DNA content
cells seen in
clb5 clb6 strains, suggesting
significant ability of Clb6-PrA to activate early origins
of replication (our unpublished data). The population of
cells with 1C DNA content was slightly increased in
clb5 CLB6-PrA
strains compared with
clb5 CLB6 strains,
suggesting a moderate reduction of Clb6-PrA function
compared with Clb6.
cln3 disruption results
in a cell volume increase of at least 50% (
Cross, 1988 ;
Nash et al., 1988 ), while
CLN3-PrA
strains exhibited at most a 10% increase in cell volume
(our unpublished data).
CLN3-PrA also rescued
cln1 cln2 cln3 inviability about as well as did
wild-type
CLN3 (the latter assay was performed
using low-copy-number plasmids, expressing
CLN3
or
CLN3-PrA from the
CLN3 promoter;
our unpublished data). Thus, Cln3-PrA was functional.
As a further functional test, we tested Cln2-PrA, Clb5-
PrA, and Clb2-PrA for binding to Cdc28 by constructing
strains expressing both the PrA-tagged cyclin and HA-tagged
Cdc28 and purifying the PrA-tagged cyclin on IgG-agarose.
Although the result was not quantitated, all three cyclins
bound Cdc28-HA roughly in accordance with the abundance of
the cyclin (our unpublished data). For all nine cyclins, we
also were able to recover IgG-agarose–purified histone H1
kinase activity, indicating that the tagged cyclins were
able to activate enzymatic activity of bound Cdc28.
Thus, the PrA fusions generally exhibit significant
biological and biochemical function and in most cases
function similarly to the untagged wild-type genes.
Moderate reductions in function cannot be ruled out in most
cases, and this leads to a caveat in the use of the tagged
proteins for quantitation. An additional subtle caveat
could be that if the PrA addition simultaneously weakens
biological function but increases protein stability, the
net effect could be to hide the loss of activity, while
confounding the quantitative measurements of protein
abundance.
Average Copies per Cell in Asynchronous Culture
To determine copies per cell of the PrA-tagged
proteins, we used the following procedure. We produced
recombinant His-GST-PrA fusions in E. coli,
purified the fusion on nickel beads, and quantitated the
yield. We then performed serial dilutions of the
recombinant protein and compared the signal obtained to
that from serial dilutions of yeast protein extracts from
known numbers of yeast cells. We used dilutions yielding
signal in a linear range of detection using digital camera
detection from exposed film (Figure
). The results of this
quantitation are presented in Table
.
Validation of the Quantitation
As an independent test of our data set, we
constructed a recombinant GST-myc standard and quantitated
myc-tagged Cln2, Cln3, and Clb5 (Table
). As a second independent
test of our data set, we compared the abundance of
endogenous Clb2 to recombinant standard MBP-Clb2, using
anti-Clb2 antibody (Table ). These independent comparisons
agree with the PrA data set, within a factor of two or
three. Given the number of experimental manipulations and
calculations involved, we consider this agreement
reasonable.
We have been able to find only one literature value to
compare with our data: for Cdc28, 10
ng/10
7 haploid cells (
Funakoshi
et al., 1997 ), translating to 16,000 copies per
haploid cell. We calculate 12,000 copies per diploid cell
(Table ). Diploids have two copies of the Cdc28 gene and
are about twice as big
as haploids. One might therefore expect to find twice as
much Cdc28 in diploid cells (although a systematic
examination of the consequences of ploidy changes on
individual protein levels has not been carried out to our
knowledge). Thus, our estimate is in a similar range to the
published one, although probably a few-fold lower.
Cells simultaneously expressing Clb2 and Clb5 C-terminally
tagged with an HA epitope, from the endogenous promoters,
show a moderate (although unquantitated) excess of Clb2
over Clb5 (
Schwab et al., 1997 ), consistent with
our results (Tables and ).
The approximately twofold difference between Cln2 and Cln1
levels that we detect is slightly greater than might be
expected, based on the nearly identical levels of Cln1- and
Cln2-associated kinase activity
reported previously using HA-tagged cyclins (
Tyers et
al., 1993 ).
Tyers et al. (1993) reported a
200-fold difference between Cln2-associated and Cln3-
associated kinase activity, compared with a 15-fold
difference in protein abundance detected in our
experiments. Cln3-associated kinase activity is relatively
low under the extraction conditions used by Tyers, and
different conditions improve Cln3-associated kinase
compared with Cln2 (
Jeoung et al., 1998 ;
Miller
and Cross, 2000 ).
Tyers et al. (1993) did not
quantitate their Western signal for Cln3 compared with Cln1
and Cln2, but a value of 7% does not seem unreasonable
from inspection of their data. Thus, overall we consider
our G1 cyclin quantitation to be in reasonable agreement
with published data.
Grandin and Reed (1993) concluded that Clb3 accounted for
about two thirds of the total Cdc28 histone H1 kinase
activity in asynchronous cells, based on recovery of Cdc28-
associated kinase from a
clb3 deletion mutant.
This result is not consistent with our finding that Clb3-
PrA is present at less than one third the level of the
other Clbs added together and at an even lower level when
Cln1 and Cln2 are included (Table ). This discrepancy
might suggest that Clb3-PrA levels are under-reporting true
Clb3 levels. Alternatively, the effects reported for the
clb3 deletion mutant (
Grandin and Reed, 1993 )
could be indirect effects of
clb3 deletion on
levels of other cyclins, or the Clb3-associated kinase
could be unusually active relative to other cyclin-
associated Cdc28 kinase because of posttranslational
effects. The last explanation is unlikely, although, since
using IgG-agarose purification, we recover similar levels
of histone H1 kinase activity and similar amounts of PrA-
tagged cyclin from cells expressing Clb2-PrA and Clb3-PrA
(our unpublished results).
Overall, it appears likely that the data obtained by PrA
tagging (Table ) are reasonably accurate. For purposes of
discussion we will take the PrA quantitation literally,
although the caveats discussed above (both functional and
quantitative) should be kept in mind.
Correlation between Abundance and Functional Importance
in B-type Cyclins
The six B-type cyclins derive by gene duplication from
a single ancestor and more recent relationships can be
observed. The B-type cyclins can be classed by sequence
homology and time of expression in the cell cycle into the
CLB5,6,
CLB3,4, and
CLB1,2
pairs (
Fitch et al., 1992 ;
Grandin and Reed,
1993 ;
Schwob and Nasmyth, 1993 ). Recent work (
Lynch and
Conery, 2000 ) suggests that some gene duplications may be
found in modern genomes simply as a consequence of their
recent generation. To evaluate the functional significance
of the six
CLB genes, we performed competition
growth experiments between various
clb gene
deletions and wild-type strains. We found that deletion of
the three
CLB genes with the least abundant
products,
CLB1, CLB4, and
CLB6,
resulted in no significant selective disadvantage in
competition with wild type, whereas deletion of the three
CLB genes with more abundant products,
CLB2,
CLB3, and
CLB5,
yielded clear selective disadvantages (Figure
). (Note that these selective
disadvantages are unlikely to be entirely due to differences
in exponential growth rate, based on previous data, but we
have not attempted to determine the sources of the
disadvantages.) This result suggests that although the three
sequence classes are functionally distinct and all
maintained by natural selection, one member of each class
(satisfyingly, in each case the one expressed at a lower
level) may not be under strong selection, at least in
vegetative culture in rich medium. It is important to note,
although, that
CLB1 and
CLB4 have
significant roles in meiosis (
Grandin and Reed, 1993 ;
Dahmann and Futcher, 1995 ), which imposes a distinct
selective pressure for their maintenance.
Of the mitotic cyclins
CLB1,2,3,4,
clb2 deletion alone results in a significant cell
cycle delay before mitosis, with consequent cell enlargement
and reduction of length of G1; in contrast,
single deletions of other mitotic
CLB genes
(
CLB1,3,4) have only minor phenotypes. If these
cyclins are fully overlapping in all functional aspects and
differ only quantitatively, then the data in Table allow
the conclusion that
clb2-deleted cells should
result in a reduction of ~40% in total mitotic Clb level.
This rather moderate reduction can be easily modeled using
the
Chen et al. (2000) parameters by lowering
Clb2 synthesis parameters ksb2′ and ksb2" by 40%, yielding
about a 12% increase in predicted cell volume at cell
division. This increase is significantly less than is
observed with
clb2 deletion (
Surana et
al., 1991 ). These quantitative considerations may
suggest only partial functional overlap among the mitotic
cyclins. For example, suppose Clb1 completely overlaps in
function with Clb2 (consistent with the high sequence
conservation between Clb1 and Clb2), whereas other cyclins
are not considered at all. Then the
clb2 deletion
will result in about a 70% decrease in Clb1/2 functional
protein, which is predicted by the model to yield a nearly
twofold increase in cell volume at cell division. An
increase of this magnitude is more consistent with
observation (
Surana et al., 1991 ). Simple
quantitative considerations of this sort may therefore have
implications for cyclin functional specificity (see
DISCUSSION).
Abundance through the Cell Cycle and the Role of Cdh1
To analyze fluctuations of the PrA-tagged
cyclins through the cell cycle, we separated cells on the
basis of cell size. In this elutriation method, cultures
growing rapidly in rich medium are quickly chilled and then
directly fractionated, such that no further physiological
response of the culture is required after chilling (
Levine
et al., 1996 ;
Oehlen et al., 1996 ).
The entire culture is recovered and analyzed in this way.
The strategy and sample data are shown in Figure
A.
This elutriation method
loses resolution in the larger size cell fractions. This is
in part due to loss of accuracy of size resolution in the
fractions containing larger cells, which is evident from a
somewhat variable increase in the peak width in electronic
cell volume measurements (normalized to peak position) for
later fractions (our unpublished data). It is also possible
that cell size does not correlate as tightly with later cell
cycle events. The largest fractions contain cells that have
started the next cell cycle before cell separation is
complete, as evidenced microscopically by occasional
rebudding of already budded cells (our unpublished data).
Similarly, FACS analysis shows that the fractions of modal
cell volume > 125 fl contain a significant 1C DNA
content population upon resonication.
Thus, this
method gives an accurate separation of cells in early
periods of the cell cycle, from birth until after DNA
replication. Fractions with the largest cell sizes (>150
fl) are closer to being asynchronous averages due to loss of
resolution of the elutriation.
Multiple diploid
strains were analyzed with similar volume distributions and
dependence of budding on cell volume (Figure , B and C).
cdh1 mutant diploid strains reproducibly budded
and initiated DNA replication at ~10 fl smaller volume
than the wild type (arrows in Figure C) and initiated
nuclear division at ~25 fl smaller than wild type
(arrowheads in Figure C). An increase in the population of
anaphase
cdh1 mutants was noted previously
(
Visintin et al., 1998 ).
We elutriated a triply heterozygous diploid, in which
coding sequences for Clb2, Clb5 and Sic1 were tagged with
PrA on one of the two alleles of each. This allowed a direct
comparison of the abundance of the three proteins with the
same tag, within the same experiment. We express the units
in this experiment relative to peak Clb2 concentration. If
peak Clb2 expression corresponds to two times the average
asynchronous level (Table ), one unit on these graphs
should correspond to ~35 nM (2400 copies/120 fl cell).
As a cross-check, it is possible to predict asynchronous
levels of the tagged proteins by integrating across the
elutriation profile, multiplying the observed amount of the
protein in the size fractions
(Figure , A and C) by the
proportion of the mass of the culture recovered in these
fractions (Figure A). This can then be compared with the
levels directly obtained in asynchronous cells (Table ).
This calculation from the two elutriations quantitated in
Figure yields predicted asynchronous Clb2:Clb3:Clb5:Sic1
ratios of 1:0.91:0.91:0.27, compared with ratios from Table
of 1:0.76:0.70:0.19. This agreement suggests that the
quantitation of the elutriation is reasonably accurate, with
most of the proteins recovered and assigned to the different
cell size classes.
Although Sic1 was found at quite low levels in asynchronous
culture (Table ), it was abundant in the smallest cells in
the culture, where it was in molar excess over the levels of
Clb5 and Clb2 coexpressed in the same cells (Figures , A
and D, and 7A). These cells contributed a very small
proportion of the total mass of the culture (Figure B), and
this could account for the low relative yield of Sic1 in
asynchronous total culture (Table ). If Sic1 inhibits Clb-
Cdc28 complexes in a 1:1 stoichiometric ratio, this suggests
that under these growth conditions Sic1 is only present at
levels sufficient for Clb inhibition for a brief period
early in the cell cycle. The onset of DNA replication in
cells of ~60 fl (black arrow, Figure C) correlates with
the increase of Clb5 above the Sic1 threshold (Figure A).
We find that limiting the growth rate of the culture by
changing the carbon source from glucose to glycerol
increases the duration of the period when Sic1-PrA is high.
Thus, growth limitation may expand the high Sic1 pre-Start
period of the cell cycle (M.K. and F.C., unpublished data).
This expansion is expected based on the known mechanisms for
coordinating growth and division in yeast (
Hartwell and
Unger, 1977 ;
Cross et al., 1989 ;
Cross, 1995 ).
By comparison with coexpressed cyclins, it appears that the
highest concentration of Sic1 found in the smallest cells
analyzed is ~0.4 times the peak concentration of Clb2
(Figure A). Clb2 peaks in the vicinity of 2400 copies per
cell (estimating that peak concentration is two times the
average concentration reported in Table ), in cells of
~120 fl (Figure A), yielding a concentration of 35 nM.
Thus, peak Sic1 concentrations should be ~15 nM. The
Ki determined for purified
Sic1 on Clb-Cdc28 kinase activity was 1.6 nM (
Mendenhall,
1993 ). This will allow Sic1 to be effective at inhibiting
Clb kinase, provided there is even a moderate excess of Sic1
over Clbs (assuming 1:1 stoichiometry for inhibition). This
effect becomes much stronger if Sic1 is
concentrated in the nucleus, but we are unaware of data on
this point.
The
Chen et al. (2000) model
predicts qualitatively patterns of accumulation of these
different proteins similar to what we observe, with several
potentially significant differences (Figure B). First,
the model predicts a long period of time when Sic1
accumulates stably. We observe, in contrast, very little
Sic1 accumulating, for only a short time (translating cell
volume increments into time, based on the fact that yeast
cells probably increase approximately exponentially in cell
mass throughout the cell cycle;
Elliott and McLaughlin,
1979 ). Second, the model calls for a high level of Clb2
compared with Clb5, although we observe nearly comparable
levels of these cyclins. Third, Clb2 accumulation appears
significantly “peakier” in the model than in the
experiment, but this could be a consequence of the poor
synchrony in the larger-cell fractions noted above. Overall,
the model clearly does a very good job of qualitatively
predicting times of accumulation, but the lack of common-
scale quantitative information prevented relative levels of
different components from being appropriately specified. The
more accurate numbers provided here will have consequences
for the predicted efficiency with which different cyclins
carry out different tasks (see DISCUSSION).
Cdh1 is known to be important for restricting Clb2 protein
accumulation, especially in postmitotic cells (
Schwab
et al., 1997 ;
Visintin et al., 1998 ;
Zachariae et al., 1998 ). We elutriated a
cdh1 strain triply heterozygous for PrA-tagged
CLB2,
CLB5, and
SIC1 genes
and found strong deregulation of Clb2
accumulation, with only minor effects on Clb5 and Sic1
accumulation. (The minor fluctuations in Clb2 levels that we
observe are not very reproducible; cf. Figure A with 7C).
It was notable in this background that even in the smallest
cells that we could isolate, Sic1 was most likely not in
stoichiometric excess over Clb cyclins (because it was not
even in clear excess of Clb2 considered alone, without
including Clb5, Clb3, and other cyclins). Thus, in the
absence of Cdh1, Sic1 regulation of Clb kinase in
postmitotic cells may be inefficient. This may account for
the entry into DNA replication of these strains at a smaller
cell size (gray arrow, Figure C).
We approximately standardized the scale of the
cdh1 experiments to the CDH1
experiments by determining that the signal from peak Clb2
levels in cdh1 strains was about two times the
level in a CDH1 strain. Thus, all the graphs in
Figure , A and C, are similarly scaled to a value of 1 for
peak Clb2 expression in a CDH1 strain. (Note that
this is an approximation to allow rough quantitative
comparison between the experiments and is intrinsically less
accurate than the within-experiment comparisons, which are
standardized by coexpression of PrA-tagged genes within the
same cell.)
The effects of
cdh1 deletion are generally
similar to those predicted by the model (Figure B), except
that a more significant residual regulation of Clb2 is
predicted than we observe. These oscillations are
predicted because the model assumes very strong
transcriptional positive feedback for
CLB2 and
cyclical degradation of Clb2 by Cdc20. Both of these ideas
are supported by experimental data (
Amon et al.,
1993 ;
Baumer et al., 2000 ;
Yeong et
al., 2000 ), but the strength of one or both of the
effects may be overstated in the model. Alternatively, if
Cdc20-dependent Clb2 degradation becomes ineffective at low
Clb2 levels (
Yeong et al., 2000 ), detection of
cdh1-independent degradation could be quite
difficult at normal Clb2 expression levels. It will be
interesting to implement the proposed biphasic Clb2
degradation (Cdc20-dependent degradation to an intermediate
level, followed by Cdh1-dependent degradation;
Yeong
et al., 2000 ) in a computational model (see
DISCUSSION).
The model predicts oscillations of Clb5 and Sic1 in the
cdh1 strain that are similar to wild type,
essentially as we observe. The Clb5 oscillations are
predicted to be of lower amplitude and those of Sic1 of
higher amplitude. These are less than twofold effects, and
we are not sure if our data confirm these small changes,
especially
because of the extra correction involved in putting wild-
type and cdh1 data on a common scale (see
above). The Sic1 prediction seems better confirmed than the
Clb5 prediction (Figure B).
The model does not include the Clb3 cyclin. Clb3 overlaps
functionally with both the Clb5/6 S cyclins and the Clb1/2
M cyclins (
Fitch et al., 1992 ;
Schwob and
Nasmyth, 1993 ) and is also present in asynchronous culture
at levels similar to Clb5 and Clb2 (Table ). We determined
the pattern of Clb3 and Clb2 accumulation by elutriating
doubly tagged diploid strains and observed similar timing
and levels of these two cyclins (Figure C). Clb3-PrA
reproducibly accumulated in slightly smaller cells than
Clb2-PrA, possibly because of earlier transcriptional
activation of
CLB3 than
CLB2 (
Fitch
et al., 1992 ;
Richardson et al.,
1992 ).
Grandin and Reed (1993) reported somewhat earlier
accumulation of Clb3 than of Clb2. In the experiment in
Figure C, we did not observe a significant fall-off of
Clb2 or Clb3 levels in the largest cells, unlike the
results seen in Figure A for Clb2; this difference was not
reproducible. In experiments (with the same doubly tagged
Clb2-PrA, Clb3-PrA strain) where a fall-off of Clb2 was
observed in larger cells, a parallel fall-off of Clb3 was
also observed (our unpublished data). We attribute the
variability to the loss of resolution of the elutriation
method in larger cells (see above).
We determined the pattern of accumulation of Clb1-PrA in a
diploid doubly heterozygous for tagged CLB1 and
CLB3. Clb1 accumulated with periodicity similar
to Clb3, but accumulated to
only ~60% the peak level of Clb3 (our unpublished
results), as expected from the asynchronous values in Table
.
We observed similar deregulation of both Clb2-PrA and Clb3-
PrA by
cdh1 deletion (Figure C). This
observation suggests that Cdh1 controls both Clb2 and Clb3
accumulation similarly, in disagreement with another report
using induced synchrony and overexpressed Clb3 (
Baumer
et al., 2000 ). Consistent with our findings,
Zachariae et al. (1998) showed that ectopic Cdh1
can induce Clb3 degradation, and
Alexandru et
al. (1999) proposed that Clb3 might be under control
of both Cdc20 and Cdh1.
Effects of Constitutive Undegradable Clb2 on
Accumulation of Other Cell Cycle Regulators
The model allows explicit predictions to be
made about the consequences of interfering with the cell
cycle oscillator, not only for cell cycle events but also
for accumulation of cell cycle regulators. The availability
of a comprehensive set of tagged regulators allows these
predictions to be tested. Overexpression of Clb2 lacking
its destruction box causes cell cycle arrest late in
mitosis (
Surana et al., 1993 ). This genetic
manipulation can be simulated in the model (Figure
A). The model predicts that
Clb2-db overexpression should eliminate Cln2, Clb5, and
Sic1 proteins. We introduced a
GAL-CLB2-db
cassette or a control
GAL-CLB2 cassette into
strains expressing various PrA fusions and tested the
effect of a 3.5-h incubation in galactose medium (enough to
give efficient cell cycle arrest with
GAL-CLB2-
db). The predicted disappearance of Cln2, Clb5, and
Sic1 (Figure A) was observed in this experiment (Figure
B), whereas expression of
GAL-CLB2 containing
the destruction box was without significant effect, also as
the model predicts.
Effects of Unregulated Cdh1
To examine the effect of making Clb2
degradation constitutive, we constructed strains containing
various PrA fusions and also expressing an unregulatable
Cdh1 mutant under
GAL control (
GALL-HA3-
HCT1-m11::TRP1;
Zachariae et al.,
1998 ). The galactose-induced mutant Cdh1 protein expressed
from this construct is mutated in its Cdk phosphorylation
sites, and so negative control by cyclin-Cdc28 is lost.
Thus, this construct results in constitutive Clb2 and Clb3
degradation and blocks the cell cycle (
Zachariae et
al., 1998 ). We modeled expression of this construct by
simulating Cdh1 not subject to negative regulation by
phosphorylation and determined the predicted effects on
abundance of Cln2, Clb2, Clb5, and Sic1 (Figure
A). The model predicts cell
cycle arrest with very low levels of Sic1 and Clb2 and very
high levels of Cln2 and Clb5. Experimentally, we observed a
three- to fourfold increase in Cln2-PrA and disappearance
of Clb2-PrA and Sic1-PrA, all in accordance with the
model's predictions (Figure B). We observed no
significant increase in Clb5-PrA, in disagreement with the
model, but in agreement with previously published data
(
Schwab et al., 1997 ;
Zachariae et
al., 1998 ).
In this experiment, the effects of unregulated mutant Cdh1
(
GALL-HA3-HCT1-m11) on Clb2 are likely to be
primarily due to direct promotion of Clb2 ubiquitination
(leading to its degradation) by Cdh1 (
Zachariae et
al., 1998 ). The effects of the mutant Cdh1 on Cln2 and
Sic1, in contrast, are likely to be indirect. In the model,
unregulated Cdh1 leads to Cln2 accumulation through (1)
loss of Clb2, with consequent loss of repression of
CLN2 transcription, leading to (2)
hyperaccumulation of Cln2. The hyperaccumulated Cln2
contributes to very efficient Sic1 phosphorylation and SCF-
dependent ubiquitination, leading to Sic1 proteolysis.
The incorrectly predicted strong increase in Clb5-PrA by
unregulated Cdh1 is also an indirect effect in the model
and is predicted for two reasons. First, the model
implements Clb2-dependent stimulation of
Cdc20 synthesis (
Prinz et al., 1998 ), and Cdc20
is required for efficient Clb5 proteolysis in the model.
Second, the model assumes that Clb2 is required to turn off
CLB5 transcription in the same way as it is
required to turn off
CLN2 transcription. These
two hypothetical mechanisms will make removal of Clb2 by
unregulated Cdh1 lead to increased Clb5 levels. There is
some information supporting the first assumption (
Prinz
et al., 1998 ), but the second assumption is
probably incorrect (
Amon et al., 1993 ), as indeed
was noted by
Chen et al. (2000) .
We observed a
strong reduction in Clb3-PrA levels upon expression of
unregulated Cdh1, consistent with the results of
Zachariae
et al. (1998) , although the reduction was not as
effective as the reduction in Clb2-PrA or Sic1-PrA (with
longer exposures, in several experiments; our unpublished
data).
Thus, for Cln2, Clb2, and Clb3, we observe opposing effects
of cdh1 deletion (lowering Cln2 and increasing
Clb2 and Clb3) and expression of unregulated Cdh1
(increasing Cln2, and strongly reducing Clb2 and Clb3).
This article has been 
fWend/fWbeg)/ln(
I ![[triple prime]](/corehtml/pmc/pmcents/x2034.gif)
= 0.01, kdb2p =
0). To model GAL-HCT1-m11 (unregulated
Cdh1), GAL promoter expression was neglected,
because CDH1 expression is not considered in the
model. Instead the nonphosphorylatable status of the mutant
Cdh1 encoded by this construct was reflected by setting
kit1" to zero, eliminating the effect of Cdk
phosphorylation.
