The control of cell proliferation under steady-state conditions in the budding yeast, Saccharomyces cerevisiae, is well described by either the tandem or sloppy size control models, both of which suggest that differences in cycle time between individual cells or between parents and daughters is largely due to differences in birth size. These models have been investigated further under conditions in which cell size has not been a rate-determining factor for cell cycle initiation. Two approaches have been used. The first involves the growth of cells in low concentrations of hydroxyurea (HU), which has the effect of prolonging the duration of DNA synthesis. This leads to a lengthening of the budded period, which in turn leads to daughter cells being larger at division than the normal cell cycle initiation size of daughters in steady-state populations. The second approach involves the accumulation of cells at the key control point of the cycle, called start, using the pheromone α-factor. Since growth is unaffected, all cells eventually become larger than the volume at which they would normally initiate the cell cycle. The kinetics of proliferation were followed after release from α-factor arrest. The results from both approaches were broadly consistent with the predictions of both models. However, abolition of birth-size differences between parents and daughters in the presence of HU did not lead to a complete disappearance of differences in either cycle time or proliferation kinetics. Furthermore, following release from α-factor arrest, the rate of cell cycle initiation of parent cells was slower than in steady-state culture and the daughters’ cells behaved as if comprising two separate populations. These discrepancies suggest that besides a size difference, there are additional physiological differences between parent and daughter cells.

Start is defined as the stage, in the G1 period of the cell cycle of Saccharomyces cerevisiae, the completion of which commits a cell to a sequence of events (the cell division sequence) culminating in a mitotic division (Hartwell, 1974). All the known events of the cell cycle are dependent on the prior occurrence of start (Pringle & Hartwell, 1981), which thus represents the major point of control in the cell cycle of this yeast. Johnston, Pringle & Hartwell (1977) produced evidence that the attainment of a critical cell size is an important prerequisite for the completion of start. An important implication of a size control is that much of the duration of the cell cycle is determined by the birth-size of the cell. In the case of yeast cells this means that it is the portion of G1 between cell division and start whose duration is determined by birth-size. Since S. cerevisiae cells divide asymmetrically into large parents and smaller daughters (Johnson & Gibson, 1966; Hartwell & Unger, 1977) and since, at division, parent cells are already above the critical size, it is only the duration of the Gi period of daughter cells that is subject to the size control (Hartwell & Unger, 1977).

Support for the view that much of the G\ period is due to the fulfilment of a growth requirement was given by Singer & Johnston (1981). They showed that when the.S’ phase of yeast cells is lengthened, by incorporating a low concentration of hydroxyurea (HU) in the growth medium, the G1 period is shortened (particularly that part of G’i between cytokinesis and start). They also reported that daughter cells tended to produce buds at the same time as their sibling parent cells, in the presence of HU. Their formal explanation for these results was that daughter cells are born at a larger size due to the extended budded period (which is due to the lengthened S phase) and, therefore, need less time to attain a critical size for traversing start than daughter cells grown in the same medium but without HU.

The importance of cell size in triggering start was questioned by Shilo, Shilo & Simchen (1976). They released yeast cells from start arrest and showed that these cells traversed start at a similar rate to exponentially growing cells, both showing first-order kinetics. They proposed that start is triggered in the manner suggested in the Transition Probability hypothesis of Smith & Martin (1973). That is, that cells initiate the cell division sequence with constant probability per unit time. However, to account for the difference between parent and daughter cycle times, Shilo, Shilo & Simchen (1977) accepted the notion that cells must attain a minimum cell size before they can traverse start.

We termed the proposal of Shilo et al. (1976, 1977) the Tandem model (Lord & Wheals, 1981) since it implies that there are two mechanisms, which operate in tandem to trigger start (i.e. a size mechanism followed by a probabilistic mechanism). We showed that this model adequately describes the kinetics of yeast cell proliferation as long as it is further assumed that there is considerable variation in critical cell size (Lord & Wheals, 1981; Wheals, 1982). We also showed that another model of cell proliferation control, which combines the ideas of a size control and a probabilistic traverse of start, provides a good description of yeast cell cycle kinetics. In this sloppy size control (SSC) model (Wheals, 1982), the probability of traverse of start increases smoothly with increasing cell size. We have used the methods of Singer & Johnston (1981) and of Shilo et al. (1976) as further means of testing the Tandem and the SSC models by analysing their effect on individual cells.

Using time-lapse cinephotomicrography we have measured the size and cycle times of yeast cells growing in steady state in low concentrations of HU. Under these conditions daughter cells should be large enough at birth to prevent size being ratedetermining for start. Both the Tandem and the SSC models predict that in low concentrations of HU: (1) the mean daughter cycle time should approach the mean parent cycle time; and (2) the rate of traverse of start should be the same for parent and daughter cells, α-Factor prevents the traverse of start in a strains of S. cerevisiae without inhibiting growth (Hereford & Hartwell, 1974; Throm & Duntze, 1970). We have used α-factor to accumulate cells at start and released them after sufficient time for daughter cells to attain a size at which they should be as competent as parent cells to traverse start. We have compared the kinetics of the traverse of start following release, of parent and daughter cells, by following the kinetics of bud emergence using time-lapse cinephotomicrography. Shilo et al. (1976) showed that the rate of bud emergence provides a good estimate of the rate of emergence from start. The Tandem and SSC models predict that after release from start arrest, parent and daughter cells should traverse start with the same kinetics.

Although the difference between parent and daughter cycle times in exponentially growing populations of S. cerevisiae can be broadly explained by the asymmetrical mode of division and the presence of a size control over start (Hartwell & Unger, 1977), we recently found indirect evidence that part of the duration of the unbudded period of daughter cells is not determined by their size (Lord & Wheals, 1981). The experiments reported here provide more direct evidence for this period.

Organism

A haploid strain of S. cerevisiae, A364A (Hartwell, 1967) obtained from L. H. Hartwell was used throughout.

Media

YEP-galactose-PVP medium consisted of 15g yeast extract, 30g bacteriological peptone, 30g galactose, 280 g polyvinylpyrrolidone (PVP-40, Sigma) and 50 μ g adenine in 11 distilled water. This was sterilized by autoclaving. Hydroxyurea was obtained from Sigma. Synthetic α-factor was obtained from the Peptide Institute, Osaka, Japan.

Culture chamber

A Powell chamber (Powell, 1956) was used. In this, cells are grown on a piece of cellophane and liquid medium is passed underneath. The chamber was set up in the following manner. The cellophane (Cuprophan 150PM, 11· 5 μm thick, Medicell International Ltd) and its supporting PVC washers were sterilized by soaking them for 10 min in 70% ethanol and then for 5 min in sterile distilled water. The cellophane was placed in position between the washers on the chamber, the top was screwed on and the vacuum (provided by an electric vacuum pump) applied. Sterile distilled water was pumped (using a LKB Vario-perpex pump) through slowly for approx. 30 min to leach out plasticizers in the cellophane. After that, medium was pumped through at the maximum flow rate. A small drop of cell suspension was placed on the cellophane surface, which was then made concave by tightly squeezing the outlet tube, and a coverslip was placed on top of the cellophane. The pressure on the outlet tube was slowly released. The latter operations ensured a firm even contact between the cellophane and the coverslip. Once the covershp was in place the flow rate was reduced to 4ml/h. Cells were grown for several generations to ensure that they were growing exponentially, then redistributed prior to filming. Redistribution was accomplished by introducing a small amount of liquid medium (not containing PVP) underneath the coverslip and then twice raising and lowering the coverslip. The latter was achieved by setting the flow rate to maximum, applying and then releasing pressure (by squeezing) on the outlet tube. After redistributing the cells, the flow rate was reduced to 4ml/h.

Filming equipment

The microscope was a Wild M20 fitted with a long-working-distance phase condenser. A 10 × eyepiece and 20 × phase objective were used throughout. The camera was a Bolex H165BM controlled by a Bolex/Wild Variotimer timing system. An electromagnetic shutter, operated by the timer unit, was fitted beneath the condenser so that cells were not continuously exposed to light. Films were taken at a rate of 1 frame/min. on Eastman Ektachrome Commercial 7252 16 mm film. All operations were carried out at 30 °C in a temperature-controlled room. Unless otherwise stated the films were analysed as previously (Lord & Wheals, 1981).

Kinetics of cell proliferation in low concentrations of hydroxyurea

Time-lapse cine films were made of A364A cells growing on YEP-galactose-PVP medium with and without HU, in a Powell chamber at 30 °C. This medium was chosen because there is a large difference between the cycle times of parent and daughter cells growing on this medium (Lord & Wheals, 1981).

Three films were analysed: of cells growing in the absence of HU (1), and in the presence of (2) 1· 5 mg/ml and (3) 2· 5 mg/ml HU. In each case the cells were judged to be in exponential growth by some or all of the criteria of Lord & Wheals (1981). The values of the population doubling time (τ) and of the population volume doubling time (τV) are given in Table 1. As in previous kinetic analyses of this strain τ< τv (Lord & Wheals, 1981).

Table 1.

Values of τ* and τv in different concentration of hydroxyurea

Values of τ* and τv in different concentration of hydroxyurea
Values of τ* and τv in different concentration of hydroxyurea

The mean durations of the cell cycle and its constituent periods for parent and daughter cells are listed in Table 2. Cells grown in the presence of HU have longer budded periods than cells grown in the absence of HU. The periods from nuclear migration to cell separation showed little increase in duration with increasing concentrations of HU. These results are consistent with S phase being lengthened by the addition of HU to the medium (Singer & Johnston, 1981). Nuclear division, and consequently cytokinesis and cell separation, are thus delayed since nuclear division is dependent on the completion of DNA synthesis (Hartwell, 1974). Nuclear migration was also delayed so there may be some dependency for this event on the completion of DNA synthesis. The parent cycle time increased with increasing concentration of HU due to the expansion of the budded period. The parental unbudded period was unaffected by the presence of HU. The increased variance of the parent cycle times in the presence of HU is due to the increased variance of the budded period. The mean parent cycle time was less than the mean daughter cycle time in the presence or in the absence of HU, although the difference between the means was less for cells grown in the presence of HU. In the absence of HU and in the presence of 1-5 mg/ml HU, all daughter cells had a longer unbudded period than their sibling parent cells, whereas in the presence of 2· 5 mg/ml HU all except six daughter cells had longer unbudded periods than their sibling parent cells (data not shown). The mean daughter cycle time in the presence of 1· 5 mg/ml HU was slightly less than that in the absence of HU. There was a marked increase in the mean length of the daughter cycle time in the presence of 2· 5 mg/ml HU. The mean duration of the unbudded period of daughter cells decreased with increasing concentrations of HU. The variability of the unbudded period contributed more to the variability of the daughter cycle time with increasing concentrations of HU.

Table 2.

Mean duration of the cell cycle and constituent periods for parent and daughter cells in each concentration of hydroxyurea

Mean duration of the cell cycle and constituent periods for parent and daughter cells in each concentration of hydroxyurea
Mean duration of the cell cycle and constituent periods for parent and daughter cells in each concentration of hydroxyurea

The rationale behind these experiments was to increase the size of daughter cells at birth so that they were born at a size either above a ‘critical size’ (in terms of the Tandem model) or with a transition probability as high as parent cells (in terms of the SSC model). It can be seen from Table 3 that the mean birth size of daughter cells growing in the presence of 1· 5 mg/ml HU is larger than the mean daughter cell size at bud emergence in the absence of HU. It is also evident that in the presence of HU the mean increase in cell volume of daughter cells from birth to bud emergence was less than that in the absence of HU. The distributions of daughter cell size at birth and at bud emergence in the absence and in the presence of HU are presented in Fig. 1. The majority of daughter cells in the presence of HU were born at a size greater than the mean daughter cell size at bud emergence in the absence of HU. The difference in the timing of start between parent and daughter cells, which is due to a size control, should therefore be negligible at the concentration of HU used.

Table 3.

Mean size of daughter cells, at three stages in the cell cycle, in the absence and in the presence of hydroxyurea

Mean size of daughter cells, at three stages in the cell cycle, in the absence and in the presence of hydroxyurea
Mean size of daughter cells, at three stages in the cell cycle, in the absence and in the presence of hydroxyurea
Fig. 1.

The distribution of the sizes of daughter cells at two stages of the cell cycle, in the absence and in the presence of hydroxyurea. Histograms show the sizes of daughter cells at birth (solid line) and at bud emergence (broken line), A. Cells growing in the absence of HU; B, cells growing in the presence of 1· 5 mg/ml HU.

Fig. 1.

The distribution of the sizes of daughter cells at two stages of the cell cycle, in the absence and in the presence of hydroxyurea. Histograms show the sizes of daughter cells at birth (solid line) and at bud emergence (broken line), A. Cells growing in the absence of HU; B, cells growing in the presence of 1· 5 mg/ml HU.

Cell cycle kinetics of parent and daughter cells are best compared by plotting the distributions of cycle times as α plots (Lord & Wheals, 1981). An α plot is the percentage of cells with cycle times greater or equal to t plotted (on a logarithmic scale) against t (Smith & Martin, 1973). α plots of the duration of the unbudded period give a more accurate indication of the kinetics of initiation of cell cycle events (i.e. of traverse of start) since the pre-start period forms part of the unbudded period and since variation in the duration of the budded period can have a pronounced effect on the slope of the a plot of cycle times, particularly when the unbudded period is short. In this study it is especially important to compare theαplots of the duration of the unbudded period since the budded period was more directly affected by HU. It is clear from Table 2 that HU increased both the length and the variability of the budded period and, consequently, with increasing concentrations of HU the distributions of the lengths of the budded period had an increasing effect on the shape of the α plots of cycle times. The distributions of the lengths of the unbudded periods of parent and daughter cells in the absence and in the presence of HU are presented as α plots in Fig. 2.

Fig. 2.

α Plots of the unbudded periods of parent and daughter cells, growing in the absence and in the presence of hydroxyurea. The percentage of cells with unbudded periods of duration, tub, greater than or equal to 1, is plotted against t. Data are cells growing: in the absence of HU (○, •); in the presence of 1· 5mg/ml HU (ɛ, ▴); and of 2-5mg/ml HU (◻, ◼). Open symbols, parent cells; closed symbols, daughter cells.

Fig. 2.

α Plots of the unbudded periods of parent and daughter cells, growing in the absence and in the presence of hydroxyurea. The percentage of cells with unbudded periods of duration, tub, greater than or equal to 1, is plotted against t. Data are cells growing: in the absence of HU (○, •); in the presence of 1· 5mg/ml HU (ɛ, ▴); and of 2-5mg/ml HU (◻, ◼). Open symbols, parent cells; closed symbols, daughter cells.

The α plot of parent unbudded periods were unaffected by the presence of HU. HU had a considerable effect on the shape of the α plot of daughter unbudded periods. In the absence of HU the α plot had a pronounced initial downward curvature, which included about 50% of the data, before becoming approximately linear. This initial curvature was greatly reduced in the presence of HU. All the daughter unbudded periods were shorter in the presence than in the absence of HU, with the α curves being shifted more to they-axis as the concentration of HU was increased. There was little difference in the slopes of the (approximately) linear portions of the three curves of the daughter unbudded periods, but in each case the slope was less steep than the slope of the corresponding parent α curve.

The relationship between cell size at cell separation and the length of the subsequent unbudded period is shown in Fig. 3 for cells grown in the absence and in the presence of 1· 5 mg/ml HU. In both cases there was no correlation between the size at cell separation of parent cells and their subsequent unbudded period. There was a correlation between the birth size of daughter cells and the length of their unbudded period (r =—0’66, which is significantly different from 0 at the 04 % level) in the absence of HU. In the presence of 1· 5 mg/ml HU there was less correlation between these parameters (r =—0’42, which is not significantly different from 0). Size, therefore, plays less of a role in determining the length of the unbudded period for cells grown with HU. The data points for HU-grown daughter cells merge into the data points of HU-grown parent cells because of the broader distribution of birth sizes and the shorter unbudded periods.

Fig. 3.

Cell size at cell separation versus the duration of the subsequent unbudded period in different concentrations of HU. A. Cells growing in the absence of HU; B, cells growing in the presence of 1· 5 mg/ml HU; (○) parent cells; (• daughter cells. The correlation coefficients of daughter cell size at cell separation versus the duration of the unbudded period were: A, -0· 66; B, -0· 42.

Fig. 3.

Cell size at cell separation versus the duration of the subsequent unbudded period in different concentrations of HU. A. Cells growing in the absence of HU; B, cells growing in the presence of 1· 5 mg/ml HU; (○) parent cells; (• daughter cells. The correlation coefficients of daughter cell size at cell separation versus the duration of the unbudded period were: A, -0· 66; B, -0· 42.

Release from α-factor arrest

For this experiment cells of A364A were filmed growing on YEP-galactose-PVP medium at 30 °C in the Powell chamber. At t = 200 min α-factor was added. This was achieved by replacing the medium in the reservoir with YEP-galactose-PVP medium containing α-factor at a concentration of 5 μ g/ml at t = 198 min and adjusting the flow rate to maximum. After 5 min the flow rate was returned to the original setting. This procedure ensured that the a-factor-containing medium came into contact with the cells at t = 200 min and that all the medium without α-factor was fully replaced in the chamber. a-Factor was removed at t = 395 min by repeating the above procedure in reverse. The cells were exposed to α-factor for a time at least as long as the longest daughter cycle time, so that on release most or all daughter cells should be as large or larger than daughter cells at bud emergence in medium without a-factor. Filming was stopped when it was judged that all cells had produced a bud following α-factor release.

In the analysis of the film all cells of each clone in focus were scored. The cells in even the largest clone was easily identified and followed, since after release the cells produced buds orientated away from the centre of the clone in a radial array. Complete cessation of division occurred 100 min after addition of a-factor. The population doubling time was calculated to be 113 min.

The mean durations of the measured periods in the cell cycle of cells prior to afactor arrest and of cells after α-factor release are compared in Table 4. It should be noted that the unbudded period of cells following α-factor release refers to the period of time from α-factor release (i.e. t = 395 min) to bud emergence. The mean duration of the periods between nuclear migration and cell separation were equivalent for cells before α-factor arrest and after α-factor release. The budded period of cells after αfactor release was, however, about 10 min shorter than that of cells before α-factor arrest. Since the period between bud emergence and nuclear migration is shorter for cells after α-factor release, either bud emergence may be delayed or those events that occur during this period may be completed more quickly. The most interesting feature of these data was that parent cells had a shorter unbudded period than daughter cells both before α-factor arrest and after α-factor release, the mean differences being 36-1 and 34-7 min, respectively.

Table 4.

Mean duration of constituent periods of the cell cycle prior to and following release from α-factor arrest

Mean duration of constituent periods of the cell cycle prior to and following release from α-factor arrest
Mean duration of constituent periods of the cell cycle prior to and following release from α-factor arrest

The mean size of daughter cells at the time of α-factor release was 58’3 μm3, which is larger than the mean size of daughter cells at bud emergence (47-7 μm3) before a-factor arrest, although the distributions of the two sizes overlap completely (Fig. 4). Since there may be a substantial lag period after α-factor release during which cells are unable to traverse start (Samokhin et al. 1981; and Fig. 5), it is likely that all daughter cells will be above a critical size (Tandem model) or will be in the high-transition-probability size range (SSC model). After α-factor release, therefore, daughter cell size should not be a determining factor for traverse of start. Indeed there is no significant correlation between the size of daughter cells at α-factor release and the time from α-factor release to bud emergence (r=—0-38).

Fig. 4.

The distributions of daughter cell size at two stages of the cell cycle and at the time of α-factor release, A. Histograms of the sizes of daughter cells at birth (solid line) and at bud emergence (broken line) prior to α-factor arrest, B. Histogram of the sizes of daughter cells at t = 395 min (i.e. the time of removal of α-factor from the medium).

Fig. 4.

The distributions of daughter cell size at two stages of the cell cycle and at the time of α-factor release, A. Histograms of the sizes of daughter cells at birth (solid line) and at bud emergence (broken line) prior to α-factor arrest, B. Histogram of the sizes of daughter cells at t = 395 min (i.e. the time of removal of α-factor from the medium).

Fig. 5.

α Plots of the unbudded periods of parent and daughter cells prior to α-factor arrest and following release from α-factor arrest. The percentage of cells with unbudded periods of duration, tub, greater than or equal to t versus t, prior to α-factor arrest (○, •); and the percentage of cells with tr (time from removal of α-factor to bud emergence) greater than or equal to t versus t (△, ▴) are shown. Open symbols, parent cells; closed symbols, daughter cells.

Fig. 5.

α Plots of the unbudded periods of parent and daughter cells prior to α-factor arrest and following release from α-factor arrest. The percentage of cells with unbudded periods of duration, tub, greater than or equal to t versus t, prior to α-factor arrest (○, •); and the percentage of cells with tr (time from removal of α-factor to bud emergence) greater than or equal to t versus t (△, ▴) are shown. Open symbols, parent cells; closed symbols, daughter cells.

Assuming that the lag period after α-factor release is approximately the same for each cell (i.e. the lag period has little variability), the period of time from α-factor release to bud emergence is comparable to the time from start to bud emergence, since the duration of each is determined mainly by the rate of completion of start. Both the Tandem and the SSC model provide the same clear prediction about the shape of the α plots of the distributions of the length of time from α-factor release to bud emergence for parent and daughter cells; namely, that after a lag period, approximately constant for all cells, the α plots of this period should become linear and should be the same for parent and daughter cells, and the linear portions of these α plots should be approximately parallel to the α plot of the lengths of the unbudded periods of parent cells prior to α-factor arrest. These α plots are presented in Fig. 5.

The following features are evident from Fig. 5. (1) The α plot of the parent unbudded periods is approximately linear. (2) The α plot of daughter unbudded periods is not linear. (3) There is a lag period, of about 50 min for parent cells and of about 60 min for daughter cells, after α-factor release before bud emergence occurs. (4) After the initial lag and an initial downward curvature the α plot for parent cells, after α-factor release, becomes approximately linear but the slope is much less steep than the slope of the α plot of parent unbudded periods. (5) The α plot of the time from α-factor release to bud emergence of daughter cells is not linear.

The distributions of the periods of time from α-factor release to bud emergence, for parent and daughter cells, are presented more conventionally as histograms in Fig. 6. The distribution for parent cells is skewed as was expected since the α plot was mainly linear. In contrast, the distribution for daughter cells is bimodal, suggesting that the daughter cells are not a homogeneous population but are composed of at least two subsets. The origin of the bimodality is not apparent from any of these data. Neither cell size at the time of α-factor release nor the length of time that daughter cells, after birth, were exposed to α-factor determined the length of time from α-factor release to bud emergence (data not shown). There is slight evidence (data not shown) that, after α-factor release, daughter cells from the same clone produce buds after a time that falls in the same half of the distribution in Fig. 6B. However, any explanation of clonal variation cannot satisfactorily explain why the data for parent cells appear homogeneous (Fig. 6A).

Fig. 6.

The distributions of the times between release from α-factor arrest and bud emergence of parent and daughter cells. A. Histogram of the duration of the period between removal of α-factor and bud emergence of parent cells. B. Histogram of the duration of the period between removal of α-factor and bud emergence of daughter cells.

Fig. 6.

The distributions of the times between release from α-factor arrest and bud emergence of parent and daughter cells. A. Histogram of the duration of the period between removal of α-factor and bud emergence of parent cells. B. Histogram of the duration of the period between removal of α-factor and bud emergence of daughter cells.

These results seem to be inconsistent with the results of Shilo et al. (1977). They showed that the kinetics of bud emergence in an exponentially growing culture and in a cell population following α-factor release were similar. They did not, however, distinguish between parent and daughter cells. Fig. 7 is equivalent to fig. 1 of Shilo et al. (1977). The α plot of the lengths of the unbudded periods of cells (both parent and daughter cells) prior to α-factor arrest is equivalent to the α plot of the % unbudded cells against the time after plating exponentially growing cells. The α plot of the lengths of the period from α-factor release to bud emergence is equivalent to the a plot of the % unbudded cells against time after α-factor release. As shown in Fig. 7, by pooling the data for parent and daughter cells as was, in effect, done by Shilo et al. (1977), the kinetics of bud emergence of exponentially growing cells do appear to be similar to the kinetics of bud emergence following α-factor release.

Fig. 7.

α Plots of the unbudded periods of cells prior to α-factor arrest and following removal of α-factor. The data of parent and daughter cells were pooled for these plots. (◻) The percentage of cells with unbudded periods of a duration greater than or equal to t versus t, prior to α-factor arrest. (◼) The percentage of cells with tr (time from removal of α-factor to bud emergence) greater than or equal to t versus t.

Fig. 7.

α Plots of the unbudded periods of cells prior to α-factor arrest and following removal of α-factor. The data of parent and daughter cells were pooled for these plots. (◻) The percentage of cells with unbudded periods of a duration greater than or equal to t versus t, prior to α-factor arrest. (◼) The percentage of cells with tr (time from removal of α-factor to bud emergence) greater than or equal to t versus t.

As expected, low concentrations of HU in the growth medium increased the length of the budded period and increased the size of daughter cells at birth. Whereas in the similar experiments of Singer & Johnston (1981) the population doubling time (τ) was unaltered by the presence of HU, in these experiments τ increased as the concentration of HU in the medium increased. The population volume doubling time (τv) in the presence of 1 · 5 mg/ml HU was approximately the same as in the absence of HU, which suggests that this concentration of HU does not alter the (volume) growth rate.

There are two possible reasons for the increase in τ. (1) If the sole effect of HU is to expand S phase and if the sum of the lengths of G 1, G2 and M phases cannot be decreased below a minimum value, then beyond a threshold concentration of HU when the sum of G 1, G2 and M phases becomes minimal, 1 would increase due to the expansion of S phase with increasing concentrations of HU. (2) HU also slows down synthesis of RNA and protein, although to a much smaller extent than it slows DNA synthesis and, consequently, could have slowed down other processes. The latter explanation is unlikely since the concentrations of HU used were low (0’02 M and 0 · 03 M) and Slater (1973) found that these concentrations of HU had little effect on RNA and protein synthesis.

Apart from increasing the length of the budded period (between bud emergence and nuclear migration) the presence of HU has little effect on the duration of the other periods in the parent cycle (Table 2). The delayed occurrence of nuclear division, cytokinesis and cell separation in the presence of HU (Table 2) was expected, since these events are dependent on completion of DNA synthesis (Hartwell, 1974). Although it has been proposed that nuclear migration is independent of DNA synthetic events (Hartwell, Culotti, Pringle & Reid, 1974), the delay in the occurrence of nuclear migration in the presence of HU (Table 2) suggests that this event is dependent on completion of DNA synthesis. The proposal of Hartwell et al. (1974) was based on the observations of Hartwell (1973) and Slater (1973) that nuclear migration takes place when completion of DNA synthesis is prevented. However, their observations were on fixed, Giemsa-stained cells and it is possible that the fixation procedure affected the position of the nucleus. This possibility could be tested by repeating their experiments on unfixed cells using time-lapse cinephotomicrography and immersion refractometry.

The rate of bud emergence (i.e. the rate of exit from the unbudded period; Fig. 2) of parent cells is also little affected by HU. This observation and Table 2 suggest that, even in the absence of HU, the length of G1is minimal and the rate of traverse of start is maximal in parent cells. It is clear that the unbudded period is shorter for daughter cells in the presence of HU (Table 2). It is not clear whether the rate of traverse of start of daughter cells (rate of exit from the unbudded periods; Fig. 2) is altered by the presence of HU, since the shape of the α plot of the lengths of the unbudded period of daughter cells in the absence of HU is determined to some extent by the variation in the birth size of daughter cells.

The results are consistent with there being a size control early in the cell cycle, since the difference between the cycle times (and in particular, between the lengths of the unbudded periods) of parent and daughter cells is reduced when the birth size of daughter cells is increased. However, there is still a difference between parent and daughter cells in the durations of their unbudded periods in the presence of HU. The cause of this is the difference in rate of exit from the unbudded period and, by inference, the rate of traverse of start, for parent and daughter cells. This observation is inconsistent with both the Tandem and the SSC models. These models predict that the length of the unbudded period and the rate of traverse of start should be the same for parent and daughter cells in the presence of HU (provided that the daughter cells are born large enough, which they are; see Table 3 and Fig. 1).

Either model can be modified to account for the results. The inclusion of the assumption that there is an additional period in the daughter cycle prior to bud emergence is one adequate way of modifying both models. This period would have to be of variable duration to account for the α plots in Fig. 2, but the shape of the distribution and the exact temporal location of this period cannot be deduced from the data.

As shown by Fig. 7 the results of the a-factor-release experiment are not too dissimilar from the results of Shilo et al. (1977). However, we have looked at the kinetics of α-factor release in more detail by distinguishing between parent and daughter cells, and the conclusions from these results are quite different from the conclusions of Shilo et al. (1976, 1977). The rate of bud emergence of parent cells follows approximately first-order kinetics both before α-factor arrest and following release from the arrest, although the rate of bud emergence is not the same. Samokhin et al. (1981) have shown that the rate of bud emergence following complete arrest is decreased when cells are transferred to medium containing low concentrations of αfactor. This suggests the possibility that α-factor was not completely washed out of the Powell chamber. Since α cells actively degrade α-factor (Ciejek & Thorner, 1979), and since any residual α -factor within the chamber will have been continuously diluted by α-factor-free medium, the concentration of residual α -factor in the chamber should have decreased with time. Even if the decrease in the concentration of αfactor was slow, the α plot of the time from release to bud emergence of parent cells (Fig. 5) would not be linear (after the initial plateau) as was observed. Instead, it would be a curve with increasing (negative) slope. It is perhaps more likely that the traverse of start following release from α -factor arrest does not occur at the same rate as in steady-state conditions, owing to some property intrinsic to the mode of action of α -factor. The question then arises as to what the cells are doing during the lag period following removal of α -factor from the medium, a lag period very similar in length to that observed by Shilo et al. (1977) and Samokhin et al. (1981).

To complicate the issue further, the kinetics of bud emergence of daughter cells following α -factor release are strikingly different from the kinetics of bud emergence of: (1) daughter cells prior to α -factor arrest; (2) parent cells prior to arrest; and (3) parent cells after release (Fig. 5). The distribution of the times from α -factor release to bud emergence of daughter cells is bimodal (Fig. 6B), which suggests that there is a difference in the kinetics of release from α -factor arrest not only between parent and daughter cells, but also between at least two subsets within the daughter cell population. The basis of the heterogeneity of the daughter cell population following α -factor release remains a mystery, although it is possible that a proportion of the daughters enter a G 1 -like state, as can occur in slow-growing or stationary-phase cultures (B. Carter, personal communication).

The duration of the budded period following α-factor release is equivalent for parent and daughter cells, but is some 10 min shorter than for cells in a steady state. This does not necessarily mean that the time between completion of start and cell separation is shorter in cells following α-factor release, although it is a possible reason for the shorter budded period. A second possibility is that events specific to the emergence of the bud (e.g. microfilament-ring formation) are executed at a slower rate because of the changes in the cell wall produced by the action of α-factor (Lipke, Taylor & Ballou, 1976). This is plausible since the bud is formed, in most cases, at the ‘shmooing tip’ and the Calcofluor-stainable ring at the base of the bud has a larger diameter on ‘shmoos’ than on steady-state cells (unpublished observation).

These experiments were designed to reveal how much influence ‘pre-start’ cell size has on the timing of start. Under the conditions of the experiments the pre-start cell size of all cells was large enough in theory to essentially remove the effect of cell size in determining the timing of start. In the case of the timing of start in parent cells in balanced growth, size has little or no effect. Cell size is an important determining factor for the timing of start in daughter cells in balanced growth. The experiments with HU confirm this and reveal that an additional factor influences the timing of start in daughter cells but not in parent cells. The experiments with HU also support the interpretation of the results presented previously (Lord & Wheals, 1981), that the daughter cell cycle contains an additional period, called Gw, whose duration is not influenced by cell size. Gw is unique to daughter cells and may be due to an event (or events) distinct from, but a prerequisite for, start events. If this were true then, during α-factor arrest, not only will the effect of cell size be reduced (by continued growth) but the effect due to this pre-start event will also be reduced, assuming that α-factor block start events and not the hypothetical pre-start event. In view of the difference in the kinetics of α-factor release between parent and daughter cells, a pre-start event unique to daughter cells is unlikely.

This leaves two further possibilities for Gw. It may be due to an event that lies between start and bud emergence or it may lie within the complex of start events (Nurse, 1982; Pringle & Hartwell, 1981). In the former case the rate of traverse of the start complex would be the same for parent and daughter cells, but the rate of bud emergence following start would be different for parent and daughter cells. In the latter case the rate of traverse of start would be different, but the rate of bud emergence after start would be the same for parent and daughter cells. The rate of traverse of start was not directly monitored in the α-factor arrest experiment and, apart from this, there is a pronounced qualitative difference in the kinetics of bud emergence after α-factor release between parent and daughter cells, which is difficult to interpret. The α-factor release experiment, therefore, does not provide evidence to discriminate between these two possibilities.

It is held that the difference between the mean cycle times of parent and daughter cells of S. cerevisiae is due to the asymmetrical mode of division and the presence of a ‘size control’ (Hartwell & Unger, 1977; Carter & Jagadish, 1978). Furthermore, it is held that the difference is due to the difference in the mean pre-start period of parent and daughter cells (Hartwell & Unger, 1977; Singer & Johnston, 1981). The results presented here imply that, whilst the difference in cell size at division is the major cause of the difference in the mean pre-start cycle time of parent and daughter cells, it is not the sole cause. The difference in the mean pre-start period of parent and daughter cells does appear, in the light of this evidence, to be caused solely by the difference in cell size at division. However, an additional source of the mean cycle time difference is apparent in daughter cells that, if not within the start complex, lie immediately after start.

These results further emphasize the need to treat populations of S. cerevisiae cells as comprising two distinct sub-populations. Treating them as homogeneous populations in cell cycle experiments can lead to misleading, if not erroneous, conclusions.

We thank the SRC for financial support.

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