The timing of initiation of DNA synthesis in Paramecium tetraurelia is established during the preceding cell cycle as cells become committed to cell division

Experimental

Cell Research 174 (1988) 355-366

The Timing of Initiation of DNA Synthesis in Paramecium tetraurelia Is Established during the Preceding Cell Cycle as Cells Become Committed to Cell’ Division JAMES D. BERGER’ and ADA S.-L. CHING Departmenf

of Zoology, University of British Columbia, British Columbia, Canada V6T 2A9

Vancouver,

The timing of initiation of DNA synthesis (IDS) in Paramecium is established before cell division at a point located at about 0.75 in the preceding cell cycle. This point occurs about 90 min prior to fission and coincides with the point at which cells become committed to cell division. The location of the point at which the timing of IDS is set was deduced from a series of nutrient-shift experiments. Changes in nutrient level lead to changes in the duration of the subsequent Gl interval when they occur more than 90 min prior to fission. Perturbation of the cell cycle so that the timing of commitment to cell division is altered, results in a parallel shift in the point at which the timing of IDS is established. 0 1988 Academic

Press, Inc.

Initiation of macronuclear DNA synthesis (IDS) is one of the earliest cell cycle landmarks in Paramecium and the first indication that cells have become committed to the DNA replication pathway. IDS in Paramecium normally occurs at 0.25 in the cell cycle [3, 5, 12, 16, 24, 27, 281. Although IDS regularly occurs at a precise and characteristic position within the cell cycle under conditions of equilibrium growth, the timing of IDS depends on a number of variables, as in many eukaryotes. These variables include cell mass, macronuclear gene dosage, and nutrient levels [12, 24, 271. The variation in the’timing of IDS under different conditions reflects the operation of regulative processes which govern the entry of cells into the DNA replication pathway and ‘establish the timing of IDS [12]. This function is the first of two conceptually distinct processes which regulate the cell cycle in this organism. The second process regulates commitment to cell division. This study examines the temporal relation between these processes and shows that they coincide, both in normal and in perturbed cell cycles. This suggests that in this organism both control functions, though conceptually distinct, may be aspects of a single complex process. Previous experiments have shown that the first cell cycle control function, regulating IDS, acts prior to fission during the preceding cell cycle [12, 271. This differs from the usual situation in eukaryotes in which the initial cell cycle control point occurs just prior to IDS in the latter part of the Gl interval [19, 20, 23, 34, 351.This conclusion is based on the effects of perturbation of cell cycle variables on the timing of IDS. For example, increase in cell mass leads to proportional shortening of the Gl interval of the subsequent cell cycle, or its entire elimination ’ To whom reprint requests should be addressed. 24-888332

355

Copyright @ 1988 by Academic Press, Inc. All rights of reproduction m any form reserved 0014-4827188 $03.00

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if initial cell mass equals or exceeds the cell mass normally present at IDS 124, 271. However, if cell mass is increased during the Gl interval, the duration of the remaining portion of the Gl interval is not affected [27]. Similarly, drastic changes in macronuclear gene dosage introduced at fission lead to no change in the timing of the subsequent IDS [9,27]. On the other hand, when change in gene dosage is introduced at the preceding fission there is a slight decrease in the duration of the Gl interval in the progeny of cells with smaller than average macronuclear gene dosage [27]. The timing of IDS is also influenced by nutrient levels. In nutrient-limited cells the duration of the Gl interval is extended. However, changes in nutrient level at fission do not lead to changes in the timing of IDS in the following cell cycle [ 121. Thus, when dividing cells from an equilibrium chemostat culture with a generation time of approximately 24 h are transferred to medium with excess food, IDS occurs about 6 h after fission, at the time typical of IDS under the preshift conditions. In the second postshift cell cycle the timing of IDS is typical for wellfed cells. Similarly, when well-fed cells are transferred to nutrient-limited conditions at fission, IDS occurs about 1.5 h after fission, as it does under well-fed conditions. These observations indicate that the timing of IDS is established prior to fission, during the parental cell cycle. Further information about the location of the initial cell cycle control point can be obtained by determining the point at which initial commitment to meiosis occurs. In other organisms, for example yeasts [15] or Tetrahymena [34], the point from which cells enter the meiotic pathway is located just prior to the point of commitment to vegetative replication, and occurs shortly before IDS. In Paramecium the point of initial commitment to meiosis (autogamy) occurs during the latter part of the preceding cell cycle and is linked with the point at which cells become committed to division [lo]. If the association between the points of commitment to meiosis and commitment to vegetative replication is also valid for Paramecium, then the timing of IDS is probably established at or just prior to the point at which cells become committed to division in the preceding cell cycle. We have therefore mapped the temporal location of the point at which timing of IDS is set by examining the consequences of nutrient-level shifts carried out at various points in the cell cycle on the timing of IDS in the subsequent cell cycle. In the same experiments the position of the point of commitment to cell division was mapped by shifting cell samples to conditions which block fission in cells not already committed to division. This point occurs late in the cell cycle in Paramecium, about 90 min prior to fission (0.73kO.02 in well-fed cells [21, 261, and depends on macronuclear DNA synthesis [13]). This study shows that the two conceptually distinct cell cycle control functions are temporally coincident in both normal and perturbed cell cycles. MATERIALS

AND METHODS

Paramecium tetraurelia [30] was grown in phosphate-buffered Cerophyl medium with Enterobacter aerogenes as the food organism [29]. The cells used (stock d4-1002) carry a temperature-sensitive gene mutation ccl which completely blocks cell cycle progression and DNA synthesis at 34.4”C [21,

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251.Synchronous samples of cells were obtained by hand selection of dividing cells from exponential growth-phase cultures over an interval of less than 5 min. Heat treatments were carried out in a water bath equipped with an electronic thermostat which maintained the temperature within 0.02”C of the set level. Cell cycle duration was determined by isolation of a set of 40 synchronous cells into drops of medium in glass depression slides. The cells were examined frequently during the latter part of the cell cycle and the cumulative number of cells having reached division was plotted against time since fission. The median time of division was estimated from the plot of the cumulative distribution. The median time of division was used as an estimator for the mean time of division. The standard deviation of the mean time of division was also estimated from the same cumulative plot. The time interval subtended by the central 38% of the distribution (31 to 69%) was taken to correspond to 1 standard deviation. A similar approach was used to estimate the mean time of commitment to cell division. Synchronous cell samples were placed in 0.5 ml of medium in 1J-ml plastic centrifuge tubes and immersed in a waterbath at 34.4”C, the restrictive temperature for the ccl mutation. One hour after a parallel cell sample had completed division at the permissive temperature, the fraction of cells which had divided in the samples at the restrictive temperature was determined. The fraction of cells completing division was taken to be the fraction of cells which had passed the point of commitment to cell division at the time of the temperature shift. These values were plotted against time after fission. The median time of commitment to division and its error were determined as described above. The kinetics of initiation of DNA synthesis were similarly established. Sets of 40 synchronous cells were allowed to feed on [3H]thymidine-Iabeled bacteria [5] for 20 min at intervals from 0.75 to 3.25 h after fission and were then fixed and stained with acriflavine [14]. Autoradiographs were prepared and the fraction of cells showing significant incorporation (twice background level) of labeled material into their macronuclei was plotted against time since fission. The median time of onset of DNA synthesis and its error were determined as described above. Nutrient down-shift experiment. Eight to twelve sets of 40 synchronous cells were selected from exponentially growing cultures. These cells were individually transferred by micropipet from normal growth medium to a 1% dilution of growth medium in Dryl’s buffer at a point in the later part of the cell cycle (2.5 to 5.0 h after fission). The cells were washed twice and allowed to remain in diluted medium until fission. At that point eight groups of 40 synchronous cells were selected from the experimental samples and placed in diluted medium. At intervals between 0.75 and 3.5 h after fission, individual sets of 40 synchronous cells were labeled and the median time of IDS was determined as described above. A separate set of synchronous cells was allowed to remain in growth medium and was used to determine the duration of the control cell cycle. Nutrient up-shift experiment. Synchronous cell samples were collected and subjected to nutrient down-shift between 0.5 and 0.6 in the cell cycle as described above. At a later point in the cell cycle (ranging from 250 to 0 min prior to fission, in different experiments) cells were refed by adding normal growth medium to the depression slide cultures so that the initial volume was more than doubled. Dividers were later selected from these synchronous cell samples, and the timing of IDS in the next cell cycle was determined as described above. The control for each experiment consisted of an entire set of synchronous cell samples, subjected to the same down-shift regimen as the experimental cells, but not refed until fission. Means are shown with their standard errors. Compounded errors were calculated according to Beers [2].

RESULTS The Timing of IDS Is Set Approximately

90 min Prior to Fission

The duration of the Gl interval is established during the parental cell cycle in [12]. The location of the point within the cell cycle at which the timing of IDS is set was estimated by examining the effects of nutrient downshifts on the duration of the Gl interval in the subsequent cell cycle. Nutrient down-shift prior to the point at which the timing of IDS is established should result in extension of the Gl interval of the subsequent cell cycle. Conversely, nutrient down-shift after the timing of IDS is set should result in no extension of the following Gl period.

Paramecium

358 Berger and Ching Nutrient down-shift to diluted medium (1%) was carried out between 200 and 0 min prior to the median time of fission of a control cell sample which remained in growth medium throughout the cell cycle. The duration of the subsequent Gl interval in experimental cells was expressed as a fraction of the control Gl interval (estimated as 25 % of the control cell cycle duration) and plotted against the time of nutrient down-shift (Fig. 1). The validity of the assumption that the normal G 1 interval can be estimated by 25 % of the control cell cycle duration is established by the observation that the Gl duration following nutrient down-shift at fission is normal, as previously observed [12]. When nutrient down-shift occurred less than 90 min prior to fission there was no significant effect on the timing of IDS in the next cell cycle. However, when nutrient down-shift occurred more than 90 min prior to fission the duration of Gl interval was extended (Fig. 1). These observations suggest that the timing of IDS is established about 90 min prior to fission. The scatter of the points from experiments in which nutrient down-shift occurred more than 90 min after fission is likely a consequence of minor differences in the concentration of food available to the cells in the different experiments. This would affect the degree of starvation, and consequently the duration of the subsequent Gl interval. The experimental design provided a control for variation in the duration of the unextended Gl interval due to differences in the overall cell cycle length. It did not, however, provide control for variation due to differences in the degree of starvation which could alter the extent to which the Gl interval was increased. Thus, when nutrient down-shift occurred 90 min prior to fission, or later, all experiments showed similar Gl durations because the timing of the Gl interval had already been set, and was unaffected by the reduced nutrient level. The Time at Which the Duration of the Gl Period Is Set Coincides with Commitment to Cell Division The foregoing experiment indicates that the timing of IDS is set about 90 min prior to fission in the normal, unperturbed cell cycle. This timing coincides with the position of the major cell cycle control point acts late in the cell cycle. At this point cells become committed to cell division, as indicated by their ability to proceed to division in the presence of conditions which would otherwise block cell cycle progression [13, 21, 261. The median time of commitment to cell division occurs approximately 90 min prior to division, regardless of the length of the cell cycle (Table 1). This confirms the previous observation that commitment to cell division occurs at a fixed interval prior to fission rather than at a fixed relative position within the cell cycle [13]. Typical patterns of commitment to division are shown in Figs. 2 (filled circles) and 3. In Fig. 1 the fraction (%) of cells in each experiment which had reached the point of commitment to division is indicated by a small number near the data point. In general, if the cells had reached the point of commitment to division, the duration of the following Gl interval was not altered by nutrient down-shift, while nutrient down-shift prior to the point of commitment to cell division results in extension of the following Gl interval.

Paramecium cell cycle

50'

I

I

250 200 MINUTES

__, .

I

150 loo BEFORE

11

50 FISSION

0

100

I 250

200

MINUTES

p +I'

359

I

150 loo BEFORE

50 FISSKIN

0

Fig. I. Effects of nutrient down-shift on the duration of the subsequent Gl interval. Time of nutrient down-shift is indicated as minutes prior to fission. The duration of the subsequent GI interval is expressed as a percentage of the control G1 interval. The numbers besides the data points indicate the fraction of cells (%) in the samples from the individual experiments which were committed to division at the time of the nutrient shift. Fig. 2. Effects of nutrient up-shift on the duration of the subsequent Gl interval in cells which were subjected to nutrient down-shift in the middle of the cell and later refed. Time of refeeding is shown as minutes prior to fission. The resulting G 1 duration is plotted as a percentage of the normal G I interval (open circles). The cumulative fraction of cells committed to division in a parallel experiment is shown for comparison (tilled circles).

The Association betwen Commitment to Cell Division and Establishment of the Timing of IDS Is Maintained in Perturbed Ceil Cycles If the setting of the timing of IDS is linked to commitment to division, then perturbations of the cell cycle which result in extension of the cell cycle and a shift in the time of commitment to division (Fig. 3) should produce a parallel shift in the point at which the timing of IDS is set. When cells growing in the presence of excess food were subjected to nutrient down-shift between 0.5 and 0.6 in the cell cycle, the duration of the cell cycle is extended by 15+2% or an average of 55+7 min in 11 independent experiments. Although the point of commitment to division is delayed by the nutrient down-shift (Fig. 3), the interval between the point of commitment to division and fission (Table 2) is similar to that in unperturbed cells (Table 1). The small difference (6 min) appears to be a consistent feature of the experiments but is not significant at the 0.05 level by a group comparison t test. TABLE 1 Timing of commitment to cell division Expt NO.

86-5 86-10 86-11 86-12 86-63

Median time of commitment (h after fission)

Median time of division (h after fission)

4.YO+O.18 5.8SkO. 10 4.75&O. 10 6.65kO.25 4.55kO.22

6.4 1.2 6.1 8.2 6.0

Mean

Difference (min) YO+_IY 82+16 802 16 Y3+23 87k20 8Yk5

360 Berger and Ching

345678910 HOURS

AFTER

FISSION

Fig. 3. Pattern of commitment to division and fission in normal and perturbed cell cycles in Paramecium. Filled circles, percentage committed to division; open circles, percentage divided. (A) Control cell cycle. (B) Nutrient down-shift at 3 h after fission. (0 Nutrient down-shift at 3 h after fission followed by up-shift to normal medium at 5 h.

Nutrient up-shifts were used to determine the point at which the timing of IDS was set in these experimentally elongated cell cycles. In cells growing under nutrient-poor conditions, the duration of the following Gl period is longer than normal and is not altered by nutrient up-shift at the time of fission [12]. Thus, if up-shift occurs after the timing of IDS is set, the duration of the following Gl interval should not be reduced. However, if up-shift occurs prior to the point at which the timing of IDS is set, the duration of the subsequent Gl interval should be shortened and reach the mean level for normal cells when none of the cells in the sample have reached the point at which the timing of IDS is established. Synchronous cell samples were subjected to nutrient down-shift between 0.5 and 0.6 in the cell cycle and were refed later in the same cell cycle. The precision of the experiment was improved by the incorporation of a complete set of control samples which were subjected to nutrient down-shift at the same time as the experimental cell samples. These control samples, however, were not refed until fission. The length of the Gl interval in the control cells was approximately 1.9 TABLE 2 Timing of commitment to division following nutrient down-shift Expt No.

Time of shift (h after fission)

Median time of commitment (h after fission)

Median time of division (h after fission)

Difference (min)

86-36 86-7 1 86-7 1 86-72 86-73 86-74

3.5 1.5 1.0 2.5 3.0 3.0

6.3OkO.25 5.4OkO.27 5.80f0.27 5.65f0.37 6.1OkO.80 5.68k0.35

7.70 6.82 7.48 7.35 7.75 7.48

84+21 85rt22 101+22 102+29 99+26 100+28

Mean

95+4

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times the normal Gl interval. The length of the subsequent Gl interval in the experimental cells was expressed as a percentage of the normal Gl interval (Fig. 2).

The results show that the duration of the following Gl interval is normal (89f7 min) when experimental cells were subjected to nutrient up-shift 120 min or more prior to fission. When up-shift occurred at later points, the duration of the Gl interval increased, and reached the control level (that of cells which were not refed until fission) by 50 min prior to the median time of division. The pattern of commitment to division in a separate parallel experiment is also shown (tilled circles). Nutrient up-shift prior to the point that any of the cells have become committed to division results in a subsequent Gl interval of normal duration. When all cells have become committed to division, the following Gl interval is of control duration (maximum length). At intermediate points, intermediate levels are obtained. The pattern of increase in Gl duration in the experimental cells parallels the increase in the fraction of the cells committed to division (Fig. 2). The median point of commitment to division in a parallel experiment coincides with the midpoint of the interval during which the change in duration of the subsequent Gl interval occurs. Both points occur just less than 90 min prior to fission. The results of the two sets of nutrient-shift experiments are consistent. In both cases is a strong association between the point of commitment to cell division and the point at which the timing of the subsequent Gl interval is established. The observation that this relationship is maintained following perturbation of the cell cycle suggests that the association between the two events is not simply coincidental. DISCUSSION This study demonstrates that the duration of the Gl interval in Paramecium is set during the parental cell cycle, approximately 90 min prior to fission. Subsequent changes in nutrient level, gene dosage, or cell mass do not alter the timing of initiation of DNA synthesis (IDS) [12, 261. It appears that cells become committed to enter the vegetative replication pathway when the timing of IDS is set. In this respect Paramecium differs from most eukaryotes in which commitment to replication occurs in the latter part of the G 1 interval [35]. The notion that the initial cell cycle control point occurs about 90 min prior to fission is strengthened by the observation that the point of initial commitment to meiosis (autogamy) also occurs at the same position in the cell cycle [lo]. At this point the nature of the next cell cycle is determined (vegetative vs meiotic) and, if the next cell cycle is to be vegetative, the duration of the subsequent Gl interval is established. The occurrence of both control functions at the same point within the cell cycle suggests that a complex of events analogous to the “start” function in Saccharomyces acts in Paramecium. This function acts about 90 min prior to fission and gates cells into either the vegetative replication pathway or the alternative meiotic pathway. The point from which cells enter meiosis or the vegetative replication pathway

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coincides with the point at which they become committed to division. Both the point at which the timing of IDS is set and the point of initial commitment to meiosis show strong linkage to the point of commitment to cell division. When the cell cycle is perturbed so that the point of commitment to division is shifted, there are parallel shifts in the locations of the control points for meiosis 1101or vegetative replication (this study). The close temporal association of the cell cycle functions governing entry to meiosis and vegetative replication and the point of commitment to cell division in Paramecium may be more than coincidental. In the well-studied cell cycles of the yeasts Saccharomyces and Schizosaccharomyces the two major cell cycle control points, which govern commitment to vegetative replication and commitment to mitosis, respectively, are functionally related. In both organisms the “start” function, cdc28 in Saccharomyces [22] and cdc2 in Schizosaccharomyces [18], acts at two different points within the cell cycle. The earlier point of action is associated with commitment to replication, and the later with commitment to mitosis. In Paramecium this control complex might act to control both initiation of cell division in the present cell cycle and commitment to vegetative replication or meiosis in the next. The linkage of these two conceptually distinct control processes in Paramecium suggests that, as in yeasts, both control functions may be aspects of a single complex control system. The unusual feature of the Paramecium cell cycle is the occurrence of both control points at the same position within the cell cycle at 90 min prior to fission. Major cell cycle control points occur late in the cell cycle in some other organisms, for example the myxomycete, Physarum. In this organism commitment to mitosis occurs at about 0.9 in the cell cycle (45 min prior to mitosis [31]). However, the point of commitment to spherulation (as opposed to vegetative mitosis) occurs in the middle of the G2 interval at about 0.7 in the cell cycle [17]. Commitment to sporulation is more complex. Competence to sporulate is acquired following a final mitosis which is not followed by DNA replication as in the vegetative cell cycle [ 1l] suggesting that sporulation is entered from the Gl portion of the cell cycle. The point of commitment to sporulation is, however, not known. Although cell cycle control appears to be exerted at only one point in the cell cycle in Paramecium, about 90 min prior to fission, the two conceptually distinct control functions governing the timing of IDS and commitment to cell division divide the cell cycle into three segments. The first segment extends from the point of commitment to replication (when the duration of the Gl interval is fixed) until IDS. This period is variable and depends on gene dosage, cell mass, and nutrient level at the time of commitment to the new cell cycle. The second period is also variable and appears to depend on synthesis of a threshold increment of macronuclear DNA [4, 6, 7, 131. The level of the threshold is variable and depends on cell mass, gene dosage, and nutritional state [7; J. D. Berger and A. S.-L. Ching unpublished data]. The third segment is fixed and occurs between the point of commitment to division and fission. It corresponds to the period of prefission morphogenesis.

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The observation that the duration of the Gl interval is established prior to the beginning of the Gl interval, and is unaffected by subsequent changes in cell mass, gene dosage, or nutrient level occurring at fission or during the Gl interval, suggests that the Gl interval is measured out by a timer mechanism which is insensitive to changes in these variables. This is especially interesting as cell mass, gene dosage, and nutrient level all influence the timing of IDS at or prior to the control point [12, 271. The basis of the timer mechanism is not known. Its action, however, can be reversibly blocked by the action of the ccl mutation when cells are placed under restrictive conditions during the Gl interval [25, 271 but not during the interval between commitment to division and fission (A. S.-L. Ching and J. D. Berger, unpublished data). A number of models have been suggested to rationalize the timing of IDS and its dependence on cell mass increase in various organisms. Among the more successful of these are bimolecular, activator-inhibitor models which have been applied to Physarum [32, 331 and Saccharomyces [l]. These models successfully account for the major experimental observations on the effects of cell cycle perturbation in these organisms. The incorporation of a bimolecular activator-inhibitor mechanism for control of the timing of IDS similar to that of Alberghina et al. [l] into the growth-controlled cell cycle model developed previously for Paramecium [8] successfully reproduces the major effects of cell cycle perturbation on cell mass, macronuclear DNA content, and cell cycle duration but does not adequately account for the timing of IDS in all situations. In particular, the model indicates that macronuclear DNA synthesis should begin immediately following release of cell cycle blockage when blockage occurs during the Gl interval (Appendix). Observations, however, indicate that the unelapsed portion of the Gl interval is postponed and must be traversed following release of the cell cycle block before IDS can occur [27]. This observation is difticult to reconcile with concentration-dependent regulatory mechanisms and suggests that the basis of the timing of the Gl interval may be more complex than a simple bimolecular regulatory mechanism will allow. APPENDIX Simulation

of the Paramecium Cell Cycle

Model

This model is based on the activator-inhibitor cell cycle model of Alberghina et al. [l] and an earlier Paramecium cell cycle model [8]. Rate constants. kO=rate of decay of protein synthesizing system; kl=rate of synthesis of protein synthesizing system; kZ=rate of production of activator; k3=rate of reaction of activator and inhibitor; k4=rate of mass increase; k6=rate of DNA synthesis; k5=rate of inhibitor production; k,=growth rate as fraction of maximal rate. Threshold levels. T1=Minimum activator concentration for initiation of DNA synthesis; T*=Maximum inhibitor concentration for inhibition of DNA synthesis; T3=DNA increment required for initiation of DNA synthesis.

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Variables. M=cell mass; D=macronuclear DNA content; D;=initial macrocnuclear DNA content; A=amount of activator; Z=amount of inhibitor; P=size of the cell’s protein synthesizing system. Cell growth. Selection of variable-limiting rate of increase in size of protein synthesis system. RLV =

M when M>D D { when DsM *

Decay and growth of protein synthesizing system dPldt = -koP + k, RLV.

Activator is made with amount being proportional to either cell mass (3) or size of protein synthesizing system (4) dAldt = k2 M-k3AZIM

(3)

dAldt = k2 P-k3AZIM.

(4)

Inhibitor reacts with activator and both are lost. dlldt = - k3AZ/M.

(5)

dMldt = k4P,

(6)

dDldt = k5P.

(7)

The cell grows:

DNA is synthesized:

Initiation

of DNA synthesis.

Initiation of DNA synthesis occurs when AsT 1 and Z
DNA synthesis is terminated at a fixed time interval (18 % of normal cell cycle) after point of commitment to division. Commitment to cell division. Commitment to cell division occurs when Termination

of DNA synthesis.

Inhibitor is pulse synthesized at the point of commitment to cell division in an amount proportional to either the size of the protein synthesizing system (8) or the macronuclear DNA content (9). Production

of inhibitor.

dZ= k6P

(8)

dZ= k6D

(9)

Results

Figure 4 shows the pattern of increase in DNA content and cell mass during a steady-state cell cycle, along with the concentrations of activator and inhibitor.

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365

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-123 wloo(3 2 80-

:$

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10 2030405060 708090100 STAGE IN CELL CYCLE (‘lo)

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Fig. 4. Simulation of steady state Paramecium cell cycle. Macronuclear DNA content (larger open circles) and cell mass (larger tilled circles) as percentages of the initial value (left abscissa). Concentration of inhibitor (smaller tilled circles) and activator (smaller open circles) in arbitrary units (right abscissa). All variables are expressed as functions of stage in the cell cycle (as %). k,,=O.10337; k,=0.1112; k,=O.1112; /c,=o.2; /r,=o.O0730; ,&=O.Oll; /rh=l.o; k,=l.O; T,=0.22; T*=O.lS; T,=66. Fig. 5. Simulation of increase in cell mass by blockage of the cell cycle for a period equivalent to 75% of the duration of a normal cell cycle. The values shown are initial values for successive cell cycles. The perturbation occurs in cell cycle 1. DNA content (larger open circles) and cell mass (larger tilled circles) are expressed as percentages of the initial values for the normal cell cycle. Cell cycle duration (small circle with dot) and Gl duration (crosses) are expressed as a percentage of the normal cell cycle duration. Inhibitor concentration (smaller tilled circles) and activator concentration (smaller open circles) are in arbitrary units.

The sudden rise in inhibitor concentration at 0.72 in the cell cycle corresponds to the pulse synthesis of inhibitor at the point of commitment to cell division. The corresponding drop in activator concentration is a consequence of the reaction of inhibitor and activator to produce an inactive product (Eqs. (3~(5), above). Threshold inhibitor and activator concentrations were chosen so that IDS occurs at 0.25 in the normal, unperturbed cell cycle. Pulse synthesis of inhibitor at the time of commitment to division rather than at fission was required to simulate the observed elimination of the Gl interval when cells began the cell cycle with mass greater than the normal mass at IDS [24]. Several variations of the model were examined. These differed in the rules for generation of the activator and inhibitor. Activator was produced at rates proportional to either cell mass (Eq. (3)) or the size of the protein synthesizing system (Eq. (4)). Inhibitor was pulse synthesized in amounts proportional to either DNA content (Eq. (8)) or the size of the protein synthesizing system (Eq. (9)). There was little difference between these models in the patterns of change in cell mass and DNA content during the course of the normal cell cycle. However, all variations of the model failed to account for two important observations. First, observations indicate that when the cell cycle is blocked during the Gl interval, the unelapsed portion of the normal Gl interval is executed following the removal of the cell cycle block prior to IDS 1271.In the models IDS occurs immediately upon termination of cell cycle blockage (Fig. 5). This is a consequence of the attainment of threshold levels of activator and inhibitor prior to release of the cell cycle blockage. Second, the duration of the

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Berger and Ching

Gl interval is proportionally lengthened when the cell cycle is extended by reduction of growth rate [ 121. None of the models produced proportional extension of the Gl interval when the growth rate (k,) was reduced. When inhibitor is produced in an amount proportional to DNA content the Gl interval remains approximately constant. When inhibitor production is proportional to the size of the protein synthesizing system, the Gl interval is eliminated at reduced growth rates. Because the models did not produce appropriate extension of the Gl interval at reduced growth rates, it was not possible to realistically simulate the effects of nutrient shifts at various points in the cell cycle on the timing of IDS in the subsequent cell cycle. This study was supported by Grant A-6308 of NSERC Canada to J. D. Berger.

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