patterns of protein synthesis during the cell cycle of the fission yeast ... · 2005. 8. 22. ·...

J. Cell Sci. 5», 263-285 (1982)Printed in Great Britain © Company of Biologists Limited 1982

PATTERNS OF PROTEIN SYNTHESIS

DURING THE CELL CYCLE OF THE FISSION

YEAST SCHIZOSACCHAROMYCES POMBE

J. CREANOR AND J. M. MITCHISON*Department of Zoology, University of Edinburgh, West Mams Road, Edinburgh EHg 2JT,Scotland

WITH A STATISTICAL APPENDIX BY D. A. WILLIAMS,

Department of Statistics, University of Edinburgh

SUMMARYThe rate of protein synthesis through the cell cycle of Schizosaccharomyces pombe has been

determined from the incorporation of pulses of [JH]tryptophan in synchronous culturesprepared by selection in an elutriating rotor. This selection procedure caused minimal per-turbations as judged by asynchronous control cultures, which had also been put through therotor. The rate of synthesis showed a periodic pattern rather than a smooth exponential increase.There was a sharp increase in the rate at an 'acceleration point' at about 0-9 of the cycle.Model-fitting by a novel procedure suggests that the average single cell has an increasing rateof protein synthesis for the first 60 % of the cycle and a constant rate for the remaining 40 %.

The same pattern was shown in less extensive experiments with PHjleucine and [3H]phenyl-alanine. It was also shown in a series of size mutants, which indicates that the pattern is notsize-related, in contrast to earlier work on the rates of synthesis of messenger RNA. However,one large mutant (ede 2.M35T2O) had a significantly earlier acceleration point.

Care was taken to justify the assumption that the rate of incorporation of tryptophan was avalid measure of the rate of protein synthesis. A tryptophan auxotroph was used to eliminatethe problem of endogenous supply and the size of the metabolic pool was measured throughth; cycle. This pool did not show cell-cycle related fluctuations. An operational model of thepools is presented.

INTRODUCTION

The cell cycle of the fission yeast Schizosaccharomyces pombe has been extensive-ly studied over the last 25 years in terms both of division control and of growthduring the cycle. Nevertheless, the pattern of total protein synthesis, a majorcomponent of growth, has not been defined clearly. An early study by Mitchison &Wilbur (1962) on autoradiographs using a method equivalent to ' age-fractionation'showed an increasing rate of incorporation of labelled amino acids through the cyclebut the method, like most other age-fractionations, was not sufficiently sensitive toshow the fine detail of rate changes. We therefore set out to measure the rate of syn-thesis using pulse labels of amino acids in synchronous cultures prepared by selectionwith an elutriating rotor (Creanor & Mitchison, 1979). This method causes less

• Author for correspondence.

264 J- Creanor andj. M. Mitchison

perturbations than other methods of synchronization in S. pombe and also allows theproduction of asynchronous controls.

There were two particular reasons for undertaking this study. The first was to seewhether protein synthesis followed one or ether of two simple patterns - a smoothexponential without periodicities in rate or a 'linear' pattern with a doubling in rateonce per cycle (Mitchison, 1969). Linear patterns with periodic rate doubling havebeen found in S. pombe for total dry mass (Mitchison, 1957), enzyme activity (Mitchi-son & Creanor, 1969), messenger and ribosomal RNA (Fraser & Moreno, 1976) andcarbon dioxide production (Creanor, 1978). Periodic pattern are of interest becausethey pose questions about the nature of the rate controls and whether they are tightlylinked to the DNA-division cycle. In the case of carbon dioxide production (Creanor,1978) and enzyme potential (Benitez, Nurse & Mitchison, 1980), the controls do notappear to be closely linked since the rate changes continue for a time after the DNA-division cycle has been delayed or blocked. The second reason for examining proteinsynthesis stemmed from the work of Fraser & Nurse (1978, 1979). Their evidencesuggested that the cycle position of the rate-doubling step in the linear pattern formessenger and ribosomal RNA varied according to cell size. In cells small at division,for example wee mutants, the step was later in the cycle than in wild-type cells. Ifthese steps generate periodicities in the rate cf protein synthesis, then the predictionwould be that the timing of these periodicites would also be size-related.

In the first half of this paper, we present evidence that the rate of incorporation ofamino acids, primarily tryptophan, dees show cell cycle periodicity, though it doesnot follow the simple linear pattern. The pattern is also not size-related. In thesecond half, we show the rate of incorporation is a valid measure of the rate of proteinsynthesis and examine the tryptophan pools and the balance between endogenousand exogenous supply of the precursor.

MATERIALS AND METHODS

Organisms

Some experiments were done with strain N.C.Y.C. 132 (A.T.C.C. 24751) of S. pombe.Most experiments, however, were done on a wild-type strain 972h~ (originally obtained fromProfessor U. Leupold, Bern) and its mutants. The mutants wee 1.50 and wee 2.1 divide atabout half the size of the wild-type strain (Thuriaux, Nurse & Carter, 1978). wee 1.302 ispartially defective in the wee 1 gene and is intermediate in size between wee 1.50 and wild type(Fantes, 1981). ede 2.M35 is an allele of ede 2 (Nurse & Thuriaux, 1980), which divides at alarger size than wild type when grown at 25 °C but is blocked at nuclear division when transferedto 35 °C. ede 2.M35T2O is likely to be a revertant in this gene. It was obtained by selecting forgrowth and large size at 35 °C after ultraviolet irradiation of ede 2.M35. After backcrossing towild type and tetrad dissection, there was no reappearance of the cdc~ phenotype in fivetetrads. This was confirmed with free spore analysis where there was no cdc~ segregants in565 progeny colonies. Of 100 colonies examined, 51 had cells of normal size and 49 had largecells, indicating that a single gene was involved, trp 4.47 is a tryptophan auxotroph (providedby P. Thuriaux) with a defective phosphoribosyl transferase (Schweingruber & Dietrich, 1973).

Protein synthesis in the yeast cell cycle 265

Media and growth conditions

Strain 132 was grown in a minimal medium with acetate buffer, EMM2 (Mitchison, 1970).Strain 972 and its mutants were grown in EMM3, a modified version of EMM2 with a phtha-late buffer to reduce clumping with this strain. Its composition was (per litre): glucose, 10 g;NH4C1, 5 g; Na,SO4, 0.1 g; MgCl,.6 H,O, 1 g; CaCl,.2 H,O, 15 mg; KH phthalate, 3 g;Na,HPO4, i-8 g; vitamins and trace elements as in EMM2. The 'EMM3-glutamate' used forthe trp 4 mutant experiments had sodium glutamate at 5 g/1 in place of the NH4C1. Cultureswere shaken or stirred and, except where specified, the growth temperature was 35 °C. Some ofthe earlier experiments, especially with 132, were done at 32 °C but the doubling time was thesame (145 min).

Synchronous cultures and asynchronous control cultures

Synchronous cultures were prepared by selecting small cells in a Beckman JE-6 elutriatorrotor. In summary, an exponential-phase culture was pumped through the rotor and theyeast cells accumulated in the rotor cell. When sufficient cells had accumulated, the pumpspeed was increased and the first fraction of the effluent contained small cells early in the cycle.These were diluted, if necessary, with the same medium and grown on as a synchronous culture.Asynchronous control cultures were made in the same way except that the whole contents ofthe rotor cell was used.

This method has been described in detail by Creanor & Mitchison (1979). The only changein technique was that the rotor, after treatment with diethyl pyrocarbonate, was washed outwith 1 1 sterile distilled water followed by 1 1 warm growth medium.

Radioactive tracers, cell collection and cell counting

The following radioactive amino acids were used: L-[G-'H]rryptophan, 93-326 GBq/mmol(Radiochemical Centre, Amersham and New England Nuclear); L-[4,s-3H]leucine, 1-96-2-15 TBq/mmol; and L-phenyl-[2,3-*H]alanine, 592 GBq/mmol (both from RadiochemicalCentre, Amersham). It was necessary to filter off fine paniculate matter in the ['H]tryptophansolution, immediately before use, with a Millex-GS filter (Millipore, 0-22 /tm pore size).

Cells were collected on glass fibre (Whatman GF/C). For total uptake samples, the filterswere washed four times with the appropriate non-radioactive amino acid at 1 mg/ml, and fourtimes with water. For acid-insoluble incorporation, the preceding washes were followed bytreatment with 10 % trichloracetic acid for 10 s and then two further washes with water. Thefilters were then dried, immersed in 0.56 % butyl-PDB in toluene and counted in a Packardmodel 2425 liquid scintilation spectrometer.

Cell numbers were determined on a Coulter Counter (Industrial model D) with a 100/tmaperture.

RESULTS

Pools and perturbation

The only satisfactory method of determining the fine detail of the rate of synthesisof macromolecules is to use pulse labels of an appropriate precursor. Given certainassumptions, the amount of percursor incorporated over a short period is a measureof the rate of synthesis of the macromolecule. An important assumption is that thereis only a small pool of precursor, which is used directly for synthesis. This pool wecall the ' metabolic pool'. If this pool is small, incorporation will rise linearly from theorigin in a time-course experiment in which incorporation is followed after theaddition of label. If the pool is large, incorporation will proceed at an increasing rateuntil the pool reaches a constant specific activity. A single pulse measurement is not a

266 ]f. Creanor and J. M. Mitchison

20 40 0

Time (min)INT

40

Fig. i. Kinetics of total uptake (A —A) and incorporation (O—O) of labelledamino acids added to asynchronous exponential-phase cultures, A. f'HJleucine instrain 132 growing in EMM2 at 32 °C; 0-5 ml samples of a culture treated at timeo with 19 kBq/ml. Initial cell number 2-4x10' cells/ml. B. [sH]phenylalanine instrain 972 growing in EMM3 + 1 gh/ml phenylalanine at 35 °C; 0-25 ml samples of aculture treated at time o with 93 kBq/ml. Initial cell number, I-I x io 1 cells/ml.C. [3H]tryptophan in strain 972 growing in EMM3 + 10 /tg/ml tryptophan at 35 CC;0-25 ml samples of a culture treated at time o with 740 kBq/ml. Initial cell number,2-0 x 10" cells/ml. D. [aH]tryptophan in Up 4.47 growing in EMM3-glutamate +I2'S j"g/ml tryptophan at 35 °C; 02 ml samples of a culture treated at time o with463 kBq/ml. Initial cell number, 2-9 x 10' cells/ml. ( ) Backward extrapolationof the line through the points between 30 and 50 min. It intercepts the abscissa atINT (12 min).

satisfactory measurement of synthesis in a situation where the pool is large and theincorporation rate is still increasing, since its value will depend on pool size as wellas on rate of synthesis.

Fig. 1 A, B, c shows that the metabolic pool is small with leucine in strain 132 andwith phenylalanine and tryptophan in strain 972. Incorporation rises linearly from theorigin, or nearly so. These experiments were dene with asynchronous cultures andwe consider later whether there may be changes in the size of the metabolic poolthrough the cycle. There is a marked contrast between these curves and that for thetrp 4.47 mutant in Fig. 1 D. In the mutant, the pool is large since it takes 30 minbefore the incorporation achieves a constant rate. As with the other experiments,


100 1-

50 -

0 1 2 3 4 5 6Time(h)

Fig. 2. Rate of leucine incorporation in strain 132 at 32 °C in EMM2. Each point isthe mean of two samples. Curve A, synchronous culture. Samples (025 ml) labelledfor 14 min with 93 kBq [*H]leucine. Arrows indicate acceleration points. 10 arbitraryunits (a.u.) = 4420 c.p.m. Curve B, cell numbers in synchronous culture A. 10 a.u. =1-50x10' cells/ml. Curve C, synchronous culture. Labelling as for A. 10 a.u. =1150 c.p.m. Curve D, cell numbers in synchronous culture C. 10 a.u. = 4-06 xio8 cells/ml. Curve E, asynchronous control culture. Samples (1 ml) labelled for13 min with 148 kBq [3H]leucine. 1 a.u. = 4550 c.p.m. Curve F, cell numbers incontrol culture (E). 1 a.u. = 152 x io* cells/ml.

there is a divergence between uptake and incorporation, though it is larger here. Weconsider the problem of this radioactive pool later.

Synchronous cultures have certain advantages over age-fractionation techniquesin the analysis of cell-cycle events, but they do suffer from the problems of perturba-tions caused by the selection procedure (Mitchison, 1977). It is essential therefore toexamine control cultures that have been put through all the synchronizing procedureapart from the final step of selecting small cells. These cultures should show a smoothexponential rise in cell number and also in cellular parameters such as rate of incor-

268 J. Creanor and y. M. Mitchison

100

50

3

gI

10

0 1 2 3 4 5 6Time (h)

Fig. 3. Rate of tryptophan incorporation in strain 972 at 35 °C in EMM3 + 10 /ig/mltryptophan. Each point in curves A and C is the mean of two samples. Curve A, syn-chronous culture. Samples (0-25 ml) labelled for 12 min with 307 kBq [JH]tryptophan.Arrows indicate acceleration points. 10 arbitrary units (a.u.) = 1560 c.p.m. Curve B,cell numbers in synchronous cultured. 10 a.u. = 0-92 x 10* cells/ml. Curve C, syn-chronous culture. Labelling as for A. 1 a.u. = 682 c.p.m. Curve D, cell numbers insynchronous culture (C). 1 a.u. = 0-35 x 10' cells/ml. Curve E, asynchronous controlcultures. Samples labelled for 14 min with 370 kBq [JH]tryptophan. 1 a.u. = 4170c.p.m. Curve F, cell numbers in control culture E. 1 a.u. = 1-85 x 10' cells/ml.

poration. As will be shown, such cultures can be obtained, but even so there may besome initial perturbation lasting for the first 45 min.

We started this work some four years ago using selection from sucrose gradients(Mitchison & Vincent, 1965) but found marked perturbations in the controls withcarrier-free [3H]leucine incorporation in strain 132. We then developed a method ofusing the elutriator rotor to select small growing cells and also to produce controlcultures. This method avoided collecting, and perhaps starving, the cells on a filterand also centrifuging through a sucrose gradient. It very largely eliminated theperturbations in strain 132 but it did not do so with strain 972 in EMM3 (Creanor &


100 r-

50

3

g 10!5

0 1 2 3 4 5 6Time (h)

Fig. 4. Rate of tryptophan incorporation in mutant toee 2.1 at 35 °C in EMM3 +1 0 /*g/ml tryptophan. Each point is the mean of two samples. Curve A, synchronousculture. Samples (0-25 ml) labelled for 12 min with 307 kBq [3H]tryptophan. Arrowsindicate acceleration points. 10 arbitrary units a.u. = 1520 c.p.m. Curve B, cell num-bers in synchronous culture A. 10 a.u. = 2-0 x io* cells/ml. Curve C, synchronousculture. Labelling as for A, except 266 kBq were used. 1 a.u. = 600 c.p.m. Curve D,cell numbers in synchronous culture C. 1 a.u. = 0-77 x io ' cells/ml. Curve E,asynchronous control culture. Labelling as for A, except 370 kBq were used. 1 a.u. =1870 c.p.m. Curve F, cell numbers in control culture E, 1 a.u. = 1-82 x 10* cells/ml.

Mitchison, 1979). Further experiments showed that the perrubations in 972 could beeliminated by adding leucine to the growth medium, but this expanded the metabolicpool and produced incorporation kinetics similar to Fig. 1 D. Carrier-free pHJphenyl-alanine gave smaller perturbations than leucine and a few experiments were done withthis tracer, but the controls were usually more perturbed than the example shownlater (Fig. 3E). Eventually we settled en pHJtryptophan as the best of the tracers weexamined in 972. To avoid the perturbations found with carrier-free tracer, themedium contained 10/jg/ml tryptophan. At this level of exogenous tryptophan, the

270 J. Creanor and J. M. Mitchison

1

1

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l r

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972

132

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Fig. 5. Cell-cycle maps of the acceleration points. Each solid triangle marks the cellcycle position of an acceleration point in a synchronous culture, those above the linebeing in the first cycle and those below in the second cycle. The cell cycle is fromcell division to division. The arrow and cross-bar show the mean and standard error.T, with tryptophan; PA, with phenylalanine; L, with leucine. The bottom left mapgives the approximate position of nuclear division (ND) and the stages of the DNAcycle (G,, S and G,).

metabolic pool was not significantly expanded (Fig. 1 c). We have no cogentexplanation for the differences between the strains or of the cause of the perturbations.It is possible that they may be connected with variations in the endogenous supply,since they are least marked when this supply is cut off or diminished by the presenceof exogenous amino acid. It will be shown later that the endogenous supply of trypto-phan is probably shut off when the exogenous concentration is io/tg/ml.

Synchronous cultures and asynchronous control cultures

We have measured the rate of amino acid incorporation in some 45 synchronouscultures using different strains and size mutants, and different amino acids. All theexperiments were of the same form. A sample (sometimes in duplicate) was takenfrom the culture, incubated at the growth temperature for 12-14 min with the labelledamino acid, and a measurement was then made of the incorporated counts. This isproportional to the rate of incorporation during that period. This procedure wasrepeated every 15 min for 6-6-5 h at 32-35 °C (rather more than two cell cycles formost strains). Cell numbers were also counted. Asynchronous control cultures thathad been through the elutriator rotor were treated in the same way, except that theywere usually followed for a shorter time. Some 70 of these controls had to be examinedbecause of the problems of reducing perturbations.

The results from a limited number of cultures are shown in Figs. 2-4, each ofwhich has two synchronous and one control culture. Fig. 2 shows leucine pulses in


Table 1. Protein content of size mutants at 350 C in EMM-$

Mean protein(pg)/cell at

Strain division

wee 1.50 io-owee 2.1 10-0

wee 1.302 I2'4972 h- (WT) 178Cdc 2.M3ST2O 26-6

Measurements by S. G. Elliot (unpublished) using the folin reaction (Lowry, Rosebrough,Farr & Randall, 1951).

strain 132 growing in EMM.2 at 32 °C. These are the strain and growth conditionsused in much of the earlier work on S. pombe in this laboratory. It is clear that there areperiodic changes in the rate of incorporation. At, or a little before, the mid-point ofrise in cell number in the synchronous cultures there is a sharp rise in the rate ofincorporation. We call this the 'acceleration point'. The rate of rise tends to fall offafter the acceleration point and may reach zero before the next acceleration point.These periodic changes appear to be cell-cycle events, since their period is nearlyequal to the cell cycle and they are absent in the asynchronous control.

These patterns of incorporation rate are clearly not in accord with a smooth exponen-tial increase in rate through the cycle. Nor are they in accord with the linear patternmentioned earlier. If there was a linear pattern in single cells, incorporation rateshould show the same symmetrical sigmoid curve as number increase. The ratecurves are not symmetrical on either side of their point of half rise and, on average,they rise less sharply than the number curves. The interpretation of these rate curveswill be discussed later.

Fig. 3. shows the pattern of incorporation of tryptophan for strain 972 at 35 °C in aslightly different minimal medium, EMM3. The rate patterns are basically the sameas those in Fig. 2, though it is worth pointing out that one of the synchronous cultureshas a more sharply defined pattern than the other even though there is little differencein the degree of synchrony shown in the number curves. We have found this happeninga number of times in synchronous cultures and cannot explain it. The incorporation ofanother amino acid, phenylalanine, was examined in strain 972 at 32 °C and thepatterns were similar to those in Fig. 3.

A conclusion from these results is that the same pattern of incorporation occurs withthree different amino acids. This makes it more likely that this is the pattern of totalprotein synthesis and that it is not distorted by periods of slow or rapid incorporationof any one amino acid.

Fig. 4 shows the pattern of incorporation of tryptophan for the small mutant wee2.1. Here again, there are the same pattern and approximately the same position of theacceleration points.


2 13x

I 1230 60

Time (min)

90

5 -oX

Ea.6

Time(h)

Fig. 6. Kinetics of total uptake (A —A) and incorporation (O—O) with a 4-hpulse of labelled tryptophan. [3H]tryptophan (93 kBq/ml) was added at o h to trp4.47 growing at 35 °C in EMM3-glutamate + 15 /ig/tryptophan. Initial cell number0-9 x 10' cells/ml. Sample size, 02 ml. At 4 h, the cells were washed free of tracer andresuspended in the original medium. Inset: incorporation only after resuspension,in an identical experiment except that the initial cell number was 2-nx ioe cells/mland the [8H]tryptophan level was 111 kBq/ml.

Figs. 2-4 illustrate patterns that were found in all the experiments on synchronouscultures. The cell-cycle maps in Fig. 5 show the timing of the acceleration points in awider range of experiments including 972 at 25 °C, 972 at 32 °C, three other sizemutants, wee 1.50, wee 1.302 and cdc 2.M35r2O, and also trp 4.47. The method ofdetermining the rate of incorporation in trp 4.47 was somewhat different and will bedescribed later. Except for the large size mutant cdc 2.M3sr2O, which has an earlytiming (074 of the cycle), all other strains have mean values for the accelerationpoint which lie in G1 or early S phase between o-8i and 093 of the cycle. Thesemeans do not differ significantly from the mean of 0-85 of the cycle for strain 972with [3H]tryptophan at 35 °C (f-test, P > 0-05). There is no consistent differencebetween the timing of the acceleration points in the first and the second cycle.

The main purpose of using the size mutants was to see whether the incorporationpatterns were related to cell size. One model would be to have the acceleration pointtriggered by attaining a critical size. However, comparison of Fig. 5 and Table 1shows that there is no simple relationship between cell size and the acceleration point.The timing of the acceleration points is the same in wild-type cells and in the threewee mutants that vary between 56 % and 70 % of the protein content of wild type. Thelarge mutant cdc 2.M35r2O does have an acceleration point that is 01 of the cycleearlier than wild-type cells. But this point should have been 06 of the cycle earlier, if


Endogenous supply

IMetabolic

pool• Protein

Exchangeablepool

Outsidecell

Insidecell

Fig. 7. Diagram of tryptophan pools.

it occurred when the mutant cells were the same size as wild-type cells at division(assuming exponential increase of protein).

Tryptophan mutant, pools model and pools through the cycle

There are several reasons why the amounts of label incorporated after pulses mightnot reflect the rate of protein synthesis during the cycle. First, the metabolic poolmight vary in size through the cycle. Secondly, the relative proportions of the exo-genous and endogenous contributions to the pool might vary. Thirdly, there mightbe variable contributions to the metabolic pool from other storage pools. These couldall alter the specific activity of the metabolic pool and distort the relation betweenmeasured incorporation and actual synthesis. In principle, the best way of avoidingthese problems is to measure directly the specific activity of the metabolic pool, butin practice it is difficult to find a way of extracting the metabolic pool by itself. Wewere unable to find such a way with the tryptophan pool in S. pombe, and we thereforefollowed an alternative course using a tryptophan auxotroph trp 4.47 and kineticexperiments. The use of an auxotroph eliminates the endogenous supply except froma storage pool.


100 r

50

<

10

0 1 2 3 4 5 6 7Time (h)

Fig. 8. Rate of tryptophan incorporation in mutant trp 4.47 at 35 °C. Each incorpora-tion point is the slope of a regression line through samples started at 30 min afteradding [3H]tryptophan to a sample of the culture (see text). The timing of this pointis taken as the mid-point of the sample times. Curve A, synchronous culture inEMM3-glutamate+ 125 /tg/ml tryptophan. Portions (07 ml) taken at 30, 35, 40-5and 45 min after labelling the sample with 618 kBq/ml [3H]tryptophan. Arrowsindicate acceleration points. 10 arbitrary units (a.u.) = 29-0 c.p.m.1 Curve B, cellnumbers in culture A. 10 a.u. = o-86 x io* cells/ml. Curve C, synchronous culturein EMM3-glutamate+ 15 /*g/ml tryptophan. Samples taken at 30, 34, 38, 42, 47 and52 min after labelling with 833 kBq/ml |3H] tryptophan. 1 a.u. = 16-0 c.p.m.1

Curve D, cell numbers in culture C. 1 a.u. = 0.56 x io8 cells/ml.

The auxotroph grew better in a medium containing glutamate and it required notless than i2fig/m\ tryptophan as a supplement. At i2-5/£g/ml, the metabolic poolwas expanded, as shown by the curved incorporation kinetics in Fig. 1D. The poolproperties of the auxotroph appeared to be slightly different from those of wild-typecells since the latter showed a much smaller metabolic pool with exogenous tryptophanat 10 fig/m\ (Fig. ic) and at 15/fg/ml. It is unlikely that the glutamate mediumaltered the pool size, since wild-type cells showed identical uptake and incorporationkinetics in EMM-glutamate (+ io/ig/ml tryptophan) as in EMM3 (Fig. ic).


10

fte2

OB

1 6

Time (h)Fig. 9. Changes in the size of tryptophan and leucine metabolic pools in synchronouscultures. The intercept is proportional to the size of the metabolic pool (see text).Curve A, means (and standard errors) from three synchronous cultures of mutanttrp 4.47 at 35 °C in EMM3-glutamate + 125 to 15 /tg/ml tryptophan. Two of thecultures are those shown in Fig. 8 and experimental details are given in the legend.Arrows mark the beginning and end of the cell cycle (mid-points of the cell number'steps'). Curve B, synchronous culture of strain 972 at 32 CC in EMM3 + 20 /*g/mltryptophan. Experimental details similar to those for Fig. 8, curve A, but labellingwas with 1-48 MBq/ml [3H]tryptophan and initial cell number was 1-3 x 10* cells/ml.Curve C, synchronous culture of strain 132 at 32 °C in EMM2. Experimental detailssimilar to those for Fig. 8, curve A, but labelling was with 185 kBq/ml[3H]leucine and initial cell number was 1-7 x io* cells/ml. Sampling of the portionwas started at 4-5 min since there was little curvature in the incorporation kinetics.

Pulse experiments can provide useful information about the pools. In Fig. 6, aculture of the auxotroph was labelled with [3H]tryptophan for 4 h. During that time,the radioactive pool increased and there was upward curvature in both total uptakeand incorporation due mainly to growth in a period equal to 1 -4 times the doublingtime of the auxotroph (170 min). After 4 h, the tracer was removed by suspending thecells in non-radioactive conditioned medium. The incorporated counts rose for afurther 20 min and then remained constant for 2-5 h until the end of the experiment.A repeat experiment on this part of the incorporation curve, giving better detail, isincluded in Fig. 6. The total accumulated uptake dropped for the first 50 min andthen remained constant leaving an appreciable radioactive pool, which also stayedconstant.

276 J. Creanor andj. M. Mitchison

Table 2. Rate of incorporation of exogenous tryptophan in trp 44.7 auxotroph and inwild-type 972 at different concentrations of tryptophan and at 32-35 °C

Tryptophan Rate of incorporationStrain (jig/m\) (amol/cell per min)

trp 4.47972972972972972972

12-20

0 7 1

1-2

51 0

IS

SO

152 (0-22; 13)

O - I I I

O-OI2

O781-47 (018; s)i-6o1-61 (0-06; 3)

Where there are replicate experiments, the numbers in parenthesis give the standard devia-tion and number of experiments. The absolute rates are less certain than the relative ratesbecause of the difficulties of determining the efficiency of counting incorporated radioactivity.

The ratio of the maximum rate of incorporation/min in 972 (i"6i) to that in trp 4.47 (1.52)is 1 -06. But 972 has a shorter generation time (145 min) than trp 44.7 (172 min). If this isallowed for, the ratio becomes 0-90.

In operational terms, we interpret this experiment in terms of three pools (Fig. 7).The first is the metabolic pool on the way to protein. Amino acids enter this poolfrom the medium or from the endogenous pathways (except in the auxotroph). Thispool is expandable since experiments with wild-type cells (not shown) gave curvedincorporation data similar to Fig. 1D when the tryptophan in the medium wasincreased from 1 o to 50/^g/ml. The second pool is the storage pool. This fills up duringthe labelling period but it does not empty after the removal of the tracer and, inradioactive terms, accounts for the constant difference between uptake and incorpora-tion in the last hours of the experiment. The third pool is exchangeable with themedium and accounts for the fall in total counts for the first 50 min after the removal.As with many pool models, the location and chemical nature of the pools are un-certain. So also is the positioning of some of the arrows; for example, the storage poolmight well be fed from the metabolic pool. But what is important for our argumentis the evidence that the storage pool does not feed into the metabolic pool, at any rateunder these conditions of growth. This follows from the absence of any increase inincorporated counts after the first 20 min following removal of the tracer. What thenis happening during these first 20 min ? It is likely that this represents the emptyingof the radioactivity of the metabolic pool into protein. It followed approximatelyfirst-order kinetics with a time to half-saturation cf 7-5 min. The inverse situationoccurred in the first part of the incorporation curve in Fig. 1D when the pool radio-activity was becoming saturated. The kinetics were similar and the time to half-saturation was 9-5 min (mean of 6 experiments).

Given the assumption that the rise in incorporated counts after tracer removal inFig. 6 came from the metabolic pool, then the counts in this pool at removal were16% of the total pool counts. If it is further assumed that there was no increase in theradioactivity in the storage pool during the first 50 min, then it contained 49% of the


total pool counts, leaving the remaining 35% in the exchangeable pool. These pro-portions will of course change with varying pulse lengths. Similar curves to those inFig. 6 were obtained with pHJtryptophan (carrier-free and with 10 fig/ml tryptophan)in strain 972 and with carrier-free pHJleucine and [3H]phenylalanine in strain 132(data not shown). The most conspicuous difference was the absence of detectablecounts in the contracted metabolic pools, as might be expected from Fig. 1 A, B, c.

In order to follow the pattern of tryptophan incorporation through the cycle of theauxotroph, it was necessary to change the method of measuring the rate of incorpora-tion because of the size of the metabolic pool (Fig. 1 D). Instead of a single sample, anumber of samples were taken starting at 30 min after adding the label when theincorporation had become linear. A regression line was calculated and its slope gavethe rate of incorporation. Provided the incorporation has become linear, this slope isindependent of pool size. The size of the metabolic pool is given by the intercept (/)of this line with the abscissa. With first order kinetics, the time of half-saturation =/In 2.

The incorporation rates in two synchronous cultures of the auxotroph are shownin Fig. 8. There is the same pattern as in the earlier graphs (Figs. 2-4) with accelera-tion points towards the end of the cycle (Fig. 5). There are rather fewer points perhour, a necessary disadvantage of this method.

We also used the intercept values to see whether there was evidence of fluctuationsin the metabolic pool related to the cell cycle. Fig. 1 shows the means from threesynchronous cultures of the auxotroph. Although there are fluctuations, they do nothave the periodicity of the cell cycle. Fig. 9 also shows the application of the samemethod to strain 972 growing with a partially expanded metabolic pool in 20 /*g/mltryptophan and to strain 132 labelled with carrier-free pHJleucine. Again, there is noevidence of cell-cycle periodicity.

Although the tryptophan auxotroph was likely to have a very marked reduction inthe endogenous supply of tryptophan, it also appeared that this supply was largely cutoff in wild-type cells growing in tryptophan. Table 2 shows that the amount of exo-genous tryptophan incorporated by the mutant was about the same as that of wild-typecells growing in concentrations of tryptophan of 10/ig/ml and above.

DISCUSSION

We have been at some pains to try to justify the assumption that the patterns ofincorporation reflect the patterns of protein synthesis through the cycle. The samepatterns are shown with three different amino acids, so it is unlikely that there isdifferential incorporation, e.g. tryptophan-rich protein synthesized at a particularstage of the cycle. The trp auxotroph also showed the same incorporation patternusing a method that is not influenced by the size of the metabolic pool. Although theexperiments in Fig. 6 showed no overall flow from the storage pool to the metabolicpool, a small flow at one stage of the cycle would not have been detected. Such a flow,however, is unlikely in view of the absence of cell-cycle fluctuations in pool size shownin Fig. 9. Although strain 972 has its endogenous supply of tryptophan cut off when


the tryptophan in the medium is at 10/ig/ml or more (Table 2), it is conceivable thatthis control is relaxed at one stage of the cycle, and that there is a burst of tryptophansynthesis that is fed into the metabolic pool. But evidence against comes from thepool measurements in Fig. 9, which show no cell-cycle fluctuation in the tryptophanpools of strain 972 measured by intercept. It remains a remote possibility that instrain 972 (but not in the auxotroph) the balance between the exogenous supply anda small surviving endogenous supply varies during the cycle even though the poolis constant. We have less information about the other two amino acids, but leucineand phenylalanine behave much like tryptophan in experiments similar to that inFig. 6, and Fig. 9 shows a small leucine pool without cell-cycle fluctuations. As aresult of all these experiments, we think it reasonable to assume that bulk proteinsynthesis has the same rate patterns as amino acid incorporation.

The pattern of protein synthesis that emerges from these results is not a smoothexponential increase with a doubling of rate spread over the whole cycle. Nor is it alinear pattern with a sharp rate-doubling at one point in the cycle. If it was, the ratecurve would be the same shape as the cell number curve. Instead, the pattern liesbetween these two simple alternatives. This makes it more difficult to achieve the realobject of cell cycle analysis of imperfect synchronous cultures, the definition of thecycle pattern of the average single cell. The single cell pattern cannot be derived bydirect numerical analysis of the synchronous culture results without making toomany simplifying assumptions. It is however, possible to get an approximate answerby model-fitting and we present a novel approach in the Appendix. Two curves forthe average single cell pattern of protein synthesis are shown in the Appendix (Fig. A1D and E). They are much sharper than the patterns in the synchronous culturesbecause the imperfect synchrony of the cultures has been allowed for. They are alsosharper because they are fairly simple models. The exact shape of the rate curve forthe average single cell would be difficult to define but it is reasonable to concludethat most of the rate increase takes place in about the first 60% of the cycle and thatthereafter there is a plateau with little or no increase in rate.

This pattern of increase for total protein may also be shown by individual proteins,or at any rate by the majority of abundant proteins. Some evidence for this comes fromthe measurements of Elliott (unpublished observations) of ribosomal RNA synthesisduring the cell cycle of S. pombe. The rate of RNA synthesis does not show a sharpstep-doubling and is similar to the protein pattern. If the synthesis of ribosomal pro-teins is controlled concomitantly with ribosomal RNA (Warner & Gorenstein, 1978)then this group of proteins (which comprise about one third of the total protein) willshow a pattern of rate increase similar to bulk protein. A second simple alternative isthat individual proteins have sharp step-doublings in rate but the timing of the stepsis different. A cascade of sharp steps through the first 60 % of the cycle would givethe observed pattern for total protein. Some evidence for this is provided by the findingthat three enzyme activities appeared to show sharp steps in rate early in the cycle(Mitchison & Creanor, 1969), though it is difficult to be precise about the sharpness ofa rate increase from absolute measurements of activity. Nor of course does enzymeactivity necessarily reflect the amount of enzyme protein. A critical test of these two


alternatives will have to wait until rate measurements can be made on individualproteins.

A third possible alternative comes from the following argument. It is well known thatRNA synthesis ceases during mitosis in higher eukaryotes and that there is often aresulting reduction in protein synthesis at the same time (Mitchison, 1971). Forunknown reasons, this does not appear to happen in yeast. Most of the methods thathave been used however, are not sufficiently discriminating to detect a gap of only afew minutes in RNA or protein synthesis. P. A. Fantes (unpublished) has shown bymodelling that such a gap combined with exponential synthesis of protein in therest of the cycle will give a pattern in a synchronous culture not unlike those describedin this paper. We have therefore re-examined the data of Mitchison & Lark (1962) ongrain counting in autoradiographs of S. pombe cells pulse-labelled with pHJadenine.A gap in synthesis should cause an increase in variation of the grain counts in cellstowards the end of the cycle. We found no significant change in the coefficient ofvariation through the cycle after a 1 min pulse label. We also found no change insimilar autoradiographs after a 10 min pulse label with f^HJleucine. It seems there-fore that this third alternative is unlikely.

Can this periodic pattern of protein synthesis rate be related to other cycle events?The results from the size mutants show that it is not related to cell size. This is incontrast to the results of Fraser & Nurse (1978, 1979) on messenger RNA and mayimply that the rate of protein synthesis through the cycle is not directly related to therate of messenger RNA synthesis. The pattern is also not related temporally to DNAsynthesis, wee mutants have an S phase that is later than that in wild-type cells. Inwee 1.50 the 5 phase is 0-29 of a cycle later than wild type, and in wee 2.1 it is 0-23of a cycle later (Nurse & Thuriaux, 1977). Yet the acceleration points of the proteinpatterns of the mutants in Fig. 5 are not significantly different from wild-type cells.The most likely temporal relation is with mitosis or cell division. For wild-type 972cells, the acceleration point is at 0-9 of the cycle. This is later than mitosis, which isat about 0-75 of the cycle, and is near the time when the cell plate (septum) hascompleted the physiological separation of the two daughter cells. The relationbetween the protein pattern and the events of mitosis and division can be investigatedin greater detail in cdc mutants and this work is in hand.

Net accumulation of protein will be less than protein synthesis if there is degradationand turnover. There is no direct evidence about this in S. pombe, but results withSaccharomyces cerevisiae suggest that there is little protein breakdown in growingcells. Halvorson (1958) found that proteins have an average half-life of 18 days incells in the exponential phase of growth. Elliott & McLaughlin (1979) showed thatperiodic degradation or modification of proteins is not a general feature of the cellcycle of budding yeast.

It is not easy to compare the detailed pattern of protein synthesis in 5. pombe withthose in most other eukaryotic cells. In general, they show an increase in rate duringinterphase following either an exponential pattern or a linear pattern with a ratedoubling (Mitchison, 1971). The methods used, however, were not sufficientlysensitive in most cases to discriminate between either of these two simple patterns

280 J. Creanor and y. M. Mitchison

and the intermediate one that we have found in S. pombe. Nor has much attentionbeen paid to the pool problem and the assumption that the incorporation of pulselabels of amino acids is a valid measure of the rate of protein synthesis. In addition,there is the problem of the fall-off of protein synthesis at the time of mitosis, which isevident in, for example, mammalian cell cultures (Scharff & Robbins, 1965; Martin,Tomkins & Granner, 1969; Ronning, Pettersen & Seglen, 1979). This spreads intothe apparent Gx and G2 phases of synchronous cultures and may distort the ends ofthe interphase pattern.

It is easier to compare the protein patterns in S. pombe and Saccharomyces cerevisiaesince both yeasts appear to show no diminution in synthesis during mitosis. A recentcareful study by Elliott & McLaughlin (1978), using age-fractionation in an elutriatingrotor and double-labelling, showed that exponential synthesis gave a better fit to thedata than a linear or a periodic pattern. The two yeasts may indeed have differentpatterns, but we have some doubts as to whether the elutriation.technique coulddiscriminate between exponential synthesis and a pattern similar to that in S. pombe,particularly since the main difference between them is towards the end of the cyclewhere the age-fractionation is least efficient.

Finally, a comparison should be made with earlier work on S. pombe from thislaboratory. Two papers are particularly relevant. The first, by Mitchison & Wilbur(1962), described the pattern of amino acid incorporation through the cycle usinggrain counting on autoradiographs and age-classification from cell length. Themethod is less sensitive than synchronous cultures, both because cells have to begrouped in large length classes to reduce the variations in grain counts and becauseof uncertainty about the beginning and end of the cycle. This latter problem isinherent in all age-fractionations. The results gave a better fit to an exponentialpattern than to a linear pattern, but the fit to an exponential was not particularlygood. They are certainly not inconsistent with the pattern found in the present work;indeed all the amino acid patterns (leucine, glycine and methionine at 25 °C) showedan upwards rise in rate after an acceleration point towards the end of the cycle.

The second paper, by Stebbing (1971), described some of the characteristics of theamino acid pools and how they changed through the cycle. His results were similarthough his interpretation of two kinetic experiments was slightly different from ours.He also called our metabolic pool the' internal pool' and our storage pool the ' expand-able pool'. The results showed that there were no fluctuations in the relative size ofthe internal amino acid pool during the cell cycle in minimal medium. A later paper(Stebbing, 1972) extended the analysis to individual amino acids, and also found nofluctuations. This is in accord with cur results on tryptophan and leucine.

We would like to express our thanks to Peter Fantes, Steve Elliot and Harlyn Halvorson forhelpful discussions; and to Yvonne Bisset, Linda Farrar and Cathy McDougall for experttechnical assistance. This work was supported by a grant from the Science and EngineeringResearch Council.


REFERENCES

BENITEZ, T., NURSE, P. & MITCHISON, J. M. (1980). Arginase and sucrase potential in thefission yeast Schizosaccharomyces pombe. J. Cell Set. 46, 399-431.

CREANOR, J. (1978). Carbon dioxide evolution during the cell cycle of the fission yeast Schizo-saccharomyces pombe. J. Cell. Set. 33, 385-397.

CREANOR, J. & MITCHISON, J. M. (1979). Reduction of perturbations in leucine incorporationin synchronous cultures of Schizosaccharomyces pombe. J. gen. Microbiol. 112, 385-388.

ELLIOTT, S. G. & MCLAUGHLIN, C. S. (1978). Rate of macromolecular synthesis through thecell cycle of the yeast Saccharomyces cerevisiae. Proc. natn. Acad. Set. U.S.A. 75, 4384-4388.

ELLIOTT, S. G. & MCLAUGHLIN, C. S. (1979). Synthesis and modification of protein during thecell cycle of the yeast Saccharomyces cerevisiae. J. Bad. 137, 1185-1190.

FANTES, P. A. (1981). Isolation of cell size mutants of a fission yeast by a new selective method:characterization of mutants and implications for division control mechanisms. J. Bact. 146,746-754-

FRASER, R. S. S. & MORENO, F. (1976). Rates of synthesis of polyadenylated messenger RNAand ribosomal RNA during the cell cycle of Schizosaccharomyces pombe. J. Cell Set. 21,497-521-

FRASER, R. S. S. & NURSE, P. (1978). Novel cell cycle control of RNA synthesis yeast. Nature,Land. 271, 726—730.

FRASER, R. S. S. & NURSE, P. (1979). Altered patterns of ribonucleic acid synthesis during thecell cycle: a mechanism compensating for variation in gene concentration. J. Cell Set. 35,25-4°-

HALVORSON, H. (1958). Studies in protein and nucleic acid turnover in growing cultures ofyeast. Biochim. biophys. Acta 37, 267-276.

LOWRY, O. H., RosEBROUGH, N. J., FARR, A. L. & RANDALL, R. J. (1951). Protein measure-ment with the folin phenol reagent. J. biol. Chem. 193, 256-275.

MARTIN, D., TOMKINS, G. M. & GRANNER, D. (1969). Synthesis and induction of tyrosineaminotransferase in synchronized hepotoma cells in culture. Proc. natn. Acad. Set. U.S.A.62, 248-255.

MITCHISON, J. M. (1957). The growth of single cells. I. Schizosaccharomyces pombe. Expl CellRes. 13, 244-262.

MITCHISON, J. M. (1969). Enzyme synthesis in synchronous cultures. Science 165, 657-663.MITCHISON, J. M. (1970). Physiological and cytological methods for Schizosaccharomyces

pombe. In Methods in Cell Pkysiology, vol. 4 (ed. D. M. Prescott), pp. 131-165. New York,London: Academic Press.

MITCHISON, J. M. (1971). The Biology of the Cell Cycle. London: Cambridge University Press.MITCHISON, J. M. (1977). Enzyme synthesis during the cell cycle. In Cell Differentiation in

Microorganisms, Plants and Animals (ed. L. Nover & K. Mothes), pp. 377-401. Jena: VEBGustav Fischer Verlag.

MITCHISON, J. M. & CREANOR, J. (1969). Linear synthesis of sucrase and phosphatases duringthe cell cycle of Schizosaccharomyces pombe. J. Cell Set. 5, 373-391.

MITCHISON, J. M. & LARK, K. G. (1962). Incorporation of JH-adenine into RNA during thecell cycle of Schizosaccharomyces pombe. Expl Cell Res. 28, 452-455.

MITCHISON, J. M. & VINCENT, W. S. (1965). Preparation of synchronous cell cultures bysedimentation. Nature, Lond. 205, 987-989.

MITCHISON, J. M. & WILBUR, K. M. (1962). The incorporation of protein and carbohydrateprecursors during the cell cycle of a fission yeast. Expl Cell Res. 26, 144-157.

NURSE, P. & THURIAUX, P. (1977). Controls over the timing of DNA replication during thecell cycle of fission yeast. Expl Cell Res. 107, 365-375.

NURSE, P. & THURIAUX, P. (1980). Regulatory genes controlling mitosis in the fission yeastSchizosaccharomyces pombe. Genetics 96, 627-637.

RUNNING, O. W., PETTERSEN, E. O. & SEGLEN, P. O. (1979). Protein synthesis and proteindegradation through the cell cycle of human NHIK 3025 cells in vitro. Expl Cell Res. 123,63-72-

SCHARFF, M. D. & ROBBINS, E. (1965). Synthesis of ribosomal RNA in synchronized HeLacells. Nature, Lond. 208, 464-466.

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SCHWEINGRUBER, M. E. & DIETRICH, R. (1973). Gene-enzyme relationships in the tryptophanpathway of Schtzosaccharomyces pombe. Experientia 29, 1152-1153.

STEBBING, N. (1971). Growth and changes in pool and macromolecular components of Schizo-saccharomyces pombe during the cell cycle. J. Cell Set. 9, 701-717.

STEBBING, N. (1972). Amino acid pool components as regulators of protein synthesis in thefission yeast Schtzosaccharomyces pombe. Expl Cell Res. 70, 381-389.

THURIAUX, P., NURSE, P. & CARTER, B. (1978). Mutants altered in the control co-ordinatingcell division with cell growth in the fission yeast Schizosaccharomyces pombe. Molec. gen.Genet. 161, 215-220.

WARNER, J.R. & GORENSTEIN, C. (1978). Yeast has a true stringent response. Nature, Land.375. 338-339-

(Received 21 March 1982)

APPENDIXA STATISTICAL ANALYSIS TO INFER THE PATTERNOF PROTEIN SYNTHESIS IN A SINGLE CELL

INTRODUCTION

The aim of this analysis is to infer a simple deterministic model for the increase inthe rate of protein synthesis over the lifetime of a single cell. The data compriseestimates of the total number of cells, N(t), and the rate of protein synthesis, S(t), in asynchronous culture at times t, at intervals of 15 min over approximately 6 h, duringwhich time three generations develop.

The first stage of the analysis makes simple assumptions about the random processunderlying the joint distribution of birth and division times in each generation, andestimates the parameters of these distributions from the cell counts, N(t). The secondstage assumes a family of deterministic models for the increase in rate of proteinsynthesis during the lifetime of a single cell, and identifies that member of the familywhose expectations with respect to the estimated distributions of birth and divisiontimes best fit the observed rates, S(t).

To represent the analysis mathematically let ij,<^ denote the times of birth anddivision in a typical single cell of the tth generation, and \etf(biyd{) denote their jointprobability density function. Introduce function n(b,d,t), which takes a value ofunity if b < / < d, and s(b,d,t), which measures the rate of protein synthesis at timet in a single cell that was born at time t and will divide at time d. Both functions take avalue of zero for t outside the interval b ̂ t ^ d. Then, assuming that all cells areviable, so that the m first generation cells form 2 m second generation cells and 4 mthird generation cells, the expected values (E) of N(t) and S(t) are given by:

E[N(t)] = I 2*->m fn(M«')/(Mi)dW. (0

E[S(t)] = 2 2<-'m Ubt,di,t)f(bt,dt)dbiddi- (2)<-i J

The first stage of the analysis estimates the density functions f{bitd^) by fitting theregression equation (1). The second stage substitutes these estimates into regressionequation (2) and then fits the regression to estimate the parameters of s(b,d,t).


Estimation of the probability density functions f (b,, dj)

The following model is assumed. All cells of the first generation were born at time,/ib. In each generation the cycle times, ci = di — bi, are distributed Normally withmean fic and variance <J\. There is a negative correlation, p, between the cycle time, ct,of an tth generation cell and the cycle times, ci+1, of its daughters. Under theseassumptions equation (1) reduces to:

where <1> denotes the Normal distribution function.This non-linear regression was estimated iteratively by weighted least-squares,

assuming that the variances of observed cell counts are proportional to their expec-tations. Given estimates of fib, /i^ <rc and p the bivariate normal density functions

f), are simply determined.

Estimation of the rate function, s(b, d, t), for a single cell

It is not unreasonable to assume that the rate function is a monotonically increasingsigmoid curve doubling in value as t increases from t = b to t = d. The simplestsuch function comprises three linear segments. The lifetime of the cell is divided intothree periods of length: (d-b)plt (d~b)pi and (d-b)p3, where/>1+/>2+/>3 = 1. Duringthe first period s(b,d,t) remains constant at an initial value a, during the secondperiod it increases linearly from a to 2a, and during the third period it remainsconstant at its final value of za. For any given set of fractions pv p2, p3 the values of(ma)-1 E[S(t)] can be calculated by numerical integration. These values then formthe explanatory variable, and the observed S(t) forms the response variable, in asimple linear regression through the origin that can be fitted by least-squares toestimate the slope ma. The process is repeated for different sets of values of pi todetermine the set of values that minimize the residual sum of squares about thisregression.

Some shortcomings of the model

The three plateaux in the observed N(t) curves were often not at heights in theratios 1:2:4. ^n particular, the first plateau was usually 5-10% higher than expected,relative to the second and third plateaux. This suggests that a proportion of first-generation cells are not viable and although they contribute to all cell counts they donot divide. An extra parameter representing this proportion was introduced intoequation (1) and estimated to allow for this discrepancy.

The distribution of cell-cycle times was assumed Normal despite suggestions in theliterature that an asymmetric distribution, such as the log-normal or gamma, is moreappropriate. The Normal distribution is easier to handle and there was no consistentsuggestion, from graphical study of the fit of equation (3), that an asymmetric distri-bution would provide a better fit. Certainly, the observations are inadequate to esti-mate any parameter that measures the asymmetry of the distribution of cycle times.


10

Q.6

Time(h)

Fig. Ai. Comparison of observed rate of protein synthesis with curve given by theestimated equation (2), for three synchronous cultures. The vertical scale is log10c.p.m. to within an arbitrary additive constant. Curves A and B are the culturespreviously plotted in Figs. 3 A and C, respectively (O, measured point). Curve Cis a third culture run under similar conditions. Curves D and E represent the esti-mated function s(b,d,t), the rate of protein synthesis of a single cell corresponding tocurves A and C, respectively.

Doubtless it would be more realistic to allow for some variation in the initial birthtimes, b, by assuming them to vary Normally about fib with variance cr*. If this isdone the parameters 0%, a\ and p cannot be uniquely identified from the fit of equa-tion (1). The effect of assuming p = o, rather than <r\ = o, was in fact investigated.Although the estimated density functions, f{bt,d^, are somewhat altered this has anegligible effect on the second stage cf the analysis.

In some cultures the agreement between the best fitting model (2) and the obser-vations, S(t), was inadequate because of a mismatch between the heights of the


plateaux. Although no convincing explanation can be offered it appears that the rateof protein synthesis does not exactly double in each generation. In some generationsthe increase is less than 100%, in others it exceeds 100%. Accordingly, the modelwas modified, allowing s(b{,di,t') to increase by a factor that varies between generationsand is estimated from the data. This modification allowed a substantial improvementin the fit of equation (2) in some cultures.

Results

The Normal distribution function adequately models the observed relation betweenN(t) and t during cell division so the assumptions underlying the choice of a bivariateNormal density function for/(b^df) are not incompatible with these data. Interestfocuses on whether the use of a ' constant-then-linear increase-then-constant model'for the rate of protein synthesis during the lifetime of a single cell provides, throughregression equation (2), an adequate fit to the observed S(t) values. Three cultures areillustrated in Fig. Ai where the observed and fitted log S(t) values are plotted againstt values. The fits are not perfect, for the residuals still display some systematic relation-ship with t, and we must report that some other cultures analysed gave a poorer fitthan those illustrated here. However, we regard the agreement as good enough tojustify the retention of the s(b,d,t) function as an adequate simple approximation toreality.

Interest then centres on the estimates of the p{ values, and there is encouragingagreement between the estimates obtained from different cultures. The estimates ofpx are mostly zero, and the estimates of p2 are mostly in the range from 0-5 to 07.From this we can conclude that the rate of protein synthesis begins to increase verysoon after birth and continues to increase until 50-70% through the lifetime of thecell, after which it remains constant.

patterns of protein synthesis during the cell cycle of the fission yeast ... · 2005. 8. 22. ·...

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