JOURNAL OF BACTERIOLOGY, Feb. 1970, p. 561-567Copyright © 1970 American Society for Microbiology

Vol. 101, No. 2Printed in U.S.A.

Growth in Volume of Euglena gracilis Duringthe Division Cycle1E. S. KEMPNER AND A. G. MARR

National Institute ofArthritis and Metabolic Diseases, Bethesda, Maryland 20014 andDeDartment ofBacteriology, University ofCalifornia, Davis, California 95616

Received for publication 14 November 1969

The distribution of volumes of Euglena gracilis cells was measured conducti-metrically. The volume spectrum of cultures in balanced growth was analyzed by themethod of Collins and Richmond. The kinetics of volume increase of Euglena isneither linear nor exponential; the growth rate of small and large cells is low, but in-termediate size cells show the largest growth rate.

The most direct method of estimating thekinetics of growth of cells during their divisioncycle is to record periodically the image formedby light microscopy of a growing cell; the volumeis estimated from a silhouette by assuming thatthe cell has a regular geometric form. Unfortu-nately, this direct method has serious limitations:it is difficult to maintain a constant local environ-ment in microcultures (18); the errors in deter-mination of volume are large, particularly forcells as small as bacteria, but also for larger cells,because of the error in assuming a regulargeometric form; and minimizing error by poolingdata taken on several cells is not possible (8).

Conductimetric measurement of volumes ofcells has much higher precision and, if coupledwith automatic pulse height analysis (10, 14),permits measurement of the volume of largenumbers of cells. Conductimetric analysis is notnecessarily destructive, but, with contemporaryequipment, it is not possible to measure atintervals the volume of a particular growing cell.The analysis of Collins and Richmond (5)

permits a calculation of growth rate as a functionof size from a measurement of the distribution ofvolume of a sample of cells drawn from a culturein balance growth. This analysis has been appliedto conductimetric measurements of volumedistributions of bacteria (11), and of mammaliancells in culture (1).

Microscopic determinations of the cellularvolumes of two protozoa, amoeba (20) andTetrahymena (4), have been reported. The dis-tribution of volumes of Euglena cells has beenmeasured conductimetrically (6), but the dis-tribution was not analyzed.

1 Sixth paper in a series entitled "The Molecular Biology ofEuglena gracilis."

MATERIALS AND METHODS

Axenic cultures of E. gracilis Klebs ATCC 12716were grown in 150 ml of liquid culture in cotton-plugged 500-ml Erlenmeyer flasks on a shaker in awater bath at 26 C. The cultures were illuminated foran interval of 12 hr per day by two 40-w "cool white"fluorescent lamps providing 1,000 lux at the watersurface. The composition of the culture medium was asfoIlows (in milligrams per liter): L-glutamic acid,3,000; KCI, 3,000; MgSO4-7H20, 39; KH2PO4, 44;NH4Cl, 79; CaCl2-2H20, 7.35; FeCl3-6H20, 5.0;ZnCl2, 41.72; CuCl2, 0.404; MnCl2*4H20, 72.0;CoCl2-6H20, 1.62; NaMoO4-2H20, 20.2; H3BO3,0.56; Nal, 0.024; thiamine hydrochloride, 1.0; andvitamin B12, 0.0002. This medium differs from thatused previously (12) by a reduced concentration ofcalcium and the addition of KCI to facilitate conducti-metric measurements. Neither of these changes alteredthe growth rate of the population.

Counting and volume measurements were done withthe electronic apparatus previously developed formeasuring bacteria (10). A sample of the culture waspassed through a small orifice (150-,um diameter "Elec-trozone" orifice; Particle Data Corp., ElmhurstIll.) at a flow rate of 6.0 ml/min (mean velocity 5.7m/sec). A constant electric current of 0.25 ma wasmaintained throughout the orifice; the passage of acell generates a signal which is a function of the cellularvolume. This signal was amplified, shaped, and fed to apulse-height analyzer to obtain the volume distribu-tion. Approximately 104 cells were measured in 1 min.

Conductimetric counting of Euglena cells was donewith the equipment described above and agreed withhemocytometer counts within the sampling error ofthe microscopic method (4% SE).

Extracted ragweed (Ambrosia) pollen (a gift fromR. H. Berg, Particle Data Corp.) was used as a volu-metric standard. Because of the difficulty of wetting,the pollen was first extracted with acid alcohol (con-centrated HCI-95% ethyl alcohol; 1:1; v/v). Thevolume distribution of the pollen was measuredperiodically during the extraction procedures; the

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pollen shrank progressively and the distribution ofvolume sharpened as indicated by a decreasing meanand coefficient of variation. After 3 to 5 hr in acidalcohol, the pollen was washed several times and sus-pended in culture medium, in which it remained stableat room temperature for at least several months.The time constants used for shaping the pulses gen-

erated by particles of the order of 1 ,um3 (10) werefound to be inappropriate. Optimal time constantswere established by comparing the electronic measure-ment with optical measurements of pollen grains. Thetime constants for the first differentiator affected onlythe scale not the shape of the pulse-height distribution;if large, the time constants for integration and seconddifferentiation caused only minor changes. For theresults reported the time constants were as follows:first differentiator, 8 ,Asec; integrator, 1.6 ,Asec or 1msec; second differentiator, 12.8 JAsec or 1 msec. Thesesettings were found to have no appreciable effect onthe distribution of pulse heights. Pollen volume, meas-ured electronically, was compared with the volumescalculated from photomicrographs of 1,001 pollengrains, assuming a spherical shape. A comparison ofthe volume distribution obtained by these two methodsis shown in Fig. 1. Our results agree with similarmeasurements reported by Anderson and Petersen (2).

Photomicrographs were taken of wet mounts ofof pollen or Euglena cells using a Zeiss 25X (0.45numerical aperture) objective. The negatives were pro-jected to an overall enlargement of approximately1000 X for measurement or tracing.

FIG. 1. Distribution of volume of ragweed pollendetermined electronically (+) compared with a histo-gram based on measurement of photo.nicrographs of1,001 pollen grains. The mean, mode, and standarddeviation of volume by microscopy were, respectively,3,309,3,240, and 595.3 pm3. The electronic measurementswere scaled to normalize the mean; the mode andstandard deviation were, respectively, 3,497 and403.8 1m3.

Numerical data were analyzed with an IBM 7044computer.

RESULTS

Volume distribution of cells of E. gracilis. Theaccuracy of the conductimetric measurement ofthe volume distribution of Eaglena cells wasassessed by comparing the results of conducti-metric and microscopic estimates. Samples weretaken from a culture growing exponentially at adensity of 105 cells/ml. One sample was analyzedconductimetrically, and several photomicro-graphs were made of wet mounts prepared from asecond sample. Silhouettes of the cells in photo-micrographs were traced, and the digital co-ordinates of several hundred points defining theoutlines were recorded on magnetic tape. Themajor axis of each profile was located as a line,about which rotation of the points gave a mini-mal volume. Two estimates of the volume werecomputed assuming symmetry about this axis,first for the points above and then for the pointsbelow the axis. The volume was taken as theaverage of the two estimates. The distribution ofvolumes of 285 cells obtained in this manner iscompared with the electronic spectrum in Fig. 2.The values of the means of the two distributionswere 3,322 and 2,966 ,um3, respectively. Afternormalization of the means, the probability that

FIG. 2. Distribution of volume of cells of Euglenagracilis determined electronically (+) compared with a

histogram (...... ) of volumes obtained from the

analysis of photomicrographs of 285 cells. The mean,mode, and standard deviation were, respectively, 3,322,2,450, and 1,089 jum3 from microscopy and 2,966, 2,150,and 804.3 pAm3 from electronic measurement by usingragweed pollen as a reference.

562 J. BACmERioL.

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KEMPNER AND MARR

the two distributions differ by chance is 0.059(chi-square).

Effect of shape on conductimetric determinationof volumne. It has been reported that conducti-metric measurement of volume is biased by theshape of the objects (3, 9). If so, the distributionof volumes determined conductimetrically issystematically biased by the distribution of shapesof Euglena cells. Growing cells of E. gracilis areclosely approximated by prolate elipsoids withan axial ratio of 2 or 3 to 1; typical cells are shownin Fig. 3a. When suspensions of such cells areshaken on a "vortex" mixer for 60 sec, the cellsassume a nearly spherical shape (Fig. 3b). After10 to 20 min, the cells resume their original shape.Conductimetric volume distributions obtainedfrom normal and from treated cells (within 60sec after treatment) are shown in Fig. 4. The twospectra do not differ detectably, indicating thatthe volume measurement is independent of theshape of the cell.Volume distribution during balanced exponential

563

FIG. 4. Distribution of volwne of cells of Euglenagracilis. (0) Untreated cells and (+) cells immediatelyafter agitation.

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a.

Fio. 3. Photomicrographs of cells of Euglena

gracilis. (a) Untreated cells and (b) cells immediately

after agitation.

growth. In liquid culture, populations of E.gracilis grow exponentially to a concentrationnear 106 cells/ml (12). The distribution ofvolumes of the cells in such cultures was invariantuntil the population neared the end of expo-nential growth. The constancy of the volumedistribution is indicated by periodic estimates ofthe mean cell volume (Fig. 5). Approximatelyone generation before the specific growth ratebegins to decline the mean cell volume increases;as the specific growth rate declines, the mean cellvolume decreases until stationary phase isreached.Over a period of several months a number of

cultures of E. gracilis were analyzed (Table 1).The volume distribution of cells in independentcultures varied somewhat more than in samplesfrom the same culture; however, neither thedoubling time nor volume distribution variedgreatly. Table 1 also shows that growth of E.gracilis in the dark (actually dim light) does notalter the growth rate or the volume distribution.

Analysis of Euglena volume distribution. Theanalysis described by Collins and Richmond (5)was applied to the data obtained for E. gracilis.The equation of Collins and Richmond, equation1, may be written as

Y(x) = x(x) [2#(e) - (e) x(e)] de

in which V(x) is the rate of growth of cells of sizex; k is the specific growth rate of the population;and A(x), qo(x), and X(x) are the frequency

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GROWTH IN VOLUME OF E. GRACILIS

functions of size of newly formed, dividing, andextant cells, respectively. The equation requiresthat k, X, (p, and i/ are independent of time. Bothk and X have been shown by experiment to beconstant, and the constancy of X implies con-stance of s° and y6 (17).The functions p and i,/ were not measured. The

calculation of V(x) from equation 1 was basedon approximating V(x) by an incomplete gammafunction of given mean and variance, and 41(x)was computed as equation 2, +(x) = 2(p(2x),which is precise if division produces two daughtersof equal size (5) and is a good approximationif division is not equal (19).

In practice, a guess was made for the meanand variance of S(x); the experimental values forX(x) were displayed by the computer on anoscilloscope together with the calculated valuesof p(x), +t(x), and V(x). Inspection of the resultsled to new choices of mean or variance, or both,of sp(x). An optimal choice was based on thecriteria used by Collins and Richmond (5) andHarvey et al. (11). These involved the range of

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X, s, and y6 and the bounds of the function V. Theexperimental values of X(x) and the optimalchoice for the functions sp(x) and y6(x) are shownin Fig. 6.The calculated growth rate, V(x), is shown in

Fig. 7. The growth rate of small cells is low; asthe volume of the cell increases, the growth rateincreases until a maximal growth rate of 205,um3/hr is reached at a volume of 3,000 ,um3.

Effect of starvation on cell volume. From the

TABLE 1. Analysis of independent culturesof E. gracilis

Volume parametersRatio Doubling- ___ ______

of light timeto dark Ma Moe CoefficienttodarkDoublingMean Mode of variation

hr hr pm3 sm

12:12 2,912a 2,062 0.38215.0 3, 000a 2,200 0.40613.8 2,925a 2,081 0.411

3,388b 2,427 0.3660:24 14.1 3X215b 2,397 0.367

aTime constants were: first differentiator, 8jAsec; integrator, 1.6 ,usec; second differentiator,12.8,Asec.bTime constants were: first differentiator, 8

,usec; integrator, 1 msec; second differentiator,1 msec.

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HQ=MFIG. 5. Exponential growth of Euglena gracilis.

(a) Number of cells per milliliter (logarithmic scale)as a function of time in hours; (b) mean cell volume(cubic micrometers) determined conductimetrically.During exponential growth, the specific growth ratewas0.0484 1 0.0013 hr-1; themean volume was 2,985 ±32 Am'; and the standard deviation about the mean was1,207 :i 20 pom.

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FIG. 6. Distributions of volumes of cells, X, deter-mined conductimetrically, and of newly formed, V/, anddividing cells, zp, estimated as indicated. The functionip was an incomplete gamma function with a mean of3,800 um' and coefficient of variation of0.22.

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KEMPNER AND MARR

constancy in volume distribution and exponen-tiality of increase in number of cells (Fig. 5), itappears that the culture was in balanced growth.The sensitivity of the index of mean volume ofthe cells was examined by depriving cells of theirsource of carbon and energy. The cells werewashed with a medium free of glutamic acid andbuffered with citrate to maintain the same pH ascomplete medium. The washed cells were sus-pended to a density of 104 cells/ml in this glutamicacid-free medium. Under these conditions, thecells are starved for carbon and energy. Cellnumber remained constant (Fig. 8, circles), andthe mean cell volume rapidly fell to approxi-mately 50% of the normal value. After 100 hr ofstarvation, glutamic acid was added back to theculture; cell division was resumed, and thespecific growth rate rapidly approached theoriginal rate. Mean cell volume increased withno detectable lag and appears to have overshotthe original mean cell size.

DISCUSSION

The certainty of the calculated growth ratedepends upon (i) the realization of a steady state,(ii) the accuracy of the measurement of thevolume distribution, X, and (iii) the assumptionsregarding (p and 4,6.The experimental results support the conten-

tion that the population under the conditions ofcultivation was in a steady state; i.e., the intrinsicproperties of the population were constant. Thedistribution of volumes of cells and the specificgrowth rate were constant during the growth of agiven culture up to a population density of atleast 101 cells/ml and varied only slightly amongindependent cultures over a period of severalmonths. The biochemical profile of Euglena isalso constant under these conditions (12). Itmight appear surprising that the alternate 12-hrperiods of light and dark did not perturb meas-urably the physiological state of the cells. How-ever, both the specific growth rate and thevolume distribution are not significantly affectedby cultivation in the dark (Table 1). Our resultson the lack of photic effects for cells growing withglutamic acid as a nutrient are in general agree-ment with the results of Edmunds (7). Thesensitivity of the volume distribution to physi-ological perturbation is shown clearly by theresponse to starvation for the source of energy(Fig. 8).A bias in conductimetric measurement of the

volume distribution would affect seriously thecalculated kinetics of growth (13). One source ofbias is the variation in form of the cells (ap-proximately prolate ellipsoids with axial ratios

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FIG. 7. Growth rate of cells ofEuglena gracilis as afunction of cellular volume. The ordinate, V(x), isgrowth rate in cubic micrometers per hour and theabscissa is cellular volume in cubic micrometers.Growth rate was computed from the data shown in Fig.6 according to equation 1.

ranging from 1:1 to 3:1). The measurementsmade by Gregg and Steidley (9) suggest asignificant effect of shape in conductimetricsizing. Anderson et al. (3) have interpreted as ashape effect the change resulting from celldivision on the distribution of pulse-heights ob-tained by conductimetric sizing. Hurley (un-published results) has obtained an analyticsolution for the resistivity of prolate spheroidswhich predicts a significant effect of shape.Nevertheless, the experiment shown in Fig. 3and 4 demonstrates that a large difference in theshape of cells before measurement does not affectthe volume distribution measured conducti-metrically. Either the cells are distorted to acommon shape by the measurement itself or theinstrument used in our measurements minimizesthe effect of shape of the cells. Of course, sourcesof bias other than shape are not eliminated.The error in assuming a function p for calcula-

tion of growth rates has been discussed in pre-vious reports (5, 11), in which it was shown thatother reasonable functions for qp do not alter thegrowth rate calculations. The validity of theassumption for Escherichia coli has been con-firmed by measurement (15). Unfortunately we

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GROWTH IN VOLUME OF E. GRACILIS

have been unable to devise a technique fordirect estimation of the distribution of volumesof dividing or of newly formed cells of E. gracilis.The exponential kinetics of growth of micro-

bial populations reveals nothing about thekinetics of growth of individual cells beyond thefact that the average time for a cell to double itsbirth size is closely approximated by the doublingtime of the population.

It is frequently assumed a priori that kineticsof growth of individual cells is either linear(constant rate) or exponential (rate proportionalto size). Although these are by no means theonly alternatives, it is of interest whether a givenset of data can distinguish them. The microscopicdata shown as the histogram in Fig. 2 cannot. Astatistical test was made by comparing (chi-square) the microscopic data with a theoreticalsolution X computed from equation A-8 inreference 11. The probability was 0.49 for differ-ence by chance, assuming either exponential orlinear kinetics of growth. It is clear that a samplemuch larger than 285 cells is required to dis-tinguish these alternatives.The conductimetric analysis shown in Fig. 2

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FIG. 8. Effect of starvation and restoration ofL-glutamic acid. (a) number of cells per milliliter(logarithmic scale); (b) mean volume (cubic microm-eters) of cells. At 9 hr (first arrow) the culture wasdivided. One portion of the culture (+) served as a

control. The cells from the remainder were washed andresuspended in medium free of glutamic acid (0); at103 hr (second arrow) glutamic acid was restored.

am I ~~~~I I

++

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function of age. The volume was computed from therates shown in Fig. 7, assuming a volume of 1,200 Mm3

at zero time.

is based on 146,000 cells, a sample size more thanadequate to distinguish between linear andexponential kinetics. Assuming hypothetically abirth size of 1,200 jAm3, we can compute thevolume of a cell as a function of age from thegrowth rates given in Fig. 7; the calculation isshown in Fig. 9, from which it is apparent thatgrowth of cells of E. gracilis is neither linear norexponential. Rather, the kinetics resemble thekinetics of growth computed for Escherichia coliand Azotobacter agilis (10, 16).

This complex growth pattern suggests thatthere may not be a single simple mechanismregulating cell growth, but that a series of inde-pendent events controls the process.

LITERATURE CITED

1. Anderson, E. C., G. I. Bell, D. F. Petersen, and R. A. Tobey.1969. Cell growth and division. IV. Determination of vol-ume growth rate and division probability. Biophys. J. 9:246-263.

2. Anderson, E. C., and D. F. Petersen. 1967. Celi growth anddivision. II. Experimental studies of cell volume distribu-tions in mnammalian suspension cultures. Biophys. J.7:353-364.

3. Anderson, E. C., D. F. Petersen, and R. A. Tobey. 1967. Aneffect of cell shape on apparent volume as determined witha Coulter aperture. Biophys. J. 7:975-977.

4. Cameron, I. L., and D. M. Prescott. 1961. Relations betweencell growth and division. V. Cell and macronuclear volumesof Tetrahymena pyriformis HSM during the cell life cycle.Exp. Cell Res. 23:354-360.

5. Collins, J. F., and M. H. Richmond. 1962. Rate of growth of

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Bacillus cereus between divisions. J. Gen. Microbiol. 28:15-33.

6. Cook, J. R. 1961. Euglena gracilis in synchronous division.I. Dry mass and volume characteristics. Plant Cell Physiol.2:199-202.

7. Edmunds, L. N., Jr. 1965. Studies on synchronously dividingcultures of Euglena gracilis Klebs (Strain Z). I. Attainmentand characterization of rhythmic cell division. J. Cell.Comp. Physiol. 66:147-158.

8. Errington, F. P., E. 0. Powell, and N. Thompson. 1965.Growth characterisitcs of some gram-negative bacteria.J. Gen. Microbiol. 39:109-123.

9. Gregg, E. C., and K. D. Steidley. 1965. Electrical Countingand Sizing of Mammalian Cells in Suspension. Biophys.J. 5:393-405.

10. Harvey, R. J., and A. G. Marr. 1966. Measurement of sizedistribuions of bacterial cells. J. Bacteriol. 92:805-811.

11. Harvey, R. J., A. G. Marr, and P. R. Painter. 1967. Kineticsof growth of individual cells of Escherichla col and Azoto-bacter agills. J. Bacteriol. 93:605-617.

12. Kempner, E. S., and J. H. Miller. 1965. The molecular biologyof Eugkna gracilis. I. Growth conditions and cellularcomposition. Biochim. Biophys. Acta 104:11-17.

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13. Koch, A. L. 1966. Distribution of cell size in growing cul-tures of bacteria and the applicability of the Collins-Richmond principle. J. Gen. Microbiol. 45:409-417.

14. Kubitschek, H. E. 1958. Electronic counting and sizing ofbacteria. Nature (London) 182:234-235.

15. Marr, A. G., R. J. Harvey, and W. C. Trentini. 1966. Growthand division of Escherichia coli. J. Bacteriol. 91:2388-2389.

16. Marr, A. G., P. R. Painter, and E. H. Nilson. 1969. Growthand division of individual bacteria, p. 237-261. In P. M.Meadow and S. J. Pirt (ed.). Microbial growth, 19th Symp.Soc. Gen. Microbiol. Cambridge Univ. Press, Cambridge,England.

17. Painter, P. R., and A. G. Marr. 1968. Mathematics of micro-bial populations. Annu. Rev. Microbiol. 22:519-548.

18. Powell, E. 0. 1956. An improved culture chamber for thestudy of living bacteria. J. Roy Microsc. Soc. 75:235-243.

19. Powell, E. 0. 1964. A note on Koch and Schaechter's hypoth-esis about the growth and fission of bacteria. J. Gen. Micro-biol. 37:231-249.

20. Prescott, D. M., 1955. Relations between cell growth and celldivision. I. Reduced weight, cell volume, protein contentand nuclear volume of Amoeba proteus from division todivision. Exp. Cell Res. 9:328-337.

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