[16] Measurement of size distribution with the coulter counter

[16]

MEASUREMENTOF SIZEDISTRIBUTION

171

[16] M e a s u r e m e n t o f Size D i s t r i b u t i o n w i t h t h e Coulter Counter By KAZUO SHIBATA

The instrument, the Coulter counter, 1 measures the number of particles above a preset particle volume which are present in a suspension. One can, therefore, determine the particle-size distribution from the counts at different preset threshold volumes as well as the total particle number per unit volume of the suspension. With this instrument, the errors in counting the number of particles can be greatly reduced, and the size distribution can be measured much more accurately and quickly than by light or electron microscopy. The instrument, which was originally designed for routine counting of red blood cells, I-4 have recently been applied to other cells or subcellular particles as well as to particles produced in industry. In this section the technique for use of the instrument and its applications to isolated chloroplasts and photosynthetic microorganisms are described. Illustrations are made mostly on the technique of using Model A, a simpler model for manual operation. The more advanced instrument, Model B, with a recorder or pulse-height analyzer can be used with minor modification of the technique. Principle and Operation The instrument is diagrammatically illustrated in Fig. 1. One electrode (E2) is placed in a beaker (B, 50-250 ml) containing a sample suspension (F); into the beaker is placed a vertical glass tube (D), sealed from the suspension except at the point where an orifice or aperture (A) is located. The second electrode (El) is contained in this tube. The instrument is based upon the principle that each particle or cell in the suspension, when passing through the aperture, causes a momentary increased impedance (or pulse) to the steady flow of electric current through the aperture between the two electrodes. The aperture limits the volume of the medium (electrolyte) in which the change of impedance takes place. To operate the instrument, stopcock C1, which is connected to a bottle under a constant reduced pressure, is first opened so that the level of ~W. H. Coulter, Proc. Nat. Electron. Conf. 12, 1034 (1956). 2G. Brecher, M. Shneiderman, and G. J. Williams, Amer. J. Clin. Pathol. 26, 1439 (1956). 3C. F. T. Mattern, F. S. Brackett, and B.J. Olson,J. Appl. Physiol. 10, 56 (1957). 4j. L. Grant, M. C. Britton, and T. E. Kurtz, Amer.J. Clin. Pathol. 33, 138 (1960).

172

METHODOLOGY

[16]

I To Pump Ci C~ Medium

M

FIG. 1. Simplifieddrawing of the Coulter counter, showing aperture (A), sample suspension (F) in a beaker (B), stopcocks (Ca and C2), aperture tube (D), electrodes (El and E2) for pulses, electrodes (To, T1, and T2) for switching, and manometer (M).

mercury in the right arm of m a n o m e t e r M is raised and balanced at a higher level. W h e n the stopcock is closed, the mercury falls back, drawing the particle suspension into the tube t h r o u g h the aperture. When particles pass t h r o u g h the aperture, they cause electrical pulses, and the n u m b e r of pulses during the passage of mercury from switch T1 to T2 (0.5 ml in volume between these electrodes for switching) is counted automatically. Stopcock C2, which is for flushing or filling up the tube with the medium, is kept closed during this procedure. T h e wall of the aperture plate cemented on tube D is thicker than the aperture diameter, so that the aperture is, in fact, a cylindrical tunnel. Consequently, the current between the two electrodes depends entirely on the resistance of the fluid in the tunnel. In the absence of particles, this resistance is constant, but, when a particle enters the tunnel, the current between the electrodes drops. T h e magnitude of this drop is proportional to the volume of the particle, provided that the particle diameter is less than one-third the diameter of the aperture; the measurement of particle volumes below this size is i n d e p e n d e n t of their shape. It is fairly simple to convert the current pulses into voltage pulses and to count the pulses above any given voltage. T h e voltage of particle size over which counts are made can be limited by means of a threshold control composed of electrical filters. An oscilloscope is provided so that a r o u g h visual check can be made of the particle size distribution, and

[16]

M E A S U R E M E N T OF SIZE D I S T R I B U T I O N

173

the threshold level is displayed on the oscilloscope as a brightness modulation; the pulses above the threshold level are brighter than those below it. A microscope is mounted on the side of the sample beaker to examine the condition of the aperture. Caution has to be exercised to avoid the use of a medium or a buffer containing a large number of dust particles, 'which would block the aperture. Chemicals or salts for the preparation of buffers or electrolytes often contain such foreign dust particles. Centrifugation, distillation, or filtration of the medium is helpful in removing such large particles as well as small particles which would raise the background count. A large particle blocking the aperture can be removed in the following manner. The inside of tube D is first flushed with the medium by opening both stopcocks, C1 and C~, and sudden stoppage of the medium flow by turning off stopcock C1 builds a shock of positive pressure inside the tube, which will push out the blocking particle. Another way is to open stopcock C2 quickly while stopcock C1 is closed, this will release the negative pressure suddenly. Bubbling of air in the tube through the aperture by lowering the container of suspension is helpful to clean the aperture after removal of the blocking particle. The main variables to be adjusted are the particle concentration, the conductivity of medium (or diluent), the aperture diameter and the degree of amplification of pulses controlled by a sensitivity switch. The sample suspension is diluted appropriately with a medium having a conductivity to provide an optimum electric current or resistivity through the aperture. The best signal voltage is obtained at higher resistivities, so that a relatively weak electrolyte is desirable. However, excessive resistivity raises the noise level. Resistivities of 100-2000 ohm-cm are usually chosen; 1% saline at 20 ° is about 50 ohm-cm. The use of buffers is recommended because the pH value of the medium greatly affects the resistivity. For example, 0.04 M phosphate buffer at pH 7.0 is suitable as a medium for chloroplasts, and 0.9% NaCl solution is usable for counting blood cells. The amplification can be varied stepwise from S (sensitivity) = 1 to S = 8 (or ][0), and the degree of amplification changes by a factor of approximately 2 on each step (AS = 1) of switching. Therefore, the count at S -- 2 and Vt (the threshold value) = 20, for example, is approximately equal to the count at S --- 3 and Vt --- 40. Replaceable tubes with an aperture of 30 p~ to 2000 /~ in diameter are available, and the diameter determines the counting period as well as the particle size to be measured. Particles in the range between 0.5 ~ and 1000 p~ in diameter can be measured by appropriate choice of these variables.

174

METHODOLOGY

[ 16]

Most o f the distribution measurements are made on an arbitrary relative scale (expressed by V~) of volume or in the scale (expressed by Vt) on the threshold dial u n d e r certain conditions o f the above variables. T h e s e relative scales of volume can be converted to an absolute scale (V) o f volume by use o f data on particles with a known d i a m e t e r measured u n d e r the same conditions. Plastic spheres and pollens, which are listed in Table I, are available for this purpose. A suspension o f pollen grains is p r e p a r e d by putting the grains in a m e d i u m with a d r o p o f a d e t e r g e n t solution, followed by shaking at intervals for 1 h o u r and standing overnight. T h e addition o f d e t e r g e n t is helpful to minimize the formation o f doublets or higher aggregates of grains.

TABLE I PLASTIC SPHERES AND POLLENS FOR STANDARDIZATION

Material

Approximate size (~)

Aperture to be calibrated (~)

Plastic spheres (Dow Chemical Co.) Puffball spores Ragweed pollen Pecan pollen Sweet vernal grass pollen Corn pollen Crab eggs

3.49

30 and 50

4.8 19-20 45-50 45-50

30 and 50 100-280 280-560 280-560

85-90 400

400-1000 2000

M e a s u r e m e n t s and Corrections

Total Cell Number T h e total n u m b e r , Ns, o f cells in a suspension can be c o u n t e d at an a p p r o p r i a t e setting o f sensitivity, S, and threshold volume, Vt. T h e value o f / I t suitable for this purpose is indicated by vertical arrows in Fig. 2 where the u p p e r curve shows the count, N (the count after the correction described below) or N' (the count before the correction) vs Vt and the lower curve shows -AN (the decrease o f N for a constant i n c r e m e n t o f Vt) versus Vt which is proportional to --dN/dVt. T h e b a c k g r o u n d count, Nb, o f small dust or contaminating cells can be thus eliminated. T h e direct count, N', o f cell n u m b e r , however, includes a systematic e r r o r due to the coincidence counting loss, which is caused by the phen o m e n o n that m o r e than one particle pass t h r o u g h the a p e r t u r e at the same time when particle concentration is high. T h e count, N', must

[16]

MEASUREMENTOF SIZE DISTRIBUTION

175

<~

Fro. 2.

T h e N ' (or N) vs Vt curve r e l a t e d to the --AN vs Vt curve.

t h e r e f o r e be corrected for this effect. T h e correction is made according to the following equation; N = N' + a(N') 2

(1)

where a is a function o f the a p e r t u r e diameter and the m a n o m e t e r volume and must be d e t e r m i n e d for each i n s t r u m e n t with the a p e r t u r e and the m a n o m e t e r to be used. Determination o f a can be m a d e in the following manner. P r e p a r e a concentrated cell suspension, and dilute it to obtain a series o f suspensions o f known relative concentrations, Nr; X ~- f i N r (2) where fl is the proportionality constant for the series o f suspensions. F r o m these equations, we obtain /3Nr = N' + a(N') 2

(3)

Dividing this equation by f i N ' N r / N ' = (1/B) + ( a / f l ) N ' .

(4)

T h e r e f o r e , plotting ( N r / N ' ) against N' gives a straight line, f r o m which the value o f a can be d e t e r m i n e d . Tables showing the values o f N versus N' for c o m m o n l y used a p e r t u r e s are very useful. A high count o f N ' for a concentrated cell suspension provides a high statistical accuracy but requires a greater correction, so that the best c o u n t is a c o m p r o m i s e between these opposite conditions. With a 100-/z a p e r t u r e for the 0.5 ml m a n o m e t e r , for example, the counts between 20 × 10a and 80 × 10a are preferable.

176

METHODOLOGY

[161

Size Distribution A volume-distribution curve can be obtained by simple subtraction o f successive counts, Ni and Ni + a, for a constant shift o f Vt, and by plotting the drop, N~ +1 -- Ni =--AN, against Vt, which is proportional to the particle volume, V. In this case, again, each count has to be corrected for the coincidence count loss b e f o r e subtraction. T h e --AN vs Vt curve can be c o n v e r t e d to the --AN vs V curve in an absolute unit o f volume if we know the conversion factor o f V/Vt, which can be estimated f r o m data for particles with known volumes. In the m e a s u r e m e n t o f a distribution curve in terms o f volume, an a p p r o p r i a t e value o f sensitivity, S, has to be chosen. Curves A, B, and C in Fig. 3 illustrate the data that would be obtained for the same sample at different sensitivities, S -= 2, 3, and 4, for the same shift o f Vt. Since the d e g r e e o f amplification o f the pulse height is approximately d o u b l e d by raising the sensitivity by one step, the volume-distribution curve is flattened by a factor of 1/2 by the increase o f sensitivity by one step. W h e n the sensitivity is lowered, on the o t h e r hand, the curve is s h a r p e n e d and shifted toward smaller values o f Vt. T h e r e f o r e , a small difference in setting the value of Vt introduces a greater e r r o r in the reading o f --AN at the lower sensitivity, while the fractional e r r o r in the value o f - A N is greater at the h i g h e r sensitivity. An a p p r o p r i a t e setting o f sensitivity in the case o f Fig. 3 may t h e r e f o r e be S = 3. T h e data shown in Fig. 4 are the volume-distribution curves obtained by Bassham and Kanazawa 5 d u r i n g the synchronous culture 6 o f ChloreUa

S=2

?

Vt FIG. 3. Measurements of the --AN vs Vt curve at different sensitivities. sj. A. Bassham and T. Kanazawa, private communication, 1969. ell. Tamiya, Y. Morimura, M. Yokota, and R. Kunieda, Plant Cell Physiol. 2, 383 (1961).

[16]

177

MEASUREMENT OF SIZE DISTRIBUTION 25 .'°

2C

a

.A

,'2 o,5

•

X

Oo

I o-

o

2

4

Vr

6

8

o

~

~

Vr

~

i

10

FIG. 4. The--AN vs Vt curves determined by digital recording of--AN and Vt values with a computer connected to the Coulter counter. The points on the left side of figure indicate the distribution obtained for a suspension of daughter cells of Chlorella, and the points on the right side indicate the data obtained for a mixture of mother and daughter Chlorella cells.

cells. T h e s e curves were m e a s u r e d with the Coulter c o u n t e r o f the Model B type connected to a c o m p u t e r for digital r e c o r d i n g o f - - A N and Vt values. T h e points on the left-hand side o f this figure indicate the volume distribution o f d a u g h t e r Chlorella cells (the dark cells), and the points on the right side indicates the presence o f large m o t h e r cells (the light cells) and small d a u g h t e r cells. Fluctuation o f these points indicate the o r d e r o f e r r o r in the measurements. T h e m e a s u r e m e n t s o f distribution in terms o f volume are advantageous when dealing with the measurements in a narrow size range at a single setting o f sensitivity or when dealing with rapid measurements with a r e c o r d e r or a computer. A n o t h e r way to see the distribution is the measurements in terms o f a logarithmic scale, log V, log Vr, or log Vt; the measurements o f - - A N for a constant i n c r e m e n t o f log V, log Vr, or log Vt. This m e t h o d has the following advantages over the measurem e n t in terms o f volume. (a) T h e e r r o r in the value o f - A N is nearly constant over a wide r a n g e o f volume to be m e a s u r e d at different sensitivities. This is because roughly the same division o f Vt may be used at different sensitivities. (b) Distribution peaks are m o r e symmetrical on the logarithmic scale than o n the volume scale. (c) W h e n cells grow uniformly, the distribution peak on the logarithmic scale shifts without any change o f its shape and height, while the peak on the volume scale is flattened and d e f o r m e d . T h e s e advantages are seen in the data Tshown 7K. Shibata, Y. Morimura, and H. Tamiya, Plant Cell Physiol. 5, 315 (1964).

178

METHODOLOGY

[ 16]

in Figs. 5 and 6, which indicate the distribution changes d u r i n g the synchronous culture o f Chlorella cells as m e a s u r e d on the logarithmic scale. T h e values o f t in these figures indicate the time in hours d u r i n g the cultivation. T h e b r o a d i n g o f the peak f r o m t = 0 to t = 7 and the s h a r p e n i n g after t = 7 in Fig. 5 indicate that the growth rate is greater in the middle range o f log V, and the data in Fig. 6 indicate that the m o t h e r cells shrink uniformly in the dark b e f o r e division. A simple way to measure the curves o n a logarithmic scale is to set u p a table o f Vt values for a constant shift o f log Vt. An example is shown in Table II which illustrates the m e a s u r e m e n t s over the sensitivity r a n g e f r o m S --- 6 to S = 2. In the table, the relative volume, Vr, at Vt (the threshold value) = 10.0 and S = 6 is assumed to be Vr -- 10 (or log Vr = 1.0), and the d e g r e e o f amplification at S -- 2 or 4 relative to the d e g r e e at S = 6 is expressed by 1/f T h e value o f f a t S = 4 was estimated f r o m the value o f Vt at S = 4 giving the same c o u n t o f N' as that d e t e r m i n e d at Vt = 100.0 and S = 6, by taking overlapping counts o f a test sample at these different sensitivities. T h e values o f Vt at S = 4 for a constant shift o f log Vt between log V~ = 2.0 and 2.5 in the table were thus determined and, by the same p r o c e d u r e , the values o f Vt at S = 2 for the range between log Vr = 2.5 and 3.2 were d e t e r m i n e d . Such tables showing the relationship between Vt and log Vr over different sensitivities are very useful for a n u m b e r o f measurements. T h e figures in the f o u r t h c o l u m n show the counts (N') obtained for a suspension o f Chlorella cells, and the 5th and 6th columns include the values (N) corrected for the coincidence count loss and --AN values calculated f r o m these counts, respectively.

t=o

~'o x

23 f~30 7

t~

e~

E

I.O

1.5

2.0

Z5

log V FlG. 5. Changes of cell-size distribution as measured in terms of log V (in ~a) during 30 hours of synchronous culture of Chlorellacells in the light. The culture time in hours is shown by t.

[16]

MEASUREMENT OF SIZE DISTRIBUTION

6

179

18

E4 o.

E

5

0

i

1.0

1.5

log V

2.0

t=O

25

_.

FIG. 6. Changes of cell-size distribution as measured in terms of log V (in t~3) during 18 hours of the dark period following the synchronous culture of Chlorella cells in the light shown by the data in Fig. 5; the curve of t = 0 in this figure shows the same data as shown by the curve of t = 30 in Fig. 5.

The result obtained for spinach chloroplasts treated with dodecylbenzene sulfonate (DBS) is shown in Fig. 7, which indicates the disintegration of chloroplasts into grana by the action of this detergent, s Another example 9"1°of volume change is found when chloroplasts kept

5000

G

50 4O

0 4000 1 3000

D

? - -

x

? 3o 2 x

2000 n '\

20 ~

IOO0 o -I.O

-0.5

0

Log V ( i n

1.5 IJ3)

2.0

!0

FIG. 7 Disintegration of spinach chloroplasts into grana by the action of DBS as measured with the Coulter counter; curves D to C indicate disappearance of the peak at log V (in /~3) = 2.0 of chloroplasts swollen by the effect of DBS and appearance of a peak of grana between log V = - 1 . 0 and - 0 . 5 . 8M. hob, S. Izawa, and K. Shibata, Biochim. Biophys. Acta 69, 130 (1963). 9M. Itoh, W. Izawa, and K. Shibata, Biochim. Biophys. Acta 66, 319 (1963). 1°S. Izawa, M. Itoh, and K. Shibata, Biochim. Biophys. Acta 75, 349 (1963).

180

[ 16]

METHODOLOGY

T A B L E II THE --AN VERSUS t.O~, Vt CURVE DETERMINED FOR A Chlorella CELL SUSPENSION W I T H A 1 0 0 /A APERTURE AND A 0 . 5 ML MANOMETER

log Vr S=6 (log f = 0)

log(Vr/f)

Vr/f = Vt

N' × 10-3

N x 10 -~

--AN × 10-3

1.0

1.0

10.0

70.5

102.3

0

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

1.1 1,2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

12.6 15.9 20.0 25.1 31.6 39.8 50.1 63.1 79.4 100~0

70.5 70.5 70.8 70.4 70.7 69.8 67.8 63.5 59.1 53,5

102.3 102.7 102.9 102.0 102.7 100.7 96.6 88.2 79.9 70.0

--0.4 --0.2 0.9 --0.7 2.0 4.1 8.4 8.3 9.9

S=4 (logf =0.556)

2.0 2.1 2.2 2.3 2.4 2.5

1.444 1.544 1.644 1.744 1.844 1.944

27,8 35.0 44.1 55.5 69.8 87.9

53~2 43.9 31.5 20.2 12.3 7.7

69.4 54.5 36.6 22.2 13.0 8.0

14.9 17.9 14.4 9.2 5.0

S=2 (logf = 1.178)

2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2

1.322 1.422 1.522 1.622 1.722 1.822 1.922 2.022

21.0 26.5 33.3 41.9 52.7 66.4 83.6 105.3

7.5 4.0 2.4 1.5 0.8 0.4 0.2 0.1

7.8 4.1 2.4 1.5 0.8 0.4 0.2 0.1

3.7 1.7 0.9 0.7 0.4 0.2 0.1

in darkness are illuminated. Curve A in Fig. 8 is the volume distribution on the logarithmic scale o f chloroplasts kept in the dark, and curve B is the distribution in the light. A change as much as 50% in volume was f o u n d on the illumination. T h e count over the distribution m a x i m u m on curve A, which is expressed by the area, No*, in the figure, decreases to Nt* on illumination. T h e rather rapid change o f volume by light could be followed sensitively by measuring the change o f N* at the single setting o f Vt at the maximum. T h e Coulter counter has been used for the measurements o f other species of cells such as bacteria, 11 white and red blood cells 1-4'~ and a 11K. G. Lark a n d C. Lark, Biochim. Biophys. Acta 43, 520 (1960). 12W. J. Richar and E. S. Breakell, Amer.J. Clin. Pathol. 51, 384 (1959).

[ 17]

MEASURING CHLOROPLASTVOLUMEAND STRUCTURE 2C

t

i

i

i

181

i

A B

7 o -~lc .0

,

0 12

,

j

(X

14 16 18 20 22 P4 log 7(in ps)

FIG. 8. The distribution curves measured on the logarithmic scale for the chloroplasts incubated in the dark (curve A) and in the light (curve B).

number of photosynthetic marine organisms. 13 The applications to marine organisms have been reviewed comprehensively by Sheldon and Parsons.IS ~3R. W. Sheldon and T. R. Parsons, "A Practical Manual on the use of the Coulter Counter in Marine Research." Coulter Electronics Sales Co., Canada, 1967.

[17] Methods for the Measurement of Chloroplast Volume and Structure in Vitro and in Vivo

By LESTER

PACKER a n d SATORuMURAKAMI

The measurement of chloroplast volume (size) and other alterations of structure that affect shape (configuration) and internal structure (conformation) can be assessed by a variety of methods that are applicable to one or more of these facets of chloroplast structure. The main techniques that thus far have been applied for assessing facets of chloroplast structure are: gravimetric (packed volume, fresh weight), microscopic (light and electron microscope), and photometric (absorbance or transmission, light scattering) methods and the electronic particle (Coulter) counter.