THE MEASUREMENT OF MASS, THICKNESS, AND DENSITY IN THE ELECTRON MICROSCOPE

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T H E M E A S U R E M E N T

OF M A S S , T H I C K N E S S ,

A N D

D E N S I T Y

I N T H E E L E C T R O N

M I C R O S C O P E

R. E. B U R G E , Ph.D., and N. R. S I L V E S T E R , Ph.D.

From Wheatstone Physics Laboratory, University of London King's College, London, England

A B S T R A C T

A description is given of quantitative methods using the electron microscope which can be applied to specimens with m u c h smaller dimensions than those which can be used with the established cytochemical methods based on the use of the interference microscope and the techniques of ultraviolet and x-ray absorption. A discussion of electron scattering shows that under chosen operating conditions in the electron microscope the effective total mass-scattering coefficient S of a specimen is almost independent of its chemical composition. An order-of-magnitude agreement is observed at four accelerating voltages between experimental total scattering cross-sections for polystyrene and theoretical values for carbon. T h e contrast in a micrograph taken under standardised conditions is interpreted in terms of differences in specimen mass-thickness. T h e measurement of mass, thickness, and density of discrete particles and thin sections in the absence of sublimation is discussed in terms of relevant object models on the assumption of a constant, experimentally determined, value of S. The validity of the proposed methods was examined by measuring the masses of the heads of r a m spermatozoa (about 7 X l0 -1~ gin.) and T2 bacteriophage (about 3 X l0 -16 gin.) in the electron microscope. The values agreed reasonably well with those found by interference microscopy and sedimentation-diffusion measurements, respectively. Errors in S and magnification due to contamination and their effects on the results are considered in detail. An application of the methods to a typical electron microscope specimen was demonstrated by measuring the mass of heads of the T2 bacteriophage after staining with uranyl acetate. Errors of measurement are discussed and a minimal measurable mass estimated. Further applications of quantitative electron microscopy are proposed.

I N T R O D U C T I O N

Quantitative cytochemical measurements of mass, density, and thickness by the methods of interference microscopy, absorption of x-rays, and absorption of ultraviolet light are well known (see review articles by e.g. Davies (8), EngstrSm and Lindstr6m (11), and Walker (33), respectively). The lower limit of mass measurement in interference microscopy, which we may take as representative of the above methods, is about 10 -la gill. and there is an obvious need for a

method of mass measurement which is valid for the smaller biological organisms observable in the electron microscope (e.g. viruses, bacteri- ophages, bacteria) and for density and thickness measurement on small areas in thin sections. M a r t o n and Schiff (24) first described a method of measuring the thickness of isolated specimens in the electron microscope and implicit in their analysis is the possibility of the measurement of the mass and density of such specimens. Hall Received for publication, September 7, 1959.

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(17) m e a s u r e d the relative increase in mass- thickness (i.e. mass per u n i t area in the plane of the specimen) of two types of virus after the a p p l i c a t i o n of electron stains, and, using a pre- d e t e r m i n e d c a l i b r a t i o n of his electron microscope, was able to make estimates of the virus density. Relative m e a s u r e m e n t s similar to those of Hall have recently been m a d e by A m e l u n x e n (1). T h e theory of q u a n t i t a t i v e electron microscopy has been discussed by K r i i g e r - T h i e m e r (20) a n d Zeitler a n d B a h r (38) a n d following the latter p a p e r B a h r (2), using theoretical contrast pa- r a m e t e r s w h i c h he h a d shown to be in reasonable a g r e e m e n t w i t h e x p e r i m e n t for the conditions of m e a s u r e m e n t , d e t e r m i n e d the mass of microsomal particles to w i t h i n a n estimated e r r o r of a b o u t 30 per cent. M e a s u r e m e n t s of the mass-thickness of d i s r u p t e d cell m e m b r a n e s , a g a i n using theoretical electron-scattering cross-sections, have been m a d e by De a n d S a d h u k h a n (9). Q u a n t i t a - tive aspects of electron staining h a v e been sur- veyed in a r e c e n t p a p e r by Cosslett (6).

Both the earlier discussion of Zeitler a n d B a h r a n d their most r e c e n t p a p e r (39) are based u p o n the elastic electron-scattering theory of Leisegang (21) a n d so also are those m e a s u r e m e n t s m e n t i o n e d a b o v e w h i c h h a v e used theoretical c o n t r a s t parameters. I n the light of r e c e n t theoretical a n d e x p e r i m e n t a l work (to be m e n t i o n e d later) it seems clear t h a t inelastic scattering is as im- p o r t a n t as elastic for elements of low a t o m i c n u m b e r a n d for the o p e r a t i n g conditions w h i c h n o r m a l l y o b t a i n in the electron microscope. I n their r e c e n t p a p e r Zeitler a n d B a h r confine themselves to a c o m p a r i s o n of L i p p e r t ' s (23) e x p e r i m e n t a l values of electron-scattering cross- sections w i t h the Leisegang theory at objective a p e r t u r e s greater t h a n 10 2 radian, in w h i c h elastic scattering is the p r e d o m i n a n t factor. T h e y t h e m - selves state t h a t the deviations from this theory at smaller apertures are due to inelastic scattering but, on the o t h e r h a n d , say t h a t if apertures of 10 -3 to 10 -2 r a d i a n are used, the effect of inelastic scattering can be disregarded.

I n view of this situation we have been c o n c e r n e d to re-state some of the m a i n points of the c u r r e n t theories of electron scattering in relation to q u a n t i t a t i v e electron microscopy a n d to give some e x p e r i m e n t a l values of electron-scattering cross-sections w h i c h m a y be of use in f u r t h e r comparisons between various scattering theories. T h e m a i n purpose of this paper, however, is to show how d e t e r m i n a t i o n s of mass, density, a n d

thickness m a y be m a d e b o t h for isolated specimens and, in principle, for regions of t h i n sections w i t h o u t recourse to theoretical c o n t r a s t parameters. A q u a n t i t a t i v e e x a m i n a t i o n has b e e n m a d e of the validity a n d a c c u r a c y of the m e t h o d s described by a c o m p a r i s o n between mass measure- m e n t s m a d e in the electron microscope a n d those m a d e by other, well established, methods. A r a m spermatozoon, c a l i b r a t e d by interference microscopy, provides a n object at the u p p e r limit of size practicable for electron microscopy while a bacteriophage, c a l i b r a t e d by s e d i m e n t a t i o n a n d diffusion m e a s u r e m e n t s (31) provides a test object w i t h dimensions well below the resolving limit of the optical microscope a n d in the " n o r m a l " electron microscope range. M e a s u r e m e n t s o n b o t h these objects are reported and, in addition, the c h a n g e in mass of T 2 b a c t e r i o p h a g e after staining w i t h u r a n y l acetate is estimated as a n application of the method.

M e a s u r e m e n t s o n the density of the nucleus a n d cytoplasmic m e m b r a n e of r a m sperm, as seen in t h i n section, have already been published

(30).

E l e c t r o n S c a t t e r i n g

The contrast in the electron microscope of an image of an effectively amorphous object (i.e. one in which the effect of coherent scattering is negligible) is due almost entirely to the differential scattering of electrons by various parts of the object, which causes varying fractions of the incident beam to be pre- vented from passing through the objective aperture of the microscope and contributing to the image intensity. Under normal operating conditions the contrast at a given point of the image is governed by the exponential relation (16),

I = Le -s'° (1)

where Io is the intensity of the electron beam incident on the object of mass-thickness w, I is the intensity of the transmitted beam which reaches the image plane, and S is the effective total electron-scattering cross-section per gram of material. The mass- thickness w = pt if p is the density of the material and t the thickness of the object in a direction parallel to the incident beam. The relation (1) has been verified experimentally by Hall (15) and Hillier and Ellis (19) and more recently by Coupland (7). For scattering by a single element the atomic cross-section cr is related to S by the formula

L

S = c r - (2)

A

2 T I l E JOURNAL OF BIOPttYSIt'AL AND BIO('IIEMICAI, CYTOLOGY • VOLUME S, 1960

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where L is Avogadro's number and A the atomic weight of the element. It should be pointed out, however, that it is assumed in equation (2) that the total scattering cross-section of a body is the sum of the elastic and inelastic cross-sections of its constituent atoms. In reality, additional effects are present due to the binding of atoms in molecules, to scattering by free electrons in the case of metals, and to coherent scattering in crystalline materials.

The expressions for the elastic scattering component, S,, of S given by Leisegang (21) and Lenz (22) are similar in form and differ mainly in approxima- tions to the effective radius, R, of the scattering atom.

Leisegang uses a formula R = aoZ -1/~, where

Z4I~

ao = 0.529 A, which implies that S~cc - - f o r the

A normal range of objective apertures. Lenz uses selec- ted values of R which result in a smaller variation of Se with 2". Lenz' expressions are given in a practi- cal form by Sadhukhan (28) and tables showing the dependence of the cross-sections upon atomic number, aperture, and accelerating voltage are given by Cosslett (6).

Zeitler and Bahr, using Leisegang's theory, effectively put S = S~ which means that S should increase with atomic number. While this is encouraging from the point of view of substance differentiation (5) it would mean that to determine accurately the mass- thickness of a substance in the electron microscope its chemical composition would need to be known beforehand. On the other hand, Lenz includes in S a contribution due to inelastic scattering, i.e. S =

S,. + Si, and shows theoretically that Si is of the

same order of magnitude as S, for elements of low atomic number (e.g. carbon) and increases with decreasing aperture angle. The effect of the addition of the inelastic and elastic scattering components is that the theoretical value of S becomes almost independent of atomic number as shown by us (30) and by Cosslett (6) in his Table III. This implies that no a priori knowledge of a specimen is required for mass measurement and that, for instance, in measurements on an organic specimen the same value of S should be valid both before and after staining with heavy-metal ions. That S should be independent of 2" is thus of fundamental importance to quantitative methods of measurement.

Recent evidence for the importance of the inelastic component of S has been given by Valentine (36) who has pointed out that the variation of S with objective aperture, cL is greatest at small values of

2" (i.e. less than about 12) and that this fact may be

used experimentally to distinguish between objects of low and high mean atomic number. Since the elastic scattering cross-section (predominant for high Z) varies very little with c~, the variation of contrast observed at low Z must be due almost entirely to the

variation of Si. The magnitude of the effect observed by Valentine makes it probable that, at the smaller aperture he used, Si was at least as large as S,. An experimental determination of the variation of S with Z has lately been made by Reimer (27) who plotted the contrast ( l o g / / - 2 ) of evaporated films against their mass-thickness. For a range of elements from C to U and a range of mass-thicknesses up to 40 gg./cm. 2 he found that all the experimental points lay on a single straight line; i.e. for the condi- tions he used (60 kv. and an objective aperture of 4.6 X 10 -3 radian) S was sensibly independent of Z, a fact which has already been reported by Hall (15) for an electron microscope in which no physical aperture was used.

Four experimental values of S for accelerating potentials of 25, 50, 75, a n d 100 kv. at the apertures quoted are given in Table I a n d c o m p a r e d with the calculated values for carbon. T h e value of S was d e t e r m i n e d from electron micrographs of polystyrene spheres of k n o w n mass-thickness, a m e t h o d used by Hall and Inoue (18) whose corresponding results are shown. T h e r e is an order-

of-magnitude a g r e e m e n t between

Scale

a n d Sobs

but the experimental values are systematically lower t h a n the calculated ones; the discrepancy increases rapidly as the accelerating voltage decreases.

Theoretical values of S are calculated for single- scattering conditions in the absence of phase effects a n d lens aberrations. However, the distortion of the edge contrast of an image due to geometrical aberrations can be m a d e negligible by using a suitable objective aperture; phase and diffraction effects are minimised at the in-focus position. It has been shown experimentally t h a t the values of S d e t e r m i n e d from thick specimens in which plural scattering m a y be expected to occur are, within experimental error, the same as those d e t e r m i n e d for thin specimens. T h u s Hall (15) found that the exponential relation (1) held for values of In I o / I up to 3.0, while Hall a n d Inoue (18) a n d Zeitler and Bahr (39) b o t h publish

i,,

experimental graphs of In ~ against w w h i c h are linear up to In I o / I ~ 2.4. Bahr (2) suggests t h a t the range of mass-thickness m e a s u r e m e n t can be extended by a factor of 6 to 7 u p o n his original estimate of the limiting value w h i c h was pre-

sumably based (38) on the equation In Io _{7 = 0.53.}

BURGE AND SILVESTER Quantitative Electron Microscopy 3

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Cosslett (6) states that values of In

Io

u p to 5 m a y be used with an accuracy of 5 to 10 per cent in S. Values of the calculated transparency thickness have been included in Table I on the basis of the

1

yon Borries (3) definition, Se" T h e units have been chosen so that the numerical values show the thickness in A for a material of unit density. Hall (17) found t h a t the effective value of S

discussed below for the ideal case in w h i c h no sublimation or c o n t a m i n a t i o n of the specimen

O c c u r s .

Directly Mounted Specimens."

Consider a small homogeneous region of a specimen of thickness

t, density p, a n d area

dA

p e r p e n d i c u l a r to the

incident uniform electron beam, m o u n t e d on a film w h i c h is of uniform thickness over the area A of the specimen. Let the intensities of the electron beams transmitted by the film a n d specimen T A B L E I

Values of S

A comparison of values observed with 880 A diameter polystyrene spheres,* calculated values for C} and values reported by Hall and Inoue (18) which

are shown bracketed

a r a d i a n Se c m 3 g m . -1 1/Se g m . c m . - ~ Si c m 3 g i n . i S c a l e c m 3 g m . -1 S o b s c m . 2 g m . -~ k v . X 10 3 X 10 -4 X 10~ X 10 4 X 10 -4 )< 10 -4 100 2.56 3.21 3120 3.93 7.14 5.4 4- 0.1 [100 2.2 5.9] 75 3.49 4.20 2380 4.81 9.01 5.9 4- 0.2 50 3.68 5.91 1690 7.34 13.25 8.8 4- 0.2 [50 4.2 8.23 25 2.94 11.1:5 897 17.98 29.13 13 =t= 1

* The density of polystyrene was taken to be 1.05 gm. cm -3 (37) whereas Hall and Inoue used a value of 1.1 gm. cm. --a.

:~ Lenz' expressions were used and R was assumed to have the value 0.529.6 -1/3 A. Full relativistic corrections were made.

varied slightly with the condition of focus of the image and this observation has been confirmed in the present work. I n addition, S will d e p e n d to some extent on the convergence of the incident electron b e a m and on the electromagnetic field between the specimen and the objective aperture (7). Thus, to find the value of S obtaining d u r i n g the exposure of a m i c r o g r a p h it is necessary for quantitative work to " c a l i b r a t e " it by including objects of known mass-thickness. It is shown in the next section how the experimental value of S can be used in the d e t e r m i n a t i o n of density and mass in the electron microscope.

Object Models and the Measurement of Mass,

Thickness, and Density

T h e r e are two m a i n classes of electron microscope specimens tbr which quantitative measurements may be required, These comprise isolated specimens m o u n t e d directly on an electron microscope support film and thin tissue sections which are similarly mounted. These two object models are

together and by the film alone i m m e d i a t e l y ad- j a c e n t to the specimen be 12 a n d I1, respectively. T h e n the mass of the specimen is given by

f

A

M =

ptdA

1

f A

I1

= - In

dA,

from equation (1).

i.e.

M

S

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T h e above equation is the f u n d a m e n t a l one by which the mass of a specimen m a y be d e t e r m i n e d a n d m a y be applied only if S is i n d e p e n d e n t of atomic n u m b e r a n d mass-thickness. T h a t this i n d e p e n d e n c e m a y be achieved in practice has been shown in the previous section.

Experimentally, electron intensities are usually

recorded photographically and e q u a t i o n (3)

m a y be expressed in two forms d e p e n d i n g on the precise conditions of p h o t o g r a p h i c recording. If p h o t o g r a p h i c densities above background, Dt and D2, on the plate are linearly related to 11 a n d I2 the e q u a t i o n becomes

4 THE JOURNAL OF BIOPHYSICAL AND BIOCHEMICAL CYTOLOGY • VOLUME 8~ 1960

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1

fa

DI

M = ~ In D--~2 dA (4)

or, if D1 a n d D2 are p r o p o r t i o n a l to log / i a n d log I~, respectively, it takes the form

M = T I"1 A (DI-- D2) dA

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S J

w h e r e 3' is the p h o t o g r a p h i c constant. M e t h o d s familiar in m i c r o s p e c t r o p h o t o m e t r y (4) m a y be used to p e r f o r m the integrations above. E i t h e r e q u a t i o n (4) or e q u a t i o n (5) is suitable for the e v a l u a t i o n of the total mass of a n y isolated speci- m e n p r o v i d i n g t h a t over its a r e a v a r i a t i o n s in the thickness of the s u p p o r t i n g film are not appreci- able.

W h i l e the mass-thickness, pt, is readily deter- m i n e d for a n y p o i n t o n the specimen the density or thickness for this type of object m a y only be found indirectly. If p is k n o w n from the n a t u r e of the m a t e r i a l or from macroscopic m e a s u r e m e n t s t h e n t m a y be calculated. Alternatively, for suitable specimens, t m a y be found by m e t a l s h a d o w i n g or stereomicroscopy, thus allowing the d e t e r m i n a t i o n of p.

Thin Sections." A c o m p a r a t i v e m e t h o d for the m e a s u r e m e n t of density in t h i n sections has already been described by us (30) b u t the m a i n points will be m e n t i o n e d here for the sake of completeness. Regions of sections, to be suitable for m e a s u r e m e n t , must be of a defined thickness, i.e. they must extend t h r o u g h the entire section thickness from the u p p e r surface to the s u p p o r t i n g film. T o d e t e r m i n e the mass, thickness, a n d density of such regions it is necessary to have a measure of the intensity of the electrons t r a n s m i t t e d by the s u p p o r t i n g film alone. A hole in the section sufficiently n e a r the region of interest leaving the s u p p o r t i n g film exposed c a n n o t be expected to occur very often; however, if a reference object of k n o w n density is e m b e d d e d w i t h the specimen a n d the whole sectioned together, all three of the p a r a m e t e r s M , p, t c a n be d e t e r m i n e d u n d e r favourable conditions.

Suitable reference objects will d e p e n d on the specimen a n d in m a n y organic specimens will a l r e a d y be available in the section ( a l t h o u g h assumptions a b o u t the e m b e d d e d densities of these objects m a y have to be m a d e (compare (30)). I t is possible to mix i n t i m a t e l y reference particles in h i g h c o n c e n t r a t i o n w i t h some specimens, e.g. b a c t e r i a a n d spermatozoa. T h e particles should

preferably be i m p e r m e a b l e to the e m b e d d i n g m e d i u m (to r e t a i n a c o n s t a n t density) yet be readily e m b e d d e d a n d sectioned w i t h the speci- m e n u n d e r e x a m i n a t i o n . Small particles of plastic m a t e r i a l (e.g. polystyrene latex spheres) o r g r a p h i t e ( " a q u a d a g " ) m a y be of use in this way; we h a v e successfully sectioned colloidal g r a p h i t e particles in m e t h a c r y l a t e a n d polystyrene spheres in vestopal. T h e reference objects m u s t be sufficiently n e a r the regions of interest in the specimen for r a n d o m v a r i a t i o n s of thickness in section a n d s u p p o r t i n g film to be neglected. As pointed o u t in a previous p a p e r (30) n o n - r a n d o m v a r i a t i o n s of section mass-thickness (e.g. due to sublimation of the e m b e d d i n g m e d i u m ) will i n t r o d u c e errors in the expressions for the density of the specimen if the m e a s u r e d a n d reference densities are n o t equal. I n a r e c e n t p a p e r R e i m e r (27) has shown t h a t even in a c a r b o n - f o r m v a r " s a n d w i c h " m e t h a c r y l a t e loses a b o u t 30 per cent of its mass- thickness in the electron b e a m , while araldite a n d vestopal ( u n p r o t e c t e d ) lose a b o u t 20 per cent a n d 13 per cent, respectively. T h e best e m b e d d i n g m e d i u m at present available for q u a n t i t a t i v e m e a s u r e m e n t s is clearly vestopal, while suitable specimens will be those w h i c h o n a p p l y i n g tests such as those used by M o r g a n , Moore, a n d Rose (25) show no differential sublimation.

E X P E R I M E N T A L

Calibration of the Electron Microscope." A Metropolitan- Vickers type P.M.3. electron microscope with elec- trostatic astigmatism correction was used at accelerating voltages of 25, 50, 75, and 100 kv. T h e semi-angular apertures of the objective lens used in this work were determined by using electron diffraction conditions (with the same objective lens current used in the determination of S by normal microscopy; see Table I) and observing the angle at which the diffraction pattern from a known salt was cut off by the aperture. The aperture thus determined is the effective aperture corrected for distortion of the electron paths by the field of the objective lens.

The magnification M and total mass-scattering cross-section S valid for each micrograph were determined by including polystyrene spheres of diameter 880 4- 80 A in each specimen. Errors in M occur because of the deposit of a layer of contamination over regions of the specimen which are irradiated by the electron beam (12) while errors in S may be caused both by the effects of contamination and by sublimation of material from the spheres, caused by the electron beam.

The rate at which the contaminating layer was deposited on a surface for the beam currents used in

BURGE AND SILVESTER Quantitative Electron Microscopy 5

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this work ( < 6 m A cm. - 2 at t h e specimen) was f o u n d to be a b o u t 6 A per m i n u t e . T h e s p e c i m e n a r e a ir- r a d i a t e d at a n y one t i m e was kept to a m i n i m u m ( ~ ( 5 0 #)2) by u s i n g a screening a p e r t u r e above t h e s p e c i m e n similar to t h a t described by Page a n d A g a r (26). T h e screening a p e r t u r e a s s e m b l y was also used as a F a r a d a y cage in order to m e a s u r e t h e b e a m cur- r e n t (14). W i t h t h e types of s p e c i m e n used, i.e. m i x -

tures of polystyrene spheres w i t h r a m s p e r m a n d of polystyrene spheres w i t h b a c t e r i o p h a g e , little t i m e was lost in s c a n n i n g t h e s p e c i m e n s for suitable areas a n d it is believed t h a t t h e systematic error in t h e v a l u e of M i n t r o d u c e d b y c o n t a m i n a t i o n is n o t g r e a t e r t h a n + 4 per cent. T h i s error c o r r e s p o n d s to a b o u t 3 m i n u t e s irradiation.

Polystyrene spheres are c o m m o n l y a n d successfully u s e d for m a g n i f i c a t i o n calibration a n d t h e values of M m e a s u r e d in this work u s i n g t h e spheres were in good a g r e e m e n t w i t h those f o u n d u s i n g a replica of a diffraction grating. T h e effects of subli- m a t i o n , if this occurs, m u s t , therefore, be confined to t h e r e d u c t i o n in density of t h e spheres w i t h o u t c h a n g e in radius. T h e possibility s e e m e d to us to be small since Hall (15) a n d Hall & I n o u e (18) h a d d e t e r m i n e d S u n d e r carefully defined e x p e r i m e n t a l conditions u s i n g polystyrene spheres. It is also k n o w n t h a t polystyrene is stable in t h e absence of o x y g e n u p to a t e m p e r a t u r e of 250°C. (34); this s p e c i m e n t e m p e r a t u r e is n o t r e a c h e d in t h e electron microscope except possibly u n d e r the m o s t e x t r e m e conditions (16). However, t h e possibility of s u b l i m a t i o n was e x a m i n e d by m o u n t i n g s o m e polystyrene spheres on a n e v a p o r a t e d c a r b o n film of k n o w n mass-thickness. T h e mass-thickness of t h e c a r b o n film, o b t a i n e d by weighing, was 6.60 -t- 0.40 /~g. cm. -~. T h e mass- thickness of the c a r b o n film was m e a s u r e d f r o m electron m i c r o g r a p h s ( b e a m c u r r e n t at s p e c i m e n 6 m A c m . -2, accelerating voltage 75 kv.) u s i n g t h e m e a n v a l u e of S d e t e r m i n e d f r o m m e a s u r e m e n t s o n 12 polystyrene spheres (for m e t h o d of m e a s u r e m e n t see below) t a k i n g t h e density of polystyrene to be 1.05 gin. cm. - 3 (37). T h e electron microscope v a l u e for the mass-thickness of t h e c a r b o n film was 6.77 =t= 0.23 /~g. cm. - z . It was, therefore, c o n c l u d e d t h a t u n d e r the e x p e r i m e n t a l conditions used for m a s s m e a s u r e m e n t t h e s u b l i m a t i o n of polystyrene is negligible.

S m a y be d e t e r m i n e d in t h r e e ways, f r o m m e a s u r e - m e n t s based on t h e following e q u a t i o n s (assuming. for t h e m o m e n t , no c o n t a m i n a t i o n ) . 1 I1 S = - - l n - - 2oR (12) ,~in S = - - 1 fjo 2R In ~ dl rrpR 2 12

3fo~rR2[~2

S ~ - - In dA (8) 4~'pR a w h e r e t h e density of polystyrene (0) is 1.05 g m . cm. - 3 (37) a n d t h e spheres are of r a d i u s R. I n e q u a t i o n (6), /1 is t h e intensity t r a n s m i t t e d by t h e clear film a n d (12)rain is t h e intensity t r a n s m i t t e d at t h e centre of t h e i m a g e of t h e sphere w h e r e t h e electron p a t h l e n g t h in t h e sphere is 2R. I n e q u a t i o n (7), a c c o u n t is t a k e n of t h e variation of 12 across a d i a m e t e r of t h e sphere a n d in e q u a t i o n (8), of t h e variation in I: over t h e projected a r e a of t h e sphere. Application of e q u a t i o n (6) a s s u m e s spherical s y m - m e t r y of t h e particle a n d no distortion, e.g. flattening,

d u r i n g s p e c i m e n p r e p a r a t i o n a n d e x a m i n a t i o n . E q u a - tion (7) assumes r o t a t i o n a l s y m m e t r y of t h e particle a b o u t a line t h r o u g h its centre p e r p e n d i c u l a r to t h e s u p p o r t i n g film. E q u a t i o n (8) m a k e s no a s s u m p t i o n s . W h e n a layer of c o n t a m i n a t i o n (density fo a n d

thickness r) covers b o t h t h e sphere a n d t h e s u p p o r t i n g film, 11 a n d (12)rain (equation 6), are r e d u c e d in t h e s a m e ratio. T h e v a l u e of S o b t a i n e d u s i n g e q u a t i o n 6 is t h u s i n d e p e n d e n t of the effect of c o n t a m i n a t i o n b u t a s s u m e s a n u n d i s t o r t e d particle.

M e a s u r e m e n t s of S were m a d e for polystyrene spheres of 1500 A a n d 2700 A d i a m e t e r u s i n g e q u a - tions (6) a n d (7). T h e values of S for these spheres i n d i c a t e d t h a t t h e y were flattened by u p to 10 p e r cent. I n t h e case of 880 A d i a m e t e r spheres it was difficult to distinguish the effects of distortion f r o m those d u e to c o n t a m i n a t i o n .

T o correct for possible distortion of t h e spheres either e q u a t i o n (7) or (8) m a y be u s e d in a suitable f o r m corrected for t h e presence of t h e layer of con- t a m i n a t i o n . T h e modified f o r m of e q u a t i o n (7) is

I/

_ _

_{1 --}rn s i n 0 + ( l ~ m ) ~ l

1 - f

= S F S (1 -- 0/~') + 1 -1- rn lr 1

.re(R+ r) _

7rp(R + r) ~ ~o I n I l w h e r e (9)

2~/m

s i n 0 = a n d m = r / R . I W m

T h e right h a n d side of this e q u a t i o n m a y be evalu- a t e d e x p e r i m e n t a l l y giving t h e value of t h e p r o d u c t

S F b u t n o t S directly in t h e absence of a very carefully

s t a n d a r d i s e d c o n t a m i n a t i o n rate. I n practice t h e (6) polystyrene spheres are a s s u m e d to h a v e a r a d i u s R, since in the absence of a second m e a n s for m e a s u r i n g the magnification, r in a n y given m i c r o g r a p h c a n n o t be d e t e r m i n e d . T h e e x p e r i m e n t a l integral w h i c h is

(7)

e v a l u a t e d is therefore

6 T H E JOURNAL OF BIOPHYSICAL AND BIOCHEMICAL CYTOLOGY • VOLUME 8, 1960

(7)

9 R

S' = (1 q- m)SF = - - 1 fo- I n ~ 11 dl ( 1 0 )

~rpR 2

T h e point at issue here is how different is S' from S for given experimental conditions? Substituting f = 2,

i.e. assuming the density of the c o n t a m i n a t i o n is

approximately that of evaporated carbon, gives the

following values of (m, S'/S)--(0.01, 0.96), (0.05,

0.98), (0.07, 1.00), (0.10, 1.03), (0.20, 1.11). A variation of this form has been observed experimentally for 880 A polystyrene spheres.

T h e variation of S with variation in objective lens c u r r e n t has been examined semi-quantitatively by Hall (17). A quantitative analysis of this effect was m a d e by taking a through-focus series of polystyrene spheres at a magnification of 40,000 at 100 kv. using an objective aperture of 5 X 10 - a radian. I n the range b e t w e e n 4-1 # from focus S was found to be constant within 2 p e r cent. M i c r o g r a p h s with greater off-focus distances were not used for analysis.

It is considered unlikely that any of the micro- g r a p h s used in this work correspond to rn > 0.04,

giving S'/S ~ 0.97. T h e m e a s u r e m e n t of mass de-

1

pends on the ratio - - a n d it is i m p o r t a n t to assess

M 2 S

the effect of c o n t a m i n a t i o n on this ratio. If a n u m b e r of micrographs are used for analysis with fractional changes in magnification due to c o n t a m i n a t i o n lying b e t w e e n (1 q- ml) a n d (1 + m2) corresponding to different times of irradiation, t h e n the m e a n mass

measured for a particle of " t r u e " mass M is

M fro2 dm M

*']'-1 (m2 ~ m,)

Jml (1 + m)= (1 + m,)(l + ,.2)

if equation (6) is used to d e t e r m i n e S. Taking m l =

0.01 a n d m2 = 0.04, which are representative of the conditions used while taking the ten mierographs of r a m s p e r m a t o z o a (see next section), gives 1.05 A4 =

hi, i.e. the m e a n result is subject to a systematic error

of about - - 5 per cent due to magnification errors. Values of M calculated from a single m i c r o g r a p h using equation (10) in the d e t e r m i n a t i o n of S are subject to a m a x i m u m systematic error due to con- t a m i n a t i o n of about -- 5 per cent. This is the case for the m e a s u r e m e n t s m a d e on bacteriophage (see next section).

Photographic l~Iethods: It was shown in the previous

section that the equations for mass could take two forms according to the conditions of p h o t o g r a p h i c recording. It was decided to make use of the region of the p h o t o g r a p h i c - p l a t e characteristic where the optical density was directly proportional to the inci- d e n t intensity (corresponding to equation (4)) r a t h e r

t h a n the linear region of the H-D curve (correspond-

ing to equation (5)). This course was taken since

experience has shown that the first condition m a y be readily achieved by taking micrographs o n Ilford special lantern contrasty plates followed by s t a n d a r d processing to give optical densities less t h a n 1.5. T h e

linear region of the H-D curve occurs at higher

densities (1.7 to 3) a n d it is more difficult to m a i n t a i n a constancy of q, from plate to plate.

T h e procedure a d o p t e d in using equation (4) was to take a set of densitometer traces along equally spaced parallel lines across the image of the specimen using either a " l i n e a r " or an " e x p o n e n t i a l " (29) optical wedge a n d a d o u b l e - b e a m recording micro- densitometer (32). Optical densities were measured above the p h o t o g r a p h i c density corresponding to a specimen-grid b a r following the m e t h o d of Hall (15). T h e m e t h o d of strip-wise integration is familiar in quantitative analysis by optical methods (4). T h e integration corresponds to a d e t e r m i n a t i o n of the volume b e n e a t h a mass-thickness "profile" of t h e specimen as illustrated in Fig. l for a bacteriophage particle. T h e traces shown were m a d e with t h e " e x p o n e n t i a l " wedge.

Specimen Preparation: T h e specimens of whole r a m

s p e r m were p r e p a r e d by allowing drops of a dilute suspension of sperm a n d 880 A diameter polystyrene spheres in 70 per cent alcohol to evaporate on speci- m e n supporting films. Specimens of unstained T2 Lr+h + bacteriophage were p r e p a r e d similarly from suspension in isotonic salt solution. Specimens of bacteriophage were stained with 4 per cent uranyl acetate for 11/~ hours a n d dialysed against a large volume of glass-distilled water for 12 hours.

R E S U L T S

Mass of the Heads of Whole Ram Sperm

W h o l e r a m s p e r m d o n o t m a k e ideal s p e c i m e n s for e l e c t r o n m i c r o s c o p y since t h e d i m e n s i o n s of t h e h e a d (length, w i d t h , a n d thickness a b o u t 6/~, 3 #, a n d 0.3 ~ respectively) a r e s u c h t h a t t h e h e a d fills t h e m i c r o s c o p e field a t a m a g n i f i c a t i o n o f a b o u t 8000 times; t h e thickness difficulty w a s largely o v e r c o m e b y using a n a c c e l e r a t i n g v o l t a g e of 100 kv. A t this v o l t a g e t h e v a l u e o f In Io/I for a r a m s p e r m h e a d was a b o u t 2 w h i c h is well w i t h i n t h e r a n g e , discussed a l r e a d y , w h e r e S is i n d e p e n d e n t o f w. S u c h a large s p e c i m e n w a s r e q u i r e d to o v e r l a p t h e r a n g e of m e a s u r e m e n t o f t h e i n t e r f e r e n c e m i c r o s c o p e . T h e masses o f t h e h e a d s o f t e n w h o l e s p e r m w e r e d e t e r m i n e d using e q u a t i o n (4). T h e m e a n values of M a n d S, t h e l a t t e r using e q u a t i o n (6), w e r e d e t e r m i n e d f r o m m e a s u r e m e n t s o n t h e p o l y s t y r e n e s p h e r e s i n c l u d e d w i t h t h e s p e r m . T h e m e a n m a g n i f i c a t i o n ( i n c l u d i n g t h e effect of

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FIGURE 1

T h r e e - d i m e n s i o n a l isometric projection of the mass-thickness profile of a T 2 bacteriophage. T h e tail of the p h a g e extends in the x direction. T h e lengths of the x a n d y axes represent 1000 A a n d t h a t of

t h e mass-thickness axis

(pt)

corresponds to 1000 A for p = 1 gin. cm. -a.

c o n t a m i n a t i o n ) w a s 8 2 5 0 4- 120 ( f r o m 34 s p h e r e s ) a n d t h e m e a n S w a s 4.37 =1= 0.09 )Z 104 c m . 2 g m . - I ( f r o m 38 s p h e r e s ) . T h e m e a n m a s s o f a r a m s p e r m h e a d d e t e r m i n e d b y e l e c t r o n m i c r o s - c o p y w a s 7.74 ::t: 0.42 >( 10 -12 g m . ; t h i s v a l u e m a y be low b y a b o u t 5 p e r c e n t d u e to t h e effect o f c o n t a m i n a t i o n as a l r e a d y d i s c u s s e d .

Mass of the Heads of T2 Lr+h+ Bacteriophage

M i c r o g r a p h s w e r e t a k e n a t 75 kv. a t a m a g n i f i - c a t i o n o f 3 4 , 8 0 0 :t= 610. T h i s v a l u e i n c l u d e s t h e effect o f c o n t a m i n a t i o n . T h e v a l u e of S o b t a i n i n g w a s 5.77 =t= 0.08 X 10 -4 c m 2 g m . - 1 ; S w a s d e - t e r m i n e d u s i n g e q u a t i o n (10). B o t h ~ a n d S w e r e d e t e r m i n e d b y m e a s u r e m e n t s o n 10 poly- s t y r e n e s p h e r e s . T h e m e a n m a s s of t h e h e a d s o f t h e b a c t e r i o p h a g e ( t e n m e a s u r e m e n t s ) w a s f o u n d to be 3.00 =t= 0 . 1 4 X 10 -16 gin. T h i s v a l u e is p r o b a b l y low, d u e to t h e effects o f c o n t a m i n a t i o n , b y u p to 5 p e r c e n t . I f t h e h e a d is a s s u m e d to be h e x a g o n a l in s e c t i o n its m e a n d e n s i t y is 1.74 ::k 0.10 g m . c m 7 a (this v a l u e m a y be h i g h b y u p to 3 p e r c e n t d u e to e r r o r s in S o n l y ) . W i d e v a r i a t i o n s w e r e f o u n d in t h e m e a s u r e - m e n t s o f t h e m a s s e s o f p h a g e h e a d s s t a i n e d w i t h u r a n y l a c e t a t e . I t w a s a p p a r e n t t h a t t h e c o n d i t i o n s u s e d d u r i n g s t a i n i n g w e r e d e s t r u c t i v e a n d a n u m - b e r o f t h e p h a g e h e a d s w e r e e i t h e r p a r t l y or c o m p l e t e l y " g h o s t e d " t h r o u g h t h e loss o f d e o x y - r i b o n u c l e i c a c i d ( D N A ) . M a s s m e a s u r e m e n t s w e r e m a d e o n 25 s t a i n e d p h a g e h e a d s a n d v a l u e s of m a s s b e l o w t h e m e a n u n s t a i n e d v a l u e w e r e r e j e c t e d . T h e m e a n i n c r e a s e o f m a s s of t h e h e a d s d u e to s t a i n i n g w a s f o u n d to be a b o u t 45 p e r c e n t . D I S C U S S I O N T h e a s s e s s m e n t o f t h e v a l i d i t y o f a n e w e x p e r i - m e n t a ] m e t h o d d e p e n d s o n t h e a g r e e m e n t b e - t w e e n s i m i l a r m e a s u r e m e n t s m a d e b y t h e n e w

8 THE JOURNAL OF BIOPHYSICAL AND BIOCtIEMICAL CYTOLOGY • VOLUME 8, 1960

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m e t h o d a n d by well established ones. I n this work two c o m p a r a b l e sets of results are presented. T h e value of 7.74 -4- 0.42 X 10 -12 gm. found for the m e a n mass of a r a m s p e r m h e a d is to be c o m p a r e d w i t h the m e a n mass of 7.13 4- 0.29 X

10 -x2 gin. found b y interference microscope meas- u r e m e n t s o n ten similar h e a d s (30). T h e electron microscope value is very p r o b a b l y low by u p to 5 per c e n t due to the effects of c o n t a m i n a t i o n o n M . T h e layer of c o n t a m i n a t i o n w h i c h builds u p over the surfaces of the s p e r m heads will have little effect o n the m e a s u r e d mass since its effect will be to increase the thicknesses of the specimen a n d the s u p p o r t i n g film a t ( p r e s u m a b l y ) the same rate. T h e mass of the layer of c o n t a m i n a t i o n is, in a n y case, small c o m p a r e d w i t h the mass of the s p e r m head.

T h e mass of the h e a d of a T 2 b a c t e r i o p h a g e f o u n d b y electron microscopy is 3.00 4- 0.14 X 10 -16 gm. while Taylor, Epstein, a n d Lauffer (31) found values of 3.65 X 10 -16 gm. a n d 3.01 X 10 -16 gm. a t p H 5 a n d 7, respectively, from the c o m b i n e d results of s e d i m e n t a t i o n a n d diffusion measurements. T h e latter two values include the mass of the tail of the b a c t e r i o p h a g e particle a n d are absolute, i.e. do not d e p e n d o n a n assumed s h a p e for the particle. T h e tail has the dimensions 250 X 1000 A (35) a n d is associated w i t h a b o u t 10 per cent of the mass of the particle. T h e electron microscope value for the mass of the p h a g e particle is a g a i n very p r o b a b l y low by u p to 5 per cent due to the effects of c o n t a m i n a t i o n on M a n d S. However, it should be n o t e d t h a t the m e t h o d a d o p t e d in the m e a s u r e m e n t of mass using polystyrene spheres in order to d e t e r m i n e S involves essentially a comparison of the mass of a s p h e r e w i t h t h a t of the " u n k n o w n " particle. W h e n the two objects b e i n g c o m p a r e d are very similar in l i n e a r dimensions, as in the present case, the effect of c o n t a m i n a t i o n o n the measure- m e n t of mass will, to a large extent, cancel out. T h e mass of a n uncontaminated p h a g e h e a d should, therefore, p r o v i d i n g the rates of c o n t a m i n a t i o n of the two specimens are c o m p a r a b l e , be very close to the value o b t a i n e d w i t h o u t a p p l y i n g corrections for c o n t a m i n a t i o n , i.e. 3.00 d= 0.14 X 10 -16 gm. T h e value for the density of the m a t e r i a l of a p h a g e h e a d e v a l u a t e d o n the a s s u m p t i o n t h a t the h e a d is u n d i s t o r t e d o n d r y i n g is 1.74 d= 0.10 gin. cm. -3 (a value w h i c h includes a systematic e r r o r of u p to 3 per cent) a n d m a y be c o m p a r e d w i t h the density of dry D N A , i.e. a b o u t 1.65 gm. ~cm. -a.

W e believe the reasonable a g r e e m e n t between these electron microscope values for mass a n d density a n d those found by o t h e r m e t h o d s to be most e n c o u r a g i n g a n d t h a t u n d e r carefully controlled conditions the electron microscope c a n provide q u a n t i t a t i v e results. T h i s a g r e e m e n t , together w i t h the d e m o n s t r a t i o n t h a t polystyrene does not sublime a t low b e a m currents, gives r e a s o n a b l e evidence t h a t the p r i n c i p a l com- p o n e n t materials of the specimens used do n o t sublime in the electron microscope u n d e r the same conditions. T h e greatest systematic error to w h i c h the given m e a s u r e m e n t s are subject is due to the effect of c o n t a m i n a t i o n o n the value of M . T h i s error could be r e d u c e d or e l i m i n a t e d by using very short exposure times or by m e a s u r i n g M by a m e t h o d involving the s e p a r a t i o n of points. T h e present u n a n i m i t y of b o t h e x p e r i m e n t a l results a n d theoretical p r e d i c t i o n t h a t S is essentially i n d e p e n d e n t of Z for the usual o p e r a t i n g conditions in electron microscopy gives good reason for the supposition t h a t q u a n t i t a t i v e m e a s u r e m e n t s of the u p t a k e of electron stains by biological specimens, exemplified in this work by the m e a s u r e m e n t s on stained bacteriophage, are valid w i t h i n the present a c c u r a c y of m e a s u r e m e n t . Q u a n t i t a t i v e m e a s u r e m e n t s on t h i n sections are w i t h present e m b e d d i n g m e d i a subject to error because of the s u b l i m a t i o n of the e m b e d d i n g m e d i u m itself a n d because of the differential s u b l i m a t i o n of specimen material. T h e latter may, in fact, be due in some cases to the differential loss of e m b e d d i n g m e d i u m r a t h e r t h a n of m a t e r i a l from the specimen itself b u t this is of course no less serious.

The Minimum Mass Measurable by Electron Microscopy

T h e m i n i m u m mass d e p e n d s on the m i n i m u m l i n e a r dimensions in the p l a n e of the s u p p o r t i n g film for w h i c h phase a n d edge distortion effects are small a n d o n the accuracy w i t h w h i c h optical densities m a y be measured. T h e m i n i m u m dimensions will vary from i n s t r u m e n t to i n s t r u m e n t a n d will be a function of the coherence of the i n c i d e n t electron b e a m (13) a n d the various lens aberrations. For the present purpose a flat disc of 400 A d i a m e t e r in the plane of the s u p p o r t i n g film will be considered. T h e smallest m e a s u r a b l e density difference (DI - D~) is a function of the smoothness of the s u p p o r t i n g film, care t a k e n in specimen p r e p a r a t i o n , g r a i n in the p h o t o g r a p h i c

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plate, u n i f o r m i t y of illumination, a n d the desired accuracy of m e a s u r e m e n t . T h e effect of c o n t a m i - n a t i o n will be very i m p o r t a n t w h e n small particles are considered b u t c a n be minimised e i t h e r by short exposures of the specimen to the electron b e a m or possibly by using a specimen stage cooled to a n a p p r o p r i a t e t e m p e r a t u r e (12).

For small objects the f u n d a m e n t a l l i m i t a t i o n (neglecting c o n t a m i n a t i o n ) will be in the measure- m e n t of D, a n d D~ since these values will be almost e q u a l : for this case e q u a t i o n (4) becomes

1

fA

D l - - D,z

M = ~ j ~ d A

(11) If the r a n d o m errors in D1 a n d D~ are e q u a l a n d D, -- D ~ . of value x t h e n the fractional error in - - is

D2 2x

• If a 5 per cent error in the density ratio D2 - - D ,

is allowable on a single m e a s u r e m e n t , e q u a t i o n ( l l ) becomes, for a n object of c o n s t a n t thickness a n d density,

40x f Amin

~lmln =

SD--2

dA

(12)

A typical value of

x/D2

is 1/200 a n d for a flat disc of 400 A d i a m e t e r the m i n i m a l m e a s u r a b l e mass (to a n a c c u r a c y of 5 per cent on a single

2.5 X 10 -'2

m e a s u r e m e n t ) is a b o u t gin. For 75 S

kv. electrons the m i n i m u m mass is a b o u t 5 X l0 -17 gm. c o r r e s p o n d i n g to a m i n i m u m specimen thickness of 400 A for a material of u n i t density; from our results e q u i v a l e n t values for 25 kv. electrons would be a b o u t 2 X l0 -17 gm. a n d 160 A, respectively. For a n accuracy of l0 per cent these figures are halved.

M e a s u r e m e n t s of mass on the basis of e q u a t i o n (5) are necessarily less accurate t h a n those based o n e q u a t i o n (4) since the p h o t o g r a p h i c plate in the ,), region is less sensitive (10) to changes in image intensity.

Mass m e a s u r e m e n t s at low accelerating voltages should be more accurate (for a given specimen) t h a n m e a s u r e m e n t s m a d e at h i g h e r voltages, a n d m e a s u r e m e n t s should be possible o n t h i n n e r

specimens. However, for these a d v a n t a g e s to be realised it is necessary t h a t the resolution of the microscope at the lower voltages should be as good as t h a t n o r m a l l y achieved a t the usual o p e r a t i n g voltages of 50 to 100 kv. I t also a p p e a r s from the trend of the electron-scattering cross- sections s h o w n by our m e a s u r e m e n t s t h a t the very large increase in contrast c u r r e n t l y hoped for at low voltages m a y not occur.

A P P L I C A T I O N S

T h e q u a n t i t a t i v e methods developed here m a y be used u n d e r carefully controlled conditions to measure the mass, thickness, a n d density of suitable objects (the m a i n restriction being t h a t specimens should not sublime in the electron b e a m ) . T h e mass of a n object m a y be i m p o r t a n t of itself, or its rate of c h a n g e w i t h time or its c h a n g e w i t h chemical or physical t r e a t m e n t m a y b e of interest. As in o t h e r cytoehemieal methods a n a u t o m a t i c s c a n n i n g t e c h n i q u e m a y be desirable for the i n t e g r a t i o n of e q u a t i o n (4) in routine measure- m e n t s o n i n h o m o g e n e o u s biological materials. T h e following examples are illustrative' of the r a n g e of application.

1. T h e direct d e t e r m i n a t i o n of molecular weight by i n d i v i d u a l m e a s u r e m e n t s (lower limit a b o u t 107 at 25 kv. on the conservative estimates of the previous section) in contrast to the statistical average values found by o t h e r methods,

e.g,

u l t r a e e n t r i f u g a t i o n a n d light scattering. 2. T h e q u a n t i t a t i v e estimation of the u p t a k e of

electron stains by isolated specimens a n d regions of t h i n sections, a n d a n e v a l u a t i o n of the selectivity of such staining.

3. T h e d e t e r m i n a t i o n of specimen composition by mass m e a s u r e m e n t s before a n d after c h e m i c a l e x t r a c t i o n of a given c o m p o n e n t of the specimen.

4. T h e d e t e r m i n a t i o n of specimen thickness a n d shape a n d the thickness of t h i n sections.

We are indebted to (the late) Dr. A. Walton for the supply of ram sperm and to Dr. G. L. Brown for the bacteriophage. We are grateful to Professor J. T. Randall, F.R.S., for facilities and advice.

One of us (N. R. S.) wishes to acknowledge the receipt of a maintenance award from the Department of Scientific and Industrial Research.

10 T n n JOURNAL OF BIOPHYSICAL AND BIOCHEMICAL CYTOLOGY • VOLUME 8. 1960

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BURGE AND SILVESTER Quantitative Electron Microscopy 11