electron microscopic examination of subcellular fractions ...€¦ · electron microscopic...

ELECTRON MICROSCOPIC EXAMINATION

OF SUBCELLULAR FRACTIONS

II. Quantitative Analysis of the Mitochondrial

Population Isolated from Rat Liver

PIERRE BAUDHUIN and JACQUES BERTHET

From Laboratoire de Chimie Physiologique, University of Louvain, Louvain, Belgium

ABSTRACT

Large granule fractions, containing about 80 % of the cytochrome oxidase of the tissue, wereisolated from rat liver and used to prepare thin pellicles of packed particles which weresubmitted to quantitative electron microscopic examination. Various parameters describingthe mitochondrial population were determined by measuring the size and number of mito-chondrial profiles in sections, and the ratio of the inner to the outer membrane area. Themean particle radius and volume were found to be respectively 0.38 /p and 0.29 3; theaverage areas per mitochondrion were 2 and 5 2 for the outer and inner membranesrespectively. On the basis of the cytochrome oxidase activity recovered in the particulatefractions, the results were extrapolated to the whole liver, and it was concluded that ratliver contains about 5.1011 mitochondria per gram; this corresponds to a volume of 0.14ml/g and to an area of 2.5 and 1 m2 /g for the inner and outer membranes respectively.The validity and the accuracy of these determinations is discussed and the results are com-pared to the information which has been obtained by independent methods or by other in-vestigators.

INTRODUCTION

Since the original publication of Delesse (18)numerous theoretical studies have dealt with the

derivation of quantitative analytical data frommeasurements made on thin sections of non-

homogeneous materials (3, 4, 12, 13, 20, 22, 28,

29, 32-35, 38-42). The methods worked out

have been applied at the light microscope level,

especially in the field of mineralogy, and have

recently been extended to the analysis of electron

micrographs of biological specimens (14, 21,

29, 31). The procedures applied so far in the field

of electron microscopy have one weakness incommon, that they do not allow an estimate of

the size distribution of the particles under study.They are further complicated by the difficulty

of obtaining statistically representative specimens

when the analyzed material displays considerablemicroscopic and submicroscopic heterogeneity.The present paper describes a method based onthe original work of Wicksell (41, 42), whichpermits the size distribution of particles to bederived from measurements made on micro-graphs. It is applied here to a study of isolatedrat liver mitochondria prepared for electronmicroscopy by a filtration method which satis-fies the criterion of random sampling, and thusallows direct comparison between biochemicaland morphological data.

MATERIALS AND METHODS

Liver tissue from female rats was fractionated by theprocedure of de Duve et al. (17), abbreviated to

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Published December 1, 1967

yield a crude nuclear fraction (N), a large granulefraction (M + L), and a microsome-containingsupernatant (P + S). All fractions were analyzed forcytochrome oxidase (2) and protein (30).

Samples of M + L fractions originating from aknown weight of fresh liver were fixed with glu-taraldehyde, packed by filtration through a Milliporemembrane of 0.1 pore size, postfixed with osmiumtetroxide, dehydrated, embedded in Epon, and sec-tioned, according to the procedures described in apreceding paper (7). Ribbons of consecutive ultra-thin sections (40-60 mp), separated each time by athick section (100 u), were deposited on 200-meshgrids, and a single square of each grid was photo-graphed. This precaution ensured that each recordedtransection belonged to a different particle. Eachphotographed field included the whole thickness ofthe pellicle, and could therefore be considered asproviding a true random sample of the preparation(7). That the space between the mitochondrial pel-licle and the covering layer of erythrocytes was es-sentially void indicates that very few mitochondriabecame detached from the surface of the pellicle inthe course of the manipulation.

The micrographs were taken with a SiemensElmiskop I electron microscope at 60 kv. The finalmagnification, of the order of 15,000, was the samefor all micrographs of a given preparation, which wereenlarged at the same time. It was determined in eachcase by means of a grating replica (E. F. Fullam,Inc., Schenectady, N. Y.) which was photographedunder the same conditions as the preparation. Theonly source of error then is a difference in positionbetween the grating replica and the specimen gridin the microscope; this necessitates a different cur-rent in the objective lens. The ensuing error is small(less than 2c in our conditions), especially since theintermediary lens was used independently of the ob-jective lens. The distortion of the image owing tospherical aberration was checked and found to beless than 2o with the lens currents used. No correc-tion was introduced for compression artifacts, sincethey also were found to be small, in agreement withthe findings of Loud et al. (29) for Epon embedding.Fig. I is an example of the micrographs used forquantitative analysis.

The photographs were scanned systematically overthe whole thickness of the pellicle with a Zeiss TGZ 3particle dimension analyzer and the diameter of eachrecognizable mitochondrial profile was estimated andrecorded in the appropriate size class. The classeschosen differed by 1.l-mm increments in diameter;this corresponded to two adjacent classes foreseen inthe apparatus, since this was considered the limit ofresolution that could be achieved. Some 8 10 micro-graphs were scanned, which covered a total distanceof at least 100 p along the surface of the pellicle. Thisdistance, to be designated as the width W of transec-

tion analyzed, was also measured on the micrographs.The instrument used is constructed for the measure-

ment of circular profiles with a clearly definedcontour. As illustrated in Fig. 1, mitochondrial pro-files do not rigorously meet these conditions; thisraised some difficulties.

In the first place, many profiles are slightly ellipti-cal and some show fairly marked irregularities. In allthese cases, the size was estimated by equalizingvisually the nonoverlapping areas of the profile andof the measuring diaphragm; the diameter estimatedin this way is thus that of the circle having the samesurface area as the profile. For independent assess-ment of the degree of asymmetry of the particles, themajor and minor axes were measured with a ruler ona number of profiles chosen at random. As will beindicated in the section on Results, the average ec-centricity of the profiles was found to be small andthe measurements of surface area made in the man-ner described may be considered relatively accurate.

As shown in Fig. 1, the most easily recognizableboundary of the profile is the inner membrane orcontour of the mitochondrial matrix; the outer mem-brane is not always clearly seen and often shows acrenated or irregular appearance. When the outermembrane was sharp and close to the matrix, it wastaken as the boundary of the profile; in the placeswhere the membrane was apparently absent or obvi-ously detached from the inner membrane, the latterwas taken as the boundary. In profiles arising fromparticles cut far from the equator, the limiting mem-brane is not sharp, owing to the finite thickness of thesections; it is very likely that the area of the profilewas slightly, but systematically, underestimated inthis case. Whenever the identification was doubtful,the profile was not measured or counted. There isthus little doubt that a number of mitochondrialprofiles were excluded from the analysis because theydid not show clear evidence of a double, surroundingmembrane or of internal cristae. The profiles missedfor this reason were mostly those of near polar sec-tions. Fortunately, the mathematical proceduresapplied are such that the errors resulting from thistechnical limitation can be partly corrected for. Asusual in large granule fractions isolated from liver, afew mitochondria were swollen and had a matrix oflower than normal density. Swollen mitochondriawere counted with the others if they clearly exhibitedmorphological features which allowed them to berecognized as mitochondria; the main criterion wasthe presence of characteristic cristae.

As recorded in the instrument, the results could beused directly for the construction of a histogram ofprofile radii R, on an abscissa scale determined bythe magnification of the micrographs. Since the mag-nification varied somewhat from one experiment tothe other, whereas the size classes of the analyzer areinvariable, the divisions on the histogram were not

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FIGURE 1 Example of micrograph used for quantitative analysis. X 12.000.

PIERRE BAUDHUIN AND JACQUES BERTHET Examination of Subcellular Fractions 633

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exactly the same for different preparations; theywere of the order of 0.04 u.

A second type of measurement was made on themitochondrial profiles. An array of parallel lines wassuperimposed on the micrographs, and the number ofintersections of grid lines with the outer membraneof mitochondria and with the membranes of cristaewas counted.

MATHEMATICAL PROCEDURES

The theories on which our mathematical methods

are based have been developed by others. Werestrict their description to an outline of theprinciples and to the mathematical procedureswhich we used in their application to our measure-ments.

Theory

Let a population of n spherical particles ofvariable volume v or radius r be distributed atrandom within a given solid of volume V throughwhich an infinitely thin section of surface area Ais cut; let the radii R of the N circular profilesincluded in the section be measured; if a profileis not circular, R is the radius of the circle ofequivalent area.

(a) According to the principle established byDelesse (18), the fractional surface covered bythe profiles in the section is equal, within thelimits of sampling fluctuations, to the fractionalvolume occupied by the particles in the solid:

N n

Er-R2 E v (1)A V

which may also be written

n V = = rR (2)A

in which is the mean volume of the particles.In our experiments, the pellicles have a con-

stant area equal to 8.7 X 10' /p2. Thus

A = W X 7 (3)

and V = 8.7 X 107 X T (4)

in which I l' is the total width of the sectionsscanned and T is the thickness of the pellicle.

From equation 3 and 4 we obtain

V 8.7 X 107

A W(5)

and equation 2 becomes

8.7 X 107N

n = . E rR2. (6)

It will be noted that the pellicle thickness,which varies somewhat owing to unequal localpacking, cancels out in the derivation of equation5 and need not be known. In connection withthis, it may also be observed that the perpendicu-larity of the section with respect to the pellicleplane is not very critical. An error of 10 ° willchange the area of the pellicle section only by1.5%.

(b) As first shown by Wicksell (41), it is possibleto deduce the frequency distribution of particleradii r from that of the profile radii R. Fig. 2illustrates the principle of Wicksell's procedure asapplied to a simple case. The measured profileradii R are plotted in histogram form (Fig. 2 a).From the size and frequency of the radii in theupper class, which obviously represent the actualradii r of the largest particles of the population,one computes the size and frequency of the cor-responding class of particle radii (bar I in Fig.2 d), as well as the contribution of the particlesfrom this class to the other classes of profile radiithrough nonequatorial sections (darkened area inFig. 2 a). A new histogram is obtained by sub-traction (Fig. 2 b), and the calculation is repeatedfor the subsequent class of particles, whose equa-torial sections now form the upper class of profileradii in the new histogram. This procedure isrepeated until all profile radii have been ac-counted for, a result which is achieved at thethird step in the example of Fig. 2. In practice,these repeated subtractions are not carried outexplicitly. As shown by Wicksell, the problem canbe reduced to the solution of a set of linear equa-tions; the details of the calculations and theirtheoretical justification can be found in theoriginal paper (41).

Once the frequency distribution of particleradii r has been computed in the above manner,it is a simple matter to construct the correspondingfrequency distributions of the surface areas a andthe volumes v of the particles and also to calculatesuch relevant data as the means r, a, and and,the medians r, a, and v, as well as the corre-sponding standard deviations. The shape of these

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distributions can also be analyzed and eventuallycharacterized mathematically by fitting theappropriate statistical frequency function. Aparticularly useful parameter extracted by theanalysis is represented by the mean particlevolume i, which, when introduced in equation 2,may serve to calculate the total number of par-ticles n.

(c) If a grid is superimposed on an infinitelythin section through a two-dimensional structure,the number of intersections of the grid lines withthe structure is proportional to the area of the

urement of the area of the outer membrane,which corresponds to the area of the particles asobtained by the Wicksell procedure, equation 7may serve to calculate the mean area of the innermitochondrial membrane.

Application

In applying these methods we encounteredvarious difficulties. Some of them are inherent toelectron microscopic studies of subcellular par-ticles; others arise from the use of a particulatefraction. Since some of these problems could lead

0.2

0 0.

C

k._...i[' '

O.6

0.A

0.2

0 0.2 0.4 0-6

b~

08 0 02 0.4 0.6 08

RADIUS (p)

FIGURE Principle of the calculation ofthe particle sizes from the profile sizes. Thehistograms a, b, and c represent frequenciesof profile radii, while d represents the fre-quencies of particle radii in the correspond-ing population. See text for further explana-tions.

latter (35). This principle forms the basis of themethod used here to measure the ratio of inner-to-outer mitochondrial membrane area.

We consider, in first approximation, that theinner membrane is composed of an envelopeapposed to the outer membrane and having thesame area as the latter, and of infoldings or cristae.Then if N, is the number of intersections of thegrid lines with the boundary of the mitochondriaand if N, is the number of intersections withthe membranes of the cristae (two for each crista),we may write

area of inner membranearea of outer membrane

in which

N,q = (8)

Since we have available an independent inmeas-

to modifications in the computation procedures,they are discussed here in a systematic manner.

THE SHAPE OF THE PARTICLES IS NOT

PERFECTLY SPHERICAL: This difficulty does

not invalidate the measurement of the totalvolume (equation 6) or the determination of theratio of the membrane areas (equation 7). As toWicksell's calculations, equations valid forellipsoids of revolution have also been worked outby this author (42). When ellipsoids of axialratio smaller than 1.4 are treated as spheres, theerror on the parameters of the distribution fallsbelow that to be expected from sampling fluctua-tions if the analysis is restricted to 4,000 particles,provided that one takes as value for the radius ofthe profiles the geometric mean of the major andminor axes, as was done here. The radius of theparticle will then correspond to the radius of asphere having the same volume as the ellipsoid.This procedure, termed "spherical reduction" byWicksell, should be regarded as a mathematicaltransformation, permitting convenient handling


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of the data. It does not imply that the eccentrici-

ties of the particles are disregarded and, as will

be shown, constitutes an acceptable approxima-tion for isolated mitochondria.

NOT ALL THE PROFILES OF THE PARTI-

CLES UNDER STUDY ARE MEASURED: This

difficulty is due to a minor extent to preparative

damage that renders some profiles unrecognizable,

and to a major extent to the impossibility of iden-

tifying the smaller profiles. These include many of

the sections passing near the pole of particles of any

size, and perhaps a few equatorial sections passing

through the smaller particles. As long as the classes

where profiles are missed do not include manyequatorial profiles, the error made in estimatingthe distribution of particle sizes by the Wicksell

method will be small, since only equatorial pro-files are actually taken into account in this pro-

cedure (see Fig. 2): the calculation will simply

indicate that the number of profiles measured in

the smaller classes is less than that expected from

the contribution of the larger particles; the calcu-lated distribution of particle radii will neverthe-

less be correct. The missing nonequatorial profiles

can be retrieved by computing the expected fre-

quencies of profile radii from the known particle

radii distribution. If the population contains

particles whose radius falls within the range whereprofiles are not all recognized, it is obvious that

the data do not supply information on the fre-quencies of these small particles. Unless some

extrapolation is made, the analysis gives a trun-

cated distribution of the particle radii.

It must be pointed out that the missing profiles

have to be included in the summations of equa-

tions , 2, and 6 for a rigorous application of

Delesse's principle. Therefore, analysis of the

population by Wicksell's procedure should be

performed before an attempt is made to apply

these equations; this will provide the best estimate

of the missing profile frequencies. Fortunately,since the missing profiles are those with the small-

est radii and since the squares of the latter actually

enter into the equation, errors on this estimate are

of relatively minor importance if enough larger

profiles exist.' This will be shown to be so in the

present case.

' When sections are made at random through a sphere,86.6% of the profiles have a radius larger than one-half the radius of the sphere; the integral of the areasof these profiles represents 97.4% of the volume of thesphere. Thus, if liver mitochondria formed a homo-

THE SECTIONS ARE NOT INFINITELY THIN

BY COMPARISON TO THE SIZE OF THE

PARTICLES: The average diameter of an iso-

lated rat liver mitochondrion is about 0.8 /A; thesections used in our work have an estimated thick-

ness of about 0.05 /p. If mitochondria are consid-

ered as opaque bodies in a transparent medium,the radius of the profiles is thus overestimated,

except for sections close to the equator; on the

average, the measured profile areas would be10%/O larger than the ideal areas in infinitely thin

sections (25). However, the near polar sections of

the particles which are the main contributors tothe error are largely excluded from our measure-

ments. Moreover, when a mitochondrion is cut

far from the equator, the outline of the outer

membrane is not sharp, and as is pointed out in

Material and Methods, the actual area of the

profile was somewhat underestimated. Finally,

when the outer membrane was not clearly recog-

nizable or was very irregular, the measurementwas based on the contour of the matrix; this leads

again to some underestimation of the profilearea of the whole mitochondria.

We attempted to make approximate estima-tions of the influence of all these factors. The

analysis of the experimental data shows that

many profiles are not recognized when their

radius is smaller than 0.2 u. As explained above,

the truncated distribution of particle sizes is

independent of the frequencies, and thus of the

sizes, of the profiles smaller than the truncation

level. Almost one-half the error owing to the

thickness of the section is eliminated by the trun-

cation. The remaining error seems to be approx-

imately compensated by the other bias in the

measurements. Thus, the accuracy of our esti-

mates would probably not be improved by intro-

ducing corrections for the section thickness.THE M + L FRACTION DOES NOT CON-

TAIN ALL THE MITOCHONDRIA PRESENT IN

THE AMOUNT OF LIVER FROM WHICH IT

ORIGINATES, AND THE ISOLATION PROCE-

DURE MAY HAVE ALTERED THE CHARAC-

TERISTICS OF THE PARTICLES: Extrapola-tion of the results to the whole liver raises more

serious problems. Following the accepted practicein this laboratory, we may take advantage of the

enzymic determinations by using a correction

geneous population of spheres with a radius of 0.4 A,ignoring all profiles of radius smaller than 0.2 uwould amount to neglecting 2.6% of the profile area.


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factor based on the postulates of biochemicalhomogeneity and single location. As defined byde Duve (15), the former of these postulatesassumes that the enzymic activities per unit massor protein content (specific activities) are thesame for all subclasses of particles within a givenpopulation, and the latter that individual enzymespecies occupy a single intracellular location.Since all subcellular particles of a given type havealmost the same density, the first postulate isequivalent to the assumption of a constant en-zymic activity per unit volume.

Let E be the activity in the M + L fraction ofa reference enzyme obeying the above postulates(cytochrome oxidase 2 in the present instance),expressed in percentage of its total activity in thehomogenate; let w be the amount of the M + Lfraction included in the whole pellicle, expressedin grams of liver from which it originates; let n bethe number of particles in 1 g of liver and rtheir average volume (n and have the samemeaning as before, i.e., they refer to the numberand to the average volume in the pellicle). Therelationship between n and n is immediatelyderived from the postulates above:

nV 100n = - - (9)

w E

In addition to the postulates on which it rests,several other conditions must be satisfied for thisequation to be valid: (a) E must be a correctexpression of the relative enzymic activity of theM + L fraction; this implies both accurate deter-mination and quantitative recovery of this activ-ity in the various fractions analyzed; (b) the mito-chondrial volume must be unaltered by prepara-tive artifacts; (c) the method used to prepare theM + L fraction must not have divided the popu-lation into two groups differing in mean volume.

All three conditions must be met if the absolutenumber n of particles per gram liver is estimated(by making = ).

Only the first two must be satisfied when thetotal volume occupied by the mitochondria inthe liver, n, is computed from their total vol-ume in the pellicle, n.

2 Since cytochrome oxidase belongs to the inner mito-chondrial membrane, the postulate of homogeneityimplies that the area of the inner membrane with itsinfoldings is proportional to the volume of the par-ticles.

Computation Procedures

In early stages of this work, Wicksell's proce-dure was used as such. This required conversionof the experimental histogram of profile radii to asmooth frequency distribution curve, which wasthen redivided to form a 15 class histogram, neces-sary for application of the coefficients of equation18 of Wicksell's paper (41). After greater famili-arity with the method was achieved, a computerprogram, applicable to any number of classes andallowing direct handling of the experimentalresults, was developed on the basis of Wicksell'sequations 16 bis.

RESULTS

Shape of Mitochondria

From measurement of longer (a) and shorter(b) axes on 224 profiles chosen at random, wehave calculated the corresponding profile eccen-tricities, defined as / a2 - b2/a. These valueswere used to establish the distribution of themitochondrial eccentricities by means of Wicksell'sprocedure for prolate ellipsoids (42). The meaneccentricity was found to be 0.4 with a standarddeviation smaller than 0.1; it made very littledifference whether the eccentricity was assumedto be independent of the longer axis, the shorteraxis, or the volume of the particles. An eccen-tricity of 0.4 corresponds to an axial ratio of 1.1,well below the limit of 1.4 set by Wicksell (seeabove). It therefore seemed legitimate to use inthe calculations the method of spherical reduc-tion proposed by this author.

Size Distribution of Mitochondria

The histograms shown in the upper half of Fig.3 summarize the results of direct measurements ofprofile radii, made in each case on some ,000profiles, on four different preparations. WhenWicksell's procedure was applied to these histo-grams for derivation of the distribution of truemitochondrial radii, negative values were ob-tained for the frequency of radii smaller than 0.2pu; this indicated that the number of profile radiiin the lower classes of the experimental histo-grams was smaller than that to be expected fromthe sole contribution of nonequatorial sectionsthrough particles of larger size. This difficultywas anticipated, since, as mentioned above,many of the smaller profiles could not be identi-

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fied with certainty as belonging to mitochondriaand were for this reason neglected in the scanningof the micrographs. As a minimum correction toavoid nonsense, it was assumed that the neglectedprofiles were all nonequatorial and the computerwas programmed to treat all negative values aszero. The distributions of mitochondrial radiicalculated in this manner are shown in the lowerhalf of Fig. 3. By definition, these histogramscomprise no classes of radii smaller than 0.2 ,since this would require equatorial sections to beincluded in the corresponding classes of profileradii. The shaded areas in the upper histogramsrepresent the neglected profiles.

PROFILE RADIUS (,u)

0 04 08 0 04 0.8 0 04 0.8 0 0.4 0.8

100- -100

0 r -n W F X X I

t.u

00

' o'.~ ' 6 ' o '. ' o1 ' o'. ' o10 0. 80 0 080 0 .

chondrial volumes that can be constructed fromthe former. In these computations, the particles ineach size class have all been treated as having themean radius characteristic of the class.

The subsequent steps of the computations areeasily followed on Table I. Under total profilearea we give the sum of all the surfaces actuallymeasured, as they can be derived from the experi-mental histograms of Fig. 3. Addition of themissing profiles (shaded areas of the histograms ofFig. 3) leads to the corrected total profile area. Itis seen that this correction amounts to only a fewper cent. The total volumes of the mitochondriain the pellicle and in the liver are then derived

FIGuE 3 Size distributions of llito-chondria in the four experiments. Theupper diagrams represent the distribu-tion of profile radii while the lowerdiagrams give the distribution of theparticle radii computed according toWicksell (41). In the upper diagramsthe shaded area represents the correc-tion for the near polar sections whichwere not identified in the counting pro-cedure.

PARTICLE RADIUS (p)

Number and Average Volume

of Mitochondria

In Table I are listed other experimental dataobtained on the four preparations as well as thevarious values which could be computed fromthe results by application of the equations givenin Mathematical Procedures; and 7l are as-sumed to be equal.

On an average, the M + L fractions contained78.1% of the cytochrome oxidase activity foundon the homogenates. When corrected for therecovery, which varied between 88.7 and 98.2%(average, 93.8%), this amounted to 83.3% of thesum of the activities recovered in the three frac-tions. Most of the remainder (14.3%) was in thenuclear fraction (N), with only 2.4% in the micro-some-containing supernatant P S.

The parameters characterizing the size distri-bution of the mitochondria are those that can beobtained directly from the histograms of mito-chondrial radii or from the histogram of mito-

from the corrected total profile surface area bymeans of equations 6 and 9. Divided by the meanvolume ( and 3j are assumed to be equal), theygive the numbers n and n, of mitochondria in thepellicle and in the liver.

Areas of Mitochondrial Membranes

In Table II are listed the inner-to-outer mem-brane area ratios, as they have been measured bythe grid method and calculated by equations 7and 8. The average areas of the outer mitochon-drial membrane were computed from histogramsof mitochondrial area constructed from the distri-butions of particle radii. The numbers nl of TableI were used for computing the total areas pergram of liver.

Statistical Evaluation

The statistical evaluation of our data raisessome difficulties, even though the variance of thepopulation is known, because the relationshipbetween the number of profiles counted and the

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TABLE I

Results Pertaining to the Radius, Volume, and Number of Mitochondria

PreparationAverage

I II III IV

Cytochrome-oxidase7 of the homogenate 77.3 80.0 78.4 76.6 78.1X of total recovered activities 87.1 81.5 83.6 81.2 83.3

Amount w of fraction filtered, mg liver 2.46 2.50 2.50 2.50 2.49Total width W of sections scanned, p 105.5 120.4 136.3 129.9 123.0Number of profiles measured 959 951 966 1030 977.0Median particle radius r, [A 0.367 0.384 0.353 0.375 0.370Mean particle radius , / 0.379 0.399 0.370 0.381 0.382Standard deviation of radius, 0.098 0.102 0.103 0.106 0.102Mean particle volume , ,s(3 0.274 0.321 0.265 0.287 0.287Total profile area, pu2

uncorrected for missing profiles 380 418 383 432 403corrected for missing profiles 383 423 388 443 409

Total volume of mitochondria in pellicle, 3.16 3.05 2.47 2.96 2.91As3 X 108

Total volume of mitochondria in liver, 0.148 0.150 0.118 0.146 0.141ml/g of liver

Number n of mitochondria in 10-12 g 0.538 0.467 0.446 0.508 0.490liver

TABLE II

Results Pertaining to the Areas of Mitochondrial Membranes

PreparationAverage

I II III IV

Mean particle outer area, U2 1.92 2.13 1.86 1.96 1.97Ratio of inner to outer membrane area 2.7 2.4 2.5 2.6 2.6Surface to volume ratio, -' 7.01 6.64 7.00 6.83 6.87Total mitochondrial membrane area,

m2/g of liverouter membrane 1.03 0.99 0.83 1.00 0.96inner membrane 2.78 2.38 2.08 2.60 2.46

number of degrees of freedom is uncertain. Wick-sell (42) assumed that these numbers can betaken as equal for large samples; he implies in factthat measuring profile diameters supplies as muchinformation as measuring particle diameters. Al-though this is certainly not rigorously correct, it isprobably an acceptable approximation, especiallyif we exclude from the profiles those which arenot effectively used in the computation becausetheir radii fall below the truncation level. Thisleaves at least 800 profiles in each of our experi-ments. Since the standard deviation of particle

radius is about 0.1 u, its standard error will be ofthe order of 0.1/V/800 = 0.0035 . By thiscriterion, the values of mean radius obtained inthe four experiments are significantly different(P < 0.001).

Another and perhaps more direct way of assess-ing the significance of differences between experi-ments is to compare the profile distributions,which represent the actual experimental results.Using for this purpose the test of KolmogorovSmyrnov (26), we have also found that the fourprofile distributions are have significantly different

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5PROFILE RADIUS ()

- FREQUENCY

0.2 04 0.6 0.8PARTICLE RADIUS (p)

FIGURE 4 The open part of the upper diagram repre-sents the compound histogram derived from the fourexperiments as explained in the text. From this histo-gram, the particle size distribution shown in the lowerdiagram was computed. As in Fig. 3, the shaded areain the profile histogram corresponds to the missed pro-files. The continuous curve in the lower diagram repre-sents the log-normal function fitted to the particle sizedistribution; that in the upper diagram gives the cor-responding theoretical profile distribution.

(P < 0.01). A substantial part of the difference

arises from the frequencies of the smaller profilesbelow the truncation level of 0.2 , probably

because they were more easily recognized in some

preparations than in others. However, exclusionof the smaller profiles from the calculation led to

mean profile radii which, though falling within anarrower range, were still significantly different

(P < 0.01).Finally, we have calculated the variation co-

efficient of the total particle volume. It is given infirst approximation by the variation coefficient ofthe number of profiles measured per unit area of

section. Since this number obeys a Poisson distri-bution, with 1000 measurements, the total mito-chondrial volume is known with a precision ofabout 1/A/1000, or 3.5%. The differences foundbetween the four experiments are much largerand obviously statistically significant. Thus ac-cording to the three tests applied, it appears thatthe four preparations examined cannot be con-sidered samples of the same parent population.

Pooled Results

Although significantly different, the results ofthe four experiments may nevertheless be pooledto provide a better representation of the mito-chondrial population in an average M + L frac-tion. This is best done on the profile radii. Directsummation of the data being impossible owing toslight differences in final magnification of themicrographs, and therefore in size classes, a pre-liminary homogenization of the results had to beperformed. To do this, we divided each experi-mental histogram into equal size classes of 0.03 uand measured the mean ordinate of the fractionalareas covered by each division to obtain compa-rable frequencies. The compound histogram ofprofile radii was obtained from the sum of thecomputed frequencies (upper half of Fig. 4).These, in turn, served to calculate the corre-sponding histogram of particle radii (lower halfof Fig. 4). In addition, the total volume occupiedby the mitochondria in each size class was calcu-lated from the compound histogram of particleradii. The normalized results of this computationare represented in Fig. 5 which gives the distribu-tion of total mitochondrial volume as a functionof particle size. The main parameters estimatedfrom the pooled results are listed in Table III.They are not different from the averages given inTables I and II.

Log-Normal Fit

Following the example of Bahr and coworkers(6, 24) we have also attempted to fit a log-normalfrequency distribution to the compound histo-gram of mitochondrial radii, by using a methodof maximum likelihood which took into accountthe truncation of the histogram at the 0.2 pu level.By reversing Wicksell's method, the distributionof profile radii corresponding to the fitted log-normal function was also calculated. The com-puted curves are represented in Fig. 4, and thecorresponding parameters are listed in Table III.

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FIGURE 5 Distribution of the total

mitochondrial volume as a function ofparticle size. The histogram is deriveddirectly from the lower diagram ofFig. 4.

MITOCHONDRIAL RADIUS (u)

At first sight, the fit between the computedlog-normal function and the pooled histogramappears reasonably good. However, by applyinga X2 test to the predicted and observed values ofprofile radii (upper part of Fig. 4), above thetruncation level, we have found them to be sig-nificantly different (P < 0.01); this suggests that

a single log-normal function may not adequatelyrepresent the mitochondrial population of theliver. The discrepancy does not arise from thepooling of results obtained on possibly dissimilarpreparations, for the same conclusion was arrived

at when the results of each individual experimentwere treated in this fashion (P < 0.05). Suchdeviations are much less evident when the distri-bution is graphed in cumulative fashion on log-probit paper, as was done by Bahr and coworkers(6, 24). As shown by Table III, the values of themain parameters are the same, whether they are

calculated with or without log-normal fit.

DISCUSSION

Applicability and Validity of the Technique

Although it has been used here with isolatedparticle fractions, the technique described in thiswork can theoretically be applied equally well tointact tissue sections. The choice of one materialor the other is a matter to be decided in each case.Our own approach has been dictated by thedesire (a) to combine quantitative morphologywith the numerous resources, already exploited inthis laboratory, of quantitative biochemistry, and(b) to overcome the serious difficulty arising fromthe heterogeneity of intact tissues, by taking

TABLE III

Characteristics of the Mitochondrial PopulationDerived from the Pooled Results

Withoutlog-normal With log-

Parameter fit normal fit

Median particle radius, pA 0.371 0.368Mean particle radius, u 0.385 0.381Standard deviation of radius, 0.102

Standard deviation of logo 0.118(radius)

Mean particle area, A2 2.00 1.97Mean particle volume, 3 0.292 0.289

advantage of the randomizing effect o homoge-nization, associated with a preparative techniqueallowing random sampling. These advantageshave to be weighed against the losses and morpho-logical alterations caused to subcellular particles

by tissue disruption and fractionation in a foreignmedium. In the present application to mito-chondria, the choice of isolated fractions may notappear compelling. But it becomes more so whenit comes to evaluating the size and frequency ofrarer cytoplasmic particles that are very hetero-geneously distributed within cells, such as peroxi-somes, lysosomes, or autophagic vacuoles. Therecent work of Deter et al.3 gives a good exampleof this type of application. We decided to make

3 Deter, R. L., P. Baudhuin, and C. de Duve. 1967.Participation of lysosomes in cellular autophagy in-duced in rat liver by glucagon. J. Cell Biol., 35: Cl 1.

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rat liver mitochondria the first test object of thetechnique because considerable information, someof it mutually conflicting, has already been pub-lished on the dimensional parameters of theseparticles. Thus it was possible to evaluate criticallythe technique itself, and perhaps at the same timeto resolve some of the discrepancies occurring inthe literature.

As a biometric tool, our method rests on thesame principles utilized by other workers (14, 21,29, 31), except that it utilizes the procedure ofWicksell (41, 42) for derivation of the size distri-bution of particles from measurements of theirprofiles in thin sections, and thereby provides acomplete description of a population of particles,including their absolute number. Another mor-phological technique allowing an estimate of thisnumber, that described by Weibel and coworkers(38-40), also relies on planimetry of profiles inthin sections, but uses a different mathematicalderivation for conversion of profile to particlefrequency. With Ni being the number of profilesper unit area of section, and Vi the fractional areaoccupied by the profiles in the section, the num-ber n of particles per unit volume is given, ac-cording to Weibel et al. (40), by the formula

Ni312n = D (10)

in which : is a shape coefficient, equal to 1.382for spheres, and D is a distribution coefficientequal to

D= 3 (11)

where m, is the nth moment about the origin forthe distribution of particle radii.

Compared with the Weibel procedure, themethod described in this paper has the followingadvantages:

(a) It gives an actual size distribution of theparticles, information which is of interest in it-self, and which also allows direct calculation ofthe coefficient D. With our material, we have ob-tained D = 1.11, a value very close to the valueof 1.1 recommended by Weibel et al. (38, 40) asbeing adequate for most particle populations.

(b) It allows automatic retrieval of many of themissing profiles (shaded areas in Figs 3 and 4)and is thereby less exposed to the intrinsic limita-

tion, common to both techniques, set by thedifficulty of identifying the smaller profiles. Forthis reason, the frequency Ni of profiles, thoughprobably still underestimated, is less so with ourmethod than with that of Weibel et al.

(c) It is less dependent on the accuracy of Ni,which comes into our calculation only indirectly,whereas it enters explicitly, raised at power /3, inequation 10.

For these reasons, the Weibel procedure, inaddition to giving less information on the particlepopulation, may be expected to yield a lowervalue than ours for the particle frequency ni.With our material, the deficit was found to be ofthe order of 20%. When the profiles retrieved bythe Wicksell procedure were taken into account,equation 10 gave results identical with ours.

There is, however, one weakness to the Wick-sell procedure. As can be seen from the schematicdrawing of Fig. 2, the number of profiles remain-ing at each step and taken to belong to equatorialsections is relatively small. Thus, an excess ordeficit of even a few profile leads to an over- orunderestimation of the contribution of nonequa-torial sections to the subsequent class of profileradii, which in turn results in an under- or over-estimation of the residual profile radii, in particu-lar of those attributed to equatorial sections in theadjacent class. In this manner, oscillations of thekind most clearly seen in the first computed histo-gram of Fig. 3 are easily generated. Thus themethod is more sensitive to sampling fluctuationsthan might be expected. We believe this fact tobe mainly responsible for the irregularities occur-ring in the computed histograms of Fig. 3 and 4.It should not greatly affect the statistical param-eters of the distribution derived from the histo-grams.

As already mentioned, our technique is limited,though less so than other morphological methods,by the possibility of recognizing the smaller pro-files. According to our experience, the limit belowwhich identification becomes difficult is about0.2 gu in radius. This limit is lower for equatorialthan for polar sections; it depends also on thedegree of preservation and on the distinctivenessof the particle structure. In this respect, tissuesections may provide more favorable conditionsthan isolated fractions.

It could be argued that, as long as the structuralintegrity of the tissue is sacrificed, one might aswell take advantage of this fact and use a direct

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counting technique. However, the counting tech-niques that have been described so far are allsubject to limitations that make them at least asunsatisfactory as the indirect methods, and fre-quently more so. Counting particles in hemocy-tometer cells under the phase-contrast microscope(1, 36) appears unreliable, even for particles aslarge as mitochondria (5, 24). Up to now, count-ing with the Coulter counter does not seem to beapplicable to spheres smaller than 0.15 3 (radiussmaller than 0.33 pA) (24). The direct particlecount in sprayed droplets described by Williamsand Backus (43) and modified by Bahr et al. (5),although not subject to any theoretical size limi-tation, in practice could not be used for mito-chondria weighing less than 0.03 ng (radius smallerthan 0.26 ) (6, 24). The reason for this is that,like all other direct counting techniques, it doesnot allow any accurate identification of the par-ticles and is therefore applicable only to purefractions, a condition not likely to be frequentlyfulfilled. With mitochondrial fractions, any suchtechnique becomes unreliable in the size rangeswhere contaminants, such as lysosomes andperoxisomes, contribute significantly to the totalnumber of particles. There is thus a real justifica-tion for a counting technique applicable to sec-tions in which particle profiles can be accuratelyidentified.

A technique of this kind, applicable to isolatedfractions has been described recently by Clementiet al. (14). It consists of embedding with the par-ticles a known concentration of polystyrene beadssimilar in size to the particles under study. Withpopulations having exactly the same size distribu-tion, the relative frequency of profiles down toany size limit gives a direct measure of the numberof particles. Obviously, the accuracy of this tech-nique depends on knowledge of the size distribu-tion of the particles to be counted and on the pre-cision with which this distribution is mimicked bythe reference beads. It also requires random mix-ing of the two populations in the embeddedmaterial, as well as special qualities on the part ofthe reference beads.

From the technical point of view, our methodrelies essentially on planimetry of profiles. As isexplained in Materials and Methods, we havefound it convenient to use a particle dimensionanalyzer for this purpose. The profiles were suf-ficiently close to circular to make this possible andthe recorded results could be used directly for

computation by spherical reduction according toWicksell's procedure (42). Other planimetricmethods should lead to equally valid determina-tions of the fractional volume of particles in cells(21, 29, 39) or in subcellular fractions (31); someof these methods have a more general applicabil-ity, since they are not restricted to near circularprofiles. As long as these are not too irregular, thesize distribution of the particles can still be esti-mated by one of the procedures of Wicksell (41,42).

Validity of Results

As indicated by our statistical analysis, the fourpreparations examined differ significantly fromeach other. Although nonreproducible artifactscould be involved, this variability is more likelyto be related to individual differences in the mito-chondrial composition of the liver. This is notparticularly surprising in view of the wide varia-tions that are encountered from one animal tothe other in the hepatic level of mitochondrialenzymes and in their specific activity in purifiedfractions. The pooled results which we have ob-tained thus provide us only with some kind ofestimate of an average mitochondrial population,the precision of which is best assessed by the stand-ard deviation of the means.

In Table IV are listed the data that are avail-able in the literature concerning liver mitochondria, together with the corresponding ones de-rived from our own investigations. For derivationof the mean dry mass of mitochondria from theirmean volume, we multiply the latter by 1.10, themeasured average density of the particles in 0.25M sucrose, and by 0.347, the ratio of their dry totheir wet weight (exclusive of the sucrose presentin the sucrose space) computed from the results ofdensity gradient centrifugation experiments (9, 16).

The midpoint radius of the total volume distri-bution has been estimated from Fig. 5. It is takento apply also to the distribution of total dry mass(assuming a constant average density in all sizeclasses) and to that of mitochondrial enzymes(assuming biochemical homogeneity). It serves tocalculate the median sedimentation coefficient ofmitochondrial volume, mass or enzymes in 0.25 Msucrose at 0° , by means of the Svedberg equationfor spherical particles, with 1.10 for the particledensity, as mentioned above.

Conversion of total mitochondrial volume torelative specific activity of cytochrome oxidase is

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TABLE IV

Comparison with Other Data

Parameter This work From literatureMean SD

Mean volume, gu3 0.287 0.025 0.430 (24) 0.806 (29)Standard deviation of logo 0.354 0.278 (24)

(volume)Mean dry mass, ng 0.110 0.010 0.121 (6) 0.136 (24)Standard deviation of log1o 0.354$ 0.212 (6) 0.249 (24)

(dry mass)Midpoint radius of distribution 0.465 0.445 (19) 0.446-0.478 (37)

of total volume, protein, orenzymes, A

Median sedimentation coeffi- 1.30 1.28 (19) 1.27-1.47 (37)cient of total volume, protein,or enzymes, 10-9 sec

Surface to volume ratio, /- 6.87 4- 0.17 7.14 (29)Total volume, cm 3

/g liver 0.141 0.015Total volume, cm3 /cm3 parenchy- 0.185 (29)

mal cytoplasmTotal number per ng liver 0.490 0.041 0.330 (1) 0.119 (36)Relative specific cytochrome 4.65 0.50 4§

oxidase activity

* In parentheses, reference number.$ Taken to be equal to the standard deviation of lglo (volume).§ Combined results from this laboratory (see, for example, references 10, 17).

done as follows. We first compute the total mito-chondrial dry mass as explained above (54 mg/gliver). Of this amount 80%, or 43 mg, is taken toconsist of protein on the basis of the nitrogendetermination of Glas and Bahr (24), which hasbeen confirmed in this laboratory. Since thelivers of our animals contain about 200 mg ofprotein per gram, we conclude that the specificcytochrome oxidase activity of pure mitochondriais 200/43 or 4.65 times that of a whole liverhomogenate. For this value as for that of drymass, we have assumed the relative standarddeviation to be the same as that of the determina-tion from which it has been derived.

Considering first the results obtained by otherworkers on isolated fractions, we note that ourcalculated value for the mean dry mass agreeswithin 10 % (one standard deviation) with thatdetermined experimentally by Bahr and Zeitler(6). Actually, the agreement may be even better,since the value of Bahr and Zeitler is obtained byfitting a log-normal function to a distributiontruncated at the level of 0.03 ng or 0.26 A inradius. They thereby exclude from their analysisany excess of smaller particles over their extrapo-

lated frequency. That such an excess may exist issuggested by our results (Fig. 4). This reasonprobably also explains the smaller standarddeviation arrived at by the authors. The sameconsiderations apply to the more recent value ofmean dry mass given by Glas and Bahr (24), withthe additional point that these authors separatethe mitochondria at a speed lower than those usedby Bahr and Zeitler (6) and in this work, Thustheir measurements apply to a somewhat biasedsample of the mitochondrial population, deprivedof its smaller members by the preparative proce-dure and characterized for this reason by a highermean dry mass.

The mean mitochondrial volume given by Glasand Bahr (24) is considerably greater than our ownestimate, and does not agree with their value of drymass. The agreement claimed by the authors isspurious, since it rests on the use of two erroneousconversion factors: 1.18 (attributed to Anderson)for the mitochondrial density and 0.263 (deter-mined by the silicone technique of Glas and Bahr,reference 23), for the ratio of dry-to-wet mito-chondrial weight. It is easy to see that these factorscannot both be correct, since a particle containing

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73.7% of water and having a wet density of 1.18has a dry density of 1.68, a most unlikely value fora structure made of mostly of proteins and lipids.The value of 1.18 represents the equilibrium den-sity of mitochondria in a sucrose gradient andapplies to particles almost completely dehydratedosmotically; as already mentioned, their density in0.25 M sucrose is lower, of the order of 1.10 (10).Furthermore, as shown elsewhere (11), the methoddeveloped by Glas and Bahr (23) for the deter-mination of the water content must lead to anoverestimation of this content. Our own estimateof 0.347 (16) corresponds to a dry density of 1.315,a very plausible figure. It appears from theseconsiderations that either the mean volume or the

indicates strongly that our measurements are notvitiated by serious artifacts, and also shows that thepostulate of biochemical homogeneity, on whichour conversion of mass to enzyme distribution isbased, represents a valid approximation. In con-trast, the distributions of enzyme frequency as afunction of particle radius reported by Swick et al.(37) are more Gaussian in shape and are charac-terized by a distinctly smaller standard deviationthan those derived from our determinations andthose of Deter and de Duve (19). They also differsomewhat from one mitochondrial enzyme to theother and thus contradict the postulate of bio-chemical homogeneity.

In the discussion of their paper, Swick et al. (37)

FIGURE 6 Cumulative distribution of the

sedimentation coefficients of cytochromeoxidase. The experimental results obtained byDeter and de Duve (19) are represented bythe broken line (median sedimentation coeffi-cient, 12,800S in 0.25 M sucrose). The con-tinuous line is derived from the size distribu-tion of mitochondria observed in this work(median sedimentation coefficient, 13,000S in0.25 M sucrose). The content of the first class,on which no information is supplied by themorphological analysis, was set equal to thecytochrome oxidase activity of the P + Sfraction (2.4%).

10

SEDIMENTATION COEFFICIENT (103S)

mean dry weight value given by Glas and Bahr(24) must be incorrect. In our opinion, the meanvolume value is more suspect since it is based on theuse of the Coulter counter, which, as mentionedby the authors themselves, was used at the limitof its resolving capacity and which ceases to bereliable below a particle volume of 0.15 A3. There-fore, we tend to attach more significance to theagreement between the mean dry weight values ofBahr and coworkers (6, 24) and our own, than tothe discrepancy between the mean volumes.

As shown in Table IV, there is also good agree-ment between our calculated values for the mid-point radius of the volume, mass, or enzymedistribution and for the corresponding mediansedimentation coefficient, and those determinedexperimentally by Deter and de Duve (19) andSwick et al. (37). As shown inFig. 6, the agreementbetween our data and those of Deter and de Duve(19) extends over the entire distribution; this

state that their results agree with the value of meanmitochondrial volume of Glas and Bahr (24),which we have criticized above as being overesti-mated. They write "Glas and Bahr (1966) reporteda mean particle diameter of 0.94 /u, which agreeswith our estimates (based on sedimentation charac-teristics) of the midpoint of the protein distribu-tion, 0.938 u." This statement is misleading in tworespects. First, 0.94 A is not reported by Glas andBahr (24) as a mean diameter; it is the diameter ofa particle having the mean volume reported bythe authors, which is not the same thing. Second,the midpoint diameter of the protein distribution,assumed to be equal to that of the volume distribu-tion, characterizes a particle which is necessarilybigger than the mean volume, since the number ofparticles of smaller volume included in the left-hand half of the distribution must be greater thanthat of particles of larger volume included in theright-hand half, whichever the shape of the


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distribution. The midpoint diameter calculatedfrom the log-normal volume frequency functiongiven by Glas and Bahr (24) is 1.02 /p; that ob-tained from our results is 0.93 p (Table IV). Thus,the results of Swick et al. (37) agree much betterwith our mean volume estimate than with that ofGlas and Bahr (24).

Summarizing this part of the discussion, we findthat, except for one serious discrepancy, which webelieve to have accounted for satisfactorily, ourdata agree reasonably well with those obtained byother authors on isolated rat liver mitochondria.Our mean values tend to be somewhat smaller, andour standard deviations somewhat higher, than thecorresponding values in the literature, possiblybecause our determinations extend further into thelower size range than those of others. As alreadypointed out, all techniques become unsatisfactorybelow a radius of 0.2-0.3 . Thus, one wouldexpect frequency distribution curves to be distortedin the lower size range in a manner suggesting adeficit of smaller particles. This tendency is notseen in our histograms, whereas the dry massmeasurements of Bahr and Zeitler (6) have ac-tually provided evidence of the existence of asecond population of smaller particles. These areassumed to be nonmitochondrial, but the pos-sibility that the liver may contain a population ofsmall mitochondria, originating, for instance, fromthe Kupffer cells cannot be discounted at thepresent stage. It must be remembered that a smallbut significant fraction (2.4%) of the cytochromeoxidase activity remains in the P + S supernatant.If this activity is associated with small intactmitochondria, their total number would be ap-preciable.

The literature contains little information thatcan help to test the validity of the manner in whichour results are extrapolated to whole liver. Ourestimated number of mitochondria is much greaterthan the values obtained by direct counts underthe phase-contrast microscope (Table IV), but thelatter method is so unreliable that no significancecan be attached to this difference. On the otherhand, our estimate of the total volume occupiedby the mitochondria appears not to be incom-patible with the value obtained by Loud et al. (29)on intact tissue sections. Unfortunately, the twovalues are not directly comparable, since that ofLoud et al. (29) applies to the cytoplasm ofparenchymal cells. However, taking 1.05 for thedensity of liver (8), we find that the two values

agree if it is assumed that the cytoplasm of paren-chymal cells occupies about 80% of the livervolume and that the volume occupied by themitochondria of nonparenchymal cells is smallenough to be neglected. These assumptions are notunreasonable. Our estimate of the surface-to-volume ratio also agrees with that of Loud et al.(29), but there is marked disagreement betweenthe mean volume given by these authors and ourvalue. The reason for this discrepancy is not clear,since Loud et al. (29) do not give the details oftheir calculations, but it is obvious that their resultsare not coherent. Spherical particles forming ahomogeneous population with an average surface-to-volume ratio of 7.14 -' should have a radius of3/7.14 = 0.42 u, and therefore a volume of 0.31p3. If they are not spherical (the authors' calcula-tions apply to right cylinders), their volume canbe only smaller, not 2.6 times larger. Furthermore,multiplying the mean mitochondrial volume giventhe authors by their value for the number ofmitochondria per p3 of cytoplasm, 0.292, leads to afractional volume of 0.235 which contradicts thevalue of 0.185 found by the authors by applicationof the Delesse principle.

As shown in Table IV, the relative specificcytochrome oxidase activity of pure mitochondriapredicted from our data is higher than the averagevalue obtained experimentally in this laboratoryon the purest mitochondrial subfractions. How-ever, such fractions still contain some contami-nants, and their relative specific cytochromeoxidase activity varies within a wide range, atleast between 3 and 5. Since our predicted valuesare also quite variable, the difference is certainlynot significant.

From a theoretical point of view, the main factorthat could seriously invalidate our estimate of thetotal mitochondrial volume would be the selectiveseparation with the nuclear fraction of a group ofmitochondria differing considerably in their cyto-chrome oxidase content from those present in theM + L fraction. It can be estimated from themanner in which the nuclear fraction is separatedthat, if their selection is due to their higher rate ofsedimentation, the mitochondria in this hypothet-ical group should have a radius of 1.2 u or more.There is no evidence of the existence of a specialpopulation of large mitochondria in rat liver andit must be noted that the M + L fraction containspractically no particle with a radius greater than0.8 p (Figs. 3 and 4). It seems more likely, there-


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fore, that the mitochondria in the nuclear fraction

are a fairly random sample of the total population

and are included in this fraction by an agglutina-

tion artifact. If such is the case, the losses to thenuclear fraction should not greatly affect our

estimate of the total volume of mitochondria, orthat of their total number. However, as has alreadybeen pointed out, the small amount of mitochon-

drial material present in the P + S fraction,although of little importance for the estimate of

total mitochondrial volume, if owing to smallmitochondria, could represent a larger number of

particles than that obtained by extrapolation,which assumes randomization of sizes in thisfraction as well.

From the practical point of view, there remainsthe possibility that the mitochondria suffer a

change in size as the result of isolation. Indeed, ascan be seen in Fig. , many particles appear

somewhat condensed and a few are highly swollen.

Appreciation of the incidence these artifacts may

have on the accuracy of our determination willhave to await more accurate measurements onintact tissue sections than have been made so far.

Another difficulty, which could be corrected by

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The authors wish to thank Dr. C. de Duve for hisactive interest in the investigations reported in thispaper; his numerous suggestions for the design of theexperiments, their interpretation, and the prepara-tion of the manuscript were an invaluable help to theauthors. They also wish to thank Professor Meinguetwho allowed them to use the facilities of the Comput-ing Center of the University of Louvain. The skillfuland generous assistance of Mr. J. P. Raucq in pro-gramming and operating the computer is also grate-fully acknowledged.

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