MICROVASCULAR

The

RESEARCH

l&43-64

Quantitative Capillaries J. R. CASLEY-SMITH,

(1975)

Morphology in Relation

of Skeletal Muscle to Permeability

H. S. GREEN, J. L. HARRIS, AND P. J. WADEY

Electron Microscope Unit, and Department of Mathematical Physics, University of Adelaide, South Australia 5001, Australia Received September IO, 1974 The numbers and dimensions of skeletal blood capillaries were observed in the gastrocnemii of eight dogs. The dimensions and proportions of the close and tight junctions were also recorded. (These were adjusted to take account of the random sectioning angles and the penetration of the section by the stain.) It was found that there were -260 km of capillaries, with a total area of -2 m2 per 100 g of muscle. The close junctional length was -21 km; that of the tight junctions was -430 km. The ratio of close/(close + tight) junction was -4.8 ‘A. Using previously recorded, but newly adjusted figures for the vesicles, showed that there were -1.1 x 1Ol4 free vesicles and 2.5 x 1Ol4 attached ones per 100 g. It was considered best to calculate the resistances of the whole cross sections of each junction, obtain the flow through this, and then summate these for all the observed cross sections, corrected for the total close-junctional length per 100 g. The capillary filtration coefficient (CFC) so obtained was -0.023 ml/min/mm HgjlOO g, which is very similar to that obtained by experiment. (This is even closer when account is taken of the CFC values of vasodilated muscle.) Similar calculations were made for the capillary diffusion coefficients (CDC) for several molecules. Again it was found that the results were very similar to those obtained by experiment, especially those obtained during vasodilatation. (This is understandable since all junctions were measured, notjust those in active capillaries.) The calculated resistance of the basement membrane was negligible for small molecules. Calculations using the vesicular parameters gave results for transit times, migration percentages, and the probabilities of fusion with a membrane. These accord well both with experiment and with a hypothetical model.

One of the most important regions for the physiological study of capillary permeability, is the hind leg of dogs and cats. Hammersen (1968) has reviewed the relatively scanty literature about the quantitative morphology of capillaries in the musclesof these legs. Unfortunately, the surface area estimations, which are so vital to many physiological measurements,have rarely beenextended from those which Pappenheimer(1953) made a quarter century ago, using the light microscope. Some interesting correlations of structure and function have been made (Bruns and Palade, 1968a; Garlick and Renkin, 1970; Karnovsky, 1970; Lassenand Trap-Jensen, 1970; Perl, 1971; Karnovsky and Shea, 1970; Perry and Garlick, 1974; Sheaand Bossert, 1973),but it seemedtime to attempt to gather more accurate data, especially of the endothelial junctions. The recent advances in the applications of stereology to electron microscopy (Elias Copyright 0 1975 by Acadetak Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain

43

44

ET AL.

CASLEY-SMITH

et al., 1971; Underwood, 1970; Weibel, 1969) now mean that it is relatively simple to get quite accurate quantitative data about volumes of tissue from thin sections. The disadvantages of small volumes can be overcome to some extent by stratified random sampling techniques (Weibel, 1969), as were used here. It is possible to use the Standard Error of the Means (SE), to determine the order of accuracy being obtained. In the present investigation we achieved SE’s which were 5-10% of the Means, which were sufficiently small for the purposes to which we wished to put the data. The relative size of these SE’s to the Means implies that the samples were sufficiently large; the use of random-number tables ensured the randomness of the sections.

MATERIALS

AND

METHODS

Eight mongrel dogs (~15 kg) were anesthetized with dial-urethane and Nembutal. Biopsies (~1 mm3) were taken of their gastrocnemii, fixed in 4% glutaraldehyde in Millonig’s (1961) buffer, to which was added 7 % glucose. While this immersion fixation is inferior to perfusion fixation for fixing the capillaries distended as they are in viva, our measuring techniques for the circumference and our calculations of axes, diameters, etc., are not affected by this (Casley-Smith et nl., 1975). Thus, it was preferable to use immersion to avoid the great alterations in hydration of the connective tissue-and hence of the numbers of capill,aries~cm2-which can occur with perfusion (Bohman, 1970) even with added macromolecules, since it is impossible to be certain how much of these to add. After fixing for 12 hr at 4°C the material was postfixed in 2% osmium tetroxide for 1 hr. After acetone dehydration, it was embedded in araldite and the sections stained with lead citrate (pH 11) and uranyl acetate. Most of the sections were studied in a Siemens Elmiskop 1, but the work differentiating between close and tight junctions was performed in a Philips 300 so that the very large angle of tilt obtainable with its goniometer could be used to allow us to look down the junctions. The section thicknesses were measured with a Faraday-cage exposure meter, and photographically, using polystyrene spheres as standards (Casley-Smith and Cracker, 1975). This improved technique was also reapplied to some older sections of this material which had been used for counting and measuring vesicles (Casley-Smith and Clark, 1972). The new section thickness estimates caused us to alter these estimates slightly; these revised figures are given in Table 1 and used in this report. The magnifications used were checked with a crossed-grating replica (2160 lines/mm). Capillary numbers/cm2 were counted at a final magnification of 2310 x (12) 25; circumferences, axes, etc., and junctional numbers were estimated at 34,100 x (250) 25; junctional dimensions were measured at 126,000 x (378) 25. (Here and elsewhere the figure in brackets after the Mean is its SE, and a following number, in italics, is the number of observations upon which the estimate is based.) The blocks were sectioned randomly, using random-number tables to select the block and to determine its orientation. Where more than one section was studied these came from at least 0.2 mm away in the block. For the low-power studies, five or six random grid squares (Taab, Reading, U.K.-HR24 grids-7225 pm2 (230) 40 per square) were photographed per dog. (Here and elsewhere, no selection was made, except to reject material which was technically poor.) The numbers of capillaries were counted, neglect-

MORPHOLOGY

OF CAPILLARIES

AND

PERMEABILITY

45

ing half of those which intersected a grid bar. The criteria for a capillary were those of Rhodin (1968) except that we included any (rare) postcapillary venules, i.e., we counted all vessels with a single layer of cells (not counting pericytes), and which were not lymphatics (Casley-Smith, 1975a). In fact, the vessels were all remarkably similar. The medium magnifications (34,100 x) were used to measure the major and minor internal axes and the internal circumferences of five randomly selected cross sections of capillaries per dog. The circumferences were measured by using a map-measuring wheel, including all projections on the luminal surface. (All of these were included since it was considered that these probably represent plasma membrane which is part of the actual wall in v&---this mean came to 1.23 (0.142) 40 times the mean if the projections were ignored.) The numbers of interendothelial junctions per cross section were counted. The high magnifications (126,000 x) were of junctions, five to six from each dog. Using the goniometer, a total of 500 junctions (60-70 per dog) were studied at random at -250,000 x, using the binocular viewer. Those which could be easily recognized as tight junctions were so recorded, all the junctions which might have been close junctions were photographed. These were then categorized as tight or close, depending on the fusion or not of the two outer lamellae. (If there was any tight region present, the junction was called tight even if there was also a close region.) Additional photographs were taken to bring the total number of each class to 25. The goniometer was used to explore the junctions so that the narrowest portions could be studied and their dimensions measured. (Some 20 % of the junctions could not be seen well enough to categorize with any certainty.) Measurements were made of the various widths and depths along the junctions (Fig. 9) using a 10x magnifier and graticule for the widths and the map-measuring wheel for the depths. (The term “depth” is used for the dimensions of the junctions in the lumen-tissue axis; the term “length” is reserved for the junctional dimensions in the plane of the luminal surface.) The widths were measured by considering only the clear gaps between the outer lamellae. If more than one close region occurred, the depths of these were added. These are recorded in Table 2, as are the adjusted dimensions. These adjustments (Casley-Smith, 1975b) were made to take account of the random angles which the membranes made to the plane of section and of the resolving power of the microscope. It has been shown that such measurements must be adjusted in the present case, where measurements were made only between membranes whose unit structure was visible, by using w1 (or di) x 0.87 + 2.1 nm; for more general measurements, e.g., the vesicular numbers, etc. in Table 1,0.70 is used. Attempts were also made to follow junctions from tight to close and to tight again, in serial sections. This was possible in nine instances. Stereological calculations were done following Elias et al. (1971), Underwood (1970), and Weibel (1969); they are indicated in the Remarks column of Table 1. Row I was calculated by the method of Casley-Smith et al. (1975). Rows AG-AN in Table 2 were found by calculating the individual u$/di, etc., for each part of each junction, then finding the mean of these for each part. The Standard Errors (SE) of the various products and quotients of the Means were estimated using the methods set out in Kendall and Stuart (1966, p. 231), using large-sample theory. Table 1 records, where relevant, the data for 100 g of muscle. This was estimated from the figures per cm3 using a measured specific gravity of 1.01 (0.015) 10.

CASLEY-SMITH

ET AL.

RESULTS The general structure of the muscles and the capillaries were the same as the descriptions given by Bruns and Palade (1968a); Hammersen (1968); Karnovsky (1967, 1968, 1970); Luft (1973); and Majno (1965). In particular, it could be seen that there were a few (-5%) close junctions where the two outer lamellae of the two endothelial cells

FIG. 1. A very low power (1,350 x) micrograph of a whole grid square. Seven capillaries can be seen in the endomysium around the muscle cells.

were separatedby gapsof -4 nm, and that there were many tight junctions where these two Iamellae appeared to be fused. Some 36% of the junctions had endotheiial projections into the lumen. Representative illustrations at the various magnifications are shown in Figs. l-8. The results are presented in detail in Tables 1 and 2. The results for vesicles,from Casley-Smith and Clark (1972), are also included in Table 1. They are adjusted for the new estimations of the thickness of the section used in that work

DIMENSIONS OP CAPILLARIES,JUNCTIONSAND

1

B C D E F G H I J K L M N 0

Luminal surface area/100 g Calculated mean diameter

Calculated mean major axis Calculated mean minor axis Capillary volume/100 g Proportion “vesiculated” surface to total luminal surface

A

Row

x lo7 cm x low4 cm x 10m4cm

2.63 3.76 1.68 3.19 13.1 4.17 8.33

3.58 x lo-“ cm 1.12 x 10v4 cm 8.29 x 10-l cm3 0.872

2.19 x lo4 cm’ 2.65 x 10e4 cm

x 10F4cm x 10m4cm x 1o-4 cm

x 10m4cm

27.6

1.31 x lo5

Mean

40

from F and K from F and K n.L.M.C/4

0.864 0.193 2.49 0.053

2G/n [=S,/L,; Casley-Smith et al., 19751

D/E for each vessel

4(1/A), approximately 2.A [L” = 2P,; Weibel, 19691

Remarks

C.1 [S, = 4B,,/n; Weibel, 19691 I/n, assuming cylindrical capillaries

42 42 40 40 40 40 40 40

42

No.

VESICLES

0.223 0.235

6.17 0.132 0.325 0.143 0.540 1.16 0.309 0.739

0.0659

SE

(in 100 g of muscle, where this is relevant)

No. capillaries/cm2 of section Intercapillary distance Length of capillaries/100 g Measured internal major axis Measured internal minor axis Axial ratio Measured luminal circumference/capillary “Measured” mean internal diameter/capillary Calculated luminal circumference

Capillaries

Parameter

NUMBERSAND

TABLE

Z

No. free vesicles/cm3 of cytoplasm

4.18 x 1Ol4

5.73 x 199 4.26 x 1Or4

1.47 x 10d5 cm 6.50 x lo9

4.47 x 1O’cm 0.0479 2.14 x lo6 cm 4.26 x 10’ cm

1.70 2.08

Mean

l-continued

0.531

0.717 0.646

0.182 0.308

0.440 0.00955 0.476 0.421

0.144 0.201

SE

18

18 18

18 36

500

40 40

No.

Measured mean width x 0.7ob This no. is attached to each plasma membrane Counted no. x 0.70b Counted no. x 1.43*; this no. is attached to each plasma membrane

;SS).R

P + junctions returning to the sides from which they started P.C

Remarks

’ Values derived from Casley-Smith and Clark (1972); using new estimate of section thickness. b All these figures have been adjusted to allow for the random angles at which the sections intersected the cells and membranes (Casley-Smith, 1975b).

x Y

No. free vesicles/cm2 luminal surface No. attached vesicles/cm3 of cytoplasm

R S T U

Q

P

V w

through junctions/100 g close/(close + tight) junctions close junction/100 g tight junction/100 g

section section

Row

Vesicles” Mean cell width No. attached vesicles/cm2 luminal surface

Length of Proportion Length of Length of

Junctions No. completely through endotheIium/cross Total of all junctions in endothelium/cross

Parameter

TABLE

AC AD”

AE

AFb

AG

AH8

AI AJb

AK ALb

Widths [Gil nm

Cube root mean cube of widths

[+Y] x 1Ol4crne2

AA ABb

Row

Depths [d,] nm

Number“

Parameter

2

MEASUREMENTS OF THEWIDTHSAND DEPTHSOF PORTIONSOF THEJUNCTIONS

TABLE

%

50

CASLEY-SMITH ET AL.

FIG. 2. A low-power (35,100 x) micrograph showing a very small capillary, which was probably contracted in viva. The lumen (L) is complex: this may have been the bifurcation of two capillaries. Two junctions (J) are visible.

(mean - 81.2 nm (39) 18, in place of 51.8 (26.4) 18) and for the effects of the random angles of viewing the sections. There were no significant differences between dogs, apart from orientation, and they are grouped together. It was found that 0.86 (0.054) 42 of the volume of the muscle actually consisted of muscle cells and endomysium. The remaining 14 y0 was epimysium or perimysium. The capillaries in this tissue were similar to those in the endomysium, but fewer (0.462 x 10’ (0.103) per cm’, as compared with 1.46 x lo5 (0.0747) in the endomysium). Since it was considered that this amount of connective tissue would normally be present in the “muscles” when physiological measurements were made on them, such regions were included in the samples giving a Mean of 1.32 x lo5 (0.0659). Some of the more interesting results were: There were -260 km of capillaries per 100 g of muscle. These had a surface area of -2 m2 and major and minor internal axes of 3.6 and 1.1 /*m. The axial ratio observed (3.19) must be approximately the same as is present in the threedimensional structure-Elias et al. (1971). The various estimates of the depths and the widths of the junctions are shown in Table 2. The depths, and the widths, of regions a, b, and d (Fig. 9) were not significantly different between the close and the tight junctions, and are combined; region a was not always present. The adjustments, for random-sectioning angles, made only minor differences to the depths, and to the widths in regions a, b, and d, but had a considerable effect on the width of region c in close junctions.

MORPHOLOGY

OF CAPILLARIES

AND

PERMEABILITY

51

FIG. 3. Another small capillary (33,200 x). A portion of an erythrocyte is visible in the lumen. Two junctions (J) and adjacent endothelial luminal projections may be seen.

FIG. 4. A somewhat larger capillary (24,800 x). There is a junction (J) and a section through an erythrocyte, which nearly occupies the lumen.

52

CASLEY-SMITH ET AL.

FIG. 5. A high-power (101,000 x) micrograph showing a tight junction (cf. Fig. 9). The regions a-d are indicated. Here there are two regions c, where the outer laminae fuse. Their depths would be added together.

FIG. 6. A high-power (124,000 x) micrograph showing a tight junction on the right. The two outer laminae are clearly fused near the lumen; at a deeper level the junction was tilted relative to the section and the images of the two membranes overlap. On the left is a close junction with a 4-nm gap between the two endothelial cells. Regions b and d are very short, about equal in depth to c.

MORPHOLOGY

OF CAPILLARIES

AND

PERMEABILITY

53

FIG. 7. A close junction (158,000 x). There is a gap of -3 nm between the cells in region c. At the abluminal end, and about half-way along region d, the membranes appear to fuse, but the goniometer showed that this is only because the plane of the junction tilts at these points.

FIG. 8. A close junction (137,000 x). The regions are poorly defined, but at the narrowest part (c) there is a gap of 4nm between the cells.

54

CASLEY-SMITH ETAL.

FIG. 9. A diagram of the close junction. The nomenclature and the mean dimensions are indicated.

The efforts to determine the length of the close junctions along the vessels were not very successful. The nine junctions which it was possible to follow from tight, through close, to tight again, gave a mean length of 480 nm (250) 9. This is evidently an underestimate since only -20 of the sections, mean thickness = 62 nm (7), could be fitted on a grid. Hence, the estimate is biased against the longer lengths of close junction. The labor involved, however, did not seem to warrant more precision, particularly in view of the relatively small proportion of the sections of junctions which displayed the close structure and the fact that it was necessary to use the goniometer to examine each one. Even though it was possible to economize by photographing only the dubious junctions, the time involved speedily became quite disproportionate to the value ofthe information. There are effectively 1.09 x 1Ol4 (0.189) free vesicles per 100 g (rows J x 0 x X) and 2.48 x lOI4 (0.317) attached to both plasma membranes (rows J x 0 x W x 2), i.e., 1.24 x 1014 (0.159) to each. The use of row 0 and the word “effectively” is because the organelle and junctional regions were neglected. Although there are some vesicles present in these, they contribute little to endothelial permeability via the vesicles (Simionescu et al., 1973). DISCUSSION It was very difficult to judge the possible effects of shrinkage during processing on results such as these. It has been concluded earlier (Bruns and Palade, 1968a; CasleySmith, 1969b, 1971) that it is likely that there is very little alteration for structures the size of vesicles and fenestrae. This confidence cannot be extended to the widths of the junctions (errors in which will be magnified -3 times in CFC calculations), nor can one be certain that these gaps do not contain substances in vivo which are removed during preparation (Luft, 1973). The situation is further confused by the resolution of the microscope being only -1 nm, so that any gaps to mean the length of a junction, or a portion of one, around the cells, in the plane of the endothelium. We use the term “depth” (d) to mean the measurement perpendicular to this plane, from the lumen to the tissue. Let us consider simple, one-dimensional, filtration (and diffusion, vide infu). From Poiseuille’s equation, for flow between parallel plates (Pappenheimer, 1953) : CFC = w3Ll12qd = Kw3 L/d

(1)

(q = 7 x lop3 poise, is the viscosity; K also converts the units to mm Hg/min). For a complex slit the resistance of region i is (d,/wfLi). These must be summed, along the slit, to find the total resistance. Hence, CFC = Kl): (di/w :Li). 8

(2)

56

CASLEY-SMITH

ET AL.

Using the resistances shown in Table II, Row AJ, it can be seen that, if L, = L, = L, = hi,

CFC=KL,/[0.0132+0.0356+0.134+0.185] = KLJO.368 (0.0440)

= 0.055 (0.014) mi/min/mm

Hg/lOO g.

(3)

Here it is evident that the resistance of regions a and b are negligible, but that of region d (50 %) is of even greater importance than that of the close region, c (36 %). This is much more extreme than the finding of Per1 (1971), because of the different values we are using for di and wi, and in particular because we have used the means of the individual values of (d,/w:), rather than use d&$. Rows AB and AF, or AD, in place of that in AJ, indicate that region c is more important. However, it is more correct to use the means of the individual resistances for each region, rather than the resistances calculated from the means of dl and wi. It is even better, however, to calculate the total resistance, R, for each complete cross section, obtain K/R and find the sum of these for 100 g of muscle. This is because it uses the total resistance of each individual junctional section. Thus, CFC = KL, [1/R] KL, 25 =15-@3 j KL, 25

= 25 2 { 1I [Raj+ &j + Rcj+ &If i.e., CFC = %

$ (l/[~(~~j/w~,l)l);

i=a,

b,

c,d.

(4)

j

Using Eq. (4) and all the individual CFC=

&,‘s and wI;s:

KL, x 1.11 (0.205)

= 0.023 (0.0065) ml/min/mm

Hg/lOO g.

(5)

The considerable reduction in our results from Eq. (3) to (5) is because of the gross variations between the d*‘s and wI’s for each of the regions, between the different cross sections of the close junctions. This confirms the suggestion of Per1 (1971, p. 237) that a knowledge of the statistical distribution of the values is necessary for more precise calculations. This 0.023 ml/min/mm Hg/lOO g, is about twice that found experimentally for the hind legs of dogs by Pappenheimer and Soto-Rivera (1948), viz., 0.014. Similar values have also been observed in cats and rats (Landis and Pappenheimer, 1963; Kjellmer and Odelram, 1965; Renkin, 1969). In fact, however, we are actually measuring all the junctions in the muscle and assuming that they are all equally exposed to the induced pressure changes. This is unlikely (Renkin, 1969; Folkow and Mellander, 1970). Only during vasodilatation would this occur; in cats the CFC does increase some two to three times during exercise (Kjellmer, 1964; Kjellmer and Odelram, 1965). Hence, our calculated CFC is remarkably close to that observed experimentally.

MORPHOLOGY

Capillary Diffusion

OF CAPILLARIES

Coeficient

(CDC

AND

PERMEABILITY

57

or PS)

From considerations similar to those used to derive Eq. (4), it can be shown that the best estimate of CDC is: CDC =DL, [l/R’]

= 2 2 {1/(R:j+ RL+ Rrj+ R;j)}, j where R’ is the resistance to diffusion and D is the diffusion coefficient for some substance. i.e..

usingf(i) as an expression for the restricted diffusion of the substance as given by Per1 (1971, Eq. 68). Here i replaces his x, and 2a his d (the effective molecular diameter). i.e., f(i)j = [l - 2a/Wij]/[l + 3.4(2a)2/Wij2] (7) In Table 3 the CDC values for various test substances have been calculated. These have been done for all the individual cross sections of close junctions, summating the R;‘s for each one, and adjusting each of these by using the appropriate values off(i) for the diameters of the substances and for the Wij’S. It can be seen that the calculated CDC’s are -5.3 x the observed ones in cat’s leg. (Unfortunately, only continuous perfusion PS values are available for dog legs, and these almost certainly include a large component attributable to the interstitial tissue resistances-Landis and Pappenheimer, 1963; Renkin, 1969; Renkin and Sheehan, 1970.) The observed CDC’s may be lower because some of the muscle blood vessels were not functioning (Landis and Pappenheimer, 1963; Renkin, 1969) and because of other barriers across which osmotic flow occurs in the parenchymal plasma membranes (Landis and Pappenheimer, 1963 ; Renkin and Sheehan, 1970). (Using the mean values given in Row AN gives values ~80% of those shown in Table 3.) Vasodilatation causes increases of -2 times in the CDC’s (Renkin et al., 1966; Renkin, 1969). The values from the exercised human forearm (Trap-Jensen and Lassen, 1970) are very similar to those of Pappenheimer for the normal cat leg (Perl, 1971). Since the normal CFC values of the forearm are -l/2 those of the cat leg (Landis and Pappenheimer, 1963) this equality may be the result of the vasodilatation produced by exercise. The CFC of dog leg is -1.4 times that of cat leg (Landis and Pappenheimer, 1963), implying that the CDC of exercised dog leg should be at least 3 x the values recorded by Pappenheimer in the normal cat. Thus -60 % of the discrepancy between our calculation and physiological measurements can be accounted for by our measuring all capillaries many of which would normally be only minimally perfused. The remaining discrepancy may well be accounted for by osmotic flow at the parenchymal cell plasma membranes (Renkin and Sheehan, 1970). The values of the CDC’s calculated for regions c alone, neglecting regions a, b, d, are also shown in Table 3. It can be seen that these are -seven times greater than those for the whole slits, confirming suggestions of Per1 (1971) and Trap-Jensen and Lassen (1970).

0.96

1.14 2.7

Sucrose

Raffinose Inulin (mean of A and B)

0.64 0.23

0.70

3.4 2.5 2.0 1.95 0.90

Free diffusion coefficientb (x105 cmz/sec)

6.7 1.6

7.5

45 32 24 22 10

Observed CDC’s’ (cm3/min)

369.1

41

220 160 125 120 54

Calculated CDC’s (regions a, b, c, d) (cm3/min)

5.4 5.7

5.5

4.9 5.0 5.2 5.4 5.4

Ratio calculated observed

250 41

290

1730 1260 980 940 400

Calculated CDC’s (region c only) (cm”/min)

37 26

39

39 39 41 43 40

Ratio calculated observed

LIThe SE’s are -25 % of the mean calculated CDC’s. b From Landis and Pappenheimer (1963). c From Per1 (1971, Table IV, from Pappenheimer, 1953) and Landis and Pappenheimer (1963). These have been multiplied by the 7000 cm2, which these authors took as the surface area of the capillaries per 100 g of muscle to derive the P’s from the CDC’s they observed, and converted to minutes.

0.3 0.32 0.46 0.52 0.74

Effective molecular diameters CWJ (mm)

Water Potassium Sodium Urea Glucose

Substance

3

CALCULATED AND OBSERVEDCAPILLARY DIFFUSION COEFFICIENTS~

TABLE

b

$

c F ? B i

MORPHOLOGY

OF CAPILLARIES

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PERMEABILITY

59

There is thus a very good correlation between the calculated CFC and CDC and those obtained by observations. This allows us to be more certain about the lack of appreciable artifacts in the measurements, and about the validity of applying the laws of macrophysics to events at this scale. It also helps us in estimating how much of the observed physiological effects should be attributed to the endothelial barrier, and in analyzing the importance of the various regions of the barrier. The Basement Membrane

The basement membrane has often been considered to be an important factor in the resistance of the capillary wall. While this may be the case for macromolecules, although these do penetrate it very easily (Farquhar et al., 1961) it is very unlikely to be the case for small molecules. There is -2.5 m2 of capillary basement membrane per 100 g of muscle, -50 nm deep. If it has a similar hydraulic conductivity to the interstitial tissue in general, e.g., mesenteric connective tissue (1.9 x lo-r0 ml cm/set dyne, Intaglietta and de Plomb, 1973) that of the basement membrane will be -1 ml cm/set dyne/100 g. UsingO.O1 ml/min/mm Hg/lOO g for the CFC of muscle gives the hydraulic conductivity of the capillaries as -IO-’ ml cm/set dyne/100 g. Thus, the conductivity of the whole basement membrane is -10’ times that of the capillaries. (This assumes that the conductivity is the same as that of the connective tissue in general, but even if this is incorrect by several orders of magnitude, the conclusion is the same.) The area of the close junctions at the abluminal surface is 5 cm2-l/5000 of the basement membrane. Hence, even if the fluid could only pass directly outward, the hydraulic conductivity of this part of the membrane would still be 2 x lo3 times that of the close junctions. The spreading of the fluid laterally, beneath and through the membrane, would increase this very greatly. It should be emphasized that these remarks apply to the basement membranes and not to the whole tissues in general. In particular, they do not apply to diffusion, especially of large molecules, through these tissues (Landis and Pappenheimer, 1963; Renkin and Sheehan, 1970). Vesicular Transport

The work of Renkin and his collaborators (Carter et al., 1974; Joyner et al., 1974; Renkin et al., 1974) has provided very convincing evidence that in continuous capillaries the vesicles are a very important method by which the macromolecules, other than the smallest (Garlick and Renkin, 1970) traverse the endothelial barrier. Considerable tracer evidence has also been provided for it (Bruns and Palade, 1968b; Casley-Smith, 1969a; Casley-SmithandChin, 1971; JenningsandFlorey, 1967; Simionescuet al., 1973). A developing series of models describing this process have been proposed, based on Brownian motion (Casley-Smith, 1963; Shea and Karnovsky, 1966; Bruns and Palade, 1968a, 196gb; Palade and Bruns, 1969; Shea et al., 1969; Casley-Smith, 1969b; Karnovsky and Shea, 1970; Green and Casley-Smith, 1972; Shea and Bossert, 1973). These have been modified both by theory and by experiment (Casley-Smith and Chin, 1971). In their latest paper, Shea and Bossert (1973) criticize the model which was proposed by Green and Casley-Smith (1972) and which received considerable experimental verification (Casley-Smith, and Chin, 1971). In particular, they question the value we assigned to u (the probability that a vesicle colliding with a plasma membrane will fuse with it) and to our boundary conditions.

60

CASLEY-SMITH

ET AL.

Shea and Bossert assumed that the Stokes-Einstein relation is valid in the presence of absorbing or reflecting barriers. This is not the case, and we found it gave completely erroneous results between two adjacent walls. Because of this, these authors had to make the very unrealistic assumption that when a vesicle does not fuse with a membrane it is “instantaneously returned a distance p into the interior” (their Appendix B, iii). Their “boundary conditions” are, in fact, not boundary conditions at all, but assumptions for x > y and x < y which are designed to give a maximum near the wall. This maximum presumably represents the vesicles attached to the wall; since such vesicles are not even involved (at that time) in the diffusion process, it is wrong to try to describe them in the diffusion equation. (In our calculations they were disregarded-our transit times take no account of the attachment times.) In addition, we do not accept their criticism of our boundary conditions. In our calculations we subtracted the external radius of the vesicles from the distances of their centers from the membranes. Any “vesicle” which was closer to the membrane than this would be poking through it, and could not exist. Our boundary conditions are an exact formulation of the attachment probability assumption. The present results will modify both Shea and Bossert’s and our own calculations, as will recent data from Perry and Garlick (1975) and Carter et al. (1974). Perry and Garlick (1975) loaded rabbits with y-globulin and recorded its efflux after -18 hr. Their mean PS was 2.4 x lop3 ml/sec/lOO g. Correcting for the size of the molecules (Garlick and Renkin, 1970), this increased to -5 x 10e3 ml of interstitial fluid being transported by vesicles/sec/lOO g. This is -10 x that found by Carter et al. (1974) (5 x 10F4 ml/set) and -15 x the results of Garlick and Renkin (1970) in normal dog leg. While Perry and Garlick attribute the difference to back-diffusion in these other experiments (where the label was measured passing from the blood to the lymph), it is uncertain how much of the difference may be due to differences in the vessels of the two species, although rabbits have fewer vessels than dogs (Hammersen, 1968). Bearing these uncertainties in mind, we will use a value of 10e3 ml/set and correct for the other values. Using 1.06 x lo-l6 cm3 (Casley-Smith and Clark, 1972) as the internal vesicular volumes gives 1Ol3 vesicles which have traveled right across the cell, in one direction/ sec/lOO g. Since the effective luminal surface area is 1.9 x 1Ol2 pmZ/lOO g, this means that there will be 5.3 of such vesicles discharging/pm2/sec. (This figure is -26 using a PS of 5 x 1O-3 ml/set, and 2.6 using 5 x 10m4.) Since about half of the vesicles which start out return to the membrane from which they originated (Table 4 and Green and Casley-Smith, 1972) these figures should be doubled for the total numbers fusing with each pm2 of membrane/set. Since there are 65 vesicles attached to each pm2, this gives a median attachment time of 6.1 set (or 1.3 and 12.5 set, for the other PS’s, respectively). (Since some of the “free” vesicles may have been actually attached, but in a plane other than that of the section, these times may be slightly greater). The last value is similar to the value of -15 set found by Simionescu et al. (1973) in rat diaphragm capillaries. The times observed by CasleySmith and Chin (1971) in mouse heart endothelium and diaphragmatic mesothelium were 2-3 set, which is between those obtained using PS values of 10e3 and 5 x 10b3. The difference between the experimental estimates of Simionescu et al. and of Casley-Smith and Chin may be explained by species or site differences, or the presence of competing macromolecules in Simionescu et ul.‘s experiments, or by the different methods of applying the fixative. This last was considerably slower and less direct in the experiments of

TABLE 4

1.01

7.83

@(for PS = 5.10W3ml/set) rJ and p for ” and d = 0.073

a (for PS = 5.1 Oe4 ml/set) t, and p for fl and d = 0.073 0.020

0.19

10 0.041

50.0

42.3

48.7% 48.1 45.9 41.0

P

7.69

0.873

2.59 set 3.80 8.45 22.0

ts

0.0051

0.046

2.5 0.010

50.0

47.8

49.7 % 49.5 48.9 47.4

P

7.69

0.835

2.58 set 3.76 8.26 20.8

ts

0.0010

0.0092

0.5 0.0020

50.0

49.6

49.9%. 49.9 49.8 49.5

P

10.4

0.830

3.13 set 4.19 8.40 20.6

fs

0.00014

0.0013

0.1 0.00029

50.0

49.9

50.0 % 50.0 50.0 49.9

P

’ a is the probability that a vesicle will fuse with a plasma membrane if it collides with it. b t, is the median transit time, i.e., the time taken by half of the vesicles which traverse the cell to do so. It is approximately equal to the median time for rejoining of those vesicles which fuse with the same membrane from which they originated. ‘p is the percentage of vesicles which fuse with the membrane opposite that from which they originated. ’ d is the mean total distance between the two plasma membranes, minus the root mean square external vesicular diameter. ’ This is the actual dobserved here. The others are calculated, using the same a’s, so that comparisons can be madewith thicker or thinner cells. (These assume that the numbers of vesicles/pm’ of luminal surface area remains proportional to the new d’s.)

2.66 set 3.94 9.13 26.1

r,

0.05 (for PS = 10m3ml/set) 0.073’ 0.16 0.40

d (pm)d

Viscosity (poise) a (for PS = 10-j ml/set)

VALUESOF a,” MEDIANTRANSITTIMF..CG,~ t,, AND THE MIGRATIONPERCENTAGES: p, FOR VARIOUSAWMED VISCOSITIES

62

CASLEY-SMITH

ET AL.

Simionescu et al. as may be seen by the slowness to achieve a steady state (-60 set vs -10 set). The 5.73 (or less, uide supra) free vesicles behind each pm2 of luminal surface have 21 vesicles joining and leaving them each second (or 102 and 10.2, respectively, for the other PS’s). Thus, the figure of 11.33 set in Green and Casley-Smith (1972, p. 109) should be replaced by 5.4 set (or 1.1 and 11, respectively)--Table 4. It can be seen that the values oft, are greatly influenced by the cell width, but not very much by the viscosity. (This is because the calculated a falls greatly, as the assumed viscosity falls.) Taking Simionescu et al’s data, their cell width (as corrected-Casley-Smith, 1975b) was -0.13 pm; their t, was lo-15 set, which would fit well with a PS value of -5 x lop4 ml/set. On the other hand, Casley-Smith and Chin’s cell width (after correction) was -0.03 pm; t, was 3-5 set, which would fit with a PS value of -5 x 10m3.This difference may again reflect a difference between the species, the sites, or the techniques of fixation. It is evident that the value of a is much smaller than the values considered, and criticized, by Shea and Bossert (1973). The vesicular transit times found by experiment are within those suggested by theory, They are quite capable of accounting for the passage of macromolecules through the endothelia1 barrier. They also indicate that for small molecules, whose PS values are ~10~ x greater, some other transport system is necessary. We have shown earlier that this could be well satisfied by the close intercellular junctions. ACKNOWLEDGMENTS We are most grateful to Messrs. K. W. J. Cracker and D. W. Greig for technical assistance, to Drs. M. E. Dean and R. H. Burnell who biopsied the dogs, and for the support of the Australian Research Grants Committee. REFERENCES S. 0. (1970). Effects on tissue fine structure of variations in colloid osmotic pressure of glutaraldehyde fixatives. J. Ultrastruct. Res. 30, 1955208. BRUNS,R. R., AND PALADE, G. E. (1968a). Studies on blood capillaries. I. General organization of blood capillaries in muscle. J. Cell Biol. 37, 244-276. BRUNS, R. R., AND PALADE, G. E. (1968b). Studies on blood capillaries. II. Transport of ferritin molecules across the wall of muscle capillaries. J. CeN Biol. 37, 277-299. CARTER, R. D., JOYNER, W. L., AND RENKIN, E. M. (1974). Effects of histamine and some other substances on molecular selectivity of the capillary wall to plasma proteins and dextran. Microvasc. Res. 7, 31-48. CASLEY-SMITH, J. R. (1963). Pinocytic vesicles: an explanation of some of the problems associated with the passage of particles into and through cells via these bodies. Med. Res. (Australia) 1,58 (abstr.). CASLEY~MITH, J. R. (1969a). Endocytosis: the different energy requirements for the uptake of particles by large and small vesicles in peritoneal macrophages. J. Microsc. 90, 15-31. CASLEY-SMITH, J. R. (1969b). The dimensions and numbers of small vesicles and the significance of these for endothelial permeability. J. Microsc. 90, 251-269. CASLEY-SMITH, J. R. (1971). Endothelial fenestrae in intestinal villi: differences in their numbers etc. between the arterial and venous ends of the capillaries. Microvasc. Res. 3, 49-68. CASLEY-SMITH, .I. R. (1975a). Lymph and lymphatics. In “Microcirculation” (G. Kaley and B. M. Altura, eds.), University Park Press, Baltimore, in press. BOHMAN,

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