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Relation between myelin sheath thickness and axon size in spinal cord white matter of some vertebrate species
Journal of the Neurological Sciences, 1978, 38:421-434
421
© ElsevierfNorth-HollandBiomedicalPress
RELATION BETWEEN MYELIN SHEATH THICKNESS AND AXON SIZE IN SPINAL CORD WHITE MATTER OF SOME VERTEBRATE SPECIES
CLAES HILDEBRANDand ROBERT HAHN Department of Anatomy, Karolinska lnstitutet, 104 O1 Stockholm 60 (Sweden)
(Received 20 April, 1978) (Accepted 6 June, 1978)
SUMMARY The relation between number of myelin lamellae and axon size in the CNS was examined by electron microscopy of spinal cord white matter fibres in different vertebrate species (cat, rabbit, guinea pig, rat, mouse, frog and perch). The results show that the number of myelin lamellae increases with increasing axon size in a nonlinear fashion. Below an axon size of 4-5 #m the relation follows a fairly straight line but above this size rectilinearity is lost. The mouse and the frog differ from the pattern shared by the other animals. In the mouse the lamellar number increases more slowly with axon size and the relation is close to linear. In the frog the number of lamellae increases very slowly with axon size and the relation is markedly curvilinear. Measurements of the myelin repeating period show that in the mammals and the frog the average period of thick sheaths is about 85 % of that in thin sheaths, in accordance with previous findings in the cat. In the perch a clearcut difference in this respect between thick and thin sheaths is not found. Calculations of the g-ratio on the basis of the findings indicate that it increases with increasing fibre size. This is most pronounced in the perch and the frog in which the g-ratio for the largest fibres far exceeds the functionally optimal value defined in theoretical analyses on impulse propagation.
INTRODUCTION In both peripheral and central fibre tracts the sheaths of myelinated nerve fibres increase in thickness with the size of the axons. The relation between myelin sheath thickness and axon size has often been expressed as the ratio between axon diameter (d) and total fibre diameter (D), i.e. the g-factor. In light microscopic studies of This study was supported by grants from the Swedish Medical Research Council (Project No. 3761) and from KarolinskaInstituter.
422 peripheral nerves the g-factor has been found to vary between 0.5 and 0.7 and according to most investigators the ratio increases with fibre size (see Williams and Wendell-Smith 1971 ; Bischoff and Thomas 1975 for references). A ratio of 0.5-0.7 is in satisfactory agreement with theoretical analyses on the requirements for optimal function (Rushton 1951; Goldman and Albus 1968; Deutsch 1969; Smith and Koles 1970). A more exact measure of the relation between myelin sheath thickness and axon size is obtained by counting the number of myelin lamellae in the electron microscope and relating the lamellar number to axon circumference or cross-sectional area. In peripheral nerves the number of myelin lamellae increases with increasing axon size, and this relationship is generally considered to be rectilinear (reviewed by Friede 1972; Bischoff and Thomas 1975). According to some workers, however, it is only linear below axon sizes of 4-5/~m (Boyd and Kalu 1973; Sima 1974; Berthold and Carlstedt 1977). In the CNS the d/D-ratio of the myelinated nerve fibres appears to be similar to that in the PNS (Ogden and Miller 1966; Bishop, Clare and Landon 1971; Friede, Miyaghishi and Hu 1971; Waxman and Bennett 1972; Tapp 1974; Waxman and Swadlow 1976). According to the current view, the number of central myelin lamellae grows linearly with increasing axon size (Samorajski and Friede 1968; Friede et al. 1971; Sturrock 1975; Fraher 1976). However, in the CNS-part of the transitional region in feline dorsal roots rectilinearity is lost above an axon diameter of 4-5/~m (Berthold and Carlstedt 1977). The aim of the present study is to determine the relation between lamellar number and axon size in the white matter proper considering myelinated nerve fibre s with a wide range of sizes. Since previous studies indicate species differences (Bishop et al. 1971; Hildebrand 1977) several vertebrate species were studied. In view of the different repeating period in thin and thick feline myelin sheaths (Hildebrand 1972; Hildebrand and Miiller 1974), the possible existence of a similar variability of the myelin period in other species was examined. MATERIALAND METHODS Three adult animals of each of the following species were used: cat (European mixed breed), rabbit (New Zealand albino), guinea pig (mixed laboratory breed), frog (Rana temporaria, 5 cm body length) and perch (Perca fluviatilis, 25-40 cm body length). The mammals were anaesthetized with 40 mg/kg b.w. Nembutal intraperitoneally, artificially ventilated and perfused through the heart with 5 ~ glutaraldehyde in a 300 mOsm phosphate buffer (see Berthold 1968; Hildebrand 1971). Specimens from the spinal cord segments C1-C2 were postfixed for 4 hr in chilled perfusate. In the frog perfusion failed, and the rostral part of the spinal cord was fixed by immersion for 4 hr in the same fixative, after decapitation and rapid dissection. The fish were anaesthetized by immersion in 0.5 ~ urethane and placed in crushed ice. Perfusion fixation rendered unsatisfactory results and instead the portion of spinal cord underlying the dorsal fin was dissected out at + 4 °C and fixed by immersion in 5 ~ glutaraldehyde in a 200 mOsm phosphate buffer during 4 hr.
423 After primary fixation the spinal cord specimens were rinsed in the buffer used, osmicated in a 2 ~o solution of OsO4 in the same buffer, dehydrated in acetone and embedded in Vestopal W. Thin transverse sections from the ventrolateral funiculus were collected on one hole copper grids coated with carbon-stabilized formvar. After staining with uranyl acetate and lead citrate the sections were examined in a Philips EM 301 electron microscope. Fibres considered to present an acceptable structural preservation were free from swollen axonal mitochondria, myelin sheath splitting and empty spaces between axon and inner margin of the myelin sheath. Electron micrographs from areas containing large fibres with these characteristics were printed at a total linear magnification of × 10,000. The same areas were reexamined in the electron microscope and the number of myelin lamellae associated with fibres on the prints was counted directly in the microscope (thin sheaths), or on high magnification electron micrographs (thick sheaths). Axonal circumference and axonal area were estimated with a map meter and with an Ott planimeter respectively. The corresponding diameter values, dcire and dsrea were calculated. It should be pointed out that this represents an approximation since nerve fibres rarely form perfect circles in cross-sections. In each animal 130-220 fibres were examined. Fibres showing gross artefacts of fixation or with a highly irregular shape and fibres cut through a Schmidt-Lanterman incisure or through a node of Ranvier were excluded. The Mauthner axons in the perch were not included in the measurements. Comparisons between the two measures of axon size (deire and darea) were made by an analysis of correlation between the two sets o f values in a Nord-10 computer. Since the two approaches gave largely identical results (correlation coefficients 0.97-0.99, Table 1) only the circumference values were used for the further analysis. A numerical expression compatible with the observed relation between number of myelin lamellae and axon size was searched for in each separate animal by comparing linear (y ---- a q- bx) or linear ÷ logarithmic expressions (y = a -~ bx -Jclnx) with the observed values through regression analysis in an IBM 370-165 computer (BMD 03R biomedical computer program, University of California Press 1975, W. J. Dixon, ed.). The intraspecies and interspecies variance was determined for TABLE 1 CORRELATION COEFFICIENTS FOR THE COMPARISON delre-darea IN ONE ANIMAL OF EACH SPECIES Animal species
Correlation coefficientdcire-darea
Number of pairs of valuesexamined
Cat Rabbit Guinea pig Rat Mouse Frog Perch
0.98 0.99 0.97 0.98 0.98 0.98 0.99
183 177 174 136 138 155 152
424 TABLE 2 AVERAGE NUMBER OF MYELIN LAMELLAE (NUMBER OF OBSERVATIONS) FOUND FOR AXONAL SIZE CLASSES 0-1/~m ETC. (EXPRESSED AS deire) IN EACH OF THE EXAMINED SPECIES The values are total mean values derived from all measurements in each species. Axon size ~m) 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-17 17-19 19-21
Cat 8 (116) 19 (130) 35 (63) 49 (32) 63 (38) 76 (16) 83 (13) 92 (20) 105 (14) 108 (9) 124 (9) 120 (11) 119 (5)
Rabbit
Guinea pig Rat
Mouse
Frog
Perch
10 (116) 22 (167) 40 (66) 55 (42) 64 (30) 75 (18) 82 (20) 89 (10) 96 (6) 90 (8) 104 (6) 106 (5) 136 (2)
10 (91) 20 (165) 33 (67) 52 (42) 66 (24) 86 (23) 88 (20) 93 (19) 103 (7) 103 (6)
9 (147) 17 (128) 29 (54) 41 (41) 49 (30) 58 (10)
9 (8) 15 (126) 22 (49) 27 (53) 30 (49) 37 (37) 38 (29) 39 (16) 42 (11) 43 (11) 43 (11) 51 (5) 46 (4)
11 (67) 22 (116) 36 (54) 50 (36) 59 (34) 70 (10) 84 (16) 91 (9) 111 (7) 119 (6) 116 (4) 126 (3) 119 (3) 117 (5) 122 (6) 130 (3) 118 (5) 114 (6)
12 (150) 25 (159) 44 (57) 61 (28) 75 (15) 87 (9) 88 (14) 95 (7) 102 (5) 114 (1)
a range of circumferences corresponding to axonal diameters of 4-6/~m, by a one way analysis of variance ( B M D 0 I V biomedical c o m p u t e r program, University of California Press 1975, W. J. Dixon, ed.) and a studentisized range test of group means (Dixon and Massey 1957). F o r myelin period measurements electron micrographs were taken at a primary magnification o f × 34,000. The C N S myelin period o f the cat has been studied previously (Hildebrand 1972) and was not included. In the other species about 10 thick sheaths (/> 50 lamellae) and 10 thin sheaths (~< 10 lamellae) were examined in each individual animal at places where the myelin lamellae appeared regular and distinct and were oriented approximately parallel to the sectioning direction (Karlsson 1966). The myelin period was estimated as the average distance between the midpoints of 3-10 successive major dense lines on prints with a total magnification o f x 100,000. F o r each set of 15 plates magnification was checked with a carbon grating replica (54864 lines per inch, Ladd Res., IN, U.S.A.). The change in cross-sectional area of spinal cord ventrolateral white matter caused by the processing after primary glutaraldehyde fixation was assessed in one cat by planimetry of light micrographs from transverse Vibratome sections. RESULTS Lamellar
number
- axon size
The cat, rabbit, guinea pig, rat and perch present basically similar patterns (Fig.
425
1, Table 2). In these animals the number of myelin lamellae increases regularly with axon size up to about 4-5 #m, which corresponds to 60-70 lamellae. Above this size the relation between number of myelin lamellae and axon size is less strict and the lamellar number seems to increase progressively less with increasing axon diameter. In the size groups above 10 #m the mean number of myelin lamellae varies irregularly between 100 and 140. In the mouse, where the largest axons encountered measure 5-6 #m in diameter, a somewhat different picture is seen. The number of myelin lamellae A CAT 1
CAT 2 Y= 13.311nX + 7.56X + 4.20
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Figs• 1A--C. Graphs showing relation between number of myelin lamellae and axon size (expressed as detre) in some vertebrate species• In each case the line drawn illustrates the linear + logarithmic function (presented above the graph) which was found to be best adapted to the observed values• A: cat and rabbit; B: rat, guinea pig and mouse; C: frog and perch. increases with increasing axon diameter along a fairly straight line to a maximum of about 60 lamellae at 5-6 #m. The slope of the line is less steep in comparison with the other mammals and the fish (Fig. 1, Table 2). In the frog the number of myelin lamellae increases very slowly with increasing axon size to about 5-6/~m, corresponding to 35-40 lamellae. Above this size a further slight increase in average lamellar number is seen to a maximum of 40--50 lamellae. In all species the number of myelin lamellae shows a pronounced variability in the largest fibres (Fig. 1, Table 2). Comparisons between various linear functions (y = a + bx) and the data from each animal, showed that a good correspondance between observed and predicted values can be obtained (Table 3). However, addition of a logarithmic term to the
428 TABLE 3 CORRELATION COEFFICIENTS FOR THE COMPARISON OF THE OBSERVED RELA. TION BETWEEN NUMBER OF MYELIN LAMELLAE AND AXON SIZE WITH LINEAR OR LINEAR ÷ LOGARITHMIC FUNCTIONS Intraspecies interindividual mean lamellar number ( ± SD) representative for the axonal size range 4-6/~m are also presented. Animal No.
Correlation coefficients predicted observed values
Intraspecies interindividual mean lamellar number ( ± SD) for axonal size range 4-6/~m
y=a+bx
y-- a+bx+clnx
1 2 3
0.96 0.95 0.95
0.96 0.96 0.96
69.61 ± 1.31
1 2 3
0.91 0.89 0.95
0.94 0.92 0.96
71.99 ± 12.16
Guinea pig 1 2 3
0.91 0.94 0.95
0.91 0.95 0.95
77.82 ~ 2.42
Rat
1 2 3
0.92 0.93 0.90
0.94 0.94 0.93
82.68 4- 3.19
1 2 3
0.92 0.93 0.96
0.93 0.93 0.96
52.89 ~ 2.87
1 2 3
0.87 0.82 0.81
0.90 0.88 0.87
33.79 ± 1.50
1 2 3
0.89 0.83 0.84
0.93 0.88 0.89
65.70 ~ 3.07
Cat
Rabbit
Mouse
Frog
Perch
function (y = a -~- bx ÷ clnx, see Fig. 1) renders a better c o r r e l a t i o n between observed a n d p r e d i c t e d values, as illustrated by the c o r r e l a t i o n coefficients (Table 3). This i m p r o v e m e n t is m o s t a p p a r e n t in the frog a n d the perch b u t less clear in the m o u s e a n d the guinea pig t h a n in the o t h e r species (Table 3). A c o m p a r i s o n o f the variance within a n d between the different species, considering axons between 4 a n d 6/~m, is shown in Table 4. W i t h the exception o f the r a b b i t , where one individual differs r a t h e r distinctly f r o m the others, the interindividual " w i t h i n - v a r i a n c e " is fairly low. Analysis o f variance showed t h a t the average intraspecies v a r i a t i o n is m u c h smaller t h a n the t o t a l interspecies v a r i a t i o n ( F - r a t i o 31.5, Table 4). Pairwise c o m p a r i s o n s between the different species t h r o u g h studentisized range test showed t h a t the frog a n d the mouse differ significantly (at the level P = 0.05) f r o m the o t h e r vertebrates a n d f r o m each other. A difference between the perch a n d the rat was also indicated b y the test but no o t h e r significant differences could be f o u n d in the size range examined.
429 TABLE 4 STATISTICAL COMPARISON BETWEEN THE INTER- A N D INTRASPECIES V A R I A N C E W I T H RESPECT TO N U M B E R O F MYELIN L A M E L L A E RELATED TO AXONS WITH D I A M E T E R S OF 4-6 # m IN SPINAL CORD WHITE M A T T E R O F THE VERTEBRATE SPECIES U N D E R E X A M I N A T I O N
Between species Within species Total
Sum of squares Degrees of freedom Mean square
F-ratio
5004.4 371.1 5375.5
31.5
6 14 20
834.1 26.5
TABLE 5 A V E R A G E MYELIN PERIOD (/~) OF THIN A N D T H I C K MYELIN SHEATHS IN EACH OF T H E E X A M I N E D SPECIES The mean values presented for each species are based on the combined measurements in 3 animals. Species
Cat a Rabbit Guinea pig Rat Mouse Frog Perch
Total range
80-130 82-117 71-114 89-117 78-120 75-110 80-110
Average myelin period 4. SD (number of observations) ~< 10 lamellae
~> 50 lamellae
111 111 97 108 101 97 97
97 92 84 94 89 84 93
4- 8 4- 4 4. 7 4. 4 -4- 7 4, 7 4, 8
(109) (32) (36) (32) (32) (39) (34)
4- 8 -4- 7 4- 5 q- 4 4. 4 4- 4 -I- 4
(75) (32) (31) (31) (34) (39) (34)
Ratio between average periods of the two groups
0.87 0.83 0.87 0.87 0.87 0.87 0.96
a From Hildebrand (1972). TABLE 6 C A L C U L A T E D RATIO BETWEEN A X O N D I A M E T E R A N D TOTAL FIBRE D I A M E T E R FOR SPINAL CORD AXONS < 1/~m IN D I A M E T E R (figures to the left in each column) A N D F O R THE G R O U P OF L A R G E S T AXONS E N C O U N T E R E D (figures to the right in each column) I N SOME VERTEBRATES Values in the left column refer to the fixed and embedded state and values in the right column have been recalculated to the native state.
Cat Rabbit Guinea pig Rat Mouse Frog Perch
Estimated g-ratio in fixed and embedded state
Calculated g-ratio in native state
0.73-0.85 0.69-0.86 0.71-0.84 0.654).82 0.73-0.84 0.73-0.94 0.69-0.90
0.65-0.77 0.60-0.77 0.59-0.73 0.55-0.72 0.63-0.74 0.63-0.90 0.60-0.86
430 In the cat, rabbit and perch specimens the maximal number of myelin lamellae is about 160. The largest axons measure around 13/~m in the cat and rabbit and over 20 /zm in the perch. In the rat specimens, sheaths with more than 115 lamellae were not observed and the largest axons reach 10 /tm in diameter. The mouse and frog specimens show maximal lamellar numbers of 68 and 65 respectively. In the mouse axons larger than 5-6/~m were not found, but in the frog the largest axons measure 12-13/~m. While the maximal number of myelin lamellae varies between the species, the lower limit remains uniformly at 3-4 lamellae. The smallest myelinated axons encountered measure 0.2-0.3/~m in the mammals and the fish and 0.4-0.5 #m in the frog.
Myelin period - myelin sheath thickness The results of the myelin period measurements in thin ( ~< 10 lamellae) and thick sheaths (/> 50 lamellae) are presented in Table 5. In each animal the latter group comprises the thickest sheaths encountered and therefore contains sheaths of different thicknesses in different species. As seen from the period values in Table 5 the average radial repeating period of the thick sheaths is 83-87 ~o of that in the thin sheaths in all animals except the perch, where no clearcut difference was found. Ratio d/D Knowing the myelin period in thick and thin myelin sheaths and using the obtained data on the relation between axon size and number of myelin lamellae, the ratio d/D relevant for myelinated nerve fibres in fixed and embedded white matter was estimated. According to this estimation the ratio is 0.6--0.7 in fibres < 1 #m in diameter and 0.8-0.9 in the largest fibres (see Table 6). Shrinkage After postosmication, dehydration and embedding the area of transverse sections from feline spinal cord white matter was reduced to 85 ~ 3 ~ of the area directly after primary fixation. This represents a linear shrinkage of 7.6 ~. DISCUSSION The present results show that the relation between number of myelin lamellae and axon size follows a non-linear course in fixed and embedded spinal cord white matter, provided that a wide range of fibre sizes is considered. Thus, although a linear function with a good correspondence between observed and predicted values could be found in each case, the use of a linear + logarithmic expression resulted in an improved correlation. Comparisons between the individual animals within each species show an excellent agreement, whereas between the different species certain differences are obvious. Generally the relation between number of myelin lamellae and axon size shows a basically similar configuration in the cat, rabbit, rat, guinea pig and perch. A corresponding pattern has been observed in the CNS-part of the transitional region in feline dorsal roots (Berthold and Carlstedt 1977).
431 In the mouse no axons larger than 5-6/~m were found and within this narrow size range a rough rectilinearity is maintained. Also in the other animal species the relation between number of myelin lamellae and axon size seems to follow a straight line if only the size range below 5/~m is considered. This is in agreement with previous measurements on small myelinated fibres in various species (Samorajski and Friede 1968; Friede et al. 1971; Sturrock 1975; Fraher 1976; Waxman and Swadlow 1976). However, as shown by the present results, data obtained from small CNS fibres should not be extrapolated to large CNS fibres. The number of myelin lamellae increases comparatively slowly with increasing axon size in the mouse so that, on an average, the largest fibres have 58 myelin lamellae, whereas the same size group in the other mammals and the fish possess 70-87 lamellae. This is in agreement with previous comparisons of the relation between myelin sheath thickness and axon size in the optic nerve of the mouse and some other mammals (Bishop et al. 1971). In the sciatic nerve of the mouse Schnepp and Schnepp (1971) similarly found that the PNS myelin sheaths are unusually thin in comparison with other mammals. However, according to Friede and Samorajski (1967, 1968) the slope of the line relating lamellar number to axon size is the same in the rat and mouse sciatic nerve. The frog differs conspicuously from the prevalent pattern by having extremely thin myelin sheaths in relation to axon size, as reflected by the markedly curvilinear course of the line relating lameUar number to axon size. The difference is most pronounced in the largest fibres but is seen throughout the whole size range, except in axons below 1/tm, where the average number of myelin lamellae is similar to that in the other species. The largest frog axons, which measure 12-13/~m, possess an average number of 45-50 lamellae, which contrasts greatly with the 100-140 lamellae in comparable fibres in the cat, rabbit and perch. Similarly Bishop et al. (1971), by measuring the myelin sheath thickness directly, found that frog optic nerve axons have thinner myelin sheaths than comparable axons in the cat. If the axon controls the increase in number of myelin lamellae during development through calibre changes, as proposed by some workers (see Friede 1972; Friede and Bischhausen 1978), this control must be reset and lose greatly in precision when axons grow past a diameter of about 5/tm, in order to account for the present findings. Most likely, factors other than axon size are also involved in the control of the formation of central myelin sheaths (cf. Waxman and Swadlow 1976). In accordance with previous findings in the cat (Hildebrand 1972; Hildebrand and MiJller 1974), the myelin period was found to vary inversely with myelin sheath thickness in the examined non-feline mammals and the frog. In the perch, no clearcut difference was found. Since the period difference between thick and thin CNS sheaths is a preparative artifact (Hildebrand and Miiller 1974) counting of myelin lamellae should be employed instead of measuring myelin sheath thickness directly. It is interesting to note that, although the absolute myelin period values differ somewhat between the examined species, the average period of the thick mammalian and amphibian sheaths consistently is about 85 ~o of that in the thin sheaths. The radial repeating distances in thick and thin myelin sheaths show similar average values for the cat, rabbit and rat (about 95-110 A) and for the guinea pig, mouse and frog (about
432 85-100 A) whereas in the fish both thick and thin sheaths present a comparatively narrow average myelin period (93-97 A). Comparisons with the native period (Finean 1961) suggest that the preparative myelin sheath shrinkage amounts to 30-40 70 in the cat, rabbit and rat, 40-5070 in the guinea pig, mouse and frog and about 35 ~ in the perch. Unfortunately most previous myelin period measurements have been made on material prepared by different procedures and are therefore not directly comparable with our measurements. The obtained average period of thin sheaths in the rat (108 ± 4 A) is, however, in excellent agreement with the period found by Karlsson (1966) (109 :k 5) in the rat optic nerve prepared according to the same procedure. As discussed elsewhere (Hildebrand 1972) the different period in thick and thin sheaths after processing for electron microscopy may possibly be related to differences in lipid and protein content. Conceivably the fairly constant difference (ratio 0.83-0.87) in the various mammalian species and the frog might reflect some constant difference in chemical composition. The observation that thick and thin sheaths in the perch white matter have a similar average myelin period may be related to the atypical protein composition in fish CNS myelin (Mehl and Halaris 1970). The ratio between axon diameter and total fibre size is a parameter of prime importance for the functional properties of a myelinated nerve fibre. This ratio, which reflects the longitudinal resistance of the axon and the impedance of the myelin sheath, has been used in theoretical calculations on conduction velocity (Rushton 1951; Goldman and Albus 1968; Deutsch 1969; Smith and Koles 1970). In the present study the d/D ratio of small fixed and embedded fibres was estimated to be about 0.70 in all species. In the largest fibres the ratio was about 0.85 in the mammals, 0.90 in the fish and 0.94 in the frog. Since myelinated nerve fibres undergo dimensional changes during the preparative procedure these figures are not representative for the native state. In order to obtain figures relevant for the in vivo condition the effects of fixation, dehydration and embedding must first be considered. Since most of the cross-sectional area of the mature feline ventro-lateral funiculus is accounted for by myelinated nerve fibres the linear preparative white matter shrinkage of 7.6 ~ that takes place after primary fixation should be approximately valid also for the average individual nerve fibre. In addition the myelin sheaths decrease 3.7~ in thickness during primary glutaraldehyde fixation of feline white matter (Hildebrand and Mfiller 1974). Although a measure of axonal changes during primary fixation is not available it seems reasonable to assume that in the cat CNS the decrease in external fibre diameter during tissue preparation amounts to about 10 70 (cf. Berthold and Carlstedt 1977). Assuming further that a shrinkage factor of about 10 ~o is generally valid for myelinated CNS fibres and using the native myelin period values presented by Finean (1961) a d/D ratio of about 0.60 can be calculated for axons < 1 #m in the examined species. In the largest fibres a native ratio of about 0.75 is obtained in the mammals, 0.90 in the frog and 0.86 in the perch (see Table 6). Thus, as expected in view of the non-linear relation between lamellar number and axon size, the g-ratio seems to increase with increasing fibre size in myelinated nerve fibres of the CNS. In the PNS a shift in d/D ratio with fibre size has been described by several workers, while others claim that the ratio is constant for all sizes (reviewed by
433 Williams and Wendell-Smith 1971 ; Bischoff and Thomas 1975). With respect to the CNS most investigators advocate a constant g-ratio (Samorajski and Friede 1968; Waxman and Bennett 1972; W a x m a n and Swadlow 1976) while, according to Ogden and Miller (1966) and the present findings, the ratio increases with fibre size. This conflict of opinions is probably related to the fact that most previous workers have limited their observations to small CNS fibres. I f a large size range of central myelinated fibres is examined, a constant g-ratio is not found. Unfortunately the present estimate of the d/D ratio in the CNS cannot be directly compared with the uncorrected values presented by other workers, since the preparative procedures differ. However, our findings in the mammalian CNS are generally consistent with previous observations in the PNS (see Bischoff and Thomas 1975) and are in excellent agreement with the theoretical requirements for optimal conduction properties, as discussed by Goldman and Albus (1968) and Smith and Koles (1970). Since in the frog the g-ratio of the large fibres is very high, as a result of the slow increment in lamellar number with increasing axon size these fibres might not offer optimal conditions for impulse conduction (cf. Smith and Koles 1970). Also in the perch the d/D ratio relevant for the largest fibres is greater than in the mammals. This evokes questions as to how the large fibres of the frog and perch spinal cord compare with those of other species with respect to the internodal lengths and the structural organization of the nodes of Ranvier. ACKNOWLEDGEMENTS We wish to thank Mrs Pippi Lindquist for technical assistance and Miss Maj Berghman for drawing the graphs. The statistical calculations were made by U. Brodin and A. Olausson, Computer Department, Karolinska Institutet, which is gratefully acknowledged.
REFERENCES Berthold, C.-H. (1968) A study on the fixation of large mature feline myelinated ventral lumbar spinal root fibres, Acta Soc. Med. upsalien., 73, Suppl. 9: 1-36. Berthold, C.-H. and T. Carlstedt (1977) Observations on the morphology at the transition between the peripheral and the central nervous system in the cat, Part 3 (Myelinated fibres in $1 dorsal rootlets), Acta physioL scand., Suppl. 446: 23-42. Bischoff, A. and P. K. Thomas (1975) Microscopic anatomy of myelinated nerve fibers. In: P. J. Dyck, P. K. Thomas and E. H. Lambert (Eds.), Peripheral Neuropathy, W. B. Saunders Company, Philadelphia, PA, pp. 104-130. Bishop, G. H., M. H. Clare and W. M. Landon (1971) The relation of axon sheath thickness to fiber size in the central nervous system of vertebrates, Intern. Neurosci., 2: 69-78. Boyd, I. A. and K. U. Kalu (1973) The relation between axon size and number of lamellae in the myelin sheath for afferent fibres in groups I, II and In in the cat, J. Physiol. (Land.), 252: 31P33P. Deutsch, S. (1969) The maximization of nerve conduction velocity, LE.E.E. Trans. Systems Science Cybern., 5: 86-91. Dixon, W. J. and F. J. Massey, Jr. (1957) Introduction to Statistical Analysis, McGraw-Hill, New York, NY. Finean, J. B. (1961) Nature and stability of nerve myelin, Int. Rev. Cytol., 12: 303-336.
434 Fraher, J. P. (1976) The growth and myelination of central and peripheral segments of ventral motoneurone axons - - A quantitative ultrastructural study, Brain Res., 105:193-211. Friede, R. L. (1972) Control of myelin formation by axon caliber (with a model of the control mechanism), J. comp. NeuroL, 144: 233-252. Friede, R. L. and R. Bischhausen (1978) How do axons control myelin formation? - - The model of 6-aminonicotinamide neuropathy, J. neuroL Sci., 35: 341-353. Friede, R. L. and T. Samorajski (1967) Relation between the number of myelin lameUae and axon circumference in fibers of vagus and sciatic nerves of mice, J. comp. NeuroL, 130: 223-232. Friede, R. L. and T. Samorajski (1968) Myelin formation in the sciatic nerve of the rat - - A quantitative electron microscope, histochemical and radioautographic study, J. Neuropath. exp. Neurol., 27: 546-570. Friede, R. L., Miyaghishi, T. and K. H. Hu (1971) Axon calibre, neurofilaments, microtubules, sheath thickness and cholesterol in cat optic nerve fibres, J. Anat. (Lond.), 108 : 365-373. Goldman, L. and J. A. Albus (1968) Computation of conduction in myelinated fibers - - Theoretical basis of the velocity-diameter relation, Biophys. J., 8: 596-607. Hildebrand, C. (1971) Ultrastructural and light microscopic studies of the nodal region in large myelinated fibres of the adult feline spinal cord white matter, Acta physiol, scand., Suppl. 364: 43-81. Hildebrand, C. (1972) Evidence for a correlation between myelin period and number of myelin lamellae in fibres of the feline spinal cord white matter, J. Neurocytol., 1 : 223-232. Hildebrand, C. (1977) Presence of Marchi-positive myelinoid bodies in the spinal cord white matter of some vertebrate species, J. MorphoL, 153: 1-22. Hildebrand, C. and H. Mfiller (1974) Low angle X-ray diffraction studies on the period of central myelin sheaths during preparation for electron microscopy - - A comparison between different anatomical areas, Neurobiology, 4: 71-81. Karlsson, U. (1966) Comparison of the myelin period of peripheral and central origin by electron microscopy, J. Ultrastruct. Res., 15: 451-468. Mehl, E. and A. Halaris (1970) Stoichiometric relation of protein components in cerebral myelin from different species, J. Neurochem., 17: 659-668. Ogden, T. E. and R. F. Miller (1966) Studies of the optic nerve of the rhesus monkey - - Nerve fiber spectrum and physiological properties, Vision Res., 6: 485-506. Rushton, W. A. H. (1951) A theory of the effects of fibre size in medullated nerve, J. PhysioL (Lond.), 115: 101-122. Samorajski, T. and R. L. Friede (1968) A quantitative electron microscopic study of myelination in the pyramidal tract of rat, J. comp. Neurol., 134: 323-338. Schnepp, P. and G. Schnepp (1971) Faseranalytische Untersuchungen an peripheren Nerven bei Tieren verschiedener Gr~sse, Part 2 (Verh~iltnis Axondurchmesser/Gesamtdurchmesser und lnternodallange), Z. Zellforsch., 119: 99-114. Sima, A. (1974) Relation between the number of myelin lamellae and axon circumference in fibres of ventral and dorsal roots and optic nerve in normal, undernourished and rehabilitated rats - - An ultrastructural morphometric study, Acta physiol, scand., Suppl. 410: t-28. Smith, R. S. and Z. J. Koles (1970) Myelinated nerve fibres - - Computed effect of myelin thickness and conduction velocity, Amer. J. Physiol., 219: 1256-1258. Sturrock, R. R. (1975) A quantitative electron microscopic study of myelination in the anterior limb of the anterior commLsure of the mouse brain, J. Anat. (Lond.), 119: 67-75. Tapp, R. L. (1974) Axon numbers and distribution, myelin thickness, and the reconstruction of the compound action potential in the optic nerve of the teleost, Eugerresplurnieri, J. comp. Neurol., 153 : 267-274. Waxman, S. G. and M. V. L. Bennett (1972) Relative conduction velocities of small myelinated and non-myelinated fibres in the central nervous system, Nature (Lond.), 238: 217-219. Waxman, S. G. and H. A. Swadlow (1976) Ultrastructure of visual callosal axons in the rabbit, Exp. NeuroL, 53 : 115-127. Williams, P. L. and C. P. Wendell-Smith (1971) Some additional parametric variations between peripheral nerve fibre populations, J. Anat. (Lond.), 109: 505-526.
421
© ElsevierfNorth-HollandBiomedicalPress
RELATION BETWEEN MYELIN SHEATH THICKNESS AND AXON SIZE IN SPINAL CORD WHITE MATTER OF SOME VERTEBRATE SPECIES
CLAES HILDEBRANDand ROBERT HAHN Department of Anatomy, Karolinska lnstitutet, 104 O1 Stockholm 60 (Sweden)
(Received 20 April, 1978) (Accepted 6 June, 1978)
SUMMARY The relation between number of myelin lamellae and axon size in the CNS was examined by electron microscopy of spinal cord white matter fibres in different vertebrate species (cat, rabbit, guinea pig, rat, mouse, frog and perch). The results show that the number of myelin lamellae increases with increasing axon size in a nonlinear fashion. Below an axon size of 4-5 #m the relation follows a fairly straight line but above this size rectilinearity is lost. The mouse and the frog differ from the pattern shared by the other animals. In the mouse the lamellar number increases more slowly with axon size and the relation is close to linear. In the frog the number of lamellae increases very slowly with axon size and the relation is markedly curvilinear. Measurements of the myelin repeating period show that in the mammals and the frog the average period of thick sheaths is about 85 % of that in thin sheaths, in accordance with previous findings in the cat. In the perch a clearcut difference in this respect between thick and thin sheaths is not found. Calculations of the g-ratio on the basis of the findings indicate that it increases with increasing fibre size. This is most pronounced in the perch and the frog in which the g-ratio for the largest fibres far exceeds the functionally optimal value defined in theoretical analyses on impulse propagation.
INTRODUCTION In both peripheral and central fibre tracts the sheaths of myelinated nerve fibres increase in thickness with the size of the axons. The relation between myelin sheath thickness and axon size has often been expressed as the ratio between axon diameter (d) and total fibre diameter (D), i.e. the g-factor. In light microscopic studies of This study was supported by grants from the Swedish Medical Research Council (Project No. 3761) and from KarolinskaInstituter.
422 peripheral nerves the g-factor has been found to vary between 0.5 and 0.7 and according to most investigators the ratio increases with fibre size (see Williams and Wendell-Smith 1971 ; Bischoff and Thomas 1975 for references). A ratio of 0.5-0.7 is in satisfactory agreement with theoretical analyses on the requirements for optimal function (Rushton 1951; Goldman and Albus 1968; Deutsch 1969; Smith and Koles 1970). A more exact measure of the relation between myelin sheath thickness and axon size is obtained by counting the number of myelin lamellae in the electron microscope and relating the lamellar number to axon circumference or cross-sectional area. In peripheral nerves the number of myelin lamellae increases with increasing axon size, and this relationship is generally considered to be rectilinear (reviewed by Friede 1972; Bischoff and Thomas 1975). According to some workers, however, it is only linear below axon sizes of 4-5/~m (Boyd and Kalu 1973; Sima 1974; Berthold and Carlstedt 1977). In the CNS the d/D-ratio of the myelinated nerve fibres appears to be similar to that in the PNS (Ogden and Miller 1966; Bishop, Clare and Landon 1971; Friede, Miyaghishi and Hu 1971; Waxman and Bennett 1972; Tapp 1974; Waxman and Swadlow 1976). According to the current view, the number of central myelin lamellae grows linearly with increasing axon size (Samorajski and Friede 1968; Friede et al. 1971; Sturrock 1975; Fraher 1976). However, in the CNS-part of the transitional region in feline dorsal roots rectilinearity is lost above an axon diameter of 4-5/~m (Berthold and Carlstedt 1977). The aim of the present study is to determine the relation between lamellar number and axon size in the white matter proper considering myelinated nerve fibre s with a wide range of sizes. Since previous studies indicate species differences (Bishop et al. 1971; Hildebrand 1977) several vertebrate species were studied. In view of the different repeating period in thin and thick feline myelin sheaths (Hildebrand 1972; Hildebrand and Miiller 1974), the possible existence of a similar variability of the myelin period in other species was examined. MATERIALAND METHODS Three adult animals of each of the following species were used: cat (European mixed breed), rabbit (New Zealand albino), guinea pig (mixed laboratory breed), frog (Rana temporaria, 5 cm body length) and perch (Perca fluviatilis, 25-40 cm body length). The mammals were anaesthetized with 40 mg/kg b.w. Nembutal intraperitoneally, artificially ventilated and perfused through the heart with 5 ~ glutaraldehyde in a 300 mOsm phosphate buffer (see Berthold 1968; Hildebrand 1971). Specimens from the spinal cord segments C1-C2 were postfixed for 4 hr in chilled perfusate. In the frog perfusion failed, and the rostral part of the spinal cord was fixed by immersion for 4 hr in the same fixative, after decapitation and rapid dissection. The fish were anaesthetized by immersion in 0.5 ~ urethane and placed in crushed ice. Perfusion fixation rendered unsatisfactory results and instead the portion of spinal cord underlying the dorsal fin was dissected out at + 4 °C and fixed by immersion in 5 ~ glutaraldehyde in a 200 mOsm phosphate buffer during 4 hr.
423 After primary fixation the spinal cord specimens were rinsed in the buffer used, osmicated in a 2 ~o solution of OsO4 in the same buffer, dehydrated in acetone and embedded in Vestopal W. Thin transverse sections from the ventrolateral funiculus were collected on one hole copper grids coated with carbon-stabilized formvar. After staining with uranyl acetate and lead citrate the sections were examined in a Philips EM 301 electron microscope. Fibres considered to present an acceptable structural preservation were free from swollen axonal mitochondria, myelin sheath splitting and empty spaces between axon and inner margin of the myelin sheath. Electron micrographs from areas containing large fibres with these characteristics were printed at a total linear magnification of × 10,000. The same areas were reexamined in the electron microscope and the number of myelin lamellae associated with fibres on the prints was counted directly in the microscope (thin sheaths), or on high magnification electron micrographs (thick sheaths). Axonal circumference and axonal area were estimated with a map meter and with an Ott planimeter respectively. The corresponding diameter values, dcire and dsrea were calculated. It should be pointed out that this represents an approximation since nerve fibres rarely form perfect circles in cross-sections. In each animal 130-220 fibres were examined. Fibres showing gross artefacts of fixation or with a highly irregular shape and fibres cut through a Schmidt-Lanterman incisure or through a node of Ranvier were excluded. The Mauthner axons in the perch were not included in the measurements. Comparisons between the two measures of axon size (deire and darea) were made by an analysis of correlation between the two sets o f values in a Nord-10 computer. Since the two approaches gave largely identical results (correlation coefficients 0.97-0.99, Table 1) only the circumference values were used for the further analysis. A numerical expression compatible with the observed relation between number of myelin lamellae and axon size was searched for in each separate animal by comparing linear (y ---- a q- bx) or linear ÷ logarithmic expressions (y = a -~ bx -Jclnx) with the observed values through regression analysis in an IBM 370-165 computer (BMD 03R biomedical computer program, University of California Press 1975, W. J. Dixon, ed.). The intraspecies and interspecies variance was determined for TABLE 1 CORRELATION COEFFICIENTS FOR THE COMPARISON delre-darea IN ONE ANIMAL OF EACH SPECIES Animal species
Correlation coefficientdcire-darea
Number of pairs of valuesexamined
Cat Rabbit Guinea pig Rat Mouse Frog Perch
0.98 0.99 0.97 0.98 0.98 0.98 0.99
183 177 174 136 138 155 152
424 TABLE 2 AVERAGE NUMBER OF MYELIN LAMELLAE (NUMBER OF OBSERVATIONS) FOUND FOR AXONAL SIZE CLASSES 0-1/~m ETC. (EXPRESSED AS deire) IN EACH OF THE EXAMINED SPECIES The values are total mean values derived from all measurements in each species. Axon size ~m) 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-17 17-19 19-21
Cat 8 (116) 19 (130) 35 (63) 49 (32) 63 (38) 76 (16) 83 (13) 92 (20) 105 (14) 108 (9) 124 (9) 120 (11) 119 (5)
Rabbit
Guinea pig Rat
Mouse
Frog
Perch
10 (116) 22 (167) 40 (66) 55 (42) 64 (30) 75 (18) 82 (20) 89 (10) 96 (6) 90 (8) 104 (6) 106 (5) 136 (2)
10 (91) 20 (165) 33 (67) 52 (42) 66 (24) 86 (23) 88 (20) 93 (19) 103 (7) 103 (6)
9 (147) 17 (128) 29 (54) 41 (41) 49 (30) 58 (10)
9 (8) 15 (126) 22 (49) 27 (53) 30 (49) 37 (37) 38 (29) 39 (16) 42 (11) 43 (11) 43 (11) 51 (5) 46 (4)
11 (67) 22 (116) 36 (54) 50 (36) 59 (34) 70 (10) 84 (16) 91 (9) 111 (7) 119 (6) 116 (4) 126 (3) 119 (3) 117 (5) 122 (6) 130 (3) 118 (5) 114 (6)
12 (150) 25 (159) 44 (57) 61 (28) 75 (15) 87 (9) 88 (14) 95 (7) 102 (5) 114 (1)
a range of circumferences corresponding to axonal diameters of 4-6/~m, by a one way analysis of variance ( B M D 0 I V biomedical c o m p u t e r program, University of California Press 1975, W. J. Dixon, ed.) and a studentisized range test of group means (Dixon and Massey 1957). F o r myelin period measurements electron micrographs were taken at a primary magnification o f × 34,000. The C N S myelin period o f the cat has been studied previously (Hildebrand 1972) and was not included. In the other species about 10 thick sheaths (/> 50 lamellae) and 10 thin sheaths (~< 10 lamellae) were examined in each individual animal at places where the myelin lamellae appeared regular and distinct and were oriented approximately parallel to the sectioning direction (Karlsson 1966). The myelin period was estimated as the average distance between the midpoints of 3-10 successive major dense lines on prints with a total magnification o f x 100,000. F o r each set of 15 plates magnification was checked with a carbon grating replica (54864 lines per inch, Ladd Res., IN, U.S.A.). The change in cross-sectional area of spinal cord ventrolateral white matter caused by the processing after primary glutaraldehyde fixation was assessed in one cat by planimetry of light micrographs from transverse Vibratome sections. RESULTS Lamellar
number
- axon size
The cat, rabbit, guinea pig, rat and perch present basically similar patterns (Fig.
425
1, Table 2). In these animals the number of myelin lamellae increases regularly with axon size up to about 4-5 #m, which corresponds to 60-70 lamellae. Above this size the relation between number of myelin lamellae and axon size is less strict and the lamellar number seems to increase progressively less with increasing axon diameter. In the size groups above 10 #m the mean number of myelin lamellae varies irregularly between 100 and 140. In the mouse, where the largest axons encountered measure 5-6 #m in diameter, a somewhat different picture is seen. The number of myelin lamellae A CAT 1
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PERCH 1 Y = 20.04 InX + 3.5:'X +11.oo
PERCH 2 Y : 22.43 InX * 3.s2X * 15.oo
PERCH 3 Y = 23.'72 tnX ÷ 2.s3X * 12,0o
160.
160-
160.
i40 t
140
'i40.
120-
1
100.
%
80. 60.
40.
20
20-
20.
2 4 6 8 10 12 14 16 18 20 22 AXON DIAMETER ,urn
2 4 6 8 10 12 14 16 18 20 AXON DIAMETER ,urn
:.z
AXON DIAMETER
)Jm
Figs• 1A--C. Graphs showing relation between number of myelin lamellae and axon size (expressed as detre) in some vertebrate species• In each case the line drawn illustrates the linear + logarithmic function (presented above the graph) which was found to be best adapted to the observed values• A: cat and rabbit; B: rat, guinea pig and mouse; C: frog and perch. increases with increasing axon diameter along a fairly straight line to a maximum of about 60 lamellae at 5-6 #m. The slope of the line is less steep in comparison with the other mammals and the fish (Fig. 1, Table 2). In the frog the number of myelin lamellae increases very slowly with increasing axon size to about 5-6/~m, corresponding to 35-40 lamellae. Above this size a further slight increase in average lamellar number is seen to a maximum of 40--50 lamellae. In all species the number of myelin lamellae shows a pronounced variability in the largest fibres (Fig. 1, Table 2). Comparisons between various linear functions (y = a + bx) and the data from each animal, showed that a good correspondance between observed and predicted values can be obtained (Table 3). However, addition of a logarithmic term to the
428 TABLE 3 CORRELATION COEFFICIENTS FOR THE COMPARISON OF THE OBSERVED RELA. TION BETWEEN NUMBER OF MYELIN LAMELLAE AND AXON SIZE WITH LINEAR OR LINEAR ÷ LOGARITHMIC FUNCTIONS Intraspecies interindividual mean lamellar number ( ± SD) representative for the axonal size range 4-6/~m are also presented. Animal No.
Correlation coefficients predicted observed values
Intraspecies interindividual mean lamellar number ( ± SD) for axonal size range 4-6/~m
y=a+bx
y-- a+bx+clnx
1 2 3
0.96 0.95 0.95
0.96 0.96 0.96
69.61 ± 1.31
1 2 3
0.91 0.89 0.95
0.94 0.92 0.96
71.99 ± 12.16
Guinea pig 1 2 3
0.91 0.94 0.95
0.91 0.95 0.95
77.82 ~ 2.42
Rat
1 2 3
0.92 0.93 0.90
0.94 0.94 0.93
82.68 4- 3.19
1 2 3
0.92 0.93 0.96
0.93 0.93 0.96
52.89 ~ 2.87
1 2 3
0.87 0.82 0.81
0.90 0.88 0.87
33.79 ± 1.50
1 2 3
0.89 0.83 0.84
0.93 0.88 0.89
65.70 ~ 3.07
Cat
Rabbit
Mouse
Frog
Perch
function (y = a -~- bx ÷ clnx, see Fig. 1) renders a better c o r r e l a t i o n between observed a n d p r e d i c t e d values, as illustrated by the c o r r e l a t i o n coefficients (Table 3). This i m p r o v e m e n t is m o s t a p p a r e n t in the frog a n d the perch b u t less clear in the m o u s e a n d the guinea pig t h a n in the o t h e r species (Table 3). A c o m p a r i s o n o f the variance within a n d between the different species, considering axons between 4 a n d 6/~m, is shown in Table 4. W i t h the exception o f the r a b b i t , where one individual differs r a t h e r distinctly f r o m the others, the interindividual " w i t h i n - v a r i a n c e " is fairly low. Analysis o f variance showed t h a t the average intraspecies v a r i a t i o n is m u c h smaller t h a n the t o t a l interspecies v a r i a t i o n ( F - r a t i o 31.5, Table 4). Pairwise c o m p a r i s o n s between the different species t h r o u g h studentisized range test showed t h a t the frog a n d the mouse differ significantly (at the level P = 0.05) f r o m the o t h e r vertebrates a n d f r o m each other. A difference between the perch a n d the rat was also indicated b y the test but no o t h e r significant differences could be f o u n d in the size range examined.
429 TABLE 4 STATISTICAL COMPARISON BETWEEN THE INTER- A N D INTRASPECIES V A R I A N C E W I T H RESPECT TO N U M B E R O F MYELIN L A M E L L A E RELATED TO AXONS WITH D I A M E T E R S OF 4-6 # m IN SPINAL CORD WHITE M A T T E R O F THE VERTEBRATE SPECIES U N D E R E X A M I N A T I O N
Between species Within species Total
Sum of squares Degrees of freedom Mean square
F-ratio
5004.4 371.1 5375.5
31.5
6 14 20
834.1 26.5
TABLE 5 A V E R A G E MYELIN PERIOD (/~) OF THIN A N D T H I C K MYELIN SHEATHS IN EACH OF T H E E X A M I N E D SPECIES The mean values presented for each species are based on the combined measurements in 3 animals. Species
Cat a Rabbit Guinea pig Rat Mouse Frog Perch
Total range
80-130 82-117 71-114 89-117 78-120 75-110 80-110
Average myelin period 4. SD (number of observations) ~< 10 lamellae
~> 50 lamellae
111 111 97 108 101 97 97
97 92 84 94 89 84 93
4- 8 4- 4 4. 7 4. 4 -4- 7 4, 7 4, 8
(109) (32) (36) (32) (32) (39) (34)
4- 8 -4- 7 4- 5 q- 4 4. 4 4- 4 -I- 4
(75) (32) (31) (31) (34) (39) (34)
Ratio between average periods of the two groups
0.87 0.83 0.87 0.87 0.87 0.87 0.96
a From Hildebrand (1972). TABLE 6 C A L C U L A T E D RATIO BETWEEN A X O N D I A M E T E R A N D TOTAL FIBRE D I A M E T E R FOR SPINAL CORD AXONS < 1/~m IN D I A M E T E R (figures to the left in each column) A N D F O R THE G R O U P OF L A R G E S T AXONS E N C O U N T E R E D (figures to the right in each column) I N SOME VERTEBRATES Values in the left column refer to the fixed and embedded state and values in the right column have been recalculated to the native state.
Cat Rabbit Guinea pig Rat Mouse Frog Perch
Estimated g-ratio in fixed and embedded state
Calculated g-ratio in native state
0.73-0.85 0.69-0.86 0.71-0.84 0.654).82 0.73-0.84 0.73-0.94 0.69-0.90
0.65-0.77 0.60-0.77 0.59-0.73 0.55-0.72 0.63-0.74 0.63-0.90 0.60-0.86
430 In the cat, rabbit and perch specimens the maximal number of myelin lamellae is about 160. The largest axons measure around 13/~m in the cat and rabbit and over 20 /zm in the perch. In the rat specimens, sheaths with more than 115 lamellae were not observed and the largest axons reach 10 /tm in diameter. The mouse and frog specimens show maximal lamellar numbers of 68 and 65 respectively. In the mouse axons larger than 5-6/~m were not found, but in the frog the largest axons measure 12-13/~m. While the maximal number of myelin lamellae varies between the species, the lower limit remains uniformly at 3-4 lamellae. The smallest myelinated axons encountered measure 0.2-0.3/~m in the mammals and the fish and 0.4-0.5 #m in the frog.
Myelin period - myelin sheath thickness The results of the myelin period measurements in thin ( ~< 10 lamellae) and thick sheaths (/> 50 lamellae) are presented in Table 5. In each animal the latter group comprises the thickest sheaths encountered and therefore contains sheaths of different thicknesses in different species. As seen from the period values in Table 5 the average radial repeating period of the thick sheaths is 83-87 ~o of that in the thin sheaths in all animals except the perch, where no clearcut difference was found. Ratio d/D Knowing the myelin period in thick and thin myelin sheaths and using the obtained data on the relation between axon size and number of myelin lamellae, the ratio d/D relevant for myelinated nerve fibres in fixed and embedded white matter was estimated. According to this estimation the ratio is 0.6--0.7 in fibres < 1 #m in diameter and 0.8-0.9 in the largest fibres (see Table 6). Shrinkage After postosmication, dehydration and embedding the area of transverse sections from feline spinal cord white matter was reduced to 85 ~ 3 ~ of the area directly after primary fixation. This represents a linear shrinkage of 7.6 ~. DISCUSSION The present results show that the relation between number of myelin lamellae and axon size follows a non-linear course in fixed and embedded spinal cord white matter, provided that a wide range of fibre sizes is considered. Thus, although a linear function with a good correspondence between observed and predicted values could be found in each case, the use of a linear + logarithmic expression resulted in an improved correlation. Comparisons between the individual animals within each species show an excellent agreement, whereas between the different species certain differences are obvious. Generally the relation between number of myelin lamellae and axon size shows a basically similar configuration in the cat, rabbit, rat, guinea pig and perch. A corresponding pattern has been observed in the CNS-part of the transitional region in feline dorsal roots (Berthold and Carlstedt 1977).
431 In the mouse no axons larger than 5-6/~m were found and within this narrow size range a rough rectilinearity is maintained. Also in the other animal species the relation between number of myelin lamellae and axon size seems to follow a straight line if only the size range below 5/~m is considered. This is in agreement with previous measurements on small myelinated fibres in various species (Samorajski and Friede 1968; Friede et al. 1971; Sturrock 1975; Fraher 1976; Waxman and Swadlow 1976). However, as shown by the present results, data obtained from small CNS fibres should not be extrapolated to large CNS fibres. The number of myelin lamellae increases comparatively slowly with increasing axon size in the mouse so that, on an average, the largest fibres have 58 myelin lamellae, whereas the same size group in the other mammals and the fish possess 70-87 lamellae. This is in agreement with previous comparisons of the relation between myelin sheath thickness and axon size in the optic nerve of the mouse and some other mammals (Bishop et al. 1971). In the sciatic nerve of the mouse Schnepp and Schnepp (1971) similarly found that the PNS myelin sheaths are unusually thin in comparison with other mammals. However, according to Friede and Samorajski (1967, 1968) the slope of the line relating lamellar number to axon size is the same in the rat and mouse sciatic nerve. The frog differs conspicuously from the prevalent pattern by having extremely thin myelin sheaths in relation to axon size, as reflected by the markedly curvilinear course of the line relating lameUar number to axon size. The difference is most pronounced in the largest fibres but is seen throughout the whole size range, except in axons below 1/tm, where the average number of myelin lamellae is similar to that in the other species. The largest frog axons, which measure 12-13/~m, possess an average number of 45-50 lamellae, which contrasts greatly with the 100-140 lamellae in comparable fibres in the cat, rabbit and perch. Similarly Bishop et al. (1971), by measuring the myelin sheath thickness directly, found that frog optic nerve axons have thinner myelin sheaths than comparable axons in the cat. If the axon controls the increase in number of myelin lamellae during development through calibre changes, as proposed by some workers (see Friede 1972; Friede and Bischhausen 1978), this control must be reset and lose greatly in precision when axons grow past a diameter of about 5/tm, in order to account for the present findings. Most likely, factors other than axon size are also involved in the control of the formation of central myelin sheaths (cf. Waxman and Swadlow 1976). In accordance with previous findings in the cat (Hildebrand 1972; Hildebrand and MiJller 1974), the myelin period was found to vary inversely with myelin sheath thickness in the examined non-feline mammals and the frog. In the perch, no clearcut difference was found. Since the period difference between thick and thin CNS sheaths is a preparative artifact (Hildebrand and Miiller 1974) counting of myelin lamellae should be employed instead of measuring myelin sheath thickness directly. It is interesting to note that, although the absolute myelin period values differ somewhat between the examined species, the average period of the thick mammalian and amphibian sheaths consistently is about 85 ~o of that in the thin sheaths. The radial repeating distances in thick and thin myelin sheaths show similar average values for the cat, rabbit and rat (about 95-110 A) and for the guinea pig, mouse and frog (about
432 85-100 A) whereas in the fish both thick and thin sheaths present a comparatively narrow average myelin period (93-97 A). Comparisons with the native period (Finean 1961) suggest that the preparative myelin sheath shrinkage amounts to 30-40 70 in the cat, rabbit and rat, 40-5070 in the guinea pig, mouse and frog and about 35 ~ in the perch. Unfortunately most previous myelin period measurements have been made on material prepared by different procedures and are therefore not directly comparable with our measurements. The obtained average period of thin sheaths in the rat (108 ± 4 A) is, however, in excellent agreement with the period found by Karlsson (1966) (109 :k 5) in the rat optic nerve prepared according to the same procedure. As discussed elsewhere (Hildebrand 1972) the different period in thick and thin sheaths after processing for electron microscopy may possibly be related to differences in lipid and protein content. Conceivably the fairly constant difference (ratio 0.83-0.87) in the various mammalian species and the frog might reflect some constant difference in chemical composition. The observation that thick and thin sheaths in the perch white matter have a similar average myelin period may be related to the atypical protein composition in fish CNS myelin (Mehl and Halaris 1970). The ratio between axon diameter and total fibre size is a parameter of prime importance for the functional properties of a myelinated nerve fibre. This ratio, which reflects the longitudinal resistance of the axon and the impedance of the myelin sheath, has been used in theoretical calculations on conduction velocity (Rushton 1951; Goldman and Albus 1968; Deutsch 1969; Smith and Koles 1970). In the present study the d/D ratio of small fixed and embedded fibres was estimated to be about 0.70 in all species. In the largest fibres the ratio was about 0.85 in the mammals, 0.90 in the fish and 0.94 in the frog. Since myelinated nerve fibres undergo dimensional changes during the preparative procedure these figures are not representative for the native state. In order to obtain figures relevant for the in vivo condition the effects of fixation, dehydration and embedding must first be considered. Since most of the cross-sectional area of the mature feline ventro-lateral funiculus is accounted for by myelinated nerve fibres the linear preparative white matter shrinkage of 7.6 ~ that takes place after primary fixation should be approximately valid also for the average individual nerve fibre. In addition the myelin sheaths decrease 3.7~ in thickness during primary glutaraldehyde fixation of feline white matter (Hildebrand and Mfiller 1974). Although a measure of axonal changes during primary fixation is not available it seems reasonable to assume that in the cat CNS the decrease in external fibre diameter during tissue preparation amounts to about 10 70 (cf. Berthold and Carlstedt 1977). Assuming further that a shrinkage factor of about 10 ~o is generally valid for myelinated CNS fibres and using the native myelin period values presented by Finean (1961) a d/D ratio of about 0.60 can be calculated for axons < 1 #m in the examined species. In the largest fibres a native ratio of about 0.75 is obtained in the mammals, 0.90 in the frog and 0.86 in the perch (see Table 6). Thus, as expected in view of the non-linear relation between lamellar number and axon size, the g-ratio seems to increase with increasing fibre size in myelinated nerve fibres of the CNS. In the PNS a shift in d/D ratio with fibre size has been described by several workers, while others claim that the ratio is constant for all sizes (reviewed by
433 Williams and Wendell-Smith 1971 ; Bischoff and Thomas 1975). With respect to the CNS most investigators advocate a constant g-ratio (Samorajski and Friede 1968; Waxman and Bennett 1972; W a x m a n and Swadlow 1976) while, according to Ogden and Miller (1966) and the present findings, the ratio increases with fibre size. This conflict of opinions is probably related to the fact that most previous workers have limited their observations to small CNS fibres. I f a large size range of central myelinated fibres is examined, a constant g-ratio is not found. Unfortunately the present estimate of the d/D ratio in the CNS cannot be directly compared with the uncorrected values presented by other workers, since the preparative procedures differ. However, our findings in the mammalian CNS are generally consistent with previous observations in the PNS (see Bischoff and Thomas 1975) and are in excellent agreement with the theoretical requirements for optimal conduction properties, as discussed by Goldman and Albus (1968) and Smith and Koles (1970). Since in the frog the g-ratio of the large fibres is very high, as a result of the slow increment in lamellar number with increasing axon size these fibres might not offer optimal conditions for impulse conduction (cf. Smith and Koles 1970). Also in the perch the d/D ratio relevant for the largest fibres is greater than in the mammals. This evokes questions as to how the large fibres of the frog and perch spinal cord compare with those of other species with respect to the internodal lengths and the structural organization of the nodes of Ranvier. ACKNOWLEDGEMENTS We wish to thank Mrs Pippi Lindquist for technical assistance and Miss Maj Berghman for drawing the graphs. The statistical calculations were made by U. Brodin and A. Olausson, Computer Department, Karolinska Institutet, which is gratefully acknowledged.
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