A Quantitative morphological study of HRP-labelled cat α-motoneurones supplying different hindlimb muscles

Brain Research, 264 (1983) 1-19 Elsevier Biomedical Press

1

Research Reports A Quantitative Morphological Study of HRP-Labelled Cat a-Motoneurones Supplying Different Hindlimb Muscles B. ULFHAKE and J.-O. KELLERTH

Department of Anatomy, Karolinska lnstitutet, Box 60400, S-104 O1 Stockholm and (J.-O. K.) Department of Anatomy, University of Umed, 901 87 Umeti (Sweden) (Accepted August 31st, 1982)

Key words: cat spinal cord - - hindlimb a-motoneurone - - HRP - - light microscopy

Cat a-motoneurones supplying the quadriceps (Q), posterior biceps (PB), gastrocnemius (G), soleus (SOL) and short intrinsic plantar foot (SP) muscles were studied after retrograde or intracellular labelling with HRP. The average soma sizes were rather similar for the different pools, the SOL cells being the smallest. The median number of firstorder dendrites ranged from 10 (PB) to 12 (SOL). The median diameters of the first-order dendrites ranged from 6 (SOL) to 8.5 (PB, G) #m. The dendritic projection patterns were rather similar for the different motoneurone groups, except for a prominent dorsomedial projection of SP dendrites. A considerable fraction of the dendrites extended into the white matter. The diameter of the first-order dendrite correlated positively to the number of end branches as well as to the combined length, surface area and volume of the whole dendrite. These relations appeared to be independent of motoneurone group and dendritic orientation. The combined diameter of the first-order dendrites, which reflects the total dendritic size of a motoneurone, exhibited median values between 82 /~m (SOL) and 112 /~m (Q). With respect to the relative scaling of soma and dendrites, motoneurones with large somas tended to have proportionally larger dendritic trees. The distribution of dendritic diameters, number of branches, dendritic surface area and volume, and the combined dendritic parameter (E d 8/2) at various distances from the soma were quite similar for the different motoneurone groups. INTRODUCTION C u r r e n t ideas a b o u t t h e p h y s i o l o g i c a l p r o p e r t i e s o f central nerve ceils to a large extent derive f r o m e x p e r i m e n t s on the a - m o t o n e u r o n e s o f the spinal cord. I n c o n t r a s t to t h e r a t h e r extensive p h y s i o l o gical knowledge, however, a n a t o m i c a l d a t a a b o u t the a - m o t o n e u r o n e s have been m o r e scanty. By using i n t r a c e l l u l a r injections o f h o r s e r a d i s h p e r o x i dase ( H R P ) , it is n o w p o s s i b l e to investigate the detailed m o r p h o l o g y o f p h y s i o l o g i c a l l y defined nerve cellsg, 17,31 a n d this technique has also been used to s t u d y v a r i o u s features o f spinal a - m o t o neurones2,6,10-14,26-28,34-40. Q u a n t i t a t i v e m o r p h o l o g i c a l studies o f w h o l e am o t o n e u r o n e s , in p a r t i c u l a r the d e n d r i t i c trees, are e x t r e m e l y t i m e - c o n s u m i n g w h i c h limits the n u m b e r o f n e u r o n e s t h a t can b e analyzed. H o w e v e r , in a recent investigation o f triceps surae a - m o t o 0006-8993/83/0000-0000/$03.00 © 1983 Elsevier Science Publishers

n e u r o n e s 35 very strong relations were f o u n d to exist between a n u m b e r o f different dendritic p a r a m e t e r s , suggesting t h a t the a n a t o m y o f whole dendrites m a y to a certain extent be inferred f r o m o b s e r v a t i o n s o f only the size a n d n u m b e r o f the first-order dendrites. I n this way, q u a n t i t a t i v e analyses o f whole dendritic trees w o u l d be greatly simplified. T h e m a i n a i m o f t h e present extended study was to see w h e t h e r these o b s e r v e d relations m a y be generally valid for a - m o t o n e u r o n e dendrites. F o r this p u r p o s e , the s a m e d e n d r i t i c p a r a m e t e r s were investigated b o t h in a - m o t o n e u r o n e s b e l o n g i n g to different m o t o r p o o l s , a n d in dendrites having different p r o j e c t i o n s within the spinal cord. A n a d d i t i o n a l a i m o f the study was to see whether differences in the size or a n a t o m y o f the a - m o t o n e u r o n e s can be related to their function or l o c a t i o n within the spinal c o r d ( c o m p a r e refs. 5, 14, 29, 32 a n d 40). Special a t t e n t i o n was also p a i d to the question o f dendritic t a p e r i n g which is o f i m p o r -

tance for the validity of the neurone-equivalent cylinder model16, zl-22. MATERIALS A N D METHODS

The experiments were performed on 19 adult cats (2.5-4.0 kg body wt.). In 14 of the animals, 1-9 a-motoneurones were injected with horseradish peroxidase (HRP) by means of intracellular micropipettes, while the remaining 5 animals were used for retrograde HRP-labelling of different motoneurone pools. The procedures for animal preparation, intracellular recording and injection of HRP, tissue fixation and histochemistry have been described and discussed in detail elsewhere9, 3s. With these procedures the longitudinal tissue shrinkage of the spinal cord amounts to about 10 ~10. No correction has been made for this tissue shrinkage in the quantitative data presented below. Only those intracellularly HRP-labelled a-motoneurones which lacked light microscopic signs of damage were used for the morphological analysis. The cell bodies and proximal dendrites were reconstructed and analyzed in 63 a-motoneurones innervating the quadriceps (Q; n = 9), posterior biceps (PB; n = 9), gastrocnemius (G; n = 25), soleus (SOL; n = 9) and intrinsic short plantar muscles of the foot (SP; n ---- 11). Complete reconstructions and quantitative analysis of the entire dendritic arborizations were performed in 24 dendrites originating from PB (n == 8), G (n -= 8) and SP (n = 8) a-motoneurones. For comparison, 8 dendrites originating from Q (n -- 2), tibialis anterior (TA; n--~ 2) and SOL (n ---- 4) a-motoneurones were also analyzed in extenso. The various somatic and dendritic parameters were defined and measured as described in a previous paper 35, except for the dendritic diameters which were usually measured at shorter intervals in the present study (5-50 /~m, depending on the course and length of the particular dendritic segment). Dendritic taper was estimated by comparing the proximal and distal diameters of each segment and end-branchaS. The 5 animals used for retrograde HRP-labelling of motoneurones were anaesthetized by i.m. injections of Xylazin chloride (2 mg/kg; Rompun) and ketamin chloride (20 mg/kg; Ketalar). One muscle in each hindlimb was exposed under sterile con-

ditions and prepared for the HRP-injection. Care was taken not to interfere with the blood and nerve supplies. The muscles used for the HRP-injections were the Q, PB, G, SOL and SP. H R P (Sigma; type VI) was dissolved in sterile isotonic sodium chloride (50 mg HRP/0.5 ml) and injected at several sites in the belly muscle with a fine needle. Care was taken to avoid extramuscular deposition of HRP. After the injection, the wound was closed and the animal allowed to recover from the anaesthesia. After a survival time of approximately 72 h, the cats were re-anaesthetized and sacrificed by vascular perfusion with glutaraldehyde. The lumbosacral spinal cord was removed, cut in 30 # m thick sagittal sections and processed for HRP TM. In consecutive sections, the major and minor diameters of 100 cell bodies of each labelled motoneurone pool were measured at × 1000 magnification with an eyepiece micrometer. In each section, all labelled cell bodies where the nucleus and the nucleolus could be identified, were used for the measurements. The two soma diameters perpendicular to each other were measured in the plane of the nucleolus. The various somatic and dendritic parameters analyzed were related to each other by means of least-squares regression. Different types of functions were tested (linear, exponential, logarithmic and power functions) to obtain the best y on x fit, and the degree of fitness was judged by the differences in the fraction of explained total variance (r 2) obtained for the various functions. These differences were generally quite small ( 1 - 6 ~ ) and at most 9 ~ . Statistical differences in slope (b) values between different groups were calculated with the Student's t-test and consideration was taken, when needed, to differences in variance between the groups (separate or pooled variance estimate). In addition to these parametric tests, a non-parametric correlation test was used (Spearman rank correlation test; rs). In those cases where the parametric and non-parametric tests yielded different significance levels, both values have been presented in the text, otherwise only that of the parametric test (r). Comparison between two different sets of data was made with the Median test or the Mann-Whitney U-test (U-test). When comparing more than two sets of data the Kruskal-Wallis variance test (K-W) was used.

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Fig, l. Histograms showing the distribution of mean cell body diameters of motoneurones labelled by retrograde transport of HRP. A: Q motoneurones. B • PB motoneurones, C: G motoneurones. D: SOL motoneurones. E: SP motoneurones. Each motoneurone pool is represented by two samples of 100 cell bodies each. The two samples were obtained from different animals. Observations on a number of intracellularly labelled a-motoneurones belonging to the same pools have also been inserted in the histograms. The following symbols for the different types of motoneurones have been used in this and all subsequent figures: • = quadriceps (Q); © = posterior biceps (PB); ® = gastrocnemius (G); A = soleus (SOL); • = short plantar (SP); and • = tibialis anterior (TA) motoneurones (the TA type is not included in the above figure).

RESULTS

Cell bodies of retrogradely labelled motoneurones A total of 1000 retrogradely labelled motoneurones was sampled for the analysis. For each of the 5 motoneurone nuclei studied, 100 motoneurones were collected from each of two animals. The distribution of mean cell body diameters in each pool is shown in Fig. I. The smaller size range, up to 38/~m, is believed to include 7-motoneurones, since in intracellularly labelled 7-motoneurones the maximal mean cell body diameters are about 37-38 /~m3,12,39. With respect to the larger cells (i.e. > 38 ?~m) slight variations seem to exist between the different animals as well as between the different motoneurone pools (see Fig. 1). There was a tendency towards smaller cell bodies among the SOL motoneurones than among the Q, PB and G motoneurones (P < 0.0002). The relation between the major and minor cell body diameters indicated that an increase in the major diameter was to some extent paralleled by an increase in the minor diameter (r = -k 0.69; P < 0.001; n = 1000).

Cell bodies and first-order dendrites of intraeellularly labelled a-motoneurones The 63 a-motoneurones selected for morphological analysis showed no light microscopical signs of damage (see Fig. 2). They were all located within

Fig. 2. Photomicrograph showing the cell body, parts of the proximal dendrites and the proximal part of the axon (arrow) of an intracellularly HRP-labelled SP motoneurone. Section thickness ~ 30 pm; scale = 200 pm.

lamina IX 2¢ and the positions of the Q, PB, G and SOL a-motoneurones agreed with the locations of their respective motor nuclei as defined by Romanes2L The SP a-motoneurones were mainly located in the dorsolateral region of lamina IX ~5 but also in the central parts of lamina IX. Soma size. In the whole sample of a-motoneurones, the median value for the mean soma diameters was 58.5/~m (see Table I), with an average major-to-minor cell body diameter ratio of 1.5. A comparison between the intracellularly stained cells and the retrogradely labelled neurones (see Fig. 1), suggests that the intracellular technique introduces a bias in favour of larger neurones. In Table I various parameters of the cell bodies and first-order dendrites have been compiled. It is seen that the SOL neurones had the smallest cell body diameters, which is consistent with the observations on the retrogradely labelled motoneurones. It is also evident that the intracellularly stained SP motoneurones have an unusually large size in comparison with the retrogradely labelled cells (cf. Fig. 1E) and therefore, probably constitute the least representative sample of the present study. However, the values for these SP a-motoneurones are only slightly larger than those reported by Egger et al. 14. Number of first-order dendrites. In the whole sample of neurones the average number of firstorder dendrites was 11 (see Table I) while the mean number of dendrites occurring at 30 /~m distance from the soma was 13. This indicates that, on the average, 15 ~ of the present first-order dendrites started to branch proximally to this point. When comparing the different a-motoneurone groups, the average number of first-order dendrites ranged from 10 to 12 (see Table I) with a considerable variation within each pool (K-W; P > 0.05). The relation between the number of first-order dendrites and the mean diameter of the parent cell body (Fig. 3A), yielded a low correlation coefficient, regardless of whether the dendrites had been counted at the cell body outline or at 30 # m distance from the soma. This ratio varied more between the pools than within the pools (K-W; P < 0.01), and it was significantly larger for the SOL motoneurones (Table II) than for ithe rPB, G and SP a-motoneurones (U-test; P < 0.05).

TABLE I Quantitative data on the cell bodies and first-order dendrites of a-motoneurones supplying different hindlimb muscles For each parameter the mean (4- S.D.) and median values as well as the ranges of values have been indicated. Mean diameter of cell body (ktm)

Number of 1st-order dendrites*

Diameter of 1st-order dendrites (tim)

Diameter of largest 1st-order dendrite (l~m)

Diameter of smallest 1st-order dendrite (I~m)

Combined diameter of lst-order dendrites (I~m)

Combined dendritic parameter ( ~ d a12) (I~m812)

Q

Mean (4-S.D.) 58.1(4-4.5) Median 58.0 Range(n=9) 51.0-67.0

12.4(4-3.6) 11.0 7-18

8.3(4-3.4) 8.0 2.0-21.0 (n = 127)

15.8(4-3.2) 15.0 11.0-21.0

3.5(±1.7) 3.5 2.0-5.0

117.1(127.3) 112.0 78.5-156.5

357(4-82) 348 236-467

PB

Mean (S.D.) Median Range (n=9)

9.6(4-1.2) 10.0 8-12

9.0(±3.3) 8.5 3.5-18.5 (n = 93)

13.8(±3.9) 14.5 8.0-18.5

5.6(±1.6) 5.0 3.5-9.0

92.6(-4-23.7) 92.0 62.0-121.5

291 (4-103) 274 166-430

G

Mean (S.D.) 60.3(=t=6.3) Median 59.5 Range (n=25) 47.5-75.0

11.2(4-1.9) 11.0 8-15

8.9(4-3.7) 8.5 2.0-23.0 (n = 323)

15.8(4-3.9) 15.0 10.0-23.0

4.3(~1.3) 4.5 2.0-6.5

114.1(4-28.0) 111.5 58.5-162.0

362(4-112) 350 153-554

SOL

Mean(S.D.) Median Range (n=9)

53.4 (:]:2.6) 54.0 49.5-57.0

11.9(4-2.0) 12.0 9-15

6.0(4-2.2) 6.0 1.5-14.5) (n = 125)

10.8(4-2.1) 10.0 9.0-14.5

3.0(±1.0) 3.0 1.5~..5

82.4(4-12.0) 82.0 63.5-101.0

211 (4-39) 198 159-265

SP

Mean (S.D.) 61.5(4-4.7) Median 62.0 Range(n= 1t) 53.0-71.5

11.2(4-2.3) 11.0 6-14

8.0(4-3.1) 7.5 2.5-18.5 (n = 145)

13.6(4-2.6) 14.0 10.0-18.5

3.9(4-1.1) 3.5 2.5-5.5

104.0(4-19.0) 97.0 82.0-136.0

311(4-72) 291 216 4~8

Whole Mean (S.D.) 58.8(4-5.8) sample Median 58.5 Range (n=63) 47.5-75.0

11.3(4-2.3) 11.0 6-18

8.2(4-3.5) 7.5 1.5-23.0 (n = 813)

14.4(4-3.8) 14.0 8.0-23.0

4.1(4-1.4) 4.0 1.5-9.0

105.2(4-26.5) 102.5 58.5-162.0

321(4-104) 323 153-554

57.2(4-6.0) 55.0 49.5-65.0

* The dendrites were counted at the cell body outline.

Diameter o f first-order dendrites. In the whole s a m p l e o f n e u r o n e s the m e d i a n d i a m e t e r o f the first-order dendrites was 7.5 /~m (n = 813; see T a b l e I). T h e m e a n d i a m e t e r o f the first-order dendrites c o r r e l a t e d positively with the m e a n d i a m e t e r o f the cell b o d y (see Fig. 3B). T h e r a t i o between these two p a r a m e t e r s was quite similar for the Q, PB a n d G a - m o t o n e u r o n e s (Table II), while significantly smaller values were o b t a i n e d in the S O L cells (Utest; P < 0.01). T h e SP n e u r o n e s h a d i n t e r m e d i a t e values. T h e c o r r e l a t i o n between the m e a n d i a m e t e r o f the first-order dendrites a n d the m e a n cell b o d y d i a m e t e r was statistically significant in b o t h the PB (linear c o r r e l a t i o n : r = %- 0.89, P < 0.01;

rs = %- 0.87, P < 0.01; n = 9) a n d G groups o f m o t o n e u r o n e s (linear c o r r e l a t i o n s ; r = %- 0.48, P < 0.02; rs = %- 0.49, P < 0.02; n = 25). W h e n p l o t t i n g the d i a m e t e r o f the largest o r smallest d e n d r i t e versus the m e a n cell b o d y diameter, w e a k b u t statistically significant correlations were obt a i n e d (largest d e n d r i t e : r = %- 0.55, P < 0.001; smallest d e n d r i t e : r = %- 0.42, P < 0.001; n = 63). Combined diameter o f first-order dendrites. T h e c o m b i n e d d i a m e t e r o f all first-order dendrites o f a n e u r o n e is an i n d i c a t o r o f the size o f its entire d e n d r i t i c trees 35. I n the p r e s e n t m a t e r i a l the average value for this p a r a m e t e r was 105/~m (see also T a b l e I). T h e r e l a t i o n between the c o m b i n e d d i a m e t e r o f the first-order dendrites a n d the m e a n d i a m e t e r o f

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TABLE II Ratios between various dendritic and somatic parameters in a-motoneurones supplying different hindlimb muscles For each ratio the mean (4- S.D.) and median values as well as the ranges of values have been indicated. Motoneuronegroup

Ma]orcellbody diameter/minor cellbodydiameter

Numberoflstorder dendrites /mean diameter of cell body ( l~m-1/2)

Meandiameterof 1st-orderdendrites /meandiameter of cell body

Combineddiameter of lst-order dendrites/mean diameter of cell body

Combineddendritic trunkparameter (~d3/2)/surface area of cell body ( cm-112)

Q

Mean (±S.D.) 1.20(±0.17) Median 1.13 Range(n--9) 1.00-1.40

0.24(±0.06) 0.23 0.14-0.36

0.15(4-0.02) 0.15 0.12-0.18

2.0(±0.4) 2.0 1.4-2.7

3.4(-4-0.6) 3.3 2.74.6

PB

Mean (±S.D.) 1.42(--0.26) Median 1.46 Range (n=9) 1.10-2.00

0.18(±0.03) 0.19 0.15-0.23

0.16(4-0.02) 0.15 0.13-0.20

1.6(4-0.3) 1.7 1.2-2.0

2.8(-4-0.5) 3.0 2.1-3.4

G

Mean (±S.D.) 1.70(±0.49) Median 1.70 Range (n=25) 1.00-3.24

0.22(4-0.03) 0.21 0.14-0.29

0.15(2_0.03) 0.15 0.11-0.20

1.9(4-0.4) 1.9 1.2-2.4

3.4(±0.9) 3.5 2.1-5.1

SOL

Mean(iS.D.) 1.41(±0.16) Median 1.40 Range (n=9) 1.20-1.70

0.26(4-0.04) 0.26 0.21-0.32

0.11 (4-0.01) 0.11 0.10-0.13

1.5(:k0.2) 1.6 1.2-1.8

2.4(4-0.4) 2.4 2.0-2.9

SP

Mean(4-S.D.) 1.51 (4-0.38) Median 1.56 Range (n= l l) 1.00-2.12

0.21(±0.04) 0.22 0.13-0.25

0.13(±0.02) 0.13 0.10~.17

1.7(4-0.2) 1.6 1.3-2.0

2.7(4-0.4) 2.9 2.1-3.2

Whole Mean(4-S.D.) 1.51(4-0.40) sample Median 1.42 Range(n 63) 1.00-3.24

0.22(4-0.04) 0.22 0.13-0.36

0.14(4-0.03) 0.14 0.10-0.20

1.8(:k0.3) 1.8 1.2-2.7

3.1(:k0.8) 2.9 2.0-5.1

the cell b o d y (Fig. 3C) shows that a n increase in cell b o d y diameter is, on the average, paralleled by a n increase in the size o f the dendritic trees.

rones had significantly smaller values for this ratio t h a n the Q (P < 0.01), G (P < 0.03) a n d SP a - m o t o n e u r o n e s (P < 0.05). F u r t h e r m o r e , the Q n e u r o n e s

The values for the c o m b i n e d diameter o f the firstorder dendrites have been indicated for each of the different m o t o n e u r o n e groups i n T a b l e I. W h e n

h a d larger values t h a n the PB (P < 0.03) a n d SP

relating this p a r a m e t e r to the m e a n cell b o d y dia-

the m e a n diameter o f the cell b o d y was statistically

meter (Table II), the variations in values were f o u n d to be larger between the pools t h a n within each pool ( K - W ; P < 0.01). The largest values were f o u n d in the Q a n d G pools, a n d the smallest values in the SOL group. The U-test showed that the SOL neu-

significant in all pools (linear correlation coefficient: r = + 0 . 6 7 to + 0 . 9 5 ; 0.05 /> P >/ 0 . 0 0 1 ) a l t h o u g h in the SOL pool a significant correlation was obtained only with the n o n - p a r a m e t r i c test (rs = + 0.68, P < 0.05; n = 9).

Fig. 3. A: graph illustrating the relation between the number of first-order dendrites and the mean cell body diameter. The correlation coefficient r = + 0.26 (P < 0.05, n = 63). B: graph showing the relation between the mean diameter of the first-order dendrites and the mean cell body diameter. The values were best fitted by a power function, r = + 0.58 (P < 0.001, n = 63). C: graph showing the relation between the combined diameter of the first-order dendrites and the mean cell body diameter. This relation was significant for each of the different motoneurone groups (see text). The

strongest correlation coefficient for the whole sample r = + 0.74 was obtained with a power fit (P < 0.001, n = 63), the slope of which was 1.91 (:t: 0.45, 95700 Conf.). D: graph illustrating the relation between the combined dendritic parameter (at 30/zm distance from the soma) and the cell body surface area. The values were best fitted by a power function, r -- 4- 0.71 (P < 0.001, n = 63), the slope value of which was 1.21 (:t_ 0.30; 95 ~ Conf.). In A-D the symbols are the same as in Fig. 1.

n e u r o n e s (P < 0.05). The correlation between the c o m b i n e d diameter of the first-order dendrites a n d

Combined dendritic parameter (Zda/Z). The relation between the combined dendritic trunk parameter (Y~ d3/2, i.e. the sum of the dendritic diameters, each raised to the 3/2 power), and the surface area of the cell body (SA) is a factor of importance for the dendrite-to-soma conductance ratio. The median value for Z d a/2, measured at 30 # m distance from the soma, was found to be 323 # m (Table I). In Fig. 3D, ~3 d3/2 has been plotted against the values for cell body surface area. The latter parameter was crudely approximated as × major × minor cell body diameters. When comparing the different motonerurone groups with respect to the relation between the combined dendritic trunc parameter and the cell body surface area (Table II and Fig. 3D), the results were quite analogous to those obtained above for the relation between the combined dendritic diameter and the soma diameter. Comparison between large and small a-motoneurones. When comparing the large (mean soma diameter >58.5 #m, n ---- 32) and small (<58.5/~m, n = 31) a-motoneurones with respect to the relative anatomical scaling of soma and dendrites, the former cells were found to have proportionally larger values for the combined diameter of the firstorder dendrites (P < 0.02; n ---- 63). However, this tendency was not strong enough to become evident when the analysis was restricted to the individual motoneurone pools. Dendritic trees of intracellularly labelled a-motoneurones General observations The dendrites extended in all directions, but did not cross to the opposite side of the spinal cord. The dendrites with posterior, lateral or ventral projections had a substantial fraction o f their distal branches extending into the lateral or ventral funiculi. Between 33 ~,,, and 100 K (mean: 75 -4- 20~o S.D.; n ~ 25) of the end-branches of these dendrites terminated in the white matter, and there were no morphological characteristics distinguishing them from those branches terminating within the grey matter. The dendrites projecting medially or dorsomedially had only a few of the end-branches terminating in the white matter (mean: 7.3 zk 5 . 3 ~

S.D., range: 0--13~, n = 7). The course of the dendrites within the white matter varied considerably, some dendrites terminating shortly after entering the funiculi and others approaching the surface of the spinal cord. In the latter cases the dendrites sometimes ran parallel to the surface for some distance, after which they returned back to more central regions of the funiculi. It was also observed, especially among the SP neurones, that dendrites after having entered the white matter returned to terminate in the grey matter (see Fig. 4). Another pattern characteristic for the SP neurones was a prominent dorsomedial dendritic projection with rather closely arranged parallel dendrites extending into lamina VI and sometimes even into lamina V. The previously reported sparse occurrence of dendritic spines in adult spinal a-motoneurones 35was confirmed here, and no obvious difference in spine frequency was observed between the different motoneurone pools. The spines were usually solitary, but on a few occasions two or more spines were observed within a short distance ( < 5 0 #m). In all dendrites but two, 'beaded' branches or segments

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were observed (cf. Fig. 5 Ulfhake and Kellerth35). The frequency of beaded end-branches ranged between 0 and 100 ~o in a single dendrite (mean: 62 -I- 28 ~o S.D. ; n = 32), and there was no obvious

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10 TABLE III Quantitative data on completely reconstructed dendrites of a-motoneurones supplying different hindlimb muscles For each parameter the mean ( i S.D.) and median values as well as the ranges of values have been indicated. Diameter Number of oflstterminal order branches dendrites per ( #m) dendrite

Combined lengthof whole dendrite ( t~m)

Dendritic length from somato termination ofend-branches (#m)

Dendritic length from soma to termination of most distal end-branch (#m)

Total surface areaper dendrite (l~m 2)

Total volume per dendrite (Izm 3)

PB

Mean (±S.D.) Median Range (n=8)

7.6 (3.1) 7.0 3.3-12.5

11.9 (7.4) 9.5 5-28

6150 (3782) 4603 325014,490

934 (267) 910 367-1731 (n~95)

1410 (197) 1347 1159-1731

36,000 24,970 (20,440) (15,890) 29,010 21,710 13,360-71,100 4813-54,230

G

Mean (zES.D.) Median Range (n=8)

9.2 (4.6) 9.3 2.5-16.7

12.0 (8.3) 9.0 5-31

5136 (2957) 5134 178011,110

873 (242) 866 314-1614(n=96)

1179 (181) 1159 856-1614

39,250 (21,300) 40,100 8598-76,100

33,180 (18,940) 32,470 3762-62,270

SP

Mean (~S.D.) Median Range (n=8)

7.7 (3.7) 6.3 3.8-12.7

9.6 (6.5) 8.5 3-17

837 4560 (266) (2940) 807 3689 1355-8836341-1542(n=75)

1255 (225) 1234 946-1542

32,990 (21,030) 25,430 9868-59,630

25,250 (17,460) 18,080 687248,370

SOL

Mean (:~S.D.) Median Range (n=4)

4.9 (1.0) 4.7 3.9-6.3

8.5 (3.3) 9.0 4-12

3212 (981) 3153 2081-4460

729 (205) 716 306-1173 (n=32)

994 18,230 9959 (196) (5801) (3832) 1044 17,620 9543 7 1 4 - 1 1 7 3 12,370-25,320 6493-14,260

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1123 1134

12,554 19,954

7724 13,975

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59,403 69,560

52,400 68,646

7.9 (3.8) 6.5 2.5-16.7

10.6 (6.5) 9.0 3-31

4993 (2988) 4473 135514,430

887 (264) 881 306-1731(n=335)

34,390 (20,570) 27,950 8598-76,100

26,560 (18,750) 21,710 3762-68,650

Whole Mean sample (dzS.D.) Median Range(n=32)

1246 (226) 1209 714-1731

* Each of the two Q and TA dendrites have been listed seperately, except for the observations on dendritic length ** where the observations from the dendrites I and II have been pooled.

C o m b i n e d dendritic length. T h e c o m b i n e d length of a dendrite reflects b o t h the n u m b e r a n d lengths of the branches. T h e average value for the entire sample was close to 5 m m , a n d in Table III the values for c o m b i n e d dendritic length are shown for the different a - m o t o n e u r o n e groups. There was n o clear v a r i a t i o n between the different regions of the

spinal cord cross-sectional area. It has previously been d e m o n s t r a t e d in triceps surae a - m o t o n e u r o nes z5 a n d sciatic y - m o t o n e u r o n e s36, that the comb i n e d dendritic length correlates strongly with the diameter o f the first-order dendrite. This relation (see Fig. 7A) was highly significant also for each of the n e u r o n e pools of the present study (PB: r = -f-

II

0.94, n = i 8 ;'(3: r = + 0.94, n = 8; SP: r = + 1.0, n : 8). In order to evaluate the corresponding data from the Q, T A and SOL dendrites, the 9 5 ~ confidence interval for single observations was calculated for the linear regression of the PB, G and SP data points. It was then found that each observation from the Q, TA and SOL dendrites was located within this confidence interval. Dendritic branching pattern. No unbranched dendrites were observed. The number of dendritic endbranches was found to relate to the diameter of the first-order dendrite (Fig. 7B). The number of dendritic sub-branches increased distally to reach a maximum value at 600-800 # m distance from the cell body (Fig. 8A). The average number of endbranches per dendrite was about 11 (see Table II1). When the dendritic diameters were measured at various distances from the cell body, the average values as well as the ranges of values were found to decrease rapidly over the initial 3 0 0 4 0 0 #m distance, after which a stabilization occurred (see Fig. 8B). From Fig. 8A it is also evident that the general distribution of dendritic branches at various distances from the cell body was rather similar for the PB, G and SP neurones. The number of dendritic endbranches correlated significantly with the diameter of the first-order dendrite in each of the PB (r = + 0.96; n = 8), G (r = + 0.92; n : 8) and SP (r = + 0.97; n = 8) groups, and there was no significant difference between the groups (P > 0.10) with respect to the slope (linear fit). When calculating the 95 ~ confidence interval (for single observations) for the linear regression of the pooled observations on the PB, G and PL dendrites, each observation from the Q, TA and SOL dendrites was found to be located within this interval. Fig. 8B shows that also the distribution of dendritic diameters at various distances from the cell body was similar for the PB, G and SP dendrites. The corresponding observations on the Q, TA and SOL dendrites revealed the same pattern o f distribution. Dendritic surface area and volume. The values for dendritic surface area and volume were calculated from the length and mean diameter of each dendritic segment and end-branch according to the formula for a smooth cylinder, and these values have been indicated in Table III. The close relations between

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13 dendritic surface area and volume, on the one hand, and the diameter of the first-order dendrite on the other, which have previously been demonstrated among triceps surae a-motoneuronesZ5 and sciatic ymotoneurones 36, were found to exist also in all the presently studied motoneurone pools (see Fig. 9A and B). The relation between the dendritic surface area and the diameter of the first-order dendrite was highly significant for each of the PB (r = + 0.98; n=8),G(r=+0.99;n=8)andSP(r=+l.00; n --~ 8) pools. The slope values (linear fit) were significantly larger for the PB and SP dendrites than for the G dendrites (P < 0.01, one-tailed probability), while no difference was found between the former two groups (P > 0.10, one-tailed probability). When calculating the 95 ~ confidence interval (for single observations) for the pooled data points of the PB, G and SP dendrites, each of the observations from the Q, TA and SOL dendrites was found to be located within this interval. Also the dendritic volume was strongly related to the diameter of the first-order dendrite in each of the PB (r ---- + 0.98; n=8),G(r= +0.99;n=8) andSP(r=+0.99; n ---- 8) groups. The slope values did not differ significantly between the 3 groups (P > 0.10, one-tailed probability). However, the two TA dendrites had larger volumes than was predicted with 95 ~ confidence (as calculated for single observations). The distribution of dendritic surface area and volume at various distances from the cell body (Fig. 10A and B, respectively) was quite similar for the PB, G and SP groups of cells, and this was also the case when the observations from the Q, TA and SOL dendrites were included. The maximum value for dendritic surface area occurred at approximately 500 /zm distance from the cell body, while the corresponding peak value for dendritic volume was close to the soma.

Comparison between dendrites with different projections. Due to the limited size of the material, it was not possible to make statistical comparisons between dendrites with different projections, while simultaneously taking into consideration the type of neurone from which each dendrite originated. In order to get some quantitative information, however, all the dendrites of the present study were pooled and arranged in groups according to the main dendritic direction (i.e. anterior, n = 6;

lateral, n = 12; posterior, n ---- 8; and medial, n = 5). Doing so, no major quantitative differences were found between dendrites extending into these different regions. Like in the whole sample of dendrites, each of these different groups exhibited strong relations between the diameter of the firstorder dendrite, on the one hand, and the number of end-branches, combined dendritic length, and combined dendritic surface area and volume on the other. However, with regard to the relations between the average dendritic length and the length of the most remotely terminating end-branch, on the one hand, and the diameter of the first-order dendrite on the other, close correlations were obtained for the dendrites having a posterior projection (r ---- +0.79 and r ---- +0.92, respectively, n ~- 8), but not for those having anterior or lateral projections (r < + 0.57; n -- 6 and 12, respectively). With respect to the dendrites having a medial projection, a close relation was obtained between the length of the most remotely terminating end-branch and the diameter of the first-order dendrite (r --~ + 0.92, n = 5). Dendritic taper. In theoretical neurone models (for reviews see refs. 16, 21-22), the dendritic trees have often been reduced to equivalent cylinders. However, such models must take into account to what extent a reduction in dendritic diameters occurs between or across branching points or in the end-branches. One assumption frequently made is that the dendrites branch according to the so-called 3/2 power rule, where Z dZ/z (the summed diameter of the dendritic daughter branches, each raised to the 3/2 power) equals D3/z (the diameter of the parent branch raised to the 3/2 power). In order to test the validity of this assumption, the ratio Z d3/2/D ~/2 was calculated for 253 dendritic bifurcations, located both within 500 #m distance from the soma and distally to this point. The average ratio value for the whole sample was found to be 1.01. In Table IV the ratio values for the proximal and distal bifurcations have been listed separately for the different groups of motoneurones. The ratios for the proximally located branching points were similar for the different motoneurone groups, while the values for the distal bifurcations showed a larger variation. However, a significant difference between the proximal and distal bifurcations was found only in

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the SP group, where a rather low average ratio value was found for the distal branching points. The dendritic tapering was analyzed separately for the intersegments and the end-branches (see Methods). On the average, little or no tapering took place in the intersegments, although rather large variations occurred within each group as indicated by the values for standard deviation in Table IV. The tapering of the dendritic end-branches varied between 1/6 and 4/7 for the different groups of motoneurones. In order to illustrate the combined effects of dendritic tapering and end-branch termination in a comprehensive way, the combined dendritic parameter ratio Z d3/2/D3/~ was calculated for each dendrite at various distances from the cell body (D1 is the diameter of a first-order dendrite, and d is the diameter of each of its sub-branches occurring at a certain distance from the soma). In Fig. 10C the average values and ranges of values have been indicated for the PB, G and SP dendrites. In all 3 groups of dendrites only a slight decrease in average value took place over the initial 500/~m distance from the soma, while approximately 50 % reduction of the ratio value had occurred at about 800-900/zm distance from the cell body. This latter reduction has previously been attributed mainly to end-branch tapering and end-branch termination35, which is also consistent with the present findings (cf. Table IV and Fig. 8A). The corresponding observations on the Q, TA and SOL dendrites revealed similar patterns of tapering.

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DISCUSSION

Cell bodies and.first-order dendrites Although no systematic study was performed on the distribution and location of the retrogradely labelled motoneurones within the spinal cord, there was a general agreement between the present data and the motor pool data of Romanes 25 and Burke et al. 5. The range of soma diameters of the present triceps surae motoneurones was somewhat narrower than that reported by Burke et al. 5, but this might be explained by the smaller sample of cells analyzed in the present study. However, other factors such as tissue shrinkage or swelling and the plane of sec-

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16 TABLE IV Data showing the dendritic diameter ratio Eda/2/Da/2 across branchingpoints and the degree of dendritic tapering

The mean values ( ± S.D.) have been indicated. The proximal and distal parts of the dendrites were compared statistically (U-test), and the levels of significance of the observed differences are also shown. Zd3/2

~,da/2

3~d3/2

D 3/2 (Entiredendritictree)

D a/2 (Proximal5OOl~mof dendritic tree)

D 3/z (Distalpartofdendr±tic tree)

PB

1.02 ( ±0.28 S.D.) n =73

1.04 (n.s.) (:k 0.24 S.D.) n=40

G

0.99 (:+0.35 S.D.) n = 58

1.05 (n.s.) (±0.37 S.D.) n = 30

SP

0.98 (:--0.31 S.D.) n=59

Q

Taper of dendritic intersegments (%)

Taper of dendritic end-branches (%)

0.99 (±0.32 S.D.) n=33

0 (4-28 S.D.) n=84

26 (±32 S.D.) n=85

0.93 (+0.33 (S.D.) n = 28

0 (4-17 S.D.) n = 75

20 (-4-24 S.D.) n = 73

1.03 (P < 0.03) 0.88 ( i 0 . 2 6 S.D.) (I0.30 S.D.) n=4 n = 19

5 (4-22 S.D.) n=69

38 (±30 S.D.) n=62

0.94 (:4-0.58 S.D.) n~8

--

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0 (4-19 S.D.) n=8

41 ( i 2 6 S.D.) n=8

TA

1.00 (:L 0.37 S.D.) n=24

1.02 (n.s.) (:k0.37 S.D.) n=8

0.99 (±0.38 S.D.) n=16

3 ( + 16 S.D.) n=22

35 (4-14 S.D.) n=20

SOL

1.14 (-k0.34 S.D.) n=30

1.06 (n.s.) (:k0.21 S.D.) n=20

1.29 (4-0.48 S.D.) n = 10

0 (:4-20 S.D.) n~28

17 (±21 S.D.) n=28

1.04 (P < 0.03) 0.98 (±0.28 S.D.) (:k0.36 S.D.) n = 139 n = 106

1 (±22S.D.) n=286

27 (±28S.D.) n--276

Whole sample 1.01 ofneurones (_-k0.32 S.D.) n=253

t i o n i n g s h o u l d also be considered. So far, there are only few o b s e r v a t i o n s on the v a r i a t i o n s in s o m a shape a n d size in different section planes. Egger et al. 14 f o u n d no such v a r i a t i o n a m o n g intracellularly labelled SP a - m o t o n e u r o n e s , while R o s e 27 r e p o r t e d t h a t the largest s o m a d i a m e t e r o f cervical a - m o t o n e u r o n e s was l o c a t e d in the l o n g i t u d i n a l plane. The values for s o m a d i a m e t e r s o f the intracellularly labelled neurones generally fell within the ranges o f values o b s e r v e d for the c o r r e s p o n d i n g p o o l s o f r e t r o g r a d e l y labelled cells, a l t h o u g h the values were clearly shifted t o w a r d s the u p p e r end o f the size s p e c t r u m (see Fig. 1). This shift is p r o b a b l y due to a preferential selection o f large n e u r o n e s with the i n t r a c e l l u l a r m i c r o e l e c t r o d e technique. T h e r e was n o evidence suggesting t h a t the m o r p h o l o g y o f the intracellularly labelled cells h a d been seriously

altered due to m e c h a n i c a l t r a u m a o r o s m o t i c HRP-effects, since a n u m b e r o f the n e u r o n e s were checked also in the electron m i c r o s c o p e a n d in all cases were f o u n d to have a well preserved ultrastructure (P.-A. LagerMick, p e r s o n a l c o m m u n i cation). F o r the whole s a m p l e o f neurones, b o t h the n u m b e r o f first-order dendrites a n d the range o f d e n d r i t i c d i a m e t e r s were in g o o d a g r e e m e n t with earlier o b s e r v a t i o n s on intracellularly labelled cat a - m o t o n e u r o n e s 1,2,7-s,14,1s-2°,35,37,4°. W i t h respect to the relation between v a r i o u s d e n d r i t i c p a r a m e t e r s a n d the size o f the cell b o d y , the m a i n finding was the c o m p a r a t i v e l y large n u m b e r o f first-order dendrites in the S O L cells. T h e S O L dendrites were also t h i n n e r t h a n those f o u n d in the o t h e r a - m o t o n e u r o n e p o o l s (see also ref. 40). It m a y be n o t e d t h a t in these respects the type S m o t o n e u r o n e s o f the

17 SOL muscle differ from the type S motoneurones of the gastrocnemius muscle 40. Also, the PB a-motoneurones were found to differ from the Q, G and SP cells in that they possessed fewer first-order dendrites, although the dendritic diameters were of similar magnitude. Dendritic trees No major difference in dendritic projection patterns was observed between flexor and extensor motoneurones, nor between neurones supplying muscles of the thigh and calf. However, the prominent dorsomedial dendritic projection of the SP motoneurones (see also ref. 14) was not observed among the other groups of neurones. In general, the distribution of a single dendritic treee was limited to approximately a quarter of the ventral horn crosssectional area. This may possibly have a functional correlate in that dendrites extending into different regions may receive synaptic inputs from different sets of afferent sources, and in this way specialize in receiving and processing certain incoming data28, 30. The present values for dendritic lengths would yield total dendritic spans of the hindlimb a-motoneurones ranging between 2 and 3 mm, which agrees with earlier observations on cat spinal motoneurones 2,a5. Our values for the SP dendrites are larger than those reported by Egger et al. 14, but depending on different measuring techniques the values are not directly comparable. This range is also rather similar to that found among cervical a-motoneurones although~6, 27, in comparison, the hindlimb a-motoneurones appear to have more branches terminating at a shorter distance from the cell body. The dendritic 'receptive fields' were of rather similar size for the different a-motoneurone groups, although the PB dendrites tended to be slightly more extensive. Assuming that the length of a dendrite is in some way related to the size or remoteness of its 'receptive field '3a, however, one would rather have expected that the SP neurones, which are located in more caudal (S 1/$2) segments, would exhibit shorter dendrites depending on the smaller dimensions of this spinal cord region 33. Thus, alternative or additional factors may determine the dendritic lengths of the motoneurones which is also consistent with the observation that 'recurrent' dendritic branches were

more frequent among the SP motoneurones (see Fig. 4). The rather wide range of geometrical lengths (0.3-1.7 mm) of the present dendrites does not necessarily imply correspondingly large variations in their 'functional' (electronic) lengths. Thus, the space constant (2) of a dendritic branch is directly proportional to the square-root of its diameter, and in the present study, the dendritic branches terminating close to the soma generally had smaller diameters than those terminating further distally. In spite of large variations in the diameters of the firstorder dendrites, there were only rather small variations in the average dendritic lengths. Since the diameter of the first-order dendrite was rather closely related to the number of dendritic branches (see also ref. 35) it is obvious, therefore, that a thick first-order dendrite does not give rise to correspondingly longer branches, but rather to a more complicated system of sub-branches. This arrangement was consistent in all groups of neurones studied. The entire dendritic surface area and volume were closely related to the diameter of the first-order dendrite. These relations were independent of the direction of the dendrites and they were also basically the same in the different a-motoneurone pools studied. This finding, therefore, confirms previous observations from sciatic 7-motoneurones 36 and triceps surae a-motoneurones 35 and extends the validity of these relationships to other motoneurone pools. Furthermore, the distributions of dendritic surface area and volume at various distances from the soma were very similar for all the different groups of neurones studied. From the present data on the average number and diameters of the first-order dendrites, a 'standard' motoneurone may be computed, which will then have a total dendritic surface area in excess of 300,000 # m 2. This value is considerably larger than those reported from lumbar a-motoneurones after intracellular labelling with procion yellow 1 or [SH]leucine19-2°. If this difference is due to H R P giving a better visualization of the dendritic trees, a possible consequence would be that previous estimates of the specific membrane resistivity have been too small. Rally0, 21 concluded that a neurone can be mathematically reduced to an equivalent ~membrane

18 cylinder, if the dendrites branch according to the socalled 3/2 power rule and if no significant tapering occurs between the branching points. In the present study, the 'average' branching point o f the whole sample was f o u n d to obey the 3/2 power rule, and this was also true when analyzing each o f the m o t o neurone groups separately. This agrees with earlier findings1,2,19-20, 34-36, but it should also be emphasized that considerable variations occurred in the present material (see values for standard deviation in Table IV). The average dendritic tapering was close to 0 ~ in the intersegments and approximately 3 0 ~ in the terminal branches, b o t h in the whole sample o f cells and in each o f the different a - m o t o n e u r o n e groups. This finding is in g o o d agreement with earlier observations2,3L The c o m b i n e d effect o f dendritic tapering and end-branch termination yielded only a slight decrease in the combined dendritic parameter over the initial 5 0 0 / z m dendritic distance f r o m the soma, while a b o u t 50 ~ reduction was obtained at 800-900 # m distance. This result was quite similar for the different a - m o t o n e u r o n e groups (see Fig. 10C), and it also conforms with previous observations on triceps surae dendritesZL In the latter study a b o u t 2/3 o f this distal reduction was attributed to the tapering and termination o f end branches.

I n conclusion, the diameter o f the first-order dendrite has been f o u n d to be closely related to various size parameters o f the whole dendritic tree, in particular the combined dendritic surface area and volume. These relations were similar in all the different a - m o t o n e u r o n e pools studied and they were also independent o f the orientation o f the dendrites. Furthermore, the distributions o f these dendritic parameters at various distances from the cell b o d y were quite similar for the different am o t o n e u r o n e groups. Thus, a m o n g the hindlimb a and y - m o t o n e u r o n e s o f the cat (see also refs. 35 and 36), there appear to exist certain general rules for dendritic structure, which are closely related to the diameters o f the stem dendrites. Whether the same rules apply also to other types o f central neurones remains to be investigated.

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