Brain Research, 87 (1975) 41-53
41
() Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
THE M O R P H O M E T R Y OF THE B R A N C H I N G P A T T E R N IN D E N D R I T E S
OF THE VISUAL CORTEX P Y R A M I D A L CELLS
G. J. SMIT AND H. B. M. UYLINGS
Central lnstitute Jbr Brain Research, Amsterdam 1006 (The Netherlands) (Accepted November 21st, 1974)
SUMMARY
An analysis has been made of the three-dimensional branching structure for the basal and apical dendrites of cortical neurons in an adult rabbit. The real branching angles of basal dendrites and apical oblique branches are in the same range, but differ from those of the apical main shaft. Therefore, several different parts of the apical dendrite have to be distinguished on anatomical grounds, coincident with the presynaptic areas distinguished in the literature. The bifurcations of basal dendrites are essentially symmetrical. The mode of outgrowth, however, is non-symmetrical. Redirection of dendrites will, therefore, occur. This redirection is often not complete, so that a large variability of branching angles results. The possible significance of the observed symmetry is discussed.
1NTRODUCTION
The branching structure of dendrites has influence upon, and is under the infl uence of, a number of functional processes in neurons, e.g., electrochemical transmission and spatiotemporal integration of signals 9,1°,1"°. Morphometric analysis of dendritic branching patterns is therefore necessary. Based on data from both morphometric and physiological analysis, functional models can be developed in order to obtain insight into the above-mentioned complex interrelationship of mutual influence. Some metrical aspects of the branching pattern in basal and apical dendrites of visual cortical cells will be described in this paper. In contrast to previous anatomical analyses of dendrites1,7,11, the present data are based upon three-dimensional measurements and are differentiated in more aspects.
42 MATERIAL AND METHODS
(A) General The basal and apical dendrites of 30 pyramidal cells in the striate area of both hemispheres of a single adult rabbit were analyzed in Golgi-Cox stained sections, 80 #m thick (see ref. 14 for further technical data). These cells are representative of the pyramidal cells in cortical layers II, III and IV ~s.
(B) Measured quantities Within a rectangular three-coordinate system the following parameters were determined from the dendrites: (1) the x-, y- and z-coordinates of all the initial points, bifurcation points, end points and points where the dendrites had been cut; (2) the type of the segments, i.e. end segment or intermediate segment; and (3) the order of the segments. (1) The x- and y-coordinates were measured using 2 #m clocks mounted oll the stage of the microscope (Zeiss, type G.F.L.). It has been established from a 16-fold repetition, using an object micrometer, that the range of these measurements is about 5 #m, at room temperature ranging between 13 °C and 24 °C. The z-coordinate was determined using the fine adjustment of this microscope. The fine adjustment was operated by cog-wheels, and it too showed a variation of about 5/~m. (2) End segments run into an end point, whereas intermediate segments are closed by a bifurcation. (3) All proximal segments of the basal dendrites are called first order segments, and the order is raised by one beyond each bifurcation. This centrifugal ordering system is not strictly applicable to apical dendrites, however, since they do not have a symmetrical bifurcation structure is. Therefore, each apical dendrite was ordered in two parts (see ref. 21): (1) the main shaft, ordered starting at the perikaryon; (2) the oblique branches, ordered separately starting at the segment arising from the main shaft (Fig. 1).
( C) Calculated quantities The spatial structure of the dendritic bifurcations per order has been analyzed on the basis of the rectilinear reconstructions. The 4 measured points involved in a bifurcation are considered as vertices of a tetrahedron, with the bifurcation point (point A in Fig. 2) as the apex of the bifurcation pyramid. At each bifurcation point, two daughter segments arise from a mother segment. The bifurcation angle between the two daughter segments is called the intermediate angle (angle CAB in Fig. 2). It is distinguished from the two bifurcation angles between a daughter and the mother segment, called side angles (e.g. angle DAB in Fig. 2). For the dendritic bifurcations, the following uncorrelated quantities have been calculated by means of EL X8 and IBM 1130 computers: (a) the intermediate angle, and (b) the absolute value of the difference between the pair of the side angles. (a) There is a difference in the average length between intermediate and end segments (see ref. 14). Therefore, it would be preferable to subdivide the bifurcations,
43 opfc
dendr
'}
""4
'.3! . . . .
, 4 ~.
.... -:I'
2'
.--2 ---I
I
321" 1
s
50/~
,
~XOn
Fig. I. The projection in the x, y plane of a pyramidal neuron having 5 basal dendrites (A-EL a cut apical dendrite, and a partly stained axon. For the basal dendrites, the letters s and e refer to cutting points and end points respectively, whereas the numbers at the branchings refer to the order of the mother segment. For the apical dendrite, the numbers at the segments refer to the order of the segments.
acco r d i n g to the type o f the segments, into the 3 possible subgroups is. The n u m b e r s o f observations for each o r d e r f r o m these subgroups, however, then b e c o m e too small for the most part to allow a meaningful analysis, so this subdivision has been omitted.
44
A
D
B
Fig. 2. A schematic bifurcation. DA is the mother segment, and AB and AC are the daughter segments. Angle CAB is the intermediate angle and angles DAC and DAB are the side angles.
(b) The absolute values of the differences between the pairs of side angles have been used to examine if the bifurcations are essentially symmetrical, i.e. if on the average the side angles of a bifurcation are equal and, therefore, the differences between pairs of side angles give a symmetric distribution about a zero mean. Only the absolute values could be used, since no criteria were available to distinguish between the two side angles. A side angle equivalence test has been designed to determine if the distribution of the absolute values of the differences is compatible with a symmetric distribution about a zero mean 15. This test consists in comparing two variance estimations: (t) an estimation, not dependent on the symmetry of the bifurcations, by means of the summation law for variances: v a r ( a - - b ) - - v a r ( a ) T v a r ( b ) - 2 cov(a,b). Since the two side angles could not be distinguished we have taken var(a) -: var(b) and calculated cov(a,b) by means of the intraclass coefficient of correlation, and (2) an estimation of v a r ( a - - b ) dependent on the assumption that the differences between pairs of side angles are symmetrical about a zero mean. In case of symmetry vat(a---b) is equal to the second moment about zero of the differences.
(D) Accuracy of angle measurements In the calculations of the bifurcation angles 3 types of errors play a part: (1) the reading error, (2) the instrumental error of the fine adjustment of the ~m clocks and of the microscope, and (3) the error caused by the assumption that dendritic segments are straight. (1) and (2) The standard deviation of the reading and the instrumental error can be roughly estimated, i.e. 5 # m divided by 4 times the standard deviation of 1.25/~m for each coordinate 19. (3) Colonnier 4 and Smit et al. 15 have found that the dendritic segments generally follow a straight course. They do show a slight degree of waviness (Fig. I) however, and in a number of cases deviate strongly from a rectilinear course. The question is whether this factor significantly influences the angle calculations. To examine this, 2 sets of coordinate measurements were made at 14 bifurcations of basal dendrites in an additional pyramidal cell (the cell in Fig. 1). Besides the already described coordi-
45
(b)
(a)
B
D
D
Fig. 3. Two possible c o n f i g u r a t i o n s o f deviation f r o m a rectilinear course o f a bifurcation.
nate measurements at each bifurcation, end or cut point (to be designated as 'far'), the coordinates were also measured of a point along each of the three segments composing the bifurcation at a distance of 3-10/~m from a bifurcation (to be designated as 'near'). When the dendritic segments show negligible deviations from a rectilinear course (Fig. 3a), the angle estimations based on 'far' measurements are preferable since (a) the influence o f the measuring error is relatively smaller, (b) the influence of the waviness upon the angle estimations is smaller, and (c) the 'far' measurements demand fewer measurements for a complete description of the dendrite. When segments deviate considerably from a rectilinear course however (Fig. 3b), the angle estimations based upon 'near 'measurements are then the less sensitive of the two to the various errors, and are therefore to be preferred in this case. RESULTS
(A) Accuracy of angle measurements Based on the approximation that the standard deviation of the measuring
TABLE I M E A S U R I N G E R R O R I N F L U E N C E O N A N G L E S O F BASA L D E N D R I T E S
Order
No.
Mean (~)
S.D. ( )
Corrected S.D. ( )
75 65 57 --
32 37 36
28 35 35
122 124 ll9 125
36 41 46 44
33 38 43 43
( A) Intermediate angles (in degrees) l 2 3 4
82 72 25 7
(B) Side attgles (in degrees) 1 2 3 4
164 144 50 14
46 T A B L E ll C O M P A R I S O N ' F A R ' - - ' N E A R ~ M E A S U R E M E N T S OF A N G L E S O F C E L L IN FIG. I
Bifurcation
Intermediate angle ( )
Side ang~ (':)
Side ang~ (":
Far
Near
Far
Near
F~lr
Near
AI A2 A3
36 50 51
79 90 122
166 141 162
132 92 107
149 170 136
125 170 65
Bl B2
99 66
49 69
97 160
152 118
164 133
156 78
CI C2a C2b
82 97 49
123 120 34
159 156 144
119 118 167
Ill 102 107
lli 121 [37
DI D2 D3 D4
37 75 40 17
46 57 42 31
136 97 162 162
155 112 167 179
117 170 153 175
121 I43 126 149
E1 E2
113 46
98 29
97 108
95 69
119 148
157 98
61 28 14
70 35 14
139 26 28
126 31 28
Mean S.D. No.
error is 1.25 # m for each coordinate, the standard deviation of the bifurcation angles has been corrected. Table I shows that the influence of the measuring error on the standard deviation is small (-4 l0 To) with regard to the considerable natural standard deviation of the intermediate and side angles. It appears from Table II that the two estimations of the individual angles based on the 'far' and the 'near' measurements sometimes differ considerably. This is in agreement with the low Spearman correlation coefficients, namely, 0.58 for the 14 intermediate angles and 0.42 for the 28 side angles. It means that the individual estimations of the angles are not reliable. However, the two correlograms of, respectively, the intermediate angles and the side angles, show symmetrical distributions round the line of identical values (Fig. 4). No significant differences are present between the means of the 'far' and 'near' measurements (see Table II). In addition, the standard deviations are greater for the 'near' than for the 'far' measurements. Therefore, we conclude that the means and the standard deviations of the bifurcation angles of the 'far' measurements give a reliable description of the frequency distributions of the dendritic angles (see Material and Methods).
(B) Intermediate angles Beside the results of all bifurcations, the results of the so-called plane bifurcations (i.e. bifurcations which deviate only slightly from a plane, see ref. 20) are also given separately.
47 180 ~
4~
NEAR
Fig. 4. The two correlograms of the intermediate angles (filled circle) and the side angles (open circle) respectively, which illustrate the correlation between the 'near' and 'far' measurements.
4' 4 order1
--
a
---
b
i
2o !
o
60
120
1~) °
120
180 °
120
180 °
o/o
40" crdcr 2
20-
o 6C
order 3
2o!
60
Fig. 5. The frequency distributions of the intermediate angles of basal dendrites, a: all bifurcations. b: plane bifurcations.
48 T A B L E Ill INTERMEDIATE ANGLES
Order
All b(furcatioHs Mean (')
Plane bifurcations S.D. of mean ( )
No.
Mean ( )
S.D. O/'.u'aJt ! )
No.
O f basal dendrites 1 2 3
75 65 57
3 4 7
82 72 25
7(~ 65 67
4 5 9
55 52 16
9 8 7 1~.~
22 18 18 10
106 113 102 87
II 13 l0 9
[3 9 12 5
7 15
20 8
71 --
9
13 4
O f apical main shaft branching 1 2 3 4
97 97 100 71
Of oblique dendrites '1' '2'
69 56
Basal dendrites. The intermediate angles of the plane bifurcations of basal dendrites show unimodal, symmetrical frequency distributions for orders 1 and 3_ This does not hold true for the order 2, however; the frequency distribution here showing a certain degree of skewness to the right (Fig. 5). In Table III, the means with the standard deviation of the mean are given for the different orders. It appears that the means for the different orders o f the basal dendrites show no significant differences. Apical dendrites. The intermediate angles of the apical main shaft branchings and the oblique dendrite bifurcations display the same form of frequency distribution as do those of the basal dendrite bifurcations. The means with the standard deviation of the mean are given in Table llI. The means for the different orders of the apical main shaft angles do not show mutually significant differences. The means of the apical main shaft angles for the orders 1 and 2 of the plane bifurcations are significantly greater than those in basal dendrites. The means for the oblique dendrites lie in the range of values of the means of the basal dendrites (Table III). (C) The symmetry of bifurcation For the basal dendrites, the frequency distributions of the differences in absolute values between the pairs of side angles correspond closely with the half of a unimodal symmetric distribution with a mean of zero (see Fig. 6). This is supported by the good correspondence between the standard deviations in the side angles equivalence test (see Table IV), meaning that the differences between the pairs of side angles are compatible with a symmetric distribution about a zero mean. A similar result has been obtained before for segment lengths of the pairs of daughter segments o f the basal dendritic bifurcations 15. On this basis, we can now conclude that the assumption that the basal dendrites bifurcate essentially symmetrically can not be rejected. The frequency distribution of the absolute values of the differences between the
49 %
B
A
60
60 ¸ --Q
....
b
order1
40
r--,
20
O'
-f-I-'-1
120
order
2
18(}0
60
12D
6b
12'0
60
120
18C)°
40J
40 ¸
20
6b
~0
~86~ 60"
60 I
ord¢ r 3 40"
40
20
20
r*q
60
120
18cf'0
180°
Fig. 6. The frequency distributions of the differences in absolute values between the pairs of side angles (A) of basal dendrites (B) of the apical main shaft, a: all bifurcations, b: plane bifurcations.
pairs of side angles of the apical main shaft (Fig. 6) show a mixture of symmetrical and asymmetrical branching, except perhaps for order 2. However, we have not found that these frequency distributions are significantly asymmetrical about a zero mean (see Table IV). The frequency distributions and the side angle equivalence test of the oblique dendrites of the apical dendrites give results similar to those of the basal dendrites (Table IV). DISCUSSION
Apical dendrites can be divided into different subgroups showing different branching angles: the intermediate branching angles of the apical main shaft are larger than those of the apical oblique dendrites or of the basal dendrites (see Results and Table Ill). This distinction does not exist for the segment lengths ts.
50 T A B L E IV SIDE ANGLE EQUIVALENCE TEST
A : S.D. of the differences between the pairs o f side angles e s t i m a t e d by the s u m m a t i o n law (Stair et al.~5). B: S.D. of the differences between the pairs of side angles e s t i m a t e d a b o u t a zero m e a n value.
Order
No.
All bifurcations A (~)
B(-)
44 51 41
44 51 41
55 54 56 49
40 59
No.
Plane biJurcations A ()
~ (/
55 52 16
48 52 47
48 52 46
54 53 55 48
13 9 12 5
50 67 57 70
49 65 56 (~6
40 57
13 4
39 -
~9
For basal dendrites 1 2 3
82 72 25
For apicalmainshaftbranching 1 2 3 4
22 18 18 10
For oblique dendrites '1' '2'
20 8
All of the angle measurements for dendrites reported so far in the literature have been made on projections onto the fixed plane of sectioning and without distinguishing between the angles of apical and basal dendrites. We, on the contrary, have calculated the real angles. Moreover, the angles of the apical and basal dendrites were differentiated from one another. A direct comparison of our calculated angles with such dendritic angle measurements found in the literature is consequently not possible. Nevertheless, some comparisons with published data concerning nerve cell processes in two-dimensional tissue cultures are possible. Bray z has shown the mean intermediate angle for the nerve fibers (dendrite and/or axon) of a single sympathetic neuron from a rat to be 102°. Strassman and Wessels 16 have determined that the mean intermediate angle for the symmetric bifurcations of microspikes in nerve cells from chicken spinal ganglia and neural retina was 75 °. These values correspond with, respectively, the main shaft branchings of apical dendrites and those of the basal and apical oblique dendrites in the rabbit cortex. There are, as yet, too little data in the literature for drawing any conclusion however. In the case of symmetrical branching, the distribution of the differences between pairs of side angles is both symmetrical with a mean of zero degrees and unimodat. The side angle equivalence test (see Material and Methods) only indicates whether the distribution is symmetrical with a mean of zero or not. To examine if the branchings are actually symmetrical, the statistical test should be combined with a histogram for determining the position of the mode(s). From the results o f our test (Table IV) together with histograms (Fig. 6) we did not find significant asymmetrical branching for the apical dendrites. This is contrary
51 to our expectations. The main reason might be that only the superficial half of the cortex (see Table I in ref. 15) was examined. This probably means that the more symmetrically branching part of the apical dendrites, which occurs after the main bifurcation point in the area of laminae I and II (see Fig. 9 in ref. 8), was well represented. In addition, due to the number of angles examined, the observed bimodality was not significant. The ordering system employed here for the apical dendrite is probably not complete, since at least three parts appear ideally to have been distinguished. Firstly, the apical dendrites should be ordered in the two subgroups, as proved necessary in this paper, from the soma up to the main bifurcation point. Thereafter they should probably be ordered like the basal dendrites (see also SholV3). This subdivision in three subgroups agrees with the data of Scheibel and Scheibel as cited by Chow and Leiman 3 on the distribution of presynaptic terminals on pyramidal cells of the visual cortex. The specific sensory afferents would synapse on the apical main shaft, the commissural fibers on the oblique dendrites, and the recurrent collaterals of the pyramids on both the basal dendrites and the apical end tree (i.e. terminal tuft). As a result, completely automated tracking and measuring of pyramidal cells 5,22 will be quite difficult, since complicated differentiating criteria will be required. The interpretation of the significance of the symmetrical bifurcations in basal dendrites is difficult. To do this, more physiological data at the dendritic level would be necessary. A consequence of symmetric bifurcation is that the two daughter segments will possess equal diameters (Uylings and Stair, in preparation). It is to be expected, therefore, that the two daughter branches in a symmetrical bifurcation exercise an equivalent influence regarding electrochemical transmission upon their mother branch and vice versa (e.g. ref. 12, p. 678). There are indications that new side branches arise mainly from end segments 2,6, l~ at a considerable distance from the end of the segment in question, i.e. preterminally15, iv. Since the growth process will certainly not be deterministic 15, the branching is not symmetrical in the case of a preterminal outgrowth. Such asymmetrical outgrowth when viewed from the essentially symmetrical adult configuration of the basal dendrites reported here leads us to the hypothesis that redirection occurs during growth. Redirection to complete symmetry is not often reached, however, as is demonstrated by the large variability in the bifurcation angles. We have, in fact, found some examples of redirection in the original photos of single sympathetic rat neurons in vitro, taken at different times during the outgrowth 2, which Dr. Bray kindly put at our disposal. Some angles, for instance, are clearly more symmetric at 500 rain than at 420 rain. In contrast with our above-mentioned indications of preterminal outgrowth, however, Bray z has found that outgrowth in tissue culture as a rule occurred at the terminal tip of the fiber. Concerning this point, Bray commented that he feels 'unsure about the application of these results to normal dendritic growth. Quite obviously mechanisms exist by which new branches arise either terminally or preterminally, and the balance of the two may be easily influenced by the surrounding environment' (personal communication).
52 Th e m o d e o f o u t g r o w t h does n o t affect the possibility o f a l i g n m e n t o f a bifurc a t i o n in a flat plane. This c o r r e s p o n d s with the relatively small v ar i ab i l i t y which we f o u n d in this respect. T h e fiat plane is p r o b a b l y a strong o p t i m i z a t i o n r e q u i r e m e n t '-'°. ACKNOWLEDGEMENTS
We t h a n k M r s L. V e l d m a a t - W a n s i n k for excellent technical assistance, Drs A. v an der Stelt a n d
W. A. M. V e l t m a n f o r their suggestions an d
Dr M. A.
C o r n e r f o r reading the manuscript. We also t h a n k Mr s A. M. F e d d e m a and Mr s
S. W. L u s t - B o s b o o m f o r typing the manuscript.
REFERENCES I BERRY, M., ANDERSON, E. M., HOLLINGWORTH, T., AND FLINN, R. M., A computer technique for the estimation of the absolute three-dimensional array of basal dendritic fields using data from projected histological sections, J. Microsc., 95 (1972) 257-267. 2 BRAY,D., Branching patterns of individual sympathetic neurons in culture, J. (~,ll Biol., 56 (1973) 702-712. 3 CHOW, K. L., AND LEIMAN, A. L., The structural and functional organization of the neocortex, Neurosei. Res. Progr. Bull., 8 (1970) 153-220. 4 COLONNIER,M., The tangential organization of the visual cortex, J. Anat. (Land.), 98 (19641 327344. 5 GARVEY, C. F., YOUNG, J. H., COLEMAN, P. O., AND SIMON, W., Automated three-dimensional dendrite tracking system, Electroeneeph. clin. Neurophysiol., 35 (1973) 199-204. 6 HOLLINGWORTH, T., AND BERRY, U., Network analysis of dendritic fields of p)ramidal cells in neocortex and Purkinje cells in the cerebellum of the rat, Phil. Trans. B, in press~ 7 KEMPER, TH., L., CAVENESS, W. F., AND YAKOVLEV, P. 1., The neurographic and metric study of the dendritic arbors of neurons in the motor cortex of Macaca mulatta at birth and at 24 months of age, Brain, 96 (1973) 765-782. 8 KIRSCHE, W., KUNZ, G., WENZEL, J., WINKELMANN, A., UND WINKELMANN, E., Neurohistologische Untersuchungen zur Variabilitfit tier Pyramidenzellen des sensorischen Cortex der Ratte, J. Hirnforsch., 14 (1973) 117-135. 9 KREUTZBERG, G. W., SCHUBERT, P., TOTH, L., AND RIESKE, E., lntradendritic transport to postsynaptic sites, Brain Research, 62 (1973) 399-404. 10 LUNGS, R., AND NICHOLSON, C., Electrophysiological properties of dendrites and somata in alligator Purkinje cells, J. Neurophysiol., 34 (1971) 532-551. 11 MUNGM,J. M., Dendritic patterns in the somatic sensory cortex of the cat, J. Anal. (Lond.;, 101 (1967) 403-418. 12 RALL, W., AND R1NZEL, J., Branch input resistance and steady attenuation for input to ore branch of a dendritic neuron model, Biophys. J., 13 (1973) 648-688. 13 SHOLL,A. A., Dendritic organization in the neurons of the visual and motor cortices of the cat, J. Anat. (Lond.), 87 (1953) 387-406. 14 SMIT, G. J., AND COLON, E. J., Quantitative analysis of the cerebral cortex. I. A3electivity of the Golgi-Cox staining technique, Brain Research, 13 (1969) 485-510. 15 SMIT, G. J., UYLINGS, H. B. M., AND VELDMAAT-WANSINK~L., The branching pattern in dendrites of cortical neurons, Aeta morph, neerl.-scand., 9 (1972) 253-274. 16 STRASSMAN,R. J., AND WESSELS, N. K., Orientational preferences shown by microspikes of growing nerve cells in vitro, Tissue and Cell, 5 (1973) 401-412. 17 TEN HOOPEN, M., AND REUVER, H. A., Growth patterns of neuronal dendrites .... an attempted probabilistic description, Kybernetik, 8 (197t) 234-239. 18 UYLINGS,H. B. M., AND SMm G. J., The branching pattern in apical dendrites of cortical cells, Experientia (Basel), 30 (1974) 1187-1188.
53 19 UYLIr~GS, H. B. M,, AND SMIT, G. J., Calculation procedures of the mea, plane equation and the approximation o f the measuring error, Neth. Centr. Inst. Brain Res., Amsterdam, Res. Report 74-02, 1974, pp. I-I 1. 20 UVLINGS, H. B. M., AYD SMIT, G. J., Three-dimensional branching structure of pyramidal cell dendrites, Brahl Research, 87 (1975) 55 60. 21 WINKELMANN, E., KUNZ, G., KIRSCHI~, W., NEUMANN, l~l., WENZEL, J., UND WINKELMANN, A., Quantitative Untersuchungen an Dendriten der CA1-Pyramidenneurone des Hippocampus der adulten Albinoratte, Z. mikr.-anat. Forseh., 85 (1972) 376 396. 22 WYss, U. R., Analysis of dendrite patterns by use of an adaptive scan system, J. Microsc., 95 (1972) 269 275.
41
() Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
THE M O R P H O M E T R Y OF THE B R A N C H I N G P A T T E R N IN D E N D R I T E S
OF THE VISUAL CORTEX P Y R A M I D A L CELLS
G. J. SMIT AND H. B. M. UYLINGS
Central lnstitute Jbr Brain Research, Amsterdam 1006 (The Netherlands) (Accepted November 21st, 1974)
SUMMARY
An analysis has been made of the three-dimensional branching structure for the basal and apical dendrites of cortical neurons in an adult rabbit. The real branching angles of basal dendrites and apical oblique branches are in the same range, but differ from those of the apical main shaft. Therefore, several different parts of the apical dendrite have to be distinguished on anatomical grounds, coincident with the presynaptic areas distinguished in the literature. The bifurcations of basal dendrites are essentially symmetrical. The mode of outgrowth, however, is non-symmetrical. Redirection of dendrites will, therefore, occur. This redirection is often not complete, so that a large variability of branching angles results. The possible significance of the observed symmetry is discussed.
1NTRODUCTION
The branching structure of dendrites has influence upon, and is under the infl uence of, a number of functional processes in neurons, e.g., electrochemical transmission and spatiotemporal integration of signals 9,1°,1"°. Morphometric analysis of dendritic branching patterns is therefore necessary. Based on data from both morphometric and physiological analysis, functional models can be developed in order to obtain insight into the above-mentioned complex interrelationship of mutual influence. Some metrical aspects of the branching pattern in basal and apical dendrites of visual cortical cells will be described in this paper. In contrast to previous anatomical analyses of dendrites1,7,11, the present data are based upon three-dimensional measurements and are differentiated in more aspects.
42 MATERIAL AND METHODS
(A) General The basal and apical dendrites of 30 pyramidal cells in the striate area of both hemispheres of a single adult rabbit were analyzed in Golgi-Cox stained sections, 80 #m thick (see ref. 14 for further technical data). These cells are representative of the pyramidal cells in cortical layers II, III and IV ~s.
(B) Measured quantities Within a rectangular three-coordinate system the following parameters were determined from the dendrites: (1) the x-, y- and z-coordinates of all the initial points, bifurcation points, end points and points where the dendrites had been cut; (2) the type of the segments, i.e. end segment or intermediate segment; and (3) the order of the segments. (1) The x- and y-coordinates were measured using 2 #m clocks mounted oll the stage of the microscope (Zeiss, type G.F.L.). It has been established from a 16-fold repetition, using an object micrometer, that the range of these measurements is about 5 #m, at room temperature ranging between 13 °C and 24 °C. The z-coordinate was determined using the fine adjustment of this microscope. The fine adjustment was operated by cog-wheels, and it too showed a variation of about 5/~m. (2) End segments run into an end point, whereas intermediate segments are closed by a bifurcation. (3) All proximal segments of the basal dendrites are called first order segments, and the order is raised by one beyond each bifurcation. This centrifugal ordering system is not strictly applicable to apical dendrites, however, since they do not have a symmetrical bifurcation structure is. Therefore, each apical dendrite was ordered in two parts (see ref. 21): (1) the main shaft, ordered starting at the perikaryon; (2) the oblique branches, ordered separately starting at the segment arising from the main shaft (Fig. 1).
( C) Calculated quantities The spatial structure of the dendritic bifurcations per order has been analyzed on the basis of the rectilinear reconstructions. The 4 measured points involved in a bifurcation are considered as vertices of a tetrahedron, with the bifurcation point (point A in Fig. 2) as the apex of the bifurcation pyramid. At each bifurcation point, two daughter segments arise from a mother segment. The bifurcation angle between the two daughter segments is called the intermediate angle (angle CAB in Fig. 2). It is distinguished from the two bifurcation angles between a daughter and the mother segment, called side angles (e.g. angle DAB in Fig. 2). For the dendritic bifurcations, the following uncorrelated quantities have been calculated by means of EL X8 and IBM 1130 computers: (a) the intermediate angle, and (b) the absolute value of the difference between the pair of the side angles. (a) There is a difference in the average length between intermediate and end segments (see ref. 14). Therefore, it would be preferable to subdivide the bifurcations,
43 opfc
dendr
'}
""4
'.3! . . . .
, 4 ~.
.... -:I'
2'
.--2 ---I
I
321" 1
s
50/~
,
~XOn
Fig. I. The projection in the x, y plane of a pyramidal neuron having 5 basal dendrites (A-EL a cut apical dendrite, and a partly stained axon. For the basal dendrites, the letters s and e refer to cutting points and end points respectively, whereas the numbers at the branchings refer to the order of the mother segment. For the apical dendrite, the numbers at the segments refer to the order of the segments.
acco r d i n g to the type o f the segments, into the 3 possible subgroups is. The n u m b e r s o f observations for each o r d e r f r o m these subgroups, however, then b e c o m e too small for the most part to allow a meaningful analysis, so this subdivision has been omitted.
44
A
D
B
Fig. 2. A schematic bifurcation. DA is the mother segment, and AB and AC are the daughter segments. Angle CAB is the intermediate angle and angles DAC and DAB are the side angles.
(b) The absolute values of the differences between the pairs of side angles have been used to examine if the bifurcations are essentially symmetrical, i.e. if on the average the side angles of a bifurcation are equal and, therefore, the differences between pairs of side angles give a symmetric distribution about a zero mean. Only the absolute values could be used, since no criteria were available to distinguish between the two side angles. A side angle equivalence test has been designed to determine if the distribution of the absolute values of the differences is compatible with a symmetric distribution about a zero mean 15. This test consists in comparing two variance estimations: (t) an estimation, not dependent on the symmetry of the bifurcations, by means of the summation law for variances: v a r ( a - - b ) - - v a r ( a ) T v a r ( b ) - 2 cov(a,b). Since the two side angles could not be distinguished we have taken var(a) -: var(b) and calculated cov(a,b) by means of the intraclass coefficient of correlation, and (2) an estimation of v a r ( a - - b ) dependent on the assumption that the differences between pairs of side angles are symmetrical about a zero mean. In case of symmetry vat(a---b) is equal to the second moment about zero of the differences.
(D) Accuracy of angle measurements In the calculations of the bifurcation angles 3 types of errors play a part: (1) the reading error, (2) the instrumental error of the fine adjustment of the ~m clocks and of the microscope, and (3) the error caused by the assumption that dendritic segments are straight. (1) and (2) The standard deviation of the reading and the instrumental error can be roughly estimated, i.e. 5 # m divided by 4 times the standard deviation of 1.25/~m for each coordinate 19. (3) Colonnier 4 and Smit et al. 15 have found that the dendritic segments generally follow a straight course. They do show a slight degree of waviness (Fig. I) however, and in a number of cases deviate strongly from a rectilinear course. The question is whether this factor significantly influences the angle calculations. To examine this, 2 sets of coordinate measurements were made at 14 bifurcations of basal dendrites in an additional pyramidal cell (the cell in Fig. 1). Besides the already described coordi-
45
(b)
(a)
B
D
D
Fig. 3. Two possible c o n f i g u r a t i o n s o f deviation f r o m a rectilinear course o f a bifurcation.
nate measurements at each bifurcation, end or cut point (to be designated as 'far'), the coordinates were also measured of a point along each of the three segments composing the bifurcation at a distance of 3-10/~m from a bifurcation (to be designated as 'near'). When the dendritic segments show negligible deviations from a rectilinear course (Fig. 3a), the angle estimations based on 'far' measurements are preferable since (a) the influence o f the measuring error is relatively smaller, (b) the influence of the waviness upon the angle estimations is smaller, and (c) the 'far' measurements demand fewer measurements for a complete description of the dendrite. When segments deviate considerably from a rectilinear course however (Fig. 3b), the angle estimations based upon 'near 'measurements are then the less sensitive of the two to the various errors, and are therefore to be preferred in this case. RESULTS
(A) Accuracy of angle measurements Based on the approximation that the standard deviation of the measuring
TABLE I M E A S U R I N G E R R O R I N F L U E N C E O N A N G L E S O F BASA L D E N D R I T E S
Order
No.
Mean (~)
S.D. ( )
Corrected S.D. ( )
75 65 57 --
32 37 36
28 35 35
122 124 ll9 125
36 41 46 44
33 38 43 43
( A) Intermediate angles (in degrees) l 2 3 4
82 72 25 7
(B) Side attgles (in degrees) 1 2 3 4
164 144 50 14
46 T A B L E ll C O M P A R I S O N ' F A R ' - - ' N E A R ~ M E A S U R E M E N T S OF A N G L E S O F C E L L IN FIG. I
Bifurcation
Intermediate angle ( )
Side ang~ (':)
Side ang~ (":
Far
Near
Far
Near
F~lr
Near
AI A2 A3
36 50 51
79 90 122
166 141 162
132 92 107
149 170 136
125 170 65
Bl B2
99 66
49 69
97 160
152 118
164 133
156 78
CI C2a C2b
82 97 49
123 120 34
159 156 144
119 118 167
Ill 102 107
lli 121 [37
DI D2 D3 D4
37 75 40 17
46 57 42 31
136 97 162 162
155 112 167 179
117 170 153 175
121 I43 126 149
E1 E2
113 46
98 29
97 108
95 69
119 148
157 98
61 28 14
70 35 14
139 26 28
126 31 28
Mean S.D. No.
error is 1.25 # m for each coordinate, the standard deviation of the bifurcation angles has been corrected. Table I shows that the influence of the measuring error on the standard deviation is small (-4 l0 To) with regard to the considerable natural standard deviation of the intermediate and side angles. It appears from Table II that the two estimations of the individual angles based on the 'far' and the 'near' measurements sometimes differ considerably. This is in agreement with the low Spearman correlation coefficients, namely, 0.58 for the 14 intermediate angles and 0.42 for the 28 side angles. It means that the individual estimations of the angles are not reliable. However, the two correlograms of, respectively, the intermediate angles and the side angles, show symmetrical distributions round the line of identical values (Fig. 4). No significant differences are present between the means of the 'far' and 'near' measurements (see Table II). In addition, the standard deviations are greater for the 'near' than for the 'far' measurements. Therefore, we conclude that the means and the standard deviations of the bifurcation angles of the 'far' measurements give a reliable description of the frequency distributions of the dendritic angles (see Material and Methods).
(B) Intermediate angles Beside the results of all bifurcations, the results of the so-called plane bifurcations (i.e. bifurcations which deviate only slightly from a plane, see ref. 20) are also given separately.
47 180 ~
4~
NEAR
Fig. 4. The two correlograms of the intermediate angles (filled circle) and the side angles (open circle) respectively, which illustrate the correlation between the 'near' and 'far' measurements.
4' 4 order1
--
a
---
b
i
2o !
o
60
120
1~) °
120
180 °
120
180 °
o/o
40" crdcr 2
20-
o 6C
order 3
2o!
60
Fig. 5. The frequency distributions of the intermediate angles of basal dendrites, a: all bifurcations. b: plane bifurcations.
48 T A B L E Ill INTERMEDIATE ANGLES
Order
All b(furcatioHs Mean (')
Plane bifurcations S.D. of mean ( )
No.
Mean ( )
S.D. O/'.u'aJt ! )
No.
O f basal dendrites 1 2 3
75 65 57
3 4 7
82 72 25
7(~ 65 67
4 5 9
55 52 16
9 8 7 1~.~
22 18 18 10
106 113 102 87
II 13 l0 9
[3 9 12 5
7 15
20 8
71 --
9
13 4
O f apical main shaft branching 1 2 3 4
97 97 100 71
Of oblique dendrites '1' '2'
69 56
Basal dendrites. The intermediate angles of the plane bifurcations of basal dendrites show unimodal, symmetrical frequency distributions for orders 1 and 3_ This does not hold true for the order 2, however; the frequency distribution here showing a certain degree of skewness to the right (Fig. 5). In Table III, the means with the standard deviation of the mean are given for the different orders. It appears that the means for the different orders o f the basal dendrites show no significant differences. Apical dendrites. The intermediate angles of the apical main shaft branchings and the oblique dendrite bifurcations display the same form of frequency distribution as do those of the basal dendrite bifurcations. The means with the standard deviation of the mean are given in Table llI. The means for the different orders of the apical main shaft angles do not show mutually significant differences. The means of the apical main shaft angles for the orders 1 and 2 of the plane bifurcations are significantly greater than those in basal dendrites. The means for the oblique dendrites lie in the range of values of the means of the basal dendrites (Table III). (C) The symmetry of bifurcation For the basal dendrites, the frequency distributions of the differences in absolute values between the pairs of side angles correspond closely with the half of a unimodal symmetric distribution with a mean of zero (see Fig. 6). This is supported by the good correspondence between the standard deviations in the side angles equivalence test (see Table IV), meaning that the differences between the pairs of side angles are compatible with a symmetric distribution about a zero mean. A similar result has been obtained before for segment lengths of the pairs of daughter segments o f the basal dendritic bifurcations 15. On this basis, we can now conclude that the assumption that the basal dendrites bifurcate essentially symmetrically can not be rejected. The frequency distribution of the absolute values of the differences between the
49 %
B
A
60
60 ¸ --Q
....
b
order1
40
r--,
20
O'
-f-I-'-1
120
order
2
18(}0
60
12D
6b
12'0
60
120
18C)°
40J
40 ¸
20
6b
~0
~86~ 60"
60 I
ord¢ r 3 40"
40
20
20
r*q
60
120
18cf'0
180°
Fig. 6. The frequency distributions of the differences in absolute values between the pairs of side angles (A) of basal dendrites (B) of the apical main shaft, a: all bifurcations, b: plane bifurcations.
pairs of side angles of the apical main shaft (Fig. 6) show a mixture of symmetrical and asymmetrical branching, except perhaps for order 2. However, we have not found that these frequency distributions are significantly asymmetrical about a zero mean (see Table IV). The frequency distributions and the side angle equivalence test of the oblique dendrites of the apical dendrites give results similar to those of the basal dendrites (Table IV). DISCUSSION
Apical dendrites can be divided into different subgroups showing different branching angles: the intermediate branching angles of the apical main shaft are larger than those of the apical oblique dendrites or of the basal dendrites (see Results and Table Ill). This distinction does not exist for the segment lengths ts.
50 T A B L E IV SIDE ANGLE EQUIVALENCE TEST
A : S.D. of the differences between the pairs o f side angles e s t i m a t e d by the s u m m a t i o n law (Stair et al.~5). B: S.D. of the differences between the pairs of side angles e s t i m a t e d a b o u t a zero m e a n value.
Order
No.
All bifurcations A (~)
B(-)
44 51 41
44 51 41
55 54 56 49
40 59
No.
Plane biJurcations A ()
~ (/
55 52 16
48 52 47
48 52 46
54 53 55 48
13 9 12 5
50 67 57 70
49 65 56 (~6
40 57
13 4
39 -
~9
For basal dendrites 1 2 3
82 72 25
For apicalmainshaftbranching 1 2 3 4
22 18 18 10
For oblique dendrites '1' '2'
20 8
All of the angle measurements for dendrites reported so far in the literature have been made on projections onto the fixed plane of sectioning and without distinguishing between the angles of apical and basal dendrites. We, on the contrary, have calculated the real angles. Moreover, the angles of the apical and basal dendrites were differentiated from one another. A direct comparison of our calculated angles with such dendritic angle measurements found in the literature is consequently not possible. Nevertheless, some comparisons with published data concerning nerve cell processes in two-dimensional tissue cultures are possible. Bray z has shown the mean intermediate angle for the nerve fibers (dendrite and/or axon) of a single sympathetic neuron from a rat to be 102°. Strassman and Wessels 16 have determined that the mean intermediate angle for the symmetric bifurcations of microspikes in nerve cells from chicken spinal ganglia and neural retina was 75 °. These values correspond with, respectively, the main shaft branchings of apical dendrites and those of the basal and apical oblique dendrites in the rabbit cortex. There are, as yet, too little data in the literature for drawing any conclusion however. In the case of symmetrical branching, the distribution of the differences between pairs of side angles is both symmetrical with a mean of zero degrees and unimodat. The side angle equivalence test (see Material and Methods) only indicates whether the distribution is symmetrical with a mean of zero or not. To examine if the branchings are actually symmetrical, the statistical test should be combined with a histogram for determining the position of the mode(s). From the results o f our test (Table IV) together with histograms (Fig. 6) we did not find significant asymmetrical branching for the apical dendrites. This is contrary
51 to our expectations. The main reason might be that only the superficial half of the cortex (see Table I in ref. 15) was examined. This probably means that the more symmetrically branching part of the apical dendrites, which occurs after the main bifurcation point in the area of laminae I and II (see Fig. 9 in ref. 8), was well represented. In addition, due to the number of angles examined, the observed bimodality was not significant. The ordering system employed here for the apical dendrite is probably not complete, since at least three parts appear ideally to have been distinguished. Firstly, the apical dendrites should be ordered in the two subgroups, as proved necessary in this paper, from the soma up to the main bifurcation point. Thereafter they should probably be ordered like the basal dendrites (see also SholV3). This subdivision in three subgroups agrees with the data of Scheibel and Scheibel as cited by Chow and Leiman 3 on the distribution of presynaptic terminals on pyramidal cells of the visual cortex. The specific sensory afferents would synapse on the apical main shaft, the commissural fibers on the oblique dendrites, and the recurrent collaterals of the pyramids on both the basal dendrites and the apical end tree (i.e. terminal tuft). As a result, completely automated tracking and measuring of pyramidal cells 5,22 will be quite difficult, since complicated differentiating criteria will be required. The interpretation of the significance of the symmetrical bifurcations in basal dendrites is difficult. To do this, more physiological data at the dendritic level would be necessary. A consequence of symmetric bifurcation is that the two daughter segments will possess equal diameters (Uylings and Stair, in preparation). It is to be expected, therefore, that the two daughter branches in a symmetrical bifurcation exercise an equivalent influence regarding electrochemical transmission upon their mother branch and vice versa (e.g. ref. 12, p. 678). There are indications that new side branches arise mainly from end segments 2,6, l~ at a considerable distance from the end of the segment in question, i.e. preterminally15, iv. Since the growth process will certainly not be deterministic 15, the branching is not symmetrical in the case of a preterminal outgrowth. Such asymmetrical outgrowth when viewed from the essentially symmetrical adult configuration of the basal dendrites reported here leads us to the hypothesis that redirection occurs during growth. Redirection to complete symmetry is not often reached, however, as is demonstrated by the large variability in the bifurcation angles. We have, in fact, found some examples of redirection in the original photos of single sympathetic rat neurons in vitro, taken at different times during the outgrowth 2, which Dr. Bray kindly put at our disposal. Some angles, for instance, are clearly more symmetric at 500 rain than at 420 rain. In contrast with our above-mentioned indications of preterminal outgrowth, however, Bray z has found that outgrowth in tissue culture as a rule occurred at the terminal tip of the fiber. Concerning this point, Bray commented that he feels 'unsure about the application of these results to normal dendritic growth. Quite obviously mechanisms exist by which new branches arise either terminally or preterminally, and the balance of the two may be easily influenced by the surrounding environment' (personal communication).
52 Th e m o d e o f o u t g r o w t h does n o t affect the possibility o f a l i g n m e n t o f a bifurc a t i o n in a flat plane. This c o r r e s p o n d s with the relatively small v ar i ab i l i t y which we f o u n d in this respect. T h e fiat plane is p r o b a b l y a strong o p t i m i z a t i o n r e q u i r e m e n t '-'°. ACKNOWLEDGEMENTS
We t h a n k M r s L. V e l d m a a t - W a n s i n k for excellent technical assistance, Drs A. v an der Stelt a n d
W. A. M. V e l t m a n f o r their suggestions an d
Dr M. A.
C o r n e r f o r reading the manuscript. We also t h a n k Mr s A. M. F e d d e m a and Mr s
S. W. L u s t - B o s b o o m f o r typing the manuscript.
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