Proc. NatW Acad. Sci. USA Vol. 80, pp. 3069-3073, May 1983 Medical Sciences

Electroanatomy of a unique amacrine cell in the rabbit (horseradish peroxidase staining/intracellular electrophysiology) ROBERT F. MILLER AND STEWART A. BLOOMFIELD* Departments of Ophthalmology, Physiology and Biophysics, Washington University School of Medicine, St. Louis, Missouri 63110 Communicated by Oliver H. Lowry, February 10, 1983 ABSTRACT Intracellular electrophysiological recordings were (ii) to permit the cell to maintain a comparatively large number obtained from a specialized class of "starburst" amacrine cells by of relatively short processes without compromising the synaptic using an isolated superperfused retina-eyecup preparation of the efficiency of single distal branches. A preliminary account of rabbit. These cells were injected intracellularly with horseradish these findings has been presented (10). peroxidase and identified with light microscopy. A computer-con- trolled image-processing system was used to map and display the MATERIALS AND METHODS three-dimensional dendritic organization and provide information on length and sublaminar distribution of dendritic processes. Physiology and Anatomy. Intracellular recordings were ob- Starburst amacrines show an unusual dendritic architecture that tained from single neurons of the rabbit retina by using the iso- includes thin intermediate dendritic segments. Analysis with steady- lated superfused eyecup preparation as described (11, 12). Im- state cable equations suggests that these thin segments may pro- paled neurons were physiologically characterized and subse- vide electrical isolation of distal processes, raising the possibility quently stained with HRP. Stained cells were examined micro- that a single dendrite, which lies beyond the thin segment, may scopically in flatmount view. Well-stained neurons were fur- constitute a functional subunit of the cell. ther analyzed by using a computer-assisted image;processing system (13), which compiled structural data in three dimen- For nearly a century, silver-staining techniques applied to the sions through control of the focus adjustment and the stage mi- vertebrate retina have revealed a rich variety of neuronal cell crometers. Once the cell was logged onto the computer, its three- types that vary in size, density, and form of dendritic branching dimensional structure could be visualized in any plane through patterns (1). Variations in morphology such as the overall den- computer processing and display on a plotter. dritic spread may relate to differences in size (2); The diameters of dendritic segments were measured on a the sublaminar distribution of dendritic branching among third- Jena Amplival microscope with a Zeiss long-working-distance order neurons also may determine physiological polarity of the oil-immersion objective. A micrometer-driven filar eyepiece cell (ON, OFF, ON-OFF) (3). What about variations in the was calibrated and used for diameter measurements. The av- number of dendrites and the pattern of dendritic architecture? erage diameter of a single process was determined for three What functional significance can be attributed to the micro- adjacent regions of each dendritic segment. Although tapering scopic design of dendrites and dendritic branching? This prob- of dendrites is a property of some amacrines (14), the dendrites lem has received comparatively little attention, although a re- of starburst amacrines reasonably approximate cylinders. cent analysis of Golgi-stained ganglion cells has appeared (4). Microelectrodes were fabricated from thin-walled triangular The question of dendritic architecture is especially relevant for tubing (Glass Co. of America, Bargaintown, New Jersey) and considerations of amacrine cells because the dendrites of these filled with 10% HRP (Boehringer Mannheim) dissolved in 0.5 neurons have both post- and presynaptic anatomy (5). A ques- M potassium acetate adjusted to pH 7.6 with 0.1 M Tris. In- tion often posed concerning amacrine cells is whether single tracellular injection of HRP was done by applying an alternat- dendrites or subdendritic regions may operate independently ing current of 3 Hz at a level of 1 nA for 10 min. The use of and serve to parcel the amacrine into functional subunits. Rall alternating current minimized polarization of the microelec- (6) has pointed out that a narrowing of processes may augment trode. After several cells were stained, the retina was super- the synaptic operations upstream from the stricture, and one perfused for an additional hour, followed by fixation in 1.5% study (7), emphasizing this concept, has suggested that single glutaraldehyde/1.5% paraformaldehyde (pH 7.3 in 0.1 M varicosities of some amacrine dendrites may form functional phosphate buffer) for 10 min. Prior to fixation, the retina-pig- subunits. ment epithelium was fixed to a gelatinized cover slip to min- We have obtained intracellular recordings from a specialized imize shrinking during the histological procedure. After fixa- class of amacrine cells that have cell bodies localized on op- tion, the pigment epithelium was removed and placed in Ringer's posing sides of the . Both ON and OFF solution to wash for 16 hr at 40C. This was followed by a brief types have been observed. When these cells are stained with wash with distilled water. The HRP reaction utilized benzidene intracellularly injected horseradish peroxidase (HRP), they clearly dihydrochloride according to the method outlined by Mesulam conform to the "starburst" amacrines described previously (8, (15). 9) on the basis of Golgi-stained material. These cells possess an We estimated the amount of tissue shrinkage in several unusual dendritic organization that consists of thin interme- preparations by measuring the shrinkage of slices of retina diate segments and varicosities confined to the more distal mounted on gelatinized cover slips or the shrinkage between branches. The application of steady-state cable equations sug- two dye injection "spots" with fast Green B iontophoretically gests that these thin segments serve (i) to promote electrical applied extracellularly. If the tissue was not secured to a cover isolation of dendritic segments distal to the thin segments and slip, tissue shrinkage in the range of 20-25% was seen, but the The publication costs ofthis article were defrayed in part by page charge Abbreviation: HRP, horseradish peroxidase. payment. This article must therefore be hereby marked "advertise- * Present address: The Biological Laboratories, Harvard Univ., Cam- ment" in accordance with 18 U.S.C. §1734 solely to indicate this fact. bridge, MA. 3069 Downloaded by guest on September 27, 2021 3070 Medical Sciences: Miller and Bloomfield Proc. Nad Acad. Sci. USA 80 (1983) gelatinized cover slip reduced shrinkage to 6-14%. branches. At each branch point, Gd is evaluated as three par- Mathematical Analysis. We estimated the steady-state elec- allel conductances. The two "outward looking" terms were de- trotonic cable losses along dendritic trees using the method- rived from the initial calculation (before Gn was computed), ology of Rall (16), whose initial description also includes the whereas the soma-looking segment is solved after Gn is com- mathematical derivation of these equations. The electrotonic puted. It is worth mentioning here that the method we have lengths of dendritic segments were computed by the well-known used is an explicit solution of the dendritic tree and is not de- equation rived from any assumption about branching patterns or whether dendrites conform to equivalent cylinders as outlined by Rall A = (Rm/Ri d/4)12, [1] (16, 17). In fact, dendrites of starburst amacrines deviate con- where A = characteristic length or length constant, Rm = spe- siderably from equivalent cylinder conditions. cific membrane resistance (Q'cm2), Ri = specific internal re- To calculate steady-state voltage decay along the dendrite, sistance (fl'cm), and d = diameter. For all our calculations, we from a point of current injection, one is constrained by differ- assumed an Rm value of 4,000 fi.cm2 and an Ri value of 70 tlcm, ent boundary conditions that depend on the direction of cur- values commonly used for such calculations in mammalian neu- rent flow within the dendrite. Towards the periphery, rons. Based on the anatomical measurements of length and di- cosh (1 - x)A ameter, we calculated the following: [7] Gn = Gs + I Gd, [2] cosh l/A where Gn = whole neuron conductance, G. = soma conduc- where V = voltage at a point x and Vo = voltage at point of tance, and I Gd = summation of each individual dendritic con- application. Voltage decay towards the soma is determined by ductance at the soma. If each dendrite is similar, one need only evaluate Gd for a single dendrite and I Gd = n(Gd), where n V = number of equivalent dendrites. If dendrites show consid- =VOcosh(l/A) + B1 sinh(l/A)'[8[8] erable dissimilarity in structure, it is necessary to solve each dendrite separately. In order to solve Gd for any single den- where B1 is as in Eq. 5. drite, one begins at the distal dendritic branches and computes, collectively, towards the soma. RESULTS AND DISCUSSION The input conductance of a dendrite at the origin (Gda) is During the course of this study, we recorded from and stained given by: several types of neurons (18, 19). One type of amacrine ap- = Bo (1T/2)(Rm Ri)-12 (do)3/2 [3] peared to be unique and striking in its dendritic architecture. Gd. Fig. 1A shows a slightly retouched photograph of a HRP-stained where Bo is a computed value that expresses the conductance OFF-type starburst amacrine. In this cell and in all starburst of the dendrite as a fraction of an infinitely long extension of amacrines stained, the stain only lightly penetrated the den- the primary dendrite. Bo is determined by sequential analysis dritic tree, and some dye leakage obscured the anatomic ar- of the entire dendritic tree beginning at the most distal branches: rangement of the branches near the soma. For this reason, spe- Bj+l + tanh(l/A) cial efforts were required to obtain a photographic representation of a flat-mount view of the cell. We found it necessary to re- = + (Bj+1) tanh(l/A)' touch some of the dendritic segments with ink. These cells have where 1 = real length of each dendritic segment, A = length relatively small perikarya (estimated diameter of 11 ,m) with constant, and tanh is the hyperbolic tangent. The B,+l factor fine intermediate processes near the soma. Many of the thin expresses the conductance of the branch as a fraction of an in- intermediate dendrites branch very quickly into secondary pro- finite extension of the branch. A common assumption, and one cesses, which provide the cell with a fairly dense dendritic that we have used, is that Bj+1 = 0 at the distal end of the den- structure, particularly at the level of the most distal branches. drite, which approximates a condition in which the ends of the The dendrite marked with an asterisk in Fig. 1A is shown in dendrites are "sealed"- i.e., they have a high resistance. This Fig. LB further magnified and unretouched. The position of assumption deviates insignificantly (16, 17) from the resistance the cell body is shown as S. Note that the thin intermediate of a dendritic terminal branch with a patch of membrane at its dendrite gives rise to more peripheral dendrites, which are end. For each branch point, two factors are generated, and thicker and contain varicosities.t We have estimated the di- Bj ameter of the thin dendrite by using a micrometer-driven filar B1 = XBj (Dd/Dp)3/2, [5] eyepiece. These processes are well under 0.5 ,m and could be where Dd = the diameter of the daughter branch and Dp = the as thin as 0.1 ,m. Electron microscopy will be necessary to pro- diameter of the parent. As the calculation proceeds towards the vide a more definitive measure of these fine segments. Fig. IC soma, the two Bj terms are generated for the two daughter shows the computer printout of the cell in Fig. 1 A and B. branches, which through Eq. 5 generate a B1 term for that branch Electrophysiological recordings from starburst amacrines have point. The B1 term then becomes the B +1 term for the next revealed an interesting correlation between the light-evoked most proximal branch point. These terms Ahen lead to a B0 value response polarity, the position of the cell body, and the sub- used in expression 3 to compute the conductance of the den- laminar position of the dendrites. Starburst cells with perikarya drite at its soma origin. Once Gn is determined by Eq. 2, it is in the have processes that ramify in the outer possible to determine the conductance of the "soma looking" part of the inner plexiform layer and are physiologically OFF segment of each dendritic branch. Initially this amounts to con- cells, whereas those with cell bodies in the verting Gn into a factor for the primary dendrite, where Bj+1 t Famiglietti has examined the branching characteristics of starburst Gn-Gdo = amacrines using Golgi-stained cells in the rabbit (9). The appearance B - Good (IT/2)(RmRij)l12 (do)312, [6] G-od of the cell with the Golgi method is slightly different than that shown in Fig. 1. Golgi-stained cells do not showdistal branches thatare larger which is the same as Eq. 3 without the Bo factor. Beginning in diameterthan the thin intermediate segments. Electron microscopy with the primary dendrite, one then proceeds to more distal will be necessary to measure these processes more accurately. Downloaded by guest on September 27, 2021 Medical Sciences: Miller and Bloomfield Proc. Natd Acad. Sci. USA 80 (1983) 3071

FIG. 1. (A) Flat-mount photograph ofan off-type starburst amacrine cell, impregnated with HRP and stained with benzidene dihydrochloride. Some dye leakage at the soma prevented a clear optical defi- nition of the cell body. The thin segments near the cell body were retouched because they were lightly stained. (B) Single dendrite (same cell, same den- drite as * inA) further magnified and unretouched, with the soma near S. (C) Computer drawing of the cell in A and B after logging the cell onto the com- A B C puter-assisted image-processing system.

have processes in the inner margin of the inner plexiform layer nificant reduction in amplitude results from the electrotonic and show ON-responses. decay along the thin process; at the soma, the voltage is re- The thin processes of starburst amacrines raise several in- duced to 0.039-VB (attenuation factor = 25.6). Note also, that teresting questions concerning dendritic function. First, these current spread into other dendrites is significantly reduced; processes are thinner than any primary dendrite we have seen hence, communication between the active vs. inactive den- in other amacrine cells, which are commonly between 0.5-1.2 drites is limited. The attenuation factor between the site of cur- ,m in diameter. Further insight into a possible functional role rent injection and the first branch point of a neighboring den- for the thin dendritic segments has come from mathematical drite is 166.7. considerations of dendritic function based on the methodology When the proximal process is 1.1 pkm, the voltage decay along of Rall (16) and outlined in Materials and Methods. A single the distal dendrite is quite different. In this case, decay of po- dendrite of cell B in Fig. 1 (marked with an asterisk) was se- tential towards the soma shows a more rapid exponential be- lected for analysis. Fig. 2A illustrates the relative length and havior. Note, however, that the larger proximal process does diameter of each dendritic branch. The segments that are drawn not impose a large voltage drop across this segment so that the in thick black lines represent the longest dendrite segments and voltage in the soma is less attenuated compared to that seen are further analyzed in Fig. 2 B and C, where the electrQtonic with the thin process. In this case, the voltage in the soma is lengths are illustrated with one difference. In Fig. 2B, A was about 0. 101 VB (attenuation factor = 9.4). In addition, the com- computed (Table 1) with the diameter of the first-order den- drite taken as 1.1 Am, which would represent the diameter of .121;dioa 0.2p STARBURST AMACRINE: RABBIT the dendrite if it conformed to the "3/2 power" rule of Rall (16, .I 15;dia =0.2p 17). In Fig. 2C, the first-order dendrite was taken as 0.1 ,m, L 5 p L=41;dia 0.56p l 40;dia= 0.41h C15;da 0..2 p a value that is probably much closer to the actual diameters we ALI I see in HRP-stained material. In terms of electrotonic length, 20p 45; dia 0.84p L|63p; dia=0.52p a 1. 1-pum process means that this segment occupies less than 20; dia 0.56 the fraction occupied by the real length. In contrast, a 0. 1-im first-order process (Fig. 2C) (the other branch diameters and REAL LENGTH lengths remain constant) renders the first-order dendrite more than half of the total electrotonic length. Thus, the thin seg- ment will represent the single most significant cable-loss sec- L 0.14X B Total L =0501/ tion of the entire tree. 1.1p=FIRST L00.23A Table 1 presents the computational results of our analysis of ORDER L 0.13A the dendrite with the approach described in Materials and

Methods. .VOL0.445A L/A c Total L-0.72 Fig. 3 illustrates a second consequence of the thin proximal . 0. IJp=FIRST ORDERI.02 dendrite. In this example, Eq. 7 and 8 were used to determine L 0.13X the relative decline of a steady-state potential, contrasting the two situations where a thin (0.1 Am) and thick (1.1 pum) prox- RM 4000 OHMS-CM2; RI 70 OHMS-CM imal process connect with the soma. For these calculations, we 0.5 1.0 assumed an equal potential was applied to a terminal branch RELATIVE ELECTRONIC LENGTH (point B) indicated by the arrow. Current injected at that point will flow towards the soma and out to other branches of the FIG. 2. (A) The diameters and lengths of a single dendrite of a star- same dendrite (as indicated by the arrows). burst amacrine (samedendrite markedwith * in Fig. 1) were measured, The voltage decay along the dendritic tree is sensitive to the with the values listed. The dendritic segments drawn in thick lines were dimension of the proximal process. For the thin process, com- converted to electrotonic lengths and are displayed inB and C. (B) A of the first-order dendrite was computed that the diameter munication within the more distal segments is good; the far- by assuming of this segment conformed to the 3/2 power relationship described by thest point (G) from the site of current injection shows a voltage Rall (1.1 pm). (C) A was computed on the basis of what may be a lower decay of about 0.7 (attenuation factor = 1.4). However, be- limit to the actual process (0.1 pm). InB and C, the other segments re- tween the most proximal branch point (E) and the soma, a sig- main as measured. Downloaded by guest on September 27, 2021 3072 Medical Sciences: Miller and Bloomfield Proc. Natl. Acad. Sci. USA 80.(1983) Table 1. Starburst amacrine dendritic conductances Dia., Length, A, Dendrite Aim BIMAM B+1 B1 (Dd/SP)3/2 B1(Dd/Dp)3/2 XB1 Bo- 3,3 0.2 15 169 0 0.09 0.34 0.03 l 3,4 0.2 -15 169 0 0.09 0.34 0.03 0.06 2,1 0.2 21 169 0 0.12 0.21 0.03l 2,2 0.41 40 242 0.06 0.23 0.63 0.14 0.17 2,3 0.52 63 273 0 0.23 0.49 0.11 0.15 2,4 0.56 20 283 0 0.07 0.54 0.041 1,1 0.56 41 283 0.14 0.3 0.36* 0.11* 13.25t 3.98t 0.29* 10.55t 1,2 0.84 45 346 0.15 0.27 0.67* 0.18* 24.35t 6.57t 0,1 1.1* 55 396 0.29 0.41 1.0 0.41 0.41 0.lt 55 120 10.55 1.98 1.0 1.98 1.98 Summary of the computations described in the text for the analysis ofthe dendrite illustrated in Fig. 1. Dendrite number is determined by the branch power (the first segment is 0,1) and the branch number (top to bottom). All terminal branches have Bj "1 factors of 0 as described. The Bo factors for the two contrasting dendrites are tabulated on the lower right and are then used in Eq. 3 to calculate the conductance of the dendrite at its somal origin. Dia, diameter. * 1.1-/m process. t0l. m process.

munication between soma and the inactive dendrites is greater putations by calculating for a 1.1- vs. 0.1-,m proximal den- than that seen with the thin process. Thus, two features of the drite. At the terminal branch, the difference between the thick thin process can be seen from Fig. 3: first, it enhances voltage and thin proximal dendrite is that the (Rn) is more than double communication within the processes that lie distal to the thin (1,068 vs. 392 mil) for the thin process. Furthermore, as one segment. Second, communication between a single active den- proceeds to the soma, the disparity between the two values be- drite and the inactive dendrites is restricted because of cable comes greater. At the first branch (point A), there is more than losses along the thin process. A comparison of the attenuation a 10-fold difference between the two (834 vs. 80 mfl); at the factors for the data of Fig. 3 is presented in Table 2. soma, the Rn is 267 vs. 45 mQ. The reason for these large dif- Fig. 4 illustrates a second, physiologically more relevant ferences is that Rn is determined by the input resistance of the consequence of the thin proximal dendrite: in this figure we cell body per se (Rs) in parallel with the resistances of the den- have computed the input resistance (Rn = 1/Gn) at several in- drites that emerge from the soma (16, 17). The comparatively dicated branching points. Again we have contrasted the com- large number of dendrites in starburst amacrines would ordi- narily imply alowRn, provided thatthe branching pattern showed C Site of Current Ine a conventional decrement in diameter. Alternatively, -the thin D SOMA A]~~ ~ ~ ~ ~ ~ BA process is an effective device for reducing the dendritic con- tribution to the impedance at the soma; in turn, a higher soma impedance is less shunting for the distal segments. In this way STARBURST AMACRINE it is possible for starburst amacrines to have a dense dendritic Table 2. Attenuation factors for steady-state voltage decay*

L--IOlp Process Attenuation for 6-6 1.lp Process first-order UL U.0 . process D. 30p Branch point Thin Thick I- Rm' 4000 OHMS -CM2 B 1.0 Ri = 70 OHMS-CM 1.0 E 0.6 A 1.004 1.004 D 1.2 2.2 t E 1.3 5.1 0.4. F 1.4 5.2 u.j G 1.4 5.3 Soma 25.6 9.4 0.2. El 166.7 9.9 F1 172.4 10.4 G, 176.7 10.6

(l.p vs Q.p Dia. The attenuation factors for voltage-decay at different branch points based on the analysis illustrated in Fig. 3. In this example, we con- FIG. 3. (Upper) Current injection into a model of a starburst ama- trasted a dendrite with a thin (0.1 pm) vs. thick (1.1 ,m) first-order crine. Two contrasting models were analyzed. Both model cells con- process while the otherbranchdiameters remained as indicatedin Fig. sisted of 15 dendrites, similar to the one analyzed in Fig. 1 and 2, con- 2A. Equal voltage injections were applied at branch B, and the atten- nected to a 11-pm-diameter (dia) cell body, with Rm and Ri values in- uation factors were calculated by using Eqs. 7 and 8. It is clear that dicated. The only difference-between the models was whether the first- voltage decay distal to the first-order process is quite different when orderprocess was 0.1 /m (o) or 1.1,im (A). (Lower) Plot ofrelative volt- the thick vs. thin segments are compared. Alsoforthe thin process, much age decay from the site of current injection (point B) into other regions greater attenuation is evident at the soma and to other dendrites. of the same dendrite as well as the soma and one of the other "silent" * Equal voltage inJections into a single branch point (see Fig. 2). Thin dendrites. For further explanation, see the text. process, 0.1-,um diameter; thick process, 1.1-,pm diameter. Downloaded by guest on September 27, 2021 Medical Sciences: Miller and Bloomfield Proc. Natl. Acad. Sci. USA 80 (1983) 3073

identical computations using a diameter of 0.2 ,um and find only |834 MOHMS small differences in the results. 4~~~~~~~~~~~~~~080 MOHMS 894 MOHMS Famiglietti (9) has suggested that starburst amacrines may be < ~ ~ 85 MOH 0.4- phological studies of single neurons is a powerful method for 0.2 the analysis of neuronal function. It is clear from these studies,

SOMA A B C however, that dendritic anatomy is influenced by controlling EQUAL CURRENT INJECTIONS mechanisms that have designs other than transferring charge (Starburst Amocrine Dend. *6: Robbit) from the periphery to the soma. The microanatomy of dendritic design and structure is an important aspect of neuronal function FIG. 4. (Upper) Input resistance values for different branch points that should receive greater attention in the future. calculatedforthethick (lowervalues) vs. thin (uppervalues)first-order process. The values atthe left give the computed inputresistance at the soma. (Lower) Consequence of the differences in input resistance be- t It is possible that we failed to see spikes because of injury inactivation tween the two different dendrites. In this case, an equal current is in- from cell penetration; however, when we see this phenomenon in other cells, we usually observe a brief as jected into branch C, and the voltage decay was calculated by using Eq. period of spiking the cell is de- 7 and 8. polarized, and we have not observed this phenomena in recordings from starburst neurons. tree and presumably engage in many synaptic contacts per unit We gratefully acknowledge the assistance of Judy Dodge for figure area, while permitting efficient synaptic operations along the illustrations and Rita Drochelman for typing. This research was sup- more distal dendritic segments. ported by National Institute Grant EY03014 awarded to R.F.M.; We have attempted to illustrate this in Fig. 4 by computing S.A.B. was supported by National Eye Institute Training Grant EY07507. the voltage that would result from an equal current injection (in R.F. M. was the grateful recipient of an award from the Research to contrast to the equal voltage injection of Fig. 3) into point C. Prevent Blindness. At a is each point along the dendrite, larger potential observed 1. Cajal, S. R. Y. (1972) The Structure of the Retina (Charles C. for the thin segment; at the soma, however, the absolute volt- Thomas, Springfield, IL). age is still larger for the thick vs. thin process. This method of 2. Boycott, B. B. & Wassle, H. J. (1974)J Physiol (London) 240, 397- illustration dramatizes the increased efficiency with which den- 419. drite synapses may communicate effectively within a dendrite 3. Famiglietti, E. V. & Kolb, H. (1976) Science 194, 193-195. that is distal to the constricted process. 4. Koch, C., Poggio, T. & Torres, V. (1982) Philos. Trans. R. Soc. London, Ser. B 298, 227-264. Famiglietti has pointed out (3) that the dendritic varicosities 5. Dowling, J. E. & Boycott, B. B. (1966) Proc. R. Soc. London, Ser. ofstarburst amacrines are confined to more distal dendrites (see B 166, 80-111. Fig. 1A). It is tempting to think that the. varicosities seen in 6. Rall, W. (1981) Neurones Without Impulses (Cambridge Univ. these dendrites represent the sites of synaptic interactions, al- Press, New York), pp. 223-254. though this important point requires verification with electron 7. Ellias, S. A. & Stevens, J. K. (1980) Brain Res. 196, 365-372. microscopy. Our calculations show that electrical communi- 8. Famiglietti, E. V. & Siegfried, E. C. (1980) Invest. Ophthalmol cation a Visual Sci. Suppl. 19, 70 (abstr.). within single dendrite is reasonably good (Fig. 2, right- 9. Famiglietti, E. V. (1983) Brain Res. 261, 138-144. hand graph). It is clear that if a single dendrite were synapti- 10. Miller, R. F., Slaughter, M. & Bloomfield, S. (1981) Invest. cally activated while the other dendrites were inactive, (i.e., Ophthamol. Vis. Sci. Suppl. 20, 45 (abstr.). less depolarized), then current spread from the active to in- 11. Dacheux, R. F., Delmelle, M., Miller, R. F. & Noell, W. K. (1973) active dendrites would be negligible. In fact, the model current Fed. Proc. Fed. Am. Soc. Exp. Biol 32, 327 (abstr.). injection in Fig. 2 was based on a potential applied at a single 12. Miller, R. F. & Dacheux, R. F. (1976) J. Gen. Physiol. 67, 639- point of one dendrite. However, if we opposite 659. consider the 13. Wann, D. F., Woolsey, T. A., Dierker, M. L. & Cowan, W. M. extreme, where all but one dendrite is activated, then the cur- (1973) IEEE Trans. Biomed. Eng. 20, 223-247. rent spreading from the active to the inactive dendrite is greater 14. Boycott, B. B. & Dowling, J. E. (1969) Philos. Trans. R. Soc. Lon- because it is no longer divided at the soma by a large number don, Ser. B 255, 109-184. of inactive dendrites. In other words, the question of the func- 15. Mesulam, M.-M. (1976)J. Histochem. Cytochem. 24, 1273-1280. tional subunit of an amacrine is partially a network question. 16. Rall, W. (1959) Exp. Neurol 1, 491-527. Are the starburst amacrine dendrites independently controlled 17. Rall, W. (1962) Ann. N.Y. Acad. Sci. 96, 1071-1092. 18. Bloomfield, S. A. (1981) Dissertation (Washington Univ., St. Louis, by different synaptic inputs or are many dendrites simulta- MO). neously activated? 19. Bloomfield, S. A. & Miller, R. F. (1982)J. Comp. Neurol. 208, 288- The dimension of the thin intermediate segment described 303. in this paper is beyond quantitative resolution capabilities of 20. Masland, R. H. & Mills, J. W. (1979)J. Cell Biol 83, 159-178. the light microscope. In addition, tissue shrinkage from his- 21. Vaney, D. I., Peichl, L. & Boycott, B. B. (1981)J. Comp. NeuroL tological processing will lead to an underestimate of diameter. 199, 373-392. 22. Masland, R. H. & Ames, A., III (1976)J. Neurophysiol 39, 1220- Although tissue shrinkage is probably a minor factor, it is worth 1235. asking whether there is a critical diameter for this thin segment 23. Ariel, M. & Daw, N. W. (1982)J. Physiol. (London) 324, 135-160. without which the computations are invalid. We have made 24. Ariel, M. & Daw, N. W. (1982)J. Physiol. (London) 324, 161-185. Downloaded by guest on September 27, 2021