a. reyes et al- passive properties of neostriatal neurons during potassium conductance blockade

8/3/2019 A. Reyes et al- Passive properties of neostriatal neurons during potassium conductance blockade

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Exp Brain Res (1998) 120:7084 Springer-Verlag 1998

R E S E A R C H A R T I C L E

A. Reyes E. Galarraga J. Flores-HernndezD. Tapia J. Bargas

Passive properties of neostriatal neurons during potassiumconductance blockade

Received: 30 April 1997 / Accepted: 14 October 1997

A. Reyes E. Galarraga J. Flores-Hernndez D. TapiaJ. Bargas ())Dept. Biofsica, Instituto de Fisiologa Celular,UNAM, PO Box 70253, Mexico DF 04510, Mexicoe-mail: [email protected]: 525-622-5670, Fax 525-622-5607,

A. ReyesInstituto de Ciencias BUAP, Puebla, Mexico

Abstract Voltage recordings from neostriatal projectionneurons were obtained using in vitro intracellular tech-niques before and during K+-conductance blockade. Neu-

rons were stained with the biocytin technique. Somaticsurface area (AS) was determined by both whole-cell re-cordings in isolated somata and by measuring stainedsomata recorded in slices. Dendritic measurements weredone in reconstructed neurons. Average determinationsof dendritic (AD) and neuronal (AN) surface areas coincid-ed with previously reported anatomical data. Thus: AS 6.5 106 cm2; AD 1.9 10

4 cm2; AN AD + AS 2 104 cm2; AD/AS 30. Measurements were done beforeand after superfusion with K+-conductance blockers (K+-blockers). Cells whose neuronal morphology was not ob-viously distorted by K+-blockade were chosen for thepresent study. Electrotonic transients were matched to asomatic shunt equivalent cylinder model adjusted withthe generalized correction factor (Fdga) that constrainsthe parameters for neuronal anatomy. Neuronal input re-sistance (RN; mean SEM) increased when it was cor-rected for somatic shunt, from 49 2 MW (n = 80) to179 7 MW (n = 32). A difference was also obtained be-tween the slowest time constant, t0 = 16 0.9 ms (n =49), and the dendritic membrane time constant, tmD =33 1.6 ms (n = 36). When these electrophysiologicalmeasurements were used to calculate AN, the value ob-tained was similar to the anatomical measurements. Com-bining anatomical and electrophysiological data, somaticand dendritic input resistances were determined: RD =182 7 MW; RS (with shunt) = 74 4 MW (n = 32).The generalized correction factor, Fdga = 0.91 0.007(n = 10), implied a short effective electrotonic lengthfor dendrites: LD = 0.46 0.014 (n = 32). Saturating con-

centrations of the K+-blockers tetraethylammonium, Cs+,and Ba2+ increased RN and induced charging curves wellfitted by single exponential functions in 56% of neostri-

atal neurons. Ba

2+

greatly decreased the somatic shunt(n = 5): (RN = 216 21 MW, t0 = 46 2 ms, RD = 239 25 MW, and RS = 3.2 0.5 GW), rendering values sim-ilar to those obtained with whole-cell recordings (e.g., RN 198 MW, RS 2.62 GW) (n = 52). Cs

+ (n = 5) had lesseffect on the somatic shunt (RN = 115 19 MW, t0 = 49 13 ms, RS = 161 8 MW), although dendritic conductancewas equally blocked (RD = 261 16 MW). The Cs

+-sensi-tive conductance exhibited inward rectifying propertiesnot displayed by the Ba2+-sensitive conductance, suggest-ing that Cs+ preferentially acted upon inward rectifierconductances. In contrast, Ba2+ significantly acted uponlinear conductances making up the somatic shunt. Thissuggests a differential action of different K+-blockers onthe somato-dendritic membrane, implying a differentialdistribution of membrane conductances. Another actionof K+-blockers, in about 40% of the cells, was to inducedye and probably electrical coupling between neighboringneurons.

Key words Neostriatum Cable properties Dye coupling Brain slices Potassium blockers

Introduction

Voltage-dependent and voltage-independent ionic con-ductances may be tonically active around the restingmembrane potential (RMP). Specific membrane resis-tance (Rm) may depend on these conductances, which inthis way would participate in the shaping of the electro-tonic structure (Nisenbaum and Wilson 1995; Karschinet al. 1996; Campbell and Rose 1997). In fact, K+-conduc-tance blockade affects neuronal passive properties (e.g.,Rapp et al. 1994; Bargas et al., 1988; Campbell and Rose1997). Moreover, in many cells Rm is not uniform over thesomato-dendritic membrane: Rm on the soma (RmS) maybe much lower than Rm on the dendrites (RmD); this gen-


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erates a somatic shunt of variable magnitude (e.g., Ian-sek and Redman 1973; Brown et al. 1981a,b; Durand etal. 1983; Rose and Vanner 1988; Clements and Redman1989; Holmes and Rall 1992; Major et al. 1993; Rappet al. 1994). Besides a differential density of tonically ac-tive ionic conductances on soma and dendrites, the somat-ic shunt may be explained by electrode injury, by ionicconductances activated in response to impalement, by a

higher inhibitory activity at the soma, or by a mixtureof causes (Durand et al. 1983; Clements and Redman1989; Rall et al. 1992; Spruston and Johnston 1992; Ma-jor et al. 1993). The relative contributions of these factorsmay change according to techniques employed and neuro-nal class recorded (Spruston and Johnston 1992; Staley etal. 1992; Major et al. 1994; Campbell and Rose 1997), thesomatic shunt being reduced by gigaseal (whole-cell) re-cordings. The purpose of the present work was to investi-gate the contribution of tonically active ionic conductanc-es, particularly K+-conductances, to the somatic shunt ex-hibited by medium spiny neostriatal projection neuronsduring sharp electrode recordings.

To accomplish this goal, the overall electrotonic struc-ture of medium spiny neurons was estimated with the useof the somatic shunt equivalent cylinder model (Durand1984; Kawato 1984) that takes into account and correctsfor the somatic shunt. Then, the somatic shunt was eval-uated in the presence or absence of K+-conductanceblockers.

The somatic shunt E-C model assumes that dendriticarchitecture obeys certain rules, e.g., the three halvespower law (Rall 1977). Thus, application of this modelto experimental data obtained from cells that do not havethe architectural features of the somatic shunt E-C modelmay invalidate estimates of cable properties based on thismodel. However, a generalized correction factor (F

dga)

has recently been proposed from which an effective den-dritic electrotonic length (LD), valid for any dendritic ar-chitecture, can be obtained (Rall et al. 1992). This factoris constrained by anatomical data and, therefore, the val-ues of electrotonic structure obtained after application ofFdga are not limited by dendritic geometry (Rall et al.1992). Under these circumstances, the somatic shunt E-C model can be used to obtain a meaningful interpretationof the actions of K+-blockers on electrotonic structure(Holmes and Rall 1992; Rall et al. 1992). Therefore, thesomatic shunt E-C model adjusted by Fdgawas used to in-terpret the present experimental data. The results indicatethat tonically active ionic conductances contribute to thesomatic shunt in medium spiny neurons. Moreover, dif-ferent K+-blockers have differential blocking actions uponthe somato-dendritic membrane. In addition, it was foundthat one action of K+-blockers was to increase the proba-bility of dye and probably electrical coupling betweenneighboring neurons. A preliminary report of these datahas been presented previously (Reyes et al. 1995).

Materials and methods

Intracellular recordings

Intracellular recordings were done in vitro on adult rat brain slicescontaining the neostriatum. Our protocol has been described previ-ously (e.g., Bargas et al. 1988). It follows the Principles of labora-tory animal care (NIH publication no. 86-23, revised 1985): adult(b 3 months) Wistar rats of either sex were anesthetized and decap-itated. Parasagittal neostriatal slices (400 mm) were recorded in a

bathing solution with (in mM): 125 NaCl, 3.0 KCl, 1.0 MgCl2,2.0 CaCl2, 25 NaHCO3 and 11 glucose (saturated with 95% O2and 5% CO2for pH = 7.4; 290 mosmol/l; 3234C). Five to twentymillimolar tetraethylammonium chloride (TEA), 2.55 mM cesiumchloride (Cs+) or 15 mM of barium chloride (Ba2+) (all from Sig-ma) equimolarly substituted a part of the NaCl in some experiments.

Intracellular recordings were carried out with micropipettesfilled with either biocytin (Sigma, 12%) in 3 M potassium acetateor 3 M potassium acetate alone. Electrode d.c. resistances rangedfrom 80 to 120 MW. Records were obtained with a high input imped-ance electrometer with an active bridge circuit (Neurodata) usingstandard techniques. After recording the RMP and neuronal input re-sistance (RN) (approximately 75 mV and 3050 MW respectively;Galarraga et al. 1994), 10 min or more of continuous recording with-out any manipulation were done as a control. Afterwards, I-V plotsand electrotonic transients 15 mV hyperpolarized with respect to

the resting potential were recorded before and during the superfu-sion with K+-conductance blockers: Cs+, TEA, or Ba2+ (see above).Exchange within the recording chamber was complete in about 2min. RN was monitored continuously. K

+-blockers produced a depo-larization (27 mV) that was corrected with d.c. current, so that orig-inal RMP was maintained during the duration of the experiment.

Whole-cell recordings

Whole-cell clamp recordings were done on acutely dissociated adultneostriatal somata (see Methods in Bargas et al. 1994). This wasdone in order to have an independent method for estimating somaticcapacitance and somatic surface area (CS, AS, respectively). Briefly,two or three slices at a time were incubated in bathing saline (seeabove) for 30 min in the presence of pronase (13 mg/ml). Thereaf-

ter slices were rinsed several times with a low-Ca2+

(200 mM)HEPES-buffered saline (see below). Cells were mechanically disso-ciated with fire-polished Pasteur pipettes. The cell suspension wasthen plated on a plastic Petri dish and mounted on the stage of aninverted microscope. Recordings used whole-cell standard tech-niques (Hamill et al. 1981). External solution was (in mM): 140NaCl, 3 KCl, 2 MgCl2, 2 CaCl2, 10 HEPES, 10 glucose and 0.001tetrodotoxin (TTX), and flowed over the plated cells at a rate of 1ml/min. Electrodes were made from borosylicate glass and afterfire-polishing achieved a d.c. resistance of 36 M W. Internal solu-tion was (in mM): 115 KH2PO4, 2 MgCl2, 10 HEPES, 1.1 EGTA,2 Na2ATP, and 0.2 Na3GTP.

Recordings were obtained with an Axopatch 1-D amplifier andcontrolled and monitored with a PC-clone computer runningpClamp (v. 5.0) with a 125 kHz DMA interface (Axon Ins). Cellschosen for recordings were medium-sized somata (major diameter

614 mm) that possessed only a few or no dendritic stumps. Seriesresistance (715 MW) was compensated 80%. Current responses tosmall voltage commands from 115 to 70 mV in 10-mV steps,from a holding potential of 90 mV, were done to obtain somaticinput resistance (RS). In the present experimental conditions no ac-tive currents were detected in this voltage range and only small leakcurrents were present (Fig. 1). Subthreshold current traces weretime-averaged with the aid of Clampfit software (pClamp) and theseaverage responses were used to determine current-voltage (I-V) re-lationships. Figure 1A shows that these values are well fitted by astraight line. No sign of inward rectification was seen in these con-ditions ( 15 pA). Thus no error compensation for series resistancewas applied. Since inward rectification is a common finding in slices(e.g., Galarraga et al. 1994; Nisenbaum and Wilson 1995), and was


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not seen in the present experiments, it was concluded that thesewhole-cell clamp conditions did not favor the appearance of somesubthreshold conductances present during intracellular recordings.By integrating the capacitative transients of the smallest current re-cords (by using Clampfit; Fig. 1B), whole somatic capacitance (CS)was obtained (Yan and Surmeier 1996). CS can be used to obtain so-matic surface area (AS) (equation B2, Appendix B). In most cases,the resistive component was very small and it was not subtracted.This may explain the tail in the distribution of Fig. 1D. However,the integration method (n = 144) roughly coincided with capacitancecompensated during recording and with capacitance calculated withthe use of AS (equation B2, Appendix B; see below and Fig. 1C).

Data processing

Several voltage records of electrotonic transients after step currentstimuli were digitized and averaged. Records with spontaneous syn-aptic potentials or obvious distortions were discarded. Obtained av-erage records were also filtered and differentiated. Digitization wasdone at 40 kHz and the records stored on tape. Tapes were playedoff-line and records displayed one by one at high magnificationon a 486 PC-clone using software designed in the laboratory inthe LabView environment (National Ins.). Neuronal input resistance(RN) was obtained with the slope of the I-V relationship at the volt-age where the transient was obtained (Fig. 2A; see Galarraga et al.

1994). As previously reported (Burke et al. 1994; Rapp et al. 1994),

it was seen that main parameters obtained with fitting did not differsignificantly after the average included 1525 chosen records. Giventhe impedance of the sharp electrodes (up to 120 MW) we chose toanalyze charge transients after long current pulses. Therefore, for-mulations for long step responses were used to fit the transientsand their derivatives (e.g., Holmes and Rall 1992; Rall et al.1992). Experimental and averaged electrotonic transients were fittedto equation A1 and their derivatives to equation A2 (see Appendix Aand Fig. 2A) to obtain the exponential coefficients and time con-stants (C0, C1, t0, t1peel ; see Appendix A). Fitting used nonlinear re-gression, i.e., the Marquardt-Levenberg algorithm (Marquardt 1963;SigmaPlot, Jandel). This nonlinear regression software provides es-timation errors and 95% confidence limits; it has been used before,with success, on electrotonic transients (Campbell and Rose 1997).It finds the parameter values that minimize the sum of the squareddifferences between the observed and predicted values. A fit was

considered acceptable when the norm of the residuals (square rootof the sum of squares of the residuals), from one iteration to thenext, was less than the tolerance value (0.0001). A fit was rejectedwhen the fits between subsamples of the same data yielded signifi-cant differences (P b 0.05), or when a change in the fit intervalchanged the output. The fit interval was normally chosen between550 ms and 20 ms. After K+-blockers this interval varies and couldbe longer (normally set up to 15% before steady state). Exponentialpeeling was sometimes used to provide initial values to begin the it-eration. The coefficients and time constants obtained could be usedto get a rough approximation of Lpeel (equation A3, Appendix A).This overestimated value of the electrotonic length sets an upperlimit (Rall et al. 1992) and can be compared with those obtained pre-viously in several types of neurons.

Filtering used the adjacent averaging method, protecting theextremes of the records with a variant of the cosine window tech-

nique (Press et al. 1986; Dempster 1993). Therefore, filtering did notdistort the records (Fig. 3). This was checked by doing the analysisin both just averaged and averaged, filtered and differentiated re-cords. Also, the results obtained with subsamples of records werecompared between them and with the results from the complete sam-ple. Normally these manipulations gave the same results; if signifi-cant differences were found, data were discarded.

Differentiation was done in order to better emphasize the expo-nential components in case they were present (Jack et al. 1975; Rall1977; Johnston 1981; Brown et al. 1981a,b). Since the objective ofthis work is to make evident the changes on charge transients in-duced by K+-blockers, and since the changes detected were so large(see Results), it was decided that this data management was suffi-cient for the purposes of the present experiments.

Fig. 1A, B Measurement of somatic input resistance (RS) and so-

matic surface area (AS). A RS was calculated as the slope of the lin-ear I-V plot at subthreshold membrane potentials (see straight line).Holding potential was 85 mV and membrane current was recordedafter 15-mV command steps from 115 to 10 mV in 1 mM tetrodo-toxin (TTX). Note the voltage-dependent outward currents at mem-brane potentials more positive than 50 mV and absence of activecurrents at negative potentials where RS was obtained. B Somatic ca-pacitance (CS) was calculated by integrating capacitative transientsgenerated by a 10-mV command pulse from a holding potential of85 mV (current step not shown). The time integral of transient cur-rent is (arrows signal times 0 and t): CS %

t0IdtaV, where V is the

amplitude of the voltage command. The transient generated by elec-trode capacitance was compensated during on-cell patch just beforebreaking the seal to get the whole-cell configuration. C AS distribu-tion from anatomical measurements of filled somata from neuronsreconstructed with the biocytin technique. D AS distribution from

CS values obtained by integration of capacitative transients duringwhole-cell voltage-clamp recordings in isolated somata


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Anatomical measurements

Neurons were injected with biocytin using the method described byHorikawa and Armstrong (1988). Slices containing injected neuronswere fixed overnight in 4% paraformaldehyde, 1% picric acid in 0.1M phosphate buffer (pH 7.4). The slices were then infiltrated with30% sucrose and cut on a vibratome into 60-mm sections. The sec-tions were incubated for 24 h in a phosphate buffer solution con-taining 0.2 Triton X-100, avidin, and biotinylated horseradish perox-idase (ABC-HRP, Vectors ABC kit) for 2 h and then reacted withdiaminobenzidine and hydrogen peroxide (H2O2) to visualize thebound HRP. This enabled resolution of the intracellularly labeledprocesses through trans-illumination microscopy. Some recordedneurons were reconstructed using a camera lucida. In this work maindendritic trunks, and minor and major somata diameters, were mea-sured in order to check for anatomical distortions after K+-blockade.Thereafter, equation B1 (Appendix B) was used to calculate AS (Fig.1C) and equation B2 (Appendix B) was used to calculate CS from

the AS value. Therefore, with anatomical measurements of AS, CScould be calculated and, vice versa, with whole-cell records (seeabove) CS could be obtained and thereafter AS could be calculated.By comparing Figs. 1C and D it can be seen that the two methodscoincide (there is no statistical difference). Neurons showing anytype of abnormal morphology or biocytin leakage were discarded.

In addition, equation B3 (Appendix B) allows the determinationof the whole neuronal surface area (AN) by mixing electrophysiolog-ical and anatomical data. Therefore, if we had an independent ana-tomical measurement of AN, equation B3 becomes a constraint forelectrophysiological or model derived values, i.e., only correct val-ues of tm, RN (corrected for shunt), Fdga, and L would yield a good

AN approximation. Fortunately, average AN for projection neostriatalneurons has been reported by Wilson (1992) using high-voltageelectron microscopy. The definite integral of his figure 4 (Wilson1992) yields average AD 1.98 10

4 cm2 and, thus the sum of

mean AS (Fig. 1C, D) and AD (Wilson 1992) values yields an averageAN 2 10

4 cm2 (about 20000 mm2). Since this average value can-not easily be improved with other microscopical techniques, it wasused as a reference in the present work. However, this is an averagevalue representative of the medium spiny population. Therefore, itcan only be used with average values of tm, L, and Fdga (equationB3, Appendix B) taken from a sample of neurons (see below). None-theless, average electrophysiological and anatomical data may de-fine an average profile of medium spiny neurons electrotonic struc-ture (since the match includes mean tm and L) when equation B3 isfulfilled. Needless to say, RN directly obtained from the experiments(not corrected for the somatic shunt), t0 obtained from a direct fit-ting of equations A1 and A2 to the experimental records, and Lpeelobtained from equation A3 could not match the average AN value

obtained with anatomical methods. This shows that the original E-C model (Rall 1977) cannot be matched without correcting for so-

matic shunt and dendritic morphology. Therefore, in order to obtainmore accurate values for RN, Land tm, the corrections for the somat-ic shunt introduced by Durand (1984) and Kawato (1984) had to beused. Furthermore, the adjustments and the generalized correctionfactor (Fdga) provided by Rall et al. (1992), which are independentof dendritic architecture, were also applied (see next section).

On the other hand, Wilson (1992) has also shown that dendriticspine surface represents about halfAD. Therefore, a rough approxi-mation ofAD could be acquired from dendrograms. These were builtfrom calibrated neuronal reconstructions magnified and projected onto a screen. Dendritic lengths were measured from these projectionsand dendritic diameters were measured with an oil-immersion 100objective every 2030 mm (n = 3). The spine surface was added ac-cording to Wilsons measurements. The neurons selected had beensuperfused with high concentrations of K+-blockers. Nevertheless,this independent measurement coincided well with Wilsons average

AD (1.8 104 cm2). This shows that the anatomical measurementsof cells in high concentrations of K+ blockers were not substantiallydifferent from those recorded in more physiological solutions.

Finally, RN and membrane time constant comparable to those re-ported by others using whole-cell recordings in slices (e.g., Kawagu-chi 1993) could be obtained in the presence of 5 mM Ba2+ (see Re-sults). Therefore, several independent tests suggested that the mor-phology of the chosen medium spiny neurons was not appreciablymodified by the present methods. Additionally, average AN valuescould be obtained that matched values previously reported by inde-pendent investigators (Chang et al. 1982; Wilson 1990, 1992). Thisreinforced the view that equation B3 could be used to test averageelectrophysiological values obtained after matching the somaticshunt E-C model to the experimental transients of a sample of neu-rons.

Correcting passive parameters for somatic shunt

The block diagram shown in Fig. 2 summarizes the method of anal-ysis. The formulations used at each block are listed in the Appendi-ces. As stated in the above sections, exponential parameters from theexperimental charge transients (C0, C1, t0, t1) were obtained by fit-ting the recordings to equations described in Appendix A (Fig. 2A).Also, average anatomical measurements were obtained from recon-structed biocytin-stained neurons, from whole-cell recordings of dis-sociated somata, and from previously reported anatomical data (Fig.2B).

Thereafter, parameters obtained with the fitting of chargingcurves (equations A1, A2) were used as initial values to match the

Fig. 2AD Analysis of voltagetransients. Each block is fullyexplained in the Appendices


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somatic shunt E-C model to the experimental records (equation C1,Appendix C; Fig. 2C) (Durand 1984). The match was done by min-imizing the difference between experimental exponential coeffi-cients (Ci) and the theoretical exponential coefficients (CiT) givenby the model and defined by equations C2 and C3 (Appendix C)(Rose and Dagum 1988; White et al. 1992). This difference (equa-tion C10, Appendix C) had to be less than 1 105 to consider thatthe match was accomplished (Appendix C). In practice, to do this

match, equations C3 to C9 (Appendix C) had to be solved iterativelyand simultaneously after initial values had been given. This wasdone by using the equation-solving software Eureka (Borland). Thissoftware provides a variable number of iterations and modules toverify the solutions and estimation errors. In many cases (Fig. 3),the output of the model (continuous line in Fig. 3; equation C1) fit-ted the data points and remained well inside the 95% confidence in-terval of the exponential fitting (equation A1). Some constraintswere helpful in order to match the model, e.g.: a0 ` a1; Lb 0 ; rb 0 ; tmS ` t0 `tmD (Durand 1984; White et al. 1992). The match-ing of the model to the experimental transients yielded approxima-tions of tmD, L, e, and r (equations C19; Appendix C). e is an es-timation of the somatic shunt. tmD variations outside a small rangeimpeded the matching of the model to the experimental records.As expected, equations for the original E-C model with uniform

Rm (without a shunt) (Rall 1977) could never fit the experimental da-

ta. According to Kawato (1984) this model can only be fitted if k`2 and e = 1 (equations C39 in Appendix C; e.g., Tsukahara et al.1975; Brown et al. 1981b; Durand 1984; Kawato 1984; Bargas etal. 1988; Rose and Vanner 1988; Holmes and Rall 1992; Holmeset al. 1992; White et al. 1992). However, average kb 2 in the pres-ent sample of neostriatal neurons (Table 1).

It appeared that tmD approximation (and not L) was the mostvaluable piece of data yielded by the fitting of the somatic shuntE-C model, since according to Holmes and Rall (1992), dendriticbranches ending at different lengths and a dendritic architecture thatdoes not obey the d3/2 constraint (Rall 1977; Rall et al. 1992; Holmesand Rall 1992) may greatly overestimate L value. Moreover, tmD ap-proximations generated reasonable initial approximations for RmDand RD, specific membrane resistance and input resistance of the

dendritic arbor, respectively (equations D13 in Appendix D; Cm= 1 mF/cm2; Fig. 2). These values yielded estimations of AD in therange of that obtained by several independent methods (see aboveand Results).

Correcting passive parameters for dendritic architecture

The approximations obtained with the matching of the somatic shuntE-C model were then corrected for dendritic architecture. This im-plied finding a generalized correction factor (Fdga) valid for any den-dritic architecture (even those dendritic trees not obeying the d3/2

constraint or with branches of different lengths) and, thereafter, aneffective electrotonic length for the dendritic tree (LD), whateverits morphology (Rall et al. 1992). To do this, equations D16 (Ap-pendix D; Fig. 2E) were solved simultaneously using Eureka (Bor-land). An error larger than 1 10 5 for any of the estimated param-eters (as seen with the error estimation module of Eureka) discardedthe data. Thus, a solution was accepted when all parameters had er-rors less than this. However, if a parameters error was maintained at1 105 without a change when some of the other parameters werefixed, it was also discarded. The initial values to begin the iterativeprocedure are, on the one hand, the values obtained from the match-ing of somatic shunt E-C model (tmD, L, e and r) (Appendix C), and,

on the other hand, the anatomical values obtained by different tech-niques (Appendix B) (see above). These procedures provided andadjusted (constrained with anatomy) several parameters, either fora given neuron, or, when using average values, for a sample of neu-rons. These values are (see Appendix D): b (somatic shunt magni-tude; equation D1 in Appendix D), RS (somatic input resistance;equations D1, D2), RD (dendritic input resistance; equations D2,D3, D5), rb = 1 (a somatic shunt-independent constant that approxi-mates r in the case without shunt; equation D3), the generalized cor-rection factor, Fdga (equation D4), which allows the determination ofan effective dendritic electrotonic length (LD) that is independent ofdendritic geometry (Rall et al. 1992), and, finally, an approximationof the whole input resistance of the neuron after correcting for thesomatic shunt (RN no-shunt; equation D6).

Fig. 3AC Matching electro-tonic transients to the somaticshunt E-C model. A Filled cir-cles are the filtered average of20 records such as the oneshown in the inset. Continuousline is the model fit. Dashedlines indicate the 95% confi-dence interval. Semilogarithmicscales (top right) illustrate an

exponential peeling on the av-eraged record to show that morethan one exponential componentis present in control saline. Pa-rameters were extracted using adirect nonlinear fitting of themodel that uses initial valuesobtained by a nonlinear fittingof a sum of exponentials to theexperimental transient (see Ap-pendices). Transients averagedand filtered in this way are il-lustrated in Fig. 5. Both Lpeel (B)and RN (C) had a tendency toaggregate normally


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Statistical analysis

Since control and test conditions were compared in the same cells,the observations mainly have a comparative value, i.e., what a K+-blocker does to the electrotonic transient, RN, RS, etc. Thus, directmeasurements and model-derived parameters were compared inthe same cell samples with Wilcoxons T tests. Mann-WhitneysU-test was used when comparing the sample in control saline withsmaller samples in K+-blockers. Probability obtained from nonpara-metric statistics as well as mean, range and standard error of the

mean are reported (Tables 12).

Results

Determination of RS and AS

Whole-cell recordings from medium-sized cell bodies dis-sociated from neostriatal slices are shown in Fig. 1. A lin-ear current-voltage relationship (I-V plot) is obtained at avoltage range normally seen as subthreshold (Fig. 1A;see Materials and methods). Thus, inward rectificationis lost with commonly used intracellular solutions (Fakler

et al. 1995). Since the present work on somata did not tryto recover all subthreshold conductances present in theseneurons (Galarraga et al. 1994; Nisenbaum and Wilson1995), mean input resistance (RS) of acutely dissociatedsomata was (mean SEM): 2.62 0.32 GW (range0.7610 GW; median 1.77 GW; n = 52), which can be tak-en as an upper limit after cell dialysis. Records in Fig. 1were taken without K+-conductance blockers in either theintra- or extracellular solutions. TTX does not changesubthreshold RN (Galarraga et al. 1994). Figure 1B illus-trates a whole-cell current transient used to calculateCS. Definite integral included the trace bounded by the ar-rows. Mean CS was: 6.7 0.3 pF (n = 144), which yields amean A

Sof approximately 6.7 106 cm2 (Fig. 1D). It has

been shown that this mean somatic size corresponds to thesize of medium spiny projection neurons (Yan and Sur-

meier 1996). This was further corroborated by somaticmeasurements of biocytin-filled neostriatal neurons re-corded in slices (Fig. 1C). Since somata diameters of bothcontrol neurons and neurons treated with K+-blockers didnot show any significant difference, the AS measurementsfrom both samples were pooled. Note that these model-in-dependent results yield a striking agreement betweenwhole-cell and sharp-electrode recording methods (cf.

Fig. 1C and D). Therefore, each method validates the oth-er.

Electrotonic transients and RN correctedfor the somatic shunt

An averaged passive response is illustrated in Fig. 3. Theinset shows an actual record. Straight lines in the semilog-arithmic scale at the upper corner right-hand are the resultof exponential peeling (Rall 1977). Peeling demonstratesthat transients are not monoexponential. The longeststraight line was obtained after linearly fitting a late part

of the transient (between 15 and 20 ms). The exponentialparameters obtained from each neuron involved nonlinearfitting between 550 ms and 20 ms (see Materials andmethods; and: Durand 1984; Kawato 1984; Rose and Da-gum 1988; Holmes and Rall 1992; White et al. 1992;Campbell and Rose 1997). Data points are the filled cir-cles (after averaging and filtering). The fitting of the so-matic shunt E-C model is the continuous line displayedin linear scale (see Materials and methods and equationC1, Appendix C). Dashed lines show the 95% confidenceinterval of the exponential fitting (equation A1, AppendixA). Thus, the model function is inside the confidence in-terval for the exponential fit.

Table 1 shows average results of these fittings in a setof neurons in control saline, i.e., exponential coefficients(C0, C1) and time constants (t0, t1peel), and, in addition,

Table 1 Mean electrophysiological and anatomical data. The sec-ond and sixth rows show mean SEM values for parameters indi-cated in first and fifth rows. RN was taken at RMP (84 3 mV;n=74) from IV plots (Galarraga et al. 1994). The first two exponen-tial parameters (C0, C1, t0 and t1peel) were extracted from nonlinearfitting of the experimental transients. C0 and C1 were normalizedwith VF=1 (see equation 1) in order to be compared. The experimen-tal values (in mV) were used to fit the transients directly to the so-matic shunt E-C model (see Appendices). Note tmDbt0, AN is sim-ilar to AN obtained by anatomical methods (e.g., Wilson 1992;

AN=2.1104 cm2), RN (no shunt) (RN without shunt) is similar

to RN obtained in whole-cell conditions (Kawaguchi 1993), and RS(with shunt) (RS obtained with whole-cell recordings in isolatedsomata. Mean AS (6.510

6 cm2) is an intermediate value betweenthat found with 144 somata recorded in whole-cell conditions and44 cells filled with biocytin. Mean values were obtained from sam-ples of neurons in which anatomical (e.g., AS) and/or electrophysio-logical (e.g., tmD, RN) data were obtained. Only in ten neurons wasan AD approximation also available. These ten neurons were used toapproximate mean Fdga and rb. Also, ranges in the bottom row aretaken from this subsample of neurons

RN (MW) C0 t0 (ms) tmD (ms) C1 t1peel (ms) k b r LD

492.2 0.590.02 160.9 331.6 0.410.02 3.60.3 3.250.23 775 0.410.02 0.460.014n=80 n=50 n=49 n=36 n=49 n=49 n=36 n=32 n=32 n=3218112 0.250.93 6.633.8 2843 0.070.75 0.89.1 0.256.65 40157 0.170.72 0.350.61

rb=rb=1 Fdga RN (MW)(no shunt)

RS (MW) RD (MW) AN (104 cm2) AD (10

4 cm2) AS (106 cm2)

280.2 0.910.007 1797 744 1827 1.850.07 1.80.06 6.50.27n=10 n=10 n=32 n=32 n=32 n=32 n=32 n=144; 442729 0.890.95 119276 34122 123287 1.32.6 1.22.5 311


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the dendritic membrane time constant tmD obtained fromthe matching of the somatic shunt E-C model (Durand1984). RN was obtained from I-V plots (Fig. 4; Galarragaet al. 1994). RN and Lpeel (Rall et al. 1992) are measuresthat distribute normally (Fig. 3B, C). The present valuesare similar to those reported previously for these neurons(Bargas et al. 1988).

tmD can be used to approximate RmD (Cm = 1 mF/cm2).

Other outputs from the somatic shunt E-C model (Durand1984) are L, r and e. Anatomical measurements (AD andAS) were used to adjust these initial input values by simul-taneously solving the equations of Appendix D (see Fig. 2and Materials and methods). The solution of these equa-tions yields values for RD, RS, the shunt magnitude b,the somatic-shunt-independent constant, rb (Holmes andRall 1992; Rall et al. 1992), the generalized correctionfactor Fdga, the effective electrotonic length of the den-drites (LD), and the mean input resistance after correctingfor the somatic shunt (RN no-shunt) (Table 1). Since equa-tions in Appendix D are solved simultaneously and in-clude anatomical values, Fdga and LD values are indepen-

dent of the geometrical restrictions of the original E-Cmodel (Rall et al. 1992). In these conditions, LD turnedto be rather short, about 0.5. Note that this value underes-timates Lavg a little (Rall et al. 1992) and does not take thesoma into account.

In most neurons, AS was known but AD was not; thus,mean AD determined anatomically was used to begin theiterations. In three neurons a complete dendrogram waspossible (see Materials and methods), and in other eightneurons a less precise anatomical approximation of ADwas available with the aid of mean dendritic lengthsand diameters. In any case, the A

Dvalue was used as an

initial value, which, together with AS measurements andcomplete electrophysiological data adjusted with the so-matic shunt E-C model, was used to calculate Fdga andrb. The range of these values illustrated in Table 1 wascalculated with the subsample of neurons (n = 10) withbest AD approximations. The range for Fdgaobtained fromthis subsample encompasses the average value obtainedwith a larger neuronal sample from which only the AS val-ue was known (i.e., 0.93 0.004; n = 32).

The values obtained with equations in Appendix D areenough to approximate average AN by using equation B3in Appendix B. AD might be an output of the equations inAppendix D (if it is not fixed and its value is initiated withmean AD obtained anatomically). Also, equation B3 canbe used to obtain AD if tmD and RD are used. In any case,

AD was set to accomplish: AN AS. The value of AN cal-culated with data in Table 1 (tmD, RN no-shunt, LD) andequation B3 was similar to that obtained with previousanatomical measurements, e.g., high-voltage electron mi-croscopy (Wilson 1992). Furthermore, this value re-mained in the same range after experimental proceduresthat reduced the somatic shunt (K+-blockers; see belowand Table 2). Taken together, these results greatly validat-ed the present procedure. Moreover, RN corrected for the

Fig. 4AC Actions of K+-blockers on RN. A Actions of tetraethyl-ammonium (TEA). B Actions of Ba2+. C Actions of Cs+. Transmem-brane potential records obtained from neostriatal projection neuronsin response to depolarizing and hyperpolarizing intracellular currentsteps in control saline (column 1) and saline containing a K+-blocker(column 2) (current on top, voltage on bottom; the same cells are il-lustrated in both conditions). The I-V plots constructed with recordsin columns 1 and 2 are depicted in column 3. Note the increase in RNduring TEA and Ba2+ for the whole subthreshold voltage range (A3,B3). Cs+ changed RN only in the hyperpolarizing direction (C3).Continuous lines are polynomial fits. Column 4 shows the subtrac-tion between I-V plot fits (K+-blocker control): the result is an al-most straight line between near 100 mV to near 50 mV for bothTEA and Ba2+. In the case of Cs+ the subtraction revealed that the

Cs+-sensitive conductance was inwardly rectifying. Voltage scalefor all frames, except C2, is that of B1. Time scale is in C1


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somatic shunt (RN no-shunt; Table 1) approached RNmeasured by whole-cell recordings (Kawaguchi 1993;RN 198 MW) and was significantly different (P `0.001) than RN obtained directly from the I-V plot (Table1). This fact provides another independent validation.

The RS estimate, with the shunt, is much lower than theRS obtained by whole-cell recordings in isolated somata(Table 1). Hence, b 77, r ` 1 and kb 2 are justified(e.g., Brown et al. 1981a,b; Johnston 1981; Durand1984; Kawato 1984; Bargas et al. 1988; Rose and Dagum1988).

The action of K+-blockers on RN

As shown in Fig. 4, all K+-blockers significantly in-creased RN with respect to RN found in control saline (Ta-ble 2; P ` 0.003, P ` 0.001 and P ` 0.001 for TEA, Ba2+

and Cs+, respectively). The order of potency was: Ba2+ bCs+

bTEA (Fig. 4, Table 2, R

N). In fact, R

NBa2+ was

similar to RN reported with whole-cell recordings (Ka-waguchi 1993) and RN corrected for the shunt (RN no-shunt, Table 1) in control saline. Column 3 of Fig. 4 illus-trates I-V plots taken from medium spiny neurons beforeand during K+-blockers. While TEA and Ba2+ affected thewhole subthreshold voltage range, Cs+ only affected re-sponses in the most hyperpolarized range. I-V plots dur-ing TEA or Ba2+ cross their respective I-V plots in controlsaline (i.e., near the K+ equilibrium potential; Pacheco-Cano et al. 1996). I-V plots before and during Cs+ donot cross, but proceed together during part of the trajecto-ry (Fig. 4C3): RN obtained from Cs

+ I-V plots between 80 and 65 mV was 51 5 MW (n = 5), which is not sig-nificantly different from RN measured in control saline(Table 1) (Galarraga et al. 1994). Subtraction of I-V plots(Fig. 4, column 4) suggests that the Cs+-sensitive conduc-tance exhibits inward rectification (Galarraga et al. 1994;Nisenbaum and Wilson 1995) while TEA and Ba2+ main-ly affect linear conductances. This suggests that, at thepresent concentrations, Ba2+ effects on linear conductanc-es overwhelm Ba2+ actions on inward rectification andnonlinear conductances normally attained at lower con-centrations. Thus, these experiments show that differentK+-blockers had different actions upon the subthreshold

passive membrane, suggesting that different K+-conduc-tances may contribute to Rm at the resting membrane po-tential. Other K+-blockers (4-AP, dendrotoxin, charybdo-toxin, and apamin) did not affect subthreshold voltage-re-sponses and subthreshold RN (not shown but see Pineda et

al. 1992; Galarraga et al. 1994; Nisenbaum and Wilson1995). Note that these actions of K+-blockers on sub-threshold RN are experimental results independent of theassumptions of the model.

The action of K+-blockers on time constants

The first column of Fig. 5 illustrates neurons reconstruct-ed after several minutes of superfusion with K+-blockers.Roughly, their morphology does not obviously differ fromthat reported previously in both in vivo and in vitro stud-ies (e.g. Wilson 1990, 1992). In all reconstructed neurons,at least one dendrite differed more than 20% in lengthfrom the others. Column 2 in Fig. 5 illustrates averagedand normalized charge transients of the same neurons be-fore and during K+-blockers. The charge transients duringK+-blockers (in isolated, not coupled neurons; see below)could be well fitted by single exponential functions (Fig.5, column 3), even when the fitting was done on differen-tiated records (Fig. 5, column 4). Thus, equalizing timeconstants could not reliably be discerned in the presenceof K+-blockers, suggesting that they are small comparedwith t0. Changes in t0 for Ba

2+ and Cs+ were significantcompared with t0 in control saline (P ` 0.001 and P `0.01, respectively). Thus, t0 values in Ba

2+ and Cs+ be-come similar to tmD (corrected for somatic shunt; Table1). In fact, t0 in Ba

2+ is significantly larger than tmD (P` 0.001). Since the morphological features of the neuronswere not obviously altered, these experimental resultssuggest that the electrotonic length (L), as seen from thesoma recording site, has become more compact duringK+-blockers. In fact, LD was significantly different fromthat obtained in control saline: 0.26 0.05 (in Ba2+);0.27 0.01 (in Cs+) and 0.36 0.04 (in TEA) (cf. LD =0.46 in control saline; which means: P ` 0.001, P `0.001, and P ` 0.04 for Ba2+, Cs+ and TEA, respectively).This shows that K+-blockade reduces the effective elec-trotonic length of the dendrites.

Table 2 Action of K+-blockers on dendrosomatic input resistanceand somatic shunt. MeanSEM estimates of passive parameters in-dicated in the first row were extracted from experimental electroton-ic transients recorded in saline containing the K+-blocker indicated

in the first column. More than one exponential component cannotbe obtained in the presence of K+-blockers. b, RD, RS and AN wereobtained as described in the Appendices. Values in Cs+ were ob-tained at hyperpolarized membrane potentials

Treatment RN (MW) C0 t0 (ms) b RD (MW) RS (MW) AN(104 cm2)

TEA (10 mM) 7810.2 0.990.003 151.2 379 17013 19764 1.90.1n 9 9 9 5 5 5 5Range 54147 0.991.0 1318 1969 147219 101450 1.72.3

Ba2+ (5 mM) 20727 0.960.01 462 96 21930 3.20.5 (GW) 1.80.2n 5 5 5 5 5 5 5Range 142289 0.931.0 4250 1.334 147290 2.24.7 (GW) 1.42.2

Cs+ (5 mM) 11519 0.960.014 4913 463 26116 1618 1.90.2n 5 5 5 5 5 5 5Range 77186 0.951.0 2264 3754 219318 135177 1.62.4


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The blocking action was concentration-dependent(e.g., Fig. 5A2). Lower concentrations of blockers (e.g.,in 5 mM TEA; Fig. 5A, C) result in charging curves thatcould not be fitted by single exponential functions buthave reduced somatic shunt parameters: k = 1.7 0.2and b = 62 2.2 for six cells in 2.5 or 5 mM TEA. Similarresults were obtained with ` 1 mM Ba2+ and ` 2 mM Cs+

(not shown). That is, the presence of second-order expo-nentials depends on the concentration of blockers. LargerTEA concentrations (

b20 mM) were needed to attain t

0and RN values obtained with 5 mM Ba2+ or Cs+. This re-

inforces the view of channel heterogeneity at the sub-threshold, resting level.

The action of K+-blockers on the somatic shunt

Since t0 (in Ba2+) b tmD in control saline, it can be as-

sumed that in K+-blockers the shunt was greatly reducedso that t0 tmD. Similarly, RN values attained valuesfound in gigaseal conditions. If these t0 and RN valuesare adjusted with anatomical measurements, Fdga valuesin the presence of blockers can be approximated (equationD4, Appendix D). Although this factor is very robust andremained in the same range, differences from the valuefound in control saline were significant, indicating thatthe cells became more isopotential (Rall et al. 1992).Thus, Fdga was 0.97 0.007 (in Ba

2+), 0.97 0.002 (inCs+) and 0.96 0.008 (in TEA) (largest P = 0.041; cf. Ta-ble 1).

Once Fdga was determined, AN could be approximatedusing equation B3 for the cases in which K+-blockerswere used. For all cases, AN values are similar to those de-termined anatomically (Table 2).

As expected, Table 2 shows that RS was increased byall K+-blockers, the order of potency being: Ba2+ bbTEA Cs+. Strikingly, only in Ba2+ did RS become sim-ilar to that obtained with whole-cell recordings in a sam-ple of dissociated somata (whole-cell 2.6 GW vs sharpelectrodes in 5 mM Ba2+ 3.2 GW; Table 2). Cs+ didnot reduce the somatic shunt as much as Ba2+. In contrast,RD was increased by Ba

2+ and Cs+ in a similar way, theorder of potency being: Cs+ Ba2+ bb TEA. Thus, theorder of potency was reversed for Cs+. This makes b inCs+ larger than in Ba2+. Since the Cs+-sensitive conduc-tance was the only one exhibiting inward rectification,it is clear that the action of these blockers was not thesame.

On the contrary, TEA did not significantly enhance RD,as manifested by a lack of change in t0. Almost all the ac-tion of 10 mM TEA upon RN was due to its action on RS.This dissociation of RN and t0 has been observed before(Redman et al. 1987; Spruston and Johnston 1992). How-ever, the decrease in somatic shunt caused by TEA wasenough to eliminate the second-order exponentials fromthe charging curve.

Table 2 shows that correcting for the somatic shunt anddendritic geometry, in any condition, yields a similar ANin the range of that previously reported with anatomicalmethods (if the Cm used for these calculations were lowerthan 1 mF/cm2, the approximations may improve a little).

Dye coupling

From a data base of 200 neostriatal cells recorded in con-trol saline, only five cases exhibited dye coupling with thebiocytin technique (2.5%), confirming previous reports in

Fig. 5AC Actions of K+-blockers on electrotonic tran-sients. A Actions of TEA. BActions of Ba2+. C Actions ofCs+. The reconstructed somato-dendritic structure of neuronssuperfused with K+-blockers isdepicted in column 1. The axonsare not shown. Averaged andnormalized electrotonic tran-

sients (bottom) induced by acurrent step (top) are shown incolumn 2. Each frame comparesrecords in control saline (con-trol) with records in the pres-ence of K+-blockers in the samecells. The first 20 ms of nor-malized, averaged and filteredtransients ( filled circles) areshown plotted in semilogarith-mic scale in column 3. Contin-uous lines are fits to the somaticshunt E-C model. Differentiatedrecords plotted in a semiloga-rithmic scale are shown in col-umn 4. In the presence of K+-

blockers second-order exponen-tial components are lost


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adult neostriatal neurons (Cepeda et al. 1989). In contrast,

after K

+

-blockers the incidence of multiple staining in-creased to 44% (13 of 29; P ` 0.001). These coupled cellswere discarded from the analysis described above. Thedifference in coupling ratio with respect to cells recordedin control saline was too large to be imputed to chance orto artifactual multiple staining. Two to five neurons wererecovered from slices in which only one neuron was re-corded (Fig. 6). Only in these dye-coupled cases, and ineach of these cases, were multiexponential charge func-tions recovered after high concentrations of K+-blockers(Fig. 6B). In contrast, single-exponential charge functionswere always obtained in noncoupled neurons after highconcentrations of K+-blockers. Therefore, to record amultiexponential charge function after K+-blockade waspredictive of dye coupling; this could occur after TEA,Ba2+ or Cs+. This suggests that multiexponential chargefunctions in high concentrations of K+-blockers are amanifestation of electrical coupling. In support of this hy-pothesis, the recordings from dye-coupled cells usuallyexhibited evidence of electrical coupling. For example,they fired pairs of action potentials, so that the secondspike was inside the relative refractory period or the after-hyperpolarization of the first spike (Fig. 6B4). Also, fail-ures of the second spike could generate all-or-nothingspikelets (Fig. 6B4, arrow). This is unusual in controlconditions (e.g., Pineda et al. 1992; Galarraga et al.1994; Nisenbaum et al. 1994) but usual during electricalcoupling of neurons (e.g., MacVicar and Dudek 1982).This suggests that electrical coupling between neuronsmay be determined by Rm.

Discussion

Ba2+, Cs+ and TEA changed the passive properties of neo-striatal neurons. All blockers increased subthreshold RN.However, only 5 mM Ba2+ increased RN to values similarto those obtained in whole-cell conditions (from about 49

to about 216 MW; cf. Tables 1 and 2; Kawaguchi 1993).

In making these comparisons, it should be recognized thatanimal age is another variable (Tepper and Trent 1993),since cells used for whole-cell recordings in slices areusually younger than those used for sharp electrode re-cordings.

All K+-blockers induced electrotonic transients thatcould be well fitted to single exponential functions, indi-cating a reduction in both L and the somatic shunt. Sec-ond-order exponentials become too small to be detected.This suggests that the amplitude of second-order expo-nentials seen in control conditions is largely generatedby the somatic shunt (Wilson 1990).

K+-blockers significantly increased the probability ofdetecting dye coupling and probably electrical couplingbetween neighboring neurons. These changes were not ac-companied by obvious anatomical changes of the neuro-nal anatomy. These main findings are experimental andmodel-independent. They represent the most dramatic ef-fects of K+-blockers on passive properties so far reportedin any central neuron (cf. Redman et al. 1987; Sprustonand Johnston 1992; Rapp et al. 1994).

Average anatomical values

Average AS was determined in two ways. First, somata ofbiocytin-filled neurons were measured, and, second, CSwas determined electrophysiologically in acutely dissoci-ated somata. Both methods gave a mean AS 6.5 10

6

cm2 (650 mm2) This average is similar to that determinedpreviously (e.g., Wilson 1990, 1992). Mean AS was notsignificantly different when determined in somata super-fused with either control saline or K+-blockers. Therefore,K+-blockers did not significantly distort neuronal mor-phology. Note, however, that cells with obvious morpho-logical distortions were discarded from the present study.

Average AD has been obtained previously using high-voltage electron microscopy (1.9 104 cm2 or 19000

Fig. 6A, B Dye coupling. A1Control and A2 test (10 mMTEA) voltage responses to in-tracellular current steps from acell that was coupled to aneighboring neuron. A3 I-Vplots built before (open circles)and during TEA ( filled circles).A4 Subtraction of the I-V plots.B1. Biocytin revealed two filled

cells after recording. B2, B3Charging curves in the presenceof the K+-blocker exhibit morethan one exponential componentin these conditions. B4 Coupledcells usually exhibit pairs ofaction potentials (or spikelets;arrow) firing in close proximity


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mm2) (Wilson 1992). Our dendritic measurements in re-constructed neurons yield a similar measurement. Thisis also valid for neurons that were superfused with K+-blockers, again supporting the theory that K+-blockersdo not necessarily distort neuronal morphology. More-over, electrophysiological approximations of AN usingtmD, RN (no-shunt) and LD corrected for shunt and geom-etry, coincide well with reported anatomical measure-

ments (Tables 1, 2). This shows that the approximationofAN is kept constant in spite of dramatic changes in pas-sive parameters values and electrotonic structure. Previ-ous anatomical measurements validate the electrophysio-logical results.

LD

The somatic shunt E-C model (Durand 1984; Kawato1984), adjusted with the generalized correction factor,Fdga (Holmes and Rall 1992; Rall et al. 1992) was thesimplest model that could match the electrophysiological

data. It was surprising that mean tmD and b obtained withthis model, from cells recorded in control saline, could beused to calculate an RN without shunt very similar to thatobtained with whole-cell recordings. Furthermore, aver-age AN obtained with these data was very similar to theone obtained with anatomical methods. The average LDvalue (about 0.46; range 0.350.61; see Table 1) obtainedby this method is independent of the geometrical con-straints of the original E-C model (Rall et al. 1992) andis supported by the experimental fact that K+-blockers in-duced charging curves that could only be fitted by singleexponential functions, that is, with equalizing time con-stants too small to be detected. In fact, if an equalizingtime constant of 550 ms (of similar magnitude to the initialpart of the charge transient excluded from the nonlinearfitting procedure; see Materials and methods) is used tocalculate L, together with the average tmD obtained (about33 ms; Table 1), an L about 0.4 is obtained. This value isreduced if a larger tmD, such as that obtained with Ba

2+

and Cs+, is used. In support of this, LD decreases to a val-ue between 0.26 and 0.36 when calculated after K+-block-ade. Furthermore, it has been pointed out (Holmes andRall 1992) that a fourfold increase in RN and t0 afterblocking the somatic shunt means an L of around 0.5,which coincides well with the present calculations.

To conclude, the values for RmS (without shunt) 15000 W cm2 (equation D1, Appendix D) and RmD 3000050 000 W cm2 (equations D3 and D5, Appendix D)can be obtained by simultaneously solving the set ofequation of Appendix D. The upper RmD value was foundonly in K+-blockers. Thus, RmD would greatly depend onthe amount of inward rectification on the dendrites (seebelow). These values are in the range reported for brainneurons if Cm values remain between 0.75 and 1 mF/cm

2.

K+-blockers act differentially on the somato-dendriticmembrane

Ba2+ reduced the somatic shunt so that mean RS was sim-ilar to that found in isolated somata in whole-cell record-ing conditions. Therefore, this great reduction in somaticshunt induced RN values similar to those obtained inwhole-cell conditions in slices (Kawaguchi 1993). This

suggests that the somatic shunt is the main cause of thedifferences in RN found between sharp electrode andwhole-cell recordings.

When the shunt is reduced RN becomes a dendriticproperty. It remains to be seen whether nonspecific effectof Ba2+ such as that proposed for TEA (Stanfield 1983)plays a role in this great reduction in somatic shunt(e.g., on injury conductance). Note, however, that meanb does not become 1 after Ba2+, suggesting that even inthese conditions a uniform Rm should not be expected(Spruston and Johnston 1992).

In contrast, Cs+ did not enhance RS as much as Ba2+.

Moreover, the Cs+-sensitive conductance was inwardly

rectifying whereas the Ba

2+

-sensitive conductance wasmainly linear. Nevertheless, both Cs+ and Ba2+ increasedRD equally well, as indicated by a similar increase in t0.This suggests that the blockage of inward rectificationin the dendrites is enough to explain all the increase inRD. Therefore, inward rectification may be the main reg-ulator of RmD (Wilson 1992). However, Ba

2+ had to blocksomatic conductances in addition to the inward rectifier inorder to produce RS values similar to those found in iso-lated somata in whole-cell conditions. These conductanc-es should overwhelm the rectifying ones to induce a linearI-V relationship.

On the other hand, K+-blockers such as charybdotoxin,dendrotoxin or apamin (selective blockers of Ca2+- orvoltage-activated K+-conductances) had no effects onelectrotonic transients (not shown, but see Pineda et al.1992; Galarraga et al. 1994; Nisenbaum and Wilson1995).

It has been demonstrated previously that RN and t0 donot necessarily change simultaneously. This has beenused as additional evidence of Rm heterogeneity (Redmanet al. 1987; Rose and Dagum 1988; Spruston and Johnston1992). In particular, the present results show that TEA didnot affect dendritic conductances significantly at the con-centrations used: it increased RN without significant ef-fects on t0 (charging time, i.e., t0, greatly depends onthe amount of membrane to charge and most membranebelongs to the dendrites). As a consequence, TEA didnot change RD significantly. TEA is not a good blockerof inward rectification (Uchimura et al. 1989; Galarragaet al. 1994; Nisenbaum and Wilson 1995). In contrast,TEA did increase RS, and the TEA-sensitive conductancewas linear. Therefore, TEA acted as though it mainlyblocked the somatic shunt without blocking so much ofthe dendritic conductance. This suggests that an incom-plete reduction in somatic shunt is enough to decreasethe amplitude of the second-order exponentials in thecharge transients, suggesting again that the amplitude of


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second-order exponentials seen in control conditions islargely generated by the somatic shunt (Wilson 1990).

Coupling

Another finding of this work was that about 40% of thecells exhibited dye coupling after administration of K+-

blockers. In these cases, and only in these cases, thecharging curve could not be fitted to single exponentialfunctions. Also, dye-coupled cells had some indicationsof electrical coupling, i.e., the firing of pairs of action po-tentials (or spikelets) in close proximity (MacVicar andDudek 1982). This suggests that a multiexponentialcharging curve in these conditions may be indicative ofelectrical coupling. Therefore, the method of analysisused, designed for single neurons, cannot be applied inthese cases.

To our knowledge, this effect of K+-blockers had notbeen reported in neurons. However, an increase in thenumber of gap junctions in endocrine and muscle cells

has been reported after K

+

-blockade (Kannan and Daniel1978; Sheppard and Meda 1981).

Functional consequences

Subthreshold conductances contributing to the restingmembrane potential, as inward rectification, may be thetarget for G-protein linked receptors (Brown and Birnbau-mer 1990). This fact raises the possibility of passive prop-erties being neuromodulated in some neurons. In particu-lar, channels of the IRK family have been reported to bepresent in neostriatal neurons (Karschin et al. 1996).These channels are blocked by Cs+ (Uchimura et al.1989; Galarraga et al. 1994; Doupnik et al. 1995; Ni-senbaum and Wilson 1995), activated by the protein ki-nase A (PKA) signaling pathway and down-regulated bythe protein kinase C (PKC) signaling pathway (Fakler etal. 1994).

In neostriatal neurons, muscarinic activation of thePKC pathway increases RN and decreases inward rectifi-cation in neostriatal neurons (Dodt and Misgeld 1986; Pi-neda et al. 1995), whereas dopaminergic activation of thePKA signaling system leads to the opposite effects (Pac-heco-Cano et al. 1996). Hence, the neostriatal dopaminer-gic-cholinergic balance may control LD and thus regulatesynaptic integration (Wilson 1992, 1993, 1995).

In addition, the 40% of dye-coupled cells after K+-blockers is not only significantly different from that foundin in vitro control conditions (about 2.5%), but it is alsolarger than the percentage of dye coupling found in vivo(Onn and Grace 1995). But neuromodulation of electricalsynapses between neostriatal neurons has also been dem-onstrated. A reduction of dopaminergic tone increases theprobability of dye coupling and increases RN (Cepeda etal. 1989; Onn and Grace 1995). Is this coincidence of re-sults only casual? If not, dendritic function may be morecomplex than previously thought. Electrical coupling be-

tween neurons may be modulated together with electro-tonic length and both variables may be a function of Rm(e.g., Wilson 1992, 1993; Bargas and Galarraga 1995).The possible causal relationship between Rm and func-tional gap junctions needs further investigation.

Appendices

Appendix A. Obtaining the exponential parameters

Experimental charge transients were fitted to a sum of ex-ponential functions (Rall 1977; Rall et al. 1992):

VF V t I

i 0

Cietati A1

where VF is the asymptotic final voltage (i.e., VF = IRN,where I is the magnitude of the applied current step andRN is the input resistance of the whole neuron), V(t) isthe voltage at time t, Ci represents the exponential coeffi-

cients, and ti represents the time constants. The derivativeof the transient was fitted to:

dVadtI

i 0

Ciati etati A2

By fitting equations A1 and A2 (see Materials and meth-ods) to the averaged and filtered experimental records,initial values for exponential coefficients and time con-stants (C0, C1, t0, t1peel) were extracted. Time constantscould be used to obtain Lpeel (Rall et al. 1992):

Lpeel pt0at1peel 11a2 A3

where Lpeel apparent average electrotonic length (seeFig. 3 in Results).

Appendix B. Anatomical measurements

The somatic surface area (AS) was approximated by

As 4pab B1

where a and b are the minor and major somatic radii.Then, the somatic capacitance, CS, would be

Cs CmAs B2

where Cm = 1 mF/cm2 (Fig. 2). Neuronal surface area (AN)

can be calculated by mixing electrophysiological and an-atomical measurements (Rall 1977, eq. 5.16; Rall et al.1992):

AN tmLaCmRNtanhL tmaCmRNFdga B3

where tm is the membrane time constant and Fdga, thegeneralized correction factor that will be defined in Ap-pendix D. This equation yields accurate approximationsof AN as long as the values of tm and RN used are those


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corrected for the somatic shunt. Note that the first part ofequation B3 can also be used to calculate AD if tmD, LDand RD are used instead of tm, L and RN (Rall 1977, eq.5.9).

Appendix C. The somatic shunt E-C model

Coefficients, time constants and Lpeel obtained by fitting

the electrotonic transients to equations in Appendix Awere used as initial values to match the somatic shuntE-C model to the records (Durand 1984; also: Kawato1984):

V0Y T VF I

i 0

Bi cosaiLe1a2

itatm

VF I

i 0

Ci etati C1

Thus, the exponential coefficients (Ci) of equation A1 areequated to Bicos(aiL), and 1 + a

2i = tmD/ti. To do this, note

that (Durand 1984):

Bi [1/cos(aiL)][VF/(1a2i )]{2(r1)/[gi2e+k

Bi=[(aiLgi)2/k]} (C2)

which allows to obtain a theoretical exponential coeffi-cient (CiT) (as done by Rose and Dagum 1988; Whiteet al. 1992):

CiT[2VF(r1)ti/tmD]/[gi2ek(aigiL)2/k] (C3)

where r is the dendrites to soma conductance ratio (GD/GS), tmD is the time constant of the dendritic membrane,ti are the equalizing time constants, and ai are the rootsof the transcendental equation:

aiLgicot(aiL)rLcoth(L) = K (C4)defined as:

ai (tmD/ti1)1/2 (C5)

and:

gi[1e(1a2i )]/a21 (C6)

k can be approximated with the exponential parametersobtained from the fitting of the experimental transient asshown by Kawato et al. (1984) (see also Bargas et al.1988):

k (C1/C0)/(t1/t0) (C7)

The other terms are defined as follows (Durand 1984):e a1 tan a1L a0 tan a0L a1 a

20a1 tan a1L

1 a21a0 tan a0L C8

where e is a measure of the magnitude of the shunt thatdefines Rm heterogeneity as the ratio RmS/RmD = tmS/tmDr also defined by (Durand 1984):

r cot a0L 1 1 a20ea a0 coth L C9

where an approximation of r as defined by Brown et al.(1981a,b) can be introduced to begin the iteration.Whenthe difference (SE) between the exponential coefficients

(Ci; equation A1) and the theoretical exponential coeffi-cients (CiT; equation C3):

SE(C0TC0)2(C1TC1)

2 (C10)

is minimized to SE ` 1 105, it is considered, for thepurposes of this work, that the model has been matched.

Appendix D.Obtaining the generalized correction factor, Fdga

Initial values of AS, RmD = 1/GmD, r, and e = 1/b (outputvalues from the somatic shunt E-C model and AS from an-atomical measurements; see Materials and methods) canbe used to better estimate the somatic shunt, i.e., withthe shunt factor b dependent on anatomical and electro-physiological determinations (Holmes and Rall 1992a):

bGS/(GmD AS)GmS/GmD (D1)

GmS and GmD are specific somatic and dendritic mem-brane conductances, and GS is the somatic input conduc-tance (1/R

S). G

Sshould accomplish:

GN GSGD (D2)

The product rb, or rb = 1, which defines a somatic-shunt-independent constant for a given neuronal class (dendrit-ic conductance vs dendritic area), is obtained by(Holmes and Rall 1992a; Rall et al. 1992):

rbrb1GD/(GmDAS) (D3)

This equation may use the initial r value obtained fromthe fitting of the somatic shunt E-C model (AppendixC). Thus, given independent AD and AS measurements,the generalized correction factor is given by (Rall et al.1992):

rb1/(AD/AS)FdgatanhLD/LD (D4)

which allows an approximation of the effective electro-tonic length of the dendrites (LD) and an adjustment ofthe dendritic input conductance:

GDGmDADFdga (D5)

A putative RN, without somatic shunt, can then be esti-mated (Holmes and Rall 1992):

RN(no shunt)RN/[(rb11)/(rb1b)] (D6)

Acknowledgements This research work was partially funded bygrants from CONACyT (Mxico)# 0115P-N and DGAPA-UNAM#

IN201194 to J.B. We thank C. Vilchis for technical assistance.

References

Bargas J, Galarraga E (1995) Ion channels: keys to neuronal special-ization. In: Arbib MA (ed) The hand book of brain theory. MITPress, Cambridge, Mass, pp 496501

Bargas J, Galarraga E, Aceves J (1988) Electrotonic properties ofneostriatal neurons are modulated by extracellular potassium.Exp Brain Res 72:390398


14/15

83

Bargas J, Howe A, Eberwine J, Cao Y, Surmeier J (1994) Cellularand molecular characterization of Ca2+ currents in acutely isolat-ed, adult rat neostriatal neurons. J Neurosci 14:66676686

Brown AM, Birnbauner L (1990) Ionic channels and their regulationby G protein subunits. Annu Rev Physiol 52:197213

Brown TH, Fricke RA, Perkel DH (1981a) Passive electrical con-stants in three classes of hippocampal neurons. J Neurophysiol46:812827

Brown TH, Perkel DH, Norris JK, Peacock JH (1981b) Electrotonicstructure and specific membrane properties of mouse dorsal root

ganglion neurons. J Neurophysiol 45:115Burke RE, Fyffe REW, Moschovakis AK (1994) Electrotonic archi-tecture of cat gamma motoneurons. J Neurophysiol 72:23022316

Campbell DM, Rose PK (1997) Contribution of voltage-dependentpotassium channels to the somatic shunt in neck motoneuronsof the cat. J Neurophysiol 77:14701486

Cepeda C, Walsh JP, Hull CD, Howard SG, Buchward NA, LevineMS (1989) Dye-coupling in the neostriatum of the rat. I. Modu-lation by dopamine-depleting lesions. Synapse 4:229237

Chang HT, Wilson CJ, Kitai ST (1982) A Golgi study of rat neostri-atal neurons: light microscopic analysis. J Comp Neurol208:107126

Clements JD, Redman SJ (1989) Cable properties of cat spinalmotoneurones measured by combining voltage clamp, currentclamp and intracellular staining. J Physiol (Lond) 409:6387

Dempster J (1993) Computer analysis of electrophysiological sig-nals. Academic Press, San Diego, CalifDodt HU, Misgeld U (1986) Muscarinic excitation and muscarinic

inhibition of synaptic transmission in the rat neostriatum. J Phy-siol (Lond) 380:593601

Doupnik CA, Davidson N, Lester HA (1995) The inward rectifierpotassium channel family. Curr Opin Neurobiol 5:268277

Durand D (1984) The somatic shunt cable model for neurons. Bio-phys J 46:645653

Durand D, Carlen PL, Gurevich N, Ho A, Kunov H (1983) Electro-tonic parameters of rat dentate granule cells measured usingshort current pulses and HRP staining. J Neurophysiol50:10801097

Fakler B, Brandle U, Glowatzki E, Zenner HP, Ruppersberg JP(1994) KIR2.1 inwardly rectified K

+ channels are regulated inde-pendently by protein kinases and ATP hydrolysis. Neuron13:14131420

Fakler B, Brandle U, Glowatzki E, Weldemann S, Zenner HP, Rup-persberg JP (1995) Strong voltage-dependent inward rectifica-tion of inward rectifier K+ channels is caused by intracellularspermine. Cell 80:149154

Galarraga E, Pacheco-Cano MT, Flores-Hernndez JV, Bargas J(1994) Subthreshold rectification in neostriatal spiny projectionneurons. Exp Brain Res 100:239249

Hamill OP, Marty A, Neher E, Sakmann B, Sigworth FJ (1981) Im-proved patch-clamp techniques for high resolution current re-cording from cells and cell-free membrane patches. PflgersArch 391:85100

Holmes WR, Rall W (1992) Electrotonic length estimates in neuronswith dendritic tapering or somatic shunt. J Neurophysiol68:14211437

Holmes WR, Segev I, Rall W (1992) Interpretation of time constantand electrotonic length estimates in multicylinder or branchedneuronal structures. J Neurophysiol 68:14011420

Horikawa K, Armstrong WE (1988) A versatile means of intracellu-lar labeling: injection of biocytin and detection with avidin con-jugates. J Neurosci Methods 25:111

Iansek R, Redman SJ (1973) An analysis of the cable properties ofspinal motoneurones using a brief intracellular current pulse. JPhysiol (Lond) 234:613636

Jack JJB, Noble D, Tsien RW (1975) Electric current flow in excit-able cells. Clarendon Press, Oxford

Johnston D (1981) Passive cable properties of hippocampal CA3 py-ramidal neurons. Cell Mol Neurobiol 1:4155

Kannan MS, Daniel EE (1978) Formation of gap junctions by treat-ment in vitro with potassium conductance blockers. J Cell Biol8:338348

Karschin C, Dibmann E, Sthmer W, Karschin A (1996) IRK(13)and GIRK(14) inwardly rectifying K+ channels mRNAs aredifferentially expressed in the adult rat brain. J Neurosci16:35593570

Kawaguchi Y (1993) Physiological, morphological, and histochem-ical characterization of three classes of interneurons in rat neo-striatum. J Neurosci 13:49084923

Kawato M (1984) Cable properties of a neuron model with non-uni-form membrane resistivity. J Theor Biol 111:149169Macvicar BA, Dudek FE (1982) Electrotonic coupling between

granule cells of rat dentate gyrus: physiological and anatomicalevidence. J Neurophysiol 47:579592

Major G, Evans JD, Jack JB (1993) Solutions for transients in arbi-trarily branching cables. I. Voltage recording with somaticshunt. Biophys J 65:423449

Major G, Larkman U, Jonas P, Sakmann B, Jack JB (1994) Detailedpassive cable models of whole-cell recorded CA3 pyramidalneurons in rat hippocampal slices. J Neurosci 14:46134638

Marquardt D (1963) An algorithm for least-squares estimation ofnon-linear parameters. SIAM J Appl Math 11:431441

Nisenbaum ES, Wilson CJ (1995) Potassium currents responsiblefor inward and outward rectification in rat neostriatal spiny projection neurons. J Neurosci 15:44494463

Nisenbaum ES, Xu ZC, Wilson CJ (1994) Contribution of a slowlyinactivating potassium current to the transition to firing of neo-striatal spiny projection neurons. J Neurophysiol 71:11741189

Onn S-P, Grace AA (1995) Repeated treatment with haloperidol andclozapine exerts differential effects on dye coupling betweenneurons in subregions of striatum and nucleus accumbens. JNeurosci 15:70247036

Pacheco-Cano MT, Bargas J, Hernndez-Lpez S, Tapia D, Galarra-ga E (1996) Inhibitory action of dopamine involves a subthresh-old Cs+-sensitive conductance in neostriatal neurons. Exp BrainRes 110:205211

Pineda JC, Galarraga E, Bargas J, Cristancho M, Aceves J (1992)Charybdotoxin and apamin sensitivity of the calcium-dependentrepolarization and the afterhyperpolarization in neostriatal neu-rons. J Neurophysiol 68:287294

Pineda JC, Bargas J, Flores-Hernndez J, Galarraga E (1995) Mus-carinic receptors modulate the afterhyperpolarizing potential inneostriatal neurons. Eur J Pharmacol 281:271277

Press KC, Flannery BP, Teukolsky SA, Vetterling WT (1986) Nu-merical recipes: the art of scientific computing. Cambridge Uni-versity Press, Cambridge

Rall W (1977) Core conductor theory and cable properties of neu-rons. In: Handbook of physiology, sect 1, The nervous system,vol 1, Cellular biology of neurons. American Physiological So-ciety, Bethesda, Md, pp 3997

Rall W, Burke RE, Holmes WR, Jack JJB, Redman SJ, Segev I(1992) Matching dendritic neuron models to experimental data.Physiol Rev 72:159186

Rapp M, Segev I, Yaron Y (1994) Physiology, morphology and de-tailed passive models of guinea-pig cerebellar Purkinje cells. JPhysiol (Lond) 474:101118

Redman SJ, McLachlan EM, Hirst DS (1987) Nonuniform passivemembrane properties of rat lumbar sympathetic ganglion cells.J Neurophysiol 57:633644

Reyes A, Galarraga E, Tapia D, Bargas J (1995) Potassium channelblock induced dye coupling in neostriatal neurons. Soc NeurosciAbstr 21:913

Rose PK, Dagum A (1988) Nonequivalent cylinder models of neu-rons: interpretation of voltage transients generated by somaticcurrent injection. J Neurophysiol 60:125148

Rose PK, Vanner SJ (1988) Differences in somatic and dendriticspecific membrane resistivity of spinal motoneurons: an electro-physiological study of neck and shoulder motoneurons in thecat. J Neurophysiol 60:149166


15/15

84

Sheppard MS, Meda P (1981) Tetraethylammonium modifies gap junctions between pancreatic b-cells. Am J Physiol 9:C116C120

Spruston N, Johnston D (1992) Perforated patch-clamp analysis ofthe passive membrane properties of three classes of hippocam-pal neurons. J Neurophysiol 67:508529

Staley JK, Otis ST, Mody I (1992) Membrane properties of dentategyrus granule cells: Comparison of sharp microelectrode andwhole-cell recordings. J Neurophysiol 67:13461358

Stanfield PR (1983) Tetraethylammonium ions and the potassium

permeability of excitable cells. Rev Physiol Biochem Pharmacol97:167Tepper JM, Trent F (1993) In vivo studies of the postnatal develop-

ment of rat neostriatal neurons. Prog Brain Res 99:3550Tsukahara N, Murakami F, Hultborn H (1975) Electrical constants

of neurons of the red nucleus. Exp Brain Res 23:4964Uchimura N, Cherubini E, North RA (1989) Inward rectification in

rat nucleus accumbens neurons. J Neurophysiol 62:12801286

White JA, Manis PB, Young ED (1992) The parameter identifica-tion problem for the somatic shunt model. Biol Cybern66:307318

Wilson CJ (1990) Basal ganglia. In: Shepherd GM (ed) The synapticorganization of the brain. Oxford University Press, Oxford, pp279316

Wilson CJ (1992) Dendritic morphology, inward rectification, andthe functional properties of neostriatal neurons. In: Single neu-ron computation. Academic Press, San Diego, Calif, pp 141171

Wilson CJ (1993) The generation of natural firing patterns in neo-

striatal neurons. Prog Brain Res 99:277297Wilson C J (1995) Dynamic modification of dendritic cable proper-ties and synaptic transmission by voltage-gated potassium chan-nels. J Comp Neurosci 2:91115

Yan Z, Surmeier DJ (1996) Muscarinic (M2M4) receptors reduceN- and P-type Ca2+ currents in rat neostriatal cholinergic inter-neurons through a fast, membrane delimited, G-protein pathway.J Neurosci 16:25922604

a. reyes et al- passive properties of neostriatal neurons during potassium conductance blockade

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