Space-Clamp Problems When Voltage Clamping Neurons Expressing Voltage-Gated Conductances

J Neurophysiol 99: 1127 1136, 28. First published January 9, 28; doi:1.1152/jn.1232.27. Space-Clamp Problems When Voltage Clamping Neurons Expressing Voltage-Gated Conductances Dan Bar-Yehuda 2 and Alon Korngreen 1,2 1 The Mina and Everard Faculty of Life Sciences and the 2 Leslie and Susan Gonda Multidisciplinary Brain Research Center, Bar-Ilan University, Ramat-Gan, Israel Submitted 8 November 27; accepted in final form 8 January 28 Bar-Yehuda D, Korngreen A. Space-clamp problems when voltage clamping neurons expressing voltage-gated conductances. J Neurophysiol 99: 1127 1136, 28. First published January 9, 28; doi:1.1152/jn.1232.27. The voltage-clamp technique is applicable only to spherical cells. In nonspherical cells, such as neurons, the membrane potential is not clamped distal to the voltageclamp electrode. This means that the current recorded by the voltageclamp electrode is the sum of the local current and of axial currents from locations experiencing different membrane potentials. Furthermore, voltage-gated currents recorded from a nonspherical cell are, by definition, severely distorted due to the lack of space clamp. Justifications for voltage clamping in nonspherical cells are, first, that the lack of space clamp is not severe in neurons with short dendrites. Second, passive cable theory may be invoked to justify application of voltage clamp to branching neurons, suggesting that the potential decay is sufficiently shallow to allow spatial clamping of the neuron. Here, using numerical simulations, we show that the distortions of voltage-gated K and Ca 2 currents are substantial even in neurons with short dendrites. The simulations also demonstrate that passive cable theory cannot be used to justify voltage clamping of neurons due to significant shunting to the reversal potential of the voltage-gated conductance during channel activation. Some of the predictions made by the simulations were verified using somatic and dendritic voltageclamp experiments in rat somatosensory cortex. Our results demonstrate that voltage-gated K and Ca 2 currents recorded from branching neurons are almost always severely distorted. INTRODUCTION Address for reprint requests and other correspondence: A. Korngreen, Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan, 529, Israel (E-mail: korngra@mail.biu.ac.il). The combination of the patch-clamp technique (Hamill et al. 1981) with the acute brain slice preparation (Edwards et al. 1989; Stuart et al. 1993) ushered in a gold rush in the field of electrophysiology. Each year, thousands of investigations, if not more, are carried out using these techniques, and they have contributed immensely to our understanding of the function of single neurons and of neural networks. However, as with every gold rush, some deposits turn out to be fool s gold. For, example, one pitfall with the patch-clamp technique is the distortion of voltage-gated currents from neurons in brain slices due to space-clamp problems. Problems that occur with incomplete space-clamp have been addressed extensively (Armstrong and Gilly 1992; Augustine et al. 1985; Castelfranco and Hartline 22; Hartline and Castelfranco 23; Johnston et al. 1996; Koch 1999; Larsson et al. 1997; Major 1993; Major et al. 1993; Müller and Lux 1993; Rall and Segev 1985; Rall et al. 1992; Spruston et al. 1993; White et al. 1995). We and others have recently suggested a scheme for correcting the distortion of the ionic current recorded in the absence of space-clamp (Castelfranco and Hartline 24; Schaefer et al. 23a, 27). However, we have encountered several misconceptions of the space-clamp problem. Two main arguments may be used to justify the recording of voltage-gated channels in the absence of space clamp. The first is that the space-clamp problem is small in neurons with short dendrites, and therefore it is possible to accurately record voltage-gated currents. The second argument may be that the passive decay of the membrane potential is relatively shallow, making it possible to clamp large sections of the dendrites originating from the soma and therefore to obtain a good space-clamp. To address these lines of false argumentation, we have simulated voltage-clamp experiments in realistic morphologies of several neurons from the CNS. The simulations clearly demonstrate that the lack of space clamp considerably distorts the ionic current recorded at the soma. The major predictions made by the simulations were confirmed by somatic and dendritic voltage-clamp experiments in rat somatosensory cortex. METHODS Numerical simulations All simulations used the NEURON (versions 5.9 and 6.) simulation environment (Hines and Carnevale 1997), with an integration time step of 25 s. Shorter (1 s) and longer (5 s) integration time steps did not change the results of the simulations. Ion channel models were implemented using the NMODL extension of the NEURON simulation language (Hines and Carnevale 2). The passive parameters were R i 1 cm; R m 4, cm 2, and C m 1 Fcm 2 with a passive reversal potential of E leak 65 mv, a potassium reversal potential of E k 9 mv and a calcium reversal potential of E Ca 6 mv. All voltage-clamp simulations used the built-in MOD file SEClmp.mod. Computer representations of the morphologies of neurons from rat somatosensory cortex were derived either from neurons stained by us and reconstructed using Neurolucida (MBF Bioscience, Williston, VT) or from the NeuroMorpho data base [www.neuromorpho.org (Ascoli 26)]. The morphology of a layer 5 pyramidal neuron (A66) from a 42-day-old rat was traced from a biocytin stain using Neurolucida (MicroBrightField, Colchester, VT). The morphologies of a layer 4 interneuron (C58E2), a layer 4 spiny stellate neuron (j7_l4stellate), and a layer 2/3 bipolar interneuron (C23998A-I3) were obtained from NeuroMorpho. To reduce the complexity of the The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. Downloaded from http://jn.physiology.org/ by 1.22.33.3 on November 29, 217 www.jn.org 22-377/8 $8. Copyright 28 The American Physiological Society 1127

1128 D. BAR-YEHUDA AND A. KORNGREEN neuron, axons were removed from all reconstructions. The simulations presented in Fig. 7 were performed on a simplified neuron containing only a soma (length 1 m, diameter 1 m) and one dendrite (variable length, diameter.5 m). The diameter of the upper half of the soma was tapered to avoid impedance mismatch at the soma-dendrite connection. The code used to generate the simulations is freely available on-line at the NEURON model database web page (http://senselab.med.yale.edu/modeldb/). Slice preparation Acute brain slices (sagittal, 3 m thick) were prepared from the somatosensory cortex of 2- to 5-wk-old Wistar rats killed by rapid decapitation following shallow anesthesia with isoflurane according to the guidelines of the Bar-Ilan University animal welfare committees and using previously described techniques (Stuart et al. 1993). Slices were perfused throughout the experiment with an oxygenated artificial cerebrospinal solution (ACSF) containing (in mm) 125 NaCl, 15 NaHCO 3, 2.5 KCl, 1.25 NaH 2 PO 4, 1 MgCl 2, 2 CaCl 2, and 25 glucose (ph 7.4 with 5% CO 2, 31 mosmol kg 1 ) at room temperature (2 22 C). Pyramidal neurons from L5B in the somatosensory cortex were visually identified using infrared differential interference contrast (IR-DIC) videomicroscopy (Stuart et al. 1993). Solutions and drugs The pipette solution for recording voltage-gated K currents contained (in mm) 125 K-gluconate, 2 KCl, 1 HEPES, 4 MgATP, 1 Na-phosphocreatin,.5 EGTA,.3 GTP, and.2% biocytin (ph 7.2 with KOH, 312 mosmol kg 1 ). The pipette solution for recording voltage-gated Ca 2 currents contained (in mm) 125 Cs-gluconate, 2 CsCl, 1 HEPES, 4 MgATP, 1 Na-phosphocreatin,.5 EGTA,.3 GTP, and.2% biocytin (ph 7.2 with CsOH, 312 mosmol kg 1 ). The bath solution for single-electrode voltage-clamp experiments (SEVC) contained (in mm) 125 NaCl, 15 NaCO 3, 1 mm HEPES, 2.5 KCl, 1 MgCl 2, 2 CaCl2, 25 glucose, 1 TEA, 5 4-aminopyridine (4-AP), and 1 nm TTX (ph 7.4 with 5% CO 2, 38 mosmol kg 1 ). Tetrodotoxin (TTX, Tocris, Bristol, UK) was stored at (2(C as stock solutions in doubly distilled water and added directly to the bath solution. The bath solution of two-electrode voltage-clamp (TEVC) experiments contained (in mm): 85 NaCl, 25 NaCO 3, 2.5 KCl, 1 MgCl 2, 2 CaCl 2,25 glucose, 4 TEA, and 1 nm TTX (ph 7.4 with 5% CO 2, 33 mosmol kg 1 ). TEVC recording of voltage-gated Ca 2 currents Whole cell recordings for two-electrode voltage-clamp recordings were obtained using two patch pipettes, whose tips were positioned at the top and bottom ends of the soma. Patch pipettes (5 1 M ) were pulled from thick-walled borosilicate glass capillaries (2. mm OD,.5 mm wall thickness, Hilgenberg, Malsfeld, Germany) and were coated with silicone elastomer (Sylgard 184, Dow Corning) prior to the experiment. The distance of the dendritic recording from the soma and the distance between the tips of the current-injecting and voltagerecording electrodes were measured from video pictures taken by a frame grabber. The TEVC of voltage-gated Ca 2 currents were obtained using two HS-2Ax.1M head-stages and an Axoclamp-2B amplifier (Axon Instruments, Foster City, CA). Voltage and current were sampled using the program Pulse (Version 8.1, Heka Electronic, Lambrecht, Germany), digitized by an ITC-18 interface (Instrutech, Greatneck, NY), and stored on the hard disk of a computer. Capacitive and leak currents were subtracted off-line by scaling pulses taken at hyperpolarized potentials. SEVC recording of voltage-gated K currents Dendritic SEVC recordings were carried out using the VE-2 patchclamp amplifier (Alembic Instruments, Montreal, Quebec, Canada). In all recordings, the series resistance was fully compensated using the VE-2 virtual electrode compensation circuit. Somatic whole cell current-clamp recordings were made from the soma of layer 5 pyramidal neurons using a Multiclamp-7B amplifier (Axon Instruments). Voltage was using PClamp-9 (Axon Instruments), digitized by a Digidata-132 interface (Axon Instruments), and stored on the hard disk of a personal computer. All off-line analysis of experimental and simulated data were performed using custom-written routines in IgorPro 5 (Wavemetrics; Lake Oswego, OR) or Matlab (The Math- Works, Natick, MA). RESULTS We simulated a somatic voltage clamp in four realistic morphologies of cortical neurons to demonstrate the effect of voltage-gated K conductances on the spatial distribution of the membrane potential. Neurons with different lengths and diameters of dendrites were selected to investigate the claim that neurons with short dendrites do not suffer from spaceclamp problems. We used a layer 5 pyramidal neuron (Fig. 1A), a layer 4 interneuron (Fig. 1B), a layer 4 spiny stellate neuron (Fig. 1C), and a layer 2/3 bipolar interneuron (Fig. 1D). The neurons are drawn in Fig. 1 according to decreasing size. To address the claim that the voltage decay is shallow allowing for good spatial clamp, we deliberately selected passive membrane parameters that will generate such shallow voltage attenuation. Given the passive parameters (R i 1 cm; R m 4, cm 2 ) used in most of the simulations, the passive space constant ( ), calculated for an infinite cylinder with a diameter of 1 m was 3.16 mm. To measure the steady-state attenuation of the membrane potential in the dendrites of the neurons used, we simulated a somatic voltage clamp in all four neurons. The membrane potential at the soma was clamped to 8 mv and then stepped to mv for 1 s to allow the membrane potential in all the compartments to reach a steady-state value (displayed in Fig. 1 in gray). As predicted from cable theory, the passive voltage-attenuation was significant only in the distal apical dendrite of the L5 pyramidal neuron (Fig. 1Ai). Next a delayed rectifier-like voltage-gated K conductance with a 2 ps/ m 2 density was inserted homogenously throughout the somatodendritic tree. The activation curve of this K conductance had a voltage at half activation of 1 mv and a slope of 1 mv. The steady-state membrane potential recorded in each compartment of the neurons following the same voltage-clamp protocol is displayed in Fig. 1 (black markers). In all simula- Downloaded from http://jn.physiology.org/ by 1.22.33.3 on November 29, 217 FIG. 1. Spatial activation of voltage-gated K conductances during a voltage-clamp experiment in distributed morphologies. Left: the morphologies of the neurons used in the simulation. The neurons, from top to bottom were a L5 pyramidal neuron, a layer 4 interneuron (C58E2), a layer 4 spiny stellate neuron (j7_l4stellate), and a layer 2/3 bipolar interneuron (C23998A-I3). All the scale bars are 1 m. The membrane potential following a 1-s voltage-clamp step to mv was recorded when only passive membrane properties were inserted into the neurons (gray markings) and when a delayed rectifier with a density of 2 ps/ m 2 was homogenously inserted in all the compartments of the neurons. The figures are of the membrane potential of an L5 pyramidal neuron (Ai), a layer 4 interneuron (Bi), a layer 4 spiny stellate neuron (Ci), and a layer 2/3 bipolar interneuron (Di; black markings). In addition, the activation of the K conductance is displayed in each compartment of the same neurons [an L5 pyramidal neuron (Aii), a layer 4 interneuron (Bii), a layer 4 spiny stellate neuron (Cii), and a layer 2/3 bipolar interneuron (Dii)]. J Neurophysiol VOL 99 MARCH 28 www.jn.org

SPACE-CLAMP PROBLEMS Aii -1-2 -3-4 -5 4 8 Bii -2-3 -4-5 1 2 Cii 8 6 4 2 4 8 12 1 2 3 16 14 12 1 8 6 4 2 3-1 -2-3 -4-5 16 14 12 1 8 6 4 2-6 5 1 15 2 Dii -1 1-6 Di 12 12-1 Ci 14-6 Bi 16-2 -3-4 -5 5 1 15 2 16 14 12 1 8 6 4 2-6 5 1 15 Distance from soma (µm) J Neurophysiol VOL 99 MARCH 28 www.jn.org 5 1 15 Distance from soma (µm) Downloaded from http://jn.physiology.org/ by 1.22.33.3 on November 29, 217 Conductance (ps/mm2) Ai 1129

113 D. BAR-YEHUDA AND A. KORNGREEN tions, regardless of neuron morphology, the membrane potential decayed by 1 2 mv over the first 1 m along the dendrite away from the somatic voltage clamp. This decay is larger than the voltage decay predicted by passive cable theory alone (Fig. 1, gray markings). In addition to the marked attenuation of the membrane potential, the activation of the K conductance decreased along the dendrites of all the simulated neurons (Fig. 1, right). The strong attenuation of the membrane potential along the dendrites is due to the shunting of the membrane potential to the K reversal potential after activation of K conductances by the voltage-clamp command. As a direct result from this decay, the activation of the K conductance was marginal distal to the soma (Fig. 1). Similar results were obtained in simulations in which the voltage-clamp electrode was positioned in the dendrite (not shown) and in simulations carried out using Purkinje neuron morphology (Häusser 23). Naively, to obtain the activation curve of a voltage-gated conductance when the entire membrane of the neuron is under the control of the voltage-clamp amplifier, the experimenter records the currents at several potentials, subtracts the leak and capacitive currents, and divides the current by the driving force. Such curves are effectively the activation curves for a point neuron. We derived such curves here from the same simulation configuration as in Fig. 1 using the same activation parameters as in our simulations with the neuron morphologies. Figure 2 compared them with the activation curves from the simulations using the neuron morphologies. There is a similar deviation between the simulated activation curves from curves for a point neuron for all four morphologies. All the curves simulated in the distributed morphologies present a shallower activation slope. Additionally, all these activation curves do not reach saturation. Qualitatively similar deviations were observed when the conductance density was varied between 1 and 2 ps/ m 2 (Fig. 7) and when R m was varied between 5, and 5, cm 2 (simulations not shown). The simulations in Fig. 1 predict that the activation of a voltage-gated K conductance will generate 2 mv decay in the membrane potential over the first 1 m from the voltageclamp. To test this prediction, we performed the experiment shown in Fig. 3. Two recordings in the whole cell mode of the patch-clamp technique were simultaneously established at the soma and 9 m away from the soma along the apical dendrite of a pyramidal neuron in L5B of rat somatosensory cortex (Fig. 3A, inset). The somatic electrode passively recorded the membrane potential using the current-clamp mode of MultiClamp- 7B amplifier. The dendritic electrode was used to perform a local voltage clamp using the VE-2 amplifier. The series resistance was fully compensated using this amplifier. Large currents are expected from a somatic voltage clamp of L5 pyramidal neurons (Schaefer et al. 27). Thus even small changes to the series resistance may induce a deviation from the clamp potential. Therefore the voltage clamp was performed at the dendrite where the K current density was predicted to be lower. To increase the stability of the series resistance compensation, K currents were reduced by addition of 1 mm TEA and 5 mm 4-AP to the bath solution. Voltage-gated Na conductances were blocked with 1 nm TTX. Voltage-commands ranging from 8 to 5 mv activated outward K currents, which are presented in Fig. 3A after subtracting leak and capacitive transient. Three traces A G/Gmax G/Gmax G/Gmax G/Gmax B C D 1..8.6.4.2. -8-4 4 8 1..8.6.4.2. -8-4 4 8 1..8.6.4.2. -8-4 4 8 1..8.6.4.2. -8-4 4 8 FIG. 2. Voltage-gated K conductance activation curve distortion in nonspherical cells. Activation curves calculated by dividing the K current recorded after a 1-s voltage-clamp step by the driving force and then by the maximal conductance ( ). The activation curves simulated in a point neuron are displayed as dotted lines for comparison. A: L5 pyramidal neuron. B: layer 4 interneuron (C58E2). C: layer 4 spiny stellate neuron (j7_l4stellate). D: layer 2/3 bipolar interneuron (C23998A-I3). from this family of currents were re-plotted in Fig. 3B together with the voltage-clamp commands and the somatic membrane potential. As predicted by passive cable theory, following a voltageclamp step from 1 to 7 mv that caused no channel Downloaded from http://jn.physiology.org/ by 1.22.33.3 on November 29, 217 J Neurophysiol VOL 99 MARCH 28 www.jn.org

SPACE-CLAMP PROBLEMS 1131 A VE-2 1 na 5 ms MultiClamp 25 µm 4 mv B C 2 mv -1 mv -7 mv -1 mv 1 na 2 mv 5 ms FIG. 3. Experimental demonstration of the effect of K conductance shunting. A: voltage-clamp experiment performed 9 m along the apical dendrite of a L5 pyramidal neuron using a VE-2 amplifier. The experiment is depicted in the insert showing the somatic and dendritic electrodes superimposed on the DIC image of the neuron. The currents recorded by the dendritic voltage-clamp electrode were sampled at 2 khz and filtered at 3 khz. Leak and capacitive currents were subtracted off-line. The command potential is displayed below the recorded currents. The somatic membrane potential recorded with the MultiClamp-7B was sampled at 2 khz and filtered at 1 khz. B: selected current traces are displayed above the command potential of the dendritic electrode. The membrane potential recorded at the soma (thick lines) is superimposed on the command potential. C: average activation curve calculated by dividing the maximal K current recorded in A and in 2 other experiments by the driving force and then by the maximal conductance (smooth line). The activation curve reported in the literature (Korngreen and Sakmann 2) is displayed as a dotted line for comparison. Error bars are SE. Downloaded from http://jn.physiology.org/ G/G max activation, the somatic membrane potential closely overlapped the voltage-clamp potential applied at the dendrite (Fig. 3B). A dendritic voltage-clamp command to 1 mv generated a small outward K current. Correspondingly, a small deviation of the somatic from the dendritic potential was observed (Fig. 3B). Finally, a dendritic voltage-clamp command to 2 mv generated a larger outward K current. This K activation shunted the membrane potential, which displayed a steadystate decay of 11 mv at the soma. This is substantially larger than that predicted by passive cable theory (Fig. 3B). The average activation curve (n 3) was shifted to depolarized potentials according to the simulations in Fig. 2 and compared with the activation curve recorded in nucleated patches (Korngreen and Sakmann 2). It did not reach saturation even at 5 mv (Fig. 3C). Using simulations similar to those presented for K conductances in Fig. 1, we investigated the effect of voltage-gated Ca 2 conductances on the spatial distribution of the membrane potential (Fig. 4). A somatic voltage clamp was simulated in the four realistic morphologies of cortical neurons. Simulations included homogenous passive properties and a spatially homogenous voltage-gated Ca 2 conductance with a5ps/ m 2 density. The activation curve of this Ca 2 conductance had a voltage at half activation of 1 mv and a slope of 1 mv. These values were deliberately selected similar to those for the K conductance to better demonstrate the effect of the different reversal potentials. The membrane potential at the soma was clamped to 8 mv and then stepped to mv for 1sto allow the membrane potential in all the compartments to reach a steady-state value. The value of the membrane potential (black markings) is displayed in Fig. 4 in comparison to the value of the membrane potential simulated using only passive membrane properties (gray markings). Figure 4 also displays the activation of the Ca 2 conductance in all compartments of the neurons. In all simulations, regardless of neuron morphology, the membrane potential was depolarized by 1 mv more over the first 1 m along the dendrite away from the somatic voltage-clamp. Furthermore, the Ca 2 conductance by 1.22.33.3 on November 29, 217 J Neurophysiol VOL 99 MARCH 28 www.jn.org

1132 D. BAR-YEHUDA AND A. KORNGREEN Ai Aii 5. 6 3 4 8 12 Bi 4 8 12 1 2 3 Bii 5. 6 3.5 3-3 4.5 4. 3.5 3. 1 2 3 Ci Cii 5. 6 3 4.5 4. 3.5 3. -3 5 1 15 2 Di 5 1 15 2 Dii 5. 6 3 4.5 4. 3.5 3. -3 5 1 15 Distance from soma (µm) J Neurophysiol VOL 99 MARCH 28 www.jn.org 5 1 15 Distance from soma (µm) Downloaded from http://jn.physiology.org/ by 1.22.33.3 on November 29, 217 4. 3. -3 4.5

SPACE-CLAMP PROBLEMS 1133 displayed greater activation along the dendrite than at the soma (Fig. 4). These effects cannot be explained by passive cable theory alone. Passive cable theory predicts a small decay of the membrane potential within the first 1 m along the dendrite. Although the impact of voltage-gated Ca 2 conductances appears opposite to that of voltage-gated K conductances, the basic mechanism is identical. Following activation of Ca 2 conductance, the membrane potential is shunted to the Ca 2 reversal potential, leading to the observed dendritic depolarization. The shunting of the membrane potential to the Ca 2 reversal potential induces the generation of a dendritic regenerative Ca 2 potential. Because no voltage-gated K conductances were present in the simulation to hyperpolarize the dendritic membrane, the dendrites remained constantly depolarized at or close to the Ca 2 reversal potential. The impact of this dendritic regenerative Ca 2 potential on the steady-state activation curves recorded at the soma is clearly seen in Fig. 5. In all simulations, the curves displayed conductance activation at more hyperpolarized potentials ( ) than the activation curves for point neurons ( ) and, similarly to the K conductance activation curves, did not reach saturation even at 5 mv (Fig. 5). Qualitatively similar deviations were observed when the conductance density was varied between 1 and 2 ps/ m 2 (Fig. 7) and when R m was varied between 5, and 5, (cm2 (simulations not shown). Figure 6 shows another manifestation of the shunting of the dendritic membrane potential to the Ca 2 reversal potential and the generation of dendritic Ca 2 spikes. Simulating a somatic voltage-clamp experiment in an L5 pyramidal neuron containing a homogenous distribution of a high-voltage-activated Ca 2 conductance generated a family of currents in response to voltage steps ranging from 8 to 4 mv (Fig. 6A). A similar simulation was carried out in a spherical cell for comparison (Fig. 6B). As previously shown for voltage-gated K conductances (Schaefer et al. 23a), the apparent activation of the currents simulated in the distributed morphology was slower than that simulated in a spherical cell. Moreover, one of the traces displays a kink or a current escape during the voltage-clamp command (Fig. 6A). This current escape is the hallmark of a regenerative activation of voltage-gated Ca 2 conductance in the dendrite. To test the predictions from the simulations, we performed TEVC recordings from the soma of L5 pyramidal neurons (Fig. 6C, inset). Voltage-gated K currents were reduced by complete substitution of K with Cs in the recording pipette and by bath application of 4 mm TEA. Voltage-gated Na conductance was blocked with 1 nm TTX. The currents recorded following a series of voltage-clamp steps display activation kinetics similar to the space-clamp distorted simulated currents displayed in Fig. 6A. Moreover, one of the current traces displays a clear current escape similar to the simulated currents displayed in Fig. 6A. Calculating the average steadystate activation curve from the deactivating part of the recording in Fig. 6C and from that of three other similar experiments generated a curve (Fig. 6D) similar to the simulations in Fig. 5. The curves displayed activation at more hyperpolarized potentials than the activation curves obtained from the literature (Hamill et al. 1991) and, similarly to the K conductance activation curves, did not reach saturation even at 8 mv (Fig. 6D). All of the simulations presented in the preceding text were carried out with fixed voltage-gated K (2 ps/ m 2 ) and Ca 2 (5 ps/ m 2 ) conductance densities. To quantitatively investigate the effect of conductance density and the length of the dendrite on space-clamp distortions, we repeated the simulations displayed in Figs. 2 and 5 using a simple ball and stick morphology (see METHODS). The density of the voltage-gated K conductance was varied systematically from to 2 ps/ m 2 while the length of the dendrite was varied from to 4 m. For each pair of these two values, we simulated the steady-state activation curve using conditions similar to those used to simulate the curves displayed in Fig. 2. The mean square error (MSE) between these curves and the curve simulated in a point neuron is displayed in Fig. 7A. The MSE displayed a shallow dependence on the conductance density and on the length of the dendrite. Similarly, the density of the voltage-gated Ca 2 conductance was varied systematically fromto2ps/ m 2 while the length of the dendrite was varied from to 4 m. For each pair of these two values, we simulated the steady-state activation curve using conditions similar to those used to simulate the curves displayed in Fig. 5. Contrary to the asymptotic dependence of the MSE calculated for the K conductance, the MSE calculated for the Ca 2 conductance increased in a highly nonlinear fashion as a function of both the conductance density and the length of the dendrite (Fig. 7B). DISCUSSION The simulations and experiments presented here demonstrate the effect of voltage-gated K and Ca 2 channels on the membrane potential during a voltage-clamp experiment in a neuron with distributed morphology. The simulations show that activation of these conductances shunts the membrane potential distal to the voltage-clamp electrode to the reversal potential of the respective ion. The experiments demonstrate some of the side effects of this shunting effect. We conclude that recording voltage-gated Ca 2 and K conductances from distributed morphologies may induce severe errors in the interpretation of the results and understanding of neuronal physiology. A simple biophysical mechanism is responsible for all the effects described here. Activation of a membrane conductance that is specific to one type of ion will shunt the membrane potential to the reversal potential of that ion. This effect has considerable consequences in synaptic integration because shunting inhibition and saturation of excitatory synapses both derive directly from this mechanism. During a voltage-clamp Downloaded from http://jn.physiology.org/ by 1.22.33.3 on November 29, 217 FIG. 4. Spatial activation of voltage-gated Ca 2 conductances during a voltage-clamp experiment in distributed morphologies. The membrane potential following a 1-s voltage-clamp step to mv was recorded when only passive membrane properties were inserted into the neurons (gray markings) and when a voltage-gated Ca 2 conductance with a density of 5 ps/ m 2 was homogenously inserted in all the compartments of the neurons. The figures are of the membrane potential of an L5 pyramidal neuron (Ai), a layer 4 interneuron (Bi), a layer 4 spiny stellate neuron (Ci), and a layer 2/3 bipolar interneuron (Di; black markings). In addition, the activation of the Ca 2 conductance is displayed in each compartment of the same neurons [an L5 pyramidal neuron (Aii), a layer 4 interneuron (Bii), a layer 4 spiny stellate neuron (Cii), and a layer 2/3 bipolar interneuron (Dii)]. J Neurophysiol VOL 99 MARCH 28 www.jn.org

1134 D. BAR-YEHUDA AND A. KORNGREEN A B C D 1..8.6.4.2. -8-4 4 1..8.6.4.2. -8-4 4 1..8.6.4.2. -8-4 4 1..8.6.4.2. -8-4 4 FIG. 5. Distortion of voltage-gated Ca 2 conductance activation curves in nonspherical cells. Activation curves were calculated by dividing the Ca 2 current recorded after a 1-s voltage-clamp step by the driving force and then by the maximal conductance ( )., the activation curves simulated in point neurons. A: L5 pyramidal neuron. B: layer 4 interneuron (C58E2). C: layer 4 spiny stellate neuron (j7_l4stellate). D: layer 2/3 bipolar interneuron (C23998A-I3). experiment, the membrane potential is clamped to a specific value for long periods of time. Thus the shunting effect, which is transient during synaptic transmission, lasts longer and has greater consequences. Interestingly, the shunting of the membrane potential distal to the voltage-clamp electrode is responsible for the observation that the K conductance activation curve does not saturate. When the membrane at the recording location is depolarized to positive potentials, the local K conductance reaches maximal open probability and does not contribute additional current to the recording. Because the voltage distal to the recording site is lower, due to the shunting of the membrane potential to the K reversal potential, the K conductance distal to the recording site does not reach maximal open probability. The axial current flowing to the soma from all the more distal locations in which the K conductances are partially activated both distorts the apparent kinetics of the K conductance and generates an increase in the apparent K conductance, which does not saturate even when the membrane is very depolarized. A similar logic, although with a positive reversal potential, can explain the shape of the activation curve obtained for the voltage-gated Ca 2 conductance (Figs. 5 and 6). The simulations here assumed that in addition to the leak conductance, only one voltage-gated conductance was expressed in the membrane of the simulated neurons. This is rarely the case in an experiment. It is possible to obtain a clean recording of the voltage-gated K conductances by blocking voltage-gated Ca 2 and Na conductances. However, recording clean voltage-gated Ca 2 currents from a distributed morphology encounters several pitfalls. The standard pipette solution for recording Ca 2 currents contains Cs instead of K. Because many K conductances are slightly permeable to Cs, some residual K current will almost always contaminate the Ca 2 current recordings. Moreover, due to incomplete diffusion from the soma to the dendrite, it is hard to guarantee a full internal block of K conductances by the Cs ions. Thus it is likely that the experimenter records a current that is the linear combination of the Ca 2 and K currents. Distal to the recording electrode, the membrane potential is set by two opposing forces, the K and Ca 2 driving forces, and settles to a value reflecting a combination of them. The resulting axial currents that flow to the recording electrode are severely distorted and cannot be subjected to analysis. Finally, in all the simulations performed in this study, the conductance density was assumed to be homogenous. However, in real nerve cells, K and Ca 2 channels distributed inhomogenously (Migliore and Shepherd 22). For example, in CA1 pyramidal neurons the density of an A-type K conductance density increases with density from the soma (Hoffman et al. 1997), whereas in L5 neocortical pyramidal neurons, the density of the sustained K conductance decreases along the apical dendrite (Schaefer et al. 27). We have previously shown that paradoxically due to the shunting of the membrane potential to the K reversal potential, the effect of K conductance gradient is small (Schaefer et al. 23b). This cannot, for similar reasons, be true for the case in which a gradient of voltage-gated Ca 2 is expressed in the dendrites. We have shown that even in neurons with relatively short dendrites the distortion of the recordings by the lack of space clamp was substantial. Even 5 m from the cell body there was a considerable deviation of the membrane potential from the voltage clamp command applied at the soma. Thus our results indicate that measuring Downloaded from http://jn.physiology.org/ by 1.22.33.3 on November 29, 217 J Neurophysiol VOL 99 MARCH 28 www.jn.org

SPACE-CLAMP PROBLEMS 1135 A B 1 na 1 ms 1. C D 1 na 5 ms 2 mv -1 mv G/G max.8.6.4.2. -8-4 4 8 FIG. 6. Activation of voltage-gated Ca 2 conductance in distributed morphologies distorts the time course of voltage-clamp recordings. A: simulation of a voltage-clamp experiment in the soma of a reconstructed L5 pyramidal neuron containing a homogenous distribution of 5 ps/ m 2 voltage-gated Ca 2 conductance model. B: a simulation using the same voltage-gated Ca 2 conductance model in a spherical neuron. C: a 2-electrode voltage-clamp experiment performed at the soma of a L5 pyramidal neuron using an AxoClamp-2B amplifier. The experiment is depicted in the inset showing the current injecting and voltage-sensing electrodes superimposed on the DIC image of the neuron. Scale bar is 2 m. The currents recorded by the Two-electrode voltage clamp (TEVC) were sampled at 1 khz and filtered at 3 khz. Leak and capacitive currents were subtracted off-line. The command potential is displayed below the recorded currents. D: activation curve calculated from the deactivating part of the experiment displayed in C and from three other experiments ( )., the activation curve reported in the literature (Hamill et al. 1991) for comparison. Error bars are SE. A.4 B 3 Downloaded from http://jn.physiology.org/ by 1.22.33.3 on November 29, 217 MSE.3.2.1 MSE 2 1 2 15 1 5 1 2 3 Length (µm) 4 2 15 1 5 1 2 3 Length (µm) 4 FIG. 7. Quantitative estimation of space clamp distortions. A: mean square error (MSE) calculated by taking the sum of squares of the difference between the steady-state activation curves of the voltage-activated K conductance calculated in a ball and stick model and a point neuron. The MSE is plotted as a function of the conductance density and the length of the dendrite in the ball and stick model. B: same calculation as in A performed for the voltage-gated Ca 2 conductance. J Neurophysiol VOL 99 MARCH 28 www.jn.org

1136 D. BAR-YEHUDA AND A. KORNGREEN voltage-gated currents from cells with distributed morphologies may lead to severe errors in the interpretation of the results. It may be prudent to investigate neuronal voltage-gated conductances using the cell-attached and excised patch configurations of the patch-clamp technique or correct the distortion of whole cell currents (Castelfranco and Hartline 24; Schaefer et al. 23a, 27). ACKNOWLEDGMENTS We thank Dr. Andreas Schaefer for expressing an opinion on an early version of this manuscript, N. Peled for Matlab programming tips, and H. Ben-Porat for excellent technical assistance. GRANTS This work was supported by Israeli Science Foundation Grant 345/4. REFERENCES Armstrong CM, Gilly WF. Access resistance and space clamp problems associated with whole-cell patch clamping. Methods Enzymol 27: 1 122, 1992. Ascoli GA. Mobilizing the base of neuroscience data: the case of neuronal morphologies. Nat Rev Neurosci 7: 318 324, 26. 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