AII amacrine cells in the mammalian retina are connected via electrical synapses to on-cone bipolar cells and to other AII amacrine cells. To understand synaptic integration in these interneurons, we need information about the junctional conductance (gj), the membrane resistance (rm), the membrane capacitance (Cm), and the cytoplasmic resistivity (Ri). Due to the extensive electrical coupling, it is difficult to obtain estimates of rm, as well as the relative contribution of the junctional and nonjunctional conductances to the total input resistance of an AII amacrine cell. Here we used dual voltage-clamp recording of pairs of electrically coupled AII amacrine cells in an in vitro slice preparation from rat retina and applied meclofenamic acid (MFA) to block the electrical coupling and isolate single AII amacrines electrically. In the control condition, the input resistance (Rin) was ∼620 MΩ and the apparent rm was ∼760 MΩ. After block of electrical coupling, determined by estimating gj in the dual recordings, Rin and rm were ∼4,400 MΩ, suggesting that the nongap junctional conductance of an AII amacrine cell is ∼16% of the total input conductance. Control experiments with nucleated patches from AII amacrine cells suggested that MFA had no effect on the nongap junctional membrane of these cells. From morphological reconstructions of AII amacrine cells filled with biocytin, we obtained a surface area of ∼900 μm2 which, with a standard value for Cm of 0.01 pF/μm2, corresponds to an average capacitance of ∼9 pF and a specific membrane resistance of ∼41 kΩ cm2. Together with information concerning synaptic connectivity, these data will be important for developing realistic compartmental models of the network of AII amacrine cells.
AII amacrine cells play a central role for transmission and integration of signals in the network of neurons that constitute the rod pathway (reviewed by Bloomfield and Dacheux 2001), and recent results suggest important roles for AII amacrines in photopic vision as well (Manookin et al. 2008; Münch et al. 2009). AII amacrine cells are postsynaptic to and receive glutamatergic input from the axon terminals of rod bipolar cells and some off-cone bipolar cells (Singer and Diamond 2003; Strettoi et al. 1992, 1994; Veruki et al. 2003). They are presynaptic to and transmit their signals to off-cone bipolar cells via glycinergic, inhibitory synapses (Pourcho and Goebel 1985; Sassoè-Pognetto et al. 1994; Strettoi et al. 1992, 1994). In addition, AII amacrine cells are connected via gap junctions to on-cone bipolar cells (heterologous connections) and to other AII amacrine cells (homologous connections) (Chun et al. 1993; Kolb 1979; Kolb and Famiglietti 1974; McGuire et al. 1984; Strettoi et al. 1992, 1994). Functionally, both types of gap junctions correspond to electrical synapses (Trexler et al. 2005; Veruki and Hartveit 2002a,b).
While the electrical synapses between AII amacrine cells and on-cone bipolar cells are considered to play a role in the direct transmission of scotopic visual signals, the electrical synapses between AII amacrine cells are thought to be important for removing noise from the visual signal (Smith and Vardi 1995; Vardi and Smith 1996). The magnitude of the junctional conductance (gj) between AII amacrine cells and between AII amacrine and on-cone bipolar cells is important for the functional consequences of electrical coupling (Veruki et al. 2008), and it is important to obtain experimental measurements of these parameters. However, to fully understand synaptic integration in AII amacrine cells, we need knowledge of additional passive membrane parameters such as membrane resistance (rm), membrane capacitance (Cm), and cytoplasmic resistivity (Ri). There is currently not sufficient quantitative information to construct compartmental models of the network of AII amacrine cells with a high level of morphological and physiological realism. It is essential to construct such models that can serve as electrical skeletons onto which active, voltage-gated conductances can be added with the goal of building up a realistic computational model (Major 2001). For example, it is unknown how much of the total input conductance of a single cell the junctional and nonjunctional conductances account for. This question can be addressed experimentally for a pair of electrically coupled cells, using a two-cell circuit model (Bennett 1966, 1977), but in the case of the network of AII amacrine cells, this model ignores the fact that a single cell is connected by electrical synapses to several other AII amacrine cells and on-cone bipolar cells. There are few agents that block gap junction channels, and several of these have nonspecific effects on other channel types. Recently, however, the compound meclofenamic acid (MFA) was demonstrated to block tracer coupling and electrical coupling between AII amacrine cells and between AII amacrines and on-cone bipolar cells (Pan et al. 2007; Veruki and Hartveit 2009). The block is complete and reversible, but the time required for complete block is typically 20–40 min. This suggests that MFA can be used in experiments that seek to measure physiological properties of electrically isolated AII amacrine cells but that the required recording durations can be technically challenging. Here we have used high-resistance pipettes to obtain long-lasting voltage-clamp recordings of electrically coupled pairs of AII amacrine cells where gj is stable over time under control conditions (Veruki and Hartveit 2009; Veruki et al. 2008). We obtained estimates of rm and Rin at regular intervals, first in the control condition and then during block of electrical coupling with MFA. Because we performed dual recordings of electrically coupled pairs of AII amacrines, we obtained measurements of gj in parallel with rm and Rin and could determine when the electrical coupling was blocked (gj = 0). By combining the measurements of rm under conditions of blocked coupling with measurements of membrane surface area based on quantitative morphological reconstructions of single AII amacrine cells, we obtained estimates for the specific resistance of the nongap junctional membrane. These results will be important for our ability to model the integrative properties of the network of electrically coupled AII amacrine and on-cone bipolar cells under conditions of changing gj.
General aspects of the methods have previously been described in detail (Veruki and Hartveit 2002a, 2009). Albino rats (4–7 wk postnatal) were deeply anesthetized with isoflurane in oxygen and killed by cervical dislocation (procedure approved under the surveillance of the Norwegian Animal Research Authority). Retinal slices were visualized with a ×40 water-immersion objective (Olympus BX51WI) and infrared gradient contrast videomicroscopy (Luigs and Neumann, Ratingen, Germany) (Dodt et al. 1998). Recordings were carried out at room temperature (22–25°C).
Solutions and drugs
The extracellular perfusing solution was continuously bubbled with 95% O2-5% CO2 and had the following composition (in mM): 125 NaCl, 25 NaHCO3, 2.5 KCl, 2.5 CaCl2, 1 MgCl2, and 10 glucose, pH 7.4. Whole cell recordings were performed with pipettes pulled from thick-walled borosilicate glass (GC150-11; Harvard Apparatus, Edenbridge, UK). For paired whole cell recordings and for nucleated patch recordings, the pipettes were filled with the following solution (in mM): 125 K-gluconate, 5 KCl, 8 NaCl, 0.2 EGTA, 10 HEPES, and 4 MgATP (pH was adjusted to 7.3 with KOH). Lucifer yellow was added at a concentration of 1 mg/ml. In single-cell recordings for morphological reconstructions (see following text), the pipettes were filled with the following solution (in mM): 125 K-gluconate, 10 KCl, 8 NaOH, 5 EGTA, 1 CaCl2, 10 HEPES, 4 MgATP, and 0.3 NaGTP (pH was adjusted to 7.3 with KOH). Lucifer yellow was added at a concentration of 1 mg/ml, and biocytin was added at a concentration of 3 mg/ml. Theoretical liquid junction potentials were calculated with the computer program JPCalcW (Molecular Devices, Sunnyvale, CA) and membrane holding potentials (Vhold) were corrected for liquid junction potentials on- or off-line.
During recordings, AMPA, GABAA and glycine receptors were blocked by 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX), bicuculline, and strychnine, respectively. Voltage-gated Na+ channels were blocked by tetrodotoxin (TTX). Drugs were added directly to the extracellular solution used to perfuse the slices. The concentrations of drugs were as follows (in μM; supplier Tocris Bioscience, Avonmouth, UK, unless otherwise noted): 10 bicuculline methchloride, 10 CNQX disodium salt, 100 2-[(2,6-dichloro-3-methylphenyl)amino]benzoic acid sodium salt [meclofenamic acid (MFA) sodium salt; Sigma], 1 strychnine, and 0.3 TTX. MFA sodium salt was stored as a stock solution in water (100 mM) at −20°C and diluted to the final concentration on the day of the experiment.
Electrophysiological recording and data acquisition
For paired, whole cell recordings between AII amacrine cells, we used high-resistance pipettes (25–35 MΩ) with long, thin tips. The accompanying reduced intracellular perturbation allowed us to obtain stable and long-lasting recordings of electrically coupled cell pairs (Veruki and Hartveit 2009). Voltage clamp was achieved by using two discontinuous (switched) single-electrode voltage-clamp (DSEVC) amplifiers (SEC-05LX-BF; npi Electronic, Tamm, Germany), each controlled by one of two instances of PatchMaster software (HEKA Elektronik, Lambrecht/Pfalz, Germany) in a “master-slave” configuration with both instances running on the same computer (Mac OS X version 10.4). These amplifiers switch between current injection and potential measurement at high frequency (e.g., Halliwell et al. 1994). Because the potential is measured at a time when no current flows across the recording electrode, problems caused by voltage drops across nonzero series resistance (Rs) are reduced and potentially totally avoided. The switching frequency was set to 35–40 kHz, synchronized between the two amplifiers (Müller et al. 1999), and the duty cycle was set to 1/4. Before sampling, current and voltage signals were low-pass filtered (analog 4-pole Bessel filter) with corner frequency of 2 kHz (−3 dB; 1/5 of the inverse of the sampling interval of 100 μs). The voltage-clamp gain and the proportional-integral controller were adjusted to give the fastest possible voltage response with minimal overshoot and ringing. The headstage output voltage signal from both amplifiers was monitored on an oscilloscope throughout each recording. For each amplifier, application of voltage protocols and digital sampling of the analog signals were performed by an LIH8+8 laboratory interface (HEKA Elektronik). The start of sampling by the slave interface was hardware triggered from the master interface via a digital line.
For single-cell, whole cell recordings (for morphological reconstructions; see following text) and for nucleated patch recordings, we used lower-resistance pipettes (∼5 MΩ for whole cell recording; ∼9 MΩ for nucleated patch recording) and an EPC9-dual patch-clamp amplifier (continuous single-electrode voltage-clamp; CSEVC; HEKA Elektronik) controlled by PatchMaster software. To establish nucleated patch recordings, the pipette was slowly withdrawn after establishing the whole cell configuration while continuous light suction (50–100 mbar) was applied to the pipette. Before sampling, signals were low-pass filtered (analog 3- and 4-pole Bessel filters in series) with a corner frequency (−3 dB) of 2 kHz (1/5 of the inverse of the sampling interval of 100 μs). Currents caused by the recording pipette capacitance (Cfast) and the cell membrane capacitance (Cslow) were measured with the automatic capacitance neutralization circuitry of the amplifier.
In all experiments, cells and patches were voltage clamped at a holding potential (Vhold) of −60 mV.
Dynamic clamp electrophysiology
We implemented artificial electrical synapses between pairs of electronic model cells by conductance injection (dynamic clamp) electrophysiology (Robinson and Kawai 1993; Sharp et al. 1993; reviewed by Goaillard and Marder 2006). The conductance injection was performed with real-time software (SM-2; Cambridge Conductance, Royston, UK) (Robinson 2008) running on a digital signal processing (DSP) analog board (Toro-8; Innovative Integration, Simi Valley, CA) interfaced with a host PC. A current command signal was generated from a user-specified conductance value and the instantaneous values of the time-varying membrane potentials of the cells. For an electrical synapse connecting two electronic model cells (cells a and b) in an artificial network, the current injected into each cell [Ia(t) in cell a, Ib(t) in cell b] was calculated according to the following equations (1) (2) where gj is the junctional conductance and Va(t) and Vb(t) are the instantaneous values of the membrane potentials of cells a and b, respectively. The same conductance value was used for each direction of coupling (cell a → cell b, cell b → cell a). The SM-2 system was run with a sampling interval of 50 μs. The conductance injection experiments were performed with two clustered EPC10-triple amplifiers (CSEVC) in the current-clamp configuration, using 100% bridge-balance compensation (10 μs time constant).
Histology and three-dimensional reconstruction
In single-cell recording experiments, AII amacrine cells (n = 6) were filled with biocytin for staining the cells and subsequent off-line morphological reconstruction. After 5–10 min of whole cell recording, the recording pipette was removed, and the slice was immediately fixed for 2 min in 2% paraformaldehyde (PFA; 4% PFA in 0.1 M phosphate buffer was added to an equal volume of HEPES-buffered extracellular solution). Thereafter the slice was fixed in 4% PFA in phosphate buffer at room temperature for 30 min and at 4°C overnight. To minimize problems with tissue shrinkage, we did not dehydrate or resection the slices. Development of a reaction product with avidin-biotinylated horseradish peroxidase complex (VECTASTAIN ABC-elite kit; Vector Laboratories, CA) and diaminobenzidine was done as described in detail in Oltedal et al. (2009).
Quantitative morphological reconstruction of the labeled cells was done with a motorized microscope (Olympus BX 51) equipped with a ×100 oil-immersion objective (NA 1.25; Olympus), a digital CCD camera (MicroFire S99808, Optronics) and Neurolucida software (v7; MicroBrightField Bioscience, Williston, VT). The soma of each cell was traced as a single contour. The surface area of the three-dimensional (3D)-reconstructed cells was calculated with the help of the software program Neurolucida Explorer (MicroBrightField Bioscience). No attempt was made to correct for errors in morphological measurements due to shrinkage and consequent distortion.
To estimate the steady-state gj between the two cells of a physiologically coupled pair, we used current responses obtained with dual voltage-clamp recordings. For the calculations, we assumed an equivalent-circuit model (Fig. 1A). For recordings using DSEVC amplifiers, we assumed that Rs was effectively zero. This means that the junction current (Ij) corresponds to the current evoked in the postsynaptic cell and gj can be calculated directly from Ohm's law (Hartveit and Veruki 2010; Müller et al. 1999) according to Eq. 3 for voltage pulses applied to cell a and according to Eq. 4 for voltage pulses applied to cell b (3) (4) where Ia is Ij measured in cell a, Ib is Ij measured in cell b, and Va and Vb are the voltages of cells a and b, respectively. Previous work with electronic model cells has demonstrated that voltage-clamp recordings with DSEVC amplifiers can correctly estimate gj with errors of <5% for Rs values up to ≥200 MΩ (Hartveit and Veruki 2010). For dynamic clamp recordings with CSEVC amplifiers, we mathematically corrected for nonzero Rs and finite rm according to published procedures (van Rijen et al. 1998). Each measurement of gj was obtained by plotting Ij versus the junction voltage (Vj) and by calculating gj as the slope of a straight line fitted to the Ij-Vj relationship. For a given cell pair, gj was calculated as the average of the gj values obtained for both directions of coupling.
The membrane resistance (apparent or real) was estimated according to Eq. 5 when stepping cell a (rm1) (5) and according to Eq. 6 when stepping cell b (rm2) (6) Each measurement of rm was obtained by plotting the voltage versus the current and by calculating rm as the slope of a straight line fitted to the V-I relationship.
In dual recordings of electrically coupled cells, the input resistance (Rin) of each cell was obtained indirectly by calculating it from the apparent membrane resistances (rm1, rm2) and gj according to Eq. 7 for cell a (Rin1) and Eq. 8 for cell b (Rin2) (7) (8) where rm1 is the apparent membrane resistance of cell a (estimated from Eq. 5), rm2 is the apparent membrane resistance of cell b (estimated from Eq. 6), and rj is the inverse of the junctional conductance (estimated from Eqs. 3 and 4).
Off-line data analysis was performed with FitMaster (HEKA Elektronik), IGOR Pro (WaveMetrics, Lake Oswego, OR) and Excel (Microsoft, Seattle, WA). Data are presented as means ± SE (n = number of cells or cell pairs), and percentages are presented as percentage of control. Statistical analysis was performed using Student's two-tailed t-test (paired). For illustration purposes, most raw data-records were low-pass filtered (digital nonlagging Gaussian filter; −3 dB at 0.5–1 kHz).
Equivalent electrical circuits for electrical coupling
A pair of electrically coupled cells can be represented by the equivalent electrical circuit illustrated in Fig. 1A (Bennett 1966, 1977; van Rijen et al. 1998). Each cell is represented by a simple resistor-capacitor (RC) circuit with a single lumped resistance (rm1 or rm2) and capacitance (Cm1 or Cm2). The resistance of the electrical synapse is represented by rj (junctional resistance), corresponding to a junctional conductance gj (= 1/rj). The parameters rm1, rm2, and gj can be estimated with dual voltage-clamp recording of a pair of electrically coupled cells. When the two cells are embedded in a larger network of electrically coupled cells, with each of the two cells coupled to additional cells, the two-cell circuit is an obvious simplification. For a simple two-dimensional network and low to moderate values of gj, the two-cell circuit can still be used as an approximation to obtain reasonably accurate estimates of gj between two neighboring cells (Veruki et al. 2008). However, when the two coupled cells are each coupled to other cells, we can no longer use the two-cell circuit to estimate the true membrane resistance. Specifically, when each cell is connected via electrical synapses to additional cells, the estimated values for rm1 and rm2 will represent apparent membrane resistances instead of true membrane resistances. Irrespective of these complicating factors, the two-cell circuit serves as an important analytical model and will be used in the present study to estimate the true rm of AII amacrine cells when gj is reduced pharmacologically.
Recent results demonstrated that electrical synapses between AII amacrine cells and between AII amacrine and on-cone bipolar cells are blocked completely, although slowly, by the drug MFA (Veruki and Hartveit 2009). This suggests that we can use MFA to electrically isolate AII amacrine cells and measure their passive membrane properties under varying degrees of coupling. With normal electrical coupling, the estimated rm (an apparent rm) reflects current flow across both the nongap junctional and gap junctional membrane. As the electrical synapses are gradually blocked by MFA, the apparent rm should gradually approach the true rm, and when gj is zero, the two should be equal. A similar change is expected for Rin, such that Rin is lower than rm under conditions of normal electrical coupling and equal to rm when gj is zero.
In the following, we first report results to validate our use of the two-cell circuit model to analyze electrical coupling when a pair of coupled cells is embedded in a larger network. Specifically, we wanted to verify the ability of our experimental recording procedures to extract the correct membrane parameters in situations with variable strength of the electrical coupling. For this, we used patch-clamp amplifiers and model cells with known circuit parameters and implemented electrical coupling with dynamic clamp electrophysiology. Next we report results obtained with paired recordings of electrically coupled AII amacrine cells where we monitored gj, rm, and Rin as electrical coupling was gradually blocked by MFA. Finally, we relate the measurements of rm obtained in the absence of electrical coupling to the measurements of membrane surface area obtained for morphologically reconstructed AII amacrine cells, allowing us to estimate upper and lower limits for the specific membrane resistance of AII amacrine cells.
Validation of two-cell circuit model to analyze passive membrane properties in a network of electrically coupled cells
We used dynamic clamp electrophysiology to implement an artificial network of electrically coupled model cell circuits (Fig. 1B). The network consisted of four model cells arranged in a linear array, and we used six patch-clamp amplifiers for controlling and recording the activity. Four amplifiers, one for each model cell, were used in the current-clamp configuration (CC1–CC4) with conductance injection to implement the electrical coupling (Fig. 1B). Two amplifiers were connected to cells 2 and 3 in the voltage-clamp configuration (VC2, VC3), thus mimicking dual voltage-clamp recording of a pair of electrically coupled cells embedded in a network of coupled cells.
To measure the influence of the magnitude of gj on the apparent passive membrane properties of the model cells, we applied voltage pulses alternatingly to the two cells in voltage clamp (cells 2 and 3; Fig. 1B) and estimated gj, rm1, rm2, Rin1, and Rin2 from the evoked currents. The same procedures were used to analyze the responses of the model cells and the biological cells. To correct for the effect of Rs and rm (in the model cells), we applied the procedures developed by van Rijen et al. (1998). Dynamic clamp, implemented with the SM-2 software and the patch-clamp amplifiers in current-clamp configuration (see methods), was used to vary gj of each virtual electrical synapse between 0 and 3,000 pS. For each condition, gj was identical for all the virtual electrical synapses. When the network was completely uncoupled (gj = 0), rm and Rin were identical and equal to ∼511 MΩ. With increasing strength of the electrical coupling, the values of rm and Rin gradually dropped (Fig. 1C). When Rin for a cell drops with increasing gj, it reflects the increasing flow of current to other electrically coupled cells relative to the current flowing through the cell's real membrane resistance. When rm for a cell drops with increasing gj, it reflects that the network of electrically coupled cells is larger than the simple two-cell network illustrated in Fig. 1. While rm estimated for a simple two-cell network reflects the real membrane resistance, the presence of other cells electrically coupled to the two cells in a dual recording (e.g., in the 4-cell network illustrated in Fig. 1B) means that the estimated rm will be an apparent membrane resistance. When gj increases, an increasing amount of current will flow to the electrically coupled cells not directly recorded from, appearing as a drop in rm. As expected, Rin was smaller than rm for all values of gj > 0, with an increasing difference between the two parameters for increasing values of gj (Fig. 1C). The experimentally determined values for rm and Rin corresponded very well with the values for both parameters calculated directly from the exact values of the model cell resistors and the values of the conductances injected by dynamic clamp (Fig. 1C). This indicated that our experimental methods were well suited for revealing the relevant equivalent circuit parameters.
Passive membrane properties of electrically coupled AII amacrine cells
In dual voltage-clamp recordings of electrically coupled AII amacrine cells with DSEVC amplifiers and high-resistance pipettes (Veruki et al. 2008), we tested for electrical coupling by applying voltage pulses to one cell (“presynaptic”; Fig. 2A) and recording the current responses in both the pulsed and the nonpulsed (“postsynaptic”) cell (Fig. 2, B and C) (Veruki and Hartveit 2002a). When cells were electrically coupled, the hyper- and depolarizing voltage pulses applied to the presynaptic cell evoked outward and inward currents, respectively, in the postsynaptic cell (Fig. 2, B and C). For each direction of coupling, we plotted Ij versus Vj and calculated gj as the slope of a straight line fitted to the Ij-Vj relationship (Fig. 2, D and E). For each cell, we also calculated the current flowing through the apparent nongap junctional membrane (Im; Eqs. 5 and 6), plotted Im versus Vj and calculated the apparent rm as the slope of a straight line fitted to the Im-Vj relationship (Fig. 2, F and G). All current measurements for rm were obtained from responses to hyperpolarizing voltage pulses and were within the linear range without activation of voltage-activated conductances (Fig. 2, F and G). Rin was calculated from the values of rm1, rm2, and rj (Eqs. 7 and 8). rm and Rin were calculated individually for both cells in a pair (rm1, rm2, Rin1, and Rin2), whereas gj for a cell pair was calculated as the average of the conductance values measured in each direction. For the AII cell pair illustrated in Fig. 2, gj was 390 pS, rm1 was 1,170 MΩ, rm2 was 1,490 MΩ, Rin1 was 910 MΩ, and Rin2 was 1,070 MΩ.
Under optimal conditions, recordings with high-resistance pipettes and DSEVC amplifiers could be maintained for ≤3 h. During the recordings, we repeatedly estimated gj, rm, and Rin, with one set of measurement points obtained at intervals of ∼20 s. For most cells, all three parameters were stable over time, as is illustrated in Fig. 3 for a coupled cell pair recorded for >120 min. For five cell pairs, we calculated an average value for each parameter from all measurement points obtained within a period of stable recording (110–150 min; average: 130 ± 7 min). gj was 320 ± 18 pS (n = 5), rm was 520 ± 34 MΩ (n = 10), and Rin was 460 ± 25 MΩ (n = 10). The average holding current was 2.6 ± 3.4 pA (n = 10) and changed little over the time course of the recordings (Fig. 3D).
Changes of passive membrane properties of AII amacrine cells during pharmacological block of electrical coupling
We next examined the changes in passive membrane properties of AII amacrine cells when the gap junction coupling between these cells, and between these cells and on-cone bipolar cells, was gradually blocked. To achieve this, we applied the gap junction blocker MFA (100 μM) during paired recordings of coupled AII amacrines. MFA blocks both tracer coupling (Pan et al. 2007) and functional electrical coupling between AII amacrine cells (Veruki and Hartveit 2009). An example of the action of MFA can be seen in Fig. 4 where the electrical coupling was completely blocked after ∼20 min of application. For each measurement of gj, we also calculated rm (average of rm1 and rm2) and Rin (average of Rin1 and Rin2) and monitored Ihold (Fig. 4). During application of MFA, rm and Rin slowly increased and reached a maximum at approximately the point in time when the electrical coupling was abolished (gj ∼0). For this cell pair, rm1 changed from ∼390 MΩ in the control condition to ∼1,560 MΩ after complete block of electrical coupling and Rin1 changed from ∼330 MΩ in the control condition to ∼1,560 MΩ after complete block by MFA (Fig. 4B). Similar changes were observed for rm2 and Rin2 (Fig. 4C). For six cell pairs, rm changed from 760 ± 104 MΩ (range: 390–1,490 MΩ) in the control condition to 4,430 ± 510 MΩ (range: 1,500–6,460 MΩ) after complete block of electrical coupling with MFA (monitored by repeated measurements of gj; n = 12; P = 8.2 × 10–6; Fig. 4E). For Rin, the corresponding change was from 620 ± 76 MΩ (range: 330–1,070 MΩ) in the control condition to 4330 ± 490 MΩ (range: 1,500–6,450 MΩ) after complete block of electrical coupling with MFA (P = 6.2 × 10–6; Fig. 4E). Rin was 83 ± 1% of the value of rm in the control condition and 98 ± 1% of the value of rm after complete block of electrical coupling with MFA (n = 12). Comparing Rin in the control condition with rm after complete block of electrical coupling, indicated that the nongap junctional conductance was 16 ± 2% of the total input conductance. Following application of MFA, Ihold of both cells changed to a more positive level (Fig. 4D), reaching a peak near the point in time when gj = 0. Ihold of both cells returned to a more negative value during wash-out of MFA. For the 12 cells, Ihold changed from −4.5 ± 3.4 pA in the control condition to 10.7 ± 2.9 pA in the presence of MFA (P = 1.2 × 10−4).
Does MFA have a direct effect on membrane resistance of AII amacrine cells?
The increase of rm and Rin for AII amacrine cells evoked by MFA is consistent with and can be explained by block of electrical coupling. From previous work we know that MFA blocks electrical coupling not only between AII amacrine cells but also between AII amacrine cells and on-cone bipolar cells (Veruki and Hartveit 2009). However, it is also known that MFA and related fenamates modulate a diversity of ion channels in addition to connexons. For example, MFA inhibits hKv2.1 potassium channels (Lee and Wang 1999), opens KCNQ2/Q3 potassium channels (Peretz et al. 2005), and stimulates BKCa channel activity (Wu et al. 2001).
To investigate the potential effect of MFA on ion channels active in AII amacrine cells at the voltages used for measurement of gj, and separate such effects from the effect of MFA on electrical coupling, we isolated nucleated patches from AII amacrine cells. For each patch, we sampled I-V curves repeatedly with application of voltage pulses from a Vhold of −60 mV (−30 to +10 mV relative to Vhold; 10-mV increment per sweep; Fig. 5). A complete I-V curve was sampled approximately every 20 s. After a baseline period of 3–5 min, we applied MFA (100 μM) for 5–15 min, followed by a recovery period. As illustrated by the example in Fig. 5, MFA had no consistent effect on either rm or Ihold. Similar results were observed for six other nucleated patches. rm was 14 ± 5 GΩ in the control condition and 13 ± 5 GΩ in the presence of MFA. Ihold was −3.9 ± 1.4 pA in the control condition and −3.6 ± 1.6 pA in the presence of MFA (P > 0.3 for both rm and Ihold; n = 7 patches). The period of MFA application was shorter than that required for complete block of gj but longer than the time required for onset of block of gj (Veruki and Hartveit 2009).
Passive membrane properties of AII amacrine cells
To obtain a simple estimate of the specific membrane resistance of AII amacrine cells, we need measurements of both the total rm and the total membrane surface area. Because our measurements of rm were obtained under conditions of blocked electrical coupling, they should reflect properties of the nongap junctional membrane. Because recordings with DSEVC amplifiers do not provide estimates of cell capacitance, we filled AII amacrine cells with biocytin to obtain morphological estimates of the surface area. To minimize diffusion of tracer from the recorded cell to other coupled cells, cells were only kept for 5–10 min in the whole cell configuration after which the slices were fixed and processed to develop a visible reaction product. With such brief periods of whole cell recording, we never observed evidence for tracer coupling from the injected cell. Following morphological reconstruction, surface areas were calculated with Neurolucida Explorer. The morphological projections of six successfully reconstructed AII amacrine cells are illustrated in Fig. 6. The average surface area was 923 ± 42 μm2 (range: 803–1,106 μm2). If we assume the standard value of 0.01 pF/μm2 for specific membrane capacitance (Gentet et al. 2000; Hille 2001; Major 2001), this corresponds to an average capacitance of 9.2 ± 4.2 pF (range: 8.0–11.1 pF) for noncoupled AII amacrine cells.
With rm for isolated AII amacrine cells ranging between 1.5 and 6.5 GΩ and the surface area ranging between 803 and 1,106 μm2, the specific membrane resistance (Rm) can be estimated as 17–52 kΩ cm2 (assuming that surface area and rm are inversely correlated). From the average values of surface area and rm, we obtain an average value for Rm of 41 kΩ cm2. From these results, we can estimate a membrane time constant (τm = Rm × Cm) of 41 ms (range: 17–52 ms), again assuming a specific membrane capacitance of 0.01 pF/μm2.
In this study we have presented estimates of the passive membrane properties of AII amacrine cells in the rat retina. Because these cells are electrically coupled to each other and to on-cone bipolar cells, it is technically challenging to estimate their passive membrane properties. We used MFA to completely block the electrical synapses between AII amacrine cells and between AII amacrine and on-cone bipolar cells (Pan et al. 2007; Veruki and Hartveit 2009) and used voltage-clamp responses measured after complete block of coupling to estimate the total resistance of the nongap junctional membrane of AII amacrine cells which ranged from 1.5 to 6.5 GΩ. In a parallel set of experiments, we filled single AII amacrine cells with biocytin and, after developing the reaction product, reconstructed the morphology of AII amacrine cells. From the quantitative morphological data, we obtained estimates of total surface area which ranged from ∼800 to ∼1,100 μm2 with an average of ∼920 μm2. Combining the estimates of membrane resistance and surface area allowed us to constrain the specific membrane resistance to the range 17–52 kΩ cm2 and the single-cell capacitance to 8–11 pF.
Passive responses in the presence and absence of electrical coupling
There is strong evidence from ultrastructural studies that AII amacrine cells are coupled via gap junctions to other cells of the same type and to on-cone bipolar cells (Chun et al. 1993; Kolb 1979; Strettoi et al. 1992, 1994; Vardi and Smith 1996). Corresponding to this, injection of single AII amacrine cells with neurobiotin or biocytin can demonstrate tracer coupling to other AII amacrines and to on-cone bipolars in whole-mount preparations (Hampson et al. 1992; Mills and Massey 1995; Vaney 1991), and there is evidence that electrical coupling is present in in vitro slice preparations as well (Trexler et al. 2005; Veruki and Hartveit 2002a,b).
In the present study, we observed a strong increase of apparent membrane resistance after application of a concentration of MFA (100 μM) that has been demonstrated to be sufficient to completely block electrical coupling between AII amacrine cells and between AII amacrine and on-cone bipolar cells (Veruki and Hartveit 2009). Because we recorded from pairs of electrically coupled AII amacrine cells, we could directly correlate the increase of apparent rm with the block of electrical coupling by monitoring gj between the recorded cells. If we make the reasonable assumption that MFA blocks not only the electrical synapses between the two coupled AII amacrine cells in the recorded pair, but all other electrical synapses in the slice potentially sensitive to MFA, including those between either recorded cell and the other nonrecorded cells to which they are directly coupled, one would indeed expect that the apparent membrane resistance of each cell would increase.
The DSEVC amplifiers used in these recordings do not provide explicit information about the capacitance of the recorded cells. However, if the apparent capacitance “seen” by a CSEVC amplifier in a conventional whole cell recording of an electrically coupled AII amacrine cell is measurably influenced by the electrical coupling, it is reasonable to expect that the apparent capacitance should be reduced after application of MFA. Although capacitative currents evoked by square-wave pulses in AII amacrine cells decay with a time course that cannot be satisfactorily described by a single-exponential function (Veruki and Hartveit, unpublished observations), the estimate of apparent capacitance obtained by the neutralization circuitry of a CSEVC amplifier should still reflect the effective surface area. In several previous studies with presumed normal electrical coupling, we have obtained whole cell capacitance measurements of AII amacrine cells with CSEVC amplifiers of ∼14.5 pF [14.6 ± 0.4 pF; n = 89 cells (Veruki et al. 2003); 14.4 ± 0.4 pF; n = 62 cells (Veruki et al. 2008)]. With a specific membrane capacitance of 0.01 pF/μm2, this corresponds to an average surface area of ∼1,450 μm2, a value that is ∼160% of the value obtained from quantitative, morphological reconstruction after filling cells with biocytin (average: ∼920 μm2) and suggests that the measurements obtained in the control condition do indeed reflect the presence of electrical coupling. Because cells used for morphological reconstruction were kept in the whole cell configuration for a short time (5–10 min), it is likely that the light-microscopic morphology was relatively unaffected by diffusion of biocytin across electrical synapses to processes of neighboring coupled cells.
Specific resistance of nongap junctional membrane of AII amacrine cells
The results obtained in this study suggest that for AII amacrine cells, the nongap junctional conductance constitutes ∼16% of the total input conductance of a single cell. We obtained an approximate estimate for the specific membrane resistance of the nongap junctional membrane of AII amacrine cells by relating the total membrane resistance measured after blocking electrical coupling to the total surface area obtained after light-microscopic morphological reconstruction of single cells. The estimated range, 17–52 kΩ cm2, is similar to estimates from rod bipolar cells (average: 25 ± 19 kΩ cm2), obtained with considerably more accurate methods, involving compartmental modeling and directly fitting the current responses of individual models (based on morphological reconstruction) evoked by voltage pulses to the physiologically recorded responses from the same cells (Oltedal et al. 2009).
Experiments where we applied MFA to nucleated patches from AII amacrine cells suggested that MFA had no effect on the nongap junctional membrane, but there remains the possibility that MFA might have an effect on nonconnexon ion channels expressed in the dendrites of these cells (which would not be contained in nucleated patches). It will be difficult to investigate this experimentally as it does not seem possible to isolate AII amacrine cells intact from the retina.
Passive membrane parameters of AII amacrine cells
Cytoplasmic resistivity (Ri), Cm, and Rm are important parameters that influence the integrative properties and summation of synaptic inputs in single neurons. While there seems to be little variability in estimates of Cm, which is often regarded as a biological constant (Hille 2001; Major 2001), there is considerably more variability in estimates of Rm and Ri (Major 2001; Spruston et al. 2008). With respect to Ri, it has been difficult to design experiments that can estimate this parameter with high accuracy. In experiments with simultaneous somatic and dendritic whole cell recordings from layer 5 neurons in cerebral cortex (Stuart and Spruston 1998), CA1 pyramidal neurons (Golding et al. 2005), and cerebellar Purkinje neurons (Roth and Häusser 2001), computer modeling has indicated values for Ri between 70 and 200 Ω cm. The values obtained from these experiments have been considered to represent the most reliable estimates of Ri because the filtering of transient voltage changes in dendrites is very sensitive to the value of Ri (Spruston et al. 2008). Consistent with this, the modeling study of Oltedal et al. (2007) found that the decay of capacitative charging transients obtained in axon terminal recordings from retinal rod bipolar cells, as opposed to somatic recordings, was strongly influenced by changes of Ri. In experiments with axon terminal recordings and morphological reconstruction followed by compartmental model fitting, our average estimate for Ri was ∼130 Ω cm (Oltedal et al. 2009), very similar to the values obtained in the experiments with simultaneous somatic and dendritic recording from single cells.
It will be technically challenging to perform similar experiments to obtain more accurate estimates of Rin, Cm, and Rm for AII amacrine cells. Two obvious extensions of our experiments are unfortunately unlikely to provide the required answers. First, if one attempts to perform correlated physiological and morphological analysis on single cells, with recording of physiological responses and morphological reconstruction after filling the cells with biocytin, the long time required for MFA to block electrical coupling (Veruki and Hartveit 2009) means that biocytin would have time to diffuse to electrically coupled cells and ambiguate the cellular identity of filled processes during morphological reconstruction. Second, while blocking electrical coupling with MFA before establishing the recording could be a feasible strategy, we have been unable to obtain GΩ seals when MFA was already added to the extracellular solution (Veruki and Hartveit, unpublished observations). An alternative strategy for correlated physiological and morphological analysis of single AII amacrine cells could be to obtain quantitative morphological analysis with high-resolution fluorescence microscopy based on multi-photon excitation microscopy (e.g., Schmidt-Hieber et al. 2007). If the fluorescent tracer used to obtain the cellular morphology does not permeate the electrical synapses between AII amacrine cells, or between AII amacrine and on-cone biplar cells, the long time required to block electrical coupling with MFA would be relatively unimportant.
Finally, it is possible that the use of genetically modified animals with deleted expression of Cx36 (e.g., Deans et al. 2002) could be helpful in estimating the passive membrane parameters of noncoupled AII amacrine cells. While potentially very informative, such experiments will require detailed verification that the genetic modification has not altered other important functional or structural parameters (see e.g., De Zeeuw et al. 2003). It is also of concern that some of the heterologous gap junctions between AII amacrine cells and on-cone bipolar cells contain Cx45 in addition to Cx36 (Dedek et al. 2006; Han and Massey 2005; Lin et al. 2005; Maxeiner et al. 2005), suggesting that electrical coupling might not be completely abolished in Cx36 knockout animals.
Passive membrane parameters and synaptic integration in AII amacrine cells
AII amacrine cells receive excitatory, glutamatergic input from rod bipolar cells at the arboreal dendrites and from some off-cone bipolar cells at the lobular appendages (Strettoi et al. 1992, 1994), and there is physiological evidence for the operation of both inputs (Singer and Diamond 2003; Veruki et al. 2003). AII amacrine cells also receive inhibitory input from amacrine cells, presumably GABAergic and glycinergic, at various cellular compartments, and there is functional evidence for glycinergic, but not yet GABAergic, synaptic input (Gill et al. 2006; Weiss et al. 2008). Little is known, however, concerning integration of the various types of chemical synaptic input to AII amacrine cells. Accurate estimates of the passive membrane properties of AII amacrine cells will be required for realistic modeling of signal integration and processing in neural networks involving these cells and their synaptic partners, including the extent and manner in which synaptic integration is influenced by the strength of electrical coupling. The importance of these questions is underscored by the extensive evidence for physiological regulation of the strength of electrical coupling between AII amacrine cells (Bloomfield and Völgyi 2009; Hampson et al. 1992; Kothmann et al. 2009; Mills and Massey 1995; Urschel et al. 2006).
This study was supported by Research Council of Norway Grants NFR 165328 and 178105.
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