Static and Dynamic Membrane Properties of Large-Terminal Bipolar Cells From Goldfish Retina: Experimental Test of a Compartment Model

Steven Mennerick, David Zenisek, and Gary Matthews

Department of Neurobiology and Behavior, SUNY Stony Brook, Stony Brook, NY 11794-5230

    ABSTRACT
Abstract
Introduction
Methods
Results
Discussion
References

Mennerick, Steven, David Zenisek, and Gary Matthews. Static and dynamic membrane properties of large-terminal bipolar cells from goldfish retina: experimental test of a compartment model. J. Neurophysiol. 78: 51-62, 1997. Capacitance measurements allow direct studies of exocytosis and endocytosis in single synaptic terminals isolated from bipolar neurons of goldfish retina. Extending the technique to intact bipolar cells, with their more complex morphology, requires information about the cells' electrotonic architecture. To this end, we developed a compartment model of bipolar neurons isolated from goldfish retina and tested the model experimentally. The isolated cells retained morphology similar to that of bipolar neurons in intact goldfish retina. In whole cell recordings, current relaxations in response to 10-mV hyperpolarizing voltage pulses decayed with a biexponential time course. This suggests that the cells may be described by a two-compartment equivalent circuit with compartments corresponding to the soma/dendrites (6-10 pF) and synaptic terminal (2-4 pF), linked by the axial resistance (30-60 MOmega ) of the axon. Four lines of evidence validate the equivalent circuit. 1) Similar estimates of somatic/dendritic and terminal capacitance were obtained whether the patch pipette was attached to the soma or to the synaptic terminal. 2) Estimates of the capacitance of the two compartments in intact cells were similar to estimates from somata and terminals that were isolated by cleavage of the connecting axon. 3) When current transients were generated from a more complete computer simulation of a bipolar neuron, analysis of the simulated transients with the use of the simple two-compartment model yielded capacitance estimates similar to those used to set up the simulation. 4) In isolated cells, the model gave estimates of depolarization-evoked increases in capacitance of the synaptic terminal that were quantitatively similar to those measured in terminals that were detached from the rest of the cell. Although in previous studies researchers have attempted to apply a similar equivalent circuit to more geometrically complex cells, morphological correlates of the equivalent-circuit compartments have been elusive. Our results demonstrate that in dissociated bipolar cells, precise morphological correlates can be assigned to the equivalent-circuit compartments. Additionally, the work shows that time-resolved capacitance measurements of synaptic transmitter release are possible in intact, isolated bipolar neurons and may also be feasible in intact tissue.

    INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References

Time-resolved capacitance measurements (Gillis 1995; Neher and Marty 1982) have proven useful in studies of exocytosis and endocytosis in a variety of secretory cells, including synaptic terminals of bipolar neurons from goldfish retina (Heidelberger et al. 1994; Mennerick and Matthews 1996; von Gersdorff and Matthews 1994a,b). These bipolar cells possess a single giant presynaptic terminal from which direct whole cell patch-clamp recordings can be made (Heidelberger and Matthews 1992). Capacitance studies of synaptic exocytosis in this preparation have utilized isolated terminals, separated from the parent soma and connecting axon. The equivalent circuit of isolated terminals is simple, consisting of parallel membrane capacitance and resistance, linked to the voltage clamp by the access resistance of the whole cell pipette (Neher and Marty 1982). However, extending the capacitance analysis to intact bipolar cells requires a quantitative description of the membrane properties of the intact cell, including the terminal, axon, and soma. The experiments reported here were carried out to establish the appropriate passive electrical model for intact bipolar neurons under conditions relevant for capacitance measurements, and to use that model to measure synaptic exocytosis in intact cells. Information about the electrotonic profile of bipolar neurons might also allow exocytosis-associated changes in membrane capacitance of the synaptic terminals to be detected in situ, in a retinal slice preparation.

Other properties of the large-terminal bipolar cells in goldfish retina provide additional impetus for a characterization of passive membrane properties in these cells. The electrotonic properties of a neuron shape the input-output characteristics of the cell and help determine the fidelity with which synaptic conductance changes in the dendrites of a neuron are propagated to the soma (Spruston et al. 1994). Bipolar cells occupy a pivotal position in visual information flow through the retina, and understanding the passive membrane properties of these cells is a necessary step in understanding how received information is transformed by bipolar cells before being passed to postsynaptic amacrine and ganglion cells. A description of the cells' electrotonic profile will also aid in interpreting voltage-clamp records of currents generated in regions distal to the recording pipette.

An additional advantage of large-terminal bipolar neurons is that the isolated cells can be experimentally manipulated to test specific aspects of the electrical model. The complexity of neuronal geometry requires simplifications in models of neuronal electrotonic structure. However, the simplifications inherent in models are rarely, if ever, experimentally testable. For example, one of the simplest electrotonic models is a two-compartment scheme that has been used to describe the membrane properties of young cerebellar cells in situ (Llano et al. 1991) and cultured hippocampal neurons (Mennerick et al. 1995). In these cases, no clear morphological correlates of the circuit components could be identified, thereby limiting the explanatory power of the proposed model. Here we exploit the relatively simple, yet fully formed, morphology of isolated bipolar cells to experimentally test a two-compartment electrotonic model. With the use of spontaneously and experimentally isolated axon terminals and somata, we show that equivalent-circuit components correspond to precise physical compartments of bipolar cells, thus lending validity to the equivalent-circuit analysis as applied to intact cells.

    METHODS
Abstract
Introduction
Methods
Results
Discussion
References

Dissociation procedure

The dissociation procedure for goldfish bipolar cells has been described in detail (Heidelberger and Matthews 1992). Unless otherwise noted, all chemicals and salts were from Sigma. Dark-adapted goldfish were killed by rapid decapitation and were enucleated. The lens and vitreous were extracted in cold, oxygenated, low-calcium saline solution containing (in mM) 102 NaCl, 2.5 KCl, 1 MgCl2, 0.5 CaCl2, 10 glucose, and 10 N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid (HEPES), pH 7.4. Eyecups were then incubated for 5-10 min in 1,100 U/ml hyaluronidase to enzymatically remove remaining vitreous. Neural retinas were freed from the epithelium in cold low-calcium saline and cut into small pieces (~1 mm2). Retinal pieces were incubated 30-40 min in the low-calcium saline with the addition of 2.7 mM D,L-cysteine (Fluka) and 40 U/ml papain (Fluka). After being rinsed in low-calcium saline, pieces were stored in an oxygenated environment at 12°C for up to 5 h before being mechanically triturated and plated onto glass coverslips for recording. Intact bipolar cells and isolated bipolar-cell terminals were easily identified on the basis of their characteristic shape and their electrophysiological profile, which exhibits no sodium current but a rapidly activating, slowly inactivating calcium current in response to pulse or ramp depolarizations.

Confocal microscope images of dissociated bipolar cells were obtained with a BioRad MRC 600 microscope and a ×50 water-immersion objective. Cells were incubated in solutions containing 2 µM Calcium Green-1 AM (Molecular Probes) for visualization. Optical sections (50-75 through a cell) were obtained in 0.4-µm increments.

Patch-clamp method

The extracellular recording solution had the same composition as the saline solution described above, with CaCl2 increased to 2.5 mM. The patch pipette solution was usually composed of (in mM) 120 cesium gluconate, 10 tetraethylammonium chloride, 10 HEPES, 0.5 ethylene glycol-bis(beta -aminoethyl ether)-N,N,N',N'-tetraacetic acid, 2 Na2ATP, 2 MgCl2, and 0.5 guanosine 5'-triphosphate, pH adjusted to 7.4 with CsOH. The cesium/tetraethylammonium chloride intracellular solution was chosen to block voltage-gated potassium conductances that would interfere with thetime-resolved capacitance measurements described below.

Voltage-clamp recordings were made with the use of an Axopatch 200A amplifier at a holding potential of -60 mV. Patch pipettes, coated with dental wax to reduce stray capacitance, were fire-polished and exhibited an open-tip resistance of 6-10 MOmega . Pipette-membrane seals were >25 GOmega before membrane rupture. Residual pipette capacitance was compensated in the on-cell configuration with the use of the compensation circuitry of the Axopatch 200A amplifier.

The output bandwidth of the amplifier's Bessel filter was set at 50 kHz in experiments in which current responses to hyperpolarizing voltage pulses were examined, and at 2 kHz for other experiments. Current transients were sampled at 100 kHz. Initial experiments examining bipolar-cell passive membrane properties employed a 10-mV hyperpolarizing voltage pulse 5 ms in duration. In later experiments the pulse duration was shortened to 2 ms, representing 4-5 times the longest time constant observed.

Analysis

Unless otherwise stated, all results are presented as means ± SE. Analyses of current transients were performed on digital averages of 5-50 traces. The small holding current at -60 mV was subtracted from each point in the trace, and current decays in response to hyperpolarizing voltage steps were fit with the use of a Marquardt-Levenberg iterative sum-of-squares minimization algorithm (Sigma Plot, Jandel Scientific). Monoexponential fits were made to the equation A(t) = A(e-t/tau ) + As, where A(t) represents the current amplitude at time t relative to the imposition of the voltage step, As is the amplitude of the steady-state current at the end of a long voltage pulse, the sum of A and As is the current amplitude at the instant of the voltage change, and tau  is the time constant of the current relaxation toward As. Fits were begun 30-40 µs after the voltage step to help avoid contamination of the fit by residual input and output filtering. The fit was extrapolated to the onset of the voltage step to estimate the instantaneous current (A + As). Biexponential fits were made to the equation A(t) = A1(e-t/tau 1) + A2(e-t/tau 2) + As, with the subscript numerals 1 and 2 denoting fast and slow components, respectively. Similarly, triexponential fits added a third exponential term.

For isolated somata and synaptic terminals, whose current transients were well described by a single exponential and whose input resistance was quite high (>1 GOmega ), we used the following equations to estimate circuit parameters (e.g., Gillis 1995) in response to an imposed voltage change, Delta V
<IT>R</IT>= <FR><NU>Δ<IT>V</IT></NU><DE>A</DE></FR> (1)
<IT>C</IT>= <FR><NU><IT>A</IT>τ</NU><DE>Δ<IT>V</IT></DE></FR> (2)
The electrical parameters of the two-compartment equivalent circuit shown in Fig. 3A can also be estimated from biexponential current relaxations with the use of the following relations
<IT>R</IT>1 = <FR><NU>Δ<IT>V</IT></NU><DE>A<SUB>1</SUB><IT>+ A</IT><SUB>2</SUB></DE></FR> (3)
<IT>R</IT>2 = <FR><NU>(<IT>A</IT><SUB>2</SUB>τ<SUB>1</SUB><IT>+ A</IT><SUB>1</SUB>τ<SUB>2</SUB>)<SUP>2</SUP>Δ<IT>V</IT></NU><DE><IT>A</IT><SUB>1</SUB><IT>A</IT><SUB>2</SUB>(<IT>A</IT><SUB>1</SUB><IT>+ A</IT><SUB>2</SUB>)(τ<SUB>2</SUB>− τ<SUB>1</SUB>)<SUP>2</SUP></DE></FR> (4)
<IT>C</IT>1 = <FR><NU>(<IT>A</IT><SUB>1</SUB><IT>+ A</IT><SUB>2</SUB>)<SUP>2</SUP>τ<SUB>1</SUB>τ<SUB>2</SUB></NU><DE>(<IT>A</IT><SUB>2</SUB>τ<SUB>1</SUB><IT>+ A</IT><SUB>1</SUB>τ<SUB>2</SUB>)Δ<IT>V</IT></DE></FR> (5)
<IT>C</IT>2 = <FR><NU><IT>A</IT><SUB>1</SUB><IT>A</IT><SUB>2</SUB>(τ<SUB>2</SUB>− τ<SUB>1</SUB>)<SUP>2</SUP></NU><DE>(<IT>A</IT><SUB>2</SUB>τ<SUB>1</SUB><IT>+ A</IT><SUB>1</SUB>τ<SUB>2</SUB>)Δ<IT>V</IT></DE></FR> (6)
A major assumption of the two-compartment model in this study is that of a very high membrane resistance. A simplification of this type is necessary to derive unique solutions for the equivalent-circuit components from the experimentally derived fit parameters. Although other simplifications of the circuit are possible (Llano et al. 1991; Mennerick et al. 1995), the assumption of a uniformly high membrane resistance is likely the most reasonable for these cells, given the high input resistance experimentally measured (see below). Also, Nodus simulations, described below, validate the idea that this simplification does not greatly affect estimates of the membrane properties.


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FIG. 3. Two-compartment model equivalent circuit and its application to bipolar cells. A: equivalent circuit consists of 2 membrane capacitance compartments, C1 and C2, defined by their proximity to recording pipette (C1 proximal). Membrane compartments are linked together by a resistance R2. Entire circuit is linked to voltage clamp by pipette access resistance R1. Vc: voltage clamp. B: average estimates for circuit parameters from a sample of 9 bipolar cells. Circuit parameters were estimated by substituting biexponential fit parameters into Eq. 3-6. Open bars: terminal-end recordings. Shaded bars: soma-end recordings from same cells.

For time-resolved capacitance measurements, estimates of passive membrane parameters were made by fitting the average current transients from five hyperpolarizing voltage pulses (amplitude 10-20 mV, duration 2 ms). Trains of voltage pulses were delivered at 20 Hz, but averaging of five current transients yielded a time resolution of 250 ms per data point. Pilot experiments showed that time-resolved capacitance estimates of synaptic terminals in soma-end recordings exhibited more baseline variability than measurements in terminal-end recordings, making detection of terminal capacitance changes in soma-end recordings more difficult. We attribute much of the baseline variability in soma-end estimates to the similar magnitudes of the time constants of biexponential fits from soma-end recordings (Fig. 2C). We suspect that the similarity of the two time constants in these recordings likely hinders the ability of the fitting algorithm to precisely estimate the fit parameters. Two experimental protocol changes reduced this problem: 20-mV (rather than the usual 10-mV) hyperpolarizing test pulses were used to increase the current sizes (thus providing a better signal-to-noise ratio), and the number of baseline and experimental capacitance data points was increased.


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FIG. 2. Current relaxations in response to 10-mV hyperpolarizing command pulses are well described by sum of 2 exponential terms. A: whole cell recording from synaptic terminal end of a bipolar cell. In this and subsequent figures, drawings associated with plots schematically illustrate recording configuration employed for the experiment. Cone attached to bipolar cell in drawing: patch pipette. A, top trace: command voltage. Numbers on trace: holding potential (-60 mV) and pulse potential (-70 mV). Filled circles in bottom trace: current in response to 10-mV voltage pulse, sampled at 10-µs intervals. Solid line: least-squares biexponential fit to current relaxation (see METHODS for equations). Fit parameters from biexponential fit were: A1 = -599.2 pA, A2 = -176.2 pA, tau 1 = 22.5 µs, tau 2 = 448 µs, As = -4.8 pA (see METHODS for explanation of variables). Insets: residual plots of difference between sum-of-squares minimized fits and raw data for a monoexponential fit (left inset), biexponential fit (middle inset), and triexponential fit (right inset; see METHODS for an explanation of residual plots). B: whole cell recording from somatic end of a bipolar cell. Conventions as in A. Fit parameters from biexponential fit were: A1 = -289.2 pA, A2 = -537.5 pA, tau 1 = 71.2 µs, tau 2 = 179.5 µs, As = -2.6 pA. C: average fit parameters for terminal-end recordings (T, n = 13 cells) and soma-end recordings (S, n = 14 cells). C, left: shaded bars represent fast time constant from each recording location; open bars represent slow time constant. C, right: relative contribution of the more rapidly decaying component (A1) to total current at the instant of the voltage step.

The quality of individual fits was assessed with the use of residual plots (e.g., Fig. 2, A and B, insets). These plots are generated by a point-by-point subtraction of the raw, experimental data from the theoretical data trace generated from the sum-of-squares minimized fit parameters. Therefore the plots represent a simple, visual way of assessing the degree to which experimental data deviate from the exponential or multiexponential model employed in the fit (Ellis and Duggleby 1978). Nonrandom deviations from the zero level in residual plots reflect a poor fit, whereas small, random deviations reflect a good fit.

Simulations

Simulations were produced with the use of Nodus software (DeSchutter 1993). Simulated bipolar cells were constructed on the basis of measured dimensions and electrophysiological parameters of isolated bipolar cells, combined with generally accepted membrane and cytoplasmic electrical properties. The bipolar-cell simulation consisted of a cylindrical somatic compartment 14.0 µm diam and 18.0 µm long connected by a cylindrical axonal compartment 35.0 µm long and 1.5 µm diam to a synaptic terminal compartment represented by a sphere 9.0 µm diam. These dimensions were based on physical measurements of bipolar cells, with the use of brightfield and confocal analyses of samples of dissociated bipolar cells. An additional cylindrical compartment was attached either to the terminal compartment or to the somatic compartment to represent the patch pipette. The diameter of the pipette compartment was adjusted to yield a typical experimental access resistance of 14.6 MOmega linking the pipette with the relevant cellular compartment. Specific membrane capacitance and cytoplasmic resistance were set to standard values of 1.0 µF/cm2 and 250 Omega /cm, respectively (Spruston et al. 1994). Membrane resistivity was set to 14.0 kOmega /cm2 to yield a cell input resistance similar to that observed in whole cell recordings.

    RESULTS
Abstract
Introduction
Methods
Results
Discussion
References

Response of intact cells to hyperpolarizing voltage pulses

Figure 1 depicts a typical isolated goldfish retinal bipolar cell. The physical appearance of cells was quite similar to cells of this class in intact retina (cf. Ishida et al. 1980; Suzuki and Kaneko 1990), with a single, large synaptic terminal, connected by a short, thick axon to a goblet-shaped soma with numerous short dendritic processes. To examine the passive membrane characteristics of bipolar cells, we examined current responses to 10-mV hyperpolarizing pulses. Figure 2 shows examples of whole cell current transients in response to hyperpolarizing pulses applied to a patch pipette sealed to either the synaptic terminal (Fig. 2A) or the soma (Fig. 2B) of two different bipolar cells. Recordings from either position produced current transients whose relaxations deviated from the monoexponential decay expected for the simple case of a spherical, isopotential cell. Rather, current transient decays were well fit by the sum of two exponentials. Fits were not improved by adding a third exponential term (Fig. 2, A and B, insets).


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FIG. 1. Confocal stereo pair of a dissociated goldfish large-terminal bipolar cell. Cell was filled with Calcium Green-1 AM for 30 min for visualization with laser-scanning confocal microscope. Projection at right was rotated 20° with respect to projection at left. Note large synaptic terminal and flask-shaped cell body. Scale bar: 6 µm.

Although two exponential terms satisfactorily described the decay of current transients in recordings made from either the synaptic terminal or the soma, the transients from the two recording locations were quite distinct. This difference can be appreciated qualitatively from inspection of the raw traces in Fig. 2, A and B, and is quantified in Fig. 2C, which shows the average fit parameters from 27 bipolar cells. Transients from terminal recordings were characterized by a fast time constant of 26.6 ± 1.1 (SE) µs, with this component representing 72 ± 4% of the total initial current amplitude. The slow time constant in terminal recordings was 433 ± 29 µs. In contrast, the fast time constant and slow time constant from somatic recordings were 52.4 ± 4.0 µs and 185 ± 13 µs, respectively, with the fast component representing 54 ± 4% of the initial current amplitude (Fig. 2C).

Two-compartment model describes intact bipolar cells

The biexponential current relaxations suggest that a two-compartment equivalent circuit may satisfactorily describe bipolar cells' electrotonic profile (Llano et al. 1991). Figure 3A shows a simplified two-compartment equivalent circuit, from which Eq. 3-6 were derived (see METHODS). C1 and C2 represent the capacitances of two membrane compartments linked in series by R2, the axial resistance of the connecting axon. The circuit representing the cell compartments is linked by the pipette access resistance, R1, to the voltage clamp, Vc. The simplified model assumes an infinitely high membrane resistance in parallel with each capacitive compartment. A similar simplification is typically applied in the case of small spherical cells with only a single electrical compartment (Gillis 1995). This simplification seems justified by the high input resistance of the cells (the median for 27 cells was 1.4 GOmega , estimated from the steady-state current at the end of a 10-mV hyperpolarizing pulse). Another simplification made in Fig. 3A is neglect of the capacitance of the connecting axon. In the following sections, we test the validity of the simplified equivalent circuit shown in Fig. 3A, both by empiric studies of isolated bipolar-cell somata and synaptic terminals and by comparing the predictions of the two-compartment model with known membrane parameters in more complete simulations of bipolar cells.

With the use of Eq. 3-6, we obtained quantitative estimates for the equivalent-circuit components of the cells represented in Fig. 2. The physical appearance of bipolar cells (Fig. 1) suggests that the morphological correlates of the two capacitive compartments (C1 and C2) are the somatic/dendritic and synaptic terminal compartments, linked by the axial resistance (R2) of the axon. Because the somatic/dendritic compartment is larger, its capacitance is expected to be greater than the synaptic capacitance. Therefore, in recordings made from the synaptic terminal, the proximal capacitance (C1) should be smaller, whereas in recordings made from the soma, the distal capacitance (C2) should be smaller. In support of this expectation, the capacitance of the synaptic terminal was estimated at 3.16 ± 0.17 pF in terminal-end recordings (C1) and 2.56 ± 0.17 pF in soma-end recordings (C2). Somatic capacitance estimates were 7.98 ± 0.55 pF in terminal-end recordings (C2) and6.16 ± 0.39 pF in soma-end recordings (C1). The calculated synaptic-terminal capacitance was similar to published values of the capacitance of isolated bipolar-cell terminals (von Gersdorff and Matthews 1994a), regardless of whether recording was made from the terminal or soma.

We noted that when recordings were made from the synaptic terminal, the estimates of both terminal and somatic capacitance were slightly higher than when recordings were made from the soma end. The differences were statistically significant for the means given in the preceding paragraph (P < 0.05, independent samples t-test). Estimates of the linking resistance (R2) were not significantly different (terminal end: 42 ± 4 MOmega ; soma end: 52 ± 5 MOmega , P > 0.1). The difference in capacitance estimates from the different recording positions could be explained by a consistent bias of the two-compartment model or of the fitting algorithm. Alternatively, an inadvertent experimenter selection bias may have been exercised toward larger cells in terminal-end recordings; larger cells possess larger synaptic terminals, which tend to be favored as targets for terminal-end whole cell recordings. To remove potential experimenter selection bias, we designed a within-cell experimental protocol to examine potential effects of recording location on membrane parameter estimates. We measured the circuit parameters first with the patch pipette attached to either the terminal end or the somatic end of a cell. The patch pipette was then gently removed, the whole cell configuration was achieved on the opposite end of the same cell, and the circuit parameters were remeasured. With the use of this within-cell design, there was no effect of recording location on the estimate of either terminal capacitance or somatic capacitance (Fig. 3B). Putative terminal capacitance estimated from the two-compartment model was 3.40 ± 0.26 pF in recordings from the terminal end and 3.29 ± 0.32 pF (n = 9) in recordings from the somatic ends of the same cells (P > 0.1, paired t-test). Putative somatic capacitance was 9.78 ± 1.47 pF in terminal-end recordings and 10.16 ± 1.28 pF in soma-end recordings (P > 0.1). Thus the small differences in the between-cell design were not due to a consistent error in the two-compartment model dependent on recording location but were instead attributable to an inadvertent selection bias in the between-cell comparison.

Current transients from isolated terminal and somatic/dendritic compartments

If a two-compartment model is sufficient to describe the passive membrane characteristics of bipolar cells, the individual, isolated compartments should display monoexponential charging transients. With large-terminal bipolar cells, individual compartments can be examined in isolation by recording from bipolar somata and terminals spontaneously isolated during the dissociation procedure. Figure 4A examines the current transients in response to 10-mV hyperpolarizing pulses from a synaptic terminal spontaneously isolated from the parent soma during dissociation. As can be seen from the residual plots in Fig. 4A, insets, a single exponential provided an adequate description of the transient decay. Average time constant of the monoexponential fit was 28.0 ± 2.0 µs, with average extrapolated initial current amplitude of -776 ± 34 pA (n = 14). These values correspond to an estimated access resistance and membrane capacitance of 13.2 ± 0.6 MOmega and 2.14 ± 0.12 pF, according to Eq. 1 and 2. 


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FIG. 4. Current relaxations from spontaneously isolated synaptic terminals and cell somata are well fit by a single exponential. A: recording from an isolated synaptic terminal. Conventions as in Fig. 2A. Fit parameters for monoexponential fit to data were: A = -945.8 pA, tau  = 30.5 µs, As = -3.4 pA. B: recording from an isolated soma devoid of axon and synaptic terminal. Fit parameters for monoexponential fit were: A = -761.4 pA,tau  = 70.8 µs, As = -4.3 pA.

Figure 4B shows the current transients from a bipolar-cell soma isolated from its axon and synaptic terminal. As with isolated terminals, a monoexponential decay provided a good fit to the current relaxations from isolated somata. The average time constant from isolated somata was 87.6 ± 7.0 µs (n = 6). Estimated somatic capacitance was 5.26 ± 0.47 pF. Perhaps surprisingly, these data suggest that the membrane voltage of the soma and entire dendritic tree of dissociated bipolar cells can be controlled with similar efficacy by a somatic voltage clamp, or at least that the contribution of distal dendritic processes to the charging transients is minor. The capacitance estimates for both isolated terminals and isolated somata were smaller than estimates from intact cells, possibly reflecting some contribution of axonal capacitance to estimates of both compartments in intact cells.

To directly assess the correspondence between capacitance estimates of the terminal compartment of intact cells to that of the isolated terminal compartment, we designed a within-cell experiment to measure putative terminal capacitance from the intact cell, followed by severing the terminal from the intact cell and measuring the membrane capacitance of the isolated terminal with the use of the single-compartment equations (Eq. 1 and 2). The patch pipette was attached to the terminal end of a cell, and the hyperpolarizing pulse protocol was performed (Fig. 5A). As previously shown (Fig. 2, insets), the best monoexponential fit to the resulting current transients was clearly inadequate (Fig. 5A, solid line). A second pipette was then used to sever the axon of the intact cell, with the recording pipette still attached to the terminal. Under optimal conditions, severing the axon resulted in only a brief (<1-s) trauma-induced inward current, followed by the apparent resealing of the axon stub and recovery of an input resistance comparable with that observed before severing the axon. After the axon was cleaved, 10-mV hyperpolarizing voltage pulses resulted in current transients that decayed with a monoexponential time course (Fig. 5B). In this cell, the estimate of putative terminal capacitance before the axon was cut was 2.90 pF, with the use of the two-compartment model. After the axon was cut, the capacitance of the isolated terminal and small residual axon stub was 2.79 pF, estimated with the use of the monoexponential fit shown in Fig. 5B.


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FIG. 5. Current transients from terminal end of an intact cell and from same terminal after isolation from cell soma. A: symbols plot current relaxation in response to a 10-mV hyperpolarizing voltage pulse in a terminal-end recording from an intact bipolar cell. Solid line: least-squares (clearly inadequate) monoexponential fit to current. B: after axon was cleaved from cell depicted in A, current transient (large filled circles) was well fit by a single exponential (solid line), tau  = 42.7 µs. Current transient from A is replotted as small filled circles to allow a more direct comparison of currents before and after axon was severed.

Two-compartment model applied to simulated bipolar cells

The two-compartment model does not account for the cable properties of the axon, nor does it account for the finite input resistance of the cell membrane (see previous section). To determine the extent to which these simplifications affect the predictions of the two-compartment model, we examined the ability of the two-compartment model to estimate the capacitance of cellular compartments of a simulated bipolar cell, where cellular properties can be defined by the experimenter and subsequently compared with the predictions of the two-compartment model.

A voltage clamp was imposed in the pipette compartment of the simulated bipolar cell, and a hyperpolarizing voltage-pulse protocol analogous to that used in experiments on real bipolar cells was performed. The resulting current transients from simulations with the pipette attached to the terminal end are shown in Fig. 6A, and current transients from soma-end simulations are shown in Fig. 6B. Comparison of the traces in Fig. 6 with those in Fig. 2 reveals a close correspondence between the shapes of the simulation current transients and those of actual experiments. The simulated transients were then analyzed in the same way as actual transients recorded from bipolar neurons. As with actual experiments, monoexponential fits (with the use of the same fitting algorithm as in actual experiments) of the simulated transients were clearly inadequate, whereas biexponential fits were nearly indistinguishable from the raw simulation data points (Fig. 6, A and B, insets).


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FIG. 6. Current transients from a simulated bipolar cell. A: conventions as Fig. 2A. Experimental protocol was performed on a simulated bipolar cell, schematically illustrated in drawing. Pipette compartment was attached to synaptic terminal compartment of simulated bipolar cell. See METHODS and RESULTS for details. Fit parameters for biexponential fit to simulation current transients were: A1 = -443.9 pA, A2 = -181.1 pA, tau 1 = 33.2 µs, tau 2 = 537.0 µs, As = -8.5 pA. B: simulation from identical simulated bipolar cell, but with pipette compartment attached to bipolar-cell soma. Compare A and B with Fig. 2, A and B, from actual bipolar cells. Fit parameters for biexponential fit to simulation current transients were: A1 -292.9 pA, A2 = -385.5 pA, tau 1 = 69.1 µs, tau 2 = 251.4 µs, As = -8.5 pA. C. biexponential residual plot from A, inset, replotted at high gain to show deviation from a perfect fit (thin trace). Thick trace: residual plot from a simulation in which axon was reduced in length and diameter to eliminate axonal capacitance but retain same axial resistance as in simulation in A.

A higher gain analysis of the biexponential residual plot from fits to simulation transients reveals a small nonrandom deviation from a perfect fit of the simulated transients (Fig. 6C). This deviation from a biexponential fit vanished when the length and diameter of the axonal compartment were reduced in the simulated cell to eliminate the capacitance of the axonal compartment but retain the axial resistance of the axon (Fig. 6C). This indicates that the capacitive and resistive properties of the axonal membrane account for a very small deviation from the two-compartment model, which would be undetectable with experimental noise levels.

Biexponential fits of the simulations in Fig. 6 resulted in fit parameters similar to those obtained in actual experiments. In terminal-end simulations, the fast and slow time constants were 33.2 and 537.1 µs, respectively, with the fast component representing 71% of the initial current amplitude. In soma-end simulations the fast and slow time constants were 69.1 and 251.4 µs, with the fast component representing 43% of the initial current amplitude (compare Fig. 2C).

Table 1 shows a comparison of the simulation input values (calculated from the membrane and cytoplasmic constants given in METHODS) with compartment estimates obtained with the use of Eq. 3-6. As in actual experiments, two-compartment estimates were generated by fitting simulated transients, as shown in Fig. 6, and by inserting the resulting fit parameters into Eq. 3-6. In the full simulation, with the physical and electrical constants outlined in METHODS, correspondence between the simulation input values and estimated values is generally good, although the two-compartment model consistently overestimated capacitance values, especially in the compartment distal to the simulated patch pipette (C2).

 
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TABLE 1. Comparison of Nodus simulation input and two-compartment model estimates

To determine whether the differences between the simulation input parameters and the estimates obtained from the two-compartment model are due to the simplifications inherent in the two-compartment model or to possible idiosyncrasies of the fitting algorithm, we examined several simplified versions of the Nodus simulation that more closely approximated the two-compartment model. The overestimation of simulation membrane capacitance (Table 1, Full simulation) by the two-compartment model appears partly due to the contributions of axonal membrane capacitance and axonal membrane resistance, which are unaccounted for by the two-compartment model. Shrinking the simulated axon to negate axonal membrane properties in the Nodus simulations resulted in reduced estimates of terminal and somatic capacitance from the two-compartment model, but in this case two-compartment capacitance values were underestimates (Table 1). Excellent correspondence between simulation input and two-compartment model predictions was obtained by shrinking the simulated cell's axon and increasing the membrane resistivity of the cell (Table 1). Together, these results suggest that, as expected, the finite membrane resistance and the axonal membrane properties (both of which are absent from the 2-compartment model) are responsible for the small deviations of the two-compartment predictions from a more realistic cell model.

Effect of axon resistance on measured calcium current

The above analysis suggests that a significant electrical feature of the bipolar-cell axon is its axial resistance. Nodus simulations revealed that this resistance was not large enough to significantly alter the steady-state voltage achieved in the compartment distal to the recording pipette during a voltage pulse (not shown), due to the high input resistance of the cell membrane relative to the axial axonal resistance. However, with an estimated axonal resistance of several tens of megohms, the series resistance imposed by the axon may be expected to cause a measurable voltage error during activation of currents in the compartment distal to the recording pipette. We examined this possibility empirically by examining the well-characterized high-voltage-activated calcium current of large-terminal bipolar cells (Heidelberger and Matthews 1992; Kaneko and Tachibana 1985; Tachibana et al. 1993). This calcium current is the predominant voltage-gated current activated in bipolar cells under the conditions of our experiments and exhibits features characteristic of an L-type calcium current, including dihydropyridine sensitivity and lack of sensitivity to peptide antagonists (Heidelberger and Matthews 1992). The current has been suggested to arise predominantly from the synaptic terminal of the cells (Heidelberger and Matthews 1992; Tachibana et al. 1993).

We first directly confirmed the previous suggestion that functional calcium channels in large-terminal bipolar cells are primarily localized to the synaptic terminal compartment. Figure 7A, left, shows the result of activating the calcium current with a voltage-ramp protocol in an intact bipolar cell (patch pipette attached to the terminal; same cell as Fig. 5). After the axon was cleaved, the calcium current evoked by the voltage ramp was virtually unchanged (Fig. 7A, right). This provides direct confirmation that the calcium current in bipolar cells is highly localized to the synaptic terminal, despite the terminal's smaller contribution to the total cell membrane capacitance.


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FIG. 7. Axonal resistance can measurably influence voltage clamp of currents arising in cellular compartment distal to recording pipette. A: inward calcium currents arise primarily from synaptic-terminal compartment. Top traces: voltage protocol. Protocol was begun at -60 mV, and between -70 and +30 mV the voltage was ramped at 200 mV/s. A, left: recording from terminal end of an intact cell (same cell as in Fig. 5). An inward calcium current (bottom trace) was elicited by the voltage-ramp protocol depicted at top. A, right: same protocol, performed after axon of cell was severed (see Fig. 5). Calcium current remained intact in the isolated terminal. Current traces are not leak subtracted. Note linearity and small amplitude of current response to voltage-ramp protocol in the voltage range of -70 to about -45 mV. This indicates that bipolar-cell membrane is passive and possesses a high input resistance in this voltage range. B, top: voltage protocol identical to that in A. B, bottom: currents from a terminal-end recording (thin trace) and a soma-end recording (thick trace) of similar peak amplitude. Current records were obtained from 2 different cells. C: average voltage at which peak current amplitude was achieved during the ramp protocol shown in A and B. C, left: soma-end recordings (n = 13 cells). C, right: terminal-end recordings (n = 12 cells). Voltage at which maximum current was observed was significantly shifted to more negative potentials in soma-end recordings (P < 0.001, independent samples t-test).

The localization of calcium channels to the terminal allows an examination of the effect of the axon on currents arising from a compartment distal to the recording pipette. Figure 7B illustrates calcium currents elicited by the same voltage-ramp protocol as that used in Fig. 7A, with the recording pipette attached to the soma (thick trace) or the terminal (thin trace). The peak of the current-voltage curve generated by the voltage ramps was shifted to the left on the voltage axis in soma-end recordings compared with terminal-end recordings (Fig. 7, B and C). The peak amplitudes of the currents from the two recording locations were similar (somatic end: -238 ± 6 pA; terminal end: -197 ± 10 pA, P > 0.3). Our interpretation of the shift in the current/voltage curves from soma-end recordings is that the axon poses a significant resistance in series with the calcium current developing in the terminal. The voltage drop across this added series resistance is an error in the clamp of the terminal membrane potential, analogous to the error imposed by the pipette resistance in whole cell recordings. As the inward current grows during the voltage ramp, the error becomes larger and leads to an escape from clamp of the terminal membrane potential. The calcium current therefore becomes partly regenerative, which results in a leftward shift of the current-voltage curve. Similar leftward shifts in the current-voltage relationships of soma-end recordings were also seen when 25-ms depolarizing pulses were used to elicit calcium current instead of ramps (n = 6, data not shown), which supports the idea that the leftward shift is due to steady-state voltage errors associated with the axonal resistance imposed in series with the current generated in the terminal.

Time-resolved measurements of exocytosis

Next, we examined whether the model for large-terminal bipolar cells would allow detection of depolarization-induced capacitance changes in the synaptic terminals of intact cells, as was done previously in isolated terminals (Heidelberger et al. 1994; Mennerick and Matthews 1996; von Gersdorff and Matthews 1994a,b). The changes in membrane capacitance are thought to reflect the calcium-dependent exocytosis of synaptic vesicles (Heidelberger et al. 1994; von Gersdorff and Matthews 1994a,b). In contrast to conventional means of measuring neurotransmission, time-resolved capacitance measurements offer a purely presynaptic means of assaying synaptic secretion. Although time-resolved capacitance measurements are typically applied to spherical cells, where a simple equivalent circuit allows straightforward estimates of membrane capacitance to be obtained (Neher and Marty 1982), extending capacitance measurements to intact bipolar cells would offer the possibility of performing these measurements in situ.

We used 10-mV hyperpolarizing pulses to monitor the membrane capacitance of the two compartments before and after a depolarizing pulse to 0 mV. The duration of the test depolarization was >1 s, to inhibit the rapid endocytosis that follows briefer voltage pulses (von Gersdorff and Matthews 1994b). In terminal-end recordings, 10-mV pulses were delivered every 50 ms and five current responses were digitally averaged to yield a capacitance estimate every 250 ms. After five baseline estimates were collected, a 2-s voltage pulse to 0 mV was delivered to activate calcium current and elicit exocytosis. Immediately after the pulse to 0 mV, 10-mV hyperpolarizing pulses were resumed. Passive properties were not measured during activation of the calcium current, to avoid invalidating the assumption of a high membrane resistance inherent in the two-compartment model. Figure 8A shows capacitance before and after the pulse to 0 mV. The filled circles represent the capacitance of the proximal (terminal) compartment estimated with the use of the two-compartment model. Figure 8B shows summary data from six terminal-end recordings from intact bipolar cells. Although the estimated change in terminal capacitance was small (157 fF), this was the only circuit component that reliably changed. The magnitude of change matches the change observed with a similar voltage protocol applied to isolated synaptic terminals (161 ± 18 fF change, n = 3 terminals), and is also similar in size to previously published capacitance responses in bipolar-cell terminals (von Gersdorff and Matthews 1994a,b). These experiments demonstrate that changes in the capacitance of the cellular compartment proximal to the recording pipette can be detected with the use of the two-compartment equivalent circuit.


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FIG. 8. Detection of synaptic membrane capacitance increases from intact bipolar cells. A: estimates of terminal capacitance from a terminal-end recording in an intact bipolar cell. Capacitance estimates were generated every 250 ms from average response of cell to 2-ms hyperpolarizing voltage pulses. At time 0 on the X-axis, a depolarizing voltage pulse to 0 mV was delivered for 2 s to elicit calcium influx and neurosecretion. After depolarizing voltage pulse, hyperpolarizing pulses were resumed. Solid lines: mean capacitance values before and after stimulation. B: summary data from 6 terminal-end recordings. Left bars in each graph: equivalent-circuit estimates before a 2-s pulse to 0 mV. Right bars: circuit estimates after 2-s pulse. Asterisk: P < 0.01, paired t-test. No other before and after comparisons showed a statistical difference.

With the use of a similar protocol, we also detected capacitance changes in the distal compartment of soma-end recordings following a 2-s voltage pulse to 0 mV. Estimated average terminal capacitance in five cells changed from3.86 ± 0.25 pF to 4.08 ± 0.31 pF (P < 0.02). Although neither estimates of somatic capacitance nor access resistance changed after calcium current activation (P > 0.2), estimates of linking resistance in the equivalent circuit decreased with stimulation from 33.3 ± 3 MOmega to 30.3 ± 4 MOmega (P = 0.03). Similar decreases in linking resistance were observed in terminal-end recordings when a 3-s pulse to 0 mV was used as a stimulus (n = 6 cells). The changes in linking resistance do not appear to be an artifact of the two-compartment model estimations, because changes in linking resistance were not correlated in magnitude with the changes in capacitance. Also, Nodus simulations of terminal capacitance changes were not associated with linking resistance changes when the two-compartment model was applied to simulation data. Therefore the change in the apparent axonal resistance associated with stimulation in some cells appears to be a real cellular response, suggesting that changes in passive electrical properties in addition to capacitance may occur with prolonged stimulation, possibly related to calcium influx.

    DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References

The present results suggest that although a simple, single-compartment description of intact bipolar cells is inadequate, these cells possess a compact electrotonic profile. The electrotonic structure of bipolar cells can be described under our recording conditions by an equivalent circuit composed of two discrete capacitive compartments linked by a resistor. Furthermore, the capacitive compartments and linking resistance correspond to the major morphological features of large-terminal bipolar cells.

Four lines of evidence suggest the validity of the two-compartment model as applied to bipolar cells. First, the two-compartment model yields similar estimates of passive membrane parameters in recordings from either the somatic end or the terminal end of bipolar cells, suggesting an internal consistency to the estimates derived from the two-compartment model. Second, spontaneously or experimentally isolated terminals and somata exhibit simple, monoexponential decays and yield capacitance estimates similar to those estimated from intact-cell recordings. Third, applying the two-compartment model to simulated bipolar cells, where axonal capacitance and finite membrane resistance can be accounted for, yields reasonable agreement between simulation input and two-compartment model estimates. Fourth, the two-compartment model yields estimates of the calcium-evoked change in membrane capacitance of the synaptic terminal that are similar in magnitude to changes evoked in isolated synaptic terminals.

One feature of bipolar cells consistent with a compact electrotonic profile is the high input resistance of the cells. Estimated from the steady-state currents during hyperpolarizing voltage pulses, the input resistance was typically >1 GOmega . It is unlikely that the cesium-based internal solutions used in the current work led to an inflated input resistance; similar input resistance estimates have been obtained from perforated-patch recordings with the use of a potassium-based internal solution (Zenisek and Matthews, unpublished observations). Our simulations of bipolar cells and measures of cell capacitance suggest that the input resistance of 1 GOmega corresponds to a membrane resistivity of ~14 kOmega /cm2, which is lower than several recent estimates in other CNS cells, where estimates of membrane resistivity have ranged from 50 to 200 kOmega cm2 (Coleman and Miller 1989; Major et al. 1994; Spruston and Johnston 1992; Thurbon et al. 1994). There may be several explanations for the difference. First, the difference may reflect real differences in membrane resistivity among different cell types. Second, it is possible that membranes of bipolar cells are compromised during the dissociation procedure, leading to a smaller membrane resistivity estimate than in situ estimates. Third, although glass/membrane seal resistances were >25 GOmega before membrane rupture in our recordings, it is possible that seal disruption during membrane rupture is responsible for a leak conductance that contributed to our estimates of cell input resistance. We observed no difference between the input resistance of isolated terminals compared with intact bipolar cells, possibly indicating that the membrane-glass seal conductance typically dominates the input conductance of the circuit. If this is the case, then the input resistance of an unperturbed bipolar neuron would be even higher than measured here. In fact, examples of cells in which the input resistance was well over 10 GOmega were observed in our studies.

Cytoplasmic resistivity also influences the overall electrotonic compactness of neurons (Spruston et al. 1994). We found that when Nodus simulations were constrained by measured physical dimensions of the axon (>1.0 µm diam, ~30 µm long), accurate simulations of current transients required a higher cytoplasmic resistivity than the standard value of ~100 Omega /cm (Stampfli and Hille 1976). Although cytoplasmic resistivity is generally a difficult parameter to estimate (Spruston et al. 1994), our results can be added to a growing list of results converging on cytoplasmic resistivity estimates between 200 and 400 Omega /cm (Major et al. 1994; Spruston and Johnston 1992; Thurbon et al. 1994; Ulrich et al. 1994).

The small membrane capacitance of bipolar cells is another feature that contributes to the compact electrotonic profile of the cells. Estimates of 2-4 pF for synaptic terminals and 5-12 pF for somatic/dendritic compartments contrast with compartment estimates of 10-40 pF for cultured hippocampal neurons (Mennerick et al. 1995) and of 100-500 pF for young cerebellar Purkinje cells (Llano et al. 1991). Although dissociated bipolar cells appear to retain a relatively complete morphology, it is possible that the cells lose fine dendritic processes in the dissociation procedure. Both Golgi stained cells (Ishida et al. 1980) and horseradish peroxidase injections (Saito and Kujiraoka 1982) show that large-terminal bipolar neurons in intact goldfish retina do not have extensive networks of fine dendrites. Nevertheless, it will eventually be necessary to compare the present estimates of capacitance and membrane resistance with estimates from cells in situ and to perform additional validation of the two-compartment model as applied to cells in the intact retina.

Our results suggest that time-resolved capacitance measurements, which have proven useful for studying exocytosis in a variety of cell types, can be extended to intact bipolar cells. For the present experiments we used rectangular voltage-pulse stimuli to estimate cell capacitance. A more common method for measuring changes in membrane capacitance utilizes sinusoidal voltage stimuli. With the use of this protocol, membrane capacitance can be measured as a function of the real and imaginary admittance of the cell for the case of a single-compartment cell (Gillis 1995). In the case of the two-compartment model used to describe the intact bipolar cell's geometry, the membrane capacitance cannot be solved for directly with the use of this technique; however, an estimate of the total membrane capacitance can be obtained from the imaginary component of the cell's impedance. The impedance is equal to the inverse of the cell's admittance, which can be determined from the two orthogonal current components measured by a lock-in amplifier (Neher and Marty 1982). The real component of the admittance corresponds to the current that is in phase with the sinusoidal voltage stimuli, whereas the imaginary component corresponds to the current that is 90° out of phase with the voltage. The complex impedance for the equivalent circuit used to describe the bipolar cells was calculated, and the imaginary component of the impedance is shown in Eq. 7
Im(<IT>Z</IT>) = − <FR><NU>ω<SUP>2</SUP><IT>R</IT>2<SUP>2</SUP>C2<SUP>2</SUP>C1 + C1 + C2</NU><DE>ω<SUP>3</SUP>R2<SUP>2</SUP>C1<SUP>2</SUP>C2<SUP>2</SUP>+ ω(C1 + C2)<SUP>2</SUP></DE></FR> (7)
where omega  is the angular frequency of the sine wave and Im(Z) is the imaginary component of the cell's impedance. Equation 7 simplifies to Eq. 8, provided both Eq. 9 and 10 are satisfied
Im(<IT>Z</IT>) ≈ <FR><NU>1</NU><DE>ω(C1 + C2)</DE></FR> (8)
C1 + C2 ≫ ω<SUP>2</SUP>R2<SUP>2</SUP>C2<SUP>2</SUP>C1 (9)
ω(C1 + C2)<SUP>2</SUP>≫ ω<SUP>3</SUP>R2<SUP>2</SUP>C1<SUP>2</SUP>C2<SUP>2</SUP> (10)
From Eq. 9 and 10, it is apparent that Eq. 8 yields better estimates of total membrane capacitance if lower-frequency sinusoidal stimuli are used. Equation 8 provides an acceptable estimate of cell capacitance when sine wave frequencies as high as 200 Hz are used to measure the cell impedance. For example, for a soma-end recording from a typical bipolar cell, C1 approx  8 pF, C2 approx  2 pF, and R2 approx  50 MOmega . With these typical values and a sine wave frequency of 200 Hz, the imaginary impedance equals 500 MOmega , which, when entered into Eq. 8, gives an estimate for the cell capacitance (C1 + C2) of 9.975 pF. A capacitance increase of 200 fF within the terminal would yield an estimated increase of 193 fF, whereas a 10% change in R2 would be sensed as only a 4.7-fF change in estimated capacitance. On the other hand, with a frequency of 800 Hz, typically used for studies of single-compartment cells, total capacitance of the typical cell above would be estimated to be 9.664 pF according to Eq. 8, and a capacitance change of 200 fF would be detected as 111 fF. A 10% change in R2 would result in a 55-fF change, clearly an unacceptable error. It is noteworthy that the utility of the sinusoidal method for other cells approximated by two electrical compartments is largely dependent on the size and morphology of the cell being investigated. Specifically, cells with a larger distal-compartment capacitance (C2) or a larger axonal resistance (R2) would yield poorer estimates of total cell capacitance.

The strategy outlined above for sinusoidal stimuli is preferred if the capacitance change of interest occurs in the distal compartment (e.g., in the terminal, with the recording pipette on the soma). If the proximal compartment is of interest, however, Eq. 7 implies that a high-frequency sine wave is preferable. For example, for a recording from the terminal of a bipolar cell (with C1 = 2 pF, C2 = 8 pF, and R2 = 50 MOmega ), a 1,000-Hz sinusoid gives an estimate of 5.535 pF for C1, and a 200-fF increase in C1 would be detected as an increase of 52 fF. A 10% change in R2 would yield a large change in the apparent capacitance of C1 by 371 fF. The performance is considerably improved by increasing the sine wave frequency to 8,000 Hz, giving estimates of 2.098 pF for C1, 193 fF for the increase in C1, and an apparent capacitance change of 17 fF in C1 for a 10% change in R2. Note, however, that a sufficiently high sine wave frequency for estimation of proximal capacitance may not in practice be attainable in a particular recording situation, because of considerations related to the values of the circuit elements, the quality and speed of voltage clamp, and frequency-dependent changes in signal/noise ratio (see Gillis 1995). Nevertheless, a high-frequency stimulus in general favors detection of proximal capacitance changes, whereas a low-frequency stimulus provides a more accurate estimate of total capacitance and thus of changes in the distal compartment.

One disadvantage of both the sinusoidal and voltage-pulse methods of time-resolved capacitance measurements in bipolar cells is that measurements can only reliably be made before and after activation of membrane conductances, to avoid invalidating the two-compartment model's assumption of a high membrane input resistance (Fig. 3A). Note that this same technical restriction is also inherent in many methods of time-resolved capacitance measurement in simple, single-compartment cells (see Gillis 1995). Despite this limitation, the ability to perform time-resolved capacitance estimates in intact bipolar cells may prove useful for extending studies of synaptic exocytosis to more intact preparations, such as retinal slices. In situ time-resolved capacitance measurements have recently been accomplished with chromaffin cells (Moser and Neher 1997) and posterior pituitary nerve terminals (Hsu and Jackson 1996). The results also offer the possibility of extending time-resolved capacitance measurements to other types of bipolar cells, which possess smaller synaptic terminals and are less amenable to direct whole cell recording from the terminal itself. Of course, salient aspects of the two-compartment model must first be confirmed for bipolar cells in situ before these studies are possible.

Bipolar cells are often thought of as a passive relay between photoreceptors and output ganglion cells (Dowling 1987). The simple electrotonic structure elucidated in the present work is consistent with the idea that bipolar cells faithfully transmit information with little modulation of the signal. However, it is known that isolated bipolar cells express a variety of voltage-gated and transmitter-gated ion channels (Heidelberger and Matthews 1991, 1992; Kaneko and Tachibana 1985). Therefore a complete understanding of bipolar-cell signal processing will require an understanding of how voltage-gated and synaptically gated conductances are superimposed temporally and spatially on the passive membrane properties examined here.

    ACKNOWLEDGEMENTS

  The authors thank Dr. Joe Fetcho (Stony Brook) for use of Nodus software and for help with confocal microscopy. The authors also thank J. Que (Washington University) for help with the equivalent circuit and H. von Gersdorff for valuable discussion.

  This work was supported by National Institutes of Health Grants NS-07371 and EY-03821.

    FOOTNOTES

   Present address of S. Mennerick: Dept. of Psychiatry, Washington University School of Medicine, 4940 Children's Place, St. Louis, MO 63110.

  Address reprint requests to G. Matthews.

  Received 7 November 1996; accepted in final form 17 March 1997.

    REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References

0022-3077/97 $5.00 Copyright ©1997 The American Physiological Society