| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
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 M
) 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.
Time-resolved capacitance measurements (Gillis 1995 Dissociation procedure
The dissociation procedure for goldfish bipolar cells has been described in detail (Heidelberger and Matthews 1992 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( 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
Simulations
Simulations were produced with the use of Nodus software (DeSchutter 1993 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
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 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
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.
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
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
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.
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
; 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.
). 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.
) 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
). 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.
-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.
60 mV. Patch pipettes, coated with dental wax to reduce stray capacitance, were fire-polished and exhibited an open-tip resistance of 6-10 M. Pipette-membrane seals were >25 G 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.
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/
) + 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 
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(et/1) + A2(et/2) + As, with the subscript numerals 1 and 2 denoting fast and slow components, respectively. Similarly, triexponential fits added a third exponential term.
), we used the following equations to estimate circuit parameters (e.g., Gillis 1995) in response to an imposed voltage change, 
V
(1)
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
(2)
(3)
(4)
(5)
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
(6)
; 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.
View larger version (28K):
[in a new window]
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.
View larger version (23K):
[in a new window]
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, 1 = 22.5 µs, 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, 1 = 71.2 µs, 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.
). Nonrandom deviations from the zero level in residual plots reflect a poor fit, whereas small, random deviations reflect a good fit.
). 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 M 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 /cm, respectively (Spruston et al. 1994). Membrane resistivity was set to 14.0 k/cm2 to yield a cell input resistance similar to that observed in whole cell recordings.
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
; 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).
View larger version (74K):
[in a new window]
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.
). 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 G, 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.
), regardless of whether recording was made from the terminal or soma.
; soma end: 52 ± 5 M, 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.
776 ± 34 pA (n = 14). These values correspond to an estimated access resistance and membrane capacitance of 13.2 ± 0.6 M and 2.14 ± 0.12 pF, according to Eq. 1 and 2.
View larger version (20K):
[in a new window]
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, = 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, = 70.8 µs, As = 4.3 pA.
View larger version (13K):
[in a new window]
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), = 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.
View larger version (18K):
[in a new window]
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, 1 = 33.2 µs, 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, 1 = 69.1 µs, 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.
View this table:
TABLE 1.
Comparison of Nodus simulation input and two-compartment model estimates
; 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).
View larger version (21K):
[in a new window]
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).
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.
; 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.
). 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.
View larger version (27K):
[in a new window]
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.
to 30.3 ± 4 M (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
. 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 G corresponds to a membrane resistivity of ~14 k/cm2, which is lower than several recent estimates in other CNS cells, where estimates of membrane resistivity have ranged from 50 to 200 k 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 G 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 G were observed in our studies.
). 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 /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 /cm (Major et al. 1994; Spruston and Johnston 1992; Thurbon et al. 1994; Ulrich et al. 1994).
) 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.
). 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
where
(7)
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
(8)
(9)
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
(10)
8 pF, C2 2 pF, and R2 50 M. With these typical values and a sine wave frequency of 200 Hz, the imaginary impedance equals 500 M, 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.
), 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.
). 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.
). 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
|
|---|
-aminobutyric acid in single synaptic terminals.
Proc. Natl. Acad. Sci. USA
88: 7135-7139, 1991.This article has been cited by other articles:
|
|
 |
|
  L. Oltedal, M. L. Veruki, and E. Hartveit Passive membrane properties and electrotonic signal processing in retinal rod bipolar cells J. Physiol., February 15, 2009; 587(4): 829 - 849. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 L. Oltedal, S. H. Morkve, M. L. Veruki, and E. Hartveit Patch-Clamp Investigations and Compartmental Modeling of Rod Bipolar Axon Terminals in an In Vitro Thin-Slice Preparation of the Mammalian Retina J Neurophysiol, February 1, 2007; 97(2): 1171 - 1187. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
Z.-Y. Zhou, Q.-F. Wan, P. Thakur, and R. Heidelberger Capacitance Measurements in the Mouse Rod Bipolar Cell Identify a Pool of Releasable Synaptic Vesicles J Neurophysiol, November 1, 2006; 96(5): 2539 - 2548. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 C. Kushmerick and H. von Gersdorff Exo-endocytosis at mossy fiber terminals: Toward capacitance measurements in cells with arbitrary geometry PNAS, July 22, 2003; 100(15): 8618 - 8620. [Full Text] [PDF]
|
|
|
|
|
|
S. Hallermann, C. Pawlu, P. Jonas, and M. Heckmann A large pool of releasable vesicles in a cortical glutamatergic synapse PNAS, July 22, 2003; 100(15): 8975 - 8980. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 M. J. Palmer, H. Taschenberger, C. Hull, L. Tremere, and H. von Gersdorff Synaptic Activation of Presynaptic Glutamate Transporter Currents in Nerve Terminals J. Neurosci., June 15, 2003; 23(12): 4831 - 4841. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
T. Euler and R. H. Masland Light-Evoked Responses of Bipolar Cells in a Mammalian Retina J Neurophysiol, April 1, 2000; 83(4): 1817 - 1829. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
E. Hartveit Reciprocal Synaptic Interactions Between Rod Bipolar Cells and Amacrine Cells in the Rat Retina J Neurophysiol, June 1, 1999; 81(6): 2923 - 2936. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
G. Neves and L. Lagnado The kinetics of exocytosis and endocytosis in the synaptic terminal of goldfish retinal bipolar cells J. Physiol., February 15, 1999; 515(1): 181 - 202. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
K. Matsui, N. Hosoi, and M. Tachibana Excitatory Synaptic Transmission in the Inner Retina: Paired Recordings of Bipolar Cells and Neurons of the Ganglion Cell Layer J. Neurosci., June 15, 1998; 18(12): 4500 - 4510. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
D. A. Protti and I. Llano Calcium Currents and Calcium Signaling in Rod Bipolar Cells of Rat Retinal Slices J. Neurosci., May 15, 1998; 18(10): 3715 - 3724. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
