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University of Bergen, Department of Biomedicine, Bergen, Norway
Submitted 22 September 2006; accepted in final form 12 December 2006
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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). During the last 20 yr, model systems for investigating synaptic transmission at the same level of mechanistic detail in the CNS have been developed. Although a model system should ideally be accessible to electrophysiological investigations both at the pre- and postsynaptic level, several systems have been limited to investigations at the postsynaptic side. Over the past decade, a few model systems with large (or even giant) presynaptic terminals have become accessible to direct electrophysiological investigations in situ, such as combined pre- and postsynaptic recording and measurement of changes in presynaptic membrane capacitance as an index of exo- and endocytosis. These model systems have greatly expanded our understanding of basic mechanisms of synaptic transmission and include hair cells in the inner ear (Moser and Beutner 2000), photoreceptors (Thoreson et al. 2004) and isolated bipolar cell axon terminals (Palmer et al. 2003) in the retina, presynaptic terminals of basket cells in the cerebellum (Southan and Robertson 1998), the calyx of Held in the auditory brain stem (e.g., Borst and Sakmann 1996; Borst et al. 1995; Forsythe 1994; Sun and Wu 2001; Taschenberger et al. 2002; Wölfel and Schneggenburger 2003), and mossy fiber terminals in the hippocampus (Geiger and Jonas 2000; Hallermann et al. 2003). Most importantly, for the calyx of Held synapse, it is possible to combine pre- and postsynaptic measurements. It has also been possible to perform dual recordings from pairs of pre- and postsynaptic cells in the retina: the photoreceptor 
bipolar cell synapse (DeVries and Schwartz 1999; DeVries et al. 2006; Thoreson et al. 2004) and the rod bipolar cell AII amacrine cell synapse (Singer and Diamond 2003; Veruki et al. 2003, 2006). By delivering physiological stimuli to the presynaptic cell, one can directly observe the input-output relationship of the synaptic connection.
An important goal is to extend the rod bipolar cell AII amacrine cell model system by being able to routinely record not only from the soma of the rod bipolar cell but directly from the axon terminal endings. First, such recordings can potentially allow improved voltage clamp of voltage- and ligand-gated ion currents generated at the axon terminal compared with recordings at the cell body. Second, by establishing whole cell recordings at the axon terminal, it should be possible to isolate outside-out patches and thereby directly study ion channels located in the terminal. Third, it might be possible to perform time-resolved capacitance measurements of exocytosis (Hallermann et al. 2003; Mennerick et al. 1997; Palmer et al. 2003; Pan et al. 2001; Zhou et al. 2006). Recordings from axon terminals of acutely isolated rod bipolar cells in culture have been reported (Pan 2001; Pan et al. 2001; Zhou et al. 2006), but recordings from axon terminals of rod bipolar cells in situ have only been reported in one previous study with an apparently low success rate (Protti and Llano 1998).
Here we report detailed methods and results from electrophysiological recordings from axon terminals of rod bipolar cells in situ using an in vitro thin slice preparation of the rat retina. These recordings, together with recordings from the soma of rod bipolar cells, were used to investigate the passive membrane properties of rod bipolar cells and analyzed with a two-compartment model of bipolar cells (Mennerick et al. 1997). The results were compared with results obtained from computer simulations of idealized models of rod bipolar cells to systematically investigate the influence of recording location and series resistance on estimates of model parameters and synaptic current kinetics. We also present physiological recordings from rod bipolar axon terminals that verify the integrity of the synaptic circuits in which they are involved. Finally, we present recordings of transmitter-evoked responses that verify the feasibility of isolating outside-out patches from rod bipolar axon terminals.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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General aspects of the methods have previously been described in detail (Hartveit 1996; Veruki et al. 2003). Albino rats (4–7 wk postnatal) were deeply anesthetized with halothane in oxygen and killed by cervical dislocation (procedure approved under the surveillance of the Norwegian Animal Research Authority). Retinal slices (Edwards et al. 1989) were cut by hand with a curved scalpel blade and were visualized with infrared differential interference contrast (IR-DIC) videomicroscopy (Axioskop FS or FS2; Zeiss) as described by Stuart et al. (1993). For axon terminal recordings, we aimed at cutting thinner slices than in experiments primarily aimed at recording from somata. We estimate roughly that the latter slices have a thickness of 
150–200 µm and that our thinner slices range from 50 to 100 µm. During experiments, cells were imaged by an analog CCD camera (VX55; TILL Photonics, Gräfelfing, Germany). For recordings from rod bipolar cell somata, we used a x40 objective (0.75 NA; working distance: 1.9 mm; Zeiss). For recordings from rod bipolar cell axon terminals, we used a x60 objective (0.9 NA; working distance: 2 mm; Olympus).
Solutions and drugs
The extracellular perfusing solution was continuously bubbled with 95% O2-5% CO2 and had the following composition (in mM): 125 NaCl, 25 NaHCO3, 2.5 KCl, 2.5 CaCl2, 1 MgCl2, and 10 glucose, pH 7.4. For some recordings of voltage-gated Ca2+ currents, we replaced 20 mM NaCl with the equivalent amount of tetraethylammonium chloride (TEA-Cl) and increased the concentration of CaCl2 to 5 mM. For whole cell recordings from cell bodies of rod bipolar cells, recording pipettes were filled with solution A, which contained (in mM) 125 CsCl, 4 NaCl, 5 HEPES, 1 CaCl2, 1 MgCl2, 5 EGTA, 15 TEA-Cl, and 4 Na2ATP. For whole cell and outside-out patch recordings from axon terminals, recording pipettes were filled with solution B, which contained (in mM): 125 CsCl, 8 NaCl, 10 HEPES, 1 CaCl2, 5 EGTA, 15 TEA-Cl, and 4 MgATP. For some whole cell recordings of synaptic currents (from cell bodies or axon terminals), recording pipettes were filled with solution C, which contained (in mM): 130 KCl, 8 NaCl, 10 HEPES, 1 CaCl2, 5 EGTA, and 4 MgATP. For all intracellular solutions, pH was adjusted to 7.3 (with CsOH or KOH) and Lucifer yellow (1 mg/ml) was added for visualization of cells with fluorescence microscopy after the electrophysiological recording. Cells were not exposed to UV-light during recording. All recordings were performed at room temperature (20–25°C).
Drugs were either added directly to the extracellular solution used to perfuse the slices or were locally applied by pressure from a multi-barreled pipette complex. The concentrations of drugs added to the perfusing solution were as follows (µM; supplied by Tocris Bioscience, Avonmouth, UK, unless otherwise noted): 10 bicuculline methchloride, 10 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX), 1 strychnine (Research Biochemicals, Natick, MA), 50 (1,2,5,6-tetrahydropyridin-4-yl)methylphosphinic acid (TPMPA), 50 D,L-threo-
-benzyloxyaspartic acid (TBOA). The concentrations (nominal) of drugs added by pressure application were as follows (in µM): 200 
-aminobutyric acid (GABA; Sigma), 200 glycine (May and Baker, Dagenham, UK). Solutions were either made up freshly for each experiment or were prepared from concentrated aliquots stored at –20°C.
Electrophysiological recording and data acquisition
Patch pipettes were pulled from borosilicate glass (GC150-11; Harvard Apparatus, Edenbridge, UK) on a two-stage vertical puller (PP-83, Narishige, Japan) and heat-polished before use. For cell body recordings, and some axon terminal recordings, electrodes were coated with dental wax (Kerr’s sticky wax) to reduce their capacitance. Pipettes for soma recordings had resistances of 5–6.5 M
(when filled with intracellular solution A). Pipettes for axon terminal recordings had resistances of 6.5–8.5 M (when filled with intracellular solution B). When establishing outside-out patch recordings, the pressure applied to the recording pipettes was continuously monitored with a Manual-Seal-Sucker (Sigmann Elektronik, Hüffenhardt, Germany). Theoretical liquid junction potentials of extracellular solutions against internal solutions were calculated with JPCalcW (Molecular Devices, Sunnyvale, CA). Holding potentials were automatically corrected for the liquid junction potentials on-line. Liquid junction potentials were +3.9, +3.3, and +3.4 mV for solutions A–C, respectively.
Voltage-clamp recordings were made with EPC9-dual amplifiers (HEKA Elektronik, Lambrecht, Germany) controlled by Pulse software (HEKA Elektronik). Cells and patches were generally held at a membrane potential of –60 mV. Application of voltage protocols and digital sampling of the analog signals were performed via an ITC-16 interface (Instrutech, Port Washington, NY) built into the amplifier. Before sampling, signals were low-pass filtered (analog 3- and 4-pole Bessel filters in series) with a corner frequency (–3 dB) automatically adjusted to 1/5–1/3 of the inverse of the sampling interval (20–250 µs depending on the protocol). Currents caused by the residual recording pipette capacitance (Cfast) and the cell membrane capacitance (Cslow) were measured with the automatic capacitance neutralization network feature of the EPC9 amplifiers that also provided on-line estimates of the series resistance (Rs). Compared with our off-line estimates, the EPC9 typically overestimated Rs, most notably for terminal-end recordings. For measurements of capacitive transients, the Cslow capacitance neutralization circuitry of the amplifier was transiently disabled and the time constant of the internal stimulus filter was reduced from 20 to 2 µs. These responses were acquired with a sampling interval of 10 µs (low-pass filter set to 30 kHz). For a few axon terminal recordings, the sampling interval was reduced to 5 µs (low-pass filter set to 100 kHz).
General data analysis
Data were analyzed with FitMaster, PulseFit and PulseTools (HEKA Elektronik), Igor Pro (WaveMetrics, Lake Oswego, OR), and AxoGraph (Molecular Devices). Capacitive transients were analyzed off-line by averaging consecutive responses (typically 20–60) and fitting the decay with exponential functions after baseline zero subtraction. For monoexponential functions we used the function
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is the time constant, and Iss is the steady-state current amplitude. The sum of A and Iss represents I(t) at time 0 (the instant of the voltage change). For biexponential functions we used the function
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1 and 2 are the time constants of the first (fast) and second (slow) exponential components. The sum of A1, A2, and Iss represents I(t) at time 0. For triexponential fits, a third exponential term was added. Fitting was started 30–60 µs after onset of the voltage step to reduce contamination of the fit by input and output filtering (Mennerick et al. 1997). For simulated data, fitting was started 50 µs after the voltage step, except where otherwise stated.
For estimating the circuit parameters of a two-compartment electrical equivalent circuit (RESULTS; Fig. 4A), we followed the approach of Mennerick et al. (1997), including the assumption of infinite membrane resistance, and used the following equations developed in their study
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50 ms), monophasic PSCs that appeared to rise in a monotonic fashion without visible deviation of the rising phase and that appeared to decay with an exponential time course were included in the ensemble averages. Any events with 10–90% rise time 2 ms were also excluded from the ensemble averages.
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Data are presented as means ± SD (n = number of cells), and percentages are presented as percentage of control. Statistical analyses were performed using Student’s two-tailed t-test (unpaired), and differences were considered statistically significant at the P < 0.05 level. For illustration purposes, data traces from physiological recordings were typically low-pass filtered (digital nonlagging Gaussian filter; –3 dB at 0.5–2 kHz). Data records displaying capacitive transients are displayed without additional off-line filtering. Unless otherwise noted, current responses in figures represent single traces.
Computer simulations
Computer simulations were performed with NEURON (version 5.8) running under Mac OS X (10.4) (Carnevale and Hines 2006; Hines and Carnevale 1997). We constructed idealized morphological models of rod bipolar cells based on published morphological data, including values for the length and diameter of cell bodies, axons, and axon terminal systems (see RESULTS). All simulations were run with a time step of 1 µs. For analysis, data were decimated to give a sampling interval of 5 µs. A single electrode voltage clamp with user-specified series resistance was connected to either the soma or the terminal compartment. Before each simulation run, the model was initialized to steady state. For measurement of charging transients, 10-mV hyperpolarizing pulses were applied from a holding potential of –60 mV. For our default model of a rod bipolar cell (see RESULTS), the cytoplasmic (internal) resistivity (Ri) was set to 160 cm, the specific membrane capacitance (Cm) was set to the standard value of 1 µF/cm2, and the specific membrane resistance (Rm) was set to 14 kcm2, corresponding to a specific membrane conductance (Gm) of 7.14 x 10-5 S/cm2 (Mennerick et al. 1997).
Synaptic conductance waveforms injected into the simulated rod bipolar cell model were calculated according to the equation
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is the decay time constant and 
is the delay to onset. |
RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Cell bodies from rod bipolar cells were targeted according to their relatively large size (cf. Hartveit 1996, 1999) and typical location in the distal part of the inner nuclear layer, immediately apposed to the outer plexiform layer (Fig. 1, A and B). Axon terminals of rod bipolar cells were targeted according to the large size of their round or pear-shaped knob-like terminal swellings in stratum 5 of the inner plexiform layer (Fig. 1, C and D). All cells were filled with Lucifer yellow, and fluorescence microscopy allowed visualization of each cell’s complete morphology at the end of the recording. This included dendrites ascending from the cell body into the outer plexiform layer and an axon descending through the inner plexiform layer with one or more characteristic large, knob-like swellings at the terminal in the proximal part of the inner plexiform layer (Fig. 1, A and B).
Establishing G-seals and whole cell recordings from cell bodies and axon terminals of rod bipolar cells
For recordings from rod bipolar cell bodies, we established G-seals in the conventional way according to published procedures (Hamill et al. 1981; Sakmann and Stuart 1995; Stuart et al. 1993). No extra cleaning of cell surfaces was attempted, apart from the action of the stream of fluid coming from the pipette tip after applying positive pressure before entering the bath (25–40 mbar) (cf. Stuart et al. 1993). Seal resistances in the G range (10 G for electrodes with heat polishing) between the electrode and cell membrane were obtained by gently positioning the electrode tip onto the cell, releasing positive pressure and applying gentle suction by mouth (–10 to –30 mbar). The whole cell configuration was established manually with suction by mouth (–80 to –120 mbar) in combination with brief voltage transients applied to the electrode ("zap," typically +400 mV for 400 µs).
For recordings from rod bipolar cell axon terminals, we found that using a x60 objective with high numerical aperture greatly increased the rate of successful recordings (see METHODS). We regularly used lightly fire-polished pipettes and in our experience this is critical for obtaining high-quality G seals. Pipette resistances from 6.5 to 8.5 M (with the standard intracellular solutions) gave the best results with respect to successfully forming a G seal and obtaining an acceptable series resistance. A pipette resistance of this magnitude corresponds to a tip diameter almost as large as an axon terminal swelling as visualized with IR-DIC videomicroscopy (Fig. 1, C and D). Monitoring the manually applied pressure in the recording pipette was very useful feedback and aided reproducibility of the pressure applied. We approached the targeted axon terminal with a slight positive pressure (5–15 mbar) in the recording pipette. When the pipette tip made contact with the terminal, we formed a G seal by removing the pressure, assisted by gentle manual suction (–10 to –20 mbar). With this approach, we have regularly been able to establish G seals with resistances 10 G. In our experience, the most challenging part of recording from rod bipolar cell axon terminals is to successfully establish the whole cell recording configuration after G-seal formation. If too much suction is applied to a terminal in the cell-attached mode, it will be sucked up into the recording pipette. We have found that a combination of brief positive pressure pulses (40–80 mbar; applied by mouth) and brief depolarizing pulses (zap; +500 mV for 100 µs) gives the highest success rate in breaking through the membrane. One aspect of terminal-end recordings that we have not been able to control is an increase in the series resistance over the first 2–3 min after establishing the whole cell recording configuration.
Current transients in soma- and terminal-end recordings
We examined the passive membrane properties of rod bipolar cells by applying 10-mV hyperpolarizing voltage pulses (10- to 15-ms duration). Figure 2A shows an example of the current transients evoked in a soma-end recording of a rod bipolar cell. We fitted the current relaxation from the initial peak to the end of the voltage pulse with either a mono- or biexponential function. The relaxation was well fitted by a biexponential function, whereas the fit obtained by a monoexponential function was clearly inadequate (Fig. 2B) (Mennerick et al. 1997). The difference between the bi- and monoexponential fits is illustrated by the curve fit residuals (Fig. 2B). Adding a third exponential component only marginally improved the fit (not shown). For soma-end recordings, we obtained a fast time constant (fast) of 39 ± 12 µs (n = 22) and a slow time constant (slow) of 349 ± 164 µs (Table 1). The amplitude contribution of the fast component was 91 ± 5%. The input resistance, calculated from the steady-state current component of the fitted curve and the amplitude of the hyperpolarizing voltage pulse, was 3.4 ± 1.7 G.
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; Palmer et al. 2003), with a fast of 50 ± 25 µs (n = 18) and a slow of 994 ± 282 µs (Table 1). The amplitude contribution of the fast component was 79 ± 8%. The input resistance was 3.0 ± 1.8 G. Although current relaxations from both soma- and terminal-end recordings were better fitted by a biexponential than a monoexponential function, the responses evoked at the two recording locations could be clearly distinguished from each other by a more prominent slow exponential component in the terminal-end recordings characterized by a larger slow and a larger-amplitude contribution. Current transients in recordings from isolated compartments
On a few occasions, we recorded from isolated cell bodies or isolated axon terminals. These structures were not targeted as isolated compartments but were identified as such with fluorescence microscopy after the recording. We assume that the axons of the cells were cut during the slicing procedure. An example of current transients recorded from an isolated cell body with a short axon stump is illustrated in Fig. 3A. The relaxation was reasonably well fitted by a monoexponential function, and the fit residual displayed a smaller nonrandom deviation (Fig. 3A) compared with monoexponential fits for intact rod bipolar cells (Fig. 2A). When the relaxation was fitted by a biexponential function, there was a slight improvement in the fit (as judged by the fit residual; Fig. 3A), but the amplitude contribution of the slow exponential component was considerably smaller compared with the relaxations observed for soma-end recordings from intact cells (Fig. 2A). Similar results were obtained for four other isolated cell bodies, three of which also had a short axon stump (Table 1). When fitted with a biexponential function, the average amplitude contribution of the slow exponential component was 3.5 ± 1.7%, significantly smaller than for soma-end recordings of intact rod bipolar cells (P = 0.026).
Similar results were seen with recordings from isolated axon terminals (Mennerick et al. 1997; Palmer et al. 2003). Figure 3B shows an example of current transients recorded from an isolated axon terminal that also included a short axon stump. The relaxation was adequately fitted with a monoexponential function. When fitted with a biexponential function (Fig. 3B), there was no obvious reduction of the fit residual and the amplitude contribution of the slow exponential component was only 8%. Similar results were obtained for two other isolated axon terminals, one of which also had a short axon stump (Table 1). When fitted with a biexponential function, the amplitude contribution of the slow exponential component was 6.4 ± 2.2%, significantly smaller than for terminal-end recordings of intact rod bipolar cells (P = 0.009).
Description of rod bipolar cells by a two-compartment model
Current relaxations were well fitted by biexponential functions, both for soma- and terminal-end recordings of intact bipolar cells in situ. Similar results were previously observed for goldfish bipolar cells, both for acutely isolated cells (Mennerick et al. 1997) and for cell in slices (Palmer et al. 2003). These authors hypothesized that the biexponential relaxation suggested that the electrotonic profile of the cells could be described by a two-compartment equivalent circuit (Fig. 4A). From this circuit, together with assumptions of infinite membrane resistance for both compartments, Mennerick et al. (1997) derived a set of equations from which they could calculate the four parameters of the circuit. C1 and C2 represent the capacitance of the proximal and distal membrane compartments, respectively. C1 and C2 are linked in series by R2, the axial resistance of the connecting axon. The proximal compartment is linked to the voltage-clamp amplifier by R1, the series resistance of the recording pipette. The capacitance of the connecting axon is not explicitly represented in the two-compartment circuit.
In their analysis of isolated goldfish bipolar cells, Mennerick et al. (1997) demonstrated that the two capacitive compartments of the electrical circuit could be correlated to the two morphological compartments, the soma/dendritic compartment and the axon terminal compartment. Because the recording pipette can be positioned at either the soma or terminal end, there is no unique correspondence between the electrical and morphological compartments. Instead, the electrical compartment C1 will correspond to the proximal compartment with the recording pipette, and the electrical compartment C2 will correspond to the distal compartment without the recording pipette (Fig. 4A). In our analysis, we followed closely the approach of Mennerick et al. (1997) and used the equations derived from the two-compartment circuit to calculate circuit parameters for both soma- and terminal-end recordings from rod bipolar cells in situ. We then performed computer simulations with idealized models of rod bipolar cells and subjected them to the same voltage protocols as the physiologically tested cells.
Using Eqs. 3–6 to analyze the current transients obtained in our soma-end recordings, the capacitance of C1 was estimated to be 3.4 ± 0.6 pF and the capacitance of C2 was estimated to be 1.6 ± 0.2 pF (n = 22; Table 2). The resistance of R1 (series resistance) was estimated to be 12.7 ± 4.4 M, and the resistance of R2 (axonal resistance) was estimated to be 208 ± 96 M. C1 was larger than C2, suggesting that for soma-end recordings, C1 corresponds to the soma/dendritic compartment and C2 corresponds to the axon terminal compartment. When we used the same equations to analyze terminal-end recordings, the capacitance of C1 was estimated to be 1.5 ± 0.2 pF and the capacitance of C2 was estimated to be 4.3 ± 0.2 pF (n = 18). The resistance of R1 (series resistance) was estimated to be 44 ± 22 M and the resistance of R2 (axonal resistance) was estimated to be 185 ± 51 M. C1 was smaller than C2, suggesting that for terminal-end recordings C1 corresponds to the axon terminal compartment and C2 corresponds to the soma/dendritic compartment. These results indicate that the estimate for the capacitance of the soma/dendritic compartment (C1 in soma-end recordings, C2 in terminal-end recordings) is larger for terminal-end recordings than for soma-end recordings (P < 0.0001). It is likely, as suggested by Mennerick et al. (1997), that this is due to a selection bias with respect to the cells recorded. On average, the terminals that are targeted and successfully recorded from are expected to be larger (with correspondingly larger membrane capacitance) than terminals not targeted or not successfully recorded from, and it is reasonable to assume that larger terminals belong to larger cells. The estimate of R1 (series resistance) was lower for soma- than terminal-end recordings. The difference in resistance between the electrodes used for soma- and terminal-end recordings (see METHODS) did not seem large enough to account for this difference. Instead we speculated that the restricted range of curve fitting (starting 30–60 µs after the onset of the voltage pulse), imposed by residual input and output filtering, was insufficient to adequately resolve the fast initial decay of the current transient in the terminal-end recordings. Even with coated pipettes and the low-pass filter set to 100 kHz (sampling interval 5 µs), curve fitting could not start earlier than 30 µs after onset of the voltage pulse (as judged by eye). When we analyzed simulated responses generated with a computer model of a rod bipolar cell, we verified that the restricted range of curve fitting can lead to overestimation of series resistance (see following text). In contrast to Mennerick et al. (1997), we found no difference between the estimates of the capacitance of the axon terminal compartment in the two recording configurations (P = 0.16).
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. In our case, two of the three isolated axon terminal compartments and four of the five isolated soma compartments also contained an axon stump of variable length. Because the current relaxations were reasonably well fitted with monoexponential functions (see preceding text), we also estimated the compartment size directly from the time constant of decay, the series resistance, and the input resistance. For isolated cell bodies, the capacitance was 2.8 ± 0.7 pF (n = 5, and for isolated axon terminals, the capacitance was 1.1 ± 0.6 pF (n = 3). These values were not significantly different from the estimates of C1 in the preceding text (P = 0.66 and 0.069, respectively). Current transients from simulated rod bipolar cells
In the absence of accurate morphological reconstructions, our simplified models of rod bipolar cells were based on approximate morphological parameters from several different sources, including Lucifer yellow-filled cells (Billups and Attwell 2002; Hartveit 1996), electron microscopic images and reconstructions of axon terminals (Chun et al. 1993), and light microscopic and confocal images of immunolabeled cells (Behrens et al. 1998; Chun et al. 1993). The axonal length can vary between 50 and 70 µm and the axonal diameter can vary between 0.5 and 1 µm. The size of axon terminal swellings was measured as the distance along the longest diameter and perpendicular to this and ranged from 2.7 x 1.5 µm (Chun et al. 1993; their Fig. 6) to 10 x 4 µm (Behrens et al. 1998; their Fig. 2A). The size of the cell body was measured the same way and ranged from 8 x 5 µm (Chun et al. 1993; their Fig. 2) to 13 x 8 µm (Hartveit 1996; his Fig. 2). When we performed similar measurements on rod bipolar cells filled with Lucifer yellow during terminal-end recording (n = 7), the soma was 11.8 ± 1.8 x 7.3 ± 0.6 µm, the length of the axon was 44.8 ± 2.5 µm, and the terminal bouton attached to the recording pipette was 3.9 ± 2.2 x 2.0 ± 0.8 µm. These seven cells had a total of 19 terminal boutons that measured 2.8 ± 1.7 x 1.7 ± 0.6 µm. Our model cell was also guided by capacitance estimates for isolated rod bipolar cell terminals with small axon stumps [1.8 pF (Pan 2001), 1.46 pF (Pan et al. 2001)]. Based on these observations, we modeled our idealized rod bipolar cell with three cylindrical compartments: soma, axon and axon terminal. Dendrites arising from the soma were not modeled as explicit compartments but were considered as part of the soma. The axon terminal compartment resulted from collapsing two to six boutons into a single terminal compartment. From an initial set of starting values, the final size of the soma and axon terminal compartments were adjusted by slightly increasing the size of each compartment until the capacitance estimates, based on the two-compartment model, were similar to those obtained from real cells (see Tables 2 and 3). The final model of a rat rod bipolar cell had the following geometry (length x diameter): soma = 11.5 x 11 µm, axon = 50 x 0.8 µm, and axon terminal = 7 x 5 µm. Our model cell had approximately half the surface area of the goldfish bipolar cell in the study of Mennerick et al. (1997) and 1.7 times the surface area of the rat bipolar cell analyzed by Billups and Attwell (2002). The input resistance of the model cell was 2.2 G, in the lower range of values measured for our biological cells.
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for both soma- and terminal-end recordings. We analyzed the resulting current transients in the same way as those from biological cells. Irrespective of whether the recording pipette was positioned at the soma or the axon terminal, the decay of the current transients was well fitted by biexponential functions (Fig. 4, B and C). The residual plots in Fig. 4, B and C, display nonrandom deviations for both mono- and biexponential fits. For the biexponential fit, the deviation is small enough that it undoubtedly would have been masked by recording noise from a biologial cell. The imperfect fit with the biexponential function is probably due to the nonzero capacitance of the axonal compartment (cf. Mennerick et al. 1997). Estimates for C1 and C2 corresponded reasonably well to the theoretical (simulation input) values (Table 3). For soma- and terminal-end simulations, we obtained an axial resistance (ri) of the axon compartment (R2) of 128 and 152 M, respectively (Table 3). These estimates were close to the theoretical value of ri, which we calculated to be 159 M according to the following equation: ri = (Ri/Ai)L (Ri is the cytoplasmic resistivity, 160 cm; Ai is the cross-sectional area of the axon, 5.03 x 10-9 cm2; L is the length of the axon, 50 µm). We next verified that our model cell gave rise to curve-fitting parameters similar to those obtained in the physiological recordings. As detailed in Table 1, this was the case for both soma- and terminal-end recordings when the series resistance was set to 10 and 40 M, respectively. Effect of series resistance on capacitance estimates
Both the soma and the axon terminal of rat rod bipolar cells are smaller than those of goldfish bipolar cells (Mennerick et al. 1997), and it can be difficult to obtain recordings with very low series resistance, particularly from the axon terminals. We therefore examined the effect of varying series resistance on estimates obtained from current transients analyzed with the two-compartment equivalent circuit model. The series resistance of the recording electrode was varied between 1 M and 1 G, and for each condition, we simulated responses evoked by both soma- and terminal-end recordings. The capacitance of each compartment (C1 and C2), the axonal resistance (R2), and the series resistance (R1) were estimated after fitting the decays of current transients with biexponential functions. Based on the surface area of each compartment and a specific membrane capacitance of 1 µF/cm2, the soma compartment had a capacitance of 4.0 pF, the axon terminal compartment had a capacitance of 1.1 pF, and the axon compartment had a capacitance of 1.3 pF. For the soma compartment, capacitance estimates from soma- and terminal-end recordings followed each other closely for series resistance values between 4 M and 1 G (Fig. 5A). Between 4 and 160 M, the estimates were within 95–107% of the theoretical value, irrespective of whether the recording electrode was located at the soma or the axon terminal (Fig. 5A). At high values of series resistance, the capacitance estimates dropped below the theoretical value (to 50% at a series resistance of 1 G). Estimates of the soma capacitance from terminal-end recordings remained close to the theoretical value for low values of series resistance (1–3 M), whereas they were below the theoretical value for soma-end recordings and dropped to <1 pF at a series resistance of 1 M (Fig. 5A). We suspected that the errors for soma-end recordings with low series resistance were caused by the restricted range of curve fitting (starting 50 µs after onset of the voltage pulse for simulated data). Indeed, when we calculated the soma capacitance by starting curve fitting at the first sampling point after onset of the voltage step, the error was eliminated for soma-end recordings (Fig. 5A; full fit).
For the axon terminal compartment, capacitance estimates differed between soma- and terminal-end recordings for all values of series resistance tested, but both recording configurations tended to overestimate the capacitance (Fig. 5B). For soma-end recordings, the capacitance of the axon terminal was overestimated except at the highest values of series resistance tested. For terminal-end recordings, the capacitance was overestimated for series resistances between 10 and 400 M, and in this range, the estimate was within 105–135% of the theoretical value. For lower (<10 M) and higher (>400 M) values of series resistance, the capacitance was underestimated compared with the theoretical value (Fig. 5B). When we calculated the terminal capacitance by starting curve fitting at the first sampling point after onset of the voltage step, the error at low values of series resistance was strongly reduced, but not completely eliminated (Fig. 5B; full fit), suggesting that even when there is no input or output filtering of the signal, a sampling interval of 5 µs can be insufficient to adequately capture a very fast initial decay of the current transient. These results indicate that whereas estimates of the soma compartment capacitance are relatively independent of the recording configuration, estimates of the axon terminal compartment capacitance can depend critically on the recording configuration with terminal recordings giving the best estimates overall.
We next considered the potential influence of series resistance on the estimates obtained from physiological recordings of rod bipolar cells based on analysis with the two-compartment model. We corrected each estimated value with respect to the series resistance calculated for the same recording. For soma-end recordings, the corrected capacitance was 3.2 ± 0.6 pF for the soma compartment and 0.92 ± 0.14 pF for the terminal compartment (n = 22). For terminal-end recordings, the corrected capacitance was 4.1 ± 0.2 pF for the soma compartment and 1.1 ± 0.2 pF for the terminal compartment (n = 18). These results support the hypothesis that there was a selection bias with respect to the cells targeted for terminal recording. In terminal-end recordings, the capacitance of the soma compartment and the terminal compartment was, on average, 1.3 and 1.2 times larger than in soma-end recordings, respectively (P < 0.0001).
Effect of series resistance on estimates of R1 and R2
The time constant of decay of the capacitive charging transient of a single (RC) compartment is given approximately by the product of the series resistance and the membrane capacitance ( = Rs x Cm). Thus for very small compartment sizes or for very small series resistances, the decay can become so fast that it cannot be adequately resolved because exponential curve fitting is limited by residual input and output filtering. To explore this for our rod bipolar model, we varied the series resistance between 1 M and 1 G and estimated R1 according to Eq. 3 for the two-compartment model. For terminal-end recordings, R1 was increasingly overestimated when the theoretical value for series resistance was less than 20 M (Fig. 6A). For soma-end recordings, R1 was increasingly overestimated when the theoretical value for series resistance was less than 4 M, but the error was generally smaller than for terminal-end recordings (Fig. 6A). As for the capacitance estimates (see preceding text), we suspected that the errors were caused by the restricted range of curve fitting (starting 50 µs after onset of the voltage pulse for simulated data). When we calculated the series resistance by starting curve fitting at the first sampling point after onset of the voltage step, the error was eliminated for soma-end recordings (Fig. 6A). For terminal-end recordings, the error was strongly reduced but not completely eliminated (Fig. 6A). When we reduced the size of the terminal compartment from 1.1 pF (5 x 7 µm) to 0.38 pF (3 x 4 µm), the overestimation of R1 for terminal-end recordings occurred for theoretical values of series resistance less than 50 M. The degree of overestimation increased and occurred for even higher theoretical values of series resistance when we removed the terminal compartment altogether (Fig. 6B). The degree of overestimation of R1 increased further when we in addition reduced the diameter of the axon (Fig. 6B).
We next examined the effect of varying the series resistance on the estimate of the axonal resistance (R2) of the two-compartment model. For soma-end recordings, R2 was underestimated when the series resistance was <320 M (Fig. 6C). For terminal-end recordings, R2 was underestimated when the series resistance was <80 M (Fig. 6C). In the range of series resistance values between 10 and 160 M, the estimates from terminal-end recordings were closer to the theoretical value than the estimates from soma-end recordings (Fig. 6C).
Effect of terminal size and axon diameter on estimates of terminal size
Because cellular morphology is subject to natural variation, we explored the consequences of varying the morphological parameters for the circuit estimates (C1, C2, R1, and R2) obtained by the two-compartment model. We varied the size of the axon terminal, the diameter of the axon, and the cytoplasmic resistivity and estimated axon terminal capacitance for both soma- and terminal-end recordings. To compare the different conditions, we normalized estimates of capacitance to the theoretical value such that values >1 correspond to an overestimation and values <1 correspond to an underestimation. We ran simulations for four different terminal sizes. The maximum axon terminal size was equal to the size of the soma compartment (relative size 1). For this condition, there was no error in the estimate of the terminal size (Fig. 7A). Our default model corresponded to a relative terminal size of 0.28. In this case, the terminal size was overestimated at 1.67 for the soma-end recording and 1.34 for the terminal-end recording (Fig. 7A). We observed that the two-compartmental model increasingly overestimated the size of the terminal compartment as its size was reduced. This was the case irrespective of whether the recording pipette was positioned on the soma or the terminal, but the error was larger for soma-end recordings than for terminal-end recordings (Fig. 7A).
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. This condition reduced the overestimation of the size of the terminal, irrespective of whether the recording pipette was positioned on the soma or the terminal (Fig. 7B). For terminal-end recordings, the error became negligible, regardless of the size of the terminal compartment. For soma-end recordings, the error increased when the size of the terminal compartment was reduced (Fig. 7B). For soma-end recordings, the reduction of axon diameter also led to an increasing underestimation of the size of the terminal compartment when it was larger than 0.5 times the size of the soma compartment (Fig. 7B).
To examine the influence of the axon membrane capacitance on the circuit estimates, we repeated the same series of simulations with the default axon diameter (0.8 µm) but with the specific capacitance of the axon compartment set to 10-6 µF/cm2 (the lowest value allowed by the NEURON simulator). This eliminated the overestimation of the terminal capacitance when its size was reduced (Fig. 7C). This condition also reduced the underestimation of the terminal capacitance for soma-end recordings when the terminal compartment was larger than 0.5 times the size of the soma compartment. Thus the observed errors seem to be a consequence of the fact that the two-compartment model explicitly neglects the capacitance of the axon compartment. Another assumption of the model was that of infinite membrane resistance. Accordingly, we tested the consequences of eliminating not only the capacitance of the axon segment but also the membrane conductance for the whole cell. In this condition, there were virtually no errors in the estimates of the terminal capacitance by the two-compartment model when the size of the terminal was varied and all estimates were within ±1% of the theoretical value (Fig. 7D).
Effect of cytoplasmic resistivity on estimate of terminal size
In our default model of a rod bipolar cell, we used a cytoplasmic resistivity of 160 cm. Cytoplasmic resistivity is in general difficult to measure accurately and estimates range from 50 to 500 cm (Hallermann et al. 2003; Major et al. 1994; Thurbon et al. 1994; Trevelyan and Jack 2002; Ulrich et al. 1994). The chosen value for cytoplasmic resistivity (Ri) is important, however, as it influences the overall degree of electrotonic compactness of a neuron (Spruston et al. 1994).
We first simulated terminal-end recordings and varied Ri between 50 and 400 cm. For each condition, we estimated terminal compartment capacitance, soma compartment capacitance, axon resistance, and series resistance. With terminal-end recordings, varying the value of Ri markedly influenced the decay time course of the current transients (Fig. 8A). However, there was no effect on the estimate for series resistance (Fig. 8B), consistent with the fact that changing Ri had no effect on the peak of the current transients (Fig. 8A). For each value of Ri, we directly calculated the corresponding value for the axonal resistance (see preceding text). The estimates from the two-compartment model closely followed these values over the range explored (Fig. 8B). Estimates for the capacitance of the terminal compartment were little influenced over the range of values tested for Ri (Fig. 8C), but estimates for the soma compartment decreased with increasing values of Ri (Fig. 8C).
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cm. In this case, the effect of varying Ri on the decay time course of the current transients was much smaller (Fig. 8D). However, for increasing values of Ri, the value of R2 was increasingly underestimated compared with the directly calculated value for axonal resistance (see preceding text; Fig. 8E). There was minimal influence of Ri on the estimates of C1 and C2 (Fig. 8F). Examples of whole cell and outside-out patch recordings from axon terminals
There is evidence that rod bipolar cells express a range of ligand-gated (e.g., Cui et al. 2003; Fletcher et al. 1998; Gillette and Dacheux 1995; Greferath et al. 1995; Karschin and Wässle 1990; Koulen et al. 1998; Pan 2001; Vaquero and de la Villa 1999) and voltage-gated (e.g., de la Villa et al. 1998; Hartveit 1999; Pan 2001; Pan and Lipton 1995; Pan et al. 2001; Protti and Llano 1998) ion channels at their axon terminals. After establishing whole cell recordings at axon terminals of rod bipolar cells, we applied GABA (200 µM) or glycine (200 µM) locally to the axon terminal using a multi-barreled pipette complex. Application of glycine evoked a strong inward current at a holding potential of –60 mV (Fig. 9A; n = 9/9 cells; peak amplitude: 30–577 pA). Application of GABA also evoked an inward current at –60 mV (Fig. 9B; n = 9/9 cells; peak amplitude: 17–488 pA). The tip of each multi-barreled pipette complex measured 20–25 µm and was displaced laterally from the axon terminal by approximately the same distance. Although it is difficult to spatially restrict the area of application with puffer pipettes, we noticed that the response amplitude was greatly reduced when we changed the position of the application pipette away from the region of the axon terminal, suggesting that glycine- and GABA-receptors located in the axon terminal region made a large contribution to the observed responses.
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, terminal-end recording; 
, soma-end recording). B: plot of estimated capacitance of terminal compartment (Cterminal (fit)) vs. theoretical value of series resistance for both terminal-end (—) and soma-end (···) recordings of simulated model of rod bipolar cell.
) and soma-end recording (
). Each pair of estimates is plotted mirror-reflected around the theoretical value of the terminal size (A–D). Series resistance set to 50 M
