INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Neurons generally have resting potentials of around 70 mV and can generate action potentials in response to stimuli. On the other hand, most of the outer retinal neurons of the vertebrate retina are depolarized in the dark and respond to light with graded potential changes. In such neurons, not only the voltage-gated ionic conductances but also the Ca²⁺ regulation mechanisms are thought to play important roles in generating the light-induced responses (Hayashida et al. 1998).

The horizontal cell is a second-order neuron of the vertebrate retina that is tonically depolarized in the dark by an excitatory transmitter, probably L-glutamate, released from the photoreceptors (Cervetto and MacNichol 1972; Dowling and Ripps 1972; Murakami et al. 1972). The membrane properties have been studied in enzymatically dissociated horizontal cells and five types of voltage-gated ionic conductances were identified under the voltage-clamp condition (e.g., Kaneko 1987; Lasater 1991 for reviews; Lasater 1986; Picaud et al. 1998; Shingai and Christensen 1983, 1986; Tachibana 1983; Yagi and Kaneko 1988). Among these voltage-gated conductances, the Ca²⁺conductance was suggested to play a crucial role in maintaining the membrane potential in the dark (Winslow 1989). More recently, some aspects concerning the Ca²⁺ regulation mechanisms were also revealed in dissociated horizontal cells by the optical measurement using the Ca²⁺-sensitive dyes (Hayashida et al. 1998; Linn and Christensen 1992; Micci and Christensen 1998; Okada et al. 1999). The Ca²⁺-regulation mechanisms are thought to affect the horizontal cell response because the voltage-gated Ca²⁺ conductance is known to be inactivated by intracellular Ca²⁺ (Tachibana 1981, 1983). Despite these previous experiments elucidating the electrochemical properties of individual physiological mechanisms, there are few quantitative analyses studying how these ionic conductances and Ca²⁺-regulation mechanisms interact each other. In the present study, we used a cable model to quantitatively study how the physiological mechanisms identified in in vitro preparations operate together to generate physiological responses of horizontal cells.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Physiological experiments

Horizontal cells were dissociated from the retinae of carp, Cyprinus carpio (10- to 20-cm body length). The dissociation procedure and the cell preparation appeared in the previous study (Hayashida et al. 1998). The dissociated cells were superfused continuously with a control solution using a "Y"-tube microflow system (Suzuki et al. 1990). The control solution contained (in mM) 120 NaCl, 7.6 KCl, 2.5 CaCl₂, 1 MgCl₂, 10 glucose, 10 HEPES with 0.1 mg/ml BSA (pH adjusted to 7.3 with 1 M NaOH). A high concentration of K⁺ was included in this control solution as was in previous studies on the dissociated cells of the cyprinid fish (Tachibana 1983, 1985; Yagi 1989; Yagi and Kaneko 1988). The general conclusions reached in the present study were not changed when a lower concentration of K⁺ (2.6 mM) was used in the control solution (data not shown). For a cobalt application, 1 mM CaCl₂ in the control solution was replaced by equimolar CoCl₂. For cadmium or caffeine application, 0.2 mM CdCl₂ or 10 mM caffeine was added to the control solution. Ca²⁺-free solution was made by removing CaCl₂ from the control solution and, in some cases, adding 5 mM EGTA. When L-glutamate was applied to the cell, sodium L-glutamate (100 µM) was dissolved in superfusates. Pharmacological agents were applied using the "Y"-tube microflow system, whose outlet (internal tip diameter, ~500 µm) was located within ~500 µm from the recorded cell.

[Ca²⁺]_i was ratiometrically measured by using the fluorescent Ca²⁺ indicator, Fura-2 (Grynkiewicz et al. 1985). Fura-2 fluorescence measurements from dissociated horizontal cells have been described in a previous study (Hayashida et al. 1998). In brief, the isolated cells were incubated in Fura-2/AM solution in the dark for 30-40 min at room temperature. The Fura-2/AM solution was made by adding the membrane-permeant analogue Fura-2 acetoxymethyl ester (Fura-2/AM) to the control solution to a final concentration of 5 µM (<0.1% vol/vol DMSO). The cells were then rinsed twice with control solution and maintained in culture medium for >30 min to convert Fura-2/AM to the Ca²⁺-sensitive form.

The 340- and 380-nm excitation light was used and the fluorescence emitted by cells was measured at 510 nm. The ratio of the fluorescence intensities elicited with the 340- and 380-nm excitation light was calculated after subtracting the background fluorescence. [Ca²⁺]_i was calculated from the fluorescence ratio (R) according to the following formula of Grynkiewicz et al. (1985)

(1)

Here K_d is the equilibrium dissociation constant for Fura-2 at 20°C (135 nM) (Grynkiewicz et al. 1985). In the present study, R_min was estimated as the ratio obtained when a cell was superfused with a Ca²⁺ ionophore, 4-Br-A23187 or A23187 (10 µM), in a Ca²⁺-free solution (10 mM EGTA and no Ca²⁺ added). The R_max value was determined as the ratio when a cell was superfused with the Ca²⁺ ionophore in a high-Ca²⁺ solution (5 mM Ca²⁺). F_free and F_bound were determined as the fluorescence intensities at 380-nm excitation when a cell was superfused with the Ca²⁺ ionophore in the Ca²⁺-free solution and the high-Ca²⁺ solution, respectively. In the text, [Ca²⁺]_i values are given when the values of F_free, F_bound, R_min, and R_max were obtained for each cell at the end of the recording. Otherwise, only the R values are given (denoted as "fluorescence ratio" in the relevant text figures).

In the voltage- and current-clamp experiments, the perforated-patch technique with the whole cell configuration was employed to minimize disruption of cytoplasmic constituents (Horn and Marty 1988).

Computer simulations

Computer simulations were carried out using the simulation software NEURON (Hines and Carnevale 1997).

Since we preferentially used horizontal cells which have round-shaped somata and a few short thin dendrites in the present experiments, a hemi-spherical cable is considered to be appropriate for modeling the dissociated horizontal cell. As shown in Fig. 1, a dissociated horizontal cell was modeled by a hemi-spherical cable with 15 µm of radius. This cable dimension mimicked a typical shape of the dissociated horizontal cells used in the present experiments. The simulation was conducted with a single cylindrical cable model as well. The diameter and length of the cable were 20 and 22.5 µm, respectively. The internal volume and surface area of the cable are the same as those of the hemi-spherical cable. There is no distinguishable difference in simulation results between these two models. Therefore only the simulation results obtained with the hemi-spherical cable are described in this paper.

View larger version (50K): [in this window] [in a new window]   Fig. 1. A hemi-spherical cable model for a dissociated horizontal cell. Radius of the cable is 15 µm. The cable is divided into 202 segments in the longitudinal direction, as indicated by seg. Internal space of each segment is divided into 101 shells in the radial direction, as indicated by j (see text for detail).

In the simulations, intracellular Ca²⁺ diffusion in the longitudinal direction was taken into account by dividing the cable into 202 segments (Hines and Carnevale 2000). Intracellular Ca²⁺ diffusion in the radial direction was also taken into account by dividing the each segment into 101 shells. The diffusion between neighboring shells is described by (Hines and Carnevale 2000)
Here, j is an integer from 0 to 100 representing the shell number; [Ca²⁺]_j is the Ca²⁺ concentration in the shell of j, e.g., j = 0 for the outer most shell; a_j,j+1 and d_j,j+1 are the area of the border and the distance between the shells of j and j + 1; D_Ca is the diffusion constant for intracellular Ca²⁺ (units of µm²/s). D_Ca used in the present simulations was assumed to be 6 µm²/s and is in the range of the apparent diffusion constant of Ca²⁺ measured in a living cell (Kushmerick and Podolsky 1969).

The number of segments and shells were increased in the simulation to estimate the error of the calculation.

A step of calculation time was 20-50 µs in all simulations.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Physiological experiments

[CA²⁺]_i CHANGE INDUCED BY L-GLU. Figure 2A shows an example of the [Ca²⁺]_i change in response to a prolonged application of L-glu (100 µM) to an isolated horizontal cell. In this experiment, the cell was first superfused with the control solution to measure [Ca²⁺]_i in the resting state. The resting potential of the isolated horizontal cell was more negative than 50 mV in the control solution [56.2 ± 6.0 (SD) mV, n = 5] (Hayashida et al. 1998; Tachibana 1981). At this voltage, voltage-gated Ca²⁺ current was not detectable by the voltage-clamp experiments (Tachibana 1983; Yagi and Kaneko 1988). [Ca²⁺]_i in the resting state was ~52 nM in this cell [75 ± 37 (SD) nM, n = 11]. The resting [Ca²⁺]_i was not affected by 200 µM Cd²⁺ (n = 5) as shown in Fig. 2B. Furthermore, application of 1 mM Co²⁺ did not have effects on [Ca²⁺]_i in the resting state (n = 4, data not shown). These observations confirm the results obtained by the voltage-clamp experiments.

View larger version (16K): [in this window] [in a new window]   Fig. 2. [Ca2+]i change measured in the isolated horizontal cell. A: 100 µM L-glutamate was applied for 324 s. The fluorescence ratio of Fura-2 was measured every 4 s (). [Ca2+]i was calculated by measuring the calibration parameters for this cell at the end of this recording (METHODS). B: 200 µM Cd2+ was applied for 60 s and then 100 µM L-glutamate was applied for 9 s. A and B were obtained in different cells. The membrane potential was not clamped and was not recorded both in A and B.

View larger version (22K): [in this window] [in a new window]   Fig. 3. Relative contribution of the voltage-gated Ca2+ conductance and the glutamate-gated conductance to the L-glu-induced [Ca2+]i change. A: L-glutamate (100 µM) was applied for 32 s during the voltage clamp in the perforated-patch configuration. The holding voltage was 75 mV (bottom) and then the membrane voltage was depolarized to 10 mV for 5 s. The whole cell membrane current (top) and the Fura-2 fluorescence ratio (middle) were simultaneously measured. · · · , the 0 pA level in the current trace. The fluorescence ratio was measured once every second. B: the holding voltage was 55 mV (bottom) and then the membrane voltage was depolarized to 5 mV for 800 s. L-Glutamate (100 µM) was applied for 240 s during the membrane potential was clamped at 5 mV. The whole cell membrane current (top) and the Fura-2 fluorescence ratio (middle) were simultaneously measured. · · · , the 0 pA level in the current trace. The fluorescence ratio was measured every 20 s.

INITIAL TRANSIENT OF [CA²⁺]_i INDUCED BY L-GLU. The transient increase of [Ca²⁺]_i shown in Fig. 2A was suppressed by a preapplication of caffeine (Fig. 4). L-Glu (100 µM) was applied to the cell repetitively as shown in the figure. In the second trial, 10 mM caffeine was applied immediately before the application of L-glu. [Ca²⁺]_i transiently increased and then decreased toward the resting level in response to the caffeine application (see inset). The transient increase of [Ca²⁺]_i induced by L-glu was partially suppressed to ~60% (61 ± 26%, mean ± SD, n = 7) when the caffeine was preapplied in seven of nine cells examined. In the remaining two cells, the initial transient was completely suppressed (Fig. 4B). The transient increase of [Ca²⁺]_i recovered in the third trial (A and B). The suppression of the transient increase of [Ca²⁺]_i by caffeine is likely to be due to a prolonged depletion of Ca²⁺ store. This observation suggests that a part of the initial transient of [Ca²⁺]_i can be explained by the Ca²⁺-induced Ca²⁺ release (CICR) from the caffeine-sensitive Ca²⁺ store (DISCUSSION). The remaining component of the initial transient, which was not blocked by the preapplication of caffeine (Fig. 4A), is explained by the Ca²⁺-dependent inactivation of the voltage-gated Ca²⁺ conductance, which will be shown later with quantitative analyses using the biophysical model of the isolated horizontal cell.

View larger version (23K): [in this window] [in a new window]   Fig. 4. Initial transient of [Ca2+]i change. L-Glutamate (100 µM) was applied repetitively for ~3 min with 2-min intervals. In the second trial, 10 mM caffeine was preapplied for ~10-20 s immediately before the L-glu application. The Fura-2 fluorescence ratio was measured every 3 s. The membrane potential was not clamped and was not recorded. A: partial suppression of the initial transient by the caffeine preapplication. The caffeine-induced Ca2+ release was shown in the inset with an expanded time scale. B: complete blockade of the initial transient by the caffeine preapplication.

Biophysical model of the isolated horizontal cell

MODELS OF PHYSIOLOGICAL MECHANISMS. The physiological mechanisms relevant to calculate [Ca²⁺]_i were the glutamate-gated cation conductance, the voltage-gated Ca²⁺ conductance, the Na⁺/Ca²⁺ exchange, the Ca²⁺ pump, and Ca²⁺ buffering. These mechanisms were described by the following equations.

(2)

(3)

(4)

(5)

View larger version (19K): [in this window] [in a new window]   Fig. 5. Inactivation curve of the voltage-gated Ca2+ conductance with different values of KCa and nCa. a, c, and e illustrate the curve with KCa = 150, 300, and 600 nM, respectively (nCa = 4). b, c, and d indicate the curve with nCa = 2, 4, and 6, respectively (KCa = 300 nM). rest and depo indicate the [Ca2+]i in the resting state and in the L-glu-induced sustained depolarization, respectively.

(6)

(7)

(8)

1

1

1

1

1

1

(9)

Estimation of parameter values of Ca²+ pump

To conduct physiologically plausible simulations, values of the parameters in the model equations describing the physiological mechanisms require appropriate estimation. As was explained in the previous section, some parameters can be directly estimated referring to previous experiments. We used the following logic to estimate parameter values that cannot be explicitly found from previous experiments. Steady state was assumed in the resting state as well as the prolonged application of L-glu for all physiological mechanisms. All cytoplasmic Ca²⁺ sequestration sites, i.e., Ca²⁺buffers and Ca²⁺ stores were also at steady state (no net release or storing of Ca²⁺ taking place). Therefore the efflux of Ca²⁺ by the Na⁺/Ca²⁺ exchange and the Ca²⁺ pump counterbalances the influx through the glutamate-gated cation and the voltage-gated Ca²⁺ conductances both in the resting state and in the L-glu-induced depolarization. Figure 6 illustrates how such steady states were achieved in the horizontal cell. The efflux of Ca²⁺ by each Ca²⁺ regulation mechanism was plotted as a function of [Ca²⁺]_i for the resting (A) and the L-glu-induced depolarized states (B). The total flux was plotted with a thick line (indicated by net). [Ca²⁺]_i in each steady state corresponds to a point where there is no net flux. The Ca²⁺ flux induced by the Na⁺/Ca²⁺ exchange (NaCa) becomes inward when [Ca²⁺]_i decreases below a value at which the electrochemical gradient reverses. Based on previous experiments, the parameters included in the glutamate-gated cation conductance, the voltage-gated Ca²⁺ conductance and the Na⁺/Ca²⁺ exchange were estimated. We selected parameter values for the Ca²⁺ pump, i.e., A_pump and K_pump of Eq. 7, so that the [Ca²⁺]_i was reproduced in the resting state (~52 nM) as well as in the prolonged L-glu application (~818 nM). The estimated values were 1.3 pmol/cm²/s for A_pump and 400 nM for K_pump.

View larger version (23K): [in this window] [in a new window]   Fig. 6. Relationships between the Ca2+ flux and [Ca2+]i in the steady states. ggcc, vgcc, NaCa and pump indicate the Ca2+ flux through the glutamate-gated cation conductance, voltage-gated Ca2+ conductance, Na+/Ca2+ exchanger, and Ca2+ pump, respectively. The Ca2+ flux was calculated with Eqs. 2 and 3 for ggcc, Eqs. 4 and 5 for vgcc, Eq. 6 for NaCa, and Eq. 7 for pump. The parameters shown in Table 1 were used for the calculations and area of the cell membrane was assumed to be 1.4 × 105cm2. net indicates the net flux of Ca2+ across the membrane. Upward deflection shows the efflux. A: the Ca2+ flux was calculated for the resting state in which the membrane voltage is about 56 mV. B: the Ca2+ flux were calculated for the L-glu-induced depolarized state in which the membrane voltage is about 5 mV.

Inactivation of Ca²+ current

The time course of the Ca²⁺-dependent inactivation observed in the isolated horizontal cell was analyzed by the model to estimate _Ca of Eq. 5. The inactivation time course of voltage-gated Ca²⁺ current during the voltage clamp was calculated with different values of _Ca using the model as shown in Fig. 7. The model includes the voltage-gated Ca²⁺ conductance, the Na⁺/Ca²⁺ exchange, the Ca²⁺ pump, the Ca²⁺ buffer, and the Ca²⁺ diffusion, and therefore the simulation mimics satisfactorily the physiological experiments conducted on the isolated horizontal cell. The experimental data () were replotted from Fig. 6 of Tachibana (1983), in which the membrane currents were measured in the isolated goldfish horizontal cell with the micro electrode. All the voltage-gated K⁺ currents were blocked and the current induced by clamping the voltage from 61 to 0 mV was measured in the absence (indicated by exp:control) and the presence of 4 mM Co²⁺ (indicated by exp:Co²⁺). The calculated current illustrates the Co²⁺-sensitive current that is composed of those through the voltage-gated Ca²⁺ conductance and the Na⁺/Ca²⁺ exchange. The calculated current decayed much faster than experimental data when _Ca was removed (indicated by a and middle trace in the inset). [Ca²⁺]_j=0, the Ca²⁺ concentration just below the membrane, increases quickly after the activation of voltage-gated Ca²⁺ conductance by the depolarization (bottom trace in the inset) and immediately inactivates the conductance if _Ca were negligibly small. The time course of calculated current provided a reasonable fit to the experimental data (indicated by b), when _Ca is 2.86 s. The experimental data could not be fitted by changing the diffusion constant of intracellular Ca²⁺.

View larger version (25K): [in this window] [in a new window]   Fig. 7. The time course of Ca2+-dependent inactivation of the voltage-gated Ca2+ current. The experimental data were replotted from Fig. 6 of Tachibana (1983) and were illustrated with . The membrane voltage of the model was depolarized from 61 to 0 mV to simulate the voltage-clamp experiment. A Co2+-sensitive current, composed of the voltage-gated Ca2+ current and the Na+/Ca2+ exchange current, was calculated with the cell model. a and b indicate the Co2+-sensitive current calculated with Ca = 0 and Ca = 2.86 s, respectively. The other parameters used for the calculations are shown in Table 1. Inset: the Co2+-sensitive current and the Ca2+ concentration just below the membrane ([Ca2+]j=0) calculated with Ca = 0 s.

Simulation of L-glu-induced [Ca²+]_i change

Using the parameter values estimated in the previous sections, we simulated the experiments shown in Fig. 2A. The densities of each physiological mechanism in the cell model, i.e., g_glu, g_Ca, k_ex, A_pump, [Buffer]_total, and D_Ca were adjusted to reproduce the profile of Fig. 2A. Fig. 8A shows the L-glu-induced [Ca²⁺]_i change calculated with the cell model (). Note that the cell model includes all the membrane conductances, the membrane capacitance, and the Ca²⁺-related physiological mechanisms introduced in the present study. In this figure, the average concentration of intracellular Ca²⁺ of the cable was illustrated to be compared with the Fura-2 fluorescence measurement. The profile of [Ca²⁺]_i change calculated with the cell model provides an appropriate fit to the experimental data () except for the initial transient. The initial transient of [Ca²⁺]_i estimated by the experiment, however, exceeded the measurable range of Fura-2 (higher than a few µM) (Grynkiewicz et al. 1985) and is likely to include a large error. The discrepancy between the experiment and the simulation probably reflects the error of the Fura-2 fluorescence measurement in such high [Ca²⁺]_i. Another possibility to explain the discrepancy is the lack of Ca²⁺ store in the model. The Ca²⁺ store was suggested to contribute to the initial transient of the [Ca²⁺]_i increase as shown in Fig. 4.

View larger version (20K): [in this window] [in a new window]   Fig. 8. Simulation of L-glu-induced [Ca2+]i change using the cable model of isolated horizontal cell. The parameters shown in Tables 1 and 2 were used for the calculations. The glutamate-gated conductance incorporated in the cable surface was calculated with Eq. 3, where gglu = 232 mS/cm2 and glu = 100 ms. A: the average [Ca2+]i of the whole cable was calculated (). , the [Ca2+]i change shown in Fig. 2A. B: the Ca2+ flux through the Ca2+ regulation mechanisms was calculated. ggcc, vgcc, NaCa, and pump indicate the Ca2+ flux through the glutamate-gated cation conductance, voltage-gated Ca2+ conductance, Na+/Ca2+ exchanger, and Ca2+ pump, respectively. The traces of Ca2+ flux are enlarged from the inset (- - -). Upward deflections show the efflux.

The amount of Ca²⁺ flux induced by each physiological mechanism was illustrated separately to examine each mechanism's contribution to the control of [Ca²⁺]_i (Fig. 8B). In this figure, the vertical axis measures the amount of Ca²⁺ extruded from the cell. When L-glu is applied, a large influx of Ca²⁺ occurs through the voltage-gated Ca²⁺ conductance that increases [Ca²⁺]_i to 9.2 µM from 52 nM transiently. The Ca²⁺ efflux mechanisms are activated simultaneously to counteract the influx. At a high [Ca²⁺]_i seen in the initial phase, Ca²⁺ is extruded mainly by the Na⁺/Ca²⁺ exchange because the Ca²⁺ extrusion rate of the Na⁺/Ca²⁺ exchange increases monotonically as [Ca²⁺]_i, yet that of the Ca²⁺ pump saturates. The influx of Ca²⁺ through the voltage-gated Ca²⁺ conductance decreases after reaching a peak (70 pA, inset) because of the Ca²⁺-dependent inactivation. The efflux through the Na⁺/Ca²⁺ exchange and the Ca²⁺ pump also decreases as [Ca²⁺]_i decreases. As a consequence, [Ca²⁺]_i reaches a steady level of 0.82 µM. These are the fundamental Ca²⁺ regulatory mechanisms of [Ca²⁺]_i in the isolated horizontal cell during the L-glu application implied by the model.

In the present model, the Ca²⁺ flux by the Na⁺/Ca²⁺ exchange is inward in the resting state. The difference of Ca²⁺ regulation properties between the Ca²⁺ pump and the Na⁺/Ca²⁺ exchange may suggest the functional difference in regulating [Ca²⁺]_i between them (DISCUSSION).

When the time constant of Ca²⁺-dependent inactivation of the voltage-gated Ca²⁺ conductance is removed from Eq. 5, the influx through the voltage-gated Ca²⁺ conductance decreases with a faster time course than that shown in the inset and a transient increase of [Ca²⁺]_i does not appear (data not shown). Therefore a part of the falling phase of [Ca²⁺]_i transient during the L-glu application can be explained by the Ca²⁺-dependent inactivation of the voltage-gated Ca²⁺ conductance.

Simulation of voltage response to L-glu application

The voltage response to the L-glu application calculated with the cell model was compared with the experimental data as shown in Fig. 9;  shows the calculated membrane potential and  show the measured voltage with the perforated-patch electrode. As shown in the figure, the membrane potential of the cell model was depolarized from 56 to 5 mV in response to the L-glu application, which is similar to the experiment. It is notable that the transient overshoot seen in the experiment is well reproduced by the model. As was shown in the previous section, the decline of the overshoot is explained by the Ca²⁺-dependent inactivation of voltage-gated Ca²⁺ current. Therefore the transient depolarization seen at the initial phase is a Ca²⁺ spike induced by the L-glu application.

View larger version (11K): [in this window] [in a new window]   Fig. 9. The voltage response to a L-glu application. The membrane voltage change was calculated with the cable model (). The parameters shown in Tables 1 and 2 were used for the calculation. The glutamate-gated conductance was calculated with Eq. 3, where gglu = 232mS/cm2 and glu = 100 ms. The membrane voltage of the isolated horizontal cell was measured under the current-clamp in the perforated-patch configuration and was shown with . L-Glutamate (100 µM) was applied for 74 s.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Computer simulation models of solitary horizontal cells with ionic currents have been previously developed (Usui et al. 1996; Winslow 1989). The biophysical model was developed in the present study based on not only electrophysiological experiments but also optical measurements. Although there are various physiological parameters to be estimated in the model, the ranges of these parameter values were determined by elucidating the results from both electrophysiological and optical measurements. Therefore the present model is physiologically realistic especially in terms of the cooperative activities of the voltage-gated conductances and the Ca²⁺ regulation mechanisms.

The horizontal cell in situ has a membrane potential of around 30 mV and responds to light with a graded potential change. Among the ionic conductances found in the horizontal cell, the voltage-gated Ca²⁺ conductance drastically changes in this voltage range and strongly affects the response of the horizontal cell. The Ca²⁺ conductance is known to be activated around 40 mV and increases prominently until ~0 mV in the horizontal cell of the lower vertebrates (Lasater 1986; Shingai and Christensen 1983, 1986; Tachibana 1983). Therefore a small amount of voltage change produces a significant change in the Ca²⁺ influx. In other outer retinal neurons, i.e., photoreceptors and bipolar cells, the Ca²⁺-activated K⁺ and Ca²⁺-activated Cl currents are thought to counteract the inward Ca²⁺ current to suppress Ca²⁺ spikes (e.g., Bader et al. 1982; Barnes and Hille 1989; Yagi and MacLeish 1994 for photoreceptors; Kaneko and Tachibana 1985; Karschin and Wässle 1990 for bipolar cells). In the horizontal cells, however, such Ca²⁺-activated outward currents were not observed (Tachibana 1983; Ueda et al. 1992) or too small to suppress the Ca²⁺ spikes (unpublished data). Our previous experiments on isolated horizontal cells have demonstrated that [Ca²⁺]_i is maintained at a high level and the voltage-gated Ca²⁺ conductance is inactivated to a large extent during the L-glu application (Hayashida et al. 1998) (see also Fig. 2A). These suggest that the feed-back control of the voltage-gated Ca²⁺ conductance by the intracellular Ca²⁺ is expected to play an essential role in stabilizing the membrane potential of the horizontal cell in situ. It was suggested that the inactivation of the voltage-gated Ca²⁺ conductance as well as the tonic synaptic input from the photoreceptors are required to account for the membrane potential in the dark and light-induced hyperpolarizing responses of horizontal cells (Winslow 1989). The quantitative analyses in the present study clearly demonstrated the underlying mechanisms to control [Ca²⁺]_i and the membrane potential.

Previous studies showed that a caffeine-sensitive Ca²⁺ store exists in horizontal cells (Linn and Christensen 1992; Micci and Christensen 1998; Yasui 1988). In the L-glu-induced sustained depolarization as well as the resting state, the Ca²⁺ store is considered to be at steady state and no net release (or uptake) of Ca²⁺ by the store takes place. In the present study, we mainly focused on the regulatory mechanism of [Ca²⁺]_i in the steady states. Therefore the Ca²⁺ store was not taken into account in the present model.

The preapplication of caffeine suppressed the transient increase of [Ca²⁺]_i induced by the L-glu application (Fig. 4), suggesting a contribution of the Ca²⁺ store to the transient phase of the L-glu-induced [Ca²⁺]_i increase in the isolated horizontal cell. The release as well as the uptake of Ca²⁺ by the Ca²⁺ store is likely to occur transiently by an abrupt Ca²⁺ influx. In the isolated horizontal cell, this abrupt Ca²⁺ influx was induced by a quick application of high concentration of L-glu or by an instantaneous voltage clamp from the resting potential to the potential in which the Ca²⁺ conductance is almost fully activated. This is not considered to be a normal physiological condition in situ. The Ca²⁺ store, however, could contribute to the depolarizing phase after the cell was fully hyperpolarized by bright light.

A possible contribution of the caffeine-sensitive Ca²⁺ store to the inactivation of the L-type Ca²⁺ channel on a long time scale has been demonstrated in rod photoreceptors (Krizaj et al. 1999). The caffeine-sensitive Ca²⁺ store in the horizontal cell might play a functional role in such inactivation of the voltage-gated Ca²⁺ conductance. The effect of caffeine on the L-glu-induced steady [Ca²⁺]_i level was examined in the isolated horizontal cell. The L-glu-induced [Ca²⁺]_i level was lowered when caffeine (2-10 mM) was applied to the cell (n = 5, data not shown). Further experiments, however, are needed to clarify the role of the Ca²⁺ store in the horizontal cell.

In horizontal cells, both the Na⁺/Ca²⁺ exchange and the Ca²⁺ pump operate together (Hayashida et al. 1998). The present simulations indicated that Ca²⁺ was extruded mainly by the Ca²⁺ pump when [Ca²⁺]_i was lower than 1 µM, but the Na⁺/Ca²⁺ exchange became dominant as [Ca²⁺]_i increased further. These two transporters cooperate to control intracellular Ca²⁺ over a wide range of concentrations. The level of [Ca²⁺]_i, however, might be different at different sites in the horizontal cell in situ. Therefore it is possible that these mechanisms control different cellular functions. The present simulation suggested that the Na⁺/Ca²⁺ exchange may operate in the reverse mode when the cell is in the resting state (Fig. 8B). This is consistent with the Ca²⁺ influx via the Na⁺/Ca²⁺ exchange demonstrated in the isolated catfish horizontal cell (Micci and Christensen 1998). Such a small amount of Ca²⁺ influx in the resting state might play an important role in loading and/or unloading the Ca²⁺ store (Blaustein 1993; Micci and Christensen 1998). Ca²⁺ possibly enters the cell through a leakage conductance. Therefore [Ca²⁺]_i at the resting state might be maintained by the balance between the efflux through the Ca²⁺ pump and the influx through the reversed Na⁺/Ca²⁺ exchange and/or the leakage conductance.

Na⁺ continuously enters the cell through the glutamate-gated cation conductance during the application of L-glu (Ishida et al. 1984; Tachibana 1985) and is assumed to be extruded by the Na⁺/K⁺ pump (Shimura et al. 1998; Yasui 1987, 1988). Therefore [Na⁺]_i is likely to be as dynamically changing and controlled as [Ca²⁺]_i. [Na⁺]_i affects the regulation of [Ca²⁺]_i via the Na⁺/Ca²⁺ exchange. In the present simulation, [Na⁺]_i was assumed to be constant (8 mM) to calculate the Na⁺/Ca²⁺ exchange current. The role of the Na⁺/K⁺ pump as well as the other Na⁺ transporters are to be studied further.

The present study revealed fundamental mechanisms to explain Ca²⁺ regulation in the horizontal cell in vitro. Further studies with experimental and computational analyses are needed to elucidate the underlying mechanisms of the light-induced response of the horizontal cell in situ. The model equations of physiological mechanisms developed in the present study are useful, when such studies are conducted.