Voltage-Dependent Uptake Is a Major Determinant of Glutamate Concentration at the Cone Synapse: An Analytical Study

Botond Roska, Lubor Gaal, and Frank S. Werblin

Division of Neurobiology, Department of Molecular and Cell Biology, University of California, Berkeley, California 94720

    ABSTRACT
Abstract
Introduction
Methods
Results
Discussion
References

Roska, Botond, Lubor Gaal, and Frank S. Werblin. Voltage-dependent uptake is a major determinant of glutamate concentration at the cone synapse: an analytical study. J. Neurophysiol. 80: 1951-1960, 1998. It was suggested that glutamate concentration at the synaptic terminal of the cones was controlled primarily by a voltage-dependent glutamate transporter and that diffusion played a less important role. The conclusion was based on the observation that the rate of glutamate concentration during the hyperpolarizing light response was dramatically slowed when the transporter was blocked with dihydrokainate although diffusion remained intact. To test the validity of this notion we constructed a model in which the balance among uptake, diffusion, and release determined the flow of glutamate into and out of the synaptic cleft. The control of glutamate concentration was assumed here to be determined by two relationships; 1) glutamate concentration is the integral over the synaptic volume of the rates of release, uptake, and diffusion, and 2) membrane potential is the integral over the membrane capacitance of the dark, leak, and transporter-gated chloride current. These relationships are interdependent because glutamate uptake via the transporter is voltage dependent and because the transporter-gated current is concentration dependent. The voltage and concentration dependence of release and uptake, as well as the light-elicited, transporter-gated, and leak currents were measured in other studies. All of these measurements were incorporated into our predictive model of glutamate uptake. Our results show a good quantitative fit between the predicted and the measured magnitudes and rates of change of glutamate concentration, derived from the two interdependent relationships. This close fit supports the validity of these two relationships as descriptors of the mechanisms underlying the control of glutamate concentration, it verifies the accuracy of the experimental data from which the functions used in these relationships were derived, and it lends further support to the notion that glutamate concentration is controlled primarily by uptake at the transporter.

    INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References

An earlier study (Gaal et al. 1998) suggested that voltage- and concentration-dependent uptake by the glutamate transporter at the cone synaptic terminal provided the essential link between cone membrane potential and glutamate concentration. The main evidence for this was the observation that the rate of glutamate removal during a light flash, measured by the rate of horizontal cell hyperpolarization, was dramatically slowed by dihydrokainate (DHK), a glutamate transporter blocker that acted specifically at the cones but not the Mueller cells. Glutamate concentration is thought to be controlled by the integral of the rates of uptake release and diffusion. This study defines the relative rates of each of these quantities and the changes that take place during the light response.

The overall system relating glutamate concentration to light intensity can be described by two relationships. One states that the rate of change of membrane potential is determined by the integral of the light-dependent current, the leak current, and the glutamate-elicited, transporter-gated chloride current over the membrane capacitance. The other states that the rate of change of glutamate concentration is determined by the integral of uptake, diffusion, and vesicular release over the volume of the space at the synapse.

The underlying functions relating currents and glutamate uptake to voltage, concentration, and light intensity were measured in earlier studies. Transport rate and the associated chloride current are known as a function of glutamate concentration and membrane voltage (Eliasof and Werblin 1993; Gaal et al. 1998; Picaud et al. 1995; Wadiche et al. 1995). A part of vesicular release depends on membrane potential (Copenhagen and Jahr 1989), but part appears to be potential independent (Rieke and Schwartz 1994). The light-elicited current was measured as a function of membrane voltage and light intensity (Attwell et al. 1982; Haynes and Yau 1985). The relationship between glutamate concentration and horizontal cell potential was also measured (Gaal et al. 1998).

The two relationships above are sufficiently complete to allow us to predict the time course of the light response in horizontal cells under normal and transporter-blocked conditions. We can also predict quantities that are unmeasurable such as the time course of glutamate concentration change and rates of diffusion, release, and transport after a light flash. We have no independent measure of the volume of the synaptic space, so we have left all results scalable to this value.

We found that the previous measurements of voltage- and glutamate-dependent uptake, voltage-dependent release, and glutamate-gated chloride current, when incorporated into the two relationships, predict time courses of glutamate removal that are very close to those actually measured. This good fit suggests that the two interdependent relationships outlined previously provide a reasonable approximation to the underlying mechanism that controls glutamate concentration as a function of cone membrane potential. The fit also supports the notion that the transporter is a significant mechanism along with vesicular release that links glutamate concentration to cone membrane potential.

    METHODS
Abstract
Introduction
Methods
Results
Discussion
References

Electrical recording, solutions, and drugs

Briefly, horizontal cells and cones were patch recorded in tiger salamander retinal slices, and solutions and drugs were applied as described by Gaal et al. (1998).

Equivalent circuit of the cone output synapse: the resistive two port model

The proposed equivalent circuit of the cone output synapse is shown in Fig. 1. The two differential equations, describing the charging of the cone membrane capacitance and the filling of the synaptic cleft with neurotransmitter, are represented by two first-order circuits. The two circuits are joined together with a resistive two-port, which represents voltage and glutamate concentration-dependent uptake. The voltage of the first circuit (Vm) represents cone voltage across the membrane capacitance (Cm), which is modulated by a light-controlled current (idark[I, Vm]) as well as leak current (ileak[Vm]) and chloride current (ichloride[Vm, Vg]). The voltage of the second circuit (Vg) represents glutamate concentration (G) in the volume of the synaptic cleft (Cg). Release, which increases glutamate concentration in the cleft, is modeled with a current source (irelease[Vm]) controlled by the state of the first circuit (Vm). Diffusion (idiffusion[Vg]) is modeled by a simple resistor in series with a voltage source that represents glutamate concentration outside the synapse. Finally uptake (iuptake[Vm, Vg]) is represented by a current flowing through a resistive two-port and controlled by both Vm and Vg.


View larger version (18K):
[in this window]
[in a new window]
 
FIG. 1. Equivalent 2-port circuit of the cone output synapse. Two differential equations, describing the charging of the cone membrane capacitance and the filling of the synaptic cleft with neurotransmitter, are represented by 2 1st-order circuits. The 2 circuits are joined together with a resistive 2-port that represents voltage and glutamate concentration-dependent uptake. Voltage of the 1st circuit (Vm) represents cone voltage across the membrane capacitance (Cm), which is modulated by a light-controlled current (idark[I, Vm]) as well as leak current (ileak[Vm]) and chloride current (ichloride[Vm, Vg]). The voltage of the 2nd circuit (Vg) represents glutamate concentration (G) in the volume of the synaptic cleft (Cg). Release, which increases glutamate concentration in the cleft, is modeled with a current source (irelease[Vm]) controlled by the state of the 1st circuit (Vm). Diffusion (idiffusion[Vg]) is modeled by a simple resistor in series with a voltage source that represents glutamate concentration outside the synapse. Finally uptake (iuptake[Vm, Vg]) is represented by a current flowing through a resistive 2 port and controlled by both Vm and Vg.

Mathematical model

The formal relationship between glutamate concentration and cone membrane potential can be described by two differential equations. The first states that the chloride, dark, and leak currents determine the electrical charging of the membrane capacitance
−<IT>C</IT>d<IT>V</IT><SUB>m</SUB>/dt = <IT>i</IT><SUB>chloride</SUB>[<IT>V</IT><SUB>m</SUB>, <IT>G</IT>] + <IT>i</IT><SUB>dark</SUB>[<IT>I</IT>, <IT>V</IT><SUB>m</SUB>] + <IT>i</IT><SUB>leak</SUB>[<IT>V</IT><SUB>m</SUB>] (1)
where Vm is the cone membrane potential (mV), G is the glutamate concentration (µM), C is the cone membrane capacitance (0.085 nf) (Attwell et al. 1982), and I is the relative (ambient minus background) light intensity (photons/µm2 s)

The second relationship states that the flows of glutamate into and out of the diffusion-limited extracellular synaptic space, caused by release, uptake, and diffusion, determine the rate of "charging" of the glutamate concentration in the synaptic region
<IT>S</IT>d<IT>G</IT>/d<IT>t</IT>= <IT>i</IT><SUB>release</SUB>[<IT>V</IT><SUB>m</SUB>] + <IT>i</IT><SUB>uptake</SUB>[<IT>V</IT><SUB>m</SUB>, <IT>G</IT>] + <IT>i</IT><SUB>diffusion</SUB>[<IT>G</IT>] (2)
where S is the volume of diffusion-limited synaptic region

For Eq. 1 we make the assumption that the cone is isopotential. This is reasonable because the electrotonic distances are small. For Eq. 2 we assume that the diffusion-limited compartment containing the glutamate concentration is compact; in other words, glutamate concentration throughout the diffusion-limited volume is uniform.

Dark current

The dark current (Fig. 2A) depends on I and Vm independently according to the following
<IT>i</IT><SUB>dark</SUB>[<IT>I</IT>] ∼ 1 − <IT>I</IT>/(<IT>I + h</IT>) (3)
which expresses the fact that light closes channels and the resulting decrease in dark current saturates with half-maximal light intensity (h) of 76 photons/µm2 s (Attwell et al. 1982).


View larger version (35K):
[in this window]
[in a new window]
 
FIG. 2. Plots of the functions used in the differential equations describing the cone output synapse. Drawing shows directions of release, diffusion, and uptake as well as dark, leak, and chloride currents. A: dark current is plotted against Vm. h = 76 photons/(µm2 s), n1 = 19, and Edark = -3 mV. The different curves are associated with relative light intensities of 1, 10, and 100 photons/(µm2 s). B: chloride current as a function of Vm. n2 = 63, KClm = 12 µM, ECl = -60 mV. The different curves are associated with glutamate concentrations of 10, 20, and 30 µM. C: leak current as a function of Vm. Slope = 2.2 nS, offset = 108 pA. D: glutamate release (dG/ dt) as a function of Vm. N1 = 370 µMs-1, xset = -35 mV, range = 1.99, slope = 0.8. E: glutamate transport (dG/dt) is plotted against G. N2 = 3.87 µMs-1, Km = 4 µM, m = 12 mV. The different curves are associated with cone membrane potentials of -55, -45, and -35 mV. F: glutamate diffusion (dG/dt) as function of G. N3 = 4.2 s-1. C, cone; B, bipolar cell; H, horizontal cell.

The I-Vm curve of the dark current was fitted by Haynes and Yau (1985) by the sum of two exponentials
<IT>i</IT><SUB>dark</SUB>[<IT>V</IT><SUB>m</SUB>] ∼ {exp[(1 − 0.35)(<IT>V</IT><SUB>m</SUB><IT>− E</IT><SUB>dark</SUB>)/12.5]
− exp[−0.35(<IT>V</IT><SUB>m</SUB><IT>− E</IT><SUB>dark</SUB>)/12.5]} (4)
Because the membrane voltage and light intensity independently influence the dark current, the overall expression is simply the weighted product of Eqs. 3 and 4
<IT>i</IT><SUB>dark</SUB>[<IT>V</IT><SUB>m</SUB>, <IT>I</IT>] = <IT>n</IT><SUB>1</SUB>[1 − <IT>I</IT>/(<IT>I + h</IT>)]{(exp[(1 − 0.35)(<IT>V</IT><SUB>m</SUB><IT>− E</IT><SUB>dark</SUB>)/12.5]
− exp[−0.35(<IT>V</IT><SUB>m</SUB><IT>− E</IT><SUB>dark</SUB>)/12.5]}
(<IT>5</IT>}
where n1 is a scaling factor, which is proportional to the number of "light-gated" channels open in dark. Fitting this function to the data measured by Attwell et al. (1982) results in n1 = 19 pA; Edark = reversal potential of the dark current (-3 mV) (Attwell et al. 1982)

Chloride current

The chloride current (Fig. 2B) is gated by glutamate (Eliasof and Werblin 1993; Picaud et al. 1995) and therefore depends on both Vm and G. The dependence on glutamate concentration can be approximated by a scaled hyperbolic function with one-half saturating concentration KClm = 12 µM (Eliasof and Werblin 1993)
<IT>i</IT><SUB>chloride</SUB>[<IT>G</IT>] ∼ <IT>G</IT>/(<IT>G + K</IT><SUB>Clm</SUB>) (6)
In the presence of a competitive inhibitor KClm(1 + i/Ki) substitutes for KClm, where i is the concentration of the inhibitor and Ki is the dissociation constant associated with it.

We fitted by the least square fit method the experimental I-Vm relationship at saturating glutamate concentrations measured by Picaud et al. (1995) with a sum of two exponentials that can be interpreted as a single energy barrier placed at gamma  = 0.91 fractional distance from the intracellular boundary of the membrane (Hille 1992)
<IT>i</IT><SUB>chloride</SUB>[<IT>V</IT><SUB>m</SUB>, ∞] = <IT>n</IT><SUB>2</SUB>{exp[(0.91<IT>V</IT><SUB>m</SUB><IT>− E</IT><SUB>Cl</SUB>)<IT>zF</IT>/<IT>RT</IT>]
− exp[−(1 − 0.91)<IT>V</IT><SUB>m</SUB><IT>zF</IT>/<IT>RT</IT>]}
(<IT>7</IT>}
where Ecl is the chloride equilibrium potential, -60 mV (Picaud et al. 1995) and n2 is a scaling factor, proportional to the number of channels. From the fitting it was determined to be 63 pA; z is the valence of the charge carrier, -1; F, R, and T have the usual meaning

The independence of Vm and G (Barbour et al. 1991) again allows us to take the product of Eqs. 6 and 7 for the overall expression
<IT>i</IT><SUB>chloride</SUB>[<IT>V</IT><SUB>m</SUB>, <IT>G</IT>] = <IT>n</IT><SUB>2</SUB><IT>G</IT>/(<IT>G + K</IT><SUB>Clm</SUB>){exp[(0.91<IT>V</IT><SUB>m</SUB><IT>− E</IT><SUB>Cl</SUB>)<IT>zF</IT>/<IT>RT</IT>]
− exp[−(1 − 0.91)<IT>V</IT><SUB>m</SUB><IT>zF</IT>/<IT>RT</IT>]}
(<IT>8</IT>}

Leak current

Leak current (Fig. 2C) refers to all other currents and is assumed to be ohmic, although it is known that a potassium current at the inner segment is outward rectifying and time dependent; a calcium current and a calcium dependent potassium and chloride current also exist. However, in the physiological operating range the leak current can be approximated by a linear curve (Attwell et al. 1982) with slope and offset adjusted to create a typical cone light response
<IT>I</IT><SUB>leak</SUB>[<IT>V</IT><SUB>m</SUB>] = 108 pA + 2.4 nS <IT>V</IT><SUB>m</SUB> (9)
Equation 2 contains three functions controlling the charging (vesicular release) and discharging (uptake and diffusion) of the diffusion limited region of the synapse. These three rates are defined below.


View larger version (32K):
[in this window]
[in a new window]
 
FIG. 3. Determination of N1, N2, N3, Km, m, range, and S parameters. A: average light response of 8 horizontal cells under control and uptake blocked [300 µM dihydrokainate (DHK)] conditions. B: same light responses as in A but the ordinate shows glutamate concentration in the cleft. C: slope of the curves in B is plotted against glutamate concentration (dots) during the time indicated by the shaded bar in B. A linear curve was fitted to the "uptake blocked" experimental data. The slope determines the relative diffusion constant, N3, and the offset determines voltage-independent release shown by the arrow at a. The curve fitted to the "control" dots is the sum of the linear "uptake blocked" curve plus a hyperbolic function (X × [G]/(Y + [G]), with X and Y unknown. D: idiffusion [G] + irelease [-50] (D + R[-50]) and iuptake [-50, G] (U[-50]) are plotted as solid curves. idiffusion [G] + irelease [-35] (D + R[-35]) and iuptake [-35, G] (U[-35]) are plotted as dashed curves. Arrows point to (a) voltage-independent release, (b) irelease [-35], (c) dark concentration of glutamate, when uptake is blocked, (d) concentration of glutamate in light when uptake is blocked, and (e) control dark concentration of glutamate.

Release

Here we describe both voltage-dependent and voltage-independent components (Rieke and Schwartz 1994) of release (Fig. 2D). This curve shows a transition near -40 mV, the activation point of L-type Ca2+ channels present in salamander cone terminals. As Vm tends from -40 to -infinity infinity, release approximates a constant (the voltage-independent component). Positive to -40 mV, release increases monotonically according to the activation curve for Ca2+. The relationship is described by the following equation
<IT>i</IT><SUB>release</SUB>[<IT>V</IT><SUB>m</SUB>] = [<IT>N</IT><SUB>1</SUB>/range − (2 − 1/range)<IT>N</IT><SUB>1</SUB>]/(1 + exp[<IT>V</IT><SUB>m</SUB><IT>− x</IT><SUB>set</SUB>]slope)
+ (2 − 1/range)<IT>N</IT><SUB>1</SUB> (10)
where xset and slope together determine the potential at which release becomes voltage dependent. Those values are chosen to be -35 mV and 0.8, respectively, to set the transition from voltage-independent to voltage-dependent release at -40 mV.

N1 is proportional to the number of release sites, number of vesicles per release site, and the number of transmitter molecules per vesicle. It determines the magnitude of release at every membrane voltage.

Range is defined as the release at -35 mV divided by the voltage independent release

Transport

Transport (Fig. 2E), as the chloride current, is affected by both voltage and glutamate concentration independently according to the following relationship (Wadiche et al. 1995)
<IT>i</IT><SUB>uptake</SUB>[<IT>V</IT><SUB>m</SUB>, <IT>G</IT>] = −<IT>N</IT><SUB>2</SUB><IT>G</IT>/(<IT>G + K</IT><SUB>m</SUB>) exp[−<IT>V</IT><SUB>m</SUB>/<IT>m</IT>] (11)
where m is a factor that determine voltage dependence of the transporter (Wadiche et al. 1995). N2 is proportional to the number of transporters at the cone terminal. The negative sign indicates that transporter removes glutamate from the synaptic region.


View larger version (25K):
[in this window]
[in a new window]
 
FIG. 4. Control light response in model and measurement. A: light response of a cone generated with the model. B: measured light response of a cone. C: light response of a horizontal cell generated with the model. D: measured light response of a horizontal cell. Saturating light (1,000 photons/(µm2 s) was "turned on" at 0.5 s and lasted 1 s for horizontal cell and 0.5 s for cone as indicated by the bars.

Diffusion

Diffusion (Fig. 2F) from the synaptic region is assumed to be linear with the concentration gradient. Glutamate concentration outside the synapse is assumed to be quite low and therefore modeled to be zero
<IT>i</IT><SUB>diffusion</SUB>[<IT>G</IT>] = −<IT>N</IT><SUB>3</SUB><IT>G</IT> (12)
where N3 is the diffusion coefficient and idiffusion is negative, suggesting that glutamate diffuses out from the synaptic region.

The horizontal cell as a glutamate electrode

Throughout the measurements the horizontal cell (which is postsynaptic to the cone) membrane potential was used to indicate glutamate concentration in the synapse. To compare the predictions of the model with the measured light response, we calibrated the horizontal cell membrane potential in the presence of different concentrations of glutamate (Gaal et al. 1998). The data can be fit by the following relationship
<IT>V</IT><SUB>h</SUB>[<IT>G</IT>] = 78<IT>G</IT>/(<IT>G</IT>+ 25) − 80 (13)
where Vh is the horizontal cell membrane potential.

Determination of N1, N2, N3, Km, m, range, and S parameters

Our strategy to find these parameters was as follows. The ordinate values of the normal light response of a horizontal cell (Fig. 3A, control) and the light response when glutamate uptake was blocked with DHK (Fig. 3A, uptake blocked) were converted to glutamate concentration units (Fig. 3B) with the calibration curve described by Eq. 13. The shaded bar in Fig. 3B indicates the time frame when cone voltage remained close to -50 mV. The change of glutamate concentration over time (-dG/dt) is plotted against glutamate concentration in Fig. 3C in the time frame indicated by the shaded bar in Fig. 3B. When uptake is blocked the ordinate values represent -idiffusion [G- irelease [-50]. The slope of the fitted linear curve determines the diffusion constant, N3 (4.2 s-1), and the offset determines the rate of voltage independent release, N1/range. When uptake is intact the data points represent -iuptake [-50,G- idiffusion [G- irelease [-50]. Because both idiffusion [G] and irelease [-50] were already determined, fitting a function of the form of iuptake [-55, G, Km, N2, m] + idiffusion [G] + irelease [-55] determines Km (3.96 µM) and sets the value of N2 exp[-55/m]. idiffusion [G] + irelease [-55] and iuptake [-55, G] are plotted as solid curves in Fig. 3D. Their intersection sets the glutamate concentration in light when cones are hyperpolarized to -50 mV. In dark, when cones are depolarized to -35 mV, the idiffusion + irelease curve is shifted to right (dashed curve) and intersects the abscissa at the dark concentration of glutamate when uptake is blocked (Fig. 3B). The offset of this shifted curve determines irelease [-35], which equals N1 (370 µM s-1). From N1 and the voltage-independent release, N1/range, range can be calculated (1.99). In dark this shifted linear curve intersects iuptake [-35, G] at the normal dark concentration of glutamate (Fig. 3B), which together with the known value of N2 exp[-55/m] sets N2 (3.87 µM s-1) and m (11.32 mV). Because we had no experimental way to determine the volume of the synaptic cleft, S, it was set to unity. The values of N1, N2, and N3 are relative to S, so the true diffusion constant and number of transporters are scaled to the (unknown) volume of the synaptic cleft. We note that horizontal cells are not ideal glutamate electrodes, so the delay caused by their capacitance is also included in S.


View larger version (24K):
[in this window]
[in a new window]
 
FIG. 5. "Hidden" or unmeasurable events of the light response. A: time course of glutamate concentration in the synaptic cleft during the light response. B: time course of release rate. At light ON hyperpolarization of cones terminates voltage sensitive release. At light OFF cone depolarization overshoots the steady-state dark potential; therefore release is accentuated. C: time course of glutamate transport. At light ON hyperpolarization of cones turns on glutamate transport, but the gradually decreasing glutamate concentration scales down the effect of hyperpolarization. D: time course of diffusion; diffusion passively follows glutamate concentration in A.

    RESULTS
Abstract
Introduction
Methods
Results
Discussion
References

Our goal was to generate simulated light responses by using the equations and functions outlined in METHODS. We then compared the simulated responses with the actual measurements under different pharmacological conditions (Gaal et al. 1998), when either release or uptake were blocked. We considered the following three experimental situations: 1) normal light response, 2) light response in the presence of different doses of DHK to block transport, and 3) light response in the presence of different doses of magnesium (Mg2+) to block release.

Normal light response

Figure 4 shows the response of the model to a light flash eliciting maximal response in cones under control conditions. The shape and range of the cone (Fig. 4A) and horizontal cell (Fig. 4B) membrane potential responses are similar to those in the living system (Fig. 4, C and D). The characteristic initial peak hyperpolarization and depolarization of the cone at light onset and offset, respectively, are illustrated on Fig. 4A.

The model can predict the change in glutamate concentration as well as the different components of the glutamate flow (release, uptake, and diffusion) during a light flash. Figure 5 shows these "hidden" events. The shape of the diffusion curve (Fig. 5D) is similar to the G response (Fig. 5A) because the diffusion depends only on G. Although glutamate release is a function of only Vm, the release curve (Fig. 5B) is different from the cone Vm response. This discrepancy is due to the fact that release is insensitive to voltages more negative than -40 mV but becomes strongly dependent on Vm around -35 mV (Fig. 2D). This asymmetry is clearly demonstrated on Fig. 5B. The initial peak hyperpolarization of the cone Vm at light onset has no effect on release, but the peak depolarization at light offset causes a large release peak.

The transport curve (Fig. 5C) reveals the dependency of uptake on G and also on Vm. The sudden increase and decrease of uptake rate at the light onset and offset is a consequence of the fast hyperpolarization and depolarization, respectively, of the cone terminal membrane.

Light response in the presence of different doses of DHK

In the model, DHK, a competitive inhibitor of the glutamate transporter (Arriza et al. 1994; Barbour et al. 1991; Eliasof and Werblin 1993; Picaud et al. 1995), changes the Km of the transporter channel to Km (1 + i/Ki), where i is the concentration of DHK and Ki is its dissociation constant (Stryer 1990).


View larger version (33K):
[in this window]
[in a new window]
 
FIG. 6. Effect of blocking uptake on the model and measured light response. A: effect of different DHK concentrations (10, 30, 100, and 300 µM) on the predicted cone light response. B: effect of the same DHK concentrations on the measured cone light response. C: effect of the DHK on the predicted horizontal cell light response. The Ki of DHK was 20 µM in the model. D: effect of DHK on the measured horizontal cell light response. Saturating light (1,000 photons/µm2 s) was "turned on" at 0.5 s and lasted 1 s as indicated by the bar. E: predicted normalized initial rate of the horizontal cell light response as a function of DHK concentration. F: measured normalized initial rate of the horizontal cell light response as a function of DHK concentration.

According to the experiments of Gaal et al. (1998), there are three important consequences of DHK to the light response: 1) cones are depolarized in dark, 2) horizontal cells are depolarized in dark and light, and 3) the rate of hyperpolarization of horizontal cells decreases at light onset.

The effect of DHK on the cone light response is shown in Fig. 6, A (model) and B (measurements). After introducing DHK (t = 0 s) in the model, there is a significant depolarization of cones in dark that increases the operating range of cones (the measurements reflect only the steady state). The depolarization of horizontal cells in dark and light and the slow down of the light response at ON are shown in Fig. 6, C (model) and D (measurement).

Figure 6, E and F, depict the results of analysis of the effect of DHK on the kinetics of the horizontal cell light response. The initial rate is defined as the average slope between t = 0.5 s and t = 0.6 s for onset and t = 1.5 s and t = 1.6 s for offset. In Fig. 6, E (model) and F (measurements), the normalized initial rate (defined as the initial rate in the presence of DHK/control initial rate × 100) is plotted against DHK concentration.

Light response in the presence of different doses of Mg2+

Magnesium decreases the calcium-dependent release of glutamate (Dowling and Ripps 1973). We can introduce this blocking effect into the model by scaling the N1 variable of release by a Boltzman function fitted to the normalized horizontal cell dark-voltage versus Mg2+ concentration experimental curve: 1/{exp[([Mg2+- 3)/0.6] + 1}. Increasing Mg2+ therefore decreases N1 with half-maximal concentration of 3 mM.

The characteristic changes in the light response of horizontal cells caused by Mg2+ were 1) hyperpolarization of horizontal cells in dark and light and 2) a decrease in rate of depolarization at the light offset and change of the onset kinetics. Our model displays both effects. Figure 7 shows the effect of Mg2+ on the light response of horizontal cells in the model (Fig. 7A) and in the measurement (Fig. 7B). The change in the kinetics of the horizontal cell light response with Mg2+ is rather complex (Fig. 7, C and D). The normalized initial rate at light OFF is monotonically decreasing with increasing Mg2+ concentrations (Fig. 7, C, dashed line for model, and D, dashed line for measurement). At light ON the normalized initial rate shows a bell-shape dependence on Mg2+ (Fig. 7, C, solid line for model, and D, solid line for measurement). This can be explained as follows. The rate of removal of glutamate from the synaptic cleft depends on the balance between inflow (release) and outflow (transport and diffusion), so the expected effect of Mg2+, a release blocker, is an increase in rate of the glutamate depletion. However Mg2+ also lowers the glutamate concentration of the cleft in dark, which decreases the rate of transport and diffusion. This decrease in removal counteracts the effect on release and slows down the onset response. At lower concentrations of Mg2+ the direct effect on release is stronger so the initial rate increases with increasing Mg2+. At higher Mg2+ concentrations the indirect effect on transport and diffusion becomes increasingly stronger, counteracting the direct effect and causing the slope of the initial rate versus Mg2+ curve to become zero then negative later. This could account for the bell-shape dependence of the initial rate curve on Mg2+.


View larger version (27K):
[in this window]
[in a new window]
 
FIG. 7. Effect of blocking release on the model and measured light response. A: effect of different (0, 1, 3, 5, and 10 mM) Mg2+ concentrations on the predicted horizontal cell light response. B: effect of the same Mg2+ concentrations on the measured horizontal cell light response. C: predicted normalized initial rate of the horizontal cell light response as a function of Mg2+ concentration. D: measured normalized initial rate of the horizontal cell light response as a function of Mg2+ concentration. Solid curve represents light onset; dashed curve represents light offset. The curves fitted to the predicted or measured normalized initial rates by hand.

    DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References

At the output synapse of cones in the tiger salamander retina the glutamate concentration is determined by the integral of three rates: release, uptake, and diffusion. The interactions that set concentration are complex because uptake is both voltage and glutamate concentration dependent. Further, the transporter appears to gate a chloride channel, generating a negative feedback signal that alters cone membrane potential. This potential controls both release and uptake.

The study of Gaal et al. (1998) proposed that the transporter is mainly responsible for setting concentration, but that study raised the more general question as to the relative contributions of each of these rates to the control of glutamate concentration. In this study we attempted to evaluate relative contribution of each of these rates in setting glutamate concentration. We used a simple pair of interrelated equations to describe these complex interactions. These equations were fitted with previously measured functions relating dark current, chloride current, leak current, release, and uptake to membrane voltage and glutamate concentration. The solution of these equations with previously measured functions generated rates of glutamate concentration change that were quite close to the quantities actually measured by Gaal et al. (1998), suggesting that the model might be a good approximation to the mechanism underlying glutamate concentration control.

Relative contributions of uptake and release are functions of membrane potential

Figure 8 shows how uptake, release, and diffusion interact to set glutamate concentration as uptake and release change with light-elicited variations in cone membrane potential. The irelease and iuptake + idiffusion curves are shown as functions of glutamate concentration. The intersection of the two curves sets the steady-state glutamate concentration in the synaptic cleft at a given cone membrane potential, which in turn is a function of light intensity. In the dark, release balanced by uptake and diffusion sets the glutamate concentration to 67 µM (Fig. 8A). When cones are illuminated they respond with hyperpolarization, which decreases release over the potential range from -35 to -40 mV and increases uptake. A downward shift in the release curve moves the intersection of the curves to the left, decreasing glutamate concentration. When the cone voltage reaches -40 mV (Fig. 8B) release is no longer voltage dependent (Rieke and Schwartz 1994), but uptake continues to increase in magnitude with hyperpolarization, steepening the uptake plus diffusion curve and pushing the intersection toward lower glutamate concentrations. When cone voltage reaches its maximum hyperpolarization of -50 mV, glutamate uptake increased to the level where the intersection of the curves moves the glutamate concentration to 5 µM (Fig. 8C).


View larger version (15K):
[in this window]
[in a new window]
 
FIG. 8. Proposed mechanism for light-controlled modulation of glutamate concentration in the cone synaptic cleft. In all figures the change of glutamate concentration with time is plotted against glutamate concentration in the cone synaptic cleft. A: in dark, the intersection of the release and uptake + diffusion curves sets the glutamate concentration around 70 µM. B: if cones are slightly illuminated they hyperpolarize; glutamate release decreases, uptake + diffusion increases, and the resultant sliding of the release and uptake + diffusion curves sets glutamate concentration to lower values. C: if the intensity of illumination further increases, cones pass -40 mV, and the release curve does not decrease further. At these intensities only the increasing uptake forces the intersection (which is equal to the steady-state glutamate concentration) to move toward lower glutamate concentrations.

Except for a narrow part of the response range where vesicular release is voltage dependent, cones appear to use a strategy different from other neurons to control transmitter concentration over most of the cone response range; cone voltage controls the rate of uptake of neurotransmitter from the synaptic cleft.

Chloride current may generate a significant negative feedback at the cone synapse

The voltage and glutamate concentration-dependent transporter not only locks glutamate concentration to cone voltage but also provides a feedback signal from glutamate concentration to cone voltage. The feedback signal is provided by a chloride channel, which is incorporated into the transporter (Picaud et al. 1995; Wadiche et al. 1995). The feedback is negative because the chloride equilibrium potential (ECl) lies negative to the cone operating range (-35 to -50 mV) (Werblin and Dowling 1969).

This negative feedback could act to accelerate the light response and help to prevent perturbations of glutamate concentration brought about by variations in rate of vesicular release. Such perturbations can be caused by change in temperature or pH, both of them shown to modulate release. (Barnes and Bui 1991; Barnes et al. 1993)

Input-output relationship of the cone-horizontal cell synapse

The rate of glutamate concentration change depends on cone voltage and glutamate concentration in the synaptic cleft. Plotting uptake, diffusion, or release as a function of cone voltage and glutamate concentration defines a three-dimensional surface. In Fig. 9A we plotted the release and uptake + diffusion surfaces. If we project the intersection of the two curves to the cone voltage-glutamate concentration plane (Fig. 9B), the resulting curve is the steady-state input-output relationship of the cone output synapse. Converting glutamate concentration units to horizontal cell voltages with the calibration curve described by Eq. 13 leads to the input-output relationship from cone voltage to horizontal cell voltage (Fig. 9C). If uptake is blocked, the steady-state input-output relationships (Fig. 9, E and F) can be obtained by projecting the intersection of the release and diffusion surfaces to the cone voltage-glutamate concentration plane. In the absence of uptake the input-output curve is highly nonlinear compared with the almost linear relationship if uptake is present (cf. Fig. 9, C and F).


View larger version (56K):
[in this window]
[in a new window]
 
FIG. 9. Input-output relationship of the cone-horizontal cell synapse with or without glutamate uptake. A: glutamate release (black surface) and transport + diffusion (shaded surface) as functions of glutamate concentration and cone voltage. B: steady-state cone voltage-glutamate concentration relationship is derived by projecting the intersection of the two surfaces in A to the glutamate concentration-cone voltage plane. C: steady-state cone voltage-horizontal cell voltage relationship. The glutamate concentration in B is scaled according to the steady-state calibration curve described in Eq. 13. D: glutamate release (black surface) and diffusion (shaded surface) as functions of glutamate concentration and cone voltage. E: steady-state cone voltage-glutamate concentration relationship when uptake is blocked is derived by projecting the intersection of the 2 surfaces in D to the glutamate concentration-cone voltage plane. F: steady-state cone voltage-horizontal cell voltage relationship when uptake is blocked.

    FOOTNOTES

  Address for reprint requests: F. Werblin, 145 Life Sciences Addition, University of California, Berkeley, CA 94720.

  Received 27 February 1998; accepted in final form 1 July 1998.

    REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References

0022-3077/98 $5.00 Copyright ©1998 The American Physiological Society