Division of Neurobiology, Department of Molecular and Cell Biology, University of California, Berkeley, California 94720
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ABSTRACT |
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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.
An earlier study (Gaal et al. 1998 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.
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
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
) 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.
; 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
).
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
.
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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.
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
(1)
), and I is the relative (ambient minus background) light intensity (photons/µm2 s)
where S is the volume of diffusion-limited synaptic region
(2)
Dark current
The dark current (Fig. 2A) depends on I and Vm independently according to the following
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(3) |
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by the sum of two exponentials
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
(4)
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
)
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(6) |
with a sum of two exponentials that can be interpreted as a single energy barrier placed at
= 0.91 fractional distance from the intracellular boundary of the membrane (Hille 1992
)
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
) again allows us to take the product of Eqs. 6 and 7 for the overall expression
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
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(9) |
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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, 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
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(10) |
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)
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(11) |
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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
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(12) |
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
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(13) |
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.
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RESULTS |
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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.
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.
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
).
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, 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.
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.
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.
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
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 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).
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.
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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
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.
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).
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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.
; 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
).
; Barnes et al. 1993
)
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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
REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References
0022-3077/98 $5.00 Copyright ©1998 The American Physiological Society