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Copyright © 2007 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 92, Issue 2, 461-472, 15 January 2007

doi:10.1529/biophysj.106.092296

Channels, Receptors, and Electrical Signaling

Effect of Substrate on the Pre-Steady-State Kinetics of the Na⁺/Glucose Cotransporter

Dominique G. Gagnon, Carole Frindel and Jean-Yves Lapointe^,  

Groupe d’étude des protéines membranaires, Université de Montréal, Montreal, Quebec, Canada

Address reprint requests to J.-Y. Lapointe, Groupe d’étude des protéines membranaires (GÉPROM), Université de Montréal, C.P. 6128, succ. Centre-ville, Montréal, Québec H3C 3J7, Canada. Tel.: 514-343-7046; Fax: 514-343-7146.

The Na⁺/glucose cotransporter SGLT1 is a member of the SLC5 family and has been the archetype of this class of Na⁺-coupled substrate transporters. Soon after its cloning 1, expression in Xenopus oocytes enabled the measurement of pre-steady-state currents, i.e., transient currents observed in the absence of substrate, which were suggestive of gating currents observed in voltage-dependent channels. As these currents were Na⁺ dependent and were absent in the presence of the specific inhibitor phlorizin (Pz) or in the presence of glucose, they were considered to represent charge displacements occurring during the voltage-dependent reorientation of the Na⁺-binding site and upon Na⁺ binding 2.

Pre-steady-state currents have been extremely useful for devising a credible transport mechanism, with quantitative estimation of the rate constants linking the different conformational states. The original model 2 proposed in 1992 has been challenged both theoretically and experimentally (3,4,5,6,7,8; for review see Wright and Turk 9), and new steps have been proposed. Recently Loo et al., using fluorescently labeled mutants 10, have reported extremely slow conformational changes (time constants on the order of 100ms) which have yet to be quantitatively explained by any proposed kinetic model. In particular, this observation is incompatible with a rate-limiting step of 50s⁻¹, which was proposed for the translocation of the fully loaded transporter in the human isoform of SGLT1 (hSGLT1) 2,11.

One characteristic observed for nearly all cotransporters studied (Na⁺/glucose cotransporters SGLT1 and SGLT2, Na⁺/myo-inositol cotransporters SMIT1 and SMIT2, Na⁺/monocarboxylate cotransporter SMCT1, Na⁺/Pi cotransporter NaPiII, Na⁺/I⁻ symporter NIS, gamma-aminobutyric acid transporters GAT1 and GAT3, H⁺/hexose cotransporter STP1, and Cl⁻-dependant K⁺/amino acids transporter KAAT1) is that addition of a saturating concentration of substrate leads to the total inhibition of pre-steady-state currents 11,12,13,14,15,16,17,18,19,20,21,22,23,24,25. Surprisingly, with the exception of GAT1, no quantitative explanation has been proposed to explain this phenomenon.

Recently, we identified a disulfide bridge between C255 and C511 in hSGLT1 26. An interesting feature of mutants C255A and C511A, which we have not previously published, is that they express pre-steady-state currents in the presence of a saturating αMG concentration, in contrast to what is observed with wild-type (wt) SGLT1. This phenomenon has prompted us to examine the dose-dependent effects of αMG on the pre-steady-state currents for the two mutants as well as for wt SGLT1 and to propose a quantitative explanation using a kinetic model displaying different rate-limiting steps for the wt SGLT1 and the mutant cotransporters.

Oocytes were surgically removed from Xenopus laevis frogs, dissected, and defolliculated as described previously 27. One day after defolliculation, oocytes were injected with 46 nl of water containing mRNA (0.1μg/μl and 0.25μg/μl for wt SGLT1 and mutants, respectively) to obtain maximal protein expression. Oocytes were maintained in Barth's solution (in mM: 90 NaCl, 3 KCl, 0.82 MgSO₄, 0.41 CaCl₂, 0.33 Ca(NO₃)₂, 5 Hepes, pH 7.6) supplemented with 5% horse serum, 2.5mM Na⁺ pyruvate, 100units/ml penicillin, and 0.1 mg/ml streptomycin for 4–7 days before electrophysiological experimentation.

The constructions prepared for obtaining the mutants C255A and C511A have been described elsewhere 26.

The saline solution normally used in our electrophysiological experiments is composed of (in mM): 90 NaCl, 3 KCl, 0.82 MgCl₂, 0.74 CaCl₂, and 10 Hepes and the pH was adjusted to 7.6 with NaOH. Two-electrode voltage-clamp experiments were performed using an Oocyte Clamp OC-725 (Warner Instruments, Hamden, CT) and a data acquisition system (Digidata 1322A and Clampex 8.2, Axon Instruments, Union City, CA). Current and voltage microelectrodes were filled with 1M KCl and had a resistance of 1–2 MΩ. The bath current electrode was an Ag-AgCl pellet, and the reference electrode was a 1M KCl agar bridge. The oocytes were clamped to a membrane potential (V_m) of −50mV, and three repetitions of V_m steps between +70 and −170mV (by increments of 20mV, 300ms duration, no series resistance compensation used) were applied with an interval of 1.7s between each step. Ninety-five percent of the command voltage step was reached in 3–4ms. Data were obtained with a sampling frequency of 10kHz, without filtering, and the three repetitions were averaged for each experiment.

Pre-steady-state current analysis was performed as described previously 26. Briefly, the transferred charge was obtained at each membrane potential (Q-V curve) by subtracting the integrated baseline-corrected currents in Pz solution (200μM) from similar currents in saline solution (either in the presence or absence of αMG). Thus, the transferred charge calculated corresponds to the total charge in one experimental condition minus the total charge in the presence of Pz. The total charge in the presence of Pz was found to be linear with voltage as expected if it was mainly due to the presence of the oocyte capacitive current. The baseline correction was obtained from the mean current measured between 50 and 80ms after the initiation of a voltage pulse. A simple Boltzmann equation was fitted to the Q-V curve to estimate V_1/2 (the voltage at which half of the charge is transferred), Q_max (the amplitude of the total charge transferred), and z (the valence of the transferred charge) 26. The time constants (τ_slow) were evaluated by fitting a double exponential on the I_transit (I_saline-I_Pz) with the Clampfit 8.2 program (Axon Instruments). Only the slow time constant (τ_slow; 2–10ms), which has the dominant amplitude, was considered.

Experiments were performed on at least six oocytes obtained from a minimum of two different donors. Data are reported as means±SE and are compared using unpaired Student's t-test; statistical significance was set at P<0.05. Errors bars were omitted when smaller than the symbol size.

In contrast to wt SGLT1, the mutants C255A and C511A clearly exhibit pre-steady-state currents in the presence of a saturating α-methyl-glucose (αMG) concentration 26, particularly at depolarizing V_m levels. Figure 1AA and Figure 2AA show the Pz-sensitive currents with different voltage steps for the two mutant proteins using several αMG concentrations (0, 1, 5, and 10mM αMG). As the capacitive currents are eliminated by subtraction of currents measured in the presence of Pz, the transient currents at each voltage step directly represent SGLT1-specific pre-steady-state currents. The integrals of the transient currents measured at different V_m are used to produce transferred charge versus V_m (Q-V) curves. The Q-V curves for the two mutants are shown in Figure 1BB and Figure 2BB. As the cotransporter conformation at very positive V_m levels is predicted to be independent of the presence of extracellular αMG (the binding site being predicted to face inside in all cases 2,4,10), each Q-V curve was shifted vertically to have Q=0 at +50mV under all conditions. This allows direct comparison of the transferred charge at different V_m; it is clear that they decrease as the αMG concentration increases. It is also clear from Figure 1BB and Figure 2BB that the voltage range over which charge can be transferred is reduced in amplitude and displaced toward more positive potentials when the αMG concentration is increased. The measured charge, at saturating αMG concentration, has reached its plateau level at −50mV and remains basically constant as V_m becomes more negative. However, a saturating αMG concentration does not totally abolish the transferred charge. A Boltzmann relation can be fitted to the Q-V curves, which yields a value for the parameter V_1/2, the V_m at which half of the mobile charge is equally balanced between the inward and outward facing positions. For both mutants, an increase in αMG concentration shifts the V_1/2 toward more positive values. For mutant C255A, the measured V_1/2 averaged −35±5mV at 0mM and 5±5mV at 10mM αMG (n=6). For mutant C511A, the corresponding values were −28±2mV at 0mM and 13±3mV at 10mM αMG (n=6).

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Figure 1

Pre-steady-state currents of mutant C255A in the presence of different αMG concentrations. (A) Pre-steady-state current traces at different V_m in the presence of various αMG concentrations (0, 1, 5, and 10mM) for a typical C255A-expressing oocyte. The currents were obtained by subtracting the currents in the presence of 200μM Pz from the currents measured in the various conditions. (B) Q-V curves in different αMG concentrations were compared to those in the absence of substrate. Values were shifted to have the same Q=0 at V_m=+50mV. The curve represents a Boltzmann equation fitted to the points (n=6). (C) Time constants of the pre-steady-state currents in different αMG concentrations were compared to those in the absence of substrate (n=6). The inset represents the double exponential fit (gray line) of the Pz-sensitive currents (black line) shown in panel A at 1mM αMG for the indicated V_m. The dotted line indicates the time at which 95% of the V_m is achieved. Means±SE are shown. Stars indicate statistical significance with respect to the values in 0mM αMG (*, P≤0.05; **, P≤0.01;***, P≤0.001).

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Figure 2

Pre-steady-state currents of mutant C511A in the presence of different αMG concentrations. (A) Pre-steady-state current traces at different V_m in the presence of various αMG concentrations (0, 1, 5, and 10mM) for a typical C511A-expressing oocyte. The currents were obtained by subtracting the currents in the presence of 200μM Pz from the currents measured in the various conditions. (B) Q-V curves in different αMG concentrations were compared to those in the absence of substrate. Values were shifted to have the same Q=0 at V_m=+50mV. The curve represents a Boltzmann equation fitted to the points (n=6). (C) Time constants of the pre-steady-state currents in different αMG concentrations were compared to those in the absence of substrate. (n=6). Means±SE are shown. Stars indicate statistical significance (see Fig. 1 legend).

The progressive addition of extracellular αMG also affected the τ_slow for pre-steady-state currents as depicted in Figure 1CC and Figure 2CC. They were obtained by fitting double exponentials to the Pz-sensitive currents. As reported previously 26, in the absence of αMG, τ_slow for the mutant proteins reached a plateau of 4–5ms at hyperpolarized V_m, which is about half of the value measured for the wt SGLT1. An increase in αMG concentration clearly produced an increase of τ_slow at positive V_m. For V_m more negative than −50mV, addition of αMG accelerated the transient currents, as shown in Figure 2C for 1mM αMG. The currents in the presence of higher concentrations can no longer be fitted accurately at these voltages (see Figure 2C for 10mM αMG and Figure 1C for 5 and 10mM αMG). Consequently, at 1mM αMG, the τ_slow versus V_m (τ_slow-V) curve has a bell shape centered around −50mV for both mutants. At 10mM αMG, τ_slow starts at very low values for negative V_m and reaches a value of 6–7ms for both mutants at depolarizing potentials.

The stability of the preparation as a function of time was tested in each experiment by comparing pre-steady-state currents in the absence of αMG measured before and after having presented the different αMG concentrations. In all cases, the Q-V and τ_slow-V curves were found identical. In addition, the effects of αMG on the pre-steady-state currents were found to be independent on the order of the αMG concentrations applied (increasing or decreasing concentrations).

Although the inhibitory effect of αMG on wt SGLT1 pre-steady-state currents has long been known 11,25, to our knowledge it has never been studied quantitatively in a dose-dependent manner nor has it been explained with the use of a kinetic model. Given our findings with the two SGLT1 mutant proteins, we sought to characterize this effect in detail on wt SGLT1 and to compare it with that observed for the mutants. Figure 3A shows Pz-sensitive pre-steady-state currents recorded from wt SGLT1 in the absence or in the presence of different αMG concentrations (0.5mM, 1mM, and 5mM). In agreement with previous reports, addition of extracellular αMG leads to a progressive decrease in the pre-steady-state currents and to the appearance of steady-state inward Na⁺/glucose flux, which have been described in detail 11,25. The Q-V curves obtained with different αMG concentrations is illustrated in Figure 3B. It is obvious that a saturating concentration of αMG (5mM) completely abolished charge transfer (n=9), at least within the time resolution provided by the two-electrode voltage-clamp technique. In the presence of 5mM αMG, the amplitude of the transferred charge that can be detected is approximately equal to that measured from a noninjected oocyte (<1 nC). The time constants of these pre-steady-state currents are shown in Figure 3C. Increased αMG concentrations produce a clear acceleration of the transient currents at negative V_m, whereas the value of the time constant remains the same at positive V_m. In the presence of 5mM αMG, the transient currents are difficult to fit to a double exponential equation because τ_slow shows only modest voltage dependence and reaches a value of ∼2.5ms (at +70mV) with very small amplitude (n=7). Both parameters are close to the limits inherent to the two-electrode voltage-clamp technique.

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Figure 3

Pre-steady-state currents of wt SGLT1 in the presence of different αMG concentrations. (A) Pre-steady-state current traces for different V_m in the presence of various αMG concentrations (0, 0.5, 1, and 5mM) containing solutions for a typical wt SGLT1-expressing oocyte. The currents were obtained by subtracting the currents in the presence of 200μM Pz to the ones in the various conditions. (B) Q-V curves in different αMG concentrations as compared to those in the absence of substrate. Values were shifted to have the same Q=0 at V_m=+50mV. The curve represents a Boltzmann relation fitted to the points (n=9). (C) Time constants of the pre-steady-state currents in different αMG concentrations as compared to those in the absence of substrate. The time constants at 5mM αMG were plotted in gray because of the small amplitude of the exponential giving uncertainty about the value of this time constant (n=7). Means±SE are shown. Stars indicate the statistical significance (see Fig. 1 legend).

Fig. 4 summarizes the effects of αMG on the V_1/2 and on the normalized amplitude of the total transferred charge for wt SGLT1 versus the two mutants. In Figure 4A, the shift in V_1/2 produced by the addition of αMG to the wt SGLT1 is compared with the shifts mentioned above for the two mutants. For wt SGLT1, V_1/2 goes rapidly from −60±5mV at 0mM to 12±12mV at 1mM αMG (n=9) and, at αMG concentrations higher than 1mM, the amplitude of the Q-V curve is reduced to such an extent that the fitting of a Boltzmann curve is not reliable. In all cases, the V_1/2 is progressively shifted toward positive V_m levels as the external [αMG] increases, but this shift is less marked for the mutants than for wt SGLT1.

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Figure 4

Effect of αMG on V_1/2 and estimation of with the transferred charge. (A) V_1/2 of C255A (open circles), C511A (open triangles), and wt SGLT1 (solid squares) in the presence or absence of different αMG concentrations. The lines represent the extracted V_1/2 values from the theoretical Q-V curves obtained with the kinetic model's current simulations (solid line: wt SGLT1, dotted line: mutants). The phenomenological parameter V_1/2 is obtained by a simple Boltzmann relation fitted to the experimental and theoretical Q-V curves (see Figure 1BBB and Figure 2BBB and Figure 3BBB). (B) Normalized αMG-dependent transferred charge in the presence of different αMG concentrations of wt SGLT1 (solid square), C255A (open circle), and C511A (open triangle) at −170mV. The line represents a simple Michaelis-Menten equation fitted to the points, and the corresponding K_m value from the fit is noted. Means±SE are shown.

To quantitatively compare the sensitivity of the pre-steady-state currents to αMG, the decreases in transferred charge caused by αMG were normalized to the total transferred charge in the absence of substrate (i.e., ). A simple Michaelis-Menten equation was fitted to taken at −170mV as a function of αMG concentration after setting Q=0 for V_m=+50mV (as done in Figure 1BBB and Figure 2BBB and Figure 3BBB). It is clear that for the wt SGLT1, a high αMG concentration inhibits 100% of the transferred charge, whereas only partial inhibition (∼65–75% inhibition) was observed for the mutant proteins. It was found that the αMG-sensitive charge is consistent with αMG affinity constants of 0.48±0.05mM for wt SGLT1 (see Figure 4B), 5±2mM for mutant C255A, and 2±1mM for mutant C511A whereas their constants, using αMG-sensitive cotransport current (steady-state values, I_ss(αMG)), were 0.97±0.1mM for wt SGLT1 26,27, 1.6±0.2mM (C255A), and 1.6±0.2mM (C511A) at −170mV 26.

A scheme of the simple five-state kinetic model used is presented in Fig. 5. The substrate-binding and -debinding steps (k₄₅ and k₅₄) are voltage independent 2,28 as are the lumped reactions k₄₁ and k₅₁, which represent the conformational changes of the Na⁺-loaded transporter (involved in the leak current) and the Na⁺- and αMG-loaded transporter, respectively, with their associated intracellular release steps. It was found that the extracellular Na⁺-binding reaction could be assumed to be a fast reaction at equilibrium without losing any fitting performance. The voltage-dependent reactions are expressed as follows (for i=1, 2, 3; j=i+1):

(1)

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Figure 5

Kinetic model of the SGLT1 for the estimation of pre-steady-state currents. The voltage-independent substrate-binding/debinding events are included (k₄₅, k₅₄) in contrast to the models previously described in Chen et al. 4 and in Gagnon et al. 26. See Table 1 for rate constant values and Results and Discussion for further details.

The affinity for intracellular Na⁺ was previously estimated for rabbit SGLT1 in giant, excised, inside-out patches and was found to vary from 44 to 70mM 28,29. In agreement with these estimates, we recently found that intracellular Na⁺ has to be increased by blocking the Na⁺/K⁺-ATPase overnight to generate a measurable outward Na⁺/glucose current upon intracellular glucose injection 30. This is consistent with an intracellular much higher than the physiological intracellular Na⁺ concentration. On the other hand, the estimation of for the intracellular site is ∼35mM 28,29. Consequently, under physiological conditions, the inverse mode of transport is highly unlikely, which is reflected by very low values of k₁₄ and k₁₅ (see Table 1). Thus, we assumed that the probability of finding the intracellular site loaded with Na⁺ and αMG was negligible, and we reduced the potential seven-state kinetic model into the five-state kinetic model shown in Fig. 5.

The numerical simulations were performed using MATLAB 6.5.0 software (MathWorks, Natick, MA). Transferred charges were calculated as the integral of the pre-steady-state currents as done during the analysis of the experimental data and were also fitted with a simple Boltzmann curve to deduce the V_1/2, Q_max, and z parameters. As the analytical expression for the time constant in the presence of substrate cannot be obtained in a five-state model, the numerical values of the time constant were obtained by taking the reciprocal of the eigenvalues of the following matrix, as previously reported 10:

Moreover, the model predicts the relaxation of pre-steady-state currents toward steady-state currents. The current (I) versus V_m curves are sigmoid, as observed for the experimental current versus membrane potential (I-V) curves in the absence and in the presence of αMG (not shown). The rate constants of the model were adjusted by trial and error to obtain a satisfactory fit to the measured Q-V curves, the V_1/2, and the τ_slows of the pre-steady-state currents. The steady-state parameters (I-V curves, , or ) were not considered as criteria for the adjustment of the model parameters but were found afterwards to be in accordance with the experimental values.

Table 1 gives the rate constants used by Chen et al. 4 and by Loo et al. 11 as well as the rate constants used by this study to simulate the time constants of the pre-steady-state currents. As shown in Figure 6A, our new set of rate constants can reproduce, in a generally satisfying manner, the currents, the Q-V curves, and the τ_slow-V curves for wt SGLT1 exposed to different αMG concentrations. In the presence of 90mM Na⁺, a k₂₁₀/k₁₂₀ ratio of ∼0.5 is required for the plateau effect seen on the τ_slow-V curve at hyperpolarizing V_m. k₂₃ is a crucial rate constant because it is voltage independent and becomes rate limiting for V_m below −70mV (at 90mM Na⁺). Indeed, the value of 1/k₂₃ closely corresponds to the plateau value reached by τ_slow at very negative V_m. The ratio k₂₃/k₃₂ is also responsible for the voltage dependence of τ_slow observed at depolarizing V_m. At 0mV, K₃₄ (the ratio k₄₃/k₃₄) is 0.1M² for wt SGLT1 and 0.07M² for the mutants and is largely responsible for the Na⁺ affinity measured at low αMG concentration. This ratio also has a large influence on the position of the V_1/2 of the Q-V curve. The K₃₄ and the k₂₃ values were modified for simulation of transferred charges through the mutant proteins to account for the faster τ_slow at negative V_m and the new V_1/2 of −30mV (instead of −50mV), which was observed for both mutants 26. These two simple modifications yielded the fit for the Q-V curve of Figure 6B (left panel), shown for mutant C511A, and the τ_slow-V curve shown in Figure 6B (right panel) at 5mM αMG.

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Figure 6

Predictions of the kinetic model. (A) Predictions of the kinetic model superimposed on the experimental data for wt SGLT1. The left panel shows simulated currents (gray line) superimposed on the experimental current (black line) at 1mM αMG for the indicated V_m; the vertical dotted line indicates the beginning of the voltage step. The middle panel illustrates the Q-V curves, and the right panel shows τ_slow as a function of V_m at different αMG concentrations. (B) Predictions of the kinetic model superimposed on the experimental data for mutants. The left panel shows the experimental current (black line) of mutant C255A superimposed on the simulated currents at 1mM αMG (gray line) for the indicated V_m; the vertical dotted line indicates the beginning of the voltage step. The middle panel illustrates the Q-V curves for mutant C511A, and the right panel shows τ_slow as a function of V_m for both mutants at 5mM αMG. The currents from wt SGLT1 and C255A come from the experiment presented in Figure 1AA and Figure 3AA, respectively. The experimental data points were represented in gray for comparison. For clarity, only data points from mutant C511A are presented for the Q-V curve. The Q-V curve was shifted vertically such that Q=0 at +50mV. As the model predicts significant amplitudes for two exponential components, the two time constants (a fast one, solid line, and a slower one, dashed line) are presented.

To interpret the effects of αMG on the pre-steady-state currents, appropriate values for the parameters k₄₅, k₅₄, and k₅₁ have to be determined. Our strategy was to start by establishing parameters that could explain the behavior of the transferred charges of wt SGLT1 in the presence of different αMG concentrations. Our first criterion was that the transferred charge had to disappear in the presence of a saturating αMG concentration. The k_ij of the four-state model established in the absence of αMG were maintained constant, and we investigated the effects of the three new k_ij on the simulated Q-V curve. We started with the parameters proposed by Loo et al. 11 (see Table 1) but needed to increase the value of k₅₁ by up to 40-fold over the original value (2000 vs. 50s⁻¹) to reproduce the charge disappearance observed at high αMG concentration. It was also clear that the ratio k₄₅/k₅₄ influenced the V_1/2 of the Q-V curve: an increase in this ratio shifts the V_1/2 toward more positive V_m. However, the absolute values of k₄₅ and k₅₄ (and not only their ratio) were also important in the global behavior of the Q-V curve as a function of αMG concentration. With respect to the values proposed by Loo et al. 11, the values of k₄₅ and k₅₄ had to be increased by factors of 30 and 50, respectively.

For the mutants, we first established the values of the parameters k₂₁₀, k₂₃, and K₃₄₀ to account for the faster time constants and the positive shift in V_1/2 in the absence of αMG. Changes in k₂₁₀ and k₂₃ were necessary along with more modest changes in the remaining parameters describing the αMG-independent steps of the kinetic model. The new values of k₄₅, k₅₄, and k₅₁ found for the wt transporter could not reproduce the observed Q-V and τ_slow-V curves of the mutants. We found that the reactions describing αMG binding and debinding had to be reduced by an order of magnitude and the reorientation of the fully loaded carrier (k₅₁) had to be massively decreased from 2000 to 80s⁻¹. The best parameter set found is presented in Table 1 for wt SGLT1 and the mutants.

The simulated wt SGLT1 Q-V curves are shown in Figure 6A (middle panel), superimposed on the experimental data points (in gray). Although, the shapes of the theoretical and experimental Q-V curves differ slightly, the general decrease due to external αMG concentration is well represented. Three parameters were used to measure the accuracy of the model predictions: the V_1/2 of the Q-V curves, the normalized transferred charge curves in the presence of different αMG concentrations , as well as the τ_slow-V curve. Figure 4A illustrates the phenomenological parameter V_1/2 as a function of αMG concentration extracted from the fits of a simple Boltzmann relation to our theoretical Q-V curves (solid line). Although the theoretical Q-V curve differs slightly from a simple Boltzmann relation, the model correctly represents the voltage shift produced by αMG addition. The model also correctly predicts the total inhibition of the transferred charge by a saturating αMG concentration. We estimated an apparent affinity for αMG , using the remaining charge in the presence of αMG , to compare it with that obtained experimentally. The parameters given in Table 1 yield a value of 0.40±0.07mM at −170mV, which is not significantly different from the experimental value reported above. Finally, Figure 6A (right panel) shows that the τ_slow-V curve values are close to the experimental values as the model reproduces very well the acceleration of the transient currents at hyperpolarizing V_m and shows the bell-shaped curve peak shifting toward more positive V_m as the αMG concentration increases.

The simulated Q-V curves for the mutant SGLT1s are shown in Figure 6B (middle panel), superimposed on the experimental data points for mutant C511A alone (in gray) because mutant C255A produced very similar values. The charge plateau value reached at hyperpolarizing V_m, at 5 and 10mM αMG, is reproduced very well by the modeled Q-V curve. The dotted line on Figure 4A illustrates V_1/2 as a function of αMG concentration for the mutants. It is clear that the estimated V_1/2 for the modeled Q-V curves of the mutants closely reproduced the characteristics of both mutants. The model accounts for the partial inhibition of the transferred charge at high αMG concentrations. In addition, the was estimated with the remaining charge in the presence of αMG and provided the value of 4±2mM at −170mV, which is close to the experimental values reported above for C255A and, to a lesser extent, for C511A (5±2mM and 2±1mM, respectively). Finally, the theoretical τ_slow values were superimposed on the experimental values for both mutants at 5mM αMG in Figure 6B (right panel). The model predicts two exponentials with significant amplitudes with time constants in the range of 2–6ms in the presence of αMG. The first one is almost identical with that observed in the absence of αMG. The second one is slower at depolarizing V_m where it reaches a plateau value of ∼5.5ms. Experimentally, a single exponential with a time constant in the millisecond range could be detected. Given the limited speed of the voltage pulse, the typical noise level found in our current recording, and given the fact that the two predicted time constants are in the same order of magnitude, it is conceivable that our experimental time constant would correspond to some intermediate value between the predicted ones. Thus it is concluded that the model reproduces fairly well the experimental time constants measured in the presence of αMG.

The identification of a disulfide bridge between C255 and C511 constitutes an important step in our understanding of how the 14 transmembrane segments are located with respect to each other and in the eventual identification of the physical structure that serves as the “voltage sensor” in SGLT1 26. The two mutants C255A and C511A were found to display further interesting features which confirmed the importance of this region of the cotransporter. In this study we report that, in contrast with wt SGLT1, these two mutants exhibit pre-steady-state currents in the presence of a saturating αMG concentration. By analyzing the dose-dependent effects of αMG on the pre-steady-state currents of these mutants as well as for wt SGLT1, we sought to identify a satisfying kinetic explanation for both the partial diminution of mutant pre-steady-state currents by αMG and for the complete disappearance of the wt SGLT1 transient currents.

The pre-steady-state currents in the absence of αMG have been studied using cut open oocytes exposed to various Na⁺ concentrations, and a simple four-state kinetic model 4 was found to be consistent with the amplitudes and the time constants (τ_fast (<1ms) and τ_slow (1–10ms)) of the experimentally determined pre-steady-state currents as a function of the external Na⁺ concentration. The presence of these two time constants was more recently confirmed for rabbit SGLT1 7,8 and for hSGLT1 10. In this last study, fluorescently labeled cotransporters were also used and a slower time constant of ∼100ms was reported in addition to τ_fast and τ_slow. A seven-state model was suggested for the translocation of the free transporter and the binding of two external Na⁺ ions, but the authors could not find a parameter set that would be in quantitative agreement with their own observations. Considering the time resolution provided by the two-electrode voltage-clamp technique, we decided to use the four-state model proposed by Chen et al. 4 to explain the effects of disrupting the disulfide bridge C255-C511 on the V_1/2 of the Q-V and τ_slow-V curves in the absence of αMG 26. In the original model, it was assumed that a single Na⁺ ion was involved in the pre-steady-state currents. To incorporate αMG binding, and given that the cotransport stoichiometry is 2 Na⁺:1 glucose 31, we simply replaced the original rate constant for Na⁺ binding (k₃₄) by k₃₄/[Na⁺] to account for both Na⁺ ions and made it a second order rate constant in M⁻²s⁻¹. As the extracellular Na⁺ concentration is constant in this study, further studies will have to test whether the model used is consistent with the effects of changes in external Na⁺ concentration.

In the absence of αMG and at −50mV, the set of rate constants proposed in Table 1 leads to occupancy probabilities (C_i) of 5%, 22%, 43%, and 30% (from i=1 to 4), indicating that 73% of the Na⁺-binding sites are exposed outside either in a free or Na⁺-bound state 4,26. Obviously this situation is highly voltage dependent and, at +70mV, C₁ and C₂ now represent 52% and 40% of the cotransporter conformations, respectively. If, from state C₄ to state C₁, the total number of unitary charges that can move across the entire membrane electrical field is 2 (|z₁+z₂+z₃|=2), the occupancy probabilities at +70mV indicate that all but 11% of it has already moved into the inward facing configuration. Figure 7A presents the occupancy probabilities in the absence of αMG for an extreme voltage step from +70 to −150mV. Upon hyperpolarization, C₁ rapidly transforms into C₂ and the free binding sites exposed to the extracellular solution (C₃) become Na⁺-bound immediately. The step C₁→C₂ is considered to be mainly responsible for the fast component to the transient current. In contrast, the following slow transformation of C₂ into C₃ (which is in equilibrium with C₄(2Na⁺)) is clearly responsible for the slow component of the observed transient currents. Figure 7BC, presents the changes in occupancy probability for a similar voltage step but in the presence of αMG at 1 or 5mM. At +70mV, the starting probabilities are independent of the presence of αMG in the extracellular solution as are the fast events occurring in the first millisecond after hyperpolarization. At −150mV, the slowest rate constant in the reactions leading to the inward Na⁺/glucose current is clearly k₂₃. This is why C₂ accumulates transiently (75%) then relaxes to a value consistent with the steady-state cotransport rate allowed by the external αMG concentration. This is shown in Figure 7D where the probability of finding C₂ is plotted as a function of time for different αMG concentrations.

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Figure 7

Occupancy probability (C_i) as a function of time as calculated by the five-state kinetic model for wt SGLT1. (A) Time course of wt SGLT1 occupancy probabilities (90mM Na⁺) for a V_m pulse from +70mV to −150mV in the absence of αMG and in the presence of 1mM αMG (B) and 5mM αMG (C). (D) Time course of wt SGLT1 C₂ occupancy probability in the absence of αMG (solid line, 90mM Na⁺) or in the presence of 1mM (dashed line) or 5mM (small dashed line) αMG for a V_m pulse from +70mV to −150mV.

For the mutants, the rate constants of Table 1 lead to occupancy probabilities of 2%, 9%, 45%, and 44% (from i=1 to 4) at −50mV in the absence of αMG, which is quite similar to the C_i probabilities found for wt SGLT1. At +70mV, the distribution is slightly different from the wt SGLT1 as C₂ now dominates with a probability of 42% with respect to C₁ (34%), whereas the outward facing, free binding site (C₃) presents a significant probability of 23%. Figure 8A presents the changes in C_i as a function of time for an extreme voltage pulse from +70mV to −150mV. Once again, in the absence of αMG, C₂ is transiently accumulated before relaxing to <5% as the Na⁺-bound form (C₄(2Na⁺)) progressively rises to more than 90%. Figure 8BC, depicts the occupancy probabilities in the presence of 1.5 and 5mM αMG. Under these circumstances, and in marked contrast to wt SGLT1, C₂ continues to relax to a low value and it is C₅(2Na⁺S), the fully loaded transporter, that progressively increases and attains up to 48% (this value increases to 58% at 10mM αMG). As illustrated in Figure 8D, contrary to what was seen for wt SGLT1, the C₂ state increases (55%) and then relaxes to much lower steady-state values of 5% and 21% in the absence or presence of αMG, respectively. This simply reflects the fact that, for the mutant proteins, the slowest rate constant in the steps mediating Na⁺/glucose cotransport at −150mV is k₅₁. As the steps involved in generating the slow component of pre-steady-state currents are the transition between C₂ and C₄(2Na⁺), Figure 7DD and Figure 8DD illustrate the reason transient currents disappear in the presence of αMG for the wt transporter but not for the mutants.

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Figure 8

Occupancy probability (C_i) as a function of time as calculated by the five-state kinetic model for the mutants. (A) Time course of mutant SGLT1 occupancy probabilities (90mM Na⁺) for a V_m pulse from +70mV to −150mV in the absence of αMG, in the presence of 1.5mM αMG (B), and in the presence of 5mM αMG (C). (D) Time course of mutant C₂ occupancy probability in the absence of αMG (solid line, 90mM Na⁺) or in the presence of 1.5mM (dashed black line) or 5mM (small dashed black line) or 10mM (solid gray line) αMG for a V_m pulse from +70mV to −150mV.

We presented two distinct methods of estimating the apparent affinity for the substrate: one can use the steady-state currents (I_ss(αMG)) and obtain or the substrate-dependent charge disappearance to obtain . For the wt SGLT1, both experimental (0.97 and 0.48mM) and theoretical (0.36 and 0.40mM) approaches show that the and the are close in value. However, the two experimental K_m estimates for the mutants are significantly different, particularly for mutant C511A. It is important to specify that these two K_m are apparent K_m and depend not only on the rate constants k₄₅ and k₅₄ but also on the other rate constants. It seems that the rate-limiting step position is crucial for this discrepancy and that the two methods of obtaining an apparent affinity constant for αMG should be considered with caution. The accordance between their values for wt SGLT1 may simply be coincidental.

In a previous study, we have shown that the breakage of a disulfide bridge between C255 and C511 using dithiothreitol or by disruption through specific alanine mutations led to a displacement of the equilibrium position of the “voltage sensor” and to an acceleration of time constant of pre-steady-state current in the absence of αMG 26. In this study, we established that the disulfide bridge C255-C511 (in hSGLT1) also plays a major role in facilitating the conformational change of the fully loaded cotransporter. In addition, a minor role was also detected in the αMG-binding and -debinding reactions. In the absence of a tridimensional structure, it is impossible to know the exact position of this disulfide bridge in relation to the Na⁺ or αMG-binding sites, but it is certainly important for the mechanical structure involved in those processes.

In summary, this study has provided a quantitative explanation for the observation that transient currents disappear in the presence of αMG for the wt SGLT1 but not for the mutant transporters. In wt SGLT1 and in the presence of substrate, the rate-limiting step is from state 2 to state 3. The transferred charges are not observed in this case because, upon hyperpolarization from a very positive to a very negative V_m, the large steady-state current requires a high C₂ probability. Under these circumstances, the steady-state transporter distribution is predicted to simply move from state 1 to state 2, which should generate only a very fast transient current (τ ≈ 0.5ms). In contrast, for the mutants C255A and C511A in the presence of αMG, the rate-limiting step is from state 5 to state 1. The transporter after having reached a high C₂ probability will relax to a much lower level to reach the required C₅ probability to account for the steady-state current. As the transporter moves from state 2 to states 3–5 through electrogenic steps, a slow transient current is generated. The behavior of the mutants underscores the role played by the rate-limiting step in the possibility of observing pre-steady-state currents. It also reveals the importance of the disulfide bridge C255-C511 in facilitating the translocation of the fully loaded transporter from the outward facing to the inward facing configuration.