How Drugs Interact with Transporters: SGLT1 as a Model

Abstract

Drugs are transported by cotransporters with widely different turnover rates. We have examined the underlying mechanism using, as a model system, glucose and indican (indoxyl-β-d-glucopyranoside) transport by human Na⁺/glucose cotransporter (hSGLT1). Indican is transported by hSGLT1 at 10% of the rate for glucose but with a fivefold higher apparent affinity. We expressed wild-type hSGLT1 and mutant G507C in Xenopus oocytes and used electrical and optical methods to measure the kinetics of glucose (using nonmetabolized glucose analogue α-methyl-d-glucopyranoside, αMDG) and indican transport, alone and together. Indican behaved as a competitive inhibitor of αMDG transport. To examine protein conformations, we recorded SGLT1 capacitive currents (charge movements) and fluorescence changes in response to step jumps in membrane voltage, in the presence and absence of indican and/or αMDG. In the absence of sugar, voltage jumps elicited capacitive SGLT currents that decayed to steady state with time constants (τ) of 3–20 ms. These transient currents were abolished in saturating αMDG but only slightly reduced (10%) in saturating indican. SGLT1 G507C rhodamine fluorescence intensity increased with depolarizing and decreased with hyperpolarizing voltages. Maximal fluorescence increased ∼150% in saturating indican but decreased ∼50% in saturating αMDG. Modeling indicated that the rate-limiting step for indican transport is sugar translocation, whereas for αMDG it is dissociation of Na⁺ from the internal binding sites. The inhibitory effects of indican on αMDG transport are due to its higher affinity and a 100-fold lower translocation rate. Our results indicate that competition between substrates and drugs should be taken into consideration when targeting transporters as drug delivery systems.

Appendix

This focuses on the formulation and simulation of the kinetic model for SGLT1 in the presence of indican and αMDG, alone and together.

Kinetic Model

The model is based on extensive experimental data (Parent et al. 1992; Loo et al. 1993, 1998, 2005, 2006; Hirayama et al. 1997, 2007; Meinild et al. 2002; Eskandari et al. 2005; Mackenzie et al. 1998, Zampighi et al. 1995). The transporter has eight kinetic states: ligand-free (empty), Na⁺-bound, Na⁺- and sugar-bound, and intermediates (C_a, C_b) between the inward- and outward-facing empty conformations (Fig. 8). The empty protein has a valence of −2, and the voltage-sensitive steps are the binding of external Na⁺ (C1 to C2Na₂) and translocation of the empty carrier between the external and internal sides of the membrane (C1–C6).

Transitions between states C_i and C_j are represented by first-order (or pseudo-first-order in case of Na⁺ and sugar binding) rate constants k _ij: C_i → C_j. Eyring rate theory is used to describe the dependence of rate constants on membrane potential. k _ij = k ^o_ij exp(−ε_ij F/RT), where k ^o_ij is a voltage-independent rate, ε_ij is the equivalent charge movement (up to the transition state between C_i → C_j) and F, R and T have their usual physicochemical meanings (Parent et al. 1992). Na⁺ and sugar binding on external and internal membrane surfaces is represented by pseudo-rate constants k ₁₂ = k ^o ₁₂ [Na] ² _o exp(−ε₁₂ FV/RT), k ₂₃ = k ^o ₂₃ [αMDG]_o, k ₂₇ = k ^o ₂₇ [indican] _o , k ₆₅ = k ^o ₆₅ [Na] ² _i and k ₅₄ = k ^o ₅₄ [αMDG] _i , k ₈₅ = k ^o₈₅ [indican] _i . Na⁺ ions bind to two identical binding sites in one step before glucose (C1 + 2Na⁺ ⇄ C2Na₂), and this is considered to be valid at high [Na⁺] _o with high cooperativity between Na⁺ binding sites (Falk et al. 1998).

Pre-steady-state currents (hSGLT1 capacitive currents) are associated with the reorientation of the empty carrier between outward- and inward-facing conformations (C1 ⇄ C_a ⇄ C_b ⇄ C6) and external Na⁺ binding/dissociation (C1 ⇄ C2Na₂). There are four predicted components of pre-steady-state currents (region I, Figs. 1 and 8): C₂Na₂ ⇄ C₁, C₁ ⇄ C_a, C_a ⇄ C_b, and C_b ⇄ C₆. The current (I _ij) associated transition C_i ⇄ C_j is given by I _ij = e(ε_ij + ε_ji)(k _ijC_i − k _jiC_j), where e is elementary charge (Loo et al. 2005; Parent et al. 1992).

Total current (I) associated with SGLT1 is

$$ \begin{aligned}{} & I{\text{ = }}N_{{\text{T}}} {\text{ (}}I_{{{\text{12}}}} + I_{{{\text{1a}}}} + I_{{{\text{ab}}}} + I_{{{\text{b6}}}} {\text{)}} \\ & {\text{ = }}N_{{\text{T}}} {\text{e[(}}\varepsilon _{{{\text{12}}}} + \varepsilon _{{{\text{21}}}} {\text{)(}}k_{{{\text{12}}}} {\text{C}}_{{\text{1}}} {-k}_{{{\text{21}}}} {\text{C}}_{{\text{2}}} {\text{Na}}_{{\text{2}}} ) + (\varepsilon _{{{\text{1a}}}} + \varepsilon _{{{\text{a1}}}} {\text{)(}}k_{{{\text{1a}}}} {\text{C}}_{{\text{1}}} {-k}_{{{\text{a1}}}} {\text{C}}_{{\text{a}}} ) + (\varepsilon _{{{\text{ab}}}} + \varepsilon _{{{\text{ba}}}} {\text{)(}}k_{{{\text{ab}}}} {\text{C}}_{{\text{a}}} {-k}_{{{\text{ba}}}} {\text{C}}_{{\text{b}}} ) + \\ & {\text{(}}\varepsilon _{{{\text{b6}}}} + \varepsilon _{{{\text{6b}}}} {\text{)(}}k_{{{\text{b6}}}} {\text{C}}_{{\text{b}}} {-k}_{{{\text{6b}}}} {\text{C}}_{{{\text{6}}}} {\text{)]}} \\ & \\ \end{aligned} $$

(4)

where N _T is the total number of transporters in the oocyte plasma membrane.

Changes of fluorescence intensity (ΔF) associated with SGLT1 with step jumps in membrane voltage are assumed to be due to changes in occupancy probabilities:

$$ \Delta F \approx {\text{ }}qy_{{\text{1}}} \Delta {\text{C}}_{{\text{1}}} + qy_{{\text{2}}} \Delta {\text{C}}_{{\text{2}}} + qy_{a} \Delta {\text{C}}_{{\text{a}}} + qy_{b} \Delta {\text{C}}_{{\text{b}}} + qy_{3} \Delta {\text{C}}_{{\text{3}}} + qy_{4} \Delta {\text{C}}_{{\text{4}}} + qy_{5} \Delta {\text{C}}_{{\text{5}}} + qy_{6} \Delta {\text{C}}_{{\text{6}}} $$

(5)

where qy _j is the apparent quantum yield of the fluorophore (TMR6M) when SGLT1 is in conformation C_j (Loo et al. 2006).

Simulation of SGLT1

In the presence of two different substrates the model has 10 states (Fig. 8), with the differential equation (equation 6):

$$ d/dt\,{\left[ {\begin{array}{*{20}c} {{C1}} \\ {{C2}} \\ {{C3}} \\ {{C4}} \\ {{C5}} \\ {{C6}} \\ {{C7}} \\ {{C8}} \\ {{Ca}} \\ {{Cb}} \\ \end{array} } \right]}\, = \,{\left[ {\begin{array}{*{20}c} {{ - (k1a + k12)}} & {{k21}} & {0} & {0} & {0} & {0} & {0} & {0} & {{ka1}} & {0} \\ {{k12}} & {{ - (k21 + k23 + k25 + k27)}} & {{k32}} & {0} & {{k52}} & {0} & {{k72}} & {0} & {0} & {0} \\ {0} & {{k23}} & {{ - (k32 + k34)}} & {{k43}} & {0} & {0} & {0} & {0} & {0} & {0} \\ {0} & {0} & {{k34}} & {{ - (k43 + k45)}} & {{k54}} & {0} & {0} & {0} & {0} & {0} \\ {0} & {{k25}} & {0} & {{k45}} & {{ - (k52 + k54 + k56 + k58)}} & {{k65}} & {0} & {{k85}} & {0} & {0} \\ {0} & {0} & {0} & {0} & {{k56}} & {{ - (k65 + k6b)}} & {0} & {0} & {0} & {{kb6}} \\ {0} & {{k27}} & {0} & {0} & {0} & {0} & {{ - (k72 + k78)}} & {{k87}} & {0} & {0} \\ {0} & {0} & {0} & {0} & {{k58}} & {0} & {{k78}} & {{ - (k85 + k87)}} & {0} & {0} \\ {{k1a}} & {0} & {0} & {0} & {0} & {0} & {0} & {0} & {{ - (ka1 + kab)}} & {{kba}} \\ {0} & {0} & {0} & {0} & {0} & {{k6b}} & {0} & {0} & {{kab}} & {{ - (kba + kb6)}} \\ \end{array} } \right]}\,{\left[ {\begin{array}{*{20}c} {{C1}} \\ {{C2}} \\ {{C3}} \\ {{C4}} \\ {{C5}} \\ {{C6}} \\ {{C7}} \\ {{C8}} \\ {{Ca}} \\ {{Cb}} \\ \end{array} } \right]} $$

(6)

C_i is the occupancy probability in state i and C₁+C₂+C₃ +C₄+C₅+C₆+C₇+C₈+C_a+C_b=1. In case of a single substrate, equation 6 reduces to equation 4 of Loo et al. (2006).

Computer simulations were performed using Berkeley Madonna 8.0.1 (Loo et al. 2006). The voltage pulse protocol was simulated by determining the occupancy probabilities at holding potential (V _h = −50 mV). At each test voltage (V _t ranging between + 50 and −150 mV), the time course of the occupancy probabilities was obtained by numerically integrating equation 6. Cotransporter currents and fluorescence intensity changes (ΔF) were calculated using equations 4 and 5. Steady-state kinetic parameters (I _max, K _0.5) were simulated by generating the I–V relations for the sugar-coupled current as functions of [Na⁺] _o and [sugar] _o . At each V _m, the I vs. [sugar] _o and I vs. [Na⁺] _o curves were fitted to equation 1.

For pre-steady-state simulations, the predicted transient cotransporter currents for ON and OFF responses at each voltage (V) were integrated to obtain the charge (Q). Q−V relations were fitted with the Boltzmann relation (equation 3) to obtain Q _max, zδ ^Q and ${\text{V}}^{Q}_{{{\text{0}}{\text{.5}}}}$. Model predictions on relaxation time constants were obtained by fitting the simulated pre-steady-state currents to

$$ I{\text{(t) = }}I_{{{\text{fast}}}} {\text{ exp}(-t/}\tau _{{{\text{fast}}}} ) + I_{{{\text{med}}}} {\text{ exp}(-t/}\tau_{\text{med}}) + I_{{{\text{slow}}}} {\text{ exp}(-t/}\tau _{{{\text{slow}}}} ) + I_{{{\text{ss}}}} $$

(7)

I_fastexp(−t/τ_fast) is the fast submillisecond component and is beyond the resolution of the two-electrode voltage clamp (Loo et al. 2005).

Estimating Kinetic Parameters

In two-electrode voltage-clamp experiments, the rate constants for sugar translocation (C3Na₂S1 ⇄ C4Na₂S1) and internal ligand binding (C4Na₂S1 ⇄ C5Na₂ + S1; C5Na₂ ⇄ C6 + 2Na⁺) cannot be uniquely determined. This requires the kinetics of outward currents, using, e.g., excised patches (Eskandari et al. 2005). Here, we used kinetic parameters obtained from experiments where individual partial reactions were isolated; i.e., (1) kinetic parameters for voltage-dependent reactions (Fig. 1, region I) were obtained from fitting the pre-steady-state currents in the absence of sugar (Loo et al. 2005) and (2) kinetic parameters for αMDG on the internal membrane surface (Fig. 1, region III) were obtained from our previous study on reverse sugar transport using the excised giant patch (Eskandari et al. 2005).

Simulations were performed by varying the rate constants (initially obtained by trial and error) until a global fit (by eye) was obtained for the experimentally obtained steady-state and pre-steady-state kinetics (steady-state I–V curves, ${\text{K}}^{{{\text{Na}}}}_{{0.5}}$, ${\text{K}}^{{\alpha {\text{MDG}}}}_{{0.5}}$, ${\text{K}}^{{{\text{indican}}}}_{{0.5}}$, time course of pre-steady-state currents, Q−V and τ−V curves) and fluorescence intensity changes (ΔF−V). The objective was to obtain a single set of parameters that fit the global data set rather than those required to obtain an optimal fit to one type of experiment. Each rate was varied in turn to determine the sensitivity of the simulations to that value.

The simulations shown in Figs. 2–4, 6, 7, 9 and 10 were carried out for hSGLT1 and TMR6M-labeled mutant G507C at 20°C using the parameters of Table 1 with [Na⁺] _o  = 100 mm, [Na⁺] _i  = 5 mm, [αMDG] _i  = 0 and N_T ∼10¹¹–10¹² transporters. All simulations were performed at 0–100 mm [Na⁺]_o, 0–10 mm [αMDG] _o and 0–10 mm [indican] _o .

Model Simulations

The kinetic parameters obtained for indican and αMDG are summarized in Table 1. Simulations with one set of parameters account for the steady-state and pre-steady-state kinetics of hSGLT1 in the presence of αMDG and/or indican. This is seen from the goodness of fit for the steady-state and pre-steady-state kinetics (e.g., Figs. 2D, E, 3B, 4D–F, 6D–F and 7D–F). The sensitivity of the fit was tested by systematically changing each parameter in turn; e.g., k ₂₇ and k ₇₂ can only be varied by threefold (keeping the ratio k ₇₂/k ₂₇ constant) to account for the indican K _0.5 and the effect of indican on the time constants for the pre-steady-state currents. On the other hand, global fits are insensitive to variations in k ₈₅ from 100 to 1,000 s⁻¹: studies of outward currents as a function of internal [indican] are required to place limits on k ₈₅ (k ₅₈ is constrained by microscopic reversibility).

In order to account for the natural variation in kinetics from experiment to experiment, we determined the range in each parameter that is required (Table 1). The experimental parameters that vary include the following: (1) the V _0.5 for charge movement (${\text{V}}^{Q}_{{{\text{0}}{\text{.5}}}}$) ranges from −33 to −70 mV (Loo et al. 2005), and this is accounted for by variation of k ₁₂ of 50,000–140,000 m ⁻²s⁻¹ (Table 1); (2) the K _0.5 for indican is ∼60–100 μm, and this can be accounted for by variations in k ₂₇ of ∼1000,000–300,000 m ⁻¹s⁻¹ and in k ₇₂ of ∼12–35 s⁻¹. As previously noted, there is a poor fit of the capacitive currents recorded in the submillisecond range, and this is probably due to our assumption about the simultaneous binding of the two external Na⁺ ions to hSGLT1 (Loo et al. 2005).

The most striking differences between the kinetics of indican and glucose transport are in the turnover numbers, the competition between αMDG and indican and the effects of the sugars on the pre-steady-state kinetics. The fact that these differences can readily be accommodated may be taken as additional support for our model of Na⁺/sugar cotransport by hSGLT1 (Fig. 8).

Specifically, the simulations permit the following:

• 1. Isolation of conformation C ₇ Na ₂ S2: Namely, undersaturating external Na⁺ and indican concentrations at large negative membrane potentials, the transporter is predominantly in the C7Na₂S2 conformation (P_o = 0.8, Fig. 9B) due to the low rate of indican translocation (k₇₈ = 0.5 s⁻¹). This is in sharp contrast to that for αMDG transport, where the transporter is predominantly in the C5Na₂ conformation (P_o = 0.7, Fig. 9C) due to the higher rate for sugar translocation (k₃₄ = 50 s⁻¹) and low rate of Na⁺ dissociation (k₅₆ = 5 s⁻¹). The high population of state C7Na₂S2 in the presence of indican also accounts for (a) the charge transfer on depolarizing the membrane potential, i.e., the shift in conformation from C7Na₂S2 to C6 (C7Na₂S2 → C2Na₂ → C_a → C_b → C₆; Fig. 9B, E), and (b) the increase in time constant for both charge movement and fluorescence changes (Figs. 4 and 9). On the other hand, saturating αMDG eliminates charge movement—depolarizing the membrane potential shifts C5Na₂ to C₆ (Fig. 9C, F), an electroneutral step (see Loo et al. 2006). Implicit in the model is that the Na⁺/sugar cotransport step (C3Na₂S1 → C4Na₂S1 and C7Na₂S2 → C8Na₂S2) is electroneutral and that the only voltage-sensitive steps in the transport cycle are those involving external Na⁺ binding (C1 ⇄ C2Na₂) and the reorientation of the ligand-free transporter (C1 ⇄ C_a ⇄ C_b ⇄ C6, see Fig. 8).

• 2. Evidence for a conformational change after sugar binding: The conformational transitions monitored by fluorescence change (ΔF) when V_m is stepped from −50 mV (V_h) to + 50 mV differed in the presence of saturating concentrations of sugars: in saturating αMDG, ΔF is associated with transition from C5Na₂ → C6, whereas in saturating indican it arises from C7Na₂S2 → C6 (C7Na₂S2 → C2Na₂ → C1 → C_a → C_b → C6, Fig. 9B, C). The increase in maximal fluorescence change (ΔF_max) in saturating indican compared to NaCl buffer alone indicates that the (apparent) quantum yield of C7Na₂S2 is lower than that of C2Na₂ (qy₇ = 0.7, qy₂ = 1). This difference in quantum yields between C2Na₂ and C7Na₂S2 provides evidence for a conformational change of SGLT1 induced by sugar binding, prior to the sugar translocation step.

• 3. Substrate competition: This is simply a consequence of the large difference in the transporter turnover number for the two substrates. In the case of SGLT1, where the turnover for indican is only 10% of that for αMDG, the addition of indican causes a reduction in αMDG transport. Simulations demonstrate that this is caused by an increase in the probability of the sugar-binding site being occupied by indican (see Fig. 10) and the concomitant reduction in translocation; k₃₄ is reduced from 50 to 0.5 s⁻¹ (k₇₈). The model accurately predicts the apparent inhibition constant for indican, 210 μm (Fig. 3), and the difference between this K_i and the K_0.5 for indican transport in the absence of other substrates (0.1 mm). Simulations also predict the changes in the kinetics of αMDG transport at fixed concentrations of indican; i.e., a fixed concentration of indican produces the expected decrease in apparent affinity (increase in K_0.5) of αMDG with no change in maximum velocity, or classical competitive inhibition. Irrespective of the fixed indican concentration, a sufficiently high αMDG concentration can be obtained, in theory at least, to outcompete indican binding.