Glucose metabolism down-regulates the uptake of 6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxyglucose (6-NBDG) mediated by glucose transporter 1 isoform (GLUT1): theory and simulations using the symmetric four-state carrier model

Abstract

The non-metabolizable fluorescent glucose analogue 6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxyglucose (6-NBDG) is increasingly used to study cellular transport of glucose. Intracellular accumulation of exogenously applied 6-NBDG is assumed to reflect concurrent gradient-driven glucose uptake by glucose transporters (GLUTs). Here, theoretical considerations are provided that put this assumption into question. In particular, depending on the microscopic parameters of the carrier proteins, theory proves that changes in glucose transport can be accompanied by opposite changes in flow of 6-NBDG. Simulations were carried out applying the symmetric four-state carrier model on the GLUT1 isoform, which is the only isoform whose kinetic parameters are presently available. Results show that cellular 6-NBDG uptake decreases with increasing rate of glucose utilization under core-model conditions, supported by literature, namely where the transporter is assumed to work in regime of slow reorientation of the free-carrier compared with the ligand-carrier complex. To observe an increase of 6-NBDG uptake with increasing rate of glucose utilization, and thus interpret 6-NBDG increase as surrogate of glucose uptake, the transporter must be assumed to operate in regime of slow ligand-carrier binding, a condition that is currently not supported by literature. Our findings suggest that the interpretation of data obtained with NBDG derivatives is presently ambiguous and should be cautious because the underlying transport kinetics are not adequately established.

Keywords: GLUT; NBDG; astrocytes; four‐state carrier model; glucose.

Figure 1. The four-state carrier model in the presence of two different substrates

The definition of rate constants of glucose and 6-NBDG at the inside and outside faces of the GLUT is illustrated in left panel. Here solid lines denote binding/unbinding of the carrier to/from the ligand, whereas dashed lines denote reorientation of the carrier when it is either free or bound to the ligand. Glucose and 6-NBDG are represented by different symbols. As mentioned in the ‘Methods’ section, the symmetric model is here used, implying that the rates for forward and reverse reactions (reorientation and binding) are identical. The “o” and “i” subscripts refer to the outward- and inward-facing carrier, respectively. The microscopic parameters distinguish the transitions between different carrier states and are related to the kinetic constants for transport of glucose and 6-NBDG (Table 1). Specifically, the set of parameter values can uphold different operational regimes for the carrier, namely a slow free-carrier reorientation regime (middle panel) or a slow ligand-carrier binding regime (right panel). Note that the arrows in panels B and C portray only a partial and simplified schematic representation of net glucose and 6-NBDG fluxes pertaining to the two different regimes of the carrier. In particular, dark arrows indicates the preferential direction of net conformational change. The rate of free-carrier reorientation versus ligand-carrier binding is critical since the effect of increased glucose metabolism by HK is to remove intracellular glucose and thus up-regulate the transition from carrier state C_iGLC_i to state C_i. Thus, the velocity of the subsequent transition identifies the actual operational regime of the carrier.

Figure 2. Simulated time course of intracellular glucose and 6-NBDG concentration during changes in glucose metabolism (slow free-carrier reorientation regime - core model)

Due to the competitive inhibition of glucose uptake by 6-NBDG, the glucose concentration decreases as soon as 6-NBDG is infused at time zero (arrow, left panel). Both the extent of the glucose transport inhibition and the amount of 6-NBDG accumulated intracellularly over time depend on the added 6-NBDG concentration, which however is not a critical parameter for the conclusions of the present analysis. Increases in substrate flow through HK (black horizontal bar), i.e. increases in the rate of glucose phosphorylation, are accompanied by decreases in intracellular glucose level and increased glucose uptake. Since the carrier works in counterflow-like conditions, a decrease in cellular 6-NBDG uptake rate is observed when HK is activated (right panel). This observation implies that augmented metabolic rate actually slows down the uptake of 6-NBDG. The converse is also true, i.e. inhibition of hexokinase and subsequent increase in intracellular glucose level and decrease in glucose uptake brings about a rise in 6-NBDG influx. Note that the changes in intracellular glucose level occur on top of the decrease due to transport inhibition by 6-NBDG relative to basal conditions (left panel, dotted line). In the simulations shown in the present figure, HK velocity is increased or decreased by 50% relative to its basal reaction rate (onset at 5 minutes, duration 5 minutes). Parameter values for this figure are listed in column 1 of Table 2, and are relative to the core model conditions.

Figure 3. Simulated time course of intracellular glucose and 6-NBDG concentration during changes in glucose metabolism (slow ligand-carrier binding regime)

In these conditions (20-fold reduction in glucose dissociation constant K_D(GLC)) the up-regulation of glucose metabolism (black horizontal bar) is paralleled by a stimulation of 6-NBDG uptake (right panel). In kinetic terms this is equivalent to assuming that return of the carrier from the cytosolic side of the membrane to the cell exterior is faster when the transporter is vacant, thus no compounds are counter transported. Glucose transients (left panel) are nearly indistinguishable from those showed in Figure 3. Infusion of 6-NBDG started at time zero (arrow, left panel). Note that the changes in intracellular glucose level occur on top of the decrease due to transport inhibition by 6-NBDG relative to basal conditions (left panel, dotted line). In the simulations shown in the present figure, HK velocity is increased or decreased by 50% relative to its basal reaction rate (onset at 5 minutes, duration 5 minutes). Parameter values for this figure are listed in column 3 of Table 2.

Figure 4. Intracellular accumulation of 6-NBDG during increase in glucose metabolism for low rates of either free carrier reorientation or ligand-carrier binding

Depending on carrier parameters, the up-regulation of glucose metabolism (black horizontal bar) brings about a decrease or an increase in 6-NBDG concentration relative to conditions of unchanged or down-regulated glucose utilization. Flux of 6-NBDG varies in opposite directions whether the carrier operates in slow free-carrier reorientation regime (left panel, 10-fold reduction in f₁ = f₋₁) or slow ligand-carrier binding regime (right panel, >120-fold reduction in glucose dissociation constant K_D(GLC)). It is noted that the flux of 6-NBDG is always positive (i.e. intracellular 6-NBDG always rises) due to the positive concentration gradient of 6-NBDG between extra- and intracellular space. At 10 minutes after end of stimulation the intracellular concentration of glucose has almost returned to its basal level (which is nearly 0.85 mmol/L due to inhibition of transport by NBDG). Determination of 6-NBDG accumulation at this time gives a change of 5–6% below or above its value in absence of metabolic challenge (insets). This would mean that the difference in NBDG content in two different compartments behaving in opposite direction with respect to glucose metabolism would be in the order of 10–12%. Parameter values for this figure are listed in columns 2 and 4 of Table 2.

Figure 5. Time derivatives of glucose and 6-NBDG transport flow rates as a function of time

The time derivative of fluxes of glucose and 6-NBDG have different sign when the carrier behaves in the slow free-carrier reorientation regime. This means that the fluxes vary in opposite directions, which is true both during HK activation (top left panel) and inhibition (top right panel). When the carrier is in the slow ligand-carrier binding regime, the situation is reversed and the time derivatives of glucose and 6-NBDG fluxes share the same sign. This means that the fluxes vary in the same direction in condition of both HK activation (bottom left panel) and inhibition (bottom right panel).