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Keywords:

  • astrocytes;
  • four-state carrier model;
  • glucose;
  • GLUT ;
  • NBDG

Abstract

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Disclosure/conflict of interests
  8. References

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.

Abbreviations used:
6-NBDG

6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxyglucose

GLC

glucose

GLUT

glucose transporter

HK

hexokinase

Most mammalian cells use glucose for energy metabolism and as precursor for the synthesis of many important biological molecules. Transport of glucose is mediated by a family of ubiquitous integral membrane uniporter carriers named glucose transporter (GLUT) proteins (reviewed by Simpson et al. 2007). The fluorescent glucose analogue 6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxyglucose (6-NBDG) was introduced as a tool to quantify cell hexose uptake (Speizer et al. 1985). Most of the research using NBDG for monitoring glucose uptake in normal (i.e., non-cancer) cells has so far focused on insulin-sensitive cells. Such studies detected insulin-stimulated glucose uptake in cultured muscle cells, monocytes, adipocytes, or hepatocytes, and have conversely produced conflicting results about the effect of accelerated glucose transport on intracellular NBDG accumulation (Leira et al. 2002; Dimitriadis et al. 2005; Zou et al. 2005; Jung et al. 2011). These cell types all express the insulin-sensitive GLUT4 isoform; therefore, results obtained by studies conducted on GLUT4-expressing cells cannot be extrapolated to provide insights on 6-NBDG uptake by tissues, where GLUT4 is not expressed, such as cerebral cortex (Simpson et al. 2007). In the following, we will focus on cortical astrocytes expressing preferentially GLUT1 isoform. This choice is explained by the availability of microscopic carrier parameters for cerebral GLUT1 as well as by the fact that 6-NBDG has been recently utilized to investigate astrocytic glucose uptake during brain stimulation (see below).

In brain tissue, the relatively high (typically millimolar, mM) glucose level maintains the saturation of hexokinase (HK) under basal as well as activated conditions (Qutub and Hunt 2005 and references therein). Indeed, GLUTs are not rate limiting for metabolism of glucose, because the affinity of HK for glucose (Km = 0.05 mM) is substantially higher compared with that of GLUTs (Km = 5–10 mM) (Gruetter et al. 1992; Simpson et al. 2007). Therefore, it is the rate of glucose phosphorylation that controls net uptake of glucose. Contrary to glucose, 6-NBDG is not metabolized, yet it competes with glucose for the same carrier-binding site, although a fraction of 6-NBDG transport possibly is non-GLUT mediated (see Mangia et al. 2011). Previous studies regarding the non-metabolizable glucose analogue 3-O-methylglucose showed that brain/plasma (or intracellular/extracellular) distribution ratio for methylglucose follows tissue glucose content (see Nakanishi et al. 1996 and references therein). Specifically, when metabolism is either stimulated or reduced (for a fixed plasma glucose level), the glucose concentration and methylglucose distribution ratio either decreases or increases. In agreement with these arguments, it was recently pointed out that the kinetics of 6-NBDG transport might or might not be governed by the same supply–demand balance of glucose depending on the relation between intracellular/extracellular sugar levels and metabolic demand (Dienel 2012). Therefore, to correctly interpret fluorescence data, it is important to evaluate to what extent the transport of 6-NBDG actually reflects the cellular metabolism of glucose.

Assays of basal cerebral glucose transport using NBDG showed diffusely distributed fluorescence in the parenchyma of the mouse hippocampus (Shimada et al. 1994; Itoh et al. 2004). Accumulation of NBDG in both neurons and astrocytes was also demonstrated in vitro (Aller et al. 1997). Glutamate-induced changes in uptake of NBDG were then investigated in hippocampal astrocyte-enriched cultures (Loaiza et al. 2003) as well as neuron–astrocyte cocultures (Porras et al. 2004). These studies reported very rapid enhanced astrocytic and inhibited neuronal NBDG transport upon stimulation by glutamate. Importantly, the same group failed to observe any short-term increase of astrocytic glycolytic rate in response to glutamate using DNA-encoded Förster resonance energy-transfer (FRET)-based glucose nanosensor (Bittner et al. 2011). Using the FRET-based nanosensor, their subsequent study actually showed nearly instantaneous suppression of astrocytic glycolysis by glutamate (Ruminot et al. 2011). Together, these findings suggest that transport of glucose analogues might not reflect the concurrent utilization of glucose in brain cells. Yet, 6-NBDG has been used to examine glucose metabolism of neuronal and astrocytic perikarya in barrel cortex of anesthetized rats (Chuquet et al. 2010). An increased astrocytic but not neuronal accumulation of the fluorescent sugar was observed during whisker stimulation, and was interpreted as a proof of preferential glucose uptake and metabolism by astrocytes upon stimulation (Chuquet et al. 2010). More recently, the same outcomes were reported in hippocampal and cerebellar tissue slices (Jakoby et al. 2013). An interesting feature of this study is that measurements of glucose uptake using either FRET-based nanosensor or 6-NBDG were found to be anti-correlated in cultured neurons and astrocytes. In particular, the faster the uptake of glucose the slower the uptake of 6-NBDG. It remains to be established if this effect is as an indication of the uptake capacity of 6-NBDG in different cell types because of specific GLUT isoforms, which was the author's interpretation (Jakoby et al. 2013), or whether it underlies an intrinsic relation between uptake of the two sugars independent of the particular GLUT isoform mediating the transport. The experiments performed by Jakoby and coworkers on tissue slices and cell cultures confirm the previous observations that NBDG derivatives are preferentially taken up by glial cells during stimulation.

The aim of this work is to provide a theoretical framework to understand the results of in vitro and in vivo experiments conducted with 6-NBDG. First, the relationship between glucose and 6-NBDG transport kinetics is examined theoretically by calculating the analytical expression for flow rate changes of two substrates (i.e., glucose and 6-NBDG). Then a simple case of 6-NBDG uptake by a cellular compartment is numerically solved for varying rate of glucose utilization. Different scenarios of microscopic parameters of the carrier proteins are finally considered to resemble the behavior of GLUT1 transporter.

Methods

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Disclosure/conflict of interests
  8. References

This analysis takes advantage from the previously developed formalization of the four-state alternating-carrier model for glucose transporter (GLUT) proteins in the presence of two substrates (Deves and Krupka 1979a, b) (Fig. 1a). In particular, the substrate affinities for the cis and trans side of the membrane are assumed to be the same (i.e., symmetric model) to avoid any possible violation of thermodynamic constraints (Naftalin 2008, 2010).

image

Figure 1. The four-state carrier model in the presence of two different substrates. The definition of rate constants of glucose and 6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxyglucose (6-NBDG) at the inside and outside faces of the GLUT is illustrated in (a). 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 constants 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 (b) or a slow ligand–carrier binding regime (c). Note that the arrows in (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 indicate the preferential direction of net conformational change. The rate of free-carrier reorientation versus ligand–carrier binding is critical as the effect of increased glucose metabolism by HK is to remove intracellular glucose and thus up-regulate the transition from carrier state CiGLCi to state Ci. Thus, the velocity of the subsequent transition identifies the actual operational regime of the carrier.

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To avoid any confounding factor in the interpretation of simulations, we adopted a minimal metabolic model, which takes into account the concentration of intracellular (inside, ‘i’ subscript) and extracellular (outside, ‘o’ subscript) glucose and 6-NBDG (in equations termed NBDG to simplify notation) concentrations, and can be written as:

  • display math
  • display math
  • display math
  • display math

where it is assumed that glucose and 6-NBDG are continuously delivered into the extracellular space from the bloodstream, thus resulting in a constant extracellular concentration of these two metabolites (i.e., concentration clamp). The constancy of extracellular concentration of glucose and 6-NBDG does not alter the main conclusions of the analysis. It is noted that glucose, but not 6-NBDG, is phosphorylated by HK, which is assumed to be always saturated by its substrate.

The general rate equations for inward fluxes of glucose and 6-NBDG are (see Table 1 for the definition of the various parameters in terms of individual rate constants of the carrier model):

  • display math
  • display math

where the denominator

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is identical for the two rate equations. Combining the equations for JGLC and JNBDG by eliminating the term GLCoNBDGi − GLCiNBDGo gives:

  • display math
Table 1. Mathematical relationships between kinetic and microscopic carrier parameters
DescriptionExpressiona
  1. a

    For the derivation of these expressions, see (Deves and Krupka 1979a) and references therein. The microscopic parameters connote the conformational changes of the carrier shown in Fig. 1.

  2. The symbol Ct represents the concentration of the carrier in all forms, and therefore the tissue concentration.

Equilibrium constants for substrate–carrier complex formation inline image
Half-saturation constant for zero trans entry of glucose inline image
Half-saturation constant for zero trans entry of NBDG inline image
Half-saturation constant for zero trans exit of glucose inline image
Half-saturation constant for zero trans exit of NBDG inline image
Maximum rate of zero trans exit of glucose inline image
Maximum rate of zero trans exit of NBDG inline image
Constant for infinite trans entry of glucose inline image
Constant for infinite trans entry of NBDG inline image
Constant for infinite trans entry of glucose inline image
Constant for infinite trans entry of NBDG inline image
Maximum rate of infinite trans exit of glucose inline image
Maximum rate of infinite trans exit of NBDG inline image

The time derivative of this relation can be calculated as:

  • display math

Note that, although the consumption of glucose does not appear explicitly here, it is actually contained into the glucose gradient, which can be expressed as:

  • display math

Previous studies on GLUT kinetics showed that the free-carrier reorientates much more slowly relative to the ligand–carrier complex (Deves and Krupka 1979a; Whitesell et al. 1989; Carruthers 1990; Barros et al. 2009). This behavior implies the following conditions:

  • display math
  • display math

Normally, the flux of NBDG is about 2000- to 3000-fold lower than that of glucose (Speizer et al. 1985; Cloherty et al. 1995); therefore, inline image, which is equivalent to have the single condition:

  • display math

The latter inequality holds for very slow reorientation of the free carrier compared to the ligand–carrier complex. When this argument is taken into account, the equation of the flux derivative simplifies to:

  • display math

which identifies a condition where flux variations of glucose are accompanied by contrary flux variations of NBDG. This condition reflects a partial operational regime of the so-called counterflow or obligatory exchange. Strictly, counterflow is the uphill flow of labeled ligand driven by the downhill flow of unlabeled ligand, which applies to situations in which there is no substrate on one side. Obligatory exchange occurs when reorientation of the free carrier is prohibited. It is important to note that these conclusions are model independent, as the underlying kinetics does not require the mobile-carrier model and is also explainable using the two fixed site model (for demonstration, see Carruthers 1990; Naftalin 2010). In a straightforward manner, the mobile-carrier explanation is that the path for ligand exchange short circuits the slow path of free-carrier transit. We will refer to this behavior of the carrier as slow free-carrier reorientation regime (Fig. 1b).

On the other hand, fluxes of glucose and 6-NBDG can also change in the same direction if the above-mentioned inequality is reversed to:

  • display math

This condition implies that the rate of ligand–carrier binding is much lower than the rate of free-carrier reorientation, and therefore the return of the carrier from the inward-facing to the outward-facing configuration is favored when it is not bound to the ligand. We will refer to this behavior of the carrier as slow ligand–carrier binding regime (Fig. 1c). It is noted that the two different regimes here described are mutually exclusive, thus the slow free-carrier reorientation regime can also be defined as high ligand–carrier binding regime, and vice versa. Here, we adopted the present terminology to pinpoint where the actual changes in parameter values were made, bearing in mind that these changes have to be interpreted in relative terms. The two different regimes can be intuitively appreciated in terms of net process (remember that all transitions of the carrier are reversible) by considering that the rise in glucose metabolism (i.e., removal of intracellular glucose by HK activity) impacts on the carrier by ‘pulling’ the transition from state CiGLCi to state Ci (Fig. 1b and c). The latter state thus represents the main node point governing carrier behavior according to the relative velocity between reorientation of free carrier (from Ci to Co) and binding of the carrier to the other available substrate (from Ci to CiNBDGi).

To examine whether brain GLUT1 isoform satisfies the above theoretical predictions, the model is here applied to a cellular compartment with varying rates of glucose phosphorylation by HK. In particular, to simulate departures from steady-state conditions, the HK activity was either up- or down-regulated by 50% relative to its basal reaction rate. The core model uses the carrier parameters estimated at the blood–brain barrier (Barros et al. 2009). Notably, the glucose gradient between blood and parenchyma is much higher compared with the glucose gradient between extracellular and intracellular space within the tissue (Simpson et al. 2007). Furthermore, astrocytes express different GLUT isoform (predominance of 45-kDa GLUT-1 isoform) compared with endothelial cells (55-kDa GLUT-1 isoform) (Simpson et al. 2007). Therefore, it is likely that the microscopic parameters of astrocytic GLUT1 isoform are slightly dissimilar from those relative to blood–brain barrier GLUT1 isoform. However, we conformed to the parameter set used in previous kinetic analysis, where astrocytic and endothelial GLUT1 are assumed to be kinetically similar (Barros et al. 2009).

Model simulations were carried out by numerical integration using the software MATLAB (The Mathworks Inc., Natick, MA, USA; http://www.mathworks.com/) version 7.0.4 R14.

Results

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Disclosure/conflict of interests
  8. References

Simulations performed using available microscopic carrier parameters (i.e., core model) show that cellular uptake of 6-NBDG decreases when glucose phosphorylation is actually stimulated (Fig. 2). This indicates that a relatively low rate of free-carrier reorientation compared with the velocity of ligand binding (200/s vs. 3000/s, see column 1 in Table 2) is already sufficient to obtain opposite flux variations of glucose and NBDG. The slow reorientation of the vacant carrier is not the sole determinant in the glucose/NBDG exchange underlying this particular regime of the transporter. Indeed, a key role is played by the nearly 300-fold higher dissociation constants of glucose (40 mM) relative to that of 6-NBDG (0.13 mM), which favors rapid glucose dissociation and NBDG association from and to the carrier, respectively, and thus the counterflow-like behavior.

Table 2. Parameters values used in model simulations
ParameterUnitsValue
Low free-carrier reorientation regimeLow ligand–carrier binding regime
Fig. 2 (core model)Fig. 4aFig. 3Fig. 4b
  1. The sets of parameters are chosen to obtain a given percent difference of intracellular 6-NBDG accumulation between conditions of 50% stimulated and 50% inhibited cell glucose metabolism. In particular, this difference is ~1% for Figs 2 and 3, whereas it is ~12% for Fig. 4a and b. Note that Figs 2 and 4a identify the slow free-carrier reorientation regime, and Figs 3 and 4b identify the slow ligand–carrier binding regime.

    Changes of parameter values from core model simulation (Fig. 2) are emphasized in boldface.

    All values are taken from Barros et al. (2009), except for k±1k±2k±3k±4 that are known as ratios (i.e. KD(GLC) and KD(NBDG)). See Barros et al. (2009) for references about the experimental determination of these constants.

    Note the large decrease of the dissociation constant for glucose within the low ligand–carrier binding regime (from 40 mM to 2 mM to 0.33 mM), whereby the corresponding dissociation constant for NBDG remains unaltered (0.13 mM).

    The concentration of GLUTs in brain cells (here represented by the parameter Ct ) is estimated to be in the order of fractions of μM (~0.4 pmol/mg total protein assuming about 0.9 g/100 mL of total protein content in cerebral cortex) (see Table 1 in Simpson et al. 2007). Although there is uncertainty on these numbers, the total concentration of the carrier is possibly smaller than that used in core model. However, decreasing Ct from the value of core model simulations requires a corresponding increase of f±2 relative to f±1 (see Table 1) to maintain physiological basal and stimulation-induced glucose level (simulations not shown). In turn, increase in f±2 will result in reduced f±1/f±2 ratio, thus further confirming the conditions of slow free-carrier reorientation for GLUTs. On the other hand, the condition of slow ligand–carrier binding requires a too high tissue concentration of the transporter.

    For the kinetic significance of the various parameters, see Fig. 1.

f1 = f-1per second200 20 200200
f2 = f-2per second3000300030003000
f3 = f-3per second0.190.190.190.19
KD(GLC) = k-1/k1 = k-2/k2mM4040 2 0.33
k1 = k2per second30003000 0.00037 0.0002
k-1 = k-2mM/s120000120000 0.00074 0.000066
KD(NBDG) = k-3/k3 = k-4/k4mM0.130.130.130.13
k3 = k4per second30003000 0.0000077 0.0000077
k-3 = k-4mM/s390390 0.000001 0.000001
C t μM0.278 1.052 116.76 283.56
J HKμM/s3.33.33.33.3
GLC 0 mM1.51.51.51.5
NBDG 0 μM100 25 100100
image

Figure 2. Simulated time course of intracellular glucose and 6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxyglucose (6-NBDG) concentration during changes in glucose metabolism (slow free-carrier reorientation regime—core model). Because of the competitive inhibition of glucose uptake by 6-NBDG, the glucose concentration decreases as soon as 6-NBDG is infused at time zero (arrow, a). 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 this analysis. Increases in substrate flow through HK (black horizontal bar), that is, increases in the rate of glucose phosphorylation, are accompanied by decreases in intracellular glucose level and increased glucose uptake, and vice versa. As the carrier works in counterflow-like conditions, a decrease in cellular 6-NBDG uptake rate is observed when HK is activated (b). This observation implies that augmented metabolic rate actually slows down the uptake of 6-NBDG. The converse is also true, that is, 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 which is due to transport inhibition by 6-NBDG relative to basal conditions (a, 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 min, duration 5 min). Parameter values for this figure are listed in column 1 of Table 2, and are relative to the core model conditions.

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An accumulation of 6-NBDG inside the cell in presence of increased glucose metabolism can also be simulated (Fig. 3), but in this case, it is necessary to reduce the dissociation constant for glucose (KD(GLC), see column 3 in Table 2) by a factor of 20 and concomitantly assume very small rates of glucose and 6-NBDG binding. This particular regime of the carrier identifies a situation in which the transporter returns preferentially empty from the intracellular to the extracellular side of the membrane, and translocates either glucose or 6-NBDG with a similar probability because of the similarity of binding rates and dissociation constants. Importantly, the assumption that sugar binding is much slower than free-carrier reorientation is not supported by current literature (Carruthers 1990; Naftalin 2010).

image

Figure 3. Simulated time course of intracellular glucose and 6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxyglucose (6-NBDG) concentration during changes in glucose metabolism (slow ligand–carrier binding regime). In these conditions (20-fold reduction in glucose dissociation constant KD(GLC)) the up-regulation of glucose metabolism (black horizontal bar) is paralleled by a stimulation of 6-NBDG uptake, and vice versa (b). 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 (a) are nearly indistinguishable from those showed in Fig. 3. Infusion of 6-NBDG started at time zero (arrow, a). Note that the changes in intracellular glucose level occur on top of the decrease which is due to transport inhibition by 6-NBDG relative to basal conditions (a, 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 min, duration 5 min). Parameter values for this figure are listed in column 3 of Table 2.

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Thus, we found that the relation between 6-NBDG and concomitant glucose uptake depends on the dissociation constants of the two sugars as well as on the slowest step in the configurational changes of the carrier, whether it is the reorientation of the free carrier or the binding of the ligand to the carrier. Notably, using the currently available parameters the model supports the former situation (i.e., the parameter values satisfy the slow free-carrier reorientation regime described in the ‘Methods’ section).

The simulated departures from steady-state 6-NBDG influx during changes in metabolic demand are very small (few percent). However, a recent experiment on 6-NBDG uptake by neurons and astrocytes (Chuquet et al. 2010) showed a ~10% difference of fluorescence intensity between the two cell types after the stimulation. Therefore, we examined to what extent either the slow free-carrier reorientation regime (i.e., core model) or the slow ligand–carrier binding regime should be upset to produce the experimentally observed difference in NBDG uptake. We thus performed additional simulations by exacerbating the different regimes (see columns 2 and 4 in Table 2). We indeed found a substantial (5–6%) departure of 6-NBDG transport patterns between basal and stimulated conditions using a 10-fold lower rate of free-carrier reorientation (see Fig. 4a). Remarkably, a difference of this magnitude could be obtained in the slow ligand–carrier binding regime (Fig. 4b) only reducing the dissociation constant for glucose to an unreasonably low value (Table 2, column 4). This means that, without invoking further assumptions, the agreement with experimental data is obtained with more conservative changes within the counterflow-like behavior of the transporter.

image

Figure 4. Intracellular accumulation of 6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxyglucose (6-NBDG) during increase in glucose metabolism for low rates of either free carrier reorientation or ligand–carrier binding. Depending on carrier parameters, the changes 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 (a, 10-fold reduction in f1 = f - 1) or slow ligand–carrier binding regime (b, > 120-fold reduction in glucose dissociation constant KD(GLC)). It is noted that the flux of 6-NBDG is always positive (i.e., intracellular 6-NBDG always rises) because of the positive concentration gradient of 6-NBDG between extra- and intracellular space. At 10 min after end of stimulation, the intracellular concentration of glucose has almost returned to its basal level (which is nearly 0.85 mmol/L because of 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.

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To confirm that the simulated kinetics of glucose and 6-NBDG transport is consistent with the theoretical model described above (see ‘Methods’ section), we plotted the time derivative of the glucose and 6-NBDG flow rates as a function of time (Fig. 5). In agreement with the theory, we found that for the slow free-carrier reorientation regime, the two fluxes always change in opposite direction, that is, their time derivatives have different sign, both during HK activation (Fig. 5a) and inhibition (Fig. 5b). Conversely, for the slow ligand–carrier binding regime, the changes of the two fluxes (Fig. 5c and d) take place in the same direction, that is, their time derivatives have the same sign. These results emphasize the mutually exclusive character of the different carrier regimes and show that the time derivatives of glucose and 6-NBDG fluxes are either always correlated or always anticorrelated.

image

Figure 5. Time derivatives of glucose and 6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxyglucose (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 (a) and inhibition (b). 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 conditions of both HK activation (c) and inhibition (d).

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Discussion

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Disclosure/conflict of interests
  8. References

During enhanced energy demand, many cell types including cerebral neurons and astrocytes up-regulate oxidative metabolism and hence the substrate flow through the glycolytic pathways, which is accomplished by processing of glucose first by HK and enzymes of the glycolytic chain. In particular, the intracellular concentration of the sugar transiently decreases during conditions of increased phosphorylation of glucose. This creates a concentration gradient that in turn results in augmented flux of glucose inside the cell. As 6-NBDG cannot be metabolized, there is not a corresponding change in the concentration difference of the glucose analogue between intra- and extracellular space. Thus, uptake of glucose is actively driven by changes in metabolism, whereas that of 6-NBDG is not. It is important to remark that similar considerations might apply to the poorly metabolizable 2-NBDG derivative. However, a quantitative estimate of the effect of glucose metabolism on 2-NBDG transport requires the knowledge of the rate of 2-NBDG phosphorylation to 2-NBDG 6-phosphate as well as the rate of degradation of 2-NBDG. If phosphorylation rate of 2-NBDG is slower than its transport, the exchange between glucose and unmetabolized 2-NBDG could still produce the effect reported here for 6-NBDG, which can be further intensified by the rapid degradation of 2-NBDG to non-fluorescent products (Yoshioka et al. 1996). It should be also mentioned that retention of intracellular 2-NBDG can be overestimated because of incorporation into glycogen (Louzao et al. 2008), which is especially relevant for glycogen-rich astrocytes. Overall, it seems that the effects of changes in glucose supply and demand on NBDG resemble those on 3-O-methylglucose, although with different kinetics. Specifically, using different modeling procedures to fit experimental data (see ‘Introduction’ section), a lot of work in the past decades (Buschiazzo et al. 1970; Gjedde and Diemer 1983; Dienel et al. 1991) have arrived to conclusions similar to those we report in this study (Nakanishi et al. 1996).

Recently, it was reported that 6-NBDG accumulation significantly increases in astrocytes and slightly decreases in neurons after brain stimulation in vivo (Chuquet et al. 2010) and in vitro (Jakoby et al. 2013). With the current knowledge, the observed difference in 6-NBDG uptake surely indicates that glucose utilization is unevenly enhanced in the two cell types, provided that transport of the sugar is largely independent of the specific cellular GLUT isoforms. Yet, the results were interpreted as proof of increased uptake of extracellular glucose by astrocytes relative to neurons. Our modeling outcomes suggest that the increased flow of 6-NBDG in astrocytes actually reflects down-regulation of glucose phosphorylation. This kinetic analysis supports the latter interpretation under the commonly accepted assumption that the rate of reorientation of the free carrier is sufficiently slower than binding of the carrier with ligand and reorientation of the ligand–carrier complex (Fig. 1). The magnitude of 6-NBDG uptake departure from steady-state condition observed experimentally during metabolic challenge (Chuquet et al. 2010) could be more easily (i.e., by adopting conservative changes in parameter values) reproduced in our simulations when the transporter operates in the slow free-carrier reorientation regime, but not when it operates in the slow ligand–carrier binding regime. Thus, our results are in agreement with the notion that variations in 6-NBDG concentration follow those of glucose and hence the opposite of glucose utilization (Dienel 2012). Unfortunately, because of the lack of detailed information about neuronal GLUT3 isoform, we were unable to directly examine the fate of 6-NBDG in individual compartments under different scenarios. However, assuming GLUT3 to be kinetically similar to GLUT1 would give a > 10% difference in 6-NBDG accumulation between two adjacent compartments where, for instance, glucose uptake is oppositely modulated by the stimulation (see Fig. 4).

We have recently proposed that glycogenolysis in astrocytes after brain activation might increase intracellular glucose-6-phosphate level, thereby suppressing astrocytic glucose phosphorylation by hexokinase via product inhibition (DiNuzzo et al. 2010, 2011, 2012). Interestingly enough, this hypothesis is consistent with a reduction of astrocytic glucose metabolism and a resulting increase of both glucose and 6-NBDG in astrocytes, the latter reported by the above-mentioned studies (Chuquet et al. 2010; Jakoby et al. 2013). We have previously showed by metabolic modeling that the concentration of astrocytic glucose because of inhibition of hexokinase might transiently surpass the concentration of interstitial glucose favoring the gradient-driven efflux of the sugar by astrocytes (DiNuzzo et al. 2010). According to the present analysis, the astrocytic release of glucose would further enhance the influx of 6-NBDG in these cells.

In conclusion, we found that the transport of 6-NBDG does or does not parallel the concurrent transport of glucose depending on the microscopic parameters of the carrier proteins. Using the available parameter values relative to the cerebral GLUT1 isoform, the model predicts that the transporter behaves in the slow free-carrier reorientation regime. Therefore, the flow changes of 6-NBDG and glucose through the carrier always take place in opposite directions. While to know the exact relation between glucose and 6-NBDG transport by neuronal and astrocytic GLUT isoforms a detailed knowledge of reorientation rates of free- and ligand-bound carrier is needed, it is suggested that the utilization of intracellular 6-NBDG accumulation as a surrogate of glucose uptake and metabolism in cells preferentially expressing GLUT1 isoform (e.g., astrocytes) should await further research. Unambiguous interpretation of intracellular 6-NBDG accumulation mediated by GLUT carrier proteins requires detailed study of transport kinetics of glucose and NBDG. In the meantime, it is worthwhile to issue a word of caution regarding the interpretation of data obtained with glucose analogues, as the symmetric four-state GLUT model supports antiport not symport of glucose and NBDG.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Disclosure/conflict of interests
  8. References

S. M. thanks the support of the American Diabetes Association (grant number 07-07-DC2), along with the support of the National Center for Research Resources (Grant Number P41 RR008079) and the National Institute of Biomedical Imaging and Bioengineering (Grant Number P41 EB015894) of NIH. Additional funding supports to CMRR are Minnesota Medical Foundation, P30 NS057091 and P30 NS076408. This work was finally supported by the NIH grant UL1RR033183 and KL2 RR033182 from the National Center for Research Resources (NCRR) to the University of Minnesota Clinical and Translational Science Institute (CTSI).

Disclosure/conflict of interests

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Disclosure/conflict of interests
  8. References

The authors declare no conflict of interest.

References

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Disclosure/conflict of interests
  8. References
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