In vivo quantification of neuro-glial metabolism and glial glutamate concentration using 1H-[13C] MRS at 14.1T

Authors

  • Bernard Lanz,

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    1. Laboratory for Functional and Metabolic Imaging (LIFMET), Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
    • Address correspondence and reprint requests to Bernard Lanz, Laboratoire d'Imagerie Fonctionnelle et Métabolique (LIFMET), Ecole Polytechnique Fédérale de Lausanne (EPFL), Bâtiment CH, Station 6, CH-1015 Lausanne, Switzerland. E-mail: bernard.lanz@epfl.ch

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  • Lijing Xin,

    1. Laboratory for Functional and Metabolic Imaging (LIFMET), Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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  • Philippe Millet,

    1. Unité de Neurophysiologie et Neuroimagerie, Hôpitaux Universitaires de Genève, Geneva, Switzerland
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  • Rolf Gruetter

    1. Laboratory for Functional and Metabolic Imaging (LIFMET), Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
    2. Department of Radiology, University of Lausanne, Lausanne, Switzerland
    3. Department of Radiology, University of Geneva, Geneva, Switzerland
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Abstract

Astrocytes have recently become a major center of interest in neurochemistry with the discoveries on their major role in brain energy metabolism. An interesting way to probe this glial contribution is given by in vivo 13C NMR spectroscopy coupled with the infusion labeled glial-specific substrate, such as acetate. In this study, we infused alpha-chloralose anesthetized rats with [2-13C]acetate and followed the dynamics of the fractional enrichment (FE) in the positions C4 and C3 of glutamate and glutamine with high sensitivity, using 1H-[13C] magnetic resonance spectroscopy (MRS) at 14.1T. Applying a two-compartment mathematical model to the measured time courses yielded a glial tricarboxylic acid (TCA) cycle rate (Vg) of 0.27 ± 0.02 μmol/g/min and a glutamatergic neurotransmission rate (VNT) of 0.15 ± 0.01 μmol/g/min. Glial oxidative ATP metabolism thus accounts for 38% of total oxidative metabolism measured by NMR. Pyruvate carboxylase (VPC) was 0.09 ± 0.01 μmol/g/min, corresponding to 37% of the glial glutamine synthesis rate. The glial and neuronal transmitochondrial fluxes (Vxg and Vxn) were of the same order of magnitude as the respective TCA cycle fluxes. In addition, we estimated a glial glutamate pool size of 0.6 ± 0.1 μmol/g. The effect of spectral data quality on the fluxes estimates was analyzed by Monte Carlo simulations.

image

In this 13C-acetate labeling study, we propose a refined two-compartment analysis of brain energy metabolism based on 13C turnover curves of acetate, glutamate and glutamine measured with state of the art in vivo dynamic MRS at high magnetic field in rats, enabling a deeper understanding of the specific role of glial cells in brain oxidative metabolism. In addition, the robustness of the metabolic fluxes determination relative to MRS data quality was carefully studied.

Abbreviations used
CMRO2

cerebral metabolic rate of oxygen

FE

fractional enrichment

TCA

tricarboxylic acid

V efflux

rate of glutamine efflux from brain tissue

V Glu

rate of neuronal glutaminase

V g

rate of glial tricarboxylic acid cycle

V GS

rate of glutamine synthesis

V NT

rate of apparent glutamatergic neurotransmission

V PC

rate of pyruvate carboxylation

V tca n

rate of neuronal tricarboxylic acid cycle

V x g

exchange rate between 2-oxoglutarate and glutamate in glia

V x n

exchange rate between 2-oxoglutarate and glutamate in neurons

The brain, which is one of the most energy demanding organs in mammals, is the center of a very complex neuronal network which accomplishes the major part of the treatment of sensory information and motor functions as well as a large amount of cognitive functions, including memory, solving problems and making decisions. All these cerebral functions are the result of an intense electrochemical interaction between two major cell types, neurons and glial cells. In traditional neuroscience of the 20th century, the standard picture of brain function was that the neurons accomplish the numerous cerebral tasks, while the glial cells are simply responsible to maintain the neuronal environment in good conditions to enable proper neurotransmission. However, several studies changed this conception and showed that glial cells are active elements of the neurotransmission process (Shank et al. 1993; Yudkoff et al. 1993). Glial cells are in particular involved in the glutamate-glutamine cycle, where they are responsible for the uptake of glutamate (the major excitatory neurotransmitter) from the synaptic cleft and its conversion to the electrophysiologically inactive glutamine. The maintenance of the neurotransmission processes requires energy, delivered by glycolysis and the neuronal and glial tricarboxylic acid (TCA) cycle from glucose, which is the major energy substrate for the brain (Sokoloff 1977). However, glial cells are also fueled by alternative substrates, such as acetate (Badar-Goffer et al. 1990; Cerdan et al. 1990). More recent studies have shown evidences for the particular versatile function of astrocytes in brain energy metabolism; their capabilities to use a wide range of energy substrates (McKenna 2012) and to adapt their metabolism under pathological conditions (Gulanski et al. 2013; Jiang et al. 2013). In vivo 11C-acetate infusion experiments also showed an increased washout rate of the produced 11C-labeled metabolites under neuronal activation, pointing to an increase of astrocytic oxidative metabolism (Wyss et al. 2009), yet without demonstrating the quantitative relationship between the washout rate and glial CMRO2. Recent developments have been therefore undertaken to enable the biochemical interpretation of 11C-acetate uptake curves (Lanz et al. 2012). As a consequence, acetate might become in the near future a substrate of choice to probe modifications of glial energy metabolism in neurologic patients, insofar a detailed biochemical understanding of the observed metabolite labeling is achieved.

Two-compartment modeling combined with dynamic 13C magnetic resonance spectroscopy (MRS) has proven to be a powerful tool to probe brain oxidative metabolism and neurotransmission, both in human and rodent studies (Gruetter et al. 2001; Henry et al. 2006). Most of these studies used 13C labeled glucose as substrate to determine neuroglial metabolic fluxes (Gruetter et al. 2001; Choi et al. 2002; Henry et al. 2002; de Graaf et al. 2003a, 2004; Oz et al. 2004; Duarte et al. 2011). Since glucose is metabolized both in neurons and glial cells, the labeling of the glutamate and glutamine carbon positions is reflecting a mixture of the metabolic flow through the glial and neuronal TCA cycles. Depending on the number of measured turnover curves and on the experimental conditions, some of the determined metabolic fluxes can be subject to high uncertainties and might be unreliable as discussed by (Shestov et al. 2007; Duarte et al. 2011). This issue was especially raised for the glutamate-glutamine cycle flux.

Acetate is specifically taken up by the glia (Waniewski and Martin 1998) and thus is an ideal substrate to probe glial oxidative metabolism and to potentially increase the sensitivity of the measurement of the glutamate-glutamine cycle (Araque et al. 1999; de Graaf et al. 2003b; Henry et al. 2006). When infusing 13C labeled acetate, glutamine becomes the labeling precursor of the large neuronal glutamate pool, whose turnover dynamics is therefore very sensitive to the glutamatergic neurotransmission rate.

When infusing [2-13C]acetate, the first amino acid position to be labeled is the C4 of the small glial glutamate pool, which quickly labels the C4 of glial glutamine. The transfer of 13C to glial glutamate C4 is the result of two processes, namely the activity of the glial TCA cycle (represented by Vtcag = Vg+VPC) and the tracer exchange between 2-oxoglutarate in the glial TCA cycle and the cytosolic glutamate (represented by Vxg). If only the positions C4 of glutamate and glutamine are measured, metabolic modeling enables the determination of the composite flux Vgtg [VgtVxgVtcag/(Vxg+Vtcag)], while assumptions on the exchange flux Vxg have to be made to extract Vtcag (Uffmann and Gruetter 2007; Lanz et al. 2012).

Additional information on the individual values of the glial TCA cycle rate and the glial exchange rate Vxg requires the measurement and mathematical modeling of the C3 enrichment curves, similar to what was previously shown in one-compartment brain metabolic modeling (Henry et al. 2006; Uffmann and Gruetter 2007). The slope of the initial part of the neuronal glutamate C3 turnover curve is indicative of the Vxn/Vtcan ratio. In a similar way, the turnover of glial glutamate C3 and its direct product glutamine C3 carries information on the Vxg/Vtcag ratio. The simultaneous measurement of the time course of the C4 and C3 positions of glutamate and glutamine is therefore a necessary condition to determine both TCA cycle fluxes with minimal assumptions. With infusion of 13C labeled acetate, the precision of the estimated glial metabolic fluxes is also expected to be higher than with 13C glucose, where label incorporation into the glutamate-glutamine cycle is heavily weighted by the strong activity of the neuronal TCA cycle.

In all previous 13C MRS studies using 13C-acetate infusion in rats, the 13C uptake curves of the labeling position C3 of glutamate and glutamine could not be determined directly in vivo, preventing the determination of the exchange rates Vxg and Vxn. In some studies, the metabolic fluxes were extracted from data acquired at metabolic steady-state (Patel et al. 2005), which allows only the determination of relative metabolic rates (ratios like VNT/Vtcan). Other studies measured the glutamate and glutamine C3 enrichments ex vivo in a separate group of animals, at limited time points (typically one or two) (Patel et al. 2010) or using coinfusion of 13C labeled glucose and acetate (Deelchand et al. 2009a), which results in a higher NMR signal with a complex isotopomer pattern, to which an extended metabolic modeling approach needs to be developed (Shestov et al. 2012). Finally, sequential infusion of 13C-labeled glucose and acetate in two different animal groups were undertaken with a common modeling (van Eijsden et al. 2010), where the steady-state enrichment following [2-13C]acetate infusion was used as a constraint for the modeling of the [U-13C]glucose dynamic data.

The difficulty of acquiring dynamic labeling data directly using 13C-acetate infusion is linked to the predominant glial metabolism of acetate and the large inflow of unlabeled carbons through the dominating neuronal TCA cycle, which results in a strong dilution of the labeling in glutamate and glutamine and thus to a reduction of the measured 13C signal. Not surprisingly, most in vivo 13C-acetate brain studies were thus performed with indirect detected 13C NMR using the related increased sensitivity (Deelchand et al. 2009b; Patel et al. 2010). However, if indirect 13C detection enables a significant gain in sensitivity by measuring the protons attached to the 13C nuclei, its intrinsically low spectral resolution often makes it impossible to distinguish between certain labeling positions, like the C3 resonances of glutamate and glutamine.

The aim of this study was to take advantage of the increased spectral resolution obtained at 14.1T (see Fig. 2a) to measure in vivo and separately the turnover of the C4 and C3 positions of glutamate and glutamine to assess neuroglial metabolism, using an infusion of [2-13C]acetate. A major objective was to determine the glial and neuronal transmitochondrial exchange rates Vxg and Vxn. A second aim was to use the high sensitivity of the turnover curves to determine for the first time the glial glutamate pool size in rat brain tissue. Finally, Monte Carlo simulations were used to assess the precision of the determined metabolic fluxes and further to investigate the evolution of this precision with changes in the experimental conditions (experiment duration, SNR, and temporal resolution).

Materials and methods

The metabolic modeling presented in this study is based on MRS data previously acquired with a newly developed full signal intensity 1H-[13C] NMR sequence (Xin et al. 2010). For completeness sake, the animal preparation and NMR acquisition protocols are briefly described below.

Animal preparation

All animal experiments were approved by the veterinary authorities of the Canton of Vaud and were performed in accordance with their guidelines. The experiments were performed by licensed investigators. Six healthy male Sprague–Dawley rats (263 ± 19 g, mean ± standard deviation, Charles River Laboratories, L'Arbresle, France) were fasted overnight (15–16 h), with free access to water before the studies. Animals were intubated and ventilated with 2% isoflurane during the surgery. Both femoral veins were catheterized for continuous infusion of α-chloralose (Fisher Scientific, Pittsburgh, PA, USA) and 99% enriched [2-13C]sodium acetate (Sigma-Aldrich, St. Louis, MO, USA). One femoral artery was cannulated for blood sampling. After preparation, anesthesia was achieved by an 80 mg/kg initial bolus of α-chloralose, followed by continuous infusion at a rate of ~26.7 mg/kg/h. The animal was placed in a homemade holder and the head was stereotaxically fixed. Respiration rate and blood pressure were continuously monitored (SA Instruments Inc., Stony Brook, NY, USA ). Body temperature was measured by a rectal thermosensor and maintained at 38.0 ± 0.5°C by circulating heated water. A variable bolus of 3M 99% enriched [2-13C]sodium acetate (pH = 6) was given over two consecutive 5-min periods, with rates of 1.8 mmol/min/kg and 1.1 mmol/min/kg, respectively, and then a continuous rate of 0.3 mmol/min/kg was applied. The infused volume of acetate solution was ~5 mL in total. Arterial blood (200 μL) was sampled approximately every 30 min for monitoring blood gases (pCO2 = 39 ± 2 mm Hg, pO2 > 100 mm Hg), pH (7.41 ± 0.03), and the analysis of plasma acetate concentration and isotopic enrichment, measured with high-resolution NMR spectroscopy (Xin et al. 2010). An aliquot of arterial blood was immediately centrifuged and stored in a nearby −80°C freezer for subsequent processing. The total amount of blood withdrawn was below 10% of the total blood volume of the rat.

In vivo 13C MRS acquisition

All experiments were carried out on an animal magnetic resonance imaging system (Varian, Palo Alto, CA, USA) interfaced to a 14.1 T, 26 cm, horizontal-bore magnet (Magnex Scientific, Oxford, UK) with actively shielded gradients (12 cm inner diameter, 400 mT/m in 120 μs). A homemade 13 mm diameter geometrically decoupled quadrature 1H surface coil with a 10 mm diameter single-loop linear 13C coil was used as both transmitter and receiver. Fast spin-echo images (effective TE = 45 ms, echo train length = 8, pulse repetition time = 2.5 s, number of transitions = 2, slice thickness = 1 mm, field of view = 30 × 30 mm2, matrix = 256 × 256) were acquired for positioning of the volume of interest. Localized 1H{13C} spectra were acquired from a volume of 144 μL (8 × 3 × 6 mm3) centered in cerebral cortex of the rat brain. To optimize the magnetic field homogeneity in the volume of interest, an echo-planar imaging version of FASTMAP (Gruetter and Tkac 2000) was used to adjust all first- and second-order shims, which achieved a full width at half maximum of the water signal of 20–22 Hz in vivo. During 150 min of 99% enriched [2-13C]sodium acetate infusion, 13C enrichment (GluC4, GlnC4, GluC3, GlnC3, AceC2) and total concentration of glutamate, glutamine, and acetate were acquired using the SPECIAL-BISEP 1H{13C} NMR sequence. For a detailed description of this pulse sequence and the related spectral quantification, we refer the reader to our previously published work (Xin et al. 2010).

Metabolic modeling

Metabolic modeling was developed based on the compartmentalized neurotransmitter approach (Gruetter et al. 2001; Sibson et al. 2001). Brain tissue is mainly composed of glial and neuronal cells. It is now well established that glial cells are actively involved in glutamate neurotransmission, for example, through the uptake of the major excitatory neurotransmitter glutamate from the synaptic cleft (Arriza et al. 1994; Rothstein et al. 1996; Hertz 2011). The model therefore consists of two main metabolic compartments corresponding to each type of cell. Each compartment consists of the respective TCA cycle and both compartments are linked by the glutamate-glutamine cycle, responsible for the neurotransmission.

Acetate has the particularity to be metabolized almost purely in astrocytes (glial compartment) (Badar-Goffer et al. 1990; Hassel et al. 1995; Waniewski and Martin 1998; Lebon et al. 2002). As a consequence, the inflow of new 13C label from the substrate is occurring through the glial TCA cycle. The neuronal TCA cycle provides unlabeled carbons originating from neuronal pyruvate metabolism to the glutamate-glutamine cycle. However, 13C flow from the carbon position 4 of glutamate to the position 3 occurs both in the glial and neuronal compartment (see Appendix and Fig. 1b). The resulting model is presented in Fig. 1a. To illustrate how label is transferred within a molecule in the TCA cycle, we added the detailed scheme in Fig. 1b. 13C from [2-13C]acetate enters the glial TCA cycle at the position 4 of citrate. In the first turn of the TCA cycle, 13C-reaches the position 4 of 2-oxoglutarate with a total net flux Kdil(Vg+VPC) (Appendix, eqn (10)), where Kdil represents the affinity of glial metabolism to acetate. Kdil was fixed to 0.76, as previously found in 13C in vivo brain studies using [1,6-13C2] glucose infusion (Duarte et al. 2011). Similarly, in a previous 13C-acetate infusion study (Deelchand et al. 2009b), it was estimated that about 80% of acetyl-CoA entering the glial TCA cycle is synthesized from [2-13C]acetate, while the remaining 20% is synthesized from unlabeled glucose, in similar physiological conditions. 2-oxoglutarate exchanges label with cytosolic glutamate. This transmitochondrial label exchange, denoted by Vxg, transfers label from the carbon position 4 of 2-oxoglutarate to the position 4 of glutamate. As a result of the symmetry of the succinate molecule, the second turn of the TCA cycle brings half of the labeled carbons of the position 4 of 2-oxoglutarate to the position 3 of 2-oxoglutarate and half to the position 2 of 2-oxoglutarate, further eliminated as 13CO2. Through the transmitochondrial flux Vxg, [3-13C]glutamate is formed from [3-13C]2-oxoglutarate. Pyruvate carboxylase brings unlabeled 12C from pyruvate to oxaloacetate, which further dilutes the position C3 of glial glutamate. Pyruvate carboxylase is also responsible to maintain the balance of mass in the glial TCA cycle and compensates the label efflux from glutamine or contributes to a possible accumulation in the amino acids concentrations.

Figure 1.

(a) Schematic view of the two-compartment model used to describe the dynamic 13C MRS data acquired in the brain after [2-13C]acetate infusion. Acetate is transported across the blood brain barrier and is metabolized to acetyl-CoA, which enters the glial tricarboxylic acid (TCA) cycle at the level of citrate. Vg is the TCA cycle rate in the glia, Vtcan the TCA cycle rate in the neuronal compartment. The transmitochondrial exchange rates Vxg and Vxn model the exchange between amino acids and 2-oxoglutarate, in the glial and neuronal compartment, respectively. In the glial compartment, VPC represents the pyruvate carboxylase, responsible for anaplerosis. VGS is the glutamine synthesis flux and VGlu summarizes the transport of glutamine to the neurons and its conversion to glutamate. VNT is the apparent glutamatergic neurotransmission rate. Finally, efflux of labeling from the metabolic system occurs through the rate of glial glutamine loss Vefflux. (b) Detailed view of the label scrambling from [2-13C]acetate between the C4 and C3 positions of glutamate (Glu) in the glial and neuronal TCA cycle. 13C enters in the glial compartment, is incorporated in the glial TCA cycle and labels 2-oxoglutarate (OG) at the position C4 in the first turn of the TCA cycle. Through transmitochondrial transport, OG is in exchange with the cytosolic Glu which gets labeled at the position C4. After the second turn of the glial TCA cycle, OG C3 is labeled from OG C4. This labeling pathway is diluted by the action of pyruvate carboxylase, bringing unlabeled carbons from pyruvate to the position C3 of oxaloacetate. Through transmitochondrial, glial Glu C3 is labeled from OG C3. The neuronal TCA cycle acts similarly, with the difference that no 13C from acetate enters the first turn of the TCA cycle and that pyruvate carboxylase is absent from the neuronal compartment.

When glutamate and glutamine total concentrations are constant (metabolic steady-state), the mass balance is given by the following:

display math(1)
Steady-state of glial glutamate 
display math(2)
Steady-state of neuronal glutamate 
display math(3)
Steady-state of glutamine 

On the neuronal side, label entering the TCA cycle in the first turn from acetate is neglected, consistent with the glial-specific uptake of acetate. Nevertheless, once neuronal glutamate is sufficiently labeled by the action of the glutamate-glutamine cycle, the exchange between glutamate and 2-oxoglutarate through Vxn allows a labeling of the glutamate at position 3 from the glutamate at position 4 in the second turn of the TCA cycle, similar to what happens in the glial TCA cycle [Appendix, eqn (23)].

A system of linear differential equations was derived for this two-compartment model, assuming constant metabolic fluxes. As previously shown (Uffmann and Gruetter 2007), the temporal change in labeling of the TCA intermediates present in low concentration can be eliminated from the mathematical model without modifying the labeling dynamics of glutamate, resulting in a 6-pools model (Glu4g, Glu3g, Gln4, Gln3, Glu4n, Glu3n). The detailed derivation of the labeling equations is provided in the appendix.

The NMR-measured brain AceC2 enrichment was fitted by an exponential function multiplied with a linear function, to take into account the slow increase in AceC2 fractional enrichment (FE) in the later part of the experiment (see Fig. 2b). The fitted AceC2 curve was used as direct input function for the metabolic system. The time courses of total glutamate and glutamine were fitted with a linear function and used in the modeling as constraints in the mass balance equations. The two-compartment model was therefore adapted to include an increased mass flow through pyruvate carboxylase in the glial compartment (see Appendix). In practice, using the measured accumulation rate in glutamate (inline image) and in glutamine (inline image), the following mass balance equations were set as new constraints in the model:

Figure 2.

(a) Example of in vivo edited 1H-[13C] MRS spectrum acquired at 14.1T in a 144 μL voxel centered in cerebral cortex of a rat. The data were averaged over 45 min, about 105 min after the beginning of the [2–13C]acetate infusion. This spectrum illustrates the higher spectral resolution achieved at high magnetic field, enabling the separate quantification of AceC2, GluC4, GlnC4, GluC3, and GlnC3. See (Xin et al. 2010) for details on this MRS acquisition method. (b) Fit of the model presented in figure 1 to the time courses of fractional enrichment (FE) of glutamate and glutamine positions C4 and C3, averaged over six rats, using the measured brain AceC2 as input function. Glutamate enrichment curves represent the sum of the glial and neuronal glutamate pools, while the glutamine enrichment curves are modeled as purely glial (see 'Discussion'). AceC2 was smoothed by fitting it with a function of the type inline image to take into account the slow increase in FE measured in the second part of the curve.

display math(4)
display math(5)

where it is assumed that accumulation of glutamate and glutamine takes place in the respective larger compartment (neuronal compartment for glutamate and glial compartment for glutamine) (Storm-Mathisen et al. 1992).

With these constraints, the metabolic system is characterized by 6 independent fluxes (Vg, Vxg, VNT, Vtcan, Vxn, VPC).

The model was developed using Matlab (MathWorks, Natick, MA, USA). The model was fitted to the measured turnover curves, using a standard built-in ordinary differential equation solver and a modified Levenberg-Marquardt non-linear regression method. The fitting procedure was weighted with the square root of the inverse of the variance of the experimental noise, in order to take into account the different precisions in the measurement of the 4 turnover curves.

Glial glutamate fraction

In two-compartment modeling of brain metabolism, the glial and neuronal glutamate pools are linked to their respective TCA cycle and are therefore labeled differently. However, the proportion of the measured total glutamate which is located in the glial compartment cannot be assessed directly from 1H MRS. Usually, this concentration is assumed as a fraction of the total measured glutamate (between 1.5% (Patel et al. 2010) and 14% (Gruetter et al. 2001)), or fixed to a certain concentration (between 0.2 and 1.25 μmol/g (Sibson et al. 2001)).

Since 13C from acetate enters through the glial TCA cycle, the turnover curves are expected to be especially sensitive to glial parameters. Furthermore, the glial glutamate pool is the labeling precursor of glutamine. The early glutamate FE time points are thus expected to reflect mainly the glial component of glutamate, before the large neuronal contribution starts to dominate.

The fit of the experimental data was therefore repeated for a range of glial glutamate concentrations varying between 0.08 and 1.5 μmol/g. The weighted residual sum of squares of the fit was then calculated for each of the assumed glial concentrations. The lowest fit residual was selected as an estimate of the glial glutamate concentration in the considered brain region. For the other parts of our study, the glial glutamate pool size was then fixed to this optimized value.

Influence of the experimental conditions on the flux precision

To evaluate the effect of the experiment duration, the temporal resolution and the noise level of the turnover curves on the precision of the fluxes, an extended Monte Carlo analysis was undertaken on synthetic turnover curves. Artificial GluC4, GluC3, GlnC4, and GlnC3 FE time courses were generated with the differential system characterizing the model, using the flux values and metabolite concentrations obtained on the experimental data (Vg = 0.27, Vxg = 0.17, VNT = 0.15, Vtcan = 0.37, Vxn = 0.46, VPC = 0.087 μmol/g/min, [Gln] = 3.4 μmol/g and [Glu] = 11.5 μmol/g, from which 0.6 μmol/g was assumed to be in the glial compartment). A characteristic Gaussian noise of standard deviation σ = 0.05 μmol/g and σ = 0.10 μmol/g was added to the C4 and C3 turnover curves, respectively, as measured from the experimental data (Xin et al. 2010). A typical experiment duration of 150 min and a temporal resolution of 5 min were assumed as standard conditions.

Starting from these initial conditions, different experimental conditions were simulated by generating the GluC4, GluC3, GlnC4, and GlnC3 turnover curves varying either the length of the experiment (from 60 to 450 min), the time resolution (from 1.5 to 30 min) or by varying the noise level (from 0.2 to 5 times the original noise).

These sets of turnover curves were then fitted with the neuroglial metabolic model to obtain the best fit values for Vg, Vxg, VNT, Vtcan, Vxn, and VPC, using the same minimization procedure as for the experimental data.

Statistical analysis

The standard deviation of the fitted flux values reported in this study were obtained from Monte Carlo simulations, based on fits of at least 100 artificial data (Mason and Rothman 2004). These data are synthetic GluC4, GluC3, GlnC4, and GlnC3 enrichment time courses, generated with the flux values obtained with the best fit, to which a gaussian noise of same variance σ2 than the corresponding experimental turnover curves was added. The initial values of the fluxes were taken randomly between 0 and 1 μmol/g/min. The 95% confidence interval of the optimized glial glutamate concentration was calculated directly from the covariance matrix of the adjusted parameters obtained from the non-linear regression.

Results

To determine the precursor isotopic enrichment, plasma samples were measured with high-resolution NMR spectroscopy. The isotopic enrichment of AceC2 in blood reached 95% within 5 min after starting the infusion of [2-13C]sodium acetate and was stable at around 90% during the whole experiment. The concentration of plasma acetate during the experiment was 9 ± 3 mM.

From the analysis of the unedited 1H spectra and 13C-edited 1H spectra (64 averages), total concentration (12C + 13C) and the concentration of 13C-labeled acetate and metabolites were obtained. The average concentrations obtained on the six animals were [Gln] = 3.4 μmol/g and [Glu] = 11.5 μmol/g.

The FE of brain acetate C2, used as input function, was reaching a first step at 80% after 15 min. After this first quick increase in FE, the enrichment of acetate C2 was linearly increasing to about 90% after 150 min.

During the infusion of sodium acetate, glutamate, and glutamine total concentrations were increasing with a rate of 0.018 and 0.004 μmol/g/min, respectively. The two-compartment model was therefore adapted to include an increased mass flow through pyruvate carboxylase in the glial compartment.

To determine the metabolic fluxes from the 13C time courses, the two-compartment model presented in Fig. 1 was fitted to the FE turnover curves of the C4 and C3 positions of glutamate and glutamine (Fig. 2b) by adjusting the metabolic fluxes. The values of the determined metabolic fluxes are summarized in Table 1. Using brain acetate FE as input function, the model was able to accurately describe the measured turnover curves (R2 > 0.99). The glutamine labeling positions were the first to be labeled, consistent with the dominant glial metabolism of acetate, since most glutamate is located in the neuronal compartment (Storm-Mathisen et al. 1992), whereas astrocytes contain most of the glutamine. The C4 positions were more enriched both in glutamate and in glutamine. The maximal FE reached by GlnC4 at the end of the experiment was 34%, while GluC3, the strongest diluted labeling position measured in this study, reached only 12%. Glutamine had a larger difference between the enrichments of C4 and C3 than glutamate, indicating that the glial-specific pyruvate carboxylase, diluting specifically the position C3, had a substantial activity compared with the glutamatergic neurotransmission rate.

Table 1. Determined metabolic fluxes (μmol/g/min) with reference to the model shown in figure 1. The errors were determined by Monte Carlo simulation, based on 500 artificial data sets, using experimentally determined noise levels for the synthetic glutamate and glutamine enrichment curves
Adjusted metabolic fluxes (in μmol/g/min)
V g V x g V PC V NT V tca n V x n
0.27 ± 0.020.17 ± 0.020.087 ± 0.0120.15 ± 0.010.37 ± 0.060.46 ± 0.05
Derived metabolic fluxes (in μmol/g/min)
V GS V tca g V efflux V Glu   
0.24 ± 0.020.36 ± 0.030.065 ± 0.0180.17 ± 0.01  

An important factor in determining the metabolic fluxes is the glial glutamate concentration. To estimate its concentration, we varied the pool size of glial glutamate from 0.08 to 1.5 μmol/g and analyzed its effect on the weighted residual sum of squares of the fit (Fig. 3). It presents an optimum for a glial glutamate concentration of 0.6 ± 0.1 μmol/g. A 95% confidence interval was extracted from the fit statistics and places [Glug] in the range between 0.36 and 0.82 μmol/g.

Figure 3.

Evolution of the residual sum of squares with the assumed glial glutamate concentration. The fit error function was scaled with respect to the best fit residual sum of squares, which was found for a glial glutamate concentration of 0.6 μmol/g. Mathematically, this curve represents an orthogonal projection of the residual sum of squares function from the parameter space on the one-dimensional subspace of the glial glutamate concentration. A 95% confidence interval was estimated from the covariance matrix of the regression when adding glial glutamate concentration as a free parameter.

To determine how the precision of the metabolic fluxes depends on experimental conditions, we simulated the effect of experiment duration on the standard deviation of Vg, Vxg, VNT, Vtcan, Vxn, and VPC when varying the measurement duration, from 60 to 450 min, and keeping a temporal resolution of 5 min and an experimentally determined standard noise level of 0.05 μmol/g and 0.1 μmol/g for the C4 and C3 turnover curves, respectively (Fig. 4a). When data were measured during less than 150 min, the neuronal flux across the mitochondrial membrane, Vxn, was not reliably determined anymore. The precision of Vtcan was reduced, evident from an increase of its relative error to 60% for 80 min of acquisition. Above the 150 min threshold, all the fitted fluxes presented a coefficient of variation below 25%. The glial TCA cycle flux Vg and the neurotransmission flux VNT were throughout well determined (coefficient of variation of about 10%), even when a shorter experiment duration of less than 100 min was used.

Figure 4.

Analysis of the precision in the determination of the glial (Vg, Vxg, and VPC) and neuronal (Vtcan, Vxn, and VNT) metabolic fluxes as a function of the noise level, duration, and temporal resolution of the acquired labeling data. (a) Variation of the relative standard deviation of the 6 fitted metabolic fluxes with the experiment duration. This simulation was based on the fit of the 4 turnover curves (GluC4, GlnC4, GluC3, GlnC3), with a temporal resolution Δt of 5 min and a typical noise level of σC4 = 0.05 μmol/g for the C4 positions and σC3 = 0.1 μmol/g for the C3 positions of glutamate and glutamine. (b) Variation of the relative standard deviation of the 6 fitted metabolic fluxes with the temporal resolution. This simulation was based on the fit of the 4 turnover curves (GluC4, GlnC4, GluC3, GlnC3), with an experimental duration Texp of 150 min and a typical noise level of σC4 = 0.05 μmol/g for the C4 positions and σC3 = 0.1 μmol/g for the C3 positions of glutamate and glutamine. (c) Variation of the relative standard deviation of the 6 fitted metabolic fluxes with the noise level. This simulation was based on the fit of the 4 turnover curves (GluC4, GlnC4, GluC3, GlnC3), with an experimental duration Texp of 150 min and a temporal resolution Δt of 5 min. The noise level (in μmol/g) is equal to the noise factor multiplied with a standard noise of σC4 = 0.05 μmol/g for the C4 positions and σC3 = 0.1 μmol/g for the C3 positions of glutamate and glutamine.

When evaluating the influence of temporal resolution at a fixed experiment duration of 150 min and a noise level of 0.05 μmol/g and 0.1 μmol/g for the C4 and C3 turnover curves, respectively, we noted that the estimated value for the neuronal transmitochondrial flux Vxn diverged for a temporal resolution lower than one measurement every 15 min (Fig. 4b). For the other metabolic fluxes, the reduction in temporal resolution resulted in a progressive deterioration of their precision with a maximal coefficient of variation of 55% for the glial transmitochondrial flux Vxg at a temporal resolution of 30 min.

The effect of the noise level of the turnover curves was analyzed by multiplying the experimentally determined noise level (0.05 μmol/g for the C4 positions and 0.1 μmol/g for the C3 positions) by a noise factor N, varying between 0.2 and 5 (Fig. 4c). The transmitochondrial fluxes Vxg and Vxn were the most sensitive to the noise level. With more than a twofold increase in the noise level, the relative standard deviation of Vxg and Vxn became higher than 100%, which made their determination unreliable (Fig. 4c). Vxn diverged already for a noise factor of 1.5 (0.075 μmol/g for the C4 positions and 0.15 μmol/g for the C3 positions). The glial and neuronal TCA cycle fluxes and the neurotransmission flux as well as the pyruvate carboxylase flux were progressively losing precision with the increase of the experimental noise, without presenting a critical point above which their uncertainties would suddenly increase. As observed for the experiment duration and the temporal resolution (see above), the glial TCA flux Vg and the neurotransmission flux VNT were the most reliable fluxes determined with two-compartment modeling when infusing [2–13C]acetate, with errors below 70% and 40%, respectively, for a noise factor of 5 (0.25 μmol/g for the C4 positions and 0.5 μmol/g for the C3 positions).

Discussion

In this study, we extended the sensitivity of detection and temporal resolution of the 13C turnover curves of glutamate and glutamine under infusion of [2-13C]acetate using a recently developed 1H-[13C] MRS localized detection method at high magnetic field (14.1T). This detection method takes advantage of the higher spin polarization and spectral resolution obtained at 14.1T as well as the stronger gyromagnetic ratio of 1H, as compared to 13C. This technique enabled the measurement of the 13C turnover curves of glutamate and glutamine at position C4 and C3 as well as of acetate at position C2 with a temporal resolution of 4.5 min in a 144 μL voxel. The position C3 of glutamate and glutamine could be measured separately and used in the metabolic modeling for the first time in an in vivo 13C-acetate infusion experiment. From the two-compartment modeling of these uptake curves, a precise determination of the glial and neuronal TCA cycle fluxes, glial pyruvate carboxylase, as well as the apparent neurotransmission flux characterizing the neuroglial glutamate-glutamine exchange was possible. Moreover, based on the C3 enrichment curves, we could extend the metabolic modeling to measure separately the glial and neuronal transmitochondrial fluxes. Monte Carlo analysis demonstrated that the 6 adjusted metabolic fluxes are determined with high precision, with a maximal error of 16% for the neuronal TCA cycle flux (Vtcan). In addition, we estimated a glial glutamate concentration of 0.6 μmol/g by minimization of the weighted residual sum of squares when varying the neuroglial distribution of the total measured glutamate.

Metabolic fluxes

The measurement of the C3 positions of glutamate and glutamine is particularly challenging in 13C-acetate infusion experiments, since the large dilution of glutamate through the neuronal TCA cycle reduces considerably the FE of the turnover curves, compared to glucose infusion experiments. In the case of the C3 positions, a maximum FE of 20% was reached for GlnC3 at the end of the acquisition. This overall lower 13C signal is a strong argument toward the use of the more sensitive indirect 13C detection (de Graaf et al. 2003b). However, the lower spectral resolution of this method makes the separation of glutamate and glutamine C3 peaks difficult. Nevertheless, the higher magnetic fields NMR scanners as well as the improved shimming methodologies available today enable a reliable separation of these peaks (Xin et al. 2010), with a temporal resolution of about 4.5 min.

Glial Vg was 0.27 ± 0.02 μmol/g/min, which corresponds to more than half of the neuronal TCA cycle rate, supporting the significant role of glial resting oxidative metabolism (Danbolt 2001; Dienel 2011; Hertz 2011).

One goal of this study was to assess the transmitochondrial rate Vx, representing the exchange between cytosolic glutamate and 2-oxoglutarate in the TCA cycle, located in the mitochondrial matrix. This exchange is principally mediated by the malate-aspartate shuttle (Gruetter et al. 2001). Vx is in fact a composite representation of glutamate dehydrogenase, aspartate transaminase and transport across the membrane of the mitochondria. In previous studies, Vx was frequently assumed to be much larger than the TCA cycle rate Vtca (Hyder et al. 1996; Sibson et al. 1998; de Graaf et al. 2003a), as suggested by early results (Mason et al. 1992, 1995). This assumption leads to the fact that the labeling patterns of 2-oxoglutarate and glutamate follow each other without time lag, in both glial and neuronal compartments, which allows for simplification in the metabolic model but may lead to underestimation of the TCA cycle fluxes (Uffmann and Gruetter 2007).

The determination of the transmitochondrial fluxes requires the measurement of the C3 turnover curves of glutamate and glutamine, which are especially sensitive to the transmitochondrial fluxes in the early part of the experiment (Henry et al. 2006). The measurement of the C4 positions only allows the assessment of the composite flux Vgt (inline image)(Uffmann and Gruetter 2007), while assumptions have to be made on the value of the respective Vx. Several studies showed that the transmitochondrial flux is in the same order of magnitude than Vtca (Gruetter et al. 2001; Choi et al. 2002; Henry et al. 2002; Oz et al. 2004; Duarte et al. 2011). However, Vx was typically measured with a relatively poor precision, on the order of 30% or more. In this study, we could determine both glial and neuronal transmitochondrial fluxes Vxg and Vxn with a precision of < 12%. Both fluxes were on the same order of magnitude as the corresponding TCA cycle fluxes. This result is in very good agreement with previous in vivo 13C glucose infusion study (Duarte et al. 2011) and is supported by recent 13C glucose labeling studies in cultured astrocytes (Amaral et al. 2011) and in vivo 13C-acetate MRS studies using dynamic polarization techniques (Mishkovsky et al. 2012). The use of the glial-specific 13C-acetate substrate enabled the determination of Vxg with an increased precision, compared to labeled glucose infusion studies.

In the glial compartment, the measured transmitochondrial flux Vxg is significantly smaller than the TCA cycle flux VTCAg (VTCAg = Vg+VPC is the pyruvate dehydrogenase flux in the glial compartment), coherent with previous 13C glucose labeling studies (Duarte et al. 2011). The glial malate-aspartate shuttle represented by Vxg participates to the cytosolic NADH/NAD+ balance required for the glycolysis in the glial compartment (Hertz et al. 2007), which produces pyruvate, a TCA cycle substrate. This observation supports the fact that the glial TCA cycle is fueled in a significant proportion by substrates which do not require reducing equivalent transport, such as acetate and fatty acids (Hertz et al. 2007).

Interestingly, although acetate is not a substrate of the pyruvate carboxylation pathway, it was possible to determine a pyruvate carboxylase flux VPC = 0.087 ± 0.012 μmol/g/min. This was possible since pyruvate carboxylase dilutes specifically the position C3 of glial glutamate, while the position C4 remains unaffected (Fig. 1b). At steady-state, the FE of glutamine reaches the level of its direct precursor, glial glutamate. The effect of pyruvate carboxylase can be qualitatively observed by the C4 to C3 enrichment ratio being higher in glutamine than in glutamate at the end of the experiment. Although part of this difference could be explained by a higher Vx/Vtca ratio in the glial compartment than in the neuronal one, the metabolic model was unable to fully describe the dynamics of the 4 uptake curves without the inclusion of the pyruvate carboxylase flux (data not shown). VPC accounts for 37% of the rate of glutamine synthesis, a higher fraction than what has been recently reported in the human brain (Mason et al. 2007), but in good agreement with previous measurements in humans and in the anesthetized or awake rat brain (Gruetter et al. 2001; Sibson et al. 2001; Oz et al. 2004; Duarte et al. 2011). The value found for the pyruvate carboxylase flux under infusion of [2-13C2]acetate was 26% higher than the value found under [1,6-13C2]glucose infusion (Duarte et al. 2011), consistent with the slow increase of mass in the glutamate and glutamine pools when infusing sodium acetate.

Overall, the values found for the different fluxes are in very good agreement with the values found in previous [1,6-13C2]glucose infusion studies (Duarte et al. 2011) and with the values recently found using [1-11C]acetate infusion in positron emission studies in rats (Lanz et al. 2012) (Table 2). Compared to glucose infusion studies, fewer labeling curves (GluC4, GlnC4, GluC3, and GlnC3) were needed to achieve similar or better precision on the glial metabolic fluxes or the neurotransmission rate.

Table 2. Comparison of the determined metabolic fluxes (μmol/g/min) obtained infusing 13C-acetate, 13C-glucose (Duarte et al. 2011) or 11C-acetate (Lanz et al. 2012), a positron emitting radiotracer
Brain metabolic fluxes (in μmol/g/min) obtained with different labeled substrates
Substrate V g V x g V PC V gt g V NT V tca n V x n V gt n
  1. a

    (Duarte et al. 2011).

  2. b

    (Lanz et al. 2012).

[2-13C]acetate0.27 ± 0.020.17 ± 0.020.09 ± 0.010.17 ± 0.010.15 ± 0.010.37 ± 0.060.46 ± 0.050.21 ± 0.02
[1,6-13C2]glucosea0.23 ± 0.020.17 ± 0.060.07 ± 0.010.15 ± 0.020.12 ± 0.010.44 ± 0.010.76 ± 0.070.28 ± 0.01
[1-11C]acetateb0.14 ± 0.040.17 ± 0.10

Effect of glutamate and glutamine pool distribution

To determine the influence of differential distribution of glutamine (predominantly glial) and glutamate (predominantly neuronal), we analyzed the sensitivity of the glutamate and glutamine uptake curve to these assumptions. Replacing the glial glutamine and neuronal glutamine pools by a single kinetic compartment had a negligible effect on the dynamics of the turnover curves and, consequently, on the derived metabolic fluxes (data not shown). This can be understood by the fact that glutamine participates in only two biochemical reactions, namely glutamine synthesis in the glia (VGS) and the phosphate-activated glutaminase (PAG) in neurons, in contrast to glutamate. The large glial glutamine pool is the only precursor of the neuronal glutamine pool, which is only a small fraction of total glutamine (Storm-Mathisen et al. 1992). The labeling dynamics of neuronal glutamine is therefore much faster than glial glutamine and the neuronal pool is basically following the enrichment of its precursor, which results in very similar FEs in both glutamine pools.

It is well established that tissue glutamate in brain is unequally distributed between the neuronal and glial compartments (Storm-Mathisen et al. 1992). In early studies, the presence of two distinct glutamate pools was proposed from 14C labeling studies in mice (van den Berg and Garfinkel 1971), reporting a small glutamate pool with a concentration of 1.3 μmol/g and a large neuronal pool of 7 μmol/g. Using immunochemical methods (Ottersen et al. 1992; Storm-Mathisen et al. 1992), it was found that most of glutamate is in the neuronal compartment, while glutamine is mostly located in astrocytes. A glutamate to glutamine ratio of 0.2 in astrocytes was reported, which is in good agreement with the values found in our study, if all glutamine is assumed to be in the glial compartment (0.6 μmol/g for Glug with 3.4 μmol/g of Gln).

The dilution from pyruvate metabolism at the level of glial acetyl-CoA, represented by Kdil [Fig. 1a and Appendix, eqns (8) and (9)], could be theoretically extracted from the steady-state enrichment of the glutamine labeling positions. However, when fitting the model and including Kdil as free parameter, the value found for Kdil was subject to high uncertainty and was strongly correlated with the glial TCA cycle flux and transmitochondrial flux (data not shown). In the case of acetate infusion, Kdil is expected to be at least as high as the value found with glucose infusion [0.76 in (Duarte et al. 2011)], because of higher amount of available plasma acetate. A 10% increase in Kdil resulted in a decrease of 11% and 35% in Vg and Vxg, respectively, while all the other fluxes and the determined glial glutamate concentration were marginally affected (< 4%). The conclusions of this study are therefore not affected by the assumption on glial acetyl-CoA dilution.

The transport of acetate across the blood-brain barrier (BBB) may be rate-limiting, however, the acetate infusion of our experiments resulted in a step-wise increase in plasma acetate concentration to 9 mM, where transport across the BBB was shown not to be rate-limiting for metabolism (Deelchand et al. 2009b). Note that in this study, we used the NMR-measured brain acetate 13C enrichment as direct input to the metabolic system, which minimizes the impact of acetate transport on the metabolic flux determination.

The metabolic model used for [2-13C]acetate labeling studies is based on the assumption of the purely glial uptake and metabolism of acetate (Lebon et al. 2002; Deelchand et al. 2009b; Patel et al. 2010). At low plasma level, acetate is known to be transported primarily into glial cells (Waniewski and Martin 1998). At higher plasma acetate concentrations as used for in vivo studies, the passive diffusion of acetate through the cell membrane and its metabolism through acetate thiokinase both in the glial cells and the neurons could be possible. However, several previous 13C-acetate infusion studies showed evidences for the predominantly glial uptake and metabolism, even at higher plasma acetate levels (Badar-Goffer et al. 1990; Hassel et al. 1995). At the end of our labeling experiment, the FE of glutamate C4 reached 15%, while glutamine C4 FE was about 35%. Since about 90% of glutamate is located in the neuronal compartment, the glutamate C4 enrichment curve represents essentially the neuronal glutamate C4 pool. The large difference between the FE of neuronal glutamate and its precursor in the glutamate/glutamine cycle indicates a strong dilution of neuronal glutamate through transmitochondrial exchange with the neuronal TCA cycle and supports the fact that neurons metabolize predominantly other substrates than acetate, even at relatively high plasma acetate concentrations. Moreover, based on previously measured metabolic fluxes (Duarte et al. 2011) and the FE of Glu C4 and Gln C4 obtained in the near steady-state conditions at the end of the experiment, the FE of the neuronal acetyl-CoA was estimated to be lower than 5%, which confirms that in our experimental conditions, acetate is not or marginally used as substrate by neurons.

When infusing [2-13C]sodium acetate, we observed an increase of about 20% over 3 hours both in the total glutamate and total glutamine concentrations, consistent with previous in vivo studies (Chowdhury et al. 2007; Deelchand et al. 2009b; Patel et al. 2010), which could be related to an osmotic effect induced by the infusion of sodium acetate, as previously discussed (Deelchand et al. 2009b; Patel et al. 2010). The metabolic model was adapted to take into account the increase in pool size by assuming that new carbon chains are synthesized via pyruvate carboxylase. Note that the measured accumulation of glutamate and glutamine over 150 min, although statistically significant, was modest (24% for glutamate and 16% for glutamine) and did not affect significantly the dynamics of brain metabolism, since the measured fluxes are in good agreement with the metabolic fluxes obtained with 13C labeled glucose infusion, where no significant change in amino acid concentration was measured (Table 2). Brain metabolic fluxes determined with two-compartment modeling, and in particular the transmitochondrial fluxes Vxg and Vxn, are thus largely independent on the substrate used.

To determine the consequence of the mass increase in glutamate and glutamine on the modeling results, we adjusted the metabolic model to the measured curve, assuming constant glutamate and glutamine total concentrations, equal to their respective average value over the entire infusion time. With this assumption, the neuronal TCA cycle flux was 20% smaller, while Vxg and VPC were, respectively, increased by 40% and decreased by 50%. The changes in the remaining metabolic fluxes were within 10%. As a consequence, the increase in glutamate and glutamine pool sizes appears to be an important aspect to take into account in the metabolic model to avoid biased determination of the metabolic fluxes.

Recent studies indicated that astrocytic energy metabolism is more intense as previously believed, suggesting a major involvement of glial cells in functional activities. 14C-acetate autoradiography experiments showed that the TCA cycle activity increases in astrocytes during acoustic or visual stimulations (Dienel and Hertz 2001; Cruz et al. 2005), indicating that astrocytic respiration can be up-regulated by signaling mechanisms. The glial-specific pyruvate carboxylation increases during some but not all stimulations, while pathological conditions might also activate glial oxidative demand (Hertz et al. 2007). It remains also unclear if glial glutamate oxidation changes during activation in vivo. There are therefore many motivations to develop quantitative in vivo metabolic studies such as the presented 13C-acetate MRS approach, to better understand the particular role of astrocytic metabolism in brain function.

Conclusion

We conclude that when using [2-13C]acetate, two-compartment modeling of the C4 and C3 labeling curves of glutamate and glutamine obtained with 1H-[13C] MRS enables the measurement of mitochondrial metabolism both in the glial and neuronal compartment in vivo. In particular, the predominant glial uptake of acetate allows a precise determination of the glial metabolic fluxes and the apparent glutamatergic neurotransmission rate. In this study, the transmitochondrial exchange rates between glutamate and 2-oxoglutarate were determined separately for the glial and neuronal compartments, based on the analysis of the C3 uptake curves of glutamate and glutamine measurable at high magnetic field. Moreover, we provided the first in vivo estimation of the glial glutamate pool size in the rat brain tissue. 13C-acetate infusion studies are therefore an attractive alternative to the more widely used 13C-glucose infusions for studying pathological or physiological alterations of glial oxidative metabolism.

Acknowledgements

This study was supported by Swiss National Science Foundation (grant 131087) and by Centre d'Imagerie BioMédicale (CIBM) of the UNIL, UNIGE, HUG, CHUV, EPFL, and the Leenaards and Jeantet Foundations. The authors declare no conflict of interest.

Appendix

The mathematical model of compartmentalized cerebral metabolism was adapted from (Gruetter et al. 2001), where the reader can find an exhaustive description of the model.

The metabolic pools and fluxes of the considered model are represented in Fig 1. Metabolic steady-state was assumed for the metabolic fluxes (constant) and the metabolic pools except glutamine and the major neuronal glutamate pools, which total concentration was slightly increasing over time, as measured by 1H MRS. The in vivo measured mean glutamate and glutamine concentrations were 11.5 and 3.4 μmol/g, respectively. As determined in this study, 0.6 μmol/g of glutamate was contained in the glial compartment, while all the glutamine was assumed to be glial.

The non-steady-state conditions for glutamine and neuronal glutamate was modeled using the following mass-balance equations. dGlu/dt and dGln/dt are the slopes of the increase in total glutamate and total glutamine concentrations, respectively, as measured by 1H MRS:

display math(6)
display math(7)

The mass balance relations shown in eqns (6) and (7) were further used as constraints in the metabolic model, i.e. VNT and VPC are adjusted in the fitting of the 13C turnover curves, while Vefflux, VGlu, and VGS are then determined from eqns (6) and (7).

Transport of acetate across the blood–brain barrier was not modeled, as brain acetate FE was directly measured with 1H-[13C] MRS and used as input function for the model.

Glial compartment

Pyruvate and acetate compete for the generation of acetyl-CoA:

The position 2 of glial acetyl-CoA is labeled as follows:

display math(8)

where VAce is the net metabolic flux of acetate to acetyl-CoA and inline image is the dilution flux from the metabolism of unlabeled pyruvate in the glial compartment. Working with the small pool approximation for glial acetyl-CoA (Uffmann and Gruetter 2007) (inline image very early compared with the large glutamate pool), we obtain the following relationship between the fractional enrichment of inline image and plasma Ace2:

display math(9)

Kdil represents the affinity of glial cells to acetate as metabolic fuel. It was fixed to the value found with 13C NMR in a recent study (Duarte et al. 2011), Kdil = 0.76.

Further metabolism of acetate in the glial compartment is characterized by the glial TCA cycle flux Vg, the transmitochondrial exchange between 2-oxoglutarate and glutamate Vxg and pyruvate carboxylase VPC.

In the glial TCA cycle, the labeling of 2-oxoglutarate is given by the following equations:

display math(10)
display math(11)

The factor ½ appearing in eqn (11) is related to the fact that in each TCA cycle turn, half of the labeling from OG4g goes to OG3g and half of it goes to OG2g, because of the symmetry of the succinate molecule (Uffmann and Gruetter 2007). Similarly, half of the labeling from OG3g goes to OG2g and half of it comes back to OG3g.

The labeling of glial glutamate is given by the following equations:

display math(12)
display math(13)

Removing the (non-measurable) TCA cycle intermediates from the model

We made use of a simplification of the metabolic model by removing the TCA cycle intermediates from the labeling equations, as suggested in previous studies (Uffmann and Gruetter 2007; Duarte et al. 2011). This results in mathematical expressions which do not contain non-measurable metabolic pools, while the effect of the simplification on the determined metabolic fluxes is marginal.

By injecting in eqn (12) the expression of inline image isolated in eqn (10), we obtain the following:

display math(14)
display math(15)

In the small pool approximation, we assume that the increase in glutamate enriched carbons is much larger than the increase in 2-oxoglutarate 13C concentration, i.e. inline image. This approximation is as much better that the time after the start of the infusion gets larger, since the small pool reaches its labeling steady-state faster than the larger pool. The small pool approximation leads to the following expression for the labeling of glial glutamate C4, in which the TCA cycle intermediate pools vanished:

display math(16)

Using the same strategy for glial glutamate C3, we obtain the following expression:

display math(17)

Neuronal compartment

Acetate is considered not to be metabolized in the neuronal compartment. Pyruvate carboxylase is also absent in the neurons. 13C is therefore entering the neuronal TCA cycle through its interaction with the neuronal glutamate pool. In the neuronal compartment, the labeling of the TCA intermediates and the neuronal glutamate pools is given by:

display math(18)
display math(19)
display math(20)
display math(21)

Using the same approach as for the glial glutamate pools, the TCA cycle intermediates can be eliminated from the differential equations describing the labeling of the neuronal glutamate pools:

display math(22)
display math(23)

Glutamate-glutamine cycle

The glutamate-glutamine cycle comprises the glutamine synthesis in the glial compartment, the transfer of glutamine to neurons where it is converted back to glutamate and stored in the large neuronal glutamate pool and finally the glutamatergic neurotransmission where glutamate is released from the neurons and taken up by the glial compartment. The labeling equations of glutamine, modeled as a single large glial pool, are as follows:

display math(24)
display math(25)

where Vefflux accounts for the label loss through glutamine dilution. VGS, Vefflux, and VGlu are modeled to take into account the non-steady-state concentrations of glutamate and glutamine measured under sodium acetate infusion. They are coupled withVNT by the eqn (6) and (7) where the increase of glutamate and glutamine, measured by 1H MRS is used in the mass balance equations. Therefore, when fitting the 13C enrichment curves, only one degree of freedom is adjusted for the glutamate-glutamine cycle, namely VNT, while VGS, Vefflux and VGlu are determined from the mass balance equations.

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