Mathematical modeling of (13)C label incorporation of the TCA cycle: the concept of composite precursor function

How Energy Metabolism Supports Cerebral Function: Insights from 13C Magnetic Resonance Studies In vivo

Cerebral function is associated with exceptionally high metabolic activity, and requires continuous supply of oxygen and nutrients from the blood stream. Since the mid-twentieth century the idea that brain energy metabolism is coupled to neuronal activity has emerged, and a number of studies supported this hypothesis. Moreover, brain energy metabolism was demonstrated to be compartmentalized in neurons and astrocytes, and astrocytic glycolysis was proposed to serve the energetic demands of glutamatergic activity. Shedding light on the role of astrocytes in brain metabolism, the earlier picture of astrocytes being restricted to a scaffold-associated function in the brain is now out of date. With the development and optimization of non-invasive techniques, such as nuclear magnetic resonance spectroscopy (MRS), several groups have worked on assessing cerebral metabolism in vivo. In this context, ¹H MRS has allowed the measurements of energy metabolism-related compounds, whose concentrations can vary under different brain activation states. ¹H-[¹³C] MRS, i.e., indirect detection of signals from ¹³C-coupled ¹H, together with infusion of ¹³C-enriched glucose has provided insights into the coupling between neurotransmission and glucose oxidation. Although these techniques tackle the coupling between neuronal activity and metabolism, they lack chemical specificity and fail in providing information on neuronal and glial metabolic pathways underlying those processes. Currently, the improvement of detection modalities (i.e., direct detection of ¹³C isotopomers), the progress in building adequate mathematical models along with the increase in magnetic field strength now available render possible detailed compartmentalized metabolic flux characterization. In particular, direct ¹³C MRS offers more detailed dataset acquisitions and provides information on metabolic interactions between neurons and astrocytes, and their role in supporting neurotransmission. Here, we review state-of-the-art MR methods to study brain function and metabolism in vivo, and their contribution to the current understanding of how astrocytic energy metabolism supports glutamatergic activity and cerebral function. In this context, recent data suggests that astrocytic metabolism has been underestimated. Namely, the rate of oxidative metabolism in astrocytes is about half of that in neurons, and it can increase as much as the rate of neuronal metabolism in response to sensory stimulation.

Refined Analysis of Brain Energy Metabolism Using In Vivo Dynamic Enrichment of 13C Multiplets

Carbon-13 nuclear magnetic resonance spectroscopy in combination with the infusion of ¹³C-labeled precursors is a unique approach to study in vivo brain energy metabolism. Incorporating the maximum information available from in vivo localized ¹³C spectra is of importance to get broader knowledge on cerebral metabolic pathways. Metabolic rates can be quantitatively determined from the rate of ¹³C incorporation into amino acid neurotransmitters such as glutamate and glutamine using suitable mathematical models. The time course of multiplets arising from ¹³C-¹³C coupling between adjacent carbon atoms was expected to provide additional information for metabolic modeling leading to potential improvements in the estimation of metabolic parameters.

The aim of the present study was to extend two-compartment neuronal/glial modeling to include dynamics of ¹³C isotopomers available from fine structure multiplets in ¹³C spectra of glutamate and glutamine measured in vivo in rats brain at 14.1 T, termed bonded cumomer approach. Incorporating the labeling time courses of ¹³C multiplets of glutamate and glutamine resulted in elevated precision of the estimated fluxes in rat brain as well as reduced correlations between them.

Assessment of metabolic fluxes in the mouse brain in vivo using 1H-[13C] NMR spectroscopy at 14.1 Tesla

(13)C magnetic resonance spectroscopy (MRS) combined with the administration of (13)C labeled substrates uniquely allows to measure metabolic fluxes in vivo in the brain of humans and rats. The extension to mouse models may provide exclusive prospect for the investigation of models of human diseases. In the present study, the short-echo-time (TE) full-sensitivity (1)H-[(13)C] MRS sequence combined with high magnetic field (14.1 T) and infusion of [U-(13)C6] glucose was used to enhance the experimental sensitivity in vivo in the mouse brain and the (13)C turnover curves of glutamate C4, glutamine C4, glutamate+glutamine C3, aspartate C2, lactate C3, alanine C3, γ-aminobutyric acid C2, C3 and C4 were obtained. A one-compartment model was used to fit (13)C turnover curves and resulted in values of metabolic fluxes including the tricarboxylic acid (TCA) cycle flux VTCA (1.05 ± 0.04 μmol/g per minute), the exchange flux between 2-oxoglutarate and glutamate Vx (0.48 ± 0.02 μmol/g per minute), the glutamate-glutamine exchange rate V(gln) (0.20 ± 0.02 μmol/g per minute), the pyruvate dilution factor K(dil) (0.82 ± 0.01), and the ratio for the lactate conversion rate and the alanine conversion rate V(Lac)/V(Ala) (10 ± 2). This study opens the prospect of studying transgenic mouse models of brain pathologies.

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

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 (13) C NMR spectroscopy coupled with the infusion labeled glial-specific substrate, such as acetate. In this study, we infused alpha-chloralose anesthetized rats with [2-(13) C]acetate and followed the dynamics of the fractional enrichment (FE) in the positions C4 and C3 of glutamate and glutamine with high sensitivity, using (1) H-[(13) C] 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 (Vx (g) and Vx (n) ) 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. In this (13) C-acetate labeling study, we propose a refined two-compartment analysis of brain energy metabolism based on (13) C 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.

Metabolic Flux and Compartmentation Analysis in the Brain In vivo

Through significant developments and progresses in the last two decades, in vivo localized nuclear magnetic resonance spectroscopy (MRS) became a method of choice to probe brain metabolic pathways in a non-invasive way. Beside the measurement of the total concentration of more than 20 metabolites, (1)H MRS can be used to quantify the dynamics of substrate transport across the blood-brain barrier by varying the plasma substrate level. On the other hand, (13)C MRS with the infusion of (13)C-enriched substrates enables the characterization of brain oxidative metabolism and neurotransmission by incorporation of (13)C in the different carbon positions of amino acid neurotransmitters. The quantitative determination of the biochemical reactions involved in these processes requires the use of appropriate metabolic models, whose level of details is strongly related to the amount of data accessible with in vivo MRS. In the present work, we present the different steps involved in the elaboration of a mathematical model of a given brain metabolic process and its application to the experimental data in order to extract quantitative brain metabolic rates. We review the recent advances in the localized measurement of brain glucose transport and compartmentalized brain energy metabolism, and how these reveal mechanistic details on glial support to glutamatergic and GABAergic neurons.

In vivo enzymatic activity of acetylCoA synthetase in skeletal muscle revealed by (13)C turnover from hyperpolarized [1-(13)C]acetate to [1-(13)C]acetylcarnitine

BACKGROUND

Acetate metabolism in skeletal muscle is regulated by acetylCoA synthetase (ACS). The main function of ACS is to provide cells with acetylCoA, a key molecule for numerous metabolic pathways including fatty acid and cholesterol synthesis and the Krebs cycle.

METHODS

Hyperpolarized [1-(13)C]acetate prepared via dissolution dynamic nuclear polarization was injected intravenously at different concentrations into rats. The (13)C magnetic resonance signals of [1-(13)C]acetate and [1-(13)C]acetylcarnitine were recorded in vivo for 1min. The kinetic rate constants related to the transformation of acetate into acetylcarnitine were deduced from the 3s time resolution measurements using two approaches, either mathematical modeling or relative metabolite ratios.

RESULTS

Although separated by two biochemical transformations, a kinetic analysis of the (13)C label flow from [1-(13)C]acetate to [1-(13)C]acetylcarnitine led to a unique determination of the activity of ACS. The in vivo Michaelis constants for ACS were KM=0.35±0.13mM and Vmax=0.199±0.031μmol/g/min.

CONCLUSIONS

The conversion rates from hyperpolarized acetate into acetylcarnitine were quantified in vivo and, although separated by two enzymatic reactions, these rates uniquely defined the activity of ACS. The conversion rates associated with ACS were obtained using two analytical approaches, both methods yielding similar results.

GENERAL SIGNIFICANCE

This study demonstrates the feasibility of directly measuring ACS activity in vivo and, since the activity of ACS can be affected by various pathological states such as cancer or diabetes, the proposed method could be used to non-invasively probe metabolic signatures of ACS in diseased tissue.

Which prior knowledge? Quantification of in vivo brain 13C MR spectra following 13C glucose infusion using AMARES

The recent developments in high magnetic field 13C magnetic resonance spectroscopy with improved localization and shimming techniques have led to important gains in sensitivity and spectral resolution of 13C in vivo spectra in the rodent brain, enabling the separation of several 13C isotopomers of glutamate and glutamine. In this context, the assumptions used in spectral quantification might have a significant impact on the determination of the 13C concentrations and the related metabolic fluxes. In this study, the time domain spectral quantification algorithm AMARES (advanced method for accurate, robust and efficient spectral fitting) was applied to 13 C magnetic resonance spectroscopy spectra acquired in the rat brain at 9.4 T, following infusion of [1,6-(13)C2 ] glucose. Using both Monte Carlo simulations and in vivo data, the goal of this work was: (1) to validate the quantification of in vivo 13C isotopomers using AMARES; (2) to assess the impact of the prior knowledge on the quantification of in vivo 13C isotopomers using AMARES; (3) to compare AMARES and LCModel (linear combination of model spectra) for the quantification of in vivo 13C spectra. AMARES led to accurate and reliable 13C spectral quantification similar to those obtained using LCModel, when the frequency shifts, J-coupling constants and phase patterns of the different 13C isotopomers were included as prior knowledge in the analysis.

Cerebral glutamine metabolism under hyperammonemia determined in vivo by localized (1)H and (15)N NMR spectroscopy

Brain glutamine synthetase (GS) is an integral part of the glutamate-glutamine cycle and occurs in the glial compartment. In vivo Magnetic Resonance Spectroscopy (MRS) allows noninvasive measurements of the concentrations and synthesis rates of metabolites. (15)N MRS is an alternative approach to (13)C MRS. Incorporation of labeled (15)N from ammonia in cerebral glutamine allows to measure several metabolic reactions related to nitrogen metabolism, including the glutamate-glutamine cycle. To measure (15)N incorporation into the position 5N of glutamine and position 2N of glutamate and glutamine, we developed a novel (15)N pulse sequence to simultaneously detect, for the first time, [5-(15)N]Gln and [2-(15)N]Gln+Glu in vivo in the rat brain. In addition, we also measured for the first time in the same experiment localized (1)H spectra for a direct measurement of the net glutamine accumulation. Mathematical modeling of (1)H and (15)N MRS data allowed to reduce the number of assumptions and provided reliable determination of GS (0.30±0.050 μmol/g per minute), apparent neurotransmission (0.26±0.030 μmol/g per minute), glutamate dehydrogenase (0.029±0.002 μmol/g per minute), and net glutamine accumulation (0.033±0.001 μmol/g per minute). These results showed an increase of GS and net glutamine accumulation under hyperammonemia, supporting the concept of their implication in cerebral ammonia detoxification.

A two-compartment mathematical model of neuroglial metabolism using [1-(11)C] acetate

The purpose of this study was to develop a two-compartment metabolic model of brain metabolism to assess oxidative metabolism from [1-(11)C] acetate radiotracer experiments, using an approach previously applied in (13)C magnetic resonance spectroscopy (MRS), and compared with an one-tissue compartment model previously used in brain [1-(11)C] acetate studies. Compared with (13)C MRS studies, (11)C radiotracer measurements provide a single uptake curve representing the sum of all labeled metabolites, without chemical differentiation, but with higher temporal resolution. The reliability of the adjusted metabolic fluxes was analyzed with Monte-Carlo simulations using synthetic (11)C uptake curves, based on a typical arterial input function and previously published values of the neuroglial fluxes V(tca)(g), V(x), V(nt), and V(tca)(n) measured in dynamic (13)C MRS experiments. Assuming V(x)(g)=10 × V(tca)(g) and V(x)(n)=V(tca)(n), it was possible to assess the composite glial tricarboxylic acid (TCA) cycle flux V(gt)(g) (V(gt)(g)=V(x)(g) × V(tca)(g)/(V(x)(g)+V(tca)(g))) and the neurotransmission flux V(nt) from (11)C tissue-activity curves obtained within 30 minutes in the rat cortex with a beta-probe after a bolus infusion of [1-(11)C] acetate (n=9), resulting in V(gt)(g)=0.136±0.042 and V(nt)=0.170±0.103 μmol/g per minute (mean±s.d. of the group), in good agreement with (13)C MRS measurements.

Compartmentalized Cerebral Metabolism of [1,6-(13)C]Glucose Determined by in vivo (13)C NMR Spectroscopy at 14.1 T

Cerebral metabolism is compartmentalized between neurons and glia. Although glial glycolysis is thought to largely sustain the energetic requirements of neurotransmission while oxidative metabolism takes place mainly in neurons, this hypothesis is matter of debate. The compartmentalization of cerebral metabolic fluxes can be determined by (13)C nuclear magnetic resonance (NMR) spectroscopy upon infusion of (13)C-enriched compounds, especially glucose. Rats under light α-chloralose anesthesia were infused with [1,6-(13)C]glucose and (13)C enrichment in the brain metabolites was measured by (13)C NMR spectroscopy with high sensitivity and spectral resolution at 14.1 T. This allowed determining (13)C enrichment curves of amino acid carbons with high reproducibility and to reliably estimate cerebral metabolic fluxes (mean error of 8%). We further found that TCA cycle intermediates are not required for flux determination in mathematical models of brain metabolism. Neuronal tricarboxylic acid cycle rate (V(TCA)) and neurotransmission rate (V(NT)) were 0.45 ± 0.01 and 0.11 ± 0.01 μmol/g/min, respectively. Glial V(TCA) was found to be 38 ± 3% of total cerebral oxidative metabolism, accounting for more than half of neuronal oxidative metabolism. Furthermore, glial anaplerotic pyruvate carboxylation rate (V(PC)) was 0.069 ± 0.004 μmol/g/min, i.e., 25 ± 1% of the glial TCA cycle rate. These results support a role of glial cells as active partners of neurons during synaptic transmission beyond glycolytic metabolism.

Simplified (13)C metabolic modeling for simplified measurements of cerebral TCA cycle rate in vivo

(13)C NMR spectroscopy is a unique tool to measure the cerebral tricarboxylic acid (TCA) cycle rate in vivo. The measurement relies on metabolic modeling of glutamate C3 and C4 enrichment time courses during a (13)C-glucose intravenous infusion. Usual metabolic models require the plasma glucose and (13)C-glucose time courses as input functions, as well as the knowledge of Michaelis-Menten kinetics parameters governing passage through the blood-brain barrier. It is shown in the present work that, when using an infusion protocol yielding a rapidly stable plasma glucose fractional enrichment, metabolic modeling can be simplified in such a manner that this additional information on input function and glucose transport is no longer required, significantly simplifying the measurement of cerebral TCA cycle rate in vivo.

An integrative dynamic model of brain energy metabolism using in vivo neurochemical measurements

An integrative, systems approach to the modelling of brain energy metabolism is presented. Mechanisms such as glutamate cycling between neurons and astrocytes and glycogen storage in astrocytes have been implemented. A unique feature of the model is its calibration using in vivo data of brain glucose and lactate from freely moving rats under various stimuli. The model has been used to perform simulated perturbation experiments that show that glycogen breakdown in astrocytes is significantly activated during sensory (tail pinch) stimulation. This mechanism provides an additional input of energy substrate during high consumption phases. By way of validation, data from the perfusion of 50 microM propranolol in the rat brain was compared with the model outputs. Propranolol affects the glucose dynamics during stimulation, and this was accurately reproduced in the model by a reduction in the glycogen breakdown in astrocytes. The model's predictive capacity was verified by using data from a sensory stimulation (restraint) that was not used for model calibration. Finally, a sensitivity analysis was conducted on the model parameters, this showed that the control of energy metabolism and transport processes are critical in the metabolic behaviour of cerebral tissue.

Alteration of brain glycogen turnover in the conscious rat after 5h of prolonged wakefulness

Although glycogen (Glyc) is the main carbohydrate storage component, the role of Glyc in the brain during prolonged wakefulness is not clear. The aim of this study was to determine brain Glyc concentration ([]) and turnover time (tau) in euglycemic conscious and undisturbed rats, compared to rats maintained awake for 5h. To measure the metabolism of [1-(13)C]-labeled Glc into Glyc, 23 rats received a [1-(13)C]-labeled Glc solution as drink (10% weight per volume in tap water) ad libitum as their sole source of exogenous carbon for a "labeling period" of either 5h (n=13), 24h (n=5) or 48 h (n=5). Six of the rats labeled for 5h were continuously maintained awake by acoustic, tactile and olfactory stimuli during the labeling period, which resulted in slightly elevated corticosterone levels. Brain [Glyc] measured biochemically after focused microwave fixation in the rats maintained awake (3.9+/-0.2 micromol/g, n=6) was not significantly different from that of the control group (4.0+/-0.1 micromol/g, n=7; t-test, P>0.5). To account for potential variations in plasma Glc isotopic enrichment (IE), Glyc IE was normalized by N-acetyl-aspartate (NAA) IE. A simple mathematical model was developed to derive brain Glyc turnover time as 5.3h with a fit error of 3.2h and NAA turnover time as 15.6h with a fit error of 6.5h, in the control rats. A faster tau(Glyc) (2.9h with a fit error of 1.2h) was estimated in the rats maintained awake for 5h. In conclusion, 5h of prolonged wakefulness mainly activates glycogen metabolism, but has minimal effect on brain [Glyc].

Imaging brain activation: simple pictures of complex biology

Elucidation of biochemical, physiological, and cellular contributions to metabolic images of brain is important for interpretation of images of brain activation and disease. Discordant brain images obtained with [(14)C]deoxyglucose and [1- or 6-(14)C]glucose were previously ascribed to increased glycolysis and rapid [(14)C]lactate release from tissue, but direct proof of [(14)C]lactate release from activated brain structures is lacking. Analysis of factors contributing to images of focal metabolic activity evoked by monotonic acoustic stimulation of conscious rats reveals that labeled metabolites of [1- or 6-(14)C]glucose are quickly released from activated cells as a result of decarboxylation reactions, spreading via gap junctions, and efflux via lactate transporters. Label release from activated tissue accounts for most of the additional [(14)C]glucose consumed during activation compared to rest. Metabolism of [3,4-(14)C]glucose generates about four times more [(14)C]lactate compared to (14)CO(2) in extracellular fluid, suggesting that most lactate is not locally oxidized. In brain slices, direct assays of lactate uptake from extracellular fluid demonstrate that astrocytes have faster influx and higher transport capacity than neurons. Also, lactate transfer from a single astrocyte to other gap junction-coupled astrocytes exceeds astrocyte-to-neuron lactate shuttling. Astrocytes and neurons have excess capacities for glycolysis, and oxidative metabolism in both cell types rises during sensory stimulation. The energetics of brain activation is quite complex, and the proportion of glucose consumed by astrocytes and neurons, lactate generation by either cell type, and the contributions of both cell types to brain images during brain activation are likely to vary with the stimulus paradigm and activated pathways.