Direct assessment of hepatic mitochondrial oxidative and anaplerotic fluxes in humans using dynamic ¹³C magnetic resonance spectroscopy

Abstract

Despite the central role of the liver in the regulation of glucose and lipid metabolism there are currently no methods to directly assess hepatic oxidative metabolism in humans in vivo. By utilizing a novel ¹³C-labeling strategy in combination with ¹³C magnetic resonance spectroscopy we show that rates of mitochondrial oxidation and anaplerosis in human liver can be directly determined noninvasively. Using this approach we found the mean rates of hepatic TCA cycle flux (V_TCA) and anaplerotic flux (V_ANA) to be 0.43 ± 0.04 μmol (g-liver-min)⁻¹ and 0.60 ± 0.11 μmol (g-liver-min)⁻¹, respectively, in fourteen healthy, lean, individuals. We also found the ratio V_ANA/V_TCA to be 1.39 ± 0.22, which is several fold lower than recently published estimates using an indirect approach. This method will be useful for understanding the pathogenesis of non-alcoholic fatty liver disease and type 2 diabetes as well as assessing the effectiveness of new therapies targeting these pathways in man.

Introduction

The liver plays a central role in the regulation of normal glucose and lipid homeostasis and in the pathogenesis of type 2 diabetes. Both hepatic mitochondrial tricarboxylic acid flux (V_TCA) and anaplerotic flux (V_ANA) are critical functions in this regard given their major roles in hepatic fatty acid oxidation and gluconeogenesis. However, despite their importance, there are currently no methods to directly assess these fluxes in human liver. Indirect estimates of hepatic fluxes in humans have been obtained recently by examining the isotopomer labeling patterns of plasma glucose using a multiple tracer method in combination with ex vivo analysis by ¹³C and ²H nuclear magnetic resonance (NMR)^1–3, a method derived from techniques originally developed using radioactive tracers^4,5. The relative rate of hepatic anaplerosis to TCA cycle flux was determined from the ¹³C isotopomers of the C₂ carbon of plasma glucose following the ingestion of [U-¹³C] propionate; using this technique the ratio V_ANA/V_TCA was found to be approximately five. Absolute anaplerotic and TCA cycle fluxes were then calculated from measurements of whole body glucose turnover combined with rates of gluconeogenesis determined from deuterium labeling of C₂ and C₅ glucose from ingested ²H water. However, this approach assesses rates of anaplerosis and TCA cycle flux indirectly and the fluxes are necessarily expressed in terms of body-weight or lean body-mass, rather than per amount of liver tissue, which complicates interpretation of the data when comparing results in subjects with differing body compositions and body weights.

In contrast, in vivo magnetic resonance spectroscopy (MRS) offers the major advantage of being able to directly assess rates of intracellular metabolism in an organ specific manner^6–11. Hepatic energetics have been investigated in patients with type 2 diabetes using ³¹P-MRS techniques. Szendroedi et al. observed that the concentrations of adenosine tri-phosphate (ATP) and inorganic phosphate (P_i) were decreased in the liver of overweight individuals with type 2 diabetes and correlated inversely with hepatic insulin sensitivity¹². This group has also observed that the rate of hepatic ATP turnover (unidirectional Pi → ATP flux, assessed by ³¹P-saturation-transfer-MRS) was decreased in a similar cohort of overweight, type 2 diabetics¹³, suggesting that hepatic mitochondrial metabolism may be compromised in type 2 diabetes. While novel, the ³¹P-saturation-transfer-MRS approach does not directly assess hepatic mitochondrial oxidative function¹⁴. Studies utilizing ¹³C MRS have employed [2-¹³C] acetate infusions to directly assess mitochondrial oxidative function in skeletal muscle^7,8,11,15 and in glial cells in brain^16,17 by monitoring the rate of ¹³C label incorporation into C₄ glutamate. However, this ¹³C labeling scheme is unsuitable for liver where the presence of significant quantities of intracellular lipid obscures the detection of [4-¹³C] glutamate. To circumvent this problem we implemented a novel ¹³C labeling strategy and infused [1-¹³C] acetate and monitored ¹³C label incorporation into liver C₅- and C₁-glutamate, which, given their chemical shifts, we reasoned would be clear of interfering lipid resonances in vivo^18–20.

Using this approach we show that ¹³C enrichment in C₅- and C₁-glutamate can be directly detected in human liver without interference from intrahepatic lipid peaks and demonstrate that these data, in turn, can be used to directly assess the absolute fluxes of hepatic V_TCA and V_ANA. Assumptions underlying the MRS methodology and modeling analysis were also validated using analogous experiments in rat liver, ex vivo. The successful development of this ¹³C MRS technique has yielded the first direct measurements of hepatic mitochondrial oxidative and anaplerotic rates in man and will enhance the investigation of hepatic metabolism in normal and diabetic humans as well as the etiology and treatment of non-alcoholic fatty liver disease (NAFLD).

Results

We recruited twelve young, lean, healthy, participants from the local New Haven, CT community for these studies (see Online Methods). Subjects were screened to eliminate factors that would alter normal hepatic metabolism; all had a normal birth weight, no history of chronic metabolic diseases, were non-smokers and were not taking any medications. Body mass index for this cohort (22.8 ± 2.0 kg m⁻²) was within the normal range. All subjects had normal (<5.5%) levels of liver triglyceride content assessed by ¹H MRS (Supplementary Table 1). Written, informed consent was obtained from each subject after the purpose, nature and potential complications of the studies were explained. All procedures were approved by the Yale University Human Investigation Committee.

¹³C-MRS assessment of hepatic TCA cycle flux

During the infusion study, the plasma acetate concentration and ¹³C enrichment were elevated within 5 minutes after commencing the infusion of [1-¹³C] acetate and plateaued by 20 minutes. There were no significant differences in plasma acetate kinetics with or without a priming dose of [1-¹³C] acetate and results were combined (Fig. 1). Localized ¹³C-MRS of the liver (Fig. 2a) was performed throughout the infusion protocol, and ¹³C labeling of the hepatic glutamate and bicarbonate pools was observed (Fig. 2b) due to the oxidation of [1-¹³C] acetate via the TCA cycle. Enrichment of these metabolites could be detected without interference from the lipid carboxyl group peak at ~172.5 ppm. Using this novel labeling strategy, initial entry of ¹³C-acetate into the TCA cycle results in enrichment at the C₅ carbon of glutamate, followed by labeling at C₁-glutamate as the ¹³C label traverses a 2^nd turn of the cycle. The bicarbonate pool also becomes enriched due to the loss of ¹³C labeled carbon dioxide (CO₂) during the decarboxylation reactions of several TCA cycle intermediates as well as exchange with the plasma CO₂/bicarbonate pool. A more detailed description of the ¹³C labeling scheme can be found in the Online Methods.

Figure 1.

Plasma acetate concentration (black diamonds) and 1-¹³C enrichment (grey diamonds) during the [1-¹³C] acetate infusion protocol (n = 12).

Figure 2.

(a) Axial gradient-echo image of the torso acquired during a single breath-hold. ¹H-decoupled ¹³C MR spectra were acquired from a localized region within the liver. Voxel selection was accomplished using outer volume suppression (shaded regions) applied in 3 dimensions to suppress signals arising from outside the liver and define the volume of interest (white box). (b) Localized ¹³C spectra of the human liver acquired prior to and at the end of a 120min infusion of 1-¹³C-acetate. ¹³C-labeling at the C₅ position of glutamate (C₅-Glu) was observed due to the oxidation of [1-¹³C] acetate via the TCA cycle. Labeling at C₁-glutamate (C₁-Glu) and of the bicarbonate (HCO₃⁻) pool was also observed as the ¹³C label traversed a 2nd turn of the TCA cycle.

¹³C enrichment of the C₅-glutamate pool was detected during the initial 10 min of the [1-¹³C] acetate infusion and rapidly attained steady state (Fig. 3). ¹³C labeling at C₁-glutamate occurred more slowly but also plateaued by the end of the 120 min infusion protocol. Hepatic glutamate concentration (5.79 ± 1.31 μmol g⁻¹, n = 12) was measured by natural abundance localized ¹³C-MRS on a separate occasion.

Figure 3.

Time-courses of hepatic C₅- and C₁-glutamate enrichment determined by localized in vivo ¹³C-MRS during an infusion of [1-¹³C] acetate (n = 12). The kinetics of liver glutamate enrichment for each subject was determined by the metabolic model of hepatic metabolism. The average fit of the model to the glutamate enrichment data is superimposed.

Metabolic Modeling

C₅- and C₁- glutamate ¹³C enrichment profiles for each subject were fitted to a model of liver oxidative metabolism (Fig. 4). This model was adapted from previous schemes used to simulate acetate metabolism in muscle and brain^8,17,21 and incorporated modifications to reflect the specific biochemical pathways of hepatic metabolism. These included: 1) anaplerotic fluxes to account for the entry of metabolites into the TCA cycle; and 2) gluconeogenesis from TCA cycle intermediates via phosphoenolpyruvate (PEP). The modeling scheme is described in detail in the Online Methods.

Figure 4.

Metabolic model of liver acetate oxidative metabolism used to estimate hepatic TCA cycle flux (V_TCA) and anaplerosis (V_ANA). Carbon positional enrichment denoted in red occurs during the initial incorporation of label from 1-¹³C-acetate to glutamate on the first turn of the TCA cycle. Positional enrichment denoted in blue occurs during the 2^nd turn of the TCA cycle, with label originating from internal scrambling at succinate or from bicarbonate (HCO₃⁻)/¹³CO₂ via anaplerosis. A full description of the metabolic model can be found in the Online Methods section.

For each subject the precision in the rates of hepatic metabolism estimated by the metabolic model was determined by performing 500 Monte-Carlo simulations of the dataset followed by probability distribution analysis. Representative data for the estimates of TCA cycle flux and anaplerosis are shown for one of the subjects in the Supplementary Information (Fig. S1). For this group of lean, healthy subjects the mean rates of V_TCA and V_ANA were 0.43 ± 0.04 and 0.60 ± 0.11 μmol (g-liver-min)⁻¹, respectively; the ratio V_ANA/V_TCA was 1.39 ± 0.22 (Table 1, Supplementary Fig. S2).

Table 1.

Average hepatic mitochondrial metabolic fluxes estimated by metabolic modeling of the time-courses of liver glutamate enrichment for each subject during an infusion of [1-¹³C] acetate. V_TCA = hepatic TCA cycle flux. V_ANA = rate of anaplerosis. V_AC = rate of acetate utilization.

	n	Mean	SEM
VTCA (μmol g-min−1)	12	0.43 ± 0.04
VANA (μmol g-min−1)	12	0.60 ± 0.11
VAC (μmol g-min−1)	12	0.10 ± 0.01
VANA/VTCA	12	1.39 ± 0.22

Discussion

In this study, we have developed and applied a novel ¹³C-MRS method to directly assess rates of hepatic oxidative and anaplerotic flux in human liver in vivo. This was accomplished by utilizing a novel ¹³C labeling scheme, which enriches the carboxyl groups of liver glutamate and avoids the interfering resonances of intrahepatic lipid. Time-courses of ¹³C enrichment of hepatic glutamate were detected with sufficient sensitivity and time resolution to permit modeling of the data to yield rates of hepatic V_TCA and V_ANA in humans. To ensure accurate simulation of the kinetics of ¹³C-label turnover, a sophisticated metabolic model of liver oxidative metabolism was developed for these analyses. Using this approach we found that the mean rates of hepatic V_TCA and V_ANA were 0.43 ± 0.04 and 0.60 ± 0.11 μmol (g-liver-min)⁻¹, respectively, yielding a V_ANA/V_TCA ratio of 1.39 ± 0.22.

To validate this methodology, we performed analogous infusion experiments in adult male rats (see Supplementary Information). Positional enrichment of liver glutamate at multiple time points was determined ex vivo by ¹³C-NMR and LC/MS/MS of the extracted tissue. Profiles of ¹³C glutamate enrichment were constructed from the individual time points, and this composite dataset was fitted using our model of hepatic acetate metabolism. Using this approach we found the liver V_TCA flux was estimated to be approximately 1.2 μmol (g-liver-min)⁻¹, which is comparable to V_TCA flux rates determined by Beylot et al. in rats in vivo and in perfused livers²². We also estimated hepatic V_TCA flux rates in these animals indirectly by an independent method wherein we measured the ratio of V_ANA/V_TCA flux through steady state labeling of C₂, C₃ and C₄ glutamate during an infusion of [3-¹³C] lactate (Supplementary Table S2) and multiplied this fraction by rates of hepatic gluconeogenesis. This was calculated from endogenous glucose production, assessed by [3-³H] glucose turnover assuming a 90% contribution from the liver, and from the contribution of pyruvate to gluconeogenesis, which was determined during the infusion of [3-¹³C] lactate (see Supplementary Information). TCA cycle flux estimated using this independent method was found to be 1.4 ± 0.4 μmol (g-liver-min)⁻¹ (Supplementary Table S2), in excellent agreement with V_TCA derived using dynamic metabolic modeling of the liver C₅ and C₁ glutamate enrichment time course data.

We found the ratio of V_ANA/V_TCA in humans to be 1.39 ± 0.22, which is over 300% lower than has been recently been published by Sunny et al.³. By assessing the isotopomer splitting pattern in C₂ plasma glucose from ingested U-¹³C propionate they found rates of V_ANA to be approximately five times greater than V_TCA flux in normal subjects³. Such high rates of anaplerosis are incompatible with the extent of ¹³C labeling at C₁-glutamate that we have observed in the present study in human liver following an infusion of [1-¹³C] acetate. We believe that this discrepancy in V_ANA/V_TCA may be due to important limitations regarding the use of U-¹³C propionate as a tracer for assessing hepatic metabolism in vivo. Specifically, propionate enters the TCA cycle as an anaplerotic substrate via succinyl CoA, which requires obligate utilization via gluconeogenesis and/or pyruvate recycling. Furthermore, in contrast to acetate or lactate, Puchowicz et al. have demonstrated very large periportal-perivenous gradients for propionate uptake across the liver²³. To examine these issues we measured glucose turnover in a group of rats infused intravenously with low (333 μmol kg⁻¹) and high (666 μmol kg⁻¹) doses of [U-¹³C] proprionate that are within the range used by previous studies^2,24,25. We found that plasma glucose concentrations increased by ~25 mg dl⁻¹ during the high dose propionate infusions compared to the low dose propionate infusions. Furthermore, this increase in plasma glucose concentration during the high dose propionate infusion was associated with an ~30% increase in rates of hepatic glucose production (Supplementary Fig. S3), compared to the low dose infusion. This stimulation of hepatic glucose production by propionate is similar to the ~40% increase in rates of endogenous glucose production [from 7.3 to 10.0 mg (kg-min)⁻¹], observed when the dose of [U-¹³C] propionate given to rats was increased from 222 to 825 μmol^24,25. In contrast, doubling the infusion rates of [1-¹³C] acetate or [3-¹³C] lactate had no effects on glucose production, the ratio of pyruvate carboxylase flux (V_PC) to V_TCA or the ratio of pyruvate dehydrogenase flux (V_PDH) to V_TCA. (Supplementary Fig. S3). Taken together, these data demonstrate that [U-¹³C] propionate at doses in the range used to assess rates of mitochondrial metabolism can alter rates of anaplerosis making it unsuitable as a tracer for hepatic metabolism. These substrate driven effects of [U-¹³C] propionate on V_ANA will likely be further exaggerated when the isotope is given orally since first pass portal vein delivery will probably result in much higher concentrations of propionate being presented to the periportal hepatocytes than when administered systemically. Furthermore, in contrast to the in vivo MRS method described here, the [U-¹³C] propionate isotope method assumes negligible flux through hepatic pyruvate dehydrogenase, which is not likely to be the case in normal liver (Supplementary Table S2)²⁶ and does not account for the effects of ¹³C label recycling via CO₂ which modulates the observed labeling patterns²⁷.

The methodology described in this article uses a dynamic approach to monitor metabolite kinetics and estimate metabolic rates. While the MRS techniques involved in data acquisition are technically demanding, and the metabolic modeling analyses require high quality data collected over an extended duration (90–120 min of infusion are required to obtain sufficient time points to establish the kinetics of glutamate enrichment), the technique provides reliable, direct estimates of hepatic oxidative metabolism. Relatively modest increments in plasma acetate concentrations are observed (up to ~1 mM) minimizing the likelihood that the provision of exogenous substrate will perturb metabolism in the liver, or other organs. Metabolite enrichment in the target tissue is directly assessed avoiding assumptions about the contributions of other tissues such as the kidney, which may impact other (whole-body) techniques. Additionally, the dynamic approach does not inherently require isotopic steady-state conditions for either the substrate precursor or the target metabolite(s); however, since both the peripheral circulation and the liver were repeatedly sampled, isotopic steady-state was confirmed for these studies (Fig. 1 and 3).

We also performed a Monte-Carlo simulation for each dataset, combined with probability distribution analysis to determine the precision with which the metabolic model fitted the in vivo data (Supplementary Fig. S1). This analysis, which determined uncertainty based upon spectral noise and deviation of the data from the best fit, showed that reliable estimates of hepatic metabolism were obtained on each of the subjects in this study. It further demonstrates that this method can be used to track hepatic metabolism in individual subjects opening up the possibility of monitoring the impact of interventions which may perturb the liver. The estimated fluxes are sensitive to assumptions underlying the model of hepatic metabolism; therefore, actual error may exceed the estimates reported.

In summary, the use of traditional ¹³C-MRS techniques to measure tissue specific rates of mitochondrial V_TCA flux is not possible in liver due to the presence of dominant intrahepatic lipid peaks which obscure the detection of conventional ¹³C-labeling schemes. By using an innovative labeling strategy, in combination with localized in vivo ¹³C-MRS, we have directly observed rates of mitochondrial oxidation and anaplerosis in human liver. A sophisticated metabolic model of hepatic metabolism was developed to simulate the kinetics of ¹³C-label turnover, which generated estimates of liver oxidative fluxes. This method will be useful for understanding the potential role of altered hepatic mitochondrial fat oxidation in the pathogenesis of NAFLD and type 2 diabetes as well as for assessing the effectiveness of novel therapies aimed at increasing rates of hepatic fatty oxidation in man to reverse NAFLD.

Online Methods

Human Subjects

All procedures were approved by the Yale University Human Investigation Committee; written, informed consent was obtained from each participant after explanation of the purpose, nature and potential complications of the study. Twelve young, lean, healthy volunteers (10 male, 2 female) were recruited from the local community and were prescreened to be in good health, lean, non-smokers and taking no medications. Subjects were also selected to have normal levels of intrahepatic lipid content determined using ¹H MRS.

In vivo ¹³C MRS: general procedure

Studies were performed on a 4.0 Tesla Bruker Medspec system using a custom-built ¹³C/¹H probe consisting of a 9 cm diameter ¹³C surface coil with a pair of elliptical, 14.5 × 11 cm, ¹H coils arrayed in quadrature for imaging, shimming and decoupling. Subjects were positioned supine with the probe attached to a rigid support to minimize extraneous movement. The ¹³C/¹H probe was curved in design to site the radiofrequency coils in an optimal position over the lateral aspect of the liver. Scout images of the torso were acquired during an end-expiration breath-hold to confirm correct positioning of the probe and to define a volume for localized ¹³C spectroscopy. Field homogeneity was optimized using a respiratory-gated FASTMAP routine^{28. 1}H linewidths from an 8 cm³ volume within the region of interest, acquired using a respiratory-gated STEAM sequence, were typically ~25 Hz. Each participant underwent two MRS sessions typically separated by less than 8 days: a natural-abundance ¹³C scan to determine the hepatic concentration of glutamate, and an infusion study to assess hepatic TCA cycle flux. The natural abundance measurement was performed prior to the infusion study for eight of the 12 participants; for the remaining individuals there was a sufficient interval after the infusion study to ensure full washout of ¹³C-label before the natural abundance scan.

¹³C-MRS assessment of hepatic glutamate concentrations

Localized ¹³C spectra were acquired using a custom-written adiabatic pulse-acquire sequence with WALTZ16 decoupling and 3 dimensional outer volume suppression (OVS) to minimize signal arising from the chest wall and select a region of interest within the liver (Figure 2). The size of the localized volume varied from subject to subject depending on the morphology of the liver but was typically ~225 cm³. Due to the relatively long T₁ relaxation times of the carboxyl groups, spectra were acquired with a repetition time (T_R) of 10 s in blocks of 32 transients and repeated until sufficient signal had been acquired to detect the natural abundance glutamate signal (typically 50–60 minutes). The hepatic concentration of glutamate was determined from the in vivo C₅-glutamate signal relative to the fully-relaxed (T_R = 30 s) signal obtained from a 25 mM glutamate phantom, using a voxel of identical size and location, after correction for coil loading effects.

¹³C-MRS assessment of hepatic TCA cycle flux

Following an overnight fast, intravenous catheters were inserted into an antecubital vein in each arm. Localized ¹³C spectra were obtained over a 20 min baseline period and throughout a 120 min infusion of [1-¹³C]acetate (99% enriched, 350 mmolL⁻¹ sodium salt). Subjects underwent either a continuous acetate infusion protocol (n = 6) at a rate of 3.0 mg(kg-min)⁻¹, or a primed-continuous infusion protocol (n = 6), with a 5 min priming dose at 150% of the continuous acetate infusion rate. Spectra were acquired as described above but with nuclear Overhauser enhancement (nOe) applied during the T_R (1 ms hard-pulse every 50 ms) to increase ¹³C sensitivity. Blood samples were obtained at regular intervals throughout the infusion protocol for the measurement of plasma acetate concentration and ¹³C₁ fractional enrichment by high-field ¹H NMR at 500 MHz or by gas-chromatography/mass-spectrometry (GC/MS)²¹. To enhance signal/noise, data acquired during the infusion were summed using a four spectrum rolling average; difference spectra were created for each time point by subtracting the baseline spectrum. Glutamate enrichment at the C₅ and C₁ positions was determined from each difference spectrum relative to the baseline bicarbonate signal, which was assumed to be 1.1% enriched (i.e. natural abundance for ¹³C). Slight differences in nOe for bicarbonate and C₅ glutamate in liver and the detection efficiency of C₁ versus C₅ glutamate using this pulse-sequence were accounted for by means of correction factors determined in vivo and from a glutamate phantom experiment, respectively.

Metabolic Modeling

The time courses of hepatic glutamate enrichment for each subject were fitted to a metabolic model of the TCA cycle (Fig 4) using CWave software (developed by Dr. Graeme Mason, Yale University). This model consists of a series of isotopic and mass balance differential equations that describe the hepatic metabolism of acetate (see Supplementary Information). This model was developed from previous schemes used to examine acetate metabolism in muscle²¹ and brain^8,17,29 modified to account for liver-specific phenomena including gluconeogenesis from TCA cycle intermediates via phosphoenolpyruvate (PEP), the entry of metabolites into the TCA cycle via anaplerosis, and ¹³CO₂ recycling.

Acetate uptake occurs via the monocarboxylate transporter; under the systemic acetate concentrations in these studies (~1 mM) acetate transport is assumed to be saturated and acetate is converted to acetyl-CoA within the hepatocyte at the rate, V_AC. AcetylCoA enters the TCA cycle labeling citrate and α-ketoglutarate (α-KG) at the C₅ position. Entry of unlabeled substrates derived from fatty acids or pyruvate is accounted for by the flux V_DIL, which dilutes the enrichment of acetyl CoA. Glutamate and α-KG are in rapid exchange (V_X) via asparate-aminotransferase, and equilibration results in the enrichment of 5-¹³C-glutamate, which can be detected by ¹³C-MRS. As the TCA cycle progresses, the C₁ and C₄ positions of the TCA cycle intermediates succinate and malate are equally labeled due to the stereo-chemical symmetry of the succinate molecule. To preserve mass balance of the TCA cycle intermediates, carbon-entry from unlabeled α-KG occurs at the level of succinate.

Key branch points in this model of hepatic metabolism occur at oxaloacetate where the ¹³C-label may undergo several fates. From OAA, the ¹³C label may enter a second turn of the TCA cycle; [4-¹³C] OAA forms [1-¹³C]citrate and eventually enriches [1-¹³C] glutamate, which is also detectable by ¹³C-MRS. [1-¹³C] OAA labels the carboxyl side-chain (C₆) of citrate; 13C at this position is lost as CO₂ during the decarboxylation of citrate. Oxaloacetate may also exchange with the aspartate pool, which delays enrichment at [1-¹³C] citrate and is modeled at a rate equivalent to V_X. The action of PEP-carboxykinase (V_PEPCK) decarboxylates OAA forming ¹³CO₂ and 1-¹³C-phosphoenol-pyruvate (PEP) from ¹³C₄ and ¹³C₁-OAA, respectively. PEP is a precursor for gluconeogenesis or may be converted to pyruvate via pyruvate kinase (PK). Pyruvate can also potentially be directly formed from malate through the action of malic enzyme (ME). Our experimental data demonstrates that there is substantial dilution of [1-¹³C] with respect to [5-¹³C] glutamate, indicating that unlabeled carbons must enter the TCA cycle post-succinate via anaplerosis. We assume that any 1-¹³C-pyruvate formed via PK or ME is unavailable for recycling into OAA through pyruvate-carboxylase (V_PC). This approach is supported by experiments in rodents (see Supplementary Information) where we observe negligible labeling of [1-¹³C] lactate or alanine (surrogates for [1-¹³C] pyruvate) during a 1-¹³C-acetate infusion and in published literature which suggests compartmentation of the gluconeogenic and anaplerotic pools³⁰ and/or that the PK+ME flux is relatively low^31–33. Therefore, only unlabeled pyruvate and ¹³CO₂ may enter the TCA cycle via V_PC. Anaplerosis (V_ANA) is treated as a parameter that is equivalent to V_PC and V_PEPCK. Backwards scrambling of ¹³C-label between C₁ and C₄ OAA due to the action of fumarase is treated as a simple, rapid inter-conversion between the two species (V_FUM).

Target functions of C₅- and C₁-glutamate enrichment during the [1-¹³C] acetate infusion were created for each subject as described above. The hepatic concentration of glutamate was estimated from a natural abundance ¹³C-MRS measurement. Due to the high activity of carbonic anhydrase, liver bicarbonate enrichment estimated from the in vivo ¹³C spectra was used as a surrogate for the ¹³CO₂ input function. The liver bicarbonate concentration was calculated to be 12 mM, based on an assumed plasma bicarbonate concentration of 24 mM and a pH difference of 0.3 between liver and blood. Concentrations of the other hepatic metabolic intermediates were estimated from the literature, using average values scaled to the estimated concentration of glutamate for each subject. Due to the low concentrations of these intermediates relative to glutamate, labeling of these metabolites has a negligible impact on the kinetics of glutamate enrichment or the modeled rates of hepatic metabolism. The parameters V_AC, V_DIL, V_TCA and V_ANA were estimated by numerical simulation of the differential equations that contribute to the metabolic model. Based on previous studies, V_X was assumed to be significantly faster than V_TCA and non-limiting. Each simulated parameter was constrained to be greater than or equal to zero.

¹H MRS assessment of intrahepatic lipid content

To assess liver lipid content, localized ¹H spectra were obtained from a (15 × 15 × 15) mm³ voxel placed in 3 different locations of the liver. Spectra were acquired using a respiratory-gated stimulated echo-acquisition mode (STEAM) sequence, with chemical shift selective peak suppression (CHESS). Total intrahepatic lipid (IHL) content was estimated from comparison of a water-suppressed lipid spectrum and a lipid-suppressed water spectrum, with the appropriate peak for each spectrum on-resonance.

Statistical Analysis

Data are expressed as mean ± standard error of the mean (SEM). The precision in the fit of the metabolic model to the raw data was determined by probability distribution analysis of 500 Monte-Carlo simulations of the model with random Gaussian noise added to the fitted time courses. Probability distribution analysis was performed for each rate parameter on the resultant Monte-Carlo dataset using the distribution fitting function (dfittool) in Matlab.