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In vivo 13C magnetic resonance spectroscopy has been applied to studying brain metabolic processes by measuring 13C label incorporation into cytosolic pools such as glutamate and aspartate. However, the rate of 13C label exchange between mitochondrial α-ketoglutarate/oxaloacetate and cytosolic glutamate/aspartate (Vx) extracted from metabolic modeling has been controversial. Because brain fumarase is exclusively located in the mitochondria and mitochondrial fumarate is connected to cytosolic aspartate via a chain of fast exchange reactions it is possible to directly measure Vx from the four-carbon side of the tricarboxylic acid cycle by magnetization transfer. In isoflurane-anesthetized adult rat brain a relayed 13C magnetization transfer effect on cytosolic aspartate C2 at 53.2 ppm was detected after extensive signal averaging with fumarate C2 at 136.1 ppm irradiated using selective radiofrequency pulses. Quantitative analysis using Bloch-McConnell equations and a four-site exchange model found that Vx ≈ 13~19 μmol/g/min ( VTCA, the tricarboxylic acid cycle rate) when the longitudinal relaxation time of malate C2 was assumed to be within ±33% of that of aspartate C2. If Vx ≈ VTCA, the isotopic exchange between mitochondria and cytosol would be too slow on the time scale of 13C longitudinal relaxation to cause a detectable magnetization transfer effect.
In vivo magnetic resonance spectroscopy (MRS) has been used to follow the isotopic flow of 13C labels from an isotopically enriched substrate to many metabolites in brain including glutamate, glutamine, aspartate, γ-aminobutyric acid, and N-acetylaspartate (NAA) (e.g., Mason et al. 1992; 1995; Shen et al, 1999; Bluml et al, 2001; Moreno et al, 2001; Chhina et al, 2001; Gruetter et al, 2001; de Graaf et al, 2003; 2004; Yang et al, 2005, Yang and Shen, 2005; Xu et al, 2008). For example, by infusing exogenous [1-13C] or [1,6-13C2]glucose, the 13C labels from glucose enter into α-ketoglutarate and oxaloacetate. α-Ketoglutarate and oxaloacetate are then converted into MRS-detectable cytosolic glutamate and aspartate, respectively (see Fig. 1). From the kinetics of 13C label incorporation into predominantly cytosolic glutamate and aspartate, tricarboxylic acid (TCA) cycle flux through human and animal brain can be measured (Mason et al. 1992; 1995; Shen et al, 1999; Chhina et al, 2001; Gruetter et al, 2001; de Graaf et al, 2003; 2004; Yang and Shen, 2005).
The complete TCA cycle is known to occur exclusively in mitochondria. In brain, several enzymes from the TCA cycle machinery (pyruvate dehydrogenase, citrate synthase, fumarase, and succinate thiokinase) are exclusively located in the mitochondria (e.g., Siesjo, 1978; Akiba et al, 1984; Lai and Clark, 1989; Rodrigues and Cerdan, 2006), although many other enzymes involved in the TCA cycle (e.g., malate dehydrogenase, aconitase, and isocitrate dehydrogenase) are found in the cytosol of neurons and astroglia as well (Koen and Goodman, 1969; Siesjo, 1978, Rodrigues and Cerdan, 2006). It was noted in the use of in vivo 13C-MRS to measure the brain TCA cycle rate that glutamate C4 turnover time course data alone were not sufficient to separate the TCA cycle flux rate (VTCA) from the rate of 13C label exchange between mitochondria and cytosol (Vx, Fig. 1) (Mason et al. 1992; 1995). This is because MRS detects the total, and therefore predominantly cytosolic, glutamate signal while the mitochondrial glutamate pool is negligibly small in size. Time course data of glutamate C2 and C3 labeled during the second turn of the TCA cycle also depend on VTCA and Vx. Using metabolic models to fit the combined time course data of glutamate C4 and other position(s) can, in principle, extract both VTCA and Vx. Whether Vx is slow (Vx ≈ VTCA) or fast (Vx VTCA) in brain is a matter of considerable debate in the field of 13C MRS (e.g., Chance et al, 1983; Mason et al 1992; 1995; Gruetter et al, 2001; Patel et al, 2004; de Graaf et al, 2004; Berkich et al, 2005; Shen, 2006). The main focus of this debate has been on metabolic modeling of 13C label incorporation into glutamate and aspartate for extraction of Vx.
In vivo magnetization transfer spectroscopy allows detection of the rapid exchange of phosphate groups that occurs between phosphocreatine and adenosine triphosphate (ATP) catalyzed by creatine kinase using 31P MRS (Alger and Shulman, 1984; Leibfritz and Dreher, 2001). We hypothesized that the 13C label exchange between mitochondria and cytosol may be directly detectable using in vivo magnetization transfer spectroscopy if Vx VTCA.
The α-ketoglutarate ↔ glutamate and oxaloacetate ↔ aspartate exchange reactions catalyzed by aspartate aminotransferase have been found to be very fast and cause a marked magnetization transfer effect on glutamate and aspartate in rat brain when α-ketoglutarate and oxaloacetate were irradiated using radiofrequency pulses (Shen, 2005). When malate is irradiated, a relayed magnetization transfer effect can be detected on aspartate because of the rapid malate ↔ oxaloacetate ↔ aspartate exchange reactions (Yang and Shen, 2007). Aspartate aminotransferase, malate dehydrogenase, and their substrates reside in both cytosolic and mitochondrial compartments (Siesjo, 1978). Because of the extremely small fraction of contributions from mitochondrial pools (Sols and Marco, 1970; Wu et al, 2007), the previously detected magnetization transfer effects catalyzed by aspartate aminotransferase and/or malate dehydrogenase are predominantly cytosolic and therefore cannot be used to extract Vx. In contrast, brain fumarase is localized to mitochondria. Fumarase, malate dehydrogenase, and aspartate aminotransferase catalyze a linear chain of rapid exchange reactions in mitochondria, none of which are involved in the control of VTCA (Leong and Clark, 1984). Vx connects the mitochondrial and cytosolic exchange systems. Thus, we hypothesized that a fast Vx (Vx VTCA) between mitochondrial matrix and cytosol should cause a detectable relayed 13C magnetization transfer effect on cytosolic aspartate when fumarate is irradiated using radiofrequency pulses. On the other hand, if Vx is slow (Vx ≈ VTCA), no detectable relayed 13C magnetization transfer effect between mitochondrial fumarate and cytosolic aspartate would be expected.
Fig. 2(a) shows the diagram for the exchange between cytosol and mitochondria on the four-carbon side of the TCA cycle (Siesjo 1978). Cytosolic malate enters mitochondria via the oxoglutarate carrier (OGC, also known as the malate/α-ketoglutarate exchanger). Aspartate then leaves mitochondria via the aspartate/glutamate carrier (AGC). The rapid exchange reactions between malate and oxaloacetate and between oxaloacetate and aspartate are catalyzed by malate dehydrogenase and aspartate aminotransferase, respectively. In mitochondria, malate also rapidly exchanges with fumarate catalyzed by fumarase. In Fig. 2, only cytosolic aspartate has a significant pool size (Sols and Marco, 1970; Siesjo 1978; Wu et al, 2007) and is detectable by MRS. To estimate Vx using 13C magnetization transfer, a four-site exchange model is depicted in Fig. 2(b). The small mitochondrial fumarate, malate, oxaloacetate, and aspartate pools are lumped into a single mitochondrial site denoted by Fum, which is saturated by radiofrequency irradiation of fumarate C2 at 136.1 ppm. The cytosolic malate, oxoloacetate, and aspartate C2 carbons are denoted by Mal, Oxa, and Asp respectively. This simplified procedure attributes the loss of saturation inside the mitochondrial matrix to Vx. The Vx value calculated from this model therefore represents its lower limit.
The steady state Bloch-McConnell equations for the four-site exchange model depicted in Fig. 2(b) are:
where Asp0, Mal0, and Oxa0 are the equilibrium magnetization of cytosolic aspartate, malate, and oxaloacetate C2 carbons, respectively; fAsp Aspsteadystate/Asp0, fMal Malsteadystate/Mal0, and fOxa Oxasteadystate/Oxa0; T1Asp, T1Mal and T1Oxa are the longitudinal relaxation times of cytosolic aspartate, malate, and oxaloacetate C2 carbons, respectively, in the absence of any chemical exchange. VAAT and VMDH are the exchange flux rates catalyzed by cytosolic aspartate aminotransferase and malate dehydrogenase, respectively; Vx is the rate of isotopic exchange between cytosol and mitochondria.
In equation , Oxa0(1 − fOxa)/T1Oxa can be omitted because Oxa0/T1Oxa VAAT, VMDH, as noted previously (Yang and Shen, 2007). Equations [1–3] can be used to estimate Vx from experimentally measured fAsp upon saturation of fumarate C2:
where fOxa = (fAspVAAT − Asp0(1 − fAsp)/T1Asp)/VAAT and fMal = (fOxa(VAAT + VMDH) − fAspVAAT)/VMDH. Asp0 = 2.8 μmol/g (Siesjo, 1978; Yang and Shen, 2005). Mal0 = 0.3 μmol/g (Siesjo, 1978). Our previous work (Shen, 2005, Yang and Shen, 2007) found that VAAT (oxaloaceate ↔ aspartate) = 29 μmol/g/min, VMDH = 9 μmol/g/min, and T1Asp = 2.2 seconds. In equation , only T1Mal is unavailable because malate is below the detection threshold of in vivo MRS. Instead, Vx will be estimated by assuming T1Mal = 0.67~1.33 × T1Asp, because both malate and aspartate C2 carbons are singly protonated, and because the two molecules are small and similar in size (Wehrli, 1976).
All animal experiments were approved by the National Institute of Mental Health Animal Care and Use Committee. Male Sprague-Dawley rats (176–213 g, n = 8) that fasted for 24 hours with free access to drinking water were studied in order to measure Vx in the rat brain. The rats were orally intubated and mechanically ventilated using a mixture of 70% N2O/30% O2 and 1.5% isoflurane. The left femoral artery was cannulated for sampling blood and monitoring arterial blood pressure. Arterial blood gases (pO2, pCO2), pH, and blood glucose concentrations were measured using a blood analyzer (Bayer Rapidlab 860, East Walpole, MA). The left femoral vein was also cannulated for infusion of [1,6-13C2]glucose (1-13C, fractional enrichment: 0.99; 6-13C, fractional enrichment: 0.97, Cambridge Isotope Labs, Andover, MA). The scalp underneath the 13C transceiver coil was removed to eliminate any contamination of in vivo 13C data from extracranial tissues. For each rat, intravenous infusion of [1,6-13C2]glucose was initiated approximately one hour prior to in vivo 13C magnetization transfer data acquisition. The infusion protocol consisted of an initial bolus of 110 mg/kg/min of 0.75 M [1,6-13C2]glucose followed by an approximately constant-rate infusion of the same glucose solution at 42.8 mg/kg/min. Arterial blood was sampled every 60 minutes. Plasma glucose levels were maintained at 23 ± 8 mM. Other system physiological parameters were maintained within the normal range throughout the 13C data acquisition period with few exceptions (pH = 7.35 ± 0.04, pCO2 = 42 ± 3 mmHg, pO2 = 125 ± 16 mmHg, mean arterial blood pressure = 122 ± 13 mmHg, heart rate = 404 ± 29 bpm). End-tidal CO2 and tidal pressure of ventilation were also monitored. Body temperature was maintained at ~37.5°C using an external pump for water circulation (BayVoltex, Modesto, CA).
All experiments were performed on a Bruker 11.7 Tesla spectrometer interfaced to an 89-mm bore vertical magnet running on ParaVision 3.0.1 (Bruker Biospin, Billerica, MA). An in-house transmit/receive concentric surface 13C (circular, diameter: 10 mm)/1H (octagonal, diagonal: 25 mm) radiofrequency coil system was used. The radiofrequency coils were integrated to an animal handling system. Three-slice (coronal, horizontal, and sagittal) scout RARE images (FOV = 2.5 cm, slice thickness = 1 mm, TR/TE = 200/15 ms, rare factor = 8, 128 × 128 data matrix) were acquired to position the integrated radiofrequency probe/animal handling system inside the Mini 0.5 gradient insert (Bruker Biospin, Billerica, MA) so that the gradient isocenter was about 0–1 mm posterior to bregma. B0 inhomogeneity in the rat brain was corrected using the FASTMAP/FLATNESS methods as previously described (Chen et al, 2004 and references therein). The 90° excitation, surface-coil-localized, interleaved acquisition method was used to measure the relayed 13C magnetization transfer effect between mitochondrial fumarate and cytosolic aspartate (Shen, 2005). A 1-ms adiabatic half-passage pulse was used for non-selective 90° 13C excitation. TR = 7.4 seconds. The 13C carrier frequency was centered near aspartate C2 at 53.2 ppm. The WALTZ-4 sequence, based on a 400 μs nominal 90° rectangular pulse, was employed for proton decoupling. The decoupling pulse train was executed for a total of 106 ms. Broadband 1H→13C Nuclear Overhauser Enhancement (NOE) was generated using a train of non-selective hard pulses with a nominal flip angle of 180° spaced 100 ms apart.
When the relayed 13C magnetization transfer spectra were acquired, fumarate C2 at 136.1 ppm was saturated using a train of spectrally selective 2-ms Gaussian pulses with a nominal flip angle of 180° spaced 12 ms apart. The bandwidth of the Gaussian pulses is approximately 500 Hz (~4 ppm). The duration of the Gaussian pulse train was 7.3 seconds. When the control spectra were acquired, the saturating pulse train was placed at an equal spectral distance from aspartate C2 at 53.2 ppm but on the opposite side of fumarate C2 (−29.7 ppm). The large separation of chemical shifts among fumarate, malate, oxaloacetate, and aspartate C2 carbons allowed radiofrequency saturation of the source molecule fumarate without affecting either the relay molecules malate and oxaloacetate or the target molecule aspartate (Table 1). The saturated and control spectra were interleaved every free induction decay. The rat brain was re-shimmed after every block of 256 pairs of fumarate-saturated and control spectra were acquired in order to maintain optimal B0 homogeneity. Data were zerofilled to 16 K and apodized using a matched filter for maximum sensitivity (lb = 30 Hz) prior to Fourier transformation. The 13C signals in the 51–58 ppm region were analyzed in the frequency domain using Gaussian-Lorentzian basis functions and the MATLAB curve-fitting toolbox (The MathWorks, Inc., Natick, MA).
Fig. 3(a) depicts in vivo relayed 13C magnetization transfer results from one rat. In the control spectrum, the Gaussian saturation pulse train was placed at −29.7 ppm. NS = 256 × 5. In the displayed 46–68 ppm region, the following peaks were observed as expected: α-glucose C6 at 61.7 ppm, β-glucose C6 at 61.8 ppm, glutamate C2 at 55.2 ppm, glutamine C2 at 55.1 ppm, NAA C2 at 54.0 ppm, and aspartate C2 at 53.2. In the fumarate-saturated spectrum, the Gaussian saturation pulse train was placed at 136.1 ppm. In the difference spectrum, the relayed 13C magnetization effect on aspartate C2 at 53.2 ppm was detected with low SNR. Fig. 3(b) shows in vivo relayed 13C magnetization transfer results summed from eight rats. In the control spectrum and fumarate-saturated spectrum, each summed from eight rats, a small signal at 48.7 ppm was observed after magnification of the 47–50 ppm region and assigned to taurine (S-CH2) based on its known chemical shift position. In the difference spectrum summed from eight rats, a small but well-defined peak at the resonance frequency of aspartate C2 was clearly detected (Fig. 3(b)). In comparison, the nearby and much more intense α-glucose C6, β-glucose C6, glutamate C2, glutamine C2, and NAA C2 resonances were completely cancelled in the difference spectrum. The small taurine S-CH2 signal at 48.7 ppm was also cancelled in the difference spectrum. Because of the low signal-to-noise ratio in the individual rat results, only the spectra summed from eight rats (Fig. 3(b)) were quantitatively analyzed. Using the MATLAB curve-fitting routine and the relayed magnetization transfer spectra summed from eight rats, ΔAsp/Asp0 was determined to be 4.2%, with a relative standard deviation (rSD) of 15%. The rSD of ΔAsp/Asp0 was estimated by integrating the aspartate C2 signal and its neighboring spectral regions in the difference spectrum using the same interval length.
Using fAsp = 1−ΔAsp/Asp0 and fOxa = (fAspVAAT −Asp0(1 − fAsp)/T1Asp)/VAAT, fOxa = 84.7% was calculated. From fMal = (fOxa(VAAT + VMDH) − fAspVAAT)/VMDH, fMal = 49.1%. Note that fAsp (95.8%) > fOxa (84.7%) > fMal (49.1%) > fFum (0%) because, contrary to intuition, in saturation transfer the unidirectional flux from the observed spin to the saturated spin is measured. That is, because of the nature of the Bloch-McConnell equations, it is the transfer of unsaturated magnetization that is actually measured. In the case of the four-site exchange model depicted in Fig. 2(b), the unidirectional cytosolic aspartate → cytosolic oxaloacetate → cytosolic malate → mitochondrial fumarate relay transfers unsaturated spins from cytosolic aspartate to mitochondrial fumarate. Thus, we have fAsp > fOxa > fMal > fFum. Also notably from Eq. , the steady state aspartate magnetization (fAsp) is directly balanced by VAAT and fOxa. The direct flux from Fum to Asp in the four-site exchange model does not appear in Eq.  because it contributes fFumVx (= 0) to fAsp.
From Eq. , Vx was estimated to be 13~19 μmol/g/min for T1Mal = 1.33~0.67 × T1Asp. For T1Mal = 2.0~0.5 × T1Asp, Vx = 11~23 μmol/g/min. The sensitivity of Vx to changes in experimentally detected ΔAsp/Asp0 was plotted in Fig. 4 for T1Mal = 1.33~0.67 × T1Asp and T1Mal = 2.0~0.5 × T1Asp. From Fig. 4, if ΔAsp/Asp0 were half of the measured value (2.1%), then Vx = 3.5~7.7 μmol/g/min for T1Mal = 2.0~0.5 × T1Asp.
The present study used recently discovered in vivo 13C magnetization transfer effects to investigate Vx. Because of the exclusive localization of brain fumarase in mitochondria it was possible to directly measure Vx from the four-carbon side of the TCA cycle. The results showed that Vx is much more rapid than VTCA.
Nearly all TCA intermediates are transported out of and into mitochondria through a host of exchangers and co-transporters (Siesjo, 1979; Palmieri, 2004). Carriers such as AGC and OGC couple the exchange of glutamate between mitochondria and cytosol on the five/six carbon side of the TCA cycle to that of aspartate on the four-carbon side. In addition to the unidirectional AGC depicted in Fig. 2(a), the reversible glutamate/hydroxyl carrier is also highly functional in brain mitochondria (Berkich et al, 2005). Likewise, other mitochondria-cytosol transport mechanisms involving four-carbon dicarboxylates exist in brain (Beck et al, 1977, Passarella et al, 1984, Palmieri, 2004). For example, the dicarboxylate carrier mediates an exchange between malate and phosphate ions across the mitochondrial inner membrane (Palmieri, 2004). In addition, the TCA cycle reactions occurring in the cytosol (i.e., reactions catalyzed by cytosolic TCA cycle enzymes) undoubtedly also contribute to the overall isotopic exchange between cytosol and mitochondria during infusion of 13C-labeled substrates. In metabolic models, the single flux term denoted by Vx accounts for these exchange processes.
As noted previously, attempts to assess the rate of 13C label exchange between mitochondria and cytosol extracted from metabolic modeling of 13C MRS measurement in human and animal brains have caused considerable controversy. If Vx is comparable to VTCA, VTCA will depend on Vx (Mason et al, 1992; 1995). The validity of regarding Vx as slow (Vx ≈ VTCA) or fast (Vx VTCA) has thus been vigorously debated, and the focus of this debate has been on metabolic modeling of 13C label incorporation into glutamate and aspartate for extraction of Vx.
Using metabolic modeling approaches to extract Vx is sensitive to small errors in the measurement of 13C labeling of glutamate C3 (Shen, 2006 and references therein). Furthermore, several factors in addition to Vx are known to affect the 13C labeling of glutamate C2 and C3, and therefore the accuracy of extracted Vx. For example, the exchange of other TCA intermediates between mitochondrial matrix and cytosol causes additional label dilution at glutamate C2 and C3 (Siesjo, 1978; Lapidot and Gopher, 1994; Shen, 2006). When the additional label dilution of glutamate C2 and C3 is not included in the model, slower than expected 13C label incorporation into glutamate C2 and C3 could be compensated by the metabolic model with an artificially slower Vx. Residual incomplete label scrambling at succinate and fumarate (Sherry et al, 1994), if significant in brain, would change the 13C label distribution between glutamate C2 and C3. Partial asymmetry generated by 13C entry through neuronal pyruvate carboxylase (Merle et al, 1996) also affects the labeling of glutamate C2 and C3.
Because of the controversies surrounding metabolic modeling of Vx, a fundamentally different approach is needed to shed light on this issue. Recently, the α-ketoglutarate-glutamate exchange across the mitochondrial inner membrane was measured in vitro using suspension of isolated rat brain mitochondria (Berkich et al, 2005). It was found that the efflux of combined α-ketoglutarate and glutamate from mitochondria is slower than the rate of synthesis of mitochondrial α-ketoglutarate. Unfortunately, many brain TCA cycle intermediates (e.g., oxaloacetate and α-ketoglutarate, both of which are crucial components of the malate-aspartate shuttle) are known to be rapidly depleted upon death (Siesjo, 1978). Furthermore, using in vivo 13C magnetization transfer spectroscopy, it was found that the exchange between glutamate and α-ketoglutarate in rat brain completely ceases upon cardiac arrest (Shen, 2005). Therefore, caution is needed when extrapolating the results by Berkich and colleagues (2005), which were obtained from isolated mitochondria, to in vivo conditions.
Aconitase, isocitrate dehydrogenase, citrate, and isocitrate reside both inside and outside mitochondria. As a result, separating the magnetization transfer between mitochondrial α-ketoglutarate/glutamate and cytosolic glutamate from that within the cytosol compartment becomes impossible. In addition, mitochondrial isocitrate dehydrogenase is one of the three control sites of the TCA cycle. The irreversible mitochondrial isocitrate → α-ketoglutarate flux rate is comparable to VTCA and is expected to cause considerable loss of saturation due to longitudinal relaxation if one attempts to relay magnetization saturation between mitochondrial isocitrate and cytosolic glutamate. Therefore, the relayed 13C magnetization transfer strategy is not suitable for measuring Vx from the five/six-carbon side of the TCA cycle.
The T1s of unprotonated carboxylic carbons of aspartate C1 at 175.0 ppm and C4 at 178.3 ppm are much longer than that of the protonated aspartate C2. In principle, they could be used to significantly increase the observed relayed 13C magnetization transfer effect. However, unlike the wide chemical shift separation that occurs among the C2 carbons of fumarate (136.1 ppm), malate (71.2 ppm), oxaloacetate (201.3 ppm), and aspartate (53.2 ppm), the chemical shift separation among the carboxylic carbons is too small (oxaloacetate C1: 169.3 ppm, C4: 175.4 ppm, malate C1 and C4: 181.8 ppm, fumarate C1 and C4: 175.3 ppm, aspartate C1: 175.0 ppm, C4: 178.3 ppm) to avoid a radiofrequency spillover effect (Shen and Xu, 2006) and/or to generate the clean subtraction necessary for reliable detection of a small difference signal (Fig. 3). Unlike the C3 carbons of malate, oxaloacetate, and aspartate, which are bonded with two protons, the C2 carbons are either nonprotonated or have only a single bonded proton. The C3 carbons therefore have much shorter T1 (Wehrli, 1976). The cumulative effect of short C3 T1s can significantly reduce the efficiency of the 13C magnetization transfer relay and significantly weaken our assumption of negligible T1 relaxation inside mitochondria. Experimentally, the relay of magnetization transfer to aspartate C3 was found to be much smaller than to aspartate C2, and it was therefore not used to determine Vx. In addition, the relayed 13C magnetization transfer method cannot be used to trace the TCA cycle further upstream to succinate C2 at 35.0 ppm; the symmetrical control frequency would need to be placed at 71.7 ppm, very close to the resonant frequency of malate C2 at 71.2 ppm, therefore interfering with the relay of magnetization saturation from the more remote succinate.
Fortunately, there exists a rare combination of favorable conditions which allowed for measuring Vx from the four-carbon side of the TCA cycle: i) the control of the TCA cycle only involves citrate synthase, isocitrate dehydrogenase, and α-ketoglutarate dehydrogenase while fumarase, malate dehydrogenase, and aspartate aminotransferase catalyze near equilibrium reactions. The forward and reverse rates of fumarase-, malate dehydrogenase-, and aspartate aminotransferase-catalyzed near equilibrium reactions are much greater than the TCA cycle flux through the reactions (Hawkins and Mans, 1983); ii) Fumarase is exclusively localized to mitochondria in brain. This allows isolation of the magnetization transfer relay pathway via Vx; iii) the chemical shift separation among C2 carbons of fumarate, malate, oxaloacetate, and aspartate is unusually wide (Table 1). This large separation, attributed to the distinctly different chemical environments among the C2 carbons, allowed for the relay of 13C magnetization saturation between fumarate and aspartate without any radiofrequency interference. The completely lack of any radiofrequency spillover effect is necessary to reliably detect the small magnetization transfer effect on aspartate C2 at 53.2 ppm in the presence of immense nearby signals such as glutamate C2 at 55.2 ppm and glutamine C2 at 55.1 ppm.
The mitochondrial pools of malate, oxaloacetate, and aspartate are very small (e.g., Sols and Marco, 1970; Mason et al, 1992; Gruetter et al, 2001; Wu et al, 2007). The linear exchange from fumarate to aspartate and back—catalyzed by fumarase, malate dehydrogenase, and aspartate aminotransferase in mitochondria—is therefore very rapid. Previous brain metabolic models considered these fast-exchanging mitochondrial pools as a single pool (e.g., Mason et al, 1992; 1995; Gruetter et al, 2001). When the turnover time constant due to exchange is much shorter than T1, loss of saturation of magnetization is negligible (Yang and Shen, 2007). In the present study, this allowed us to directly measure Vx using relayed magnetization transfer and to simplify the analysis of the relayed 13C magnetization transfer results by lumping the mitochondrial fumarate, malate, oxaloacetate, and aspartate pools into a single pool as shown in Fig. 2(b). Any loss of saturation inside mitochondria would underestimate Vx. Thus, using the simplified four-site exchange model in Fig. 2(b), the lower limit of Vx is obtained.
Quantitatively, if we also ignore T1 relaxation of the fast-exchanging malate and oxaloacetate extant in the cytosolic compartment, the four-site exchange model described in Fig. 2(b) is reduced to the simpler two-site exchange model commonly used in metabolic modeling of 13C turnover kinetics for glutamate and aspartate (Fig. 1). In this further simplified two-site exchange model cytosolic aspartate is in exchange with TCA cycle intermediates with a flux rate of Vx′. Neither the pool size of cytosolic malate is negligibly small nor cytosolic VAAT and VMDH fluxes are infinitely fast. As a result, Vx′ is smaller than that given by equation  because loss of magnetization saturation via longitudinal relaxation in the cytosol is lumped into Vx′. Using this further simplified two-site exchange model as well as equation  from Alger and Shulman (1984), we find that Vx′ = ΔAsp/Asp0 × [Asp0]/T1Asp = 0.042 × 2.8 μmol/g/(2.2/60 min) = 3.2 μmol/g/min, while the actual Vx is greater than Vx′.
Under 1.5% (minimum alveolar concentration) isoflurane anesthesia, the VTCA of rat cerebral cortex is approximately 0.40–0.48 μmol/g/min (Maekawa et al, 1986). The results from this relayed 13C magnetization transfer experiment clearly demonstrate that Vx VTCA regardless of our assumptions of T1Mal. If Vx/VTCA ≈ 1, as argued by Gruetter and colleagues (2001), the observed ΔAsp/Asp0 will have to be ~0.002 for T1Mal = 0.5 × T1Asp, and ~0.003 for T1Mal = 2 × T1Asp (Fig. 4). In either case, no relayed 13C magnetization transfer effect on aspartate is detectable when mitochondrial fumarate is saturated because of slow Vx.
Our fundamental conclusion that the isotopic exchange between mitochondrial TCA cycle intermediates and cytosolic metabolites is rapid is also independent of specific exchange models used for analyzing the relayed 13C magnetization transfer data; this is because Vx has to be fast enough on the time scale of 13C T1 relaxation to be detectable using magnetization transfer spectroscopy. That is, for an exchange process to be detectable using magnetization transfer, the exchange rate multiplied by T1 of the observed signal has to be a significant fraction of the pool size of the observed signal. If Vx ≈ VTCA, Vx × T1Asp ≈ 0.44 μmol/g/min × 2.2/60 min = 0.016 μmol/g, or less than 0.6% of the pool size of aspartate.
The absence of fumarase in brain cytosol, the rapid near equilibrium reactions catalyzed by fumarase, malate dehydrogenase and aspartate aminotransferase, and the wide chemical shift separation among C2 carbons of fumarate, malate, oxaloacetate, and aspartate allowed for the relay of 13C magnetization saturation between mitochondria fumarate and cytosolic aspartate via Vx. We found that this relay was significant and detectable using in vivo 13C magnetization transfer spectroscopy after extensive signal averaging. Quantitative analysis of the in vivo 13C magnetization transfer data showed that Vx is fast (i.e., Vx VTCA).
The authors thank Mr. Christopher S Johnson for technical assistance, Ms. Ioline Henter for help with preparation of the manuscript. This work is supported by the Intramural Research Program of the NIH, NIMH.
Disclosure/Conflict of Interest
The authors have no duality of interest.