Comprehensive metabolic modeling of multiple ¹³C-isotopomer data sets to study metabolism in perfused working hearts

The present study is the first to provide comprehensive metabolic modeling for the perfused working heart using ¹³C-metabolic flux analysis. Our approach integrates 12 data sets (with 4 unique ¹³C-tracers) into a single metabolic model, identifies inconsistencies in measurement data, and improves relative flux precision compared with previous algebraic models.

Abstract

In many forms of cardiomyopathy, alterations in energy substrate metabolism play a key role in disease pathogenesis. Stable isotope tracing in rodent heart perfusion systems can be used to determine cardiac metabolic fluxes, namely those relative fluxes that contribute to pyruvate, the acetyl-CoA pool, and pyruvate anaplerosis, which are critical to cardiac homeostasis. Methods have previously been developed to interrogate these relative fluxes using isotopomer enrichments of measured metabolites and algebraic equations to determine a predefined metabolic flux model. However, this approach is exquisitely sensitive to measurement error, thus precluding accurate relative flux parameter determination. In this study, we applied a novel mathematical approach to determine relative cardiac metabolic fluxes using ¹³C-metabolic flux analysis (¹³C-MFA) aided by multiple tracer experiments and integrated data analysis. Using ¹³C-MFA, we validated a metabolic network model to explain myocardial energy substrate metabolism. Four different ¹³C-labeled substrates were queried (i.e., glucose, lactate, pyruvate, and oleate) based on a previously published study. We integrated the analysis of the complete set of isotopomer data gathered from these mouse heart perfusion experiments into a single comprehensive network model that delineates substrate contributions to both pyruvate and acetyl-CoA pools at a greater resolution than that offered by traditional methods using algebraic equations. To our knowledge, this is the first rigorous application of ¹³C-MFA to interrogate data from multiple tracer experiments in the perfused heart. We anticipate that this approach can be used widely to study energy substrate metabolism in this and other similar biological systems.

NEW & NOTEWORTHY

The present study is the first to provide comprehensive metabolic modeling for the perfused working heart using ¹³C-metabolic flux analysis. Our approach integrates 12 data sets (with 4 unique ¹³C-tracers) into a single metabolic model, identifies inconsistencies in measurement data, and improves relative flux precision compared with previous algebraic models.

the mammalian heart must sustain continuous mechanical work and respond to rapid changes in energy demand, despite its limited capacity to store chemical energy. As such, maintaining a high rate of ATP production and possessing metabolic flexibility toward substrate utilization is important to the heart's normal physiology and function. During the fasting condition in the healthy heart, fatty acids contribute ∼70–90% to ATP generation, whereas a small fraction of ATP is produced from glucose, lactate, and other sources (29, 39, 51). In the fed state, the contribution of glucose to ATP generation increases, although fatty acids are still heavily leveraged as an energy fuel. In many forms of heart disease, including heart failure and diabetic cardiomyopathies, metabolic reprogramming of energy substrate metabolism and alterations in mitochondrial energy generation play an important role in disease pathogenesis (16, 35, 48). Specifically, metabolic rearrangements occur resulting in alterations in the ratio of fatty acid to glucose oxidation (17, 26, 28). In addition, the failing heart has been shown to utilize additional oxidative fuel sources, such as ketone bodies (11, 13), and increase glucose utilization through non-ATP producing pathways, such as pyruvate anaplerosis (9, 33, 44, 50). As such, determining the contribution of various energy substrates to tricarboxylic acid (TCA) cycle inputs (i.e., pyruvate and acetyl-CoA), as well as the rerouting of carbon through anaplerotic pathways is essential for understanding the underlying mechanisms of disease pathogenesis.

Rodent heart perfusions with radioactive-labeled (14, 38, 53) and stable isotope-labeled substrates (see Ref. 46 for a detailed review) have been commonly used to investigate cardiac metabolism in isolation from complex hormone or microenvironment cues. Stable isotope tracing, commonly via ¹³C-substrates, allows for estimation of substrate contributions into the TCA cycle via oxidative and nonoxidative routes (18, 30, 37, 49). The first stable isotope approaches (40, 41, 49) focused on ¹³C-NMR techniques to measure glutamate (equilibration with α-ketoglutarate was assumed); however, due to ¹³C-NMR's limited coverage of TCA cycle metabolites, mass spectrometry (MS) approaches were also developed. With the aid of gas chromatography/mass spectrometry (GC/MS), ¹³C-enrichment of pyruvate and TCA cycle metabolites could be measured and mathematical models employed to relate relative fluxes to these enrichments (18, 31), thus making it possible to determine sources of pyruvate, sources of mitochondrial acetyl-CoA, and anaplerosis with the labeling of citrate (and its derivatives), succinate, and pyruvate (19, 34, 42). Recent developments in liquid chromatography mass spectrometry (LC-MS) have allowed multiplexing of tracers to differentially label acetyl-CoA derived from glucose/pyruvate vs. that derived from fatty acid oxidation (37) thereby refining measurement of TCA cycle turnover and the contributions of various energy substrates to the acetyl-CoA pool.

All of these methods use a predefined set of algebraic equations to relate isotopomer enrichments to various relative flux parameters including those that contribute to the pyruvate and acetyl-CoA pools and anaplerosis. Generally, only a small fraction of available isotopomer data is used for determining relative fluxes. This strategy exposes flux determination to errors accrued from potentially erroneous ¹³C-enrichment measurements. The magnitude of the error can be large. In contrast, ¹³C-metabolic flux analysis (¹³C-MFA) implements a metabolic model that is an overdetermined system to describe the relationship between relative metabolic fluxes and isotopomer data based on the complete set of isotopomer balances. An overdetermined system requires regression for parameter estimation, which will dampen potential error due to a poor measurement. Given this advantage, we anticipated that comprehensive analysis of complete data through ¹³C-MFA would improve the precision and accuracy of estimated relative fluxes.

To probe the carbon source of pyruvate and acetyl-CoA pools from multiple substrates, previous studies have employed a strategy of perfusing isolated rodent hearts (18, 32, 54) in biological replicates, each with a different isotopic-labeled substrate (i.e., identical perfusions where only the ¹³C-labeled substrate is changed). The ability to improve relative flux parameter estimation through use of multiple ¹³C-substrates relies on the premise that certain substrates can assess different metabolic pathways (23, 24). Despite the potential of this technique, no study to date has used comprehensive isotopomer measurements from various tracer perfusions to estimate relative flux parameters. For example, in the study by Khairallah et al. (32), perfusions were performed with four different ¹³C-substrates, and the labeling distributions of tissue pyruvate and several TCA cycle intermediates [citrate, α-ketoglutarate (AKG), succinate, fumarate, and malate] were measured; however, only a small fraction of the data was used in relative flux parameter estimation. Vo and Palsson (55) similarly did not use the isotopomer data from all tracer perfusions but only used data from labeled glucose perfusions (36). Notably, the relative flux results obtained in these two studies varied greatly. Thus we anticipated that by rigorously analyzing all available data using ¹³C-MFA we could improve relative flux resolution compared with previous approaches (2, 22, 23, 36). For our mathematical analysis, we used the study of Khairallah et al. (32) as it had rich isotopomer data from perfusions with four different ¹³C-labeled substrates (i.e., glucose, lactate, pyruvate, and oleate).

MATERIALS AND METHODS

Heart perfusion data.

Khairallah et al. performed perfusion experiments on working hearts from male C57BL/10 mice using a modified Krebs-Henseleit buffer containing 11 mM glucose, 1.5 mM lactate, 0.2 mM pyruvate, and 0.7 mM oleate complexed to 3% BSA as energy substrates in the presence of 0.8 nM insulin and 5 nM epinephrine (for complete details see Ref. 32). In each perfusion, one of the substrates was replaced with the corresponding uniformally ¹³C-labeled equivalent, i.e., [U-¹³C]lactate [100% molar percent enrichment (MPE)], [U-¹³C]pyruvate (100% MPE), [U-¹³C]glucose (50% MPE), or [U-¹³C]oleate (25% MPE). It is important to note that these were initial MPE and could be subject to dilution over the course of the perfusion due to release of unlabeled metabolites. For this current study, the raw mass isotopomer data sets for pyruvate, citrate, α-ketoglutarate, succinate, fumarate, and malate were obtained from the GC/MS analysis performed by Khairallah et al. [see Table 1 for complete data (32); see appendix for GC/MS fragments]. For flux analysis, the mass isotopomer data were corrected for natural isotope abundances using the method of Fernandez et al. (27). These comprehensive data sets were aptly suited for integrated flux analysis as each perfusion had a single tracer and the various tracers provided coverage of the important substrates for cardiac metabolism. To account for perfusion-to-perfusion variability in our flux analysis, which could result from inherent physiology differences, surgical procedures for heart removal, ischemia exposure and recovery, etc., three replicate data sets were used for each tracer condition.

Table 1.

GC-MS data from heart perfusion experiments

	[U-13C]Lactate			[U-13C]Pyruvate			[U-13C]Glucose			[U-13C]Oleate
	Perfusion 1	Perfusion 2	Perfusion 3	Perfusion 4	Perfusion 5	Perfusion 6	Perfusion 7	Perfusion 8	Perfusion 9	Perfusion 10	Perfusion 11	Perfusion 12
Citrate
M + 0	0.341	0.336	0.471	0.558	0.541	0.513	0.542	0.532	0.509	0.478	0.362	0.356
M1	0.237	0.231	0.233	0.239	0.241	0.246	0.240	0.241	0.243	0.235	0.233	0.233
M2	0.212	0.210	0.165	0.140	0.148	0.158	0.146	0.149	0.161	0.173	0.221	0.221
M3	0.118	0.123	0.078	0.044	0.048	0.056	0.049	0.052	0.058	0.071	0.108	0.110
M4	0.059	0.063	0.035	0.015	0.017	0.020	0.018	0.019	0.022	0.030	0.053	0.053
M5	0.024	0.028	0.014	0.003	0.004	0.005	0.005	0.005	0.006	0.010	0.018	0.020
M6	0.008	0.010	0.004	0.001	0.001	0.001	0.000	0.001	0.001	0.003	0.006	0.006
Citrate, oxaloacetate (OAC) moiety
M + 0	0.434	0.411	0.510	0.667	0.653	0.621	0.658	0.622	0.621	0.532	0.499	0.500
M1	0.271	0.273	0.248	0.209	0.215	0.227	0.211	0.223	0.225	0.254	0.261	0.261
M2	0.182	0.190	0.155	0.096	0.100	0.113	0.100	0.114	0.114	0.149	0.163	0.162
M3	0.084	0.094	0.067	0.023	0.025	0.031	0.025	0.032	0.032	0.050	0.060	0.060
M4	0.030	0.032	0.020	0.005	0.006	0.008	0.006	0.008	0.008	0.014	0.018	0.018
α-Ketoglutarate
M + 0	0.341	0.360	0.404	0.572	0.556	0.522	0.545	0.513	0.521	0.435	0.402	0.394
M1	0.238	0.222	0.240	0.240	0.242	0.248	0.247	0.246	0.244	0.247	0.248	0.248
M2	0.210	0.195	0.194	0.133	0.141	0.155	0.144	0.158	0.156	0.195	0.207	0.209
M3	0.114	0.105	0.096	0.040	0.044	0.052	0.047	0.056	0.054	0.080	0.093	0.094
M4	0.067	0.073	0.045	0.012	0.014	0.018	0.016	0.021	0.020	0.033	0.039	0.041
M5	0.029	0.045	0.021	0.003	0.003	0.004	0.001	0.006	0.005	0.009	0.012	0.013
Pyruvate
M + 0	0.652	0.549	0.567	0.677	0.702	0.693	0.682	0.662	0.665	0.748	0.746	0.745
M1	0.150	0.127	0.131	0.155	0.161	0.159	0.157	0.152	0.152	0.170	0.171	0.171
M2	0.067	0.063	0.063	0.069	0.070	0.069	0.065	0.068	0.069	0.070	0.072	0.071
M3	0.131	0.261	0.238	0.100	0.067	0.079	0.097	0.118	0.114	0.012	0.011	0.013
Malate
M + 0	0.437	0.410	0.528	0.590	0.579	0.557	0.577	0.571	0.544	0.484	0.465	0.448
M1	0.261	0.265	0.240	0.238	0.241	0.248	0.242	0.241	0.248	0.260	0.265	0.266
M2	0.178	0.189	0.146	0.126	0.130	0.138	0.129	0.133	0.142	0.168	0.174	0.181
M3	0.088	0.098	0.062	0.036	0.038	0.044	0.040	0.042	0.050	0.066	0.072	0.078
M4	0.036	0.039	0.023	0.010	0.012	0.013	0.012	0.013	0.016	0.022	0.025	0.027
Succinate
M + 0	0.471	0.480	0.553	0.683	0.672	0.639	0.655	0.627	0.612	0.559	0.522	0.506
M1	0.248	0.247	0.221	0.196	0.198	0.212	0.199	0.211	0.212	0.236	0.243	0.249
M2	0.173	0.169	0.144	0.096	0.101	0.113	0.110	0.118	0.123	0.141	0.158	0.164
M3	0.077	0.075	0.061	0.020	0.022	0.028	0.026	0.033	0.037	0.050	0.059	0.062
M4	0.031	0.029	0.022	0.005	0.007	0.008	0.009	0.011	0.016	0.014	0.019	0.019
Fumarate
M + 0	0.457	0.451	0.452	0.659	0.643	0.627	0.638	0.599	0.589	0.532	0.504	0.495
M1	0.286	0.250	0.239	0.202	0.214	0.220	0.234	0.218	0.221	0.249	0.249	0.249
M2	0.120	0.180	0.186	0.104	0.112	0.121	0.095	0.130	0.132	0.164	0.170	0.170
M3	0.100	0.084	0.086	0.024	0.028	0.029	0.032	0.039	0.039	0.053	0.060	0.063
M4	0.037	0.034	0.037	0.011	0.003	0.003	0.001	0.014	0.019	0.002	0.017	0.024

The data were not corrected for natural isotope abundances. GC/MS, gas chromatography mass spectrometry.

Nomenclature.

It is important to define and clarify the terminologies used in this work to avoid confusions with terminologies used in other fields. Here, we followed the naming conventions in the ¹³C-MFA field. In ¹³C-MFA, isotopic labeling data are fitted to a metabolic network model to estimate relative fluxes (sometimes also called “flux ratios”). Often, one reaction in the model is selected as a reference reaction (e.g., a common choice is a substrate uptake reaction, which is given an arbitrary value of 100) and all other fluxes are then expressed relative to this reference reaction flux. As such, ¹³C-MFA estimated fluxes are not true fluxes as commonly defined in physiology literature (i.e., defined as having units of mol·g⁻¹·min⁻¹) but more accurately “yield” terms. In the remainder of the text, we use the terms “relative flux” and “relative fluxes” to refer to the ¹³C-MFA estimated fluxes. For consistency with the previous study by Khairallah et al. (32), we have selected the citrate synthase reaction as the reference reaction. Thus all estimated relative fluxes in this study have the units of mol/100 mol citrate synthase flux. Note that these relative fluxes can be converted to absolute fluxes (with units of mol·g⁻¹·min⁻¹) by measuring the absolute rate of the reference reaction, in this case, the citrate synthase flux.

Metabolic network model and assumptions for ¹³C-MFA.

Figure 1 shows the metabolic network model used in this study to describe the working heart. Table 2 shows the stoichiometry for each reaction and the corresponding carbon atom transitions. The model is comprised of 23 reactions utilizing 23 metabolites, with 7 substrates (external sources: glucose, lactate, pyruvate, and oleate; and unlabeled endogenous sources: acetyl-CoA, α-ketoglutarate, and pyruvate), 3 products (citrate efflux, succinate efflux, and CO₂ efflux), 13 balanced intracellular metabolites, and several unbalanced metabolites (e.g., O₂, NAD⁺, NADH, ATP). The model includes basic pathways of primary metabolism, including a lumped glycolysis pathway, tricarboxylic acid (TCA) cycle, fatty acid oxidation, anaplerosis from pyruvate carboxylation and glutamate transamination, and cataplerosis in the form of citrate efflux and succinate efflux. It is important to note that the model cannot distinguish between pyruvate carboxylase vs. malic enzyme for pyruvate carboxylation. For simplicity, we used pyruvate carboxylase to remain consistent with the original Khairallah et al. (32) study and assumed any malic enzyme flux would result in pyruvate formation. The model also incorporates three metabolic compartments: cytosol, mitochondrion, and extracellular. Reactions in the model were assigned to specific compartments based on current knowledge. In this model, the reactions catalyzed by isocitrate dehydrogenase and aconitase were assigned to the mitochondrion and the malic enzyme reaction to the cytosol. The malate/aspartate shuttle was not included in the model. Furthermore, the model includes additional fractional labeling parameters for each measured metabolite pool, the so-called “G-parameters” that are commonly used in ¹³C-MFA field. As described previously (8), a G-value represents the fraction of a metabolite pool that is produced during the labeling experiment. In this study, the G-parameters also account for the apparent dilution of the measured metabolites by other “metabolically inactive” compartments and other metabolically inactive cell populations of the heart (see also discussion). By default, one G-value parameter was included for each measured metabolite in each data set. Reversible reactions were modeled as separate forward and backward fluxes. Net and exchange fluxes were determined as follows: v_net = v_f − v_b; v_exch = min(v_f, v_b). ¹³C-labeled substrates were assumed to have atomic purity of 99%.

Fig. 1.

Flux model for perfused working heart. The flux model consists of three compartments: external (EXT), cytosol (C), and mitochondria (M). The model includes basic pathways of primary metabolism: glycolysis, tricarboxylic acid (TCA) cycle, fatty acid (FA) oxidation, and the anaplerotic reaction from pyruvate to oxaloacetate (pyruvate carboxylase).

Table 2.

Stoichiometry and carbon transformations for reactions in the network model in Fig. 1

Reaction Number	Reaction Stoichiometry	Carbon Atom Transitions*
Sources of pyruvate
1	Glucose.ext → 2 PYR.c	abcdef → cba + def
2	PYR.ext → PYR.c	abc → abc
3	LACT.ext → LACT.c	abc → abc
4	AA_C3 → PYR.c	abc → abc
5	PYR.c ↔ LACT.c	abc ↔ abc
Amphibolic reactions
6	PYR.m → AcCoA.m + CO2	abc → bc + a
7	PYR.m + CO2 → OAC.m	abc + d → abcd
8	MAL.c → PYR.c + CO2	abcd → abc + d
9	AA_C5 → AKG.m	abcde → abcde
Tricarboxylic acid cycle (TCA)
10	AcCoA.m + OAC.m → CIT.m	ab + cdef → fedbac
11	CIT.m ↔ ICIT.m	abcdef ↔ abcdef
12	ICIT.m ↔ AKG.m + CO2	abcdef ↔ abcde + f
13	AKG.m → SUCCoA.m + CO2	abcde → bcde + a
14	SUCCoA.m ↔ SUC.m	abcd ↔ (½ abcd + ½ dcba)
15	SUC.m → FUM.m	(½ abcd + ½ dcba) → (½ abcd + ½ dcba)
16	FUM.m ↔ MAL.m	(½ abcd + ½ dcba) ↔ abcd
17	MAL.m ↔ OAC.m	abcd ↔ abcd
Fatty acid oxidation
18	Oleate.ext → 9 AcCoA.m	ababababababababab → 9 ab
19	FA → 8 AcCoA.m	abababababababab → 8 ab
Intracellular transport
20	PYR.c ↔ PYR.m	abc ↔ abc
21	MAL.c ↔ MAL.m	abcd ↔ abcd
Effluxes
22	CIT.m → CIT.sink	abcdef → abcdef
23	SUC.m → SUC.sink	abcd → abcd

^*For each compound carbon atoms are identified using lowercase letters to represent successive carbon atoms of each compound. Because fumarate and succinate are rotationally symmetric, no distinction can be made between carbon atoms 1 and 4, and carbon atoms 2 and 3.

¹³C-metabolic flux analysis.

All simulations and ¹³C-MFA calculations were performed using the Metran software (56), which is based on the elementary metabolite units (EMU) framework (7). Relative metabolic fluxes and their confidence intervals were determined by fitting of mass isotopomer abundances of citrate, α-ketoglutarate, succinate, fumarate, and malate to the described metabolic network model. For modeling purposes, it is important to note that the “oxaloacetate moiety” of citrate, as reported in the original study, is a citrate measurement (C1-2-3-6), not an oxaloacetate measurement (see appendix for full details). Fluxes were estimated using Metran by adjusting relative fluxes to minimize the variance-weighted sum of squared residuals (SSR) between the measured and model predicted mass isotopomer distributions. Metran uses a nonlinear least-squares regression algorithm to find the best solution (6). For integrated analysis of parallel labeling experiments, all data sets were fitted simultaneously to a single flux model as described previously (36). Flux estimation was repeated 10 times starting with random initial values for all relative fluxes to ensure that a global solution was found. At convergence, accurate 95% confidence intervals were computed for all estimated relative fluxes by evaluating the sensitivity of the minimized SSR to flux variations (6). To evaluate the goodness-of-fit, ¹³C-MFA fitting results were also subjected to a χ²-statistical test. In short, assuming that the model is correct and data are without gross measurement errors, the minimized SSR is a stochastic variable with a χ²-distribution (6). The number of degrees of freedom is equal to the number of fitted measurements n minus the number of estimated independent parameters p. The acceptable range of SSR values is between χ²_α/2(n − p) and χ²_1-α/2(n − p), where α is a certain chosen threshold value, e.g., 0.05 for 95% confidence interval. In this study, SSR values above the maximum acceptable threshold value were interpreted to indicate that either the model was not acceptable (e.g., the model was too simple) or that one or more fragments contained gross measurement errors. Both possibilities were considered.

RESULTS

Accounting for biological variability in unlabeled mass isotopomer fraction.

Before modeling the relative fluxes, we first analyzed the large set of mass isotopomer data for consistency [after correcting the labeling data for natural isotope abundances (27)]. As a specific example, we examined citrate's mass isotopomers for each set of replicate tracer experiments. For each set, there was large variability in the unlabeled (M + 0) mass isotopomer fraction of citrate (see Fig. 2). For example, with [U-¹³C]lactate as tracer, the three replicates had M + 0 ranging from ∼54 to 76% of the isotopomer distribution. Similarly, the [U-¹³C]oleate experiments displayed a range of M + 0 from ∼57 to 77%. Attempts to regress isotopomer data with such high variability in M + 0 fractions resulted in unacceptable model fits.

Fig. 2.

Citrate isotopomer enrichments for tracer experiment with [U-¹³C]lactate (A); [U-¹³C]pyruvate (B); [U-¹³C]glucose (C); and [U-¹³C]oleate (D). For each plot, isotopomer enrichments for the triplicate experiments are plotted with unlabeled (M + 0) fraction present, i.e., “All isotopomers” and without M + 0 fraction, i.e., “Labeled no M + 0.” Variability within triplicate experiments exist when the data includes the M + 0 fraction; however, the ratio of labeled isotopomers are consistent across triplicates when the M + 0 fraction is removed. This suggests that metabolism of a given tracer is consistent across the different heart perfusions.

To determine whether the data would be suitable for flux analysis by including appropriate dilution parameters, only the labeled isotopomer fractions were compared with each other (see Fig. 2). This is indicative of how a tracer is being metabolized, as labeled isotopomers can only result from active metabolism of the tracer and are insensitive to dilution due to unlabeled metabolite pools. When labeled isotopomers were compared, the data sets for each tracer displayed high consistency with each other (Fig. 2). This suggested that metabolism of a given tracer was consistent across the different heart perfusions and that variability in M + 0 fractions in citrate and other intermediates could be explained due to presence of metabolically inactive metabolite pools, e.g., resulting from intracellular compartmentation or the inaccessibility of a tracer to various cell populations in the perfused heart (see Fig. 3). From a modeling perspective, the apparent differences in dilution can be accounted for with the so-called “G-value parameters” commonly used in the ¹³C-MFA field for this purpose (8). Thus, based on the initial isotopomer analysis, the labeling data were determined to be amenable for flux analysis and G-parameters were included for ¹³C-MFA.

Fig. 3.

Tracing the metabolic fate of metabolite A, which is 50% M+1 and 50% M+3, to product metabolite C. In a linear pathway (A), product metabolite C has the same labeling as both A and B. If dilution occurs at an intermediate metabolite as in B, the isotopomer enrichments of metabolite B and C are the same, and are diluted compared with metabolite A. In the case where an intermediate metabolite has an active metabolite pool and an isolated, unlabeled pool (C), the label in metabolite A and C will be the same; however, B will have an “apparent” dilution. In reality, the B-pool that is metabolite active has the same label as both A and C. The G-parameter accounts for the apparent dilution due to the isolated, unlabeled B-pool.

Evaluation of metabolic model and goodness-of-fit.

To characterize the relative metabolic fluxes, a comprehensive analysis was performed on all 12 data sets (i.e., four tracers, each with triplicate perfusions) with the network model shown in Fig. 1 and Table 2. Mass isotopomer distributions for pyruvate, citrate, the oxaloacetate moiety of citrate (Cit_OAC), α-ketoglutarate, succinate, fumarate, and malate were obtained from Ref. 32. The first attempt at flux analysis (model 1) involving all metabolite data (444 fitted isotopomers) resulted in a fit that was not statistically accepted, with a SSR >2000 (see Table 3). The SSR value is a statistical measure of the lack of fit between the measured isotopomer data and the simulated isotopomer data. The SSR value has a well-defined upper threshold value that is based on the number of measurements fitted and the number of relative flux parameters estimated. From analysis of the residuals, fumarate and citrate isotopomers were found to account for >80% of the total SSR in the model fit. To determine which measurements were most problematic, ¹³C-MFA was performed again in the absence of fumarate (model 2a), citrate (model 2b), or Cit_OAC (model 2c) isotopomers. In the absence of fumarate, the model fit was unacceptable and citrate measurements were still the predominant source of error. When either of the citrate measurements was removed, the model fit was still unacceptable and the fumarate isotopomers dominated the error.

Table 3.

Evaluation of goodness-of-fit

	Model
	1	2a	2b	2c	3	4
No. of fitted mass isotopomers	444	384	360	384	324	318
No. of estimated fluxes*	9	9	9	9	9	9
No. of dilution parameters	72	60	72	72	60	59
No. of redundant measurements†	363	315	279	303	255	250
Sum of squared residuals (SSR)	2061	1163	1262	1332	435	197
Fumarate SSR	889	−	881	891	−	−
Sum of citrate SSR	806	791	27	73	63	45
Threshold value for SSR‡	421	368	330	356	303	298
Fit statistically acceptable§	No	No	No	No	No	Yes
Measurements omitted	None	Fum	Cit	CitOAC	Fum & CitOAC	Fum & CitOAC & AKG(1/12)

The complete and reduced data sets were fitted to the metabolic network model in Fig. 1. The fits were statistically evaluated for goodness-of-fit.

^*Number of estimated fluxes equals the number of independent fluxes that were statistically different from zero, as judged by 95% confidence interval. †Number of redundant measurements = (no. of fitted isotopomers) − (no. of estimated flux) − (no. of G-value parameters). ‡Threshold value for the χ²-statistical test of model adequacy at 95% confidence level. §Fit is statistically acceptable if SSR is less than the threshold value for SSR.

Based on these results, fumarate measurements were determined to contain gross errors. Note that fumarate was detected at low concentrations (see Fig. 3 in Ref. 32) and thus likely contained disproportionally large measurement errors. Our analysis also revealed that citrate and Cit_OAC were incompatible with the rest of the data if both were included. Thus we had to remove one of the citrate measurements. It is important to note Cit_OAC was obtained by postharvest treatment of the tissue lysate with ATP-citrate lyase, resulting in production of oxaloacetate, which was then measured by GC-MS. We chose to retain the full molecule citrate data for flux analysis over the oxaloacetate moiety for several reasons. First, GC-MS measurement of citrate (C1-6) is relatively more robust and reproducible than oxaloacetate due to metabolite abundance and derivatization efficiency. Second, since the citrate measurement contains the full carbon backbone, the measurement directly places constraints on precursor labeling (i.e., acetyl-CoA), where as Cit_OAC does not. Lastly, the analytical methods to obtain Cit_OAC are nontrivial and require additional processing steps before GC-MS analysis. For example, the enzymatic cleavage method may result in confounded labeling patterns, as the measured oxaloacetate is a mixture of citrate-derived oxaloacetate and any endogenous oxaloacetate.

When fumarate and Cit_OAC were removed (model 3), the model was still not acceptable. The SSR was slightly higher than the maximum allowable threshold value of 303. In this case, AKG from one data set accounted for ∼50% of the total SSR. This one AKG measurement also accounted for high SSR values in models 2a, 2b, and 2c. Based on these observations, we concluded that AKG data in this one specific data set likely contained gross errors. Upon removal, a statistically acceptable fit was obtained with an SSR of 197, well less than the maximum acceptable SSR threshold value of 298. Overall, the comprehensive model contained a total of 318 mass isotopomers for the estimation of 68 parameters (9 free fluxes and 59 G-value parameters). Thus the analysis included 250 redundant measurements. To our knowledge, this is one of the largest data sets ever used and successfully integrated by ¹³C-MFA for flux analysis in any mammalian system.

Flux estimation results and comparison to algebraic results.

The estimated flux map from ¹³C-MFA of the heart perfusion data is shown in Fig. 4 (full results are in Supplemental Table S2; Supplemental Material for this article is available online at the Journal website). Note that we report here relative flux values, in this case, relative to the citrate synthase flux, which was given the value of 100. If necessary, relative fluxes can be converted to absolute fluxes by multiplying the estimated relative fluxes with citrate synthase flux. For example, in previous studies Khairallah et al. (32) estimated a citrate synthase flux of about 9.4 ± 1.4 μmol/(min/g dry wt).

Fig. 4.

Relative metabolic fluxes from glucose, lactate, pyruvate, oleate, and endogenous sources to intracellular pyruvate and citrate. Relative fluxes were determined with ¹³C-MFA by minimizing the deviation between measured mass isotopomer distributions and mass isotopomer distributions predicted by the model. Values shown are best fit ± SD. Light gray arrows indicate that the relative flux was not statistically different from zero.

Based on the ¹³C-MFA model fit, 50.5 ± 1.4% of pyruvate was derived from perfusate lactate, whereas glucose provided about 37.5 ± 2.0% of the pyruvate, and the remaining 12 ± 0.8% was from perfusate pyruvate. Regarding contributions to acetyl-CoA, 60.2 ± 0.9% was derived from oleate oxidation, 39.8 ± 0.9% from pyruvate oxidation via pyruvate dehydrogenase (PDH), and endogenous sources did not contribute, 0.0 ± 0.4%. In addition, anaplerosis via pyruvate carboxylation was estimated to be 5.5 ± 0.5% relative to the citrate synthase flux.

A comparison of the ¹³C-MFA results to the estimates obtained in the original study using algebraic equations (32) is shown in Table 4. Overall, ¹³C-MFA results provided more precise estimates for substrate contributions to pyruvate than the algebraic method. In the prior study, it was acknowledged that the equations resulted in underestimation of glucose contribution to pyruvate and overestimation of endogenous sources to pyruvate. Our ¹³C-MFA results are consistent with this observation. Both ¹³C-MFA and the algebraic method resulted in similar estimates for oleate's contribution to acetyl-CoA; however, endogenous contributions to acetyl-CoA were drastically overestimated by the algebraic method, where ¹³C-MFA identified these contributions as negligible. Regarding anaplerotic reactions, both ¹³C-MFA and the algebraic method predicted similar values for pyruvate carboxylation (5.5 ± 0.5 vs. 4.9 ± 1.8%) and malic enzyme (0.0 ± 0.1% vs. negligible).

Table 4.

Comparison of relative fluxes estimated by ¹³C-MFA and from algebraic equations

Reaction	13C-MFA Results (This Study)	Algebraic Equations [Khairallah et al. (32)]
Sources of intracellular pyruvate
External pyruvate → pyruvate	5.4 ± 0.4 (12.0% ± 0.8)	10.7% ± 0.4
External glucose → pyruvate*	17.0 ± 0.8 (37.5% ± 2.0)	21.3% ± 3.0 (underestimate)
External lactate → pyruvate	22.8 ± 0.4 (50.5% ± 1.4)	42.0% ± 2.3
Endogenous sources → pyruvate	0.0 ± 0.4	26.0% ± 0.5 (overestimate)
Malate → pyruvate	0.0 ± 0.1	Negligible
Sources of mitochondrial acetyl-CoA
Pyruvate → AcCoA + CO2	39.8 ± 0.9	23–32
External oleate → AcCoA†	60.2 ± 0.9	63.5 ± 3.9
Endogenous sources → AcCoA	0.0 ± 0.4	9.8 ± 5.7
TCA cycle fluxes
Citrate synthase (fixed at 100)	100 (fixed)	100 (fixed)
Pyruvate carboxylase (PC)	5.5 ± 0.5	4.9 ± 1.8
Other endogenous anaplerotic sources	0.0 ± 0.2	Not significant
Efflux of citrate‡	(0–6.32)	0.8 ± 0.1
Efflux of succinate‡	(0–6.32)	Approximately 13% of anaplerosis

Fluxes are expressed as percentages of citrate synthase flux, which was given the value of 100. ¹³C-metabolic flux analysis (¹³C-MFA) results are reported as values ± SD, whereas the algebraic equations are reported as values ± SE.

^*Glucose produces 2 pyruvate molecules, i.e., (17.0 ± 0.8) = 2 × (8.5 ± 0.4.

^†Oleate produces 9 acetyl-CoA molecules, i.e., (60.2 ± 0.9) = 9 * (6.7 ± 0.1).

^‡The efflux fluxes of citrate and succinate could not be estimated independently. The combined efflux is 5.5 ± 0.5.

Evaluation of alternative design of perfusion experiments.

After completing ¹³C-MFA on the complete data set, we utilized the same model (model 4 in Table 3) and repeated flux estimation for individual tracers (n = 3 data sets for each tracer) and various combinations of two tracers (n = 6 data sets). Representative example results are shown in Fig. 5. Here, results shown are for flux analysis on data sets for 1) [U-¹³C]glucose; 2) [U-¹³C]oleate; 3) integrated analysis of [U-¹³C]glucose and [U-¹³C]oleate data; and 4) complete analysis of all data sets (i.e., Fig. 4). The [U-¹³C]glucose data set estimated glucose contribution to pyruvate with good precision. Similarly, [U-¹³C]oleate could estimate the contribution of oleate to acetyl-CoA. However, neither individual nor dual tracers could provide precise estimates of perfusate lactate contribution to pyruvate, perfusate pyruvate contribution to pyruvate, pyruvate oxidation (PDH), or pyruvate anaplerosis. Ultimately, neither the individual tracers nor the dual tracer data sets could estimate the relative fluxes with the precision obtained through comprehensive integration of all four tracers and 12 data sets. This result clearly demonstrates the power of integrated flux analysis and the need for careful tracer selection when designing ¹³C-MFA experiments to maximize relative flux resolution.

Fig. 5.

Comparison of estimated relative fluxes using the network model in Fig. 1 and the following GC-MS data sets: 1) [U-¹³C]glucose (n = 3), 2) [U-¹³C]oleate (n = 3), 3) integrated analysis of [U-¹³C]glucose and [U-¹³C]oleate (n = 6 total), and 4) all data sets, i.e., Fig. 4. Relative fluxes depicted are contribution to cytosolic pyruvate by external (A) glucose, (B) lactate, and (C) pyruvate; contributions to acetyl-CoA by (D) pyruvate dehydrogenase (PDH) and (E) oleate oxidation; anaplerosis through (F) pyruvate carboxylase. Note that the integrated analysis of all 12 data sets provided the best flux resolution for relative fluxes displayed.

DISCUSSION

With the use of the rich data set from Khairallah et al. (32), isotopomer data from multiple ¹³C-tracer perfusions in ex vivo working hearts were successfully integrated into a single comprehensive model to elucidate relative cardiac metabolic fluxes. The model incorporated >300 fitted isotopomers, included 250 redundant measurements, and estimated 68 relative flux parameters. To our knowledge, this is the first successful application of the ¹³C-MFA approach to incorporate multiple tracer data sets to determine relative cardiac fluxes in the perfused heart. Aside from the large-scale usage of mass spectrometry data, a distinguishing feature of our strategy was the implementation of data from the parallel labeling experiments (4). Parallel labeling experiments are increasingly becoming the standard for optimal flux resolution in both microbial (10, 20, 23, 36, 52) and mammalian systems (2, 3, 25). This approach employs the use of replicate biological experiments, whereby each replicate differs only by the ¹³C-tracer (labeled substrate) chosen. Mass isotopomer data from all individual replicates are then simultaneously fit into a single flux model. Because different tracers provide varying degrees of relative flux information (see Fig. 5), the integrated analysis of several tracer experiments can have an additive impact on flux resolution and result in highly precise relative flux estimates (24). The experimental design from Khairallah et al. (32) was aptly suited for the application of integrated flux analysis with parallel labeling experiments.

To reach an acceptable flux model as determined by well-established statistical measures, several modeling decisions were made based on analysis of the complete mass isotopomer data set. Upon careful inspection of the data, there was significant disagreement in the unlabeled isotopomer fraction (M + 0) for replicate tracer experiments. To investigate whether the differences in M + 0 was a result of differences in relative metabolic flux, the ratio of labeled isotopomers were compared for replicate tracer perfusions. When this was performed, minimal differences were observed and based on this observation we concluded that differences in M + 0 resulted from varying dilution between experiments. To account for differences in apparent dilution, the so-called “G-value parameters” were incorporated into the flux model as is typically done in ¹³C-MFA.

The usage of G-values serves several purposes in our flux modeling. First, the G-value corrects for variations in the fraction of an intracellular metabolite pool that is produced during the labeling experiment (8). Second, the G-parameter corrects for differences of tracer accessibility to the various cell populations in the heart. Among other explanations, this could be a result of metabolite “zonation” across the coronary arteries or dilution of the ¹³C-tracer in the perfusate over the course of the experiment (e.g., production of lactate, which dilutes ¹³C-lactate tracer). In addition, the G-parameter corrects for heterogeneity of metabolic function in the cardiac cell population. For example, variability in heart surgery and cannulation procedures may result in ischemic damage to the heart tissue, which can impact the population of cells metabolizing the tracer. Cells with low or no metabolic activity still have metabolite pools that can contribute to the apparent dilution observed in the data. Lastly, G-values correct for intracellular compartments of metabolite pools. Depending on the ¹³C-tracer used, metabolite pools in various intracellular compartments can label to varying extents. For example, peroxisomal acetyl-CoA in heart is predominantly formed from oxidation of long-chain fatty acids (15, 45), and as a result, this pool of acetyl-CoA will label from a ¹³C-oleate tracer but not from a ¹³C-glucose tracer.

In the initial flux model, we incorporated all of the metabolite data measurements (>400 fitted isotopomers); however, our initial attempts to reconcile the data were not statistically acceptable. The sum of squared residuals (SSR) was consistently larger than the threshold value for the statistical test of goodness-of-fit. Further analysis revealed that the mass isotopomer data from fumarate and the oxaloacetate moiety of citrate were incompatible with the rest of the data, suggesting the presence of gross measurement errors in these fragments. Upon removal of these fragments (and 1 extraneous AKG measurement), the reduced data set was successfully fit to a single flux model.

In regards to the relative flux results, the ¹³C-MFA approach was compared with the relative flux estimates in the initial study (32). Overall, the ¹³C-MFA method provided improved resolution of flux contributions at both the pyruvate and acetyl-CoA nodes. Relative anaplerotic flux estimates were very similar between ¹³C-MFA and the algebraic method. It was quite surprising that the ¹³C-MFA model predicted negligible contribution of endogenous sources to pyruvate (reaction 4 in Table 2), for example, from glycogen degradation or alanine transamination. To interrogate this potential discrepancy, we determined the average G-value for pyruvate across the perfusions to be 65 ± 6%. This indicates that ∼35% of pyruvate was not accounted for from the tracer labeling. The value is a known overestimate, since the tracer enrichment in the perfusate for [U-¹³C]lactate and [U-¹³C]pyruvate perfusions became diluted over the duration of the perfusion. Performing the comprehensive flux analysis with an estimated final tracer enrichment of ∼67% (based on Table 2 in Ref. 32 and pyruvate isotopomer data), the average G-value for pyruvate increased to ∼80%. Endogenous contribution to pyruvate of ∼20% is comparable to what was previously estimated (32).

Regarding the acetyl-CoA node, the algebraic method and the ¹³C-MFA approach were comparable in estimating oleate contributions to acetyl-CoA; however, the ¹³C-MFA results were in disagreement for pyruvate-derived and endogenously-derived acetyl-CoA. Khairallah et al. (32) reported that endogenous fatty acids (or amino acids) relative to citrate synthase contributed 10 ± 6% (32). Our model estimated negligible contributions of endogenous fatty acids. Based on the large standard error (∼6%) in the reported estimate, the confidence interval on this relative flux parameter would include zero. As such, our estimate from ¹³C-MFA would not be significantly different from what was reported. It is possible that the choice of perfusate substrates, hormones, and other supplements precluded the usage of endogenous acetyl-CoA substrates. Nevertheless, it is still surprising that endogenous sources of fatty acid were not a contributing factor as recent studies have shown that endogenous oxidation of fatty acids from triglycerides can contribute significantly to fatty acid oxidation even in the present of high levels of exogenous fatty acid (12, 47). To investigate this further, we defined the endogenous fatty acid contribution to acetyl-CoA as a “measured relative flux” and gradually increased the contribution of this parameter to see what the model could support (i.e., model SSR < SSR threshold). From this, it was found that 0–12% of acetyl-CoA could be derived from exogenous fatty acid. However, the optimal model fit (lowest SSR) still favored no endogenous contribution to acetyl-CoA. Recently, methods have been developed to estimate the endogenous contribution of fatty acids to acetyl-CoA (12) and measure isotopic enrichment of acetyl-CoA (37). If either of these are measured for the desired perfusion conditions, flux models can be constrained by one or both of these measurements, allowing for better resolution of contributions to acetyl-CoA.

To evaluate consistency of our results with earlier studies in mice, we estimated the ATP production from fatty acids based on our relative flux estimates (Table 4) and previously published stoichiometry (2.5 mol ATP/mol NADH and 1.5 mol ATP/mol FADH₂) in radiolabeled tracer experiments (1, 14). From the calculation we determined the ATP production from fatty acids to be ∼59%. Belke et al. (14) estimated ∼64–92% contribution to ATP from fatty acid depending on the exogenous fatty acid concentration. Khairallah et al. (32) estimated the ATP contribution from fatty acids was ∼62%. Given that the earlier works had similar but not identical perfusion conditions, and the close agreement with the estimate of Khairallah et al. (32), we believe our model results are in accordance with previous literature values.

A major difference between ¹³C-MFA and approaches based on algebraic relationships is the quantity of isotopomer data used. Previous flux methodologies have used ¹³C-NMR spectra of a single metabolite (30) or selective MS measurements (32, 37). These mathematic models are fully determined (i.e., number of equations = numbers of unknown fluxes), meaning a unique flux solution exists, which can be very sensitive to measurement error. Unlike the algebraic methods, ¹³C-MFA is not restricted to a small set of metabolite measurements but can include large amounts of isotopomer data. Prior ¹³C-MFA analysis by Vo and Palsson (55) incorporated only [U-¹³C]glucose data and utilized ∼30 isotopomers; in contrast, our study included data from all four tracer perfusions performed and all biological replicates, which resulted in more than 300 fitted mass isotopomers in the final model. ¹³C-MFA is an overdetermined mathematical system (i.e., number of measurements > numbers of unknown fluxes), which requires regression for parameter estimation. Comprehensive analysis of multiple tracer data sets through ¹³C-MFA provides opportunities to 1) identify inconsistencies in the data such as systemic gross measurement errors; 2) validate the proposed metabolic flux model; and 3) take advantage of the redundancy in the data to improve the precision and accuracy of estimated relative fluxes. Furthermore, with the current status of MS technologies (5, 43), additional measurements of TCA cycle intermediates (e.g., acetyl-CoA, aspartate as proxy for oxaloacetate, etc.) are possible that were not included in the study of Khairallah et al. (32). These additional measurements will only further improve relative flux resolution through ¹³C-MFA. Lastly, another advantage of ¹³C-MFA is the calculation of accurate confidence intervals (6). The sensitivity of the model fit (as captured by the SSR values) to changes in relative flux values is indicative of the flux precision. A large increase in SSR resulting from a small change in a relative flux value indicates a well-determined flux; conversely, a small increase in SSR would infer lower flux precision. This technique enables a rigorous evaluation of how uncertainties in the measurements are propagated to uncertainties in the estimated relative fluxes.

Despite demonstrating successful integration of parallel labeling experiments from heart perfusions, there are several experimental considerations that merit further discussion. An open question is whether biological and operational reproducibility may pose problems for flux resolution in parallel tracer experiments of perfused organs. In this study, we were able to apply the concept of G-parameter dilutions to account for differences in perfusion-to-perfusion. However, it remains unclear whether this approach will always be applicable. Furthermore, while parallel labeling efforts have been demonstrated for optimal flux estimation in microbial and mammalian systems, this approach may not be feasible for large scale studies involving animal models. For example, in this study, 12 perfusions were used to determine relative fluxes for 1 experimental condition. In studies with multiple animal treatment groups, parallel tracer labeling approaches may not be practical depending on the number of tracers interrogated and the amount of biological replicates required. In efforts to reduce the amount of perfusions required for ¹³C-MFA, mixtures of tracers may be the best option for elucidating TCA cycle fluxes in the perfused heart; however, it is likely that this will incur a cost of decreased flux resolution as shown with previous studies (21, 24). These aforementioned challenges present interesting questions for the future direction of ¹³C-MFA in perfusion studies and warrant further study. Regardless of these caveats, this current study has demonstrated that ¹³C-MFA is a powerful tool for studying relative metabolic pathway fluxes in the perfused heart.

GRANTS

S. B. Crown is supported by National Institute of Diabetes and Digestive and Kidney Diseases Grants R01-DK-089312 and P01-DK-058398.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

S.B.C., J.K.K., D.M.M., and M.A. conception and design of research; S.B.C. and M.A. analyzed data; S.B.C., J.K.K., D.M.M., and M.A. interpreted results of experiments; S.B.C. prepared figures; S.B.C. drafted manuscript; S.B.C., J.K.K., R.R., D.M.M., and M.A. edited and revised manuscript; S.B.C., J.K.K., R.R., D.M.M., and M.A. approved final version of manuscript.

APPENDIX

Appendix Table A1 shows measured GC/MS metabolite fragments.

Table A1.

Measured GC/MS metabolite fragments from Khairallah et al. (32)

Metabolite	Fragment (m/z)	Formula	C-atoms	Derivative
Citrate	459	C20H39O6Si3	1-2-3-4-5-6	TBDMS*
Citrate (OAC)	332	C13H26O5Si2N	1-2-3-6	TBDMS-methoxylamine
Pyruvate	274	C11O3H24Si2N	1-2-3	TBDMS-hydroxylamine
α-Ketoglutarate	446	C19O5H40Si3N	1-2-3-4-5	TBDMS-hydroxylamine
Succinate	289	C12O4H25Si2	1-2-3-4	TBDMS
Fumarate	287	C12O4H23Si2	1-2-3-4	TBDMS
Malate	419	C18O5H39Si3	1-2-3-4	TBDMS

Molecular formula and “active carbon” information was used for inputs into the flux modeling software, Metran.

^*TBDMS: tert-butyldimethylsilyl, a common silylation group for GC/MS analysis.