C-Metabolic flux analysis has been increasingly used to observe in vivo
fluxes in mammalian systems [34
]. However, despite recent advances in both the experimental and computational aspects of 13
C-MFA, little thought is often given to which tracers should be selected for a given network, and perhaps more importantly why these tracers are optimal.
In this contribution, we provide a new perspective for rational-based selection of 13
C-tracers. Our methodology is based on the previously described concept of EMU basis vectors [33
]. The EMU basis vector methodology is a very attractive strategy for investigating tracer selection as the tracer labeling is decoupled from the flux dependencies. In contrast to simulation-based optimal design [17
], we focused on rational grouping of the flux-dependent coefficient sensitivities such that we could maximize the sensitivity of a single isotopomer for each free flux. For each free flux, we sorted the coefficient sensitivities by sign and decreasing magnitude. We then identified the largest magnitude(s) sensitivities. In the case of multiple moderate to large sensitivities, we collapsed those of the same sign onto a single isotopomer, while keeping those of the opposite sign on different isotopomers. Subsequently, we attempted to further group same-signed sensitivities, with emphasis on maximizing the largest sensitivity. In this process, we created labeling rules, which set constraints on the basis vector matrix and hence the possible substrate labeling schemes. Using this rationale, we obtained a significant reduction in the number of tracers, from 96 in total (64 glucose and 32 glutamine) to a handful of possible candidates. We predicted two novel optimal tracers, which were not previously considered for mammalian systems. For the oxPPP flux we determined that [2,3,4,5,6-13
C]glucose would be the best tracer and [3,4-13
C]glucose would be optimal for the PC flux. When we compared these a priori
selections to simulation experiments from Henry’s PYC flux map, we observed drastic improvement in flux resolution for both the oxPPP and PC fluxes.
One practical insight this contribution provides is in the identification of feasible substrates for 13C-tracers through coefficient sensitivities. For a defined network, a flux map, and a measurement set, the dc/du values are fixed (see Eq. 2). Regardless of tracer choice and the respective labeling pattern, the coefficient sensitivities will not be affected. The method proposed in this work relies on rational grouping of the coefficient sensitivities to maximize the sensitivity of a single isotopomer for each free flux. In order to do this, it is important to choose a substrate that has large dc/du values corresponding with its respective EMU basis vectors. In essence, the coefficient sensitivities can be viewed as the potential to obtaining a large measurement sensitivity. Substrates with a larger potential are inherently better suited as tracer candidates for 13C-MFA.
To illustrate this concept, two possible substrates were considered in this work, glucose and glutamine. Glucose EMU basis vectors had large magnitude sensitivities for both the oxPPP flux (Gluc123
, -16.9) and the PC flux (Gluc123
, -5.7; Gluc456
, -6.0); in contrast, the dominant glutamine EMU basis vectors had small sensitivities for the oxPPP flux (Gln234
, +0.2) and the PC flux (Gln234
, +0.5). As glutamine sensitivities were an order of magnitude smaller than glucose sensitivities, glutamine was clearly not an optimal tracer for this network with lactate as the measured metabolite. The simulation results validated this assessment, as [U-13
C]glutamine was shown to be a poor tracer for elucidation of both the oxPPP and PC fluxes.
Intrinsically, the poor resolution of the oxPPP flux, when assessed with glutamine tracers, is reasonable as no labeling from glutamine can enter into oxPPP. More surprising is the poor resolution of the PC flux. One explanation for the poor PC flux resolution is the distance of the measurement, i.e. lactate, from glutamine and the resulting dilutions that occur at metabolites α-ketoglutarate and pyruvate. To remedy this issue, a TCA cycle intermediate (oxaloacetate or α-ketoglutarate) could be used as additional measurement; however, even if a TCA cycle intermediate is used, the measurement remains insensitive to the PC flux for [U-13C]glutamine (results not shown). We have demonstrated in this contribution that given a measurement, we can determine logical tracers for elucidation of a flux of interest; however, the converse, given a tracer, which measurements should be chosen to determine the flux is not trivial, or well understood. An understanding of both relationships will be crucial to designing optimal 13C-tracer experiments.
This work also demonstrates why it is often difficult to resolve all fluxes in a network with high confidence. In this network model, 13
C-labeling rules for resolving the oxPPP flux were inherently contradicting the rules for optimally resolving the PC flux. Thus, by trying to resolve one flux better, the resolution of the other flux worsened. For example, in this work, to resolve the oxPPP flux it was desirable to have Gluc123
; however for the PC flux, it was pressing to have Gluc123
. Both of these rules cannot be satisfied in a single tracer experiment. To select a single tracer to resolve both fluxes, the coefficient sensitivities and their magnitudes must be considered for both of the free fluxes. The most important criterion for oxPPP was that the strongly negative Gluc123
sensitivity collapsed on a different isotopomer than Gluc23
. Crucial for PC flux resolution was that Gluc123
produced the same isotopomer. These two constraints can be satisfied together, if the stipulation for the oxPPP rule set is relaxed, such that Gluc456
can differ from Gluc123
. Since the Gluc456
sensitivity is only about 2% and Gluc123
is almost −17%, this is a reasonable compromise. With the adapted rules, the first three carbons of glucose must be either  or  labeled, with the last three carbons being M
1 or M
2 labeled, respectively. Through careful selection of which tracer rules to violate, ideally ones that have a lesser impact on the maximum sensitivity for a given flux, a single tracer can be chosen to resolve both free fluxes with precision that approaches that of the optimal tracers we suggested (see Additional file 6
). Another important observation regarding flux resolution corresponds to the range of the sensitivity values. In the case of the oxPPP flux, there are three dominant sensitivities (Gluc123
, and Gluc23
). Violation of rules involving combinations of these three sensitivities, has drastic effect on the resulting confidence intervals. However, in the case where many sensitivities are of similar magnitude (e.g. the positive sensitivities for PC flux), violation of individual rules (5–9 in Figure ) can have less severe consequences. For example, [2,3,4,6-13
C]glucose in Additional file 6
violates rules 5, 7, and 9, but retains confidence intervals about twice as large as those of [3,4-13
In simple cases, such as this network, a single tracer and a single measurement may be capable of resolving all free fluxes with high fidelity; however, as the number of free fluxes increases in a network, not all sensitivity rules for each flux can be satisfied, resulting in smaller magnitudes of isotopomer sensitivity and loss of confidence in the estimated flux values. This raises an important question of how to minimize the effects of conflicting sensitivity rules, and hence improve confidence intervals. There are two feasible approaches to address this issue. The first option involves a single-tracer design with the addition of more independent measurements. The additional isotopomers may allow more flexibility when satisfying the sensitivity criteria. One concern, however, is that contradictory rules may still exist and result in poor flux resolution. In this case, additional measurements may have only marginal effect on flux resolution [35
], thus requiring another approach to achieve better flux results. A second alternative to improve flux resolution is to conduct parallel labeling experiments, where specific tracers are designed to be optimal for specific fluxes in the model. By integrating labeling data from such parallel labeling experiments, fluxes can be resolved at a high resolution that can never be achieved using any single tracer experiment. The obvious drawback to this method is tracer availability and cost, and the requirement of good biological reproducibility. The tracer selection methodology presented here gives clear insight into why flux resolution is challenging and highlights the need for investigation of not just tracer and measurement choice, but also the manner in which tracer experiments are conducted.
This work also offers some experimental insights regarding the usage of [1-13
C]glucose for oxPPP resolution. The results shown here demonstrate that [2,3,4,5,6-13
C]glucose is a more effective tracer. To further expand on this point, we numerically simulated oxPPP confidence interval for [1-13
C]glucose and [2,3,4,5,6-13
C]glucose. A grid search for the two free fluxes (oxPPP and PC) was conducted to evaluate the effect of the free fluxes on the resulting confidence intervals. Overall, for this network with lactate as the measurement, [2,3,4,5,6-13
C]glucose performed as well as, and in the majority of cases, better than [1-13
C]glucose across the entire flux space (see Additional file 7
Another insight this work provides is into experiment design with mixtures of 13
C-tracers. Often times, especially in mammalian cell culture, there will be unlabeled glucose and amino acids in the media. As shown in Additional file 5
, the addition of unlabeled glucose adversely affects the flux confidence intervals for the optimal tracers. This can be explained through the EMU basis vector sensitivities. For example, consider the sensitivity of Gluc123
for the oxPPP flux. When pure [2,3,4,5,6-13
C]glucose is used, the full sensitivity of Gluc123
(−16.9) contributes to the M
2 isotopomer; however for a 50/50 mixture of [2,3,4,5,6-13
C]glucose and unlabeled glucose, only half of the Gluc123
sensitivity (−8.5) contributes to M
2 and the other half contributes to M
0. Unlabeled glucose in this example results in a decrease in the maximum sensitivity obtainable. As a result, the flux observability suffers. Similarly, with mixtures of [2,3-13
C]glucose and [4,5,6-13
C]glucose, the maximum obtainable sensitivity was decreased, also resulting in poorer confidence intervals.
Lastly, it is important to discuss the limitations of the Henry model and how it pertains to the proposed methodology. The Henry model did not include commonly accepted reaction reversibilities, such as transketolase (TK) and transaldolase (TA) in the pentose phosphate pathway as well as malate dehydrogenase (MDH). Reversibility of TK and TA will allow back-mixing of labeling in the pentose phosphate pathway and the reversibility of MDH will result in additional pyruvate cycling via PC, MDH, and malic enzyme acting in tandem (i.e. pyruvate
pyruvate). In general, inclusion of reversible reactions may or may not increase the number of EMU basis vectors depending on whether the reversible reactions create new, independent “EMU pathways”. The fractional contributions will change, as the coefficients will be functions of additional free fluxes. The most notable change will be in the coefficient sensitivities. In addition to sensitivities with respect to the oxPPP and PC flux, each coefficient will have a sensitivity to each reversible flux. The tracer selection process based on our methodology remains the same; however, it may not be feasible to resolve all fluxes with the given measurement(s). For example, in the system described here, lactate only has three independent mass isotopomers, i.e. assuming the complete lactate molecule is measured and no other MS fragments of lactate are available. With the addition of TK, TA, and MDH reversibilities, there will be six free fluxes, and thus it will not be possible to resolve all these fluxes with lactate as the only measurement. To demonstrate this, oxPPP and PC confidence intervals were simulated for various glucose tracers, where the network model included TK, TA, and MDH. The results are shown in Additional file 8
. The uncertainty due to the inability to resolve all six free fluxes caused broadening of the confidence intervals. The best-performing tracers for the oxPPP and PC flux, however, remained the same.
In addition to reversible reactions, compartmentation was also neglected in the Henry model, meaning that parallel reactions in the cytosol and mitochondria were not distinguished in this model. Experimentally, measuring fluxes in separate compartments is difficult without isolation of metabolites located in the different cellular compartments [39
]. As advances are made to overcome this technical challenge, the methodology we have presented here will still be applicable, as the rational steps proposed are independent of the model. Regardless of the number of free fluxes, sensitivity criteria can be applied to evaluate principles for each free flux. As the model complexity increases, however, more measurements or parallel experiments may be necessary as discussed above.
In summary, the results in this paper demonstrate that optimal tracer experiment design does not need to be a pure simulation-based trial-and-error process. But rather, rational insights into tracer design can be gained through application of the EMU basis vector methodology. Through careful analysis of sensitivities, with focus on maximizing isotopomer sensitivity, labeling rules can be constructed, which guide the selection of 13C-tracers for a given network. Depending on the size and complexity of the network, the proposed methodology may provide a single optimal tracer, as in [3,4-13C]glucose for the PC flux; or perhaps more likely, the method will provide a reduced list of feasible tracers. This reduction of plausible tracer schemes, whether complete or partial, can significantly ease the computational burden for further tracer experiment design optimization. Going forward, further emphasis should be placed on understanding the interdependencies between measurements in conjunction with a rational selection of tracers and the overarching philosophy of isotopic experiment design. One important issue to address is whether a tracer experiment should be completed in isolation, i.e. one tracer experiment to elucidate all the fluxes, or whether parallel experiments are better suited, i.e. several tracer experiments with each resolving a different subset of the fluxes. Ultimately, further investigation of the correlations between flux resolution, the measurement set, and the 13C-tracer must be conducted. A deeper understanding of these relationships will allow for more powerful isotopic experiment design for 13C-MFA.