The quantitative relationship between isotopic and net contributions of lactate and glucose to the tricarboxylic acid (TCA) cycle

Whether growing cancer cells prefer lactate as a fuel over glucose or vice versa is an important but controversial issue. Labeling of tricarboxylic acid (TCA) cycle intermediates with glucose or lactate isotope tracers is often used to report the relative contributions of these two metabolites to the TCA cycle. However, this approach may not yield accurate results, as isotopic labeling may not accurately reflect net contributions of each metabolite. This may be due to isotopic exchange occurring during the conversion between pyruvate and lactate. To evaluate this quantitatively, we used an equation (CG − CG′ = CL′ − CL) assessing the relationship between isotopic labeling and net consumption measurements in vitro. CG and CL refer to the contributions of glucose and lactate to the TCA cycle as measured by their net consumption, whereas CG′ and CL′ refer to glucose's and lactate's contributions determined with isotopic labeling. We found that the isotopic labeling data overestimate the net contribution of lactate to the TCA cycle and underestimate that of glucose. The overestimated amount is equal to the isotopic exchange amount between pyruvate and lactate. After excluding the interference of isotopic exchange, the major carbon contribution (i.e. acetyl-CoA) to the TCA cycle comes from glucose rather than lactate in vitro. We propose that these relative contributions of glucose and lactate may also be present in cancer cells in vivo.

Glucose and lactate both can serve as fuels for cancer cells because they contain reduced carbons that store energy. Before they enter the TCA 2 cycle, glucose and lactate must be con-verted to pyruvate. Glucose conversion to pyruvate (glucose ϩ 2 NAD ϩ ϩ 2 ADP ϩ 2 P i 3 2 pyruvate ϩ 2 ATP ϩ 2 NADH ϩ 2 H ϩ ϩ 2 H 2 O) is thermodynamically favorable in cancer cells, with a standard change of Gibbs free energy (⌬GЈ 0 ) of Ϫ85 kJ/mol (1,2). Although the actual change of Gibbs free energy (⌬G) varies in living cells under different conditions, it is negative. In contrast, as the ⌬GЈ 0 of LDH-catalyzed reaction (lactate ϩ NAD ϩ 3 pyruvate ϩ NADH) is 25.1 kJ/mol (1,3), the reaction is thermodynamically unfavorable for lactate conversion to pyruvate. Cancer cells exhibiting the Warburg effect have a high glycolysis rate, which continuously generates pyruvate and NADH, leading to a mass action ratio (Q) of the reaction that is always larger than its equilibrium constant (K eq ), favoring pyruvate conversion to lactate. Net lactate conversion to pyruvate may occur in some extreme conditions, e.g. when glucose is deprived or glycolysis is severely inhibited.
Previous studies demonstrated that cancer cells in vitro convert about 80% of glucose to lactate and use about 5% of glucose for fuel (4 -6). It is generally recognized that glucose, rather than lactate, provides the primary carbon source (i.e. acetyl-CoA) for the TCA cycle. However, recent in vivo studies (7)(8)(9) showed that cancer cells prefer lactate as a fuel over glucose, sparking a debate about the major carbon source of the TCA cycle.
Notably, the key data to assess lactate as a preferred fuel to glucose by Faubert et al. (8) and Hui et al. (9) are the percentages of TCA cycle intermediates labeled by [ 13 C]lactate and [ 13 C]glucose. Although the experiments demonstrated unambiguously a significantly larger labeling percentage of TCA cycle intermediates labeled by [ 13 C]lactate than that labeled by [ 13 C]glucose, the net contributions of lactate and glucose carbon to the TCA cycle were not determined. Earlier, Weinman et al. (10), Haslam and Krebs (11), and Krebs et al. (12) pointed out that isotope labeling does not reflect net contributions when isotopic exchange exists. Isotopic exchange occurs in reversible reactions or reversible transports. For example, 1 mol of 13 Clabeled lactate is imported into the cells, while 2 mol of unlabeled lactate is exported to the extracellular matrix. Counting only 1 mol of 13 C-labeled lactate influx but ignoring 2 mol of unlabeled lactate efflux would lead to a conclusion that cells are consuming lactate, but the fact is that cells are producing lactate. Therefore, when isotopic exchange occurs, isotopic labeling deviates from the net flux. Given that glucose and lactate must be converted to pyruvate before entering the TCA cycle and the conversion between pyruvate and lactate is fully reversible, isotopic exchange could occur between pyruvate and lactate; thus, the isotopic contribution will deviate from the net contribution of glucose and lactate to the TCA cycle.
To measure how far the isotopic labeling data deviate from net contribution data, the two data sets need to be acquired simultaneously. Here, we did these measurements in three cultured cancer cell lines and showed that glucose rather than lactate in most cases provides a net contribution to the TCA cycle. Furthermore, we deciphered a mathematical relationship between the isotopic and net contributions of glucose and lactate to the TCA cycle.

Analysis of the net contributions of lactate and glucose to the TCA cycle based on a steady-state mathematical model
To measure isotopic labeling data and net contribution data simultaneously, we need a system in which all these data could be accurately determined. In contrast to the difficulties in measuring the net flux in real tumors (13) and the uncontrollability of the in vivo system, cultured cancer cell lines in vitro are an ideal system. Next, we need to analyze how to measure the net contributions to the TCA cycle of glucose and lactate. Fig. 1A depicts the metabolic pathways that converge to pyruvate and then to the TCA cycle in cells exposed to glucose and lactate. To A, the metabolic pathways to and from pyruvate. B, 4T1 cells were cultured in complete RPMI 1640 medium, pH 7.4, containing 10 mM glucose and 10 mM lactate for 0.5, 1, 2, 3, and 4 h. The intracellular concentrations of glucose, lactate, and pyruvate were measured at the time points. To minimize the disturbance of the residual glucose, lactate, and pyruvate after changing the medium, the cells were incubated in glucose-free medium for 1 h before the experiment. C, left panel, when lactate efflux is larger than influx, there is a net glucose carbon but no net lactate carbon into the TCA cycle. Right panel, when lactate efflux is smaller than influx, there is a net glucose carbon and a net lactate carbon into the TCA cycle. Pyruvate is produced in both conditions as RPMI 1640 medium (with ultrafiltrated FBS) contains no pyruvate. Data are mean Ϯ S.D. (error bars), n ϭ 3, from one experiment. The results were confirmed by three independent experiments. GLUT, glucose transporter.
If the concentrations of intracellular glucose, pyruvate, and lactate are almost constant during the experiments (i.e. they are at near steady state), we could deduce some equations. We show that the pre-steady state was in 1 h, after which the steady state was reached (Fig. 1B); i.e. the import rate and removal rate of intracellular glucose (or pyruvate or lactate) are nearly equal. Thus, we derived the following equations.
For glucose, import rate ϭ removal rate.
For lactate, import rate ϭ removal rate.
For pyruvate, import rate ϭ removal rate.

Substituting Equations 2 and 3 into Equation 4 and rearranging gives Equation 5
.
Integrating the left side and right side over time, respectively, gives Equation 6.
shows that net conversion from pyruvate to the TCA cycle (C 12 ) is the sum of the net conversion from glucose to pyruvate (C 6 Ϫ C 7 ), the net consumption of extracellular lactate (C 8 Ϫ C 9 ), the net consumed amount of extracellular pyruvate (C 4 Ϫ C 5 ), and the net exchange amount between pyruvate and other metabolites (C 10 ϪC 11 ).
Among the four carbon sources, when glucose is consumed by cells and glycolysis continues, (C 6 Ϫ C 7 ) is always a positive value. When we determine the net consumption of medium glucose (i.e. C 6 ), we get the upper limit of the net contribution to the TCA cycle of glucose. Because there is no pyruvate in the medium at first, all the pyruvate was generated from glucose, lactate, and other sources, so (C 4 Ϫ C 5 ) is always negative, which means medium pyruvate is a product; hence it cannot make a net contribution to the TCA cycle. Similarly, whether lactate makes a net contribution to the TCA cycle or not depends on whether or not medium lactate is consumed. When it is consumed, the consumption amount approximates the net contribution; otherwise, it cannot make net contribution to the TCA cycle. These two different conditions can be simplified as shown in Fig. 1C.
In summary, the net consumptions of medium glucose and lactate give information on the net contributions to the TCA cycle, and the net consumption data can be determined accurately. Then we performed isotopic labeling experiments in cancer cell lines, acquired both the isotopic labeling data and the net consumption data, and deduced the relationship between the two different data sets.

The contributions to the TCA cycle of glucose and lactate measured by isotopic labeling differ from that measured by net consumption
We performed parallel isotopic labeling experiments with [ 13 C 6 ]glucose or [ 13 C 3 ]lactate (i.e. [ 13 C 6 ]glucose ϩ unlabeled lactate or unlabeled glucose ϩ [ 13 C 3 ]lactate) in three different cancer cell lines: 4T1, HeLa, and NCI-H460. The two labeled substrates induced the same labeling pattern of the TCA cycle intermediates (Fig. 2, A and B). The initial concentrations of glucose and lactate were both 10 mM, and cells were incubated for 1, 3, and 5 h. We measured the isotopic labeling percentages of three TCA cycle intermediates (citrate, ␣-ketoglutarate, and malate) and determined the concentration changes of medium glucose and lactate. The results showed that the labeling efficiency of TCA intermediates with [ 13 C 3 ]lactate is always larger than that with [ 13 C 6 ]glucose in all cell lines except the labeling of citrate at 5 h in 4T1 cells (Figs. 2, D and E, S1, A and B, and S2, A and B). From the isotopic labeling data, it seems that lactate contributes more than glucose to the TCA cycle. However, the concentration curves showed that although the exogenous lactate was consumed, more glucose-derived lactate was produced, resulting in a net generation of total lactate (Figs. 2, D and E, S1, A and B, S2, A and B, lower panels). Therefore, lactate makes no net contribution to the TCA cycle.
To further confirm this, we labeled cells with [ 13 C 6 ]glucose and [3-13 C]lactate simultaneously. The glucose carbon-labeled TCA cycle intermediates are m ϩ 2 in the first cycle, whereas those labeled by lactate carbon are m ϩ 1 (Fig. 2C)

Contributions of lactate and glucose carbon to the TCA cycle
and the latter was used to calibrate m ϩ 1 isotopologues generated from [ 13 C 6 ]glucose carbon. Thus, the calibrated m ϩ 2 and m ϩ 1 isotopologues represent the labeling of [ 13 C 6 ]glucose and labeling of [3-13 C]lactate, respectively. The initial concentrations of glucose and lactate were both 10 mM, and incubation time was 1 h. The results demonstrated that, although the amount of m ϩ 1 isotopologues (labeled by lactate carbon) was significantly larger than that of m ϩ 2 isotopologues (labeled by glucose carbon), the total lactate increased (Figs. 2F, S1C, and S2C). The data are consistent with the data in Fig. 2, D and E. Therefore, when the isotopic labeling data showed that lactate is a "preferred" fuel over glucose, the net contribution was the opposite.
Nevertheless, the experiments above were all performed in one condition: initial glucose and lactate concentrations are both 10 mM, normal oxygen level, and pH 7.4. Changing these The diagrams show merely the first turn of the TCA cycle to avoid complexity. 4T1 cells were cultured in complete RPMI 1640 medium, pH 7.4, containing 10 mM [ 13 C 6 ]glucose and 10 mM lactate (D), 10 mM glucose and 10 mM [ 13 C 3 ]lactate for 1, 3, and 5 h (E), or 10 mM [ 13 C 6 ]glucose and 10 mM [3-13 C]lactate for 1 h (F) followed by determination of isotopologues of citrate, ␣-KG, and malate in cells and glucose and lactate concentrations in medium. In F, two parallel experiments were performed simultaneously using [ 13 C 6 ]glucose ϩ lactate or glucose ϩ [3-13 C]lactate (data not shown); the former was used to calibrate the contribution of [ 13 C 6 ]glucose to m ϩ 1 isotopologues, and the latter was used to calibrate the contribution of [3-13 C]lactate to m ϩ 2 isotopologues. The data shown in F were calibrated. Thus, the calibrated m ϩ 2 isotopologues represent the labeling of [ 13 C 6 ]glucose, whereas the calibrated m ϩ 1 isotopologues represent the labeling of [3-13 C]lactate. Data are mean Ϯ S.D. (error bars), n ϭ 3, from one experiment. The results were confirmed by three independent experiments. ***, p Ͻ 0.001. PEP, phosphoenolpyruvate; Ac-CoA, acetyl-CoA; OAA, oxaloacetate.

Contributions of lactate and glucose carbon to the TCA cycle
parameters may lead to different outcomes. Therefore, we next changed these parameters one by one to test whether the results could be altered.
We first changed the concentration of labeled glucose from 1 to 10 mM. Varying the concentrations of labeled glucose did not significantly change the labeling of the TCA cycle intermediates when the incubation time was short (in case that glucose was used up) (Figs. 3A, S3A, and S4A). Consistently, glucose consumption rate and lactate generation rate were comparable between cells exposed to different concentrations of glucose (Figs. 3B, S3B, and S4B). This is because the K m of HK (glucose as substrate) is about 0.2 mM (Table S1), so HK is virtually saturated at 1 mM glucose; further increasing the glucose concentration would not have a significant effect on the HK rate.
Unlike glucose, increasing the labeled lactate concentration from 5 to 20 mM increased the labeling of the TCA cycle intermediates (Figs. 3C, S3C, and S4C). This is not surprising as the K m of LDH (lactate as substrate) is about 7 mM (Table S1). Nevertheless, although increasing the concentration of labeled lactate enhanced the LDH-catalyzed reverse rate (lactate to pyruvate), the forward rate was still higher than the reverse rate as the concentration of total lactate was increasing (Figs. 3D, S3D, and S4D).

Contributions of lactate and glucose carbon to the TCA cycle
Considering that hypoxia is common in tumors, we performed labeling experiments under hypoxia conditions (0.5% O 2 ). [ 13 C 6 ]glucose and [ 13 C 3 ]lactate were used as labeling substrates, respectively. The results of 4T1 cells showed that the labeling efficiency with [ 13 C 3 ]lactate is significantly decreased under hypoxia compared with that under normoxia, whereas the labeling efficiency of [ 13 C 6 ]glucose is barely changed (Fig.  4A), and the labeling efficiency with [ 13 C 6 ]glucose exceeds that of [ 13 C 3 ]lactate under hypoxia (Fig. 4A). Conversely, H460 and HeLa cells showed no significant differences in isotopic labeling efficiency under normoxia and hypoxia, and labeling efficiency with [ 13 C 3 ]lactate was greater than that with [ 13 C 6 ]glucose even under hypoxia (Figs. S5A and S6A). The rates of glucose consumption and total lactate production in all cell lines were increased under hypoxia (Figs. 4B, S5B, and S6B).
Lactic acidosis is also common in tumors. We performed labeling experiments ([ 13 C 6 ]glucose ϩ [3-13 C]lactate) in lower pH environments, which showed that the ratio of lactate's labeling efficiency to glucose's labeling efficiency increased when pH decreased from 7.4 to 6.7 (Figs. 4C, S5C, and S6C). Thus, low pH enhanced lactate labeling but impaired glucose labeling. However, despite the glycolysis rate decreasing in low pH conditions, the total lactate still increased (Figs. 4D, S5D, and S6D). Fig. 2, D and E, show that the fraction of citrate labeled by [ 13 C 6 ]glucose increased with time, whereas the fraction of citrate labeled by [ 13 C 3 ]lactate decreased, suggesting that the percentage of the TCA cycle intermediates labeled by glucose may exceed that by lactate when the time is sufficiently extended. We used a low concentration of [3-13 C]lactate (5 mM for 4T1 and 2.5 mM for HeLa and H460). When the time reached a threshold (between 1 and 2 h, depending on cell lines), the ratio of lactate labeling efficiency to glucose labeling efficiency decreased from larger than 1 to smaller than 1 (Fig. 5A). In this situation, glucose is a preferred fuel to lactate based on both labeling data and net consumption data (Fig. 5B). In contrast, total lactate was increasing (Fig. 5B), indicating that lactate makes no net contribution to the TCA cycle.
In all the experiments above, there were a net consumption of glucose and a net generation of lactate; hence glucose makes a net contribution to the TCA cycle. As to lactate, although there was indeed a net consumption of exogenous lactate accompanied with incorporation of its carbon into the TCA cycle intermediates, the amount of glucose-derived lactate exceeded the amount of consumed exogenous lactate, resulting in a net generation of lactate. This reflects an isotopic exchange between glucose carbon and exogenous lactate carbon, which occurred at the crossover point, i.e. the conversion between pyruvate and lactate catalyzed by LDH. Isotopic exchange could cause the difference between isotopic incorporation and net conversion (11,14). To verify this, we next employed a mathematical model to analyze the problem.

The rate of isotopic exchange between pyruvate and lactate determines the relative isotopic contributions to the TCA cycle of glucose and lactate
For simplicity, we named the net contributions of glucose and lactate to the TCA cycle C G and C L , respectively, and the isotopic contributions of glucose and lactate to the TCA cycle C G Ј and C L Ј, respectively. Their corresponding flux rates were J G , J L , J G Ј, and J L Ј according to Equation 1.
The mathematical model in Fig. 1 shows that the net contributions of glucose and lactate to the TCA cycle depend on their net consumptions, but we also need to know what determines the isotopic contributions of glucose and lactate. Fig. 6A illustrates the metabolic pathways to citrate, the first TCA cycle intermediate. Apparently, C G Ј and C L Ј are determined by the percentage of glucose-derived pyruvate (named Pyr [Glc] ) and the percentage of lactate-derived pyruvate (named Pyr [Lac] ) in the total flux of pyruvate to acetyl-CoA, respectively (Fig. 6A). Therefore, we need to calculate Pyr [Glc] and Pyr [Lac] or their ratio to compare the labeling efficiency of the two substrates. Apart from glucose and lactate carbon, citrate carbon could be contributed by other carbon sources, such as fatty acids and amino acids, which would reduce the total percentage of glucose and lactate carbon incorporating into citrate but would not alter the value of C G Ј/C L Ј, so we can leave them out of consideration. Then we depicted the metabolic pathways from glucose or lactate to pyruvate (Fig. 6B).
The symbols used here have the same meaning as described in the previous section but with some modifications. The net flux J 2 and J 3 are split into two parts according to their sources.
According to the definition, we can derive Equations 7 and 8.
Similarly, the net efflux (J 5 Ϫ J 4 ) are split into two parts as well. For simplicity, we used J PG and J PL instead of (J 5G Ϫ J 4G ) and (J 5L Ϫ J 4L ), respectively. .
Equation 1 was applicable in the same way; i.e. their corresponding net conversion amounts are C 2G , C 2L , C 3G , C 3L , C PG , and C PL , respectively. According to Fig. 6B, we could derive the following equations.
N G and N L represent the amount of cellular pyruvate derived from glucose and lactate, respectively.
Because the amount of total intracellular pyruvate (named N) is far less than the amount of medium pyruvate (Table S2) and

Contributions of lactate and glucose carbon to the TCA cycle
N G and N L are just part of N, we can derive Inequalities 1 and 2.
Therefore, N G and N L could be neglected, and Equations 10 and 11 could be simplified as follows. 13) In most cases in our experiments (Figs. 2, 3, and 4B), the labeling efficiency of lactate is larger than that of glucose, thus giving us Inequality 3.
In other cases (Figs. 4A and 5), the labeling efficiency of lactate is smaller than that of glucose, thus giving us Inequality 4.
We first analyze the situation when Inequality 3 is applicable. According to Equations 12 and 13 and Inequality 3, we derive the following inequality.
Because there is a net accumulation of lactate (Figs. 2 and 3), we derive Inequality 6.
is part of C 1 , so obviously we can derive Inequality 7.
According to Inequalities 6 and 7, we can derive Inequality 8.
In the medium, glucose-derived pyruvate is less than lactatederived pyruvate (Figs. 6C and S7A); therefore, we can derive Inequality 9.
According to Inequalities 8 and 9, we could derive Inequality 10. 10) By comparing Inequality 5 with Inequality 10, we could see that the reason for C G Ј being less than C L Ј is due to (C 3G Ϫ C 2G ). Because C 1 Ͼ (C 2L Ϫ C 3L ) and C PG Ͻ C PL , glucose conversion to pyruvate is larger than lactate conversion to pyruvate. However, LDH rapidly converts glucose-derived pyruvate to lactate

Contributions of lactate and glucose carbon to the TCA cycle
(i.e. C 3G Ϫ C 2G ) so that only a minor fraction of glucose-derived pyruvate enters the TCA cycle. As a result, C G Ј is smaller than C L Ј, as reflected by the labeling efficiency (Figs. 2 and 3). The principle can be expressed as Fig. 6D. The biochemical rationale for a high (C 3G Ϫ C 2G ) is at least partly due to the high glycolysis rate and low pyruvate dehydrogenase (PDH) activity; the former is about 60 -100-fold higher than PDH (Figs. 6E and S7B). In the presence of very high LDH activity (Figs. 6E and S7B), the glucose-derived pyruvate and NADH are rapidly converted to lactate and NAD ϩ .
If (C 3G Ϫ C 2G ) or (C 2L Ϫ C 3L ) is small enough, both Inequality 10 and Inequality 11 could be satisfied. When the incubation time is long, (J 2L Ϫ J 3L ) is markedly reduced (Fig. 5B, dashed  lines); thus, (C 2L Ϫ C 3L ) is relatively small in the longer time point (e.g. 5 h), and Inequality 11 comes true. Under hypoxia, HIF1-␣ is activated, and PDH is suppressed (15,16), resulting in a decreased (C 2L Ϫ C 3L ), and then Inequality 11 is satisfied (Fig.  4A). Therefore, the factors that determine the ratio of C G Ј to C L Ј lie in (C 3G Ϫ C 2G ) and (C 2L Ϫ C 3L ), or the rate of isotopic exchange between pyruvate and lactate.
As the isotopic exchange occurs in the reaction catalyzed by LDH, if the LDH activity is reduced, the rate of isotopic exchange would be decreased, leading to an increased labeling efficiency of glucose. Using CRISPR-Cas9 technology, we obtained 4T1/LDHA KO , 4T1/LDHB KO , and 4T1/LDHA KO -LDHb KO cells (LDHA KO , LDHB KO , and LDHb KO refer to knockout of two alleles of LDHA, LDHB, and one allele of LDHB, respectively) (Fig. 7A). The LDH activity of 4T1/LD-HA KO , and 4T1/LDHB KO , and 4T1/LDHA KO -LDHb KO cells was about 60, 25, and 15% of the control cells (Fig. 7A). When the LDH activity was reduced, the ratios of m ϩ 1 isotopologues to m ϩ 2 isotopologues of citrate, ␣-ketoglutarate, and malate (or C L Ј/C G Ј) significantly decreased (Fig. 7B). The concentration changes of medium glucose and lactate validated that reduced LDH activity significantly decreased (C 3G Ϫ C 2G ) and (C 2L Ϫ C 3L ) (Fig. 7C). For 4T1/LDHA KO and 4T1/ LDHA KO -LDHb KO cells, the value of (m ϩ 1)/(m ϩ 2) is smaller than 1 (Fig. 7B). Fig. 7D describes the effect of LDH activity on the labeling. As MCT controls the shuttle of lactate, MCT knockdown may achieve a similar effect (8).

Contributions of lactate and glucose carbon to the TCA cycle
In summary, our mathematical analysis deciphered that the rapid isotopic exchange between pyruvate and lactate (i.e. (J 3G Ϫ J 2G ) and (J 2L Ϫ J 3L )) decreased C G Ј and increased C L Ј. When the exchange was reduced, C G Ј increased, and C L Ј decreased. Between C G Ј and C L Ј, one increases, another decreases, and vice versa. Next, we sought to resolve the relationship between isotopic and net contributions of glucose and lactate to the TCA cycle.

The rate of isotopic exchange between pyruvate and lactate determines the difference between isotopic contributions and net contributions of lactate and glucose to the TCA cycle
We further simplified the schematic diagram of the pyruvatecentered metabolic pathways (Fig. 8A). The pyruvate in Fig. 8A represents total pyruvate, including medium pyruvate; hence C PG and C PL become the internal interactions of the system, and we can leave them out of consideration. Therefore, in this model, we can simplify Equations 12 and 13 as follows.
The equations calculate the isotope contribution to the TCA cycle.
The conditions of Fig. 8A, left panel, are the same as that of the right panel except that the left panel shows isotopic labeling. After transforming Fig. 8A, left panel to right panel, the isotope interference is excluded, nd we can deduce the net conversion of glucose carbon (C G ) and lactate carbon (C L ) into the TCA cycle according to Equation 6 as follows. When C 3 Ͼ C 2 , i.e. when there is a generation of total lactate, lactate makes no net contribution. 16) For glucose, the net contribution to the TCA cycle is equal to its net conversion to pyruvate minus its net conversion to lactate.
When C 3 Ͻ C 2 , i.e. when there is a net consumption of lactate, the net contribution of lactate to the TCA cycle is equal to its net conversion to pyruvate.
As glucose has no net conversion to lactate in this situation, we can derive Equation 19.
For simplicity, we used two piecewise functions to express the net contributions.
is the net production of lactate; thus, C 3 Ͻ C 2 means a net consumption of lactate, and C 3 Ն C 2 means a net generation of lactate.

Contributions of lactate and glucose carbon to the TCA cycle
Calculating the values of (C G Ϫ C G Ј) and (C L Ј Ϫ C L ) in two conditions (C 3 Ն C 2 or C 3 Ͻ C 2 ) using Equation 14 and Function 1 or Equation 15 and Function 2, we get the two functions below.
Then, obviously, we get Equation 20.
The equation reveals the mathematical relationship between the isotopic and net contributions of glucose and lactate to the TCA cycle. As C 3G Ͼ C 2G and C 2L Ͼ C 3L , (C G Ϫ C G Ј) Ͼ 0 (or (C L Ј Ϫ C L ) Ͼ 0), the isotopic contribution of glucose to the TCA cycle is underestimated, whereas that of lactate is overestimated, and the underestimated fraction is just equal to the overestimated fraction. In essence, the overestimated (underestimated) fraction is equal to the amount of isotopic exchange between pyruvate and lactate (i.e. (C 3G Ϫ C 2G ) or (C 2L Ϫ C 3L )). Therefore, as long as isotopic exchange between pyruvate and lactate exists, there will be a deviation of isotopic contribution from net contribution whether total lactate is produced or consumed.
Based on what we deduced, we could estimate the isotopic and net contributions of glucose and lactate to the TCA cycle using our acquired data in three different conditions (Fig.  8B). Two of them are the conditions in Figs. 2F and 7 (the LDHA-KO cells), and the third condition is culturing 4T1 cells with 10 mM [ 13 C 6 ]glucose ϩ 20 mM lactate, pH 6.35, for 1 h where the medium glucose and total lactate are both consumed (Fig. S8). The deviations in the three conditions are different (Fig. 8B) for the conversion rates between pyruvate and lactate in the three conditions are different. In fact, the conditions represent three general conditions: the first is C G Ј Ͻ C L Ј and C L ϭ 0 (Fig. 8C, left). It is most common in the experiments. The second is C G Ј Ͼ C L Ј and C L ϭ 0 (Fig. 8C,  middle). The third is C L Ͼ 0, and C G may be larger or smaller than C L (Fig. 8C, right).
We can rearrange Equation 20 to another form.
Because the sum of the isotopic contributions of glucose and lactate are equal to the sum of their net contributions and hence are constant when the experimental condition is designated.
Thus, if C L Ј increases, C G Ј decreases and vice versa, which is consistent with our above conclusion. The biochemical principle underlying both Equations 20 and 21 is the isotopic For the estimation method, C 2 is the consumed amount of exogenous lactate, and C 3 is the amount of lactate generated from glucose. We assumed citrate Lac %/C 2 ϭ citrate Glc %/C G , then C G ϭ C 1 Ϫ C 3 ϭ citrate Glc %/citrate Lac % ϫ C 2 , and then C 1 could be calculated. Because the consumed glucose and lactate do not completely enter the TCA cycle, the values are only estimated. In addition, glucose and lactate are composed of six and three carbons, respectively, when comparing the net contribution of glucose and lactate to the TCA cycle, it is based on three carbons as a unit. C, schematic diagram of the isotopic and net contributions of glucose and lactate carbon to the TCA cycle under three general conditions: left, C L Ј is larger than C G Ј, C L is 0, and C G ϭ C G Ј ϩ C L Ј; middle, C L Ј is smaller than C G Ј, C L is 0, and C G ϭ C G Ј ϩ C L Ј; right, C L Ͼ 0, C G ϭ C 1 , and C L may be larger or smaller than C G (the figure only shows the situation when C L Ͻ C G ). The black arrows refer to various contributions, expressed in vector.
Green and blue arrows refer the net contributions of lactate and glucose carbon, respectively, into the TCA cycle, expressed in vector. The three specific conditions described in B fall into the three general conditions in C.

Contributions of lactate and glucose carbon to the TCA cycle
exchange between pyruvate and lactate (i.e. C 2 and C 3 ). In contrast, C 2 and C 3 are both divided out in the deduction process of net contribution (Equation 6); i.e. net contribution is independent of isotopic exchange. This reflects the essential distinction between net contribution and isotopic contribution.

Discussion
In summary, by means of experimentations and mathematical modeling that takes all the variables into consideration, including consumption of glucose and exogenous lactate, generation of glucose-derived lactate, isotopic exchange between pyruvate carbon and lactate carbon, glucose-derived pyruvate, and lactate-derived pyruvate into the TCA cycle, we could dissect the isotopic and the true contributions of glucose carbon and lactate carbon to the TCA cycle. The frequently observed higher labeling efficiency of TCA cycle intermediates by lactate carbon than glucose carbon is actually caused by isotopic exchange. Ignoring isotopic exchange would misinterpret the acquired data. After excluding the interference of isotopic exchange, glucose carbon is the major fuel in most conditions.
A schematic might more vividly demonstrate the isotopic exchange that occurs during the flux of glucose and lactate into the TCA cycle and how it confuses the isotopic labeling with the net flux (Fig. 9). Fig. 9A depicts the net fluxes of the metabolic pathways from glucose and lactate to the TCA cycle in cancer cells that adopt Warburg effect-type metabolism. The cells are cultured in medium containing both glucose and lactate. Obviously, glucose but not lactate makes a net contribution to the TCA cycle. Fig. 9B is the same as Fig. 9A in nature but shows the exchange between pyruvate and lactate, and it is still obvious that glucose but not lactate makes a net contribution. Fig. 9C is the same as Fig. 9A in nature but shows the isotopic labeling. If only Fig. 9C is presented, it may cause confusion; i.e. if the isotopic exchange between glucose-derived pyruvate and lactate is neglected, it would be concluded that lactate is the major carbon source for the TCA cycle because the flux of lactatederived pyruvate to the TCA cycle (the red arrow) is larger than the flux of glucose-derived pyruvate to the TCA cycle (the blue arrow). Therefore, isotopic labeling may divert the focus from the net flux to the unidirectional flux purely based on isotopic labeling, leading to a biased conclusion.
Although it has been long known that the isotopic exchange interferes with the measurement of the metabolic flux, arguments about this issue persist in the metabolic research field. Landau (17) pointed out that the isotopic labeling methods used for estimating keto body production (18) always overestimate due to the isotopic exchange. Sahlin (19) criticized the tracer technique used to determine the lactate production in exercising rats (20) and stressed that tracer methodology cannot be used to quantify lactate production or removal. Fan et al. (21) found that fatty acid labeling from glutamine in hypoxia explained by reductive carboxylation previously (22,23) could be interpreted by isotopic exchange instead of net reductive isocitrate dehydrogenase flux. The reason that isotopic labeling has been confused with net conversion may be due to a lack of mathematical expression that could unambiguously distinguish the two measurements. The equation we deduced here gives a simple quantitative relationship between isotopic con-

Contributions of lactate and glucose carbon to the TCA cycle
tributions and net contributions of lactate and glucose carbon to the TCA cycle.
Earlier, it had been recognized by Krebs et al. (12) that the discrepancy between isotopic tracing and net conversion arises from two distinct mechanisms. One, called "metabolic incorporation of isotopes," involves irreversible reactions that cross over to a common intermediate pool. The mechanism is suitable to the isotopic experiments in regard to the conversion of fatty acids to carbohydrate (10) and the production of glucose from lactate (12). The other, called "isotope exchange," lies in the exchange of carbon atoms in the reversible reactions, and this type is more common as most of the metabolic reactions are reversible. It could explain the inaccuracy in the isotopic tracing of keto body production (14,17), lactate production (19), reductive carboxylation of ␣-KG (21), and the problem described in this study. As the basic principles of the reversible reaction-related isotopic experiments are alike, our deduced equation (i.e. C G Ϫ C G Ј ϭ C L Ј Ϫ C L ) could be used in these situations in a similar way, such as keto body production (18). For example, when keto body production from fatty acids was overestimated by the isotopic tracing compared with the net balance data, the overestimated part may come from another carbon source (e.g. circulating acetoacetate), which was underestimated in an equal amount. This can be validated if all the relevant isotopic measurements and net balance data are acquired.
Theoretically, the mathematical model we introduce here is also applicable to in vivo studies because the parameters we used in the derivation process are all suitable in real tumor environment. To confirm the equation in vivo, the net consumption data must be determined along with the isotopic tracing so that the interference of isotopic exchange could be excluded and the true contribution of glucose and lactate carbon to the TCA cycle could be estimated. However, this is a daunting work because it has been recognized that it is impossible to cannulate afferent and efferent blood vessels that specifically supply tumors (8) so measuring the net flux of glucose and lactate in vivo is improbable. Nevertheless, based on the lactate concentration in tumors (ranging between 4 and 40 mM (24,25)) and in blood (about 1 mM on average at rest (26)), it could be inferred that the tumor is probably a lactate producer rather than a lactate consumer. Circulating lactate could be a candidate fuel for tumors, but to make a net consumption flux, it must overcome the huge concentration gradient to be transported into tumors.
From the isotopic distribution of citrate labeled from lactate or glucose, we could extrapolate that the labeling efficiency of lipid with lactate would be much higher than that with glucose because the acetyl-CoA needed for de novo synthesis of lipids comes from citrate (27). Nonetheless, it still does not mean that lactate contributes more than glucose to lipid biosynthesis.
However, we cannot rule out the possibility that lactate fuels the tumor under some conditions. Because the tumor environment is highly dynamic, for example glucose can be temporarily or persistently deprived (28 -31) and lactate can accumulate at high concentrations (32)(33)(34), a net flux of lactate into cells could occur when the oxygen level permits. Furthermore, some cancer cells (e.g. Siha cells) essentially feed off lactate (i.e. the reverse Warburg effect) in culture (35), which fits into the third model in Fig. 8C. It has also been reported that oxygenated tumors primarily use lactate for oxidative energy production (35,36). In these situations, lactate is consumed and fuels the tumor cells. Conversely, lactate could be considered as an important intermediate in the metabolic pathways from glucose to the TCA cycle. Most of the incoming glucose is first converted to lactate, which could be reused to feed the TCA cycle. If the LDH-catalyzed reaction is unidirectional and lactate cannot be converted back to pyruvate, substantial glucose carbon would indeed be wasted.

Materials and methods
Cell culture 4T1, NCI-H460, and HeLa cells were purchased from Cell Bank of Type Culture Collection of the Chinese Academy of Sciences (Shanghai, China) and maintained in RPMI 1640 medium with 10% FBS, 100 g/ml penicillin/streptomycin, and 2 mM L-glutamine. Cell lines were identified using DNA fingerprinting (SNP for 4T1 and short tandem repeats for H460 and HeLa) and confirmed to be Mycoplasma-free. All cells were cultured in a humidified incubator at 37°C in a 5% CO 2 atmosphere. For experiments performed at pH 7.0, 6.7, and 6.35, 2 M HCl was used to adjust the pH value. A flow cell counter (JIM-BIO) was used for cell counting and cell size measurement.

Isotope labeling experiments
[ 13 C 6 ]Glucose and sodium [ 13 C 3 ]lactate were purchased from Sigma-Aldrich, and sodium [3-13 C]lactate was from Cambridge Isotope Laboratories. The 13 C isotopes were dissolved in RPMI 1640 medium without glucose (Life Technologies) with 10% ultrafiltrated FBS so that the unlabeled glucose and lactate in FBS were eliminated. 1.2 ϫ 10 6 4T1 cells, 9 ϫ 10 5 H460 cells, or 6 ϫ 10 5 HeLa cells were seeded into a 6-well plate to allow attachment overnight. Cells were then rinsed with PBS, and the medium was replaced with the corresponding 13 C-containing medium ([ 13 C 6 ]glucose ϩ lactate, glucose ϩ [ 13 C 3 ]lactate, or [ 13 C 6 ]glucose ϩ [3-13 C]lactate). The metabolites were extracted according to the methods described previously with some modifications (37). Briefly, the medium was collected after incubation, and the cells were rinsed with ice-cold PBS twice. 600 l of 80% (v/v) methanol/well was added, and the plates were incubated at Ϫ80°C for 20 min. The plates were scraped, and the lysate/methanol mixture was vortexed and centrifuged at 25,000 ϫ g for 5 min at 4°C to remove the debris. The supernatant was evaporated completely and redissolved in 30% acetonitrile followed by LC-MS analysis. The collected medium was diluted 40-fold with 100% acetonitrile and centrifuged at 25,000 ϫ g for 15 min at 4°C, and the supernatant was aspirated for LC-MS analysis.

LC-tandem MS (LC-MS/MS) analysis
The labeling of metabolites was analyzed by an LC-MS/MS approach. LC was performed on an ACQUITY BEH Amide column (2.1 ϫ 100 mm, 1.7 m) using a Waters ACQUITY UPLC system. Mobile phase A was 10 mM ammonium acetate in 85% acetonitrile, 15% water, pH 9.0, and mobile phase B was Contributions of lactate and glucose carbon to the TCA cycle 9.0. The gradient program was as follows: 0 -0.4 min, 100% A; 0.4 -2 min, 100 -30% A; 2-2.5 min, 30 -15% A; 2.5-3 min, 15% A; 3-3.1 min, 15-100% A; 3.1-7.5 min, 100% A. The flow rate was 0.6 ml/min, the injection volume was 7.5 l, and the column was kept at 50°C. The mass spectrometer was an AB SCIEX 4000 QTRAP equipped with an electrospray ionization ion source in multiple reaction monitoring (MRM) mode. Sample analysis was performed in negative ion mode. The MRM transitions (m/z), declustering potential, collision energy, entrance potential, and collision cell exit potential were optimized for each metabolite by direct infusion of pure standards using a syringe pump and are listed in Method S1. The MRM parameters were set as follows: curtain gas, 40 p.s.i.; ion spray voltage, Ϫ4.5 kV; temperature, 500°C; ion source Gas 1, 50 p.s.i.; ion source Gas 2, 50 p.s.i. The MRM data were acquired and processed using Analyst 1.5.2 software equipped in the AB SCIEX 4000 QTRAP mass spectrometer. The peak areas of the ion fragmentations were acquired, and the observed mass isotopomer distribution (MID) of target intermediates was calculated. Afterward, the observed MID data were corrected for natural isotopic abundance using the methods described previously (38,39) to obtain the corrected MID data.

Enzymatic determination of glucose, lactate, and pyruvate
To measure the intracellular concentration of glucose, lactate, and pyruvate, cells were seeded into 10-cm dishes. The experiment was performed when the culture reached 70 -80% confluence. Cells were harvested as described above. The lyophilized sample was dissolved in 150 l of water for the following measurements. The concentrations of glucose, lactate, and pyruvate were measured using a spectrophotometer (Beckman Coulter) according to the methods described previously with some modifications (40).
Assay of glucose-10 l of medium (or 50 l of cellular sample) was added to 990 l of reaction buffer (100 mM Tris-HCl, 1 mM MgCl 2 , 500 M NAD ϩ , 500 M ATP, pH 8.1). The reaction was started by adding 0.5 unit of G6PDH (from Leuconostoc mesenteroides; Sigma-Aldrich) to measure G6P by reading at 340 nm against the blank. 0.5 unit of HK (from Saccharomyces cerevisiae; Sigma-Aldrich) was added afterward to measure glucose. Because the G6P in the medium was undetectable, the sample was added to the buffer, including HK and G6PDH, directly to measure glucose. 10 l of medium (or 50 l of cellular sample) was added to the cuvette, which contained the same ingredients but the enzyme, simultaneously to correct for the drift effect.
Assay of lactate-10 l of medium (or 50 l of cellular sample) was added to 990 l of reaction buffer (200 mM glycine, 170 mM hydrazine, 2 mM NAD ϩ , 5 units of LDH from rabbit muscle, pH 9.2). The sample was mixed well, incubated at room temperature for 1 h, and read at 340 nm against the blank. 10 l of medium (or 50 l of cellular sample) was added to the cuvette, which contained the same ingredients but the enzyme, simultaneously to correct for the drift effect.
Assay of pyruvate-50 l of sample was added to 500 l of reaction buffer (1ϫ PBS, 200 M NADH, 0.1 unit of LDH from rabbit muscle, pH 7.3). The sample was mixed well and read at 340 nm against the blank. 50 l of sample was added to the cuvette, which contained the same ingredients but the enzyme, simultaneously to correct for the drift effect.

Determination of HK, LDH, and PDH activities
The activities of HK and LDH in cells were measured by a spectrophotometer (Beckman Coulter) according to methods described previously (40). Cells were lysed with mammalian protein extraction reagent (Thermo Fisher) with protease inhibitor mixture (Thermo Fisher), and the protein concentration was measured by BCA assay kit. The experiments were all performed at 37°C.
Assay of HK-20 g of protein was added to 600 l of reaction buffer (100 mM Tris-HCl, 5 mM MgCl 2 , 1 mM NAD ϩ , 5 mM ATP, 2 mM glucose, 0.5 unit of G6PDH from L. mesenteroides, pH 8.1), and a reading at 340 nm was made every 30 s. The activity was calculated from the linear part of the curve.
Assay of LDH (from pyruvate to lactate)-2 g of protein was added to 2 ml of reaction buffer (100 mM Tris-HCl, 1 mM sodium pyruvate, 200 M NADH, pH 7.6), and a reading at 340 nm was made every 10 s. The activity was calculated from the linear part of the curve.
Assay of LDH (from lactate to pyruvate)-50 g of protein was added to 500 l of reaction buffer (200 mM glycine,170 mM hydrazine, 2 mM NAD ϩ , pH 9.2), and a reading at 340 nm was made every 10 s. The activity was calculated from the linear part of the curve.
Assay of PDH-The PDH activity was measured using a PDH Activity Assay kit from Sigma-Aldrich (catalogue number MAK183).

Determination of K m values of HK and LDH in cell lysates
The K m value of enzyme in cell lysates was determined by measuring enzyme activity at a series of substrate concentrations. For HK, the glucose concentration ladder was 0, 50, 100, 150, 200, 300, 400, 600, 800, and 1200 M. For LDH, the lactate concentration ladder was 0, 1, 2, 4, 8, 16, 32, 48, 64, and 96 mM. The K m values were calculated from the 1/V 0 Ϫ 1/[S] plot.
A pSpCas9(BB)-2A-Puro (PX459) V2.0 plasmid (Addgene plasmid number 62988) was used as sgRNA expression vector, and the constructed plasmids were transfected into cells using Lipofectamine 3000 (Invitrogen). After selection with puromycin, the cleavage efficiency was assessed by T7 endonuclease I. A single cell was isolated by limited dilution, and the monoclonal cell lines were cultured until 70 -80% confluence. The microdeletion was detected by PCR and Sanger sequencing. Candidate off-target sites were checked by sequencing to avoid an off-target effect. The result of knockout was checked by Western blotting using anti-LDHA (Cell Signaling Technology) and anti-LDHB (Santa Cruz Biotechnology) antibodies.

Contributions of lactate and glucose carbon to the TCA cycle
Enzyme activities of knockout and control cells were also measured to validate the results.