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This protocol enables quantitation of metabolic fluxes in cultured cells. Measurements are based on the kinetics of cellular incorporation of stable isotope from nutrient into downstream metabolites. At multiple time points, after cells are rapidly switched from unlabeled to isotope-labeled nutrient, metabolism is quenched, metabolites are extracted and the extract is analyzed by chromatography–mass spectrometry. Resulting plots of unlabeled compound versus time follow variants of exponential decay, with the flux equal to the decay rate multiplied by the intracellular metabolite concentration. Because labeling is typically fast (t1/2≤5 min for central metabolites in Escherichia coli), variations on this approach can effectively probe dynamically changing metabolic fluxes. This protocol is exemplified using E. coli and nitrogen labeling, for which quantitative flux data for ~15 metabolites can be obtained over 3 d of work. Applications to adherent mammalian cells are also discussed.
Kinetic flux profiling (KFP) aims to provide a practical experimental approach for measuring metabolic fluxes in live cells. The central idea of KFP is that larger metabolic fluxes are associated with faster transmission of isotopic label from added nutrient to downstream metabolites. The half-time of labeling of a metabolite will depend directly on the speed of transmission of label into the metabolite (i.e., the flux) and inversely on the size of the metabolite pool (i.e., the intracellular metabolite concentration). The KFP approach has been used to investigate nitrogen assimilation fluxes in exponentially growing E. coli1, metabolic flux changes accompanying onset of carbon starvation in E. coli2, carbon fluxes in E. coli fed with glucose versus acetate (Daniel Amador-Noguez and J.D.R., unpublished data), aromatic amino-acid pathway flux in nitrogen-starved E. coli and yeast3 and carbon flux in growing, quiescent and virally infected human fibroblasts (Hilary Coller, Johanna Scarino, Joshua Munger, Thomas Shenk, B.D.B., J.D.R., unpublished data).
This concept is illustrated in Figure 1. During exponential growth, the rate of production of each metabolite (influx) should match its rate of consumption (efflux) so that the intracellular concentration remains constant. Under this pseudosteady state, if an external nutrient is instantaneously switched from natural to isotopically labeled, for a metabolite X directly downstream of nutrient assimilation, unlabeled X (XU) will be replaced over time by its labeled counterpart (X*) and the fraction of unlabeled X (XU/XT) will decay exponentially (Fig. 1). The rate constant of this decay (kX) is determined by the ratio of the flux through X (fX) to the total pool size of X (XT) as shown in Figure 1. Therefore, one can calculate the flux through X (fX) from kX and XT. kX can be obtained experimentally by the protocol described here and XT by a diversity of literature approaches4-6, including the protocol of Bennett et al.7. For an example of quantitative analysis of data from more complex cases (which realistically involve metabolites not immediately downstream of labeled nutrient and being formed by multiple reactions), see the ANTICIPATED RESULTS section.
Accurately measuring kX is most easily achieved by rapid and complete switch of the nutrient of interest from unlabeled to isotope-labeled form, followed by fast sampling of cells1. For reliable flux measurements, both steps must be accomplished without perturbing cellular metabolism. Otherwise, the artifacts induced by the handling steps will mask the true cellular metabolic state8-12. To meet this need for nonadherent cells (e.g., E. coli1-3,13, Saccharomyces cerevisiae3), we developed a filter culture technique in which cells are grown on a membrane filter sitting on top of agarose plates loaded with media. The cells are fed by nutrient diffusion from the underlying medium up through the filter. This technique enables isotope switching by transferring the filter between agarose plates of different composition. It also allows fast metabolic quenching by transferring the filter into cold organic solvent, which stops metabolism (initially due to the temperature drop and subsequently by denaturing enzymes) and simultaneously initiates the extraction process by disrupting the cell membrane. Movements of the filter can be done in ~1 s. Minor deviations in the transfer time tend to have minimal impact, as the cells continue to receive nutrients from the filter during the transfer.
Although the overall strategy is the same, the filter culture approach is not necessary for adherent cell types like human fibroblasts. Instead, medium removal via quick aspiration is followed by addition of isotope-labeled medium for isotope switch or cold organic solvent for metabolic quenching and extraction. Specific cell-handling steps are provided in the protocol.
Overview of the workflow and experimental setups for KFP are shown in Figure 2. The step of quantifying heavy and light (i.e., labeled and unlabeled) isotopic forms can be achieved by any appropriate form of mass spectrometry (MS). Typically, we use liquid chromatography (LC)–electrospray ionization (ESI)–triple-quadrupole MS operating in multiple reaction monitoring (MRM) mode. MRM is a targeted form of tandem mass spectrometry (MS/MS) with the advantage of excellent sensitivity and linear dynamic range. LC separation before the MS/MS analysis is valuable for separating isobaric compounds. Other forms of chromatography-MS should also be applicable. These include gas chromatography–MS and LC–time-of-flight–MS. For further information on analytical options, see the protocol of Bennett et al.7. The rate constants obtained from KFP can then be combined with intracellular concentrations of metabolites determined separately to calculate fluxes.
Typically, a single replicate of KFP is informative (as even a single replicate contains multiple time points). For quantitative work where small differences between conditions are involved or precise flux estimates are desired, 3–4 replicates are preferred. As KFP experiments are internally controlled (by the multiple isotopic forms), external controls are not required. It is often useful, however, to conduct switches from unlabeled to unlabeled media to ensure against unanticipated metabolic shifts due to media change rather than isotope switch.
Kinetic flux profiling provides an approach for experimentally quantifying metabolic fluxes in live cells. The principal starting information required is the structure (connectivity) of the metabolic network being investigated (see ANTICIPATED RESULTS for an example). An advantage of the technique is that the experimental data provide a check on the pathway architecture, based on the requirement for precursor metabolites to become labeled before their downstream products. Quantitative analysis of fluxes by KFP is facilitated when the fluxes are at steady state; however, differential KFP (described below) can provide quantitative data even outside of the steady-state condition. Further quantitative assumptions are not required, as fluxes are calculated directly from the experimental results obtained as described here (kX) and in the companion protocol of Bennett et al.7 (XT).
One can choose to use basic nutrient(s) (e.g., glucose, ammonia, etc.) to introduce isotopic labels or to use special tracers for a specific pathway. We have successfully applied KFP to measure fluxes involved in nitrogen metabolism in E. coli1,2, and for this reason, this protocol uses the example of 15NH4Cl as the labeled nutrient in this model organism. The KFP approach is, however, also widely applicable to other labeled nutrients and cell types, as demonstrated by published work from our laboratory using 13C-glucose as the tracer in both E. coli and S. cerevisiae3 and unpublished data from our laboratory with cultured human cells.
It is important to note that KFP measures gross fluxes: the labeling kinetics is related to the sum of all fluxes feeding into (or, equivalently at steady state, flowing out of) a metabolite. In the case of reversible reactions, this means that the flux measured by KFP may differ significantly from the net pathway flux.
A limitation to the KFP approach is that quantitative flux information is reliably obtained only for metabolites that turn over slowly relative to their upstream precursor. Consider a case in which the isotope label is relayed from a precursor metabolite X to a downstream metabolite Y. If X turns over faster than Y, then the labeling kinetics of Y will reliably reflect the flux through Y, based on the magnitude of kY. In contrast, if X turns over at a much slower rate than Y, then the labeling kinetics of Y will mainly depend upon the labeling of X, rendering measurement of kY, and accordingly flux through Y, imprecise (a more quantitative treatment of this important case is provided in the ANTICIPATED RESULTS). For a similar reason, the uptake of the nutrient or the tracer needs to be efficient, and the nutrient must not accumulate significantly internally. Otherwise, the rate of labeling of metabolites will be largely determined by the rate of turnover of the internal pool of the nutrient/tracer, rendering it impossible to accurately quantitate the downstream fluxes.
Differential KFP provides an example of a KFP variant suitable for quantitative analysis of dynamically changing fluxes. It was developed to evaluate changes in biosynthesis and macromolecule degradation when cells are exposed to an environmental perturbation. It has been used to demonstrate that carbon starvation in E. coli results in rapid turning off of de novo biosynthetic fluxes, with protein degradation becoming the major source of intracellular amino acids2. As shown in Figure 3, differential KFP consists of two (or more) sets of the KFP experiment, with the isotope switch initiated at different times with respect to the perturbation (e.g., preceding or following the perturbation). The kinetic patterns of isotope incorporation into metabolites obtained from these experiments, in addition to the knowledge of metabolite concentration changes triggered by the perturbation, can often be used to determine the effect of the perturbation on metabolic fluxes. Carbon source withdrawal in E. coli is used as an example of a perturbation in this protocol.
Efforts at measuring cellular metabolic fluxes have been ongoing for decades and a diversity of valuable tools have been developed14-20. Several of these contain elements similar to the current KFP approach. Instead of detailing these related approaches, here we focus on two conceptually distinct alternatives: flux balance analysis (FBA)21 and metabolic flux analysis (MFA)22.
Flux balance analysis is a constraints-based computational approach that requires little experimental data and offers an estimation of the range of feasible flux distributions in steadily growing cells21,23. Although it has proven powerful, especially for E. coli24, the precise determination of fluxes by FBA relies on an objective function and related assumptions (e.g., that E. coli maximizes biomass yield per molecule of carbon source consumed23-25). For most organisms, a validated objective function is not available, limiting the ability of FBA to make quantitative flux predictions in the absence of experimental data26-28.
Metabolic flux analysis is an experimental approach that typically involves feeding cells with a mixture of different 13C-labeled glucose species (e.g., uniformly labeled and only one carbon labeled) for a prolonged period under metabolic steady state29, until the isotopic labeling pattern of the compounds to be measured (most typically proteic amino acids) reaches a steady state (>1 h). From the labeling pattern of proteic amino acids30 or primary free metabolites31, metabolic fluxes (mostly of central carbon metabolism) are then deconvolved with the aid of computer modeling32,33.
To assist in the choice of the appropriate experimental approach, MFA and KFP are compared here. MFA is well suited to measuring the ratio of fluxes at branch points when the alternative branches yield different labeling patterns of a downstream metabolite30,31. It is also suitable for large-scale studies with respect to the number of species/strains29, as the fluxes (relative to glucose uptake) of multiple pathways can be obtained from a single sample. No time courses or pool size data are needed, which reduces the experimental demand compared with KFP. However, MFA (at least in its most commonly practiced form) is largely limited to carbon metabolism, as labeling by other elements rarely produces the rich spectrum of labeling patterns of metabolites required for flux deconvolution (e.g., there are 32 theoretical C-labeling states but only 2 possible N-labeling states of glutamate—labeled or unlabeled). In contrast, KFP is more versatile in terms of what pathways can be monitored. In addition, KFP also has the following strengths compared with MFA: easy data deconvolution (in many cases, the differential equations of KFP have analytical solutions in the form of exponential functions with few free parameters, enabling direct parameter determination); short labeling time (no requirement for incorporation of isotope labels to reach steady state, which allows effective probing of dynamically changing fluxes using variants like differential KFP); and KFP can provide absolute fluxes instead of just split ratios. Each individual approach has limitations, and combining multiple approaches will generally yield the most complete understanding.
Before initiation of an experiment, cells should be handled as per typical laboratory protocols tailored to the cell type of interest. To initiate this protocol, a starter culture is required for microbes and 106–107 cells in culture for mammalian cells.
Wash the Ultrapure agarose three times with HPLC-grade water to remove trace impurities. For 30 g of agarose, use 1 liter of water for each wash. For each wash, stir the agarose–water mixture for 10 min and leave aside to settle for ~1 h. Aspirate the water with care to avoid loss of agarose. The resulting washed agarose can be used to make minimal media plates with 1.5% (wt/vol) agarose. Note: this is not necessary for adherent cell types.
Combine sterile salts, glucose (or other carbon source) and water according to the media recipe. (The exact composition of the complete minimal media we use is as follows: KH2PO4 4.7 g liter−1, K2HPO4 13.5 g liter−1, K2SO4 1 g liter−1, MgSO4 · 7H2O 0.1 g liter−1, NH4Cl 10 mM, glucose 0.4%. Use isotope labeled nutrient when appropriate.)
Combine minimal liquid medium with 1.5% (wt/vol) washed agarose. Autoclave and pour into the sterile Petri dishes to make media plates. Use 20 ml of agarose–medium mixture per 10-cm plate. Four types of plates will be used in the protocol: two types for KFP (Steps 1–8) and additional two types for differential KFP (Steps 9–22). Compositions specific to 15NH4Cl-labeling are as listed below:
Note that, as carbon starvation is used as the example of perturbation in this protocol, glucose is removed from the plate content for this purpose in Type C and D plates. Exact content of the Type C and D plates will depend on your experiment and perturbation of interest. Agarose plates are not necessary for adherent cell types.
Different groups of metabolites are extracted with different efficiency depending upon the extraction solution mixture34. Choice of extraction solution should be made according to which metabolites are of the greatest interest. Among the seven solution systems we have tested for extracting filter cultures, 40:40:20 acetonitrile:methanol:water solvent system works the best for extracting filter cultures in general; addition of formic acid to a final concentration of 0.1 M provides additional protection of nucleotide triphosphates against degradation13. NH4HCO3 solution is used to neutralize the formic acid immediately after extraction. Methanol (100% methanol at −75 °C for the first round, 80:20 methanol:water at 4 °C for the two subsequent rounds) extracts amino acids effectively while extracting fewer other components than acetonitrile:methanol:water; it is accordingly preferred for studies focused solely on amino acids and was used for our KFP study of nitrogen metabolism1. For extracting human fibroblasts, we have obtained adequate results with 80:20 methanol:water for all the three extractions. Pending more definitive studies, we recommend this solvent mixture for them.
Solvent A: 20 mM ammonium acetate + 20 mM ammonium hydroxide in 95:5 water:acetonitrile, pH 9.45; Solvent B: acetonitrile. Note that this is our mobile phase of choice when working with aminopropyl column in hydrophilic interaction chromatography mode; there are many other chromatography choices available31,35-37. Many of these have important advantages relative to the aminopropyl approach for certain classes of compounds. For more information, see Lu et al.38.
Hydrophilic interaction chromatography is performed on a 2-mm inner diameter column packed with 5-μm aminopropyl resin to 250 mm in length, using an LC-10A HPLC system (Shimadzu). The column is maintained at 15 °C with a solvent flow rate of 0.15 ml min−1, and the gradients are as follows: t = 0, 85% B; t = 15 min, 0% B; t = 28 min, 0% B; t = 30 min, 85% B; t = 40 min, 85% B. Other chromatography approaches and/or HPLC systems can be used depending on their availability and the metabolites of interest.
A Finnigan TSQ Quantum Ultra triple quadrupole mass spectrometer (Thermo Electron Corporation) is run in MRM mode and coupled to the HPLC via electrospray ionization. Electrospray ionization spray voltage is 3,200 V in positive mode. Nitrogen is used as sheath gas at 30 psi and as the auxiliary gas at 10 psi, and argon as the collision gas at 1.5 mTorr, with a capillary temperature of 325 °C. MRM scan time is 0.1 s and scan width is 1 m/z. Other forms of MS (e.g., single quadruple, time of flight, ion trap) generally provide slightly less optimal quantitation (e.g., worse signal-to-noise and reproducibility) but can nevertheless be used.
Reactions should be optimized for metabolites of interest using standards before the quantification experiment. A list of reactions used in our experiments has previously been published1. Optimization of the product ion and collision energy for a given unlabeled metabolite is achieved by infusing purified compound standard into a triple quadrupole mass spectrometer. Collision energy should be identical for labeled and unlabeled forms. For 15N labeling, the parent ion mass should be increased by the number of nitrogen atoms in the metabolite, and the product ion mass should be increased by the number of nitrogen atoms in the product ion (product ion structures can be obtained from the literature for common metabolites, or otherwise estimated based on common routes of fragmentation and confirmed experimentally by MS/MS of the labeled forms). For partially labeled forms, more than one product ion mass may be possible for each parent ion mass. The different product ion masses arise from labeling at different positions within the parent. As an example, consider the possibilities for a compound with two nitrogen atoms that gives a product ion with 1 nitrogen (e.g., glutamine): with 0 × 15N in the parent, there cannot be 15N in the product ion; with 1 × 15N in the parent, there can be 0 or 1 × 15N in the product ion; with 2 × 15N in the parent, there must be 1 × 15N in the product ion.
Δ CRITICAL Steps 1–8 enable measurement of steady-state metabolic fluxes. Steps 9–22 (Differential KFP, optional) are used for probing flux changes in response to an environmental perturbation. Steps 9–11, 12–16 and 17–22 are logistically independent of each other and can be carried out in any order.
Many of these steps have time periods dependent upon the growth rate of the cell culture. As such, these time periods may vary substantially with the cultures used.
Step 1A for E. coli:
Step 1B for human fibroblasts:
Steps 2–8 (analysis):
Differential KFP (optional steps):
Check that MRM scan events are appropriate for labeled forms of interest. A good check is to grow cells for an extended period in the labeled nutrient and make sure that the signal for the labeled forms (in the labeled cells) is similar to the signal for the unlabeled forms (in the unlabeled cells). This also provides a useful check as to whether isotopic purity of the nutrient is acceptable (such purity can also be directly measured by MS). Note that high purity is required to obtain complete labeling of compounds that assimilate the label into many positions (e.g., 98% 15N-ammonia will lead up to 98% full labeling of glutamate, 96% full labeling of glutamine (with most of the residual in the single-labeled state) and less than 13% full labeling of a 100 amino-acid protein).
Rely on chromoatographic separation. Alternatively, separate based on fragmentation pattern (product ion mass in MRM analysis) or based on exact mass (if using a mass spectrometer with very high resolving power, such as a Fourier transform instrument).
This is evident as large changes in the sum of all isotopic forms upon isotope switch. The cell handling described herein is specifically designed (and, in our hands, validated) to avoid this problem. Closely adhere to the instructions herein to avoid it. Also, avoid holding the cells in the same unlabeled media for long time periods before the switch (this can lead to accumulation of waste products in the media or depletion of nutrients) and be careful to match media pH, temperature, CO2 content and so on. Check the adequacy of cell handling via switches from unlabeled to identical unlabeled media.
This occurs when a step upstream of the pathway is slower than any of the pathway steps (i.e., the turnover of some pool between the added nutrient and the pathway is slower than turnover of any of the pathway pools). This precludes quantitative flux analysis of the pathway. There are three options: (i) accept the lower bound on the pathway flux provided by the observed data, (ii) find a way to circumvent the slow upstream step (in particular, find a way to expedite the isotope switch if it is rate limiting); (iii) apply an alternative flux measurement approach.
Make sure that the cells are at metabolic steady state at the time of the isotope switch. If the cells are not at steady state, use differential KFP to understand the ongoing flux changes. Quantitative analysis of differential KFP data does not follow a standard protocol, but an example can be found in Yuan et al.2.
When drawing biological conclusions based on partial labeling that is far from complete, correction for natural abundance of carbon 13 is required. Such corrections are generally unimportant with N-labeling of E. coli. However, we have found that they can be important in interpreting TCA cycle 13C-labeling patterns in mammalian cells. Appropriate corrections (assuming 13C labeling) are as follows:
where M0 is the amount of the monoisotopic compound, M+1 is the amount of the compound with one 13C atom, M+2 is the amount of the compound with 2 × 13C atom and so on; N is the number of carbon atoms in the molecule; and ‘real’ refers to values corrected for coincidental labeling and ‘measured’ refers to raw values determined by LC-MS/MS. The subtraction operations serve to remove the naturally occurring isotopic envelop of the less-labeled species from the ‘real’ values of the more extensively labeled species. The division operations serve to add back the isotopic envelope of the indicated species that is otherwise lost as more extensively labeled species due to the natural abundance of 13C.
Superimposed chromatograms of unlabeled and 15N-labeled glutamate from one KFP experiment, demonstrating the replacement of the unlabeled form of glutamate by its labeled counterpart when E. coli are switched from unlabeled to isotopically labeled ammonia, are shown in Figure 4a. Each chromatogram corresponds to one time point post the isotope switch. Note that glutamate has only one nitrogen atom and therefore only one labeled form. When multiple labeled forms exist for a metabolite (e.g., metabolites containing multiple nitrogen atoms for nitrogen labeling), all possible isotopically labeled forms should be taken into consideration. From each chromatogram, ‘fraction unlabeled’ is calculated as described in PROCEDURE and plotted against time in Figure 4b. This data can then be used to calculate the apparent first-order rate constant k.
The general concepts for treatment and interpretation of KFP data are discussed in the Introduction. Here, we present a more quantitative and complex example of data analysis. Imagine a pathway as shown in Figure 5: metabolite X is produced both from nutrient (by de novo synthesis) and from degradation of some macromolecules (e.g., protein, nucleic acids, glycogen and so on), and the two influxes are f1 and f2, respectively. Similarly, Y is down stream of X in the pathway and can also be produced directly from macromolecules; the fluxes are f4 and f5, respectively. Additionally, the fluxes directing X and Y out of the pathway (for biomass production and so on) are f3 and f6, respectively, as shown. Under steady state, the following conditions exist (fX and fY denote total fluxes through the pools of X and Y, respectively, superscript U stands for ‘unlabeled’, * for ‘labeled’ and T for ‘total’):
Decreasing unlabeled X and Y after switching the nutrient from natural to isotopically labeled can be described by the following differential equations (which assume that the nutrient switch is so fast as to be effectively instantaneous relative to the labeling times of X and Y):
The apparent first-order rate constant (k) for X and Y are defined as
and for simplified results, set
Therefore, by measuring fraction unlabeled (XU/XT and YU/YT) versus time, the apparent first-order rate constants (kX and kY) can be calculated. Combined with the concentrations (XT and YT), the fluxes fX and fY through X and Y can be obtained. For cases in which XT YT and fX ≈ fY, this implies kX kY, and therefore equation (4) reduces to equation (3) and kY cannot be determined. In this situation, one can only conclude that fY YT × kX.
The biexponential nature of equation (4) arises from passage of label into Y being delayed by labeling of X. For metabolites further downstream from the added nutrient, full mathematical treatment is yet more complex and often best handled by computer simulation. Alternatively, one can apply a variant of equation (4) that is more broadly applicable.
To understand this variant, consider metabolite W, downstream of metabolite V (where V is not directly downstream of the labeled nutrient). Assume that, consistent with most data that we observe in the lab, the unlabeled form of V shows approximately single exponential decay. Passage of label into W will be delayed by V, just as passage of label into Y is delayed by X. However, equation (3) (which assumes a direct connection to labeled nutrient) will not apply to V. Fit the data for V instead to a variant of equation (3), except replacing kX with k′V (equation (5)). k′V is not designed to give the flux through V, but to lay the groundwork for measuring flux through W. Knowledge of k′V allows one to fit the data for W to equation (6). This equation is equivalent to equation (4), with kX replaced by k′V and kY by kW. The parameter kW gives flux through W from fW = kW × WT. This approach can be applied repeatedly. It is important, however, to always solve for k′ for the precursor based on a single exponential approximation (equation (5)) and k based on equation (6) (i.e., to determine flux through Z, a product of W, one needs to calculate k′W and kZ, use of kW is not correct).
To demonstrate the quantitative application of KFP to a real set of metabolic pathways, we use here the nitrogen assimilation system of E. coli. Before embarking on KFP analysis per se, we provide a small amount of background that is essential to understanding the network: The central pathways of nitrogen assimilation in E. coli, as well as selected effluxes to amino acid and nucleotide biosynthesis, are shown in Figure 6. Ammonia can be directly assimilated into glutamate via the enzyme glutamate dehydrogenase (GDH). Alternatively, ammonia can condense with glutamate to form glutamine, catalyzed by the ATP-consuming enzyme glutamine synthetase (GS). Glutamine then yields two molecules of glutamate via glutamate synthase (commonly referred to as GOGAT, which stands for glutamine amide 2-oxoglutarate aminotransferase)8,40. The GS-GOGAT cycle has the same net effect as GDH, but differs in (i) burning ATP and (ii) having a lower Km (i.e., higher affinity) for ammonia8. Glutamate is the major nitrogen distributor in the cell, feeding most of the amino-acid biosynthesis via transamination41. Glutamine feeds selected other pathways41. Figure 6 shows one example of a typical transamination reaction (glutamate + α-keto-isovalerate → α-ketoglutarate + valine), and one example of a typical glutamine-consuming pathway (pyrimidine biosynthesis; glutamine enters at the first step, formation of carbamoyl phosphate).
Switching of exponentially growing E. coli into 15N-ammonia followed by kinetic sampling and LC-MS/MS analysis (as per Steps 1 option A to 8) yields data adequate to deduce most of the fluxes in Figure 6, despite the presence of cycles, branch points and compounds that cannot be directly measured by LC-MS/MS due to low abundance.
Before analyzing the KFP data itself, it is necessary to determine the turnover time of ammonia following the isotope switch. This was approximated by directly measuring the time for ammonia to diffuse onto an empty filter (Fig. 7a) and fitting the data to a single exponential saturation-binding equation, that is, A(t) = Amax (1 − exp(−k′t)) (the fit gives k′ = 7.5 min−1).
The observed value of k′ for ammonia was used in equation (6) to calculate flux through glutamine based on the data in Figure 7a. This reflected a conscious decision to treat single-labeled glutamine (the first form that appeared after the isotope switch) as the product of unlabeled glutamate and labeled ammonia. This was based on the empirical observation that glutamine labeled much faster than glutamate (t1/2 approximately 10 and 60 s, respectively) and the MS/MS-based determination that the single-labeled form of glutamine contained 15N predominantly in the amide position. The resulting k for glutamine was 14.3 min−1 and multiplication by the pool size of 3.9 μmol gCDW−1 gave a flux of 3.4 mmol (gCDW h)−1.
Flux through glutamate was calculated using equation (6), with k′ based on either ammonia or glutamine amide labeling (k′ =7.5 min−1 and 3.6 min−1, respectively). Both approaches yield similar kglutamate (1 min−1 and 1.2 min−1, respectively) because k′ k in either case. As mentioned in the previous section, when k′ k, equation (6) reduces to equation (3), and fitting glutamate data to equation (3) gives kglutamate=0.8 min−1, which is close to the k calculated from equation (6) given fitting error. With a pool size of 101 μmol gCDW−1, the fluxes for glutamate calculated from the three kglutamate values are 6, 7.2 and 4.8 mmol (gCDW h)−1, respectively.
At steady state, the total consumption and production fluxes of each metabolite must be equal. The total glutamate flux, measured to be 6 mmol (gCDW h)−1, therefore equals the sum of its two consumption fluxes: glutamine synthetase flux, measured to be 3.4 mmol (gCDW h)−1, and the flux of glutamate to biomass, which by subtraction must be 2.6 mmol (gCDW h)−1. The flux of glutamine to biomass is known (based on overall metabolic stoichiometry and the composition of E. coli) to be ~15% of the glutamate flux to biomass. Thus, it must be ~ 0.4 mmol (gCDW h)−1. The total glutamine influx of 3.4 mmol (gCDW h)−1 equals the sum of its efflux to biomass of 0.4 mmol (gCDW h)−1 and to glutamate via GOGAT, which by subtraction must be 3 mmol (gCDW h)−1. GOGAT flux from glutamine of 3 mmol (gCDW h)−1 yields 6 mmol (gCDW h)−1 of glutamate, which is the measured glutamate influx. Thus, KFP was adequate to determine that GOGAT is the major source of glutamate, despite the complexities introduced by metabolic cycling.
Flux through valine can be calculated by straightforward application of equation (5) and equation (6) to the data in Figure 7a and b (glutamate is the sole nitrogen parent of valine, and k′ is accordingly based on a fit of equation (5) to observed results for glutamate; k′ = 0.8 min−1, kvaline = 3.9 min−1, pool size = 2.4 μmol gCDW−1, flux =0.6 mmol (gCDW h)−1). Note that transamination reactions are rapidly reversible and the valine flux determined by KFP is the gross, rather than net, flux.
Calculation of pyrimidine pathway flux is complicated by the many steps involved and the inability to measure some components. It is facilitated, however, by flux into carbamoyl aspartate being essentially irreversible and by the requirement for flux at steady state to be equal for all steps of the linear portion of the pathway linking carbamoyl aspartate and UMP. Carbamoyl aspartate labels quickly after ammonia isotope switching, with the label first appearing in the carbamoyl nitrogen. Carbamoyl aspartate flux would typically be calculated using k′ based on carbamoyl phosphate. The level of carbamoyl phosphate is, however, generally too low for us to detect it in E. coli. As we have validated the method for carbamoyl phosphate, with a detection limit of 100 ng ml−1, this implies that the cellular carbamoyl phosphate concentration is very low. Therefore, the small cellular carbamoyl phosphate pool can only slightly delay the passage of nitrogen from glutamine to carbamoyl aspartate. Accordingly, pathway flux (from carbamoyl aspartate to UMP) was calculated by equation (6), with k′ based on fit of equation (5) to experimental results for glutamine and fitting to the carbamoyl aspartate data in Figure 7c (k′ = 3.6 min−1, kcarbamoyl aspartate = 4.1 min−1, pool size = 0.8 μmol (gCDW)−1, flux =0.2 mmol (gCDW h)−1). This yields net pathway flux, as the step being monitored is essentially irreversible. Extension of quantitative analysis to CMP was not feasible, however, as data on the parent of CMP (with RNA likely one major source) was not available.
Figure 8 shows a ‘fraction unlabeled’ graph generated in the same fashion as Figure 4b, from chromatograms of proline in a differential KFP experiment. Data corresponding to Steps 9–11 are shown in red and those corresponding to Steps 12–16 are shown in blue. The two data sets are aligned according to the time of isotope switch. The black arrows indicate the time of the perturbation event for each set. Note that both curves had positive slope for t > 10 min, indicating that the unlabeled fraction is increasing even though only labeled nutrient is being provided. As proline (and most other metabolites) can be produced via both de novo synthesis (which will generate labeled proline) and protein degradation (which will produce unlabeled proline), this behavior suggests that the fraction of proline production from protein degradation is increasing during carbon starvation. The fact that the two curves did not converge even at about 1 h postperturbation and isotope switch implies that the flux through proline pool is small. More quantitative information and rough estimation of flux changes can be obtained when combining these pieces of kinetic data with the concentration changes obtained via Steps 17–22. For an example of detailed data treatment and analysis in this fashion, see Yuan et al.2.
This research was supported by the Beckman Foundation, NSF DDDAS grant CNS-0540181, American Heart Association grant 0635188N, NSF CAREER Award MCB-0643859, NIH grant AI078063, and NIH grant GM071508 for Center of Quantitative Biology at Princeton University. We thank Wenyun Lu, Elizabeth Kimball, Sunil Bajad and Joshua Munger for their contributions to the development of the protocols presented here, and David Botstein for suggesting the filter culture approach which played a pivotal role in the development of KFP.