where D is the fraction of the metabolite formed by macromolecule degradation rather than from the upstream precursor X.

Transcription

1 Supplementary Methods for Yuan et al. Derivation of equations and determination of rate constants The main text presents a derivation of the fundamental equations of KPF in the ideal case of a well-mixed system in which a nutrient that is being directly converted into an intracellular metabolite is instantaneously switched to isotope-labeled form (Eq. 1 3). In practice, isotope switching is not instantaneous; other metabolites typically lie between the added nutrient and the downstream metabolite of interest. Also, some of the metabolite of interest is often formed by macromolecule degradation rather than de novo biosynthesis. Consideration of these factors leads to somewhat more complicated equations than Eq To derive these more realistic and complete equations, consider the kinetics of isotope labeling of a metabolite Y, which is downstream of another metabolite X, where Y is formed both from X (which becomes increasing labeled over time following the isotope-switch) and from macromolecule degradation (which we assume always yields unlabeled Y). Then dy U /dt = [influx from X ] X U /X T + [influx from macromolecule degradation ] [efflux] Y U /Y T (4) Assuming steady-state, i.e., total influx = total efflux = f Y, then dy U /dt = f Y [(1 D) X U /X T + D Y U /Y T ] (5) where D is the fraction of the metabolite formed by macromolecule degradation rather than from the upstream precursor X. Our data (Fig. 1 and Supplementary Fig. 1) show that X U /X T can generally be approximated, for growing E. coli, by a single exponential function exp (-k X t). Note that the term k X is used here to reflect a simple single exponential fit to the available data for X. This k X differs from k X = f X / X T, as k X takes into account the non-instantaneous labeling of the parent of X. Substituting X U /X T = exp (-k X t) (6) into Eq. (5) yields dy U /dt = f Y [(1 D) exp (-k X t) + D Y U / Y T ] (7) In this case, Y U /Y T = {[k X / ( k X - k Y )] exp (- k Y t) - [k Y / ( k X - k Y )] exp (-k X t)}(1 D) + D (8) where k Y = f Y / Y T. Yuan et al. Supplementary Methods Page 1 of 8

2 Note that, for k Y << k X and D = 0, Eq. (8) reduces to Eq. (2), i.e., the labeling of Y is determined solely by its pool size and the flux through it. For k Y >> k X, the labeling of Y mirrors that of X, reflecting the inability of a downstream compound to become labeled more rapidly than its upstream parent. The form of Eq. (8) holds even if X U /X T = (1 D ) exp (-k X t) + D, as can be shown by a derivation similar to the one above. In this case, the term D in Eq. (8) represents the sum of macromolecule degradation feeding into both X and Y. Notably, as k X can be determined directly from experimental measurements of X, Eq. (8) contains only two free parameters to fit to the data, k Y and D. All 15 N-assimilation kinetics for growing E. coli were fit to Eq. (8) using Origin (version 6.0, OriginLab Corporation, Northampton, MA) with k X determined based on the closest upstream parent of Y for which data were available. The resulting values of k Y are reported in Table 1, with inequality limits provided in cases where k X could not be determined using the immediate upstream parent of Y. Carbamoyl aspartate calculations were made as if glutamine were its immediate upstream parent. Although carbamoyl phosphate in actuality sits between glutamine and carbamoyl aspartate, carbamoyl phosphate is present in E. coli in too small an amount to alter substantially carbamoyl aspartate labeling kinetics. Bacterial strain and culture conditions Prototrophic Escherichia coli K-12 strain NCM was grown in minimal salts media 16 with 10mM NH 4 Cl (unlabeled or 15 N-labeled, as indicated) as the nitrogen source and 0.4% glucose (unlabeled or uniformly 13 C-labeled, as indicated) as the carbon source. Isotope-labeled nutrients were > 99% pure from Cambridge Isotope Laboratories (Andover, MA). To enable rapid, non-invasive alteration of the extracellular nutrient environment, E. coli were grown on nitrocellulose filters on top of the agarose plates. Ultrapure agarose (15 g; Invitrogen, Carlbad, CA) was washed three times with cartridge-filtered water (Milli-Q, to remove trace organic contaminants and then added to 1 L of minimal media, and the resulting solution was autoclaved and used to pour 100 mm plates, with each plate containing ml of agarose-media mixture. E. coli-laden filters were produced by passing 5 ml of liquid culture at early exponential phase (OD 650 ~ 0.1; produced by diluting a saturated overnight minimal media culture 50- fold and allowing to grown at 37 C for ~ 2 h) through an 82 mm nitrocellulose membrane filter ( The filter was then placed immediately face-up on the agarose plate and allowed to grow at 37 C to early log phase (OD 650 ~ 0.2; because some cells are lost during the filter-loading, this represented ~ 1.5 doublings on the filter), at which time the filter was transferred onto a new plate with the desired media composition for the purpose of the experiment. All OD values for filter-grown cells reflect the OD of a cell suspension obtained by washing the cells off of the filter into 5 ml of media (the selection to wash into 5 ml of media reflects the initial loading of the filter using 5 ml of cell culture). Complete washing of the filter required repeated and vigorous pipetting of media across the filter for ~ 2 min. Yuan et al. Supplementary Methods Page 2 of 8

3 Metabolite extraction Metabolite extraction was conducted using a procedure incorporating key features from previously published protocols 11, 17, 18 adapted to fit our filter-based culture technique. Bacteria were separated from media by peeling the filter from the plate, with the filter placed immediately into a 100 mm culture dish containing 2.5 ml of 100% methanol at dry ice temperature (-75 C) to quench metabolism. After 15 minutes on dry ice, the methanol extract, with some E. coli remnants suspended in, was transferred into a centrifuge tube. Material remaining on the filter was resuspended by washing with 1 ml methanol (-75 C) and combined with original 2.5 ml cell extract. Insoluble components in the extract were pelleted by centrifugation (4 C) and the supernatant set aside on dry ice. The pellet was then resuspended in 100 µl 80:20 methanol:water solution at 4 C and sonicated for 15 minutes at 4 C, insoluble components pelleted by centrifugation, and the new supernatant mixed with the original one on dry ice. At this point, the pellet was again resuspended in 100 µl 80:20 methanol:water, sonicated for 15 minutes at 4 C, and centrifuged to yield a clear extract that was pooled with the other soluble extracts to yield a total extract volume of 2.7 ml. A portion of this extract was then concentrated under nitrogen 10-fold to yield a sample ready for analysis. Liquid chromatography-tandem mass spectrometry (LC-MS/MS) procedure Metabolites were measured by liquid chromatography-electrospray ioniziation-triple quadrupole mass spectrometry on a Finnigan TSQ Quantum Ultra instrument (ThermoElectron Corporation, San Jose, CA) using a variant of the procedure reported in Lu et al. 11, that employs hydrophilic interaction chromatography (HILIC) as described in Bajad et al. 19. The mass spectrometer was operated in selected reaction monitoring (SRM) mode, with each SRM scan event associated with a particular isotopic form of a given metabolite. SRMs used here are provided in Supplementary Table 1. The specific HILIC conditions were as follows: aminopropyl column (250 mm x 2 mm, 5 µm particle size, Luna, Phenomenex, Torrance, CA); Solvent A: 20 mm ammonium acetate + 20 mm ammonium hydroxide in 95:5 water:acetonitrile, ph 9.45; Solvent B: acetonitrile. The gradients were as follows: positive mode t = 0, 85% B; t = 15 min, 0% B; t = 28 min, 0% B; t = 30 min, 85% B; t = 40 min, 85% B; and negative mode t = 0, 85% B; t = 15 min, 0% B; t = 38 min, 0% B; t = 40 min, 85% B; t = 50 min, 85% B. Chromatography was performed on a LC-10A HPLC system (Shimadzu, Columbia, MD) with autosampler temperature 4 C, column temperature 15 C, injection volume 10 µl, and solvent flow rate 150 µl/min. Isotope switching Transfer from unlabeled to 15 N-ammonia (N-switching) was achieved by moving an E. coli laden filter from agarose containing typical minimal media to agarose containing otherwise identical media in which the unlabeled ammonia was replaced with 15 N- ammonia. One of the filters was extracted immediately before the nitrogen switch (t = 0). The rest of the filters were allowed to grow at 37 C on the new 15 N plates followed by quenching and extracting at desired time points. The replacement of the unlabeled intracellular metabolites by their 15 N-labeled equivalents was tracked by determining via LC-MS/MS the fraction of unlabeled metabolite, which is defined by Yuan et al. Supplementary Methods Page 3 of 8

4 fraction unlabeled = peak height unlabeled form / (peak height every isotopic form ) (9) In control experiments, plate switching in the absence of isotope switching or other nutritional changes had a minimal effect. To estimate the time required for 15 N-ammonia to permeate the filter by diffusion, pre-wetted blank filters were placed onto typical minimal media plates, removed after various timepoints, and ammonia on the filter measured by the indophenol blue method. Absolute quantitation of metabolites Absolute metabolite quantitation was performed by growing E. coli in uniformly 13 C- glucose, spiking at the time of metabolism quenching with known quantities of unlabeled metabolite standards, and determining the 13 C- to 12 C-metabolite ratio in the resulting extract. This ratio is directly related to the quantity of the cellular metabolite as described previously 11, 20. E. coli were first labeled over a minimum of 20 generations by growth in minimal media liquid culture with uniformly 13 C-glucose as the sole carbon source, and subsequently grown using our filter-based methodology on top of agarose with 13 C- glucose as the sole carbon source. The bacteria were then quenched and extracted at OD 650 ~ 0.2 as described above, except that the methanol for extraction was spiked with 5 µg/ml of unlabeled standard of each metabolite of interest. Flux balance analysis FBA was performed using a stoichiometric matrix and objective function provided by the genome-scale E. coli model (ijr904) and the General Algebraic Modeling System (GAMS) code ( available on the Palsson laboratory website ( 21. In silico analysis was conducted using the GAMS program package, version The limiting reaction was glucose import, and the glucose import rate was determined so that the value of the objective function in FBA corresponded to the experimentally observed growth rate of 0.55 hr -1. Typical objective function units are mmol biomass precursors (g cell dry weight ) -1 hr -1 ; mmol biomass precursors was converted into g cell dry weight by summing the mass contribution of each component of the objective function to dry weight, where the mass contribution of each component equals the product of its growth flux coefficient and molecular weight. To determine the net flux producing/consuming each metabolite of interest, all positive fluxes for reactions containing the metabolite of interest defined as a product were added to the absolute values of all negative fluxes for reactions containing the metabolite of interest defined as a reactant. Alanine Synthesis The reaction pathways responsible for biosynthesis of most of nucleotides and amino acids in E. coli are well known. A notable exception is alanine, for which synthesis may involve direct transamination of pyruvate by glutamate, or may instead occur via valine 22. The present data are inadequate to fully resolve this issue. Nevertheless, they help clarify the following: the ultimate source of the nitrogen in alanine is likely glutamate (based on the kinetic similarity) and valine is a potential intermediate in alanine biosynthesis (valine is labeled more rapidly than alanine and the total valine flux is large enough to cover Yuan et al. Supplementary Methods Page 4 of 8

5 cellular requirements for both alanine and valine). Thus, overall, the present data favor the valine-dependent pathway. Nevertheless, to be conservative, the calculated values in Table 1 assume direct synthesis of alanine from pyruvate + glutamate (the major pathway in FBA), with inequalities indicated to account for the possibility of the valine-dependent pathway (which would yield a larger value of k ala than that shown in Table 1). Estimation of reverse fluxes To a first approximation, KPF measures gross fluxes, whereas the FBA predicts net fluxes 1. Thus, reverse fluxes can be estimated as follows: reverse flux = measured flux (KPF) predicted flux (FBA) (10) KPF measures fluxes by fitting data to equation (8). A tacit assumption in deriving equation (8) (which describes the labeling of Y) was that flux into Y from its upstream parent greatly exceeds that from its downstream products. For example, consider the reaction sequence X Y Z. Equation (8) holds for Y when X Y is reversible, but not necessarily when Y Z is reversible. In the present report, most of the reactions of interest are irreversible, with the notable exception of transamination reactions. For transamination reactions, X is glutamate, Y is another amino acid, and Z is aminoacyl trna. Thus, equation (8) holds, yielding the real gross flux, for the amino acids other than glutamate, but may not hold for glutamate itself. Indeed, equation (8) will underestimate the gross glutamate flux in the case that one or more transaminations reactions are in very fast equilibrium. In such case, the measured glutamate flux will more closely approximate the net flux. Other potential complications to consider when applying the above equations are the possibilities for metabolites to be excreted or degraded. These possibilities have not been explicitly addressed in the present manuscript. References (includes citations from both Main Text and Supplementary Methods) 1. Schilling, C.H. & Palsson, B.O. The underlying pathway structure of biochemical reaction networks. Proc Natl Acad Sci U S A 95, (1998). 2. Edwards, J.S., Ibarra, R.U. & Palsson, B.O. In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data. Nat Biotechnol 19, (2001). 3. Stephanopoulos, G. Metabolic fluxes and metabolic engineering. Metab Eng 1, 1-11 (1999). 4. Szyperski, T. Biosynthetically Directed Fractional C-13-Labeling of Proteinogenic Amino-Acids - an Efficient Analytical Tool to Investigate Intermediary Metabolism. Eur J Biochem 232, (1995). 5. Chatham, J.C., Forder, J.R., Glickson, J.D. & Chance, E.M. Calculation of absolute metabolic flux and the elucidation of the pathways of glutamate labeling in perfused rat heart by 13C NMR spectroscopy and nonlinear least squares analysis. J Biol Chem 270, (1995). Yuan et al. Supplementary Methods Page 5 of 8

6 6. Fischer, E. & Sauer, U. Metabolic flux profiling of Escherichia coli mutants in central carbon metabolism using GC-MS. Eur J Biochem 270, (2003). 7. van Winden, W.A. et al. Metabolic-flux analysis of Saccharomyces cerevisiae CEN.PK113-7D based on mass isotopomer measurements of 13C-labeled primary metabolites. FEMS Yeast Res 5, (2005). 8. Fischer, E. & Sauer, U. Large-scale in vivo flux analysis shows rigidity and suboptimal performance of Bacillus subtilis metabolism. Nat Genetics 37, (2005). 9. Ibarra, R.U., Edwards, J.S. & Palsson, B.O. Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth. Nature 420, (2002). 10. Segre, D., Vitkup, D. & Church, G.M. Analysis of optimality in natural and perturbed metabolic networks. Proc Natl Acad Sci U S A 99, (2002). 11. Lu, W., Kimball, E. & Rabinowitz, J.D. A high-performance liquid chromatography-tandem mass spectrometry method for quantitation of nitrogencontaining intracellular metabolites. J Am Soc Mass Spectrom 17, (2006). 12. Ikeda, T.P., Shauger, A.E. & Kustu, S. Salmonella typhimurium apparently perceives external nitrogen limitation as internal glutamine limitation. J Mol Biol 259, (1996). 13. Reitzer, L. Nitrogen assimilation and global regulation in Escherichia coli. Ann Rev Microbiol 57, (2003). 14. Helling, R.B. Why does Escherichia coli have two primary pathways for synthesis of glutamate? J Bacteriol 176, (1994). 15. Soupene, E. et al. Physiological studies of Escherichia coli strain MG1655: growth defects and apparent cross-regulation of gene expression. J Bacteriol 185, (2003). 16. Gutnick, D., Calvo, J.M., Klopotowski, T. & Ames, B.N. Compounds which serve as the sole source of carbon or nitrogen for Salmonella typhimurium LT-2. J Bacteriol 100, (1969). 17. Villas-Boas, S.G., Hojer-Pedersen, J., Akesson, M., Smedsgaard, J. & Nielsen, J. Global metabolite analysis of yeast: evaluation of sample preparation methods. Yeast 22, (2005). 18. Maharjan, R.P. & Ferenci, T. Global metabolite analysis: the influence of extraction methodology on metabolome profiles of Escherichia coli. Anal Biochem 313, (2003). 19. Bajad, S.U. et al. Separation and quantitation of water soluble cellular metabolites by hydrophilic interaction chromatography tandem mass spectrometry J Chrom A. in press (2006). 20. Wu, L. et al. Quantitative analysis of the microbial metabolome by isotope dilution mass spectrometry using uniformly 13C-labeled cell extracts as internal standards. Anal Biochem 336, (2005). 21. Reed, J.L., Vo, T.D., Schilling, C.H. & Palsson, B.O. An expanded genome-scale model of Escherichia coli K-12 (ijr904 GSM/GPR). Genome Biol 4, R54 (2003). 22. Csonka, L.N. Use of 3H and 14C double-labeled glucose to assess in vivo pathways of amino acid biosynthesis in Escherichia coli. J Biol Chem 252, (1977). Yuan et al. Supplementary Methods Page 6 of 8

7 Supplementary Table 1. Selected reaction monitoring scan events (SRMs) for different isotopic forms of 15 metabolites. Metabolite Neutral Formula Preferred Product Ion Number of 15 N-label Parent Mass Collision Energy (ev) Product Mass Glutamine C 5 H 10 N 2 O 3 C 4 H 6 NO Glutamate C 5 H 9 NO 4 C 4 H 6 NO Asparagine C 4 H 8 N 2 O 3 C 2 H 4 NO Aspartate C 4 H 7 NO 4 C 3 H 6 NO Alanine C 3 H 7 NO 2 C 2 H 6 N Methionine C 5 H 11 NO 2 S C 5 H 9 O 2 S Phenylalanine C 9 H 11 NO 2 C 8 H Proline C 5 H 9 NO 2 C 4 H 8 N Threonine C 4 H 9 NO 3 C 2 H 4 NO Tyrosine C 9 H 11 NO 3 C 6 H Valine C 5 H 11 NO 2 C 4 H Car-asp C 5 H 8 N 2 O 5 C 4 H 6 NO CMP C 9 H 14 N 3 O 8 P C 4 H 6 N 3 O IMP C 10 H 13 N 4 O 8 P C 5 H 5 N 4 O AMP C 10 H 14 N 5 O 7 P C 5 H 6 N Yuan et al. Supplementary Methods Page 7 of 8

8 : SRMs shown here for single labeled glutamine, asparagine, and carbamoyl aspartate correspond to the product ion being unlabeled. This is based on the experimental observation that the single labeled parent ion always yields unlabeled rather than labeled product ion. For glutamine and asparagine the product ion contains the amine but not amide nitrogen (Harrison, A.G. Fragmentation reactions of protonated peptides containing glutamine or glutamic acid. J Mass Spectrom 38, , 2003). For carbamoyl aspartate, the product ion formula matches aspartate. Yuan et al. Supplementary Methods Page 8 of 8