- Email: [email protected]
13C metabolic flux analysis in complex systems
Available online at www.sciencedirect.com
13
C metabolic flux analysis in complex systems
Nicola Zamboni Experimental determination of in vivo metabolic rates by methods of 13C metabolic flux analysis is a pivotal approach to unravel structure and regulation of metabolic networks, in particular with microorganisms grown in minimal media. However, the study of real-life and eukaryotic systems calls for the quantification of fluxes also in cellular compartments, rich media, cell-wide metabolic networks, dynamic systems or single cells. These scenarios drastically increase the complexity of the task, which is only partly dealt by existing approaches that rely on rigorous simulations of label propagation through metabolic networks and require multiple labeling experiments or a priori information on pathway inactivity to simplify the problem. Albeit qualitative and largely driven by human interpretation, statistical analysis of measured 13 C-patterns remains the exclusive alternative to comprehensively handle such complex systems. In the future, this practice will be complemented by novel modeling frameworks to assay particular fluxes within a network by stable isotopic tracer for targeted validation of well-defined hypotheses.
a model of the metabolic network; secondly, a closed carbon balance given by all rates of substrate uptake and product secretion; and thirdly, 13C-labeling patterns of metabolic intermediates or endproducts measured by mass spectrometry (MS) or nuclear magnetic resonance (NMR). In stationary 13C-MFA, alternative pathways converging to a common metabolite are resolved by their characteristic scrambling of 13C from the substrate and measured once at isotopic steady-state [1,8]. An alternative strategy is to follow the dynamics of 13C-propagation over time. This so-called non-stationary 13C-MFA also requires the measurement of metabolome concentrations and is more demanding in computations, but more informative and capable of quantifying fluxes within linear pathways [12,13,14].
Available online 15th September 2010
The core concepts underlying current methods of 13 C-MFA maturated around the turn of the Century and were further refined in the past five years. Nonetheless, 13 C-MFA is still far from being universally applicable to all cellular systems, in contrast to physical measurements like proteomics and metabolomics. In general, existing methods of 13C-MFA are well suited to investigate primary metabolism in microbes grown in minimal media, but they rely on intricate procedures to perform 13C-labeling in vivo, detect 13C-patterns, and calculate fluxes that substantially restrict experimental design and the admissible level of complexity. This article focuses on rapidly growing areas of eukaryotic cells, real-life environments, large metabolic networks, or transient systems where state of the art flux methods expose their limits, and discusses strategies to overcome them.
0958-1669/$ – see front matter # 2010 Elsevier Ltd. All rights reserved.
Compartments
Address Institute of Molecular Systems Biology, ETH Zurich, 8093 Zurich, Switzerland Corresponding author: Zamboni, Nicola ([email protected])
Current Opinion in Biotechnology 2011, 22:103–108 This review comes from a themed issue on Analytical biotechnology Edited by Matthias Heinemann and Uwe Sauer
DOI 10.1016/j.copbio.2010.08.009
Introduction 13
C metabolic flux analysis (MFA) has crystallized in the past two decades as the primary approach to quantify in vivo intracellular metabolic rates, that is, the fluxes [1]. Measured fluxes, in turn, have contributed unprecedented insights to unravel metabolic networks and their regulation, improve biotechnological processes, annotate unknown genes, assess drug toxicity, and so on (achievements recently reviewed in [2–7]). Intracellular fluxes are not directly measurable, but under given circumstances they can be inferred from the characteristic rearrangement of 13C — occasionally 15N — tracers through metabolic pathways [8,9–11]. Essentially three ingredients are used to calculate intracellular fluxes (Figure 1): firstly, www.sciencedirect.com
The existence of compartments in eukaryotic cells severely hampers calculation of fluxes. Since the same compound can exist in different subcellular spaces where it participates in different reactions, it is likely to possess compartment-specific 13C signatures. Although metabolic models can be extended to correctly describe metabolite localization and transporters, the disruptive nature of metabolite extraction before MS or NMR analysis allows only measurement of an average 13C-pattern, which in most cases must be discarded. While some compartmentspecific 13C-data can be retrieved from macromolecules, the approach has been demonstrated effective only in plant cells and embryos [15,16]. In mammalian cells, the problem is particularly acute in models of the tricarboxylic acid cycle and lower glycolysis (Figure 2). As a consequence of the increase in intertwined pathways and the reduction in measurable 13C-data, it is not possible to mathematically estimate any flux with good confidence Current Opinion in Biotechnology 2011, 22:103–108
104 Analytical biotechnology
Figure 1
Schematic summary of the algorithmic strategies to analyze data in stationary 13C-MFA. Calculation of fluxes from non-stationary experiments requires also quantification of metabolite concentrations and is done by isotopomer modeling using large systems of ordinary differential equations.
Figure 2
Stoichiometric network of lower glycolysis and tricarboxylic acid cycle reconstructed from genes listed in the HumanCyc database (www.humancyc.org). According to this model and assuming that all the enzymes encoded in the genome may be active, formally it is only possible to measure the labeling patterns of citrate, succinate, and lactate because their synthesis occurs only in one compartment, while all other metabolites are of ambiguous origin. Sparse labeling data do not allow resolving the large number of degrees of freedom given by isoenzymes in different compartments and the numerous transport reactions. The gene names are reported with the abbreviation used in the database. Current Opinion in Biotechnology 2011, 22:103–108
www.sciencedirect.com
Metabolic flux analysis in complex systems Zamboni 105
without additional assumptions. These include either the removal of reactions from the model motivated by their measured or supposed negligible activity [17], or pooling of metabolites based on hypothetical rapid equilibrium catalyzed by the continuous action of transporters [18]. A cursory glance through the amended models recently used by expert labs [17,18,19,20,21,22] reveals that there is little consensus and even some controversy, in particular with respect to reaction reversibility, localization of reactions, occurrence of gluconeogenic or anaplerotic fluxes or the presence of transporter reactions. Discrepancies can be partly ascribed to the use of differentiated cells or of specific media. This, however, also highlights the risk of transferring knowledge gained in diverse contexts, in particular when the microenvironment is not well defined or growth abnormal as in many tumor cells. As a consequence, a careful interpretation of the results has to consider the implicit model uncertainty in addition to the statistical confidence given by the parameter estimation. Although isotopically non-stationary 13C-MFA has excellent power to spot incongruences between measured concentrations and labeling data also in such underdetermined systems, to date there is no publicly available software to rigorously calculate fluxes from dynamic 13C-data. Hence, the most practicable alternative to generally validate a model for each cell type and environment is to perform preliminary experiments with ad hoc tracers tailored to test whether a given pathway is active [19,23,24].
Complex media Cellular phenotypes and evolution are best understood in the natural environment, which typically features transient and heterogeneous nutrients. The effort to calculate fluxes scales exponentially with the number of substrates, both on experimental and computational side. Multiple carbon sources also increase the danger of non-stationary metabolism or diauxic growth that depend on the availability of nutrients and the regulatory architecture of cells, for example, catabolite repression through a preferred substrate. This also applies to systems were additional nutrients must be supplemented to compensate for auxotrophies, because of the inherent risk that the secondary substrate is catabolized despite the lesion in its biosynthesis. Although published flux datasets were generated almost exclusively in media with one or sporadically two major carbon sources, quantitative 13C-MFA is at reach with the existing arsenal of techniques even for more challenging setups with multiple carbon sources. This view remains arguable in the absence of experimental proof of principle, but several factors make the problem tractable. In chemically defined media, it is possible to measure the uptake rate for all potential substrates, the production rate of byproducts confirms the completeness of physiological characterization on the basis of a closed carbon balance. If www.sciencedirect.com
the pathway of assimilation is known, it is also possible to develop a comprehensive model for flux analysis by isotopomer modeling and iterative fitting [8,10,25]. This framework is flexible with respect to substrates and network topology, but does not solve the problem that the degrees of freedom increase with the number of substrates. To compensate, additional information must be distilled from the tracer experiment to determine fluxes. This is obtained on one the hand by the measurement of 13C-labeling in the intermediates of metabolism [26,27], in particular where the catabolic pathway of different substrates convolute. On the other hand fluxes can be estimated on the basis of several labeling experiments performed with different 13C-tracers. It is possible to specifically label single substrates in separate experiments and monitor their breakdown by MS or NMR analysis while preserving the medium composition and thus the metabolic steady state. Integration of data from independent experiments is done during flux calculation using publicly available packages for stationary 13C-MFA by isotopomer modeling [28,29] which can be adjusted to estimate a single flux distribution that best fits multiple experiments [30]. Albeit computationally more demanding, this procedure returns more precise estimates compared to the independent fitting of single experiments. Provided that suitable stable isotopic tracers are commercially available, this strategy should enable calculating fluxes in chemically defined media with numerous substrates, for example, mixes of sugars and amino acids. Yet, the massive demand for experiments and resources most likely explains why it has not been accomplished thus far. Formal simulation of 13C-labeling experiments and thus quantitative flux estimation is compromised in complex and fully characterized media, such as formulations containing biomass extracts or digests. This leaves rational interpretation by the human brain as the most efficient approach to translate 13C-signatures in biological insights, as exemplarily shown by very detailed elucidations of pathogens’ metabolism within their host [31,32].
Genome-wide networks Central carbon metabolism has attracted most attention in all flux studies published so far. The primary reason was the scientific goal to characterize intracellular physiology and to quantify the largest cellular fluxes that determine cell-wide energy and redox metabolism. However, technical reasons also exist to explain this trend and, specifically, why it is difficult to expand beyond central carbon metabolism. First, fluxes in central metabolism are well resolved based on stationary 13C-data [8]. In peripheral metabolism, however, pathways form mostly branched, linear pathways where at isotopic steady-state the 13Cpatterns are independent of the flux. In fact, in 13C-MFA the purely biosynthetic fluxes are defined in the model in Current Opinion in Biotechnology 2011, 22:103–108
106 Analytical biotechnology
the form of a growth rate-dependent withdrawal of metabolites from central metabolism approximated a priori from macromolecular composition [25,33]. Second, detection of 13C-patterns in intermediates of the pathway of interest is a prerequisite, which on peripheral pathways becomes challenging because of low abundance. Third, the simulation of large(r) networks at the level of isotopologs scales poorly. Recent work suggests that these will be eventually overcome in the next years, at least for the stationary case [34,35], to rigorously estimate fluxes in mid-sized networks with hundreds of reactions. However, for branched or cyclic biosynthetic pathways such as those of fatty acids, lipids, or terpenoids, only dynamic 13C-data and thus non-stationary 13C-MFA methods are informative. Provided that it is possible to detect the 13C-enrichment and the absolute concentrations of intermediates in the pathway of interest, the flux can be quantified locally with small systems of ordinary differential equations [13] for which public, sophisticated, and yet user-friendly solvers exist [36]. In complement to the aforementioned quantitative estimation of fluxes, the model-free and qualitative analysis of 13C-patterns represents an appealing alternative also in this context [37–39]. Instead of precisely simulating all isotopologs and thus fully avoiding all scalability issues, the measured patterns are analyzed by statistical means to spot significant differences between two or more samples, in stationary [38] or dynamic data [39]. This approach is particularly suited for purposes of discovery, that is, to identify dynamic biomarkers of integrated network response to be validated in quantitative and targeted follow-ups. Noticeably, when a subset of mutants with known fluxes exist, these can be used to train a predictor capable of quantitatively estimating fluxes solely from 13 C signatures [40,41].
High resolution in time and space The highest temporal resolution achievable by flux methods is a function of multiple factors. The major determinant is the time necessary for the isotopic tracer to propagate through the network, which in turn depends on systems properties such as its topology, abundance of metabolite pools, and fluxes [8,12]. Primarily two strategies are commonly used to decrease the time necessary in a labeling experiment. The first is to measure the 13Cpatterns of intermediates directly within — or downstream of — the pathways under investigation enabling early detection [26]. The second is to calculate fluxes from the initial transients of 13C propagation, either by extrapolating stationary 13C-patterns before the isotopic steady state is established [42] or by resorting to methods of isotopically non-stationary 13C-MFA [12,43,44]. This typically reduces the minimum duration of a carbon-labeling experiment from several hours to one hour and few minutes, respectively. 13C-MFA of dynamic systems at a resolution of about one hour has been Current Opinion in Biotechnology 2011, 22:103–108
demonstrated for industrial fed batch cultivations [42,43], but with non-stationary methods it is theoretically possible to quantify fluxes also in systems where metabolism can be linearized over intervals of 10–15 min. A more futuristic application is single-cell 13C-MFA. Outstanding progress has recently been made in sensitivity using either capillary electrophoresis and electrospray [45], gas chromatography and electron impact [46], or matrix assisted laser desorption ionization [47], to pave the road for routine detection of small molecules in single cells. All these studies employed time-of-flight MS and thus collectively advocate for an extension to 13C-MFA. Tandem MS can also be employed to maximize sensitivity [48]. Further, the detection of relative 13C-labelings is even largely insensitive to poor ionization reproducibility, which is a major technical problem of using MS at such small scale and afflicts concentration measurements. Additional optimization of microfluidics, ionization efficiency, and detection will be necessary to attain the necessary signal to noise at least for some of the intermediates in central carbon metabolism or amino acids and eventually enable 13 C-MFA. This milestone is likely to be achieved within the next five years. Direct analysis of 13C patterns by flux ratio analysis [8] will enable profiling of relative fluxes in single cells even in the absence of measurable rates for substrate uptake and product formation.
Conclusions and perspectives It would be certainly invaluable for the community to gain access to a rigorous but generalized framework to independently perform non-stationary 13C-MFA at least in small-sized networks with compartments or complex environments. This would, however, always imply knowledge of most metabolite concentrations, 13C-labeling patterns and access to high performance computing. Considering also that world-wide only about a dozen groups with uneven access to instruments or know-how are pioneering novel concepts and tools for 13C-MFA, it is unlikely that such sophisticated and demanding approach will establish itself as first-line method to ubiquitously investigate fluxes in complex systems. Instead, two complementary approaches are emerging to cope with complexity, in a trend that reflects the evolution observed in proteomics [49,50] and metabolomics [51]. The first is the qualitative analysis — here of labeling patterns — by multivariate statistics and machine learning for means of profiling and thus mere data-driven discovery [37]. Although technically simple and readily applicable, the immense potential of this strategy will only be unleashed in combination with non-targeted analytical methods, for instance on MS detectors with high resolving power and accuracy. Additional experience and visions are also needed to effectively translate differential 13C-patterns into testable biological hypotheses. The second is highly targeted and quantitative assays for www.sciencedirect.com
Metabolic flux analysis in complex systems Zamboni 107
specific fluxes by stable isotopic tracers, building upon collection of 13C-data and concentration data densely around the reactions of interest and the local modeling of metabolism in the spirit of flux ratio analysis [1,52] or kinetic profiling [13]. Complexity is therefore contrasted by specialization: it is intuitively simpler to focus on one single flux rather than trying to quantify all at once. Another benefit of this approach is that the measurement of 13Cdata is also targeted to a small number of intermediates, thereby increasing sensitivity, precision, and providing more time to collect positional information by tandem MS. Frameworks to enable automated (or assisted) design of such flux assays are under development.
References and recommended reading Papers of particular interest, published within the period of review, have been highlighted as: of special interest of outstanding interest 13
1.
Sauer U: Metabolic networks in motion: analysis. Mol Syst Biol 2006, 2:62.
2.
Blank LM, Kuepfer L: Metabolic flux distributions: genetic information, computational predictions, and experimental validation. Appl Microbiol Biotechnol 2010, 86:1243-1255.
3.
Zamboni N, Sauer U: Novel biological insights through metabolomics and 13C-flux analysis. Curr Opin Microbiol 2009, 12:553-558.
4.
Niklas J, Schneider K, Heinzle E: Metabolic flux analysis in eukaryotes. Curr Opin Biotechnol 2010, 21:63-69.
5.
Heinemann M, Sauer U: Systems biology of microbial metabolism. Curr Opin Microbiol 2010, 13:337-343.
6.
Otero JM, Nielsen J: Industrial systems biology. Biotechnol Bioeng 2010, 105:439-460.
7.
Schwender J: Metabolic flux analysis as a tool in metabolic engineering of plants. Curr Opin Biotechnol 2008, 19:131-137.
C-based flux
16. Paula Alonso A, Dale VL, Shachar-Hill Y: Understanding fatty acid synthesis in developing maize embryos using metabolic flux analysis. Metab Eng 2010, 12:488-497. 17. Quek LE, Dietmair S, Kro¨mer JO, Nielsen LK: Metabolic flux analysis in mammalian cell culture. Metab Eng 2010, 12:161-171. Case study in higher cells that describes in detail the rationale of model reduction. 18. Goudar C, Biener R, Boisart C, Heidemann R, Piret J, de Graaf A, Konstantinov K: Metabolic flux analysis of CHO cells in perfusion culture by metabolite balancing and 2D [13C, 1H] COSY NMR spectroscopy. Metab Eng 2010, 12:138-149. 19. Munger J, Bennett BD, Parikh A, Feng XJ, McArdle J, Rabitz HA, Shenk T, Rabinowitz JD: Systems-level metabolic flux profiling identifies fatty acid synthesis as a target for antiviral therapy. Nat Biotechnol 2008, 26:1179-1186. A good example on how several specific tracer experiments can be merged to yield a global snapshot. 20. DeBerardinis RJ, Mancuso A, Daikhin E, Nissim I, Yudkoff M, Wehrli S, Thompson CB: Beyond aerobic glycolysis: transformed cells can engage in glutamine metabolism that exceeds the requirement for protein and nucleotide synthesis. Proc Natl Acad Sci U S A 2007, 104:19345-19350. 21. Noguchi Y, Young JD, Aleman JO, Hansen ME, Kelleher JK, Stephanopoulos G: Effect of anaplerotic fluxes and amino acid availability on hepatic lipoapoptosis. J Biol Chem 2009, 284:33425-33436. 22. Maier K, Hofmann U, Bauer A, Niebel A, Vacun G, Reuss M, Mauch K: Quantification of statin effects on hepatic cholesterol synthesis by transient 13C-flux analysis. Metab Eng 2009, 11:292-309. First systematic non-stationary flux analysis in higher cells accounting for compartments. 23. Fuhrer T, Fischer E, Sauer U: Experimental identification and quantification of glucose metabolism in seven bacterial species. J Bacteriol 2005, 187:1581-1590. 24. Metallo CM, Walther JL, Stephanopoulos G: Evaluation of 13C isotopic tracers for metabolic flux analysis in mammalian cells. J Biotechnol 2009, 144:167-174. 25. Dauner M, Bailey JE, Sauer U: Metabolic flux analysis with a comprehensive isotopomer model in Bacillus subtilis. Biotechnol Bioeng 2001, 76:144-156.
8. Zamboni N, Fendt SM, Ru¨hl M, Sauer U: 13C-based metabolic flux analysis. Nat Protoc 2009, 4:878-892. Comprehensive description of stationary flux methods, from principles to protocols and software.
26. van Winden WA, van Dam JC, Ras C, Kleijn RJ, Vinke JL, van Gulik WM, Heijnen JJ: Metabolic-flux analysis of Saccharomyces cerevisiae CEN.PK113-7D based on mass isotopomer measurements of 13C-labeled primary metabolites. FEMS Yeast Res 2005, 5:559-568.
9.
27. Toya Y, Ishii N, Hirasawa T, Naba M, Hirai K, Sugawara K, Igarashi S, Shimizu K, Tomita M, Soga T: Direct measurement of isotopomer of intracellular metabolites using capillary electrophoresis time-of-flight mass spectrometry for efficient metabolic flux analysis. J Chromatogr A 2007, 1159:134-141.
Dauner M: From fluxes and isotope labeling patterns towards in silico cells. Curr Opin Biotechnol 2010, 21:55-62.
10. Wiechert W: 3:195-206.
13
C metabolic flux analysis. Metab Eng 2001,
11. Kruger NJ, Ratcliffe RG: Insights into plant metabolic networks from steady-state metabolic flux analysis. Biochimie 2009, 91:697-702. 12. No¨h K, Gronke K, Luo B, Takors R, Oldiges M, Wiechert W: Metabolic flux analysis at ultra short time scale: isotopically non-stationary 13C labeling experiments. J. Biotechnol. 2007, 129:249-267. Seminal work on non-stationary flux analysis by iterative fitting 13. Yuan J, Bennett BD, Rabinowitz JD: Kinetic flux profiling for quantitation of cellular metabolic fluxes. Nat Protoc 2008, 3:1328-1340. This protocol describes the principles of local analysis of non-stationary data collected with 15N experiments, which are equally valid for 13C tracers. 14. No¨h K, Wiechert W: Experimental design principles for isotopically instationary 13C labeling experiments. Biotechnol Bioeng 2006, 94:234-251. 15. Allen DK, Shachar-Hill Y, Ohlrogge JB: Compartment-specific labeling information in 13C metabolic flux analysis of plants. Phytochemistry 2007, 68:2197-2210. www.sciencedirect.com
28. Quek LE, Wittmann C, Nielsen LK, Kro¨mer JO: OpenFLUX: efficient modelling software for 13C-based metabolic flux analysis. Microb Cell Fact 2009, 8:25. 29. Wiechert W, Mo¨llney M, Petersen S, de Graaf AA: A universal framework for 13C metabolic flux analysis. Metab Eng 2001, 3:265-283. 30. Masakapalli SK, Le Lay P, Huddleston JE, Pollock NL, Kruger NJ, Ratcliffe RG: Subcellular flux analysis of central metabolism in a heterotrophic Arabidopsis cell suspension using steadystate stable isotope labeling. Plant Physiol 2010, 152:602-619. Highly didactic study on resolving subcellular compartments networks by multiple stationary experiments. 31. Eylert E, Herrmann V, Jules M, Gillmaier N, Lautner M, Buchrieser C, Eisenreich W, Heuner K: Isotopologue profiling of Legionella pneumophila: role of serine and glucose as carbon substrates. J Biol Chem 2010, 285:22232-22243. Excellent example for the observation-driven interpretation of labeling experiments in a host–pathogen system. Current Opinion in Biotechnology 2011, 22:103–108
108 Analytical biotechnology
32. Eisenreich W, Dandekar T, Heesemann J, Goebel W: Carbon metabolism of intracellular bacterial pathogens and possible links to virulence. Nat Rev Microbiol 2010, 8:401-412.
glucose limitation in fed-batch culture. Biotechnol Bioeng 2010, 105:795-804.
33. Pramanik J, Keasling JD: A stoichiometric model of Escherichia coli metabolism: incorporation of growth-rate dependent biomass composition and mechanistic energy requirements. Biotechnol Bioeng 1997, 56:398-421.
43. Noack S, No¨h K, Moch M, Oldiges M, Wiechert W: Stationary versus non-stationary 13C-MFA: a comparison using a consistent dataset. J Biotechnol 2010. The first coherent and direct comparison of stationary and non-stationary flux analysis.
34. Suthers PF, Burgard AP, Dasika MS, Nowroozi F, Van Dien S, Keasling JD, Maranas CD: Metabolic flux elucidation for large-scale models using 13C labeled isotopes. Metab Eng 2007, 9:387-405.
44. Schaub J, Mauch K, Reuss M: Metabolic flux analysis in Escherichia coli by integrating isotopic dynamic and isotopic stationary 13C labeling data. Biotechnol Bioeng 2008, 99:1170-1185.
35. Suthers PF, Chang YJ, Maranas CD: Improved computational performance of MFA using elementary metabolite units and flux coupling. Metab Eng 2010, 12:123-128.
45. Lapainis T, Rubakhin SS, Sweedler JV: Capillary electrophoresis with electrospray ionization mass spectrometric detection for single-cell metabolomics. Anal Chem 2009, 81:5858-5864.
36. Maiwald T, Timmer J: Dynamical modeling and multiexperiment fitting with PottersWheel. Bioinformatics 2008, 24:2037-2043.
46. Koek MM, Bakels F, Engel W, van den Maagdenberg A, Ferrari MD, Coulier L, Hankemeier T: Metabolic profiling of ultrasmall sample volumes with GC/MS: from microliter to nanoliter samples. Anal Chem 2010, 82:156-162.
37. Zamboni N, Sauer U: Fluxome profiling in microbes. In Metabolome Analyses: Strategies for Systems Biology. Edited by Vaidyanathan S, Harrigan GG, Goodacre R. Springer; 2005:307-322. 38. Zamboni N, Sauer U: Model-independent fluxome profiling from 2H and 13C experiments for metabolic variant discrimination. Genome Biol 2004, 5:R99. 39. Godin JP, Ross AB, Rezzi S, Poussin C, Martin FP, Fuerholz A, Cleroux M, Mermoud AF, Tornier L, Arce Vera F et al.: Isotopomics: a top-down systems biology approach for understanding dynamic metabolism in rats using [1,2-13C2] acetate. Anal Chem 2010, 82:646-653. 40. Antoniewicz MR, Stephanopoulos G, Kelleher JK: Evaluation of regression models in metabolic physiology: predicting fluxes from isotopic data without knowledge of the pathway. Metabolomics 2006, 2:41-52. 41. Zamboni N: Towards metabolome-based 13C flux analysis: a universal tool for monitoring in vivo pathway activity. In Topics in Current Genetics. Edited by Nielsen J, Jewett M. Springer; 2007. 42. Ru¨hl M, Zamboni N, Sauer U: Dynamic flux responses in riboflavin overproducing Bacillus subtilis to increasing
Current Opinion in Biotechnology 2011, 22:103–108
47. Amantonico A, Oh JY, Sobek J, Heinemann M, Zenobi R: Mass spectrometric method for analyzing metabolites in yeast with single cell sensitivity. Angew Chem Int Ed Engl 2008, 47:5382-5385. 48. Kiefer P, Nicolas C, Letisse F, Portais JC: Determination of carbon labeling distribution of intracellular metabolites from single fragment ions by ion chromatography tandem mass spectrometry. Anal Biochem 2007, 360:182-188. 49. Schmidt A, Claassen M, Aebersold R: Directed mass spectrometry: towards hypothesis-driven proteomics. Curr Opin Chem Biol 2009, 13:510-517. 50. Domon B, Aebersold R: Mass spectrometry and protein analysis. Science 2006, 312:212-217. 51. Nielsen J, Oliver S: The next wave in metabolome analysis. Trends Biotechnol 2005, 23:544-546. 52. Rantanen A, Rousu J, Jouhten P, Zamboni N, Maaheimo H, Ukkonen E: An analytic and systematic framework for estimating metabolic flux ratios from 13C tracer experiments. BMC Bioinformatics 2008, 9:266.
www.sciencedirect.com
13
C metabolic flux analysis in complex systems
Nicola Zamboni Experimental determination of in vivo metabolic rates by methods of 13C metabolic flux analysis is a pivotal approach to unravel structure and regulation of metabolic networks, in particular with microorganisms grown in minimal media. However, the study of real-life and eukaryotic systems calls for the quantification of fluxes also in cellular compartments, rich media, cell-wide metabolic networks, dynamic systems or single cells. These scenarios drastically increase the complexity of the task, which is only partly dealt by existing approaches that rely on rigorous simulations of label propagation through metabolic networks and require multiple labeling experiments or a priori information on pathway inactivity to simplify the problem. Albeit qualitative and largely driven by human interpretation, statistical analysis of measured 13 C-patterns remains the exclusive alternative to comprehensively handle such complex systems. In the future, this practice will be complemented by novel modeling frameworks to assay particular fluxes within a network by stable isotopic tracer for targeted validation of well-defined hypotheses.
a model of the metabolic network; secondly, a closed carbon balance given by all rates of substrate uptake and product secretion; and thirdly, 13C-labeling patterns of metabolic intermediates or endproducts measured by mass spectrometry (MS) or nuclear magnetic resonance (NMR). In stationary 13C-MFA, alternative pathways converging to a common metabolite are resolved by their characteristic scrambling of 13C from the substrate and measured once at isotopic steady-state [1,8]. An alternative strategy is to follow the dynamics of 13C-propagation over time. This so-called non-stationary 13C-MFA also requires the measurement of metabolome concentrations and is more demanding in computations, but more informative and capable of quantifying fluxes within linear pathways [12,13,14].
Available online 15th September 2010
The core concepts underlying current methods of 13 C-MFA maturated around the turn of the Century and were further refined in the past five years. Nonetheless, 13 C-MFA is still far from being universally applicable to all cellular systems, in contrast to physical measurements like proteomics and metabolomics. In general, existing methods of 13C-MFA are well suited to investigate primary metabolism in microbes grown in minimal media, but they rely on intricate procedures to perform 13C-labeling in vivo, detect 13C-patterns, and calculate fluxes that substantially restrict experimental design and the admissible level of complexity. This article focuses on rapidly growing areas of eukaryotic cells, real-life environments, large metabolic networks, or transient systems where state of the art flux methods expose their limits, and discusses strategies to overcome them.
0958-1669/$ – see front matter # 2010 Elsevier Ltd. All rights reserved.
Compartments
Address Institute of Molecular Systems Biology, ETH Zurich, 8093 Zurich, Switzerland Corresponding author: Zamboni, Nicola ([email protected])
Current Opinion in Biotechnology 2011, 22:103–108 This review comes from a themed issue on Analytical biotechnology Edited by Matthias Heinemann and Uwe Sauer
DOI 10.1016/j.copbio.2010.08.009
Introduction 13
C metabolic flux analysis (MFA) has crystallized in the past two decades as the primary approach to quantify in vivo intracellular metabolic rates, that is, the fluxes [1]. Measured fluxes, in turn, have contributed unprecedented insights to unravel metabolic networks and their regulation, improve biotechnological processes, annotate unknown genes, assess drug toxicity, and so on (achievements recently reviewed in [2–7]). Intracellular fluxes are not directly measurable, but under given circumstances they can be inferred from the characteristic rearrangement of 13C — occasionally 15N — tracers through metabolic pathways [8,9–11]. Essentially three ingredients are used to calculate intracellular fluxes (Figure 1): firstly, www.sciencedirect.com
The existence of compartments in eukaryotic cells severely hampers calculation of fluxes. Since the same compound can exist in different subcellular spaces where it participates in different reactions, it is likely to possess compartment-specific 13C signatures. Although metabolic models can be extended to correctly describe metabolite localization and transporters, the disruptive nature of metabolite extraction before MS or NMR analysis allows only measurement of an average 13C-pattern, which in most cases must be discarded. While some compartmentspecific 13C-data can be retrieved from macromolecules, the approach has been demonstrated effective only in plant cells and embryos [15,16]. In mammalian cells, the problem is particularly acute in models of the tricarboxylic acid cycle and lower glycolysis (Figure 2). As a consequence of the increase in intertwined pathways and the reduction in measurable 13C-data, it is not possible to mathematically estimate any flux with good confidence Current Opinion in Biotechnology 2011, 22:103–108
104 Analytical biotechnology
Figure 1
Schematic summary of the algorithmic strategies to analyze data in stationary 13C-MFA. Calculation of fluxes from non-stationary experiments requires also quantification of metabolite concentrations and is done by isotopomer modeling using large systems of ordinary differential equations.
Figure 2
Stoichiometric network of lower glycolysis and tricarboxylic acid cycle reconstructed from genes listed in the HumanCyc database (www.humancyc.org). According to this model and assuming that all the enzymes encoded in the genome may be active, formally it is only possible to measure the labeling patterns of citrate, succinate, and lactate because their synthesis occurs only in one compartment, while all other metabolites are of ambiguous origin. Sparse labeling data do not allow resolving the large number of degrees of freedom given by isoenzymes in different compartments and the numerous transport reactions. The gene names are reported with the abbreviation used in the database. Current Opinion in Biotechnology 2011, 22:103–108
www.sciencedirect.com
Metabolic flux analysis in complex systems Zamboni 105
without additional assumptions. These include either the removal of reactions from the model motivated by their measured or supposed negligible activity [17], or pooling of metabolites based on hypothetical rapid equilibrium catalyzed by the continuous action of transporters [18]. A cursory glance through the amended models recently used by expert labs [17,18,19,20,21,22] reveals that there is little consensus and even some controversy, in particular with respect to reaction reversibility, localization of reactions, occurrence of gluconeogenic or anaplerotic fluxes or the presence of transporter reactions. Discrepancies can be partly ascribed to the use of differentiated cells or of specific media. This, however, also highlights the risk of transferring knowledge gained in diverse contexts, in particular when the microenvironment is not well defined or growth abnormal as in many tumor cells. As a consequence, a careful interpretation of the results has to consider the implicit model uncertainty in addition to the statistical confidence given by the parameter estimation. Although isotopically non-stationary 13C-MFA has excellent power to spot incongruences between measured concentrations and labeling data also in such underdetermined systems, to date there is no publicly available software to rigorously calculate fluxes from dynamic 13C-data. Hence, the most practicable alternative to generally validate a model for each cell type and environment is to perform preliminary experiments with ad hoc tracers tailored to test whether a given pathway is active [19,23,24].
Complex media Cellular phenotypes and evolution are best understood in the natural environment, which typically features transient and heterogeneous nutrients. The effort to calculate fluxes scales exponentially with the number of substrates, both on experimental and computational side. Multiple carbon sources also increase the danger of non-stationary metabolism or diauxic growth that depend on the availability of nutrients and the regulatory architecture of cells, for example, catabolite repression through a preferred substrate. This also applies to systems were additional nutrients must be supplemented to compensate for auxotrophies, because of the inherent risk that the secondary substrate is catabolized despite the lesion in its biosynthesis. Although published flux datasets were generated almost exclusively in media with one or sporadically two major carbon sources, quantitative 13C-MFA is at reach with the existing arsenal of techniques even for more challenging setups with multiple carbon sources. This view remains arguable in the absence of experimental proof of principle, but several factors make the problem tractable. In chemically defined media, it is possible to measure the uptake rate for all potential substrates, the production rate of byproducts confirms the completeness of physiological characterization on the basis of a closed carbon balance. If www.sciencedirect.com
the pathway of assimilation is known, it is also possible to develop a comprehensive model for flux analysis by isotopomer modeling and iterative fitting [8,10,25]. This framework is flexible with respect to substrates and network topology, but does not solve the problem that the degrees of freedom increase with the number of substrates. To compensate, additional information must be distilled from the tracer experiment to determine fluxes. This is obtained on one the hand by the measurement of 13C-labeling in the intermediates of metabolism [26,27], in particular where the catabolic pathway of different substrates convolute. On the other hand fluxes can be estimated on the basis of several labeling experiments performed with different 13C-tracers. It is possible to specifically label single substrates in separate experiments and monitor their breakdown by MS or NMR analysis while preserving the medium composition and thus the metabolic steady state. Integration of data from independent experiments is done during flux calculation using publicly available packages for stationary 13C-MFA by isotopomer modeling [28,29] which can be adjusted to estimate a single flux distribution that best fits multiple experiments [30]. Albeit computationally more demanding, this procedure returns more precise estimates compared to the independent fitting of single experiments. Provided that suitable stable isotopic tracers are commercially available, this strategy should enable calculating fluxes in chemically defined media with numerous substrates, for example, mixes of sugars and amino acids. Yet, the massive demand for experiments and resources most likely explains why it has not been accomplished thus far. Formal simulation of 13C-labeling experiments and thus quantitative flux estimation is compromised in complex and fully characterized media, such as formulations containing biomass extracts or digests. This leaves rational interpretation by the human brain as the most efficient approach to translate 13C-signatures in biological insights, as exemplarily shown by very detailed elucidations of pathogens’ metabolism within their host [31,32].
Genome-wide networks Central carbon metabolism has attracted most attention in all flux studies published so far. The primary reason was the scientific goal to characterize intracellular physiology and to quantify the largest cellular fluxes that determine cell-wide energy and redox metabolism. However, technical reasons also exist to explain this trend and, specifically, why it is difficult to expand beyond central carbon metabolism. First, fluxes in central metabolism are well resolved based on stationary 13C-data [8]. In peripheral metabolism, however, pathways form mostly branched, linear pathways where at isotopic steady-state the 13Cpatterns are independent of the flux. In fact, in 13C-MFA the purely biosynthetic fluxes are defined in the model in Current Opinion in Biotechnology 2011, 22:103–108
106 Analytical biotechnology
the form of a growth rate-dependent withdrawal of metabolites from central metabolism approximated a priori from macromolecular composition [25,33]. Second, detection of 13C-patterns in intermediates of the pathway of interest is a prerequisite, which on peripheral pathways becomes challenging because of low abundance. Third, the simulation of large(r) networks at the level of isotopologs scales poorly. Recent work suggests that these will be eventually overcome in the next years, at least for the stationary case [34,35], to rigorously estimate fluxes in mid-sized networks with hundreds of reactions. However, for branched or cyclic biosynthetic pathways such as those of fatty acids, lipids, or terpenoids, only dynamic 13C-data and thus non-stationary 13C-MFA methods are informative. Provided that it is possible to detect the 13C-enrichment and the absolute concentrations of intermediates in the pathway of interest, the flux can be quantified locally with small systems of ordinary differential equations [13] for which public, sophisticated, and yet user-friendly solvers exist [36]. In complement to the aforementioned quantitative estimation of fluxes, the model-free and qualitative analysis of 13C-patterns represents an appealing alternative also in this context [37–39]. Instead of precisely simulating all isotopologs and thus fully avoiding all scalability issues, the measured patterns are analyzed by statistical means to spot significant differences between two or more samples, in stationary [38] or dynamic data [39]. This approach is particularly suited for purposes of discovery, that is, to identify dynamic biomarkers of integrated network response to be validated in quantitative and targeted follow-ups. Noticeably, when a subset of mutants with known fluxes exist, these can be used to train a predictor capable of quantitatively estimating fluxes solely from 13 C signatures [40,41].
High resolution in time and space The highest temporal resolution achievable by flux methods is a function of multiple factors. The major determinant is the time necessary for the isotopic tracer to propagate through the network, which in turn depends on systems properties such as its topology, abundance of metabolite pools, and fluxes [8,12]. Primarily two strategies are commonly used to decrease the time necessary in a labeling experiment. The first is to measure the 13Cpatterns of intermediates directly within — or downstream of — the pathways under investigation enabling early detection [26]. The second is to calculate fluxes from the initial transients of 13C propagation, either by extrapolating stationary 13C-patterns before the isotopic steady state is established [42] or by resorting to methods of isotopically non-stationary 13C-MFA [12,43,44]. This typically reduces the minimum duration of a carbon-labeling experiment from several hours to one hour and few minutes, respectively. 13C-MFA of dynamic systems at a resolution of about one hour has been Current Opinion in Biotechnology 2011, 22:103–108
demonstrated for industrial fed batch cultivations [42,43], but with non-stationary methods it is theoretically possible to quantify fluxes also in systems where metabolism can be linearized over intervals of 10–15 min. A more futuristic application is single-cell 13C-MFA. Outstanding progress has recently been made in sensitivity using either capillary electrophoresis and electrospray [45], gas chromatography and electron impact [46], or matrix assisted laser desorption ionization [47], to pave the road for routine detection of small molecules in single cells. All these studies employed time-of-flight MS and thus collectively advocate for an extension to 13C-MFA. Tandem MS can also be employed to maximize sensitivity [48]. Further, the detection of relative 13C-labelings is even largely insensitive to poor ionization reproducibility, which is a major technical problem of using MS at such small scale and afflicts concentration measurements. Additional optimization of microfluidics, ionization efficiency, and detection will be necessary to attain the necessary signal to noise at least for some of the intermediates in central carbon metabolism or amino acids and eventually enable 13 C-MFA. This milestone is likely to be achieved within the next five years. Direct analysis of 13C patterns by flux ratio analysis [8] will enable profiling of relative fluxes in single cells even in the absence of measurable rates for substrate uptake and product formation.
Conclusions and perspectives It would be certainly invaluable for the community to gain access to a rigorous but generalized framework to independently perform non-stationary 13C-MFA at least in small-sized networks with compartments or complex environments. This would, however, always imply knowledge of most metabolite concentrations, 13C-labeling patterns and access to high performance computing. Considering also that world-wide only about a dozen groups with uneven access to instruments or know-how are pioneering novel concepts and tools for 13C-MFA, it is unlikely that such sophisticated and demanding approach will establish itself as first-line method to ubiquitously investigate fluxes in complex systems. Instead, two complementary approaches are emerging to cope with complexity, in a trend that reflects the evolution observed in proteomics [49,50] and metabolomics [51]. The first is the qualitative analysis — here of labeling patterns — by multivariate statistics and machine learning for means of profiling and thus mere data-driven discovery [37]. Although technically simple and readily applicable, the immense potential of this strategy will only be unleashed in combination with non-targeted analytical methods, for instance on MS detectors with high resolving power and accuracy. Additional experience and visions are also needed to effectively translate differential 13C-patterns into testable biological hypotheses. The second is highly targeted and quantitative assays for www.sciencedirect.com
Metabolic flux analysis in complex systems Zamboni 107
specific fluxes by stable isotopic tracers, building upon collection of 13C-data and concentration data densely around the reactions of interest and the local modeling of metabolism in the spirit of flux ratio analysis [1,52] or kinetic profiling [13]. Complexity is therefore contrasted by specialization: it is intuitively simpler to focus on one single flux rather than trying to quantify all at once. Another benefit of this approach is that the measurement of 13Cdata is also targeted to a small number of intermediates, thereby increasing sensitivity, precision, and providing more time to collect positional information by tandem MS. Frameworks to enable automated (or assisted) design of such flux assays are under development.
References and recommended reading Papers of particular interest, published within the period of review, have been highlighted as: of special interest of outstanding interest 13
1.
Sauer U: Metabolic networks in motion: analysis. Mol Syst Biol 2006, 2:62.
2.
Blank LM, Kuepfer L: Metabolic flux distributions: genetic information, computational predictions, and experimental validation. Appl Microbiol Biotechnol 2010, 86:1243-1255.
3.
Zamboni N, Sauer U: Novel biological insights through metabolomics and 13C-flux analysis. Curr Opin Microbiol 2009, 12:553-558.
4.
Niklas J, Schneider K, Heinzle E: Metabolic flux analysis in eukaryotes. Curr Opin Biotechnol 2010, 21:63-69.
5.
Heinemann M, Sauer U: Systems biology of microbial metabolism. Curr Opin Microbiol 2010, 13:337-343.
6.
Otero JM, Nielsen J: Industrial systems biology. Biotechnol Bioeng 2010, 105:439-460.
7.
Schwender J: Metabolic flux analysis as a tool in metabolic engineering of plants. Curr Opin Biotechnol 2008, 19:131-137.
C-based flux
16. Paula Alonso A, Dale VL, Shachar-Hill Y: Understanding fatty acid synthesis in developing maize embryos using metabolic flux analysis. Metab Eng 2010, 12:488-497. 17. Quek LE, Dietmair S, Kro¨mer JO, Nielsen LK: Metabolic flux analysis in mammalian cell culture. Metab Eng 2010, 12:161-171. Case study in higher cells that describes in detail the rationale of model reduction. 18. Goudar C, Biener R, Boisart C, Heidemann R, Piret J, de Graaf A, Konstantinov K: Metabolic flux analysis of CHO cells in perfusion culture by metabolite balancing and 2D [13C, 1H] COSY NMR spectroscopy. Metab Eng 2010, 12:138-149. 19. Munger J, Bennett BD, Parikh A, Feng XJ, McArdle J, Rabitz HA, Shenk T, Rabinowitz JD: Systems-level metabolic flux profiling identifies fatty acid synthesis as a target for antiviral therapy. Nat Biotechnol 2008, 26:1179-1186. A good example on how several specific tracer experiments can be merged to yield a global snapshot. 20. DeBerardinis RJ, Mancuso A, Daikhin E, Nissim I, Yudkoff M, Wehrli S, Thompson CB: Beyond aerobic glycolysis: transformed cells can engage in glutamine metabolism that exceeds the requirement for protein and nucleotide synthesis. Proc Natl Acad Sci U S A 2007, 104:19345-19350. 21. Noguchi Y, Young JD, Aleman JO, Hansen ME, Kelleher JK, Stephanopoulos G: Effect of anaplerotic fluxes and amino acid availability on hepatic lipoapoptosis. J Biol Chem 2009, 284:33425-33436. 22. Maier K, Hofmann U, Bauer A, Niebel A, Vacun G, Reuss M, Mauch K: Quantification of statin effects on hepatic cholesterol synthesis by transient 13C-flux analysis. Metab Eng 2009, 11:292-309. First systematic non-stationary flux analysis in higher cells accounting for compartments. 23. Fuhrer T, Fischer E, Sauer U: Experimental identification and quantification of glucose metabolism in seven bacterial species. J Bacteriol 2005, 187:1581-1590. 24. Metallo CM, Walther JL, Stephanopoulos G: Evaluation of 13C isotopic tracers for metabolic flux analysis in mammalian cells. J Biotechnol 2009, 144:167-174. 25. Dauner M, Bailey JE, Sauer U: Metabolic flux analysis with a comprehensive isotopomer model in Bacillus subtilis. Biotechnol Bioeng 2001, 76:144-156.
8. Zamboni N, Fendt SM, Ru¨hl M, Sauer U: 13C-based metabolic flux analysis. Nat Protoc 2009, 4:878-892. Comprehensive description of stationary flux methods, from principles to protocols and software.
26. van Winden WA, van Dam JC, Ras C, Kleijn RJ, Vinke JL, van Gulik WM, Heijnen JJ: Metabolic-flux analysis of Saccharomyces cerevisiae CEN.PK113-7D based on mass isotopomer measurements of 13C-labeled primary metabolites. FEMS Yeast Res 2005, 5:559-568.
9.
27. Toya Y, Ishii N, Hirasawa T, Naba M, Hirai K, Sugawara K, Igarashi S, Shimizu K, Tomita M, Soga T: Direct measurement of isotopomer of intracellular metabolites using capillary electrophoresis time-of-flight mass spectrometry for efficient metabolic flux analysis. J Chromatogr A 2007, 1159:134-141.
Dauner M: From fluxes and isotope labeling patterns towards in silico cells. Curr Opin Biotechnol 2010, 21:55-62.
10. Wiechert W: 3:195-206.
13
C metabolic flux analysis. Metab Eng 2001,
11. Kruger NJ, Ratcliffe RG: Insights into plant metabolic networks from steady-state metabolic flux analysis. Biochimie 2009, 91:697-702. 12. No¨h K, Gronke K, Luo B, Takors R, Oldiges M, Wiechert W: Metabolic flux analysis at ultra short time scale: isotopically non-stationary 13C labeling experiments. J. Biotechnol. 2007, 129:249-267. Seminal work on non-stationary flux analysis by iterative fitting 13. Yuan J, Bennett BD, Rabinowitz JD: Kinetic flux profiling for quantitation of cellular metabolic fluxes. Nat Protoc 2008, 3:1328-1340. This protocol describes the principles of local analysis of non-stationary data collected with 15N experiments, which are equally valid for 13C tracers. 14. No¨h K, Wiechert W: Experimental design principles for isotopically instationary 13C labeling experiments. Biotechnol Bioeng 2006, 94:234-251. 15. Allen DK, Shachar-Hill Y, Ohlrogge JB: Compartment-specific labeling information in 13C metabolic flux analysis of plants. Phytochemistry 2007, 68:2197-2210. www.sciencedirect.com
28. Quek LE, Wittmann C, Nielsen LK, Kro¨mer JO: OpenFLUX: efficient modelling software for 13C-based metabolic flux analysis. Microb Cell Fact 2009, 8:25. 29. Wiechert W, Mo¨llney M, Petersen S, de Graaf AA: A universal framework for 13C metabolic flux analysis. Metab Eng 2001, 3:265-283. 30. Masakapalli SK, Le Lay P, Huddleston JE, Pollock NL, Kruger NJ, Ratcliffe RG: Subcellular flux analysis of central metabolism in a heterotrophic Arabidopsis cell suspension using steadystate stable isotope labeling. Plant Physiol 2010, 152:602-619. Highly didactic study on resolving subcellular compartments networks by multiple stationary experiments. 31. Eylert E, Herrmann V, Jules M, Gillmaier N, Lautner M, Buchrieser C, Eisenreich W, Heuner K: Isotopologue profiling of Legionella pneumophila: role of serine and glucose as carbon substrates. J Biol Chem 2010, 285:22232-22243. Excellent example for the observation-driven interpretation of labeling experiments in a host–pathogen system. Current Opinion in Biotechnology 2011, 22:103–108
108 Analytical biotechnology
32. Eisenreich W, Dandekar T, Heesemann J, Goebel W: Carbon metabolism of intracellular bacterial pathogens and possible links to virulence. Nat Rev Microbiol 2010, 8:401-412.
glucose limitation in fed-batch culture. Biotechnol Bioeng 2010, 105:795-804.
33. Pramanik J, Keasling JD: A stoichiometric model of Escherichia coli metabolism: incorporation of growth-rate dependent biomass composition and mechanistic energy requirements. Biotechnol Bioeng 1997, 56:398-421.
43. Noack S, No¨h K, Moch M, Oldiges M, Wiechert W: Stationary versus non-stationary 13C-MFA: a comparison using a consistent dataset. J Biotechnol 2010. The first coherent and direct comparison of stationary and non-stationary flux analysis.
34. Suthers PF, Burgard AP, Dasika MS, Nowroozi F, Van Dien S, Keasling JD, Maranas CD: Metabolic flux elucidation for large-scale models using 13C labeled isotopes. Metab Eng 2007, 9:387-405.
44. Schaub J, Mauch K, Reuss M: Metabolic flux analysis in Escherichia coli by integrating isotopic dynamic and isotopic stationary 13C labeling data. Biotechnol Bioeng 2008, 99:1170-1185.
35. Suthers PF, Chang YJ, Maranas CD: Improved computational performance of MFA using elementary metabolite units and flux coupling. Metab Eng 2010, 12:123-128.
45. Lapainis T, Rubakhin SS, Sweedler JV: Capillary electrophoresis with electrospray ionization mass spectrometric detection for single-cell metabolomics. Anal Chem 2009, 81:5858-5864.
36. Maiwald T, Timmer J: Dynamical modeling and multiexperiment fitting with PottersWheel. Bioinformatics 2008, 24:2037-2043.
46. Koek MM, Bakels F, Engel W, van den Maagdenberg A, Ferrari MD, Coulier L, Hankemeier T: Metabolic profiling of ultrasmall sample volumes with GC/MS: from microliter to nanoliter samples. Anal Chem 2010, 82:156-162.
37. Zamboni N, Sauer U: Fluxome profiling in microbes. In Metabolome Analyses: Strategies for Systems Biology. Edited by Vaidyanathan S, Harrigan GG, Goodacre R. Springer; 2005:307-322. 38. Zamboni N, Sauer U: Model-independent fluxome profiling from 2H and 13C experiments for metabolic variant discrimination. Genome Biol 2004, 5:R99. 39. Godin JP, Ross AB, Rezzi S, Poussin C, Martin FP, Fuerholz A, Cleroux M, Mermoud AF, Tornier L, Arce Vera F et al.: Isotopomics: a top-down systems biology approach for understanding dynamic metabolism in rats using [1,2-13C2] acetate. Anal Chem 2010, 82:646-653. 40. Antoniewicz MR, Stephanopoulos G, Kelleher JK: Evaluation of regression models in metabolic physiology: predicting fluxes from isotopic data without knowledge of the pathway. Metabolomics 2006, 2:41-52. 41. Zamboni N: Towards metabolome-based 13C flux analysis: a universal tool for monitoring in vivo pathway activity. In Topics in Current Genetics. Edited by Nielsen J, Jewett M. Springer; 2007. 42. Ru¨hl M, Zamboni N, Sauer U: Dynamic flux responses in riboflavin overproducing Bacillus subtilis to increasing
Current Opinion in Biotechnology 2011, 22:103–108
47. Amantonico A, Oh JY, Sobek J, Heinemann M, Zenobi R: Mass spectrometric method for analyzing metabolites in yeast with single cell sensitivity. Angew Chem Int Ed Engl 2008, 47:5382-5385. 48. Kiefer P, Nicolas C, Letisse F, Portais JC: Determination of carbon labeling distribution of intracellular metabolites from single fragment ions by ion chromatography tandem mass spectrometry. Anal Biochem 2007, 360:182-188. 49. Schmidt A, Claassen M, Aebersold R: Directed mass spectrometry: towards hypothesis-driven proteomics. Curr Opin Chem Biol 2009, 13:510-517. 50. Domon B, Aebersold R: Mass spectrometry and protein analysis. Science 2006, 312:212-217. 51. Nielsen J, Oliver S: The next wave in metabolome analysis. Trends Biotechnol 2005, 23:544-546. 52. Rantanen A, Rousu J, Jouhten P, Zamboni N, Maaheimo H, Ukkonen E: An analytic and systematic framework for estimating metabolic flux ratios from 13C tracer experiments. BMC Bioinformatics 2008, 9:266.
www.sciencedirect.com