Model-independent fluxome profiling from 2H and 13C experiments for metabolic variant discrimination
© Zamboni and Sauer; licensee BioMed Central Ltd. 2004
Received: 28 August 2004
Accepted: 25 October 2004
Published: 16 November 2004
We introduce a conceptually novel method for intracellular fluxome profiling from unsupervised statistical analysis of stable isotope labeling. Without a priori knowledge on the metabolic system, we identified characteristic flux fingerprints in 10 Bacillus subtilis mutants from 132 2H and 13C tracer experiments. Beyond variant discrimination, independent component analysis automatically mapped several fingerprints to their metabolic determinants. The approach is flexible and paves the way to large-scale fluxome profiling of any biological system and condition.
Genome-wide analyses of cellular mRNA, protein or metabolite complements have become workhorses in biological research that produce unprecedented amounts of data on cellular network composition. In contrast to such compositional information, molecular fluxes through intact metabolic networks link genes and proteins to higher-level functions that result from biochemical and regulatory interactions between the components . As such, quantitative knowledge of in vivo molecular fluxes is highly relevant to functional genomics, metabolic engineering and systems biology [2, 3]. Intracellular fluxes, or in vivo reaction rates, can be assessed by methods of metabolic flux analysis that are based on stable isotopic tracer experiments [4, 5], which have successfully unraveled novel biochemical pathways [6, 7] and gene functions [8, 9]. The presently tedious and limited methodologies, however, hamper broader application to a large range of environmental conditions, isotopic tracers and higher biological systems .
We set out to overcome a principal bottleneck in metabolism-wide flux (fluxome ) analysis: the requirement for mathematical frameworks to interpret the isotopic tracer data from nuclear magnetic resonance (NMR) or mass spectrometric (MS) analyses within a detailed metabolic model [4, 5]. Constructing such models requires a priori knowledge on possible distributions of the tracer used within the network, and, more importantly, extensive labeling and physiological data to resolve all fluxes within a given model. The lack of such structural knowledge on metabolic pathways and the technical difficulty of acquiring sufficient data hamper studies of metabolism, in particular in higher cells with complex nutrient requirements and for exotic tracer molecules. Hence, fluxome analysis is largely restricted to few 13C-labeled carbon sources in microbes or plants cultivated in minimal medium [7, 11–16].
Here we discriminate mutants/conditions and assess their metabolic impact directly from 'raw' mass-isotope data by unsupervised multivariate statistics without a priori knowledge of the biochemical reaction network. To illustrate the applicability of this conceptually novel profiling method, we focused on the reactions of central metabolism in the model bacterium Bacillus subtilis, for which detailed flux data were available to validate the results [9, 11, 14].
2H and 13C tracer experiments
B. subtilis strains used
Description of deleted gene
Succinyl-CoA dehydrogenase component
Main carbon catabolite repressor
Repressor of the gapA operon
Repressor of PTS system
Identification of metabolic determinants for altered flux profiles
As well as consistency with the data in the literature, the analysis also revealed new information on pathway activity and regulation that was not previously accessible. One example is the pronounced signatures of the sdhC mutant on glucose and sorbitol. Because the sdhC mutation disrupts the tricarboxylic acid (TCA) cycle, the wild-type flux through the cycle must be similar on these substrates, both with and without CAA (Figure 3). The sdhC signatures of the TCA cycle-derived amino acids aspartate (D) and glutamate (E) were also present in the CAA profiles of the other TCA cycle mutant mdh. Their absence on ammonium indicates activity of the malic enzyme-based pyruvate bypass  in the mdh mutant.
While such a level of detailed biochemical insight is possible, it requires considerable expertise and time to retrieve. Alternatively, metabolic impacts in new mutants can be identified by comparison of the mass fingerprints in mutants with known metabolic lesions. During growth on sorbitol and pyruvate in minimal media but not with CAA, the CggR repressor of the glycolytic gapA operon, for example, appears to affect TCA cycle fluxes because the mutant profile matches those of the TCA cycle mutants sdhC and mdh (Figure 3). In contrast to glucose, sorbitol does not elicit catabolite repression; hence, comparison of sorbitol and glucose profiles can identify repression-dependent effects. Examples are the signatures of the oxaloacetate-derived amino acids isoleucine (I), threonine (T) and aspartate in the cggR profile that reveal, by the similarity to the sdhC and mdh mutants, a TCA cycle flux-promoting effect of CggR on sorbitol but not on glucose. This is consistent with the repression of cggR on glucose , and the TCA cycle effect is probably indirect, through the repression of glycolytic genes .
A significant extension beyond the canonical 13C-tracer methods is the applicability to any isotope, which broadens the observable metabolic processes. Here we used fully deuterated [U-2H]glucose that allows us to monitor dehydrogenase activities and water release. The 2H-label was present exclusively in the variable side chains, because the α-carbon hydrogen was lost in the transaminase reaction. Thus, glycine contains no label and the acidic aspartate and glutamate lose the label proximal to the carboxyl group as a result of exchange with water at the low pH during hydrolysis. The remaining amino acids provided a stable and informative 2H-pattern (see Additional data file 1). An illustrative example is the cggR mutant signatures for the pyruvate-derived amino acids valine (V), leucine (L) and, partially, alanine (A) (Figure 3) In all three cases, reduced m2 and increased m0 fractions revealed a double loss of 2H-label in their common precursor pyruvate at position C-3. This loss of 2H indicates increased exchange of 2H with water at the C-3 position of pyruvate (or any upstream triose), which is fully consistent with increased transcription of the glycolytic enolase in the cggR mutant on glucose  that could catalyze this exchange. As the enolase activity does not affect the carbon backbone, the corresponding patterns cannot be identified in 13C experiments
Independent component analysis (ICA)
For large-scale profiling studies, automated mutant classification based on metabolic function without user supervision would be desirable. Initially, we used principal component analysis (PCA), which is often used for graphical representation of multidimensional variables from profiling experiments [24, 25], as was recently described for pretreated (summed fractional labels) mass isotope data . From the raw mass isotope data, the first two PCs discriminated, under most conditions, mutants with extreme labeling patterns (see Additional data file 1). The differences become smaller with increasing PCs, and only the initial three to four PCs allowed reliable discrimination. In the present data, PCA tended to discriminate extreme singular labeling patterns in few fragments or, more frequently, combinations of altered patterns in the fragments of many amino acids, as was expected from the variance maximization of PCA. Unfortunately, the resulting complex PCs are difficult to interpret metabolically, and thus are of limited biochemical relevance.
Consequently we used independent component analysis (ICA) for unsupervised, automatic recognition of conserved labeling patterns that are biochemically relevant. The underlying assumption is that these patterns result from the superposition of independent metabolic activities. Each activity causes a specific shift in the mass distributions of one or more intermediates. ICA seeks to separate the observed variables into non-gaussian components that are statistically as independent as possible . Generally, ICA clearly discriminated mutants and conditions from the corrected (non-normalized) MS data (see Additional data file 1). While the weights in PCs were more broadly distributed among the input variables, ICs were dominated by fewer, sharper peaks (Figure 4).
Akin to PCA, ICA allowed us to discriminate mutants from the corrected MS data (Figure 5b and Additional data file 1). On sorbitol, mutants such as pgi, yqjI, pps, glcP and glcR were mostly silent, and typically projected in proximity to the parent strain. In contrast to PCA, ICs classified the mutants on the basis of specific metabolic effects. In some cases (IC2 or IC4 in Figure 5b), the IC defined well-separated clusters of mutants, usually two groups, reflecting a binary (on-off) effect. In the majority of the components, however, the even distribution between the extremes reveals progressive metabolic responses (for example, IC3, IC7 or IC10). Overall, the ICs correlated favorably with the signatures of wild-type-normalized profiles (Figure 5 and Additional data file 1). Thus, ICA clearly outperformed PCA by its capacity for unsupervised recognition of metabolic responses and its ability to correlate biochemically redundant information in the data.
Comparison of PCA and ICA with analytically determined flux ratios
For the example of central and amino-acid metabolism in B. subtilis, we show that fluxome profiling by multivariate statistics from mass isotopomer distribution analysis is meaningful for the discrimination of mutants or conditions on the basis of their metabolic behavior, and applicable to conditions that are inaccessible to previous flux analysis. In sharp contrast to metabolome concentration data [24, 25], fluxome profiles contain functional information on the operation of fully assembled networks [1, 4]. As shown here by ICA, this approach enables us to distill the essential signatures of independent metabolic activities, and supports the identification of the underlying biochemical causality. Because no model or a priori knowledge on the investigated system is required, the metabolic imprints of any tracer atom and molecule can be followed in virtually any biological system, including multicellular organisms in complex multisubstrate media.
Similarly, a priori knowledge of the number of ICs to be computed is not a prerequisite. As a matter of fact, the optimal number depends primarily on the labeling patterns and can hardly be estimated from the dataset dimensions. An underestimate will generally leave some relevant signatures unrecognized, whereas an overestimate will lead to an increased fraction of components reflecting measurement or biological noise. Although statistical significance can be assessed with duplicates, this becomes prohibitive with large datasets (that is, hundreds of mutants or analytes) or reduced availability of replicas. The bottleneck resides in the stochastic approach of most ICA algorithms, for which independent runs result in different ICs or ordering thereof. Instead, algorithmic and statistical reliability of the ICs can be evaluated by repeating the estimation several times either with randomly chosen initial guesses or by slightly varying the dataset (bootstrapping ), respectively, and then clustering all results to identify robust ICs .
Two factors directly affect the results that can be obtained by comparative fluxome profiling: the detected analytes and the choice of isotopic tracer. As well as polymer-based analytes such as the proteinogenic amino acids monitored here, fluxome profiles can be detected in any set of intra- or extracellular metabolites, thereby widening the observable metabolic processes The choice of tracer depends, to some extent, on the metabolic subsystem of interest. Uniformly labeled substrates provide a more global perspective because they allow assessment of the scrambling of any carbon backbone and, in the case of experiments performed in rich media, also allow quantification of the fraction of de novo biosynthesis from the tracer relative to the uptake of a medium component. Similarly, uniformly deuterated substrates or 2H2O are valuable for simultaneously capturing a wide number of ICs that are affected by the release, binding and exchange of water or protons. Substrates that are labeled at specific positions, in contrast, enable deeper interrogation of particular sub-networks, for example, [1-13C]hexoses for the initial catabolic reactions [8, 19] or [1-13C]aspartate to assess urea cycle activity.
The results also revealed new biological information on pathway activity, function or regulation. First, both glycolysis and the pentose phosphate pathway actively catabolized glucose in the presence of CAA, because the pgi and yqjI mutant signatures were different from the wild type and from each other. On sorbitol, in contrast, the same mutants were very similar to the wild type, suggesting that both reactions are only marginally involved in catabolism of this sugar. Second, the Krebs cycle flux was similar on glucose and sorbitol (with and without CAA), as deduced from the similarly pronounced signatures of the sdhC mutant. Third, absence of the sdhC signatures in the Krebs cycle-derived amino acids aspartate and glutamate of the mdh mutant when grown with ammonium (but not CAA) indicates activity of the malic enzyme-based pyruvate bypass . Fourth, activity of the NADP-dependent malic enzyme appears to be independent of catabolite repression because pronounced signatures of the ytsJ mutant were seen on all substrates. The gluconeogenic phosphoenolpyruvate synthetase Pps, in contrast, was inactive in the presence of the repressing glucose but active on pyruvate or sorbitol. Fifth, as discussed above the data reveal a Krebs cycle-promoting effect of the repressor CggR on sorbitol but not on glucose, most likely through the repression of glycolytic genes .
The comparative fluxome profiling presented here complements traditional flux analysis because it enables potentially rapid and automated identification of relevant mutants or conditions from large-scale datasets, for example from entire mutant libraries. The approach is quantitative in terms of the relative difference between variants, but qualitative with respect to the in vivo flux. Interesting variants are then subjected to deeper interrogation of the specific metabolic phenomenon identified. Besides mere data mining, fluxome profiling also has the potential to identify complex functional traits in higher cells where current flux methods fail, and possibly even identify the underlying biochemical mechanism of discriminant mass isotope signatures.
Materials and methods
Strains and growth conditions
Wild-type B. subtilis 168 (trpC2)  and knockout mutants containing an antibiotic marker in single genes  were grown in M9 minimal medium  at pH 7.0 with 50 mg tryptophan. Six different combinations of 2H- or 13C-labeled isotopic tracers (3 g/l) and nitrogen sources were used: (i + ii) uniformly 13C-labeled [U-13C]glucose with either 0.5 g/l CAA (Sigma) or 1 g/l NH4Cl; (iii + iv) [U-13C]sorbitol with either 0.5 g/l CAA or 1 g/l NH4Cl; (v) [U-2H]glucose ([1,2,3,4,5,6,6-2H]glucose) with 1 g/l NH4Cl; and (vi) [3-13C]pyruvate with 1 g/l NH4Cl and twofold higher concentrations of phosphate to ensure pH buffering. [U-13C]glucose (Martek Biosciences), [U-13C]sorbitol (Omicron Biochemicals), and [1,2,3,4,5,6,6-2H]glucose (Euriso-Top) were supplemented as 50:50 mixtures of labeled and unlabeled isotopomers. Pyruvate was supplied entirely as the [3-13C] isotopomer (Euriso-Top).
Aerobic batch cultures were grown in silicone-covered, deep-well microtiter plates at 37°C and 300 rpm in a 5-cm orbital shaker . Frozen stocks were used to inoculate 1 ml LB medium with selective antibiotics. After 10 h of incubation, 10 μl were used to inoculate 1 ml M9 medium with 5 g/l glucose and selective antibiotics, incubated for 12 h, and 10 μl of these precultures were used to inoculate 1.2 ml of M9 medium with isotopic tracers. Cultures were harvested upon entry into stationary phase (assessed by visual evaluation). Because the length of batch growth varied, cultures with CAA, with NH4Cl, and with pyruvate were harvested after 10, 14 and 24 h, respectively. Labeling patterns in the analyzed proteinogenic amino acids are rather stable [10, 19]; hence differences of a few hours in growth phase at harvest were irrelevant. This was also confirmed in separate (data not shown) and duplicate experiments for each combination of strain and medium that was independently started from culture stocks.
GC-MS analysis and data preprocessing
Cell harvest, protein hydrolysis and GC-MS analysis of amino acids were done exactly as described before [19, 32]. Amino-acid mass distributions were derived from the spectra after correction for the natural abundance of stable isotopes . Since amino acids are fragmented during electron impact ionization in the MS, we obtained three to five fragments with partially redundant information for each amino acid. For each fragment, a normalized vector m0, m1, ..., mn, expresses the fraction of molecules that are labeled at 0,1, ...,n positions, depending on the total number n of carbon or hydrogen atoms present. Considering all corrected fragment vectors obtained per sample, a complete dataset typically consisted of about 260 and 330 single mass values from 13C and 2H experiments, respectively, depending on the quality of the MS measurement.
Multivariate data analysis
To obtain a new representation of the multivariate MS data and to make their essential structure accessible, we applied PCA to the corrected fragment vectors. This approach projects the input variables in an orthogonal space that is spanned by the PCs. Among the infinite number of possibilities, each successive PC is selected to maximize the variance of the projected data and to be orthonormal to the previous ones . Consequently, PCA concentrates the maximum and nonredundant information of the entire dataset in the minimal number of dimensions, and thus is best suited for data compression . The computation was performed with Matlab (The Mathworks) using the princomp function of the Statistics toolbox 4.0. No input vectors were eliminated from the dataset to filter outliers in PCA, because this operation affected only PCs with higher order but only marginally PC1 and PC2.
To reveal hidden information in the labeling patterns, the corrected MS vectors were subjected to ICA , which is frequently used in the neurosciences [34, 35] and in gene-expression studies [36, 37]. For ICA, we assume that independent metabolic processes such as reactions or pathways produce characteristic fingerprints in the labeling pattern. These metabolic fingerprints are defined by m fundamental components S = (s1, ..., s m )T, each of which is represented by a vector of p MS-signals. We assumed that the experimental data X = (x1, ..., xn)T, with n vectors of p corrected MS signals for each mutant/condition, result from a linear combination of the m fundamental processes, given by x i = ai1s1 +...+ aimsm. In matrix notation, this leads to X p × n = A p × m S m × n , with A as the mixing or loading matrix. ICA seeks to estimate the unknown terms A and S from the observed values X but has different objectives from PCA. Briefly, ICA identifies statistically ICs by selecting those with maximum non-gaussianity . Hence, ICs are nonlinearly decorrelated and assumed to have non-gaussian distributions. Because of the central limit theorem, which states that the sum of non-gaussian random variables is closer to gaussianity than the original ones, ICs are identified by selecting the linear combinations of the observed variables that have maximum non-gaussianity . In particular, we used the publicly available FastICA 2.1 algorithm  to estimate the number of components that were equal to the number of strains in the dataset, excluding duplicates. The data dimension was not reduced (by PCA) before IC computation.
Additional data files
The following additional data is available with the online version of this paper. Additional data file 1 contains three figures (Additional Figure 1 shows the mass distribution in the 2H experiment; Additional Figure 2 shows mutant discrimination by PCA (less relevant than by ICA); Additional Figure 3 is a complete representation of the 660 ICs (10 ICs in 6 experiments for 11 strains). All the raw data is contained in six Excel tables in Additional data file 2.
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