Specifics of MetaNetwork

Similar to the approach used in gene expression studies, the genetic determinants of variation for metabolite abundance (mQTL) can be mapped. However, algorithms used for the analysis of transcript abundance have to be accommodated to the specifics of metabolite abundance. In the work of Keurentjes et al.³, one-third of the mass peaks segregating were not present in the parental lines, presumably caused by new allelic combinations. Likewise, many segregating mass peaks were not present in an appreciable proportion of the segregants, causing clear spikes at zero in the corresponding metabolite abundance distributions. Standard parametric approaches for QTL mapping (e.g., t-test¹², ANOVA^{6, 7, 10}, maximum likelihood¹³) make use of the assumption that the residual variation follows a normal distribution and departure from this assumption due to a spike can inflate errors of type I and II¹⁸. Standard non-parametric approaches for QTL mapping (Wilcoxon–Mann–Whitney test^{5, 14}) can solve this problem, but they are less useful in consideration of multiple QTL models¹⁸. A more suitable approach is to perform QTL analysis on the binary trait defined by whether an individual has a non-zero abundance, and on the quantitative trait for those individuals who have non-zero abundance. To combine these two analyses, MetaNetwork implements a two-part parametric model¹⁸ for mQTL mapping and outputs QTL profiles (- ¹⁰log P significance values plotted at marker positions along the genome).

Network reconstruction approaches based on the correlation of transcript abundance^{15, 16} may also be suitable for metabolite abundance. However, whereas transcripts are translated into molecules of another type (proteins), metabolites are transformed by enzymes into molecules of the same type (other metabolites). Therefore, if one metabolite is the precursor of another metabolite, an mQTL involved in the transformation will exert reversed effects for the precursor and its successor. Counterbalancing of positive and negative effects of multiple mQTLs may make it difficult to infer associations between metabolites from abundance correlations. Metabolites in the same pathway will show similar peaks in their QTL profiles, so that a correlation analysis based on QTL profiles may overcome this problem. MetaNetwork subsequently uses such correlations to determine associations between metabolites and to re-construct metabolic networks.

Challenges in MetaNetwork

Within the context of the genetical genomics experimental space, MetaNetwork encounters numerous challenges due to the size and the scope of the data set and the complexity of metabolic networks. Testing multiplicity is obviously a general challenge in QTL mapping¹⁹. The genome-wide mapping of each of many (correlated) mass peaks can result in a large number of false positives and/or false negatives. MetaNetwork uses Storey's method²⁰ to control false discovery rate (FDR). Candidate gene multiplicity is another challenge: an mQTL may still harbor hundreds of candidate genes²¹. Incorrect connections between metabolites affected by different enzymes may be predicted if the genes for those enzymes appear to colocalize on the genome. To predict or to prioritize candidates among many potential genes in a mQTL region requires additional strategies such as fine mapping and/or follow-up laboratory experiments. Appropriate information can also be derived from the use of assumedly independent (in silico) information in databases with metabolic pathway information, such as KEGG²², MetaCyc²³ or AraCyc²⁴, or data on eQTL studies, enzyme activity assays, or phenotypic data on the same segregants. Mass peak multiplicity, that is, metabolites represented by multiple mass peaks, is another challenge²⁵. For example, a metabolite with mass m can have one or more charges and peaks can appear at masses m, m/2, m/3 and so on. Or different isotopes of this metabolite have different numbers of neutrons and peaks appearing at m + 1, m + 2, m + 3 and so on. Unfortunately, error-free assignment of different mass peaks to a single metabolite is still difficult with today's mass spectrometry methods²⁶. However, MetaNetwork can provide important independent information to improve on this: it can predict possibly related peaks based on highly correlated mQTL profiles (r > 0.95).

Applications of MetaNetwork

To date, our MetaNetwork applications have been based on untargeted metabolite abundance data collected from recombinant inbred lines (RILs) of Arabidopsis thaliana plants using liquid chromatography–mass spectrometry technology³. It measures a large range of different metabolites mainly involved in secondary metabolism, including phenylpropanoids, flavonoids and glucosinolates²⁷. Many of these metabolites show a spike in their abundance distribution and MetaNetwork was specifically developed to handle such data. However, the MetaNetwork protocol can equally well handle abundance data without spikes. Moreover, it can handle data obtained from other mass spectrometry techniques, such as gas chromatography–mass spectrometry²⁸ that can detect polar primary metabolites.

In addition to mass spectrometry technologies for targeted or untargeted measuring amounts of metabolites^{3, 29}, other high-throughput technologies for measuring amounts of other molecular entities, such as microRNAs, proteins and their post-translational modifications, are rapidly being developed³⁰. The methodology described here is directly applicable to these and other quantitative types of data and helps biologists to understand how biological systems function.

Implementation of MetaNetwork

MetaNetwork is implemented in R, an open source software environment for statistical computing and graphics³¹. MetaNetwork is executed via a command line. However, users with little experience of command-line-driven applications and/or computer programming can easily run MetaNetwork using default parameter settings. An advanced user of R can change parameter settings or modify the underlying protocol, for example, by replacing the module for calculation of correlations by one for calculation of mutual information³², or the module for QTL analysis on RILs by one for QTL analysis on other types of segregating or natural populations. Future MetaNetwork releases will offer more options, for example, multiple QTL analysis^{33, 34} in the two-part model, combined analysis of metabolite abundance data with other types of biomolecular data¹¹ and direct access of the R-tools to a metabolite abundance database. A seamless software infrastructure that supports MetaNetwork data management and analysis workflows is under development using code generation techniques³⁵. For more implementation details, please consult the Supplementary Manual online.

Algorithm of MetaNetwork

The flowchart of the MetaNetwork protocol is shown in Figure 1. Given the scope of this manuscript, we will limit ourselves to the definition of the two main steps in the procedure: QTL mapping of metabolite abundances; and reconstruction of metabolic networks from correlations of QTL profiles. It should be noted that MetaNetwork does not offer data pre-processing, for example, alignment of mass peaks has to be performed by external applications such as METALIGN²⁷.

Figure 1: MetaNetwork flowchart.

The shaded squares represent computational steps where names of R-functions are indicated between parentheses and the superscript numbers refer to steps in Box 1. The ellipses represent significance thresholds and cylinders represent biological results where the result names as R objects are indicated between accolades. The solid line represents the step that is by default "on" in MetaNetwork and the dashed line represents the step that is by default "off" in MetaNetwork.

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MetaNetwork detects the genetic determinants underlying variation in metabolite abundance with the help of a two-part QTL analysis. Part one tests whether the presence/absence of metabolites has a genetic basis: whether different genotype classes at a given marker differ in their numbers of non-zero observations. Part two tests whether quantitative variation in non-zero abundances has a genetic basis: whether the non-zero observations for each of these genotype classes at a given marker differ in mean abundance. The "P-value" of the QTL is computed as the product of the two "P-values" in the two parts. With binary data only (no quantitative data) or quantitative data only (no spike), the "P-value" of the missing part is set to one. These "P-values" are not yet corrected for multiple testing at many markers and also not for testing multiple metabolites. MetaNetwork can run simulation and FDR procedures²⁰ to set an empirical threshold for the "P-values" at desired multiple-testing significance levels. MetaNetwork will output all relevant information such as the estimated effect of each mQTL, its support interval on the genome and the proportion of variance explained by it (see Box 1).

MetaNetwork explores the associations between metabolites by comparing their QTL profiles based on correlations. A permutation procedure sets an empirical threshold for the correlation at a desired significance level. MetaNetwork generates files with network connections that can be visualized using Cytoscape, an open source software suite for visualization of biomolecular interactions³⁶ (see Box 1).

Mapping genetic determinants

The QTL likelihood along the genome as stored in "qtlProfiles" is visualized with the function "qtlPlot," loaded by > data(qtlProfiles) and visualized by > qtlPlot(markers,qtlProfiles,4.11). At the empirical - ¹⁰log P threshold 4.11 (=0.05, FDR=0.0003), the glucosinolate mQTLs map to two major loci, which were confirmed by a previous targeted study³⁹: gene AOP at 9.0 cM of chromosome 4 is responsible for glucosinolate side-chain modification³⁷, and gene MAM at 35 cM of chromosome 5 is responsible for chain elongation³⁹. The observation that all glucosinolates have a QTL at MAM but only some of them have a QTL at AOP suggests that AOP acts downstream of MAM (Fig. 3a). The mQTL at MAM exerts the same sign of effect for all glucosinolates that are in the same branch of the network, whereas the mQTL at AOP exerts reversed effects on precursors and their successors. Six flavonols showed strong mQTLs at 88.6 cM of chromosome 1, where a not previously known glycosyl transferase or regulator was suggested³ (Fig. 3b).

Figure 3: The visualization of metabolic QTL profiles and networks.

(a) The mQTL profiles for ten aliphatic glucosinolates before AOP catalysis (upper part) and eight after AOP catalysis (lower part). The mQTL at 303.3 cM on chromosome 4 is at the AOP locus. The mQTL at 409.4 cM on chromosome 5 is at the MAM locus. A positive (negative) sign indicates that individuals carrying the Cvi allele have higher (lower) abundance than individuals carrying the Ler allele. The different colors represent different carbon chain lengths (black 3C; red 4C; green 5C; blue 6C; light blue 7C). (b) The mQTL profiles for six glycosylated flavonols. The mQTL at 88.6 cM on chromosome 1 is a putative glycosyl transferase, catalyzing the production of flavonoldihexosides. The different colors represent different aglycone classifications (black: quercetin; red: kaempferol; green: isorhamnetin), different line types represent different glycosylation patterns (solid line: dihexoside; dashed line: hexoside). (c) The detected mQTLs explain a percentage of the total variation observed between the RILs: the percentage of variance explained for the binary presence/absence of metabolite is on the x axis; the percentage of variance for the non-zero quantitative metabolite abundance is on the y axis. The green dots represent MAM mQTLs for glucosinolates; the red dots represent AOP mQTLs for glucosinolates; the blue triangles represent mQTLs for flavonols. (d) Visualization of the metabolic network using Cytoscape. The nodes represent different metabolites and the edges represent significant correlations. Glucosinolates are presented in a different color based on their carbon chain length—Hgray (3C), red (4C), green (5C) and blue (6C)—and flavonols are presented in pink.

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The mQTLs can underlie binary variation of presence/absence of the metabolite, quantitative variation of metabolite abundance or both types of variation in the segregants (Fig. 3c). For the detected 52 mQTLs, 22 mQTLs only underlie quantitative variation; seven mQTLs predominantly underlie binary variation and the rest underlies both types of variation. For example, two flavonols showed mQTLs 88.6 cM of chromosome 1 that underlie only quantitative variation, whereas the four other flavonols showed mQTLs at that position that underlie both binary and quantitative variation. Further interpretation of these mQTLs can be obtained from the QTL summary "qtlSumm," loaded by > data(qtlSumm).

A combined analysis of mass data and QTL profiles predicted that a single glucosinolate can have up to six mass peaks (1.2 on average, 6 glucosinolates had 3–6 mass peaks); a single flavonol can have up to four mass peaks.

Metabolic network (re)-construction

MetaNetwork computes the zero-order correlation "corrZeroOrder" and second-order partial correlation "corrSecondOrder" between pairs of metabolites, loaded by > data(corrSecondCorr) and > data(corrZeroOrder), respectively. Thirty-one second-order correlations were significant at a Bonferroni-corrected =0.05 level ("corrThres"=0.14 from 20,000 simulations). These significant correlations are plotted using Cytoscape (Fig. 3d). We can observe that glucosinolates and flavonols are separated into two networks because they have different mQTLs.

The similarities between the reconstructed and known glucosinolate pathway validate the approach, and the dissimilarities may suggest (but do not prove) possible previously unknown steps in the formation of glucosinolates. In the constructed network for glucosinolates (left in Fig. 3d), edges for the known transformation between the methylthio group and the methylsulfinyl group were always observed. But novel edges between metabolites were also observed, for example, the edge linking 2-propenyl to 4-methylthiobutyl (but the biochemical linkage may be indirect, that is, due to coregulation by the same mQTL). The reverse additive effect of the AOP locus for 4-hydroxybutyl, 2-propenyl and 4-benzoyloxybutyl formation shows that regulation can be completely different for different growth stages³.

Except one flavonol, all pairwise partial correlations among the other five flavonols remain significant (right in Fig. 3d). Colocation of mQTLs of these six flavonols suggests that the biochemical linkages are indirect, that is, variation in their abundance is attributable to a single locus affecting glycosylation of the basic flavonoid backbone³.

These results show how the combined genetic and metabolomic approach allows the (re)construction of metabolic pathways. It can provide an independent line of evidence to create new knowledge or to validate or modify current knowledge. Even an untargeted approach can therefore facilitate the annotation of metabolites and show that they play a role in existing or new pathways³. Although MetaNetwork can identify meaningful associations between metabolites, it can obviously not prove causality (i.e., that there are true biochemical linkages between highly correlated metabolites). Any output should therefore be treated as an independent source of information solely for the use of hypothesis formation and be used as guidelines for future experimental confirmation.

Although MetaNetwork is developed for and has been applied to metabolite data, its theoretical basis readily extends to other high-throughput quantitative measurements such as gene and protein expression. We expect that MetaNetwork will prove increasingly useful in elucidating systems genetics.

Note: Supplementary information is available via the HTML version of this article.