1. Supporting Materials and Methods
Chemicals
All chemicals were purchased in analytical grade from Sigma-Aldrich (Taufkirchen,
Germany) and Merck (Darmstadt, Germany), respectively.
Terminology
Analytics: Throughout this text we use the term ‘peak’ to designate a mass spectral
feature which is described by a mass-to-charge ratio (m/z) and a retention index (RI). The
term ‘analyte’ designates a chromatographic peak which is the convolute of a single or
many mass spectral features. For downstream analysis each analyte is represented by a
single mass spectral feature using its peak height for analyte quantification.
Datasets: The ‘metabolite dataset’ comprises the normalized measured peak heights
(analyte abundances) for each evaluated peak across the metabolite profiles and contains
missing values (Tab. S3). The ‘quantification dataset’ designates the metabolite dataset
where the replicates of the replicate groups with completely missing values are replaced
by random values sampled from a Gaussian distributed as simulated background / noise
distribution. This dataset still contains missing values. The ‘complete dataset’ designates
the quantification dataset with fully imputed missing values.
GC/MS data processing and compound identification
Peak alignment: An initial non-targeted metabolite fingerprint alignment was generated
using msPeak to construct a targeted peak library for further quantitative analyses. For
this, the GC/MS chromatograms were exported using Leco ChromaTOF software
(version 3.25) as NetCDF files (Andi MS format) with the following settings: baseline
subtraction just above the noise, peak width broadening using width-to-time (w/t) of 3.5 /
0 sec – 6.0 / 1 400 s. Peak smoothing (as running mean with 7 data points), peak apex
search (as local maxima search with 11 data points) and alignment using peak spread and
peak gap to neighboring peaks were performed within msPeak for each mass trace
separately. The peak list for each chromatogram was exported for post-processing.
Peak redundancy: To reduce the redundancy of peaks potentially derived from the same
analyte, a time - similarity (T/S) clustering approach was used (Krueger et al 2011). In
detail, peaks were grouped according to their RI (adjusted retention time based on FAME
retention) into time groups with 0.25s resolution. The similarities among time group
members were computed on raw peak heights using Pearson and Spearman correlation
(Sokal 1995). Both similarity matrices were averaged (sØ) and converted into a distance
range using the equation (1 – sØ) / 2. The distance matrices were then clustered using
hierarchical average linkage clustering (Legendre 1998) and the resulting trees cut at
0.146 heights (sØ = 0.707). Thus, the obtained clusters reflect about 50% of the local
variance among assigned peaks within a cluster. The T/S clusters were manually
evaluated and curated (i) to remove ambiguous or badly shaped peaks, (ii) to identify a
single peak as reliable quantification fragment for an analyte, and (iii) to remove already
known analytical byproducts and artifacts. The resultant peak library consists of 643
quantification peaks including analytical standards and thus represents 4.5% of the initial
peak set. This peak library was used for targeted peak extraction with narrow time
windows (on average ±0.8s around the peak specific average RI) using the exported peak
lists.
Peak annotation: Compound identification was performed using several reference
compound libraries of commercially available authentic standards measured as described
(Huege et al 2011, Kopka et al 2005, Krall et al 2009). All annotations were manually
curated and linked to the quantification peak-dataset.
GC/MS data analyses
Data normalization: In subsequent data analyses steps various profile-wise normalization
approaches were applied. To keep the normalized peak heights within the original
measurement scale, each sample profile was divided by the ratio of its corresponding
profile-specific scale parameter to the mean of estimated scale parameters across all
profiles.
Data pre-processing: To account for analytical variations during sample derivatization
and extraction the quantification peak-dataset was normalized first to the total ion count
of the RI markers and secondly to the U-13C-Sorbitol peak height. All 14 analytical
standards were afterwards removed. To further filter the dataset for relevant peaks,
following criteria were applied:
(i) peaks detected in at least 50% of the measured biological replicates (3 out of 5,
majority rule),
(ii) peaks clearly above their corresponding blank peaks, i.e. the average sample peak
height minus 2 times standard error is larger than the corresponding blank
average peak height plus 2 times standard error,
(iii)peaks revealing an average fold change greater than the robust average fold
change within the blank replicates with a lower and upper fold-change bound
of 1.5 and 3,
(iv) peaks revealing an average peak height of ≥1000 arbitrary units
All criteria must be fulfilled in at least one out of the nine replicate groups (genotype ×
treatment) to consider a peak as being validly measured. This filtering resulted in 529
quantification peaks that are kept for further downstream analysis. Subsequently, the
blank samples were removed resulting in a filtered data matrix of 529 peaks and 45
profiles. To account for sample amount variations, the profiles were normalized using the
optical density as biomass equivalent.
Data post-processing: To further correct for experimental and technical variations a
modified version of the Progenesis CoMet normalization was applied (Nonlinear
Dynamics Limited, 2014). This approach aims to identify robust, non-changing peaks
considered as "spikes" for estimating a robust scaling factor. Briefly, peaks were
expressed as log2-ratios to their corresponding groupwise reference profile, estimated
using one-step Tukey's biweight (Affymetrix, 2002) over the five biological replicates.
Outliers were removed globally using a full (n-step) Tukey's biweight until no further
outlying ratios were detected. In total, 90 peaks were considered robust, as no outlying
ratio was detectable, and thus, were used for profile normalization. The scaling factor for
each profile was estimated and applied as the anti-log of the mean of the log-ratios. The
resultant dataset was further normalized using variance-stabilizing transformation without
calibrating (Huber et al 2002).
Data evaluation: The resultant dataset was evaluated for univariate outliers over all peaks
within each of the nine replicate groups. Only values detected by both, a boxplot statistics
and one-step Tukey's biweight are considered as outliers. In total, 944 (3.97%) univariate
outliers were detected and treated as missing values. Subsequently, the peaks were
evaluated for reliable quantification using their groupwise coefficient of variation (CV).
For this, the mean average, the Tukey's biweight, and the median over all groupwise CV
values were estimated and outliers were removed by iterative boxplot statistics. Peaks
revealing outlying values in the majority of cases (2 out of 3) were removed from further
analysis. The final metabolite dataset (Tab S3) comprises 501 peaks and 45 sample
profiles with a total of 2082 (9.23%) missing values.
Data imputation: For 93 out of all 4509 combinations of peak and replicate group no
measureable peak was detectable in the 5 biological replicates, illustrating qualitative
differences between genotypes and / or treatments. These peaks are most likely below the
detection level or within the noise of the method rather than truly absent. For those 93
combinations a simulation approach was chosen to simulate values within the methods
background / noise for missing value imputation. To estimate global noise, the median
and the 95% quantile were computed for combinations with ≤2 measurements (minority
rule), resulting in 437 and 1419 arbitrary units respectively. The standard error (SE) was
estimated as 95% quantile for all combinations with >3 measurements (majority rule)
revealing a groupwise maximum peak height of less than 1419 arbitrary units. The
resulting global noise was considered as 437 ± 212 (as mean and SE) and used to random
generate values from a normal distribution constrained with the global noise parameter.
The resultant quantification dataset contains 7.17% missing values. The remaining
missing values were imputed by principal component analyses (PCA) on log2transformed and mean-centered data using Bayesian model, probabilistic model as well
as by a linear combination of the k most significant eigengenes (Stacklies et al 2007) and
the resulting complete datasets were back-transformed. The robust mean estimated using
one-step Tukey’s biweight of the three different imputation outcomes was used to finally
replace missing values.
Statistical analyses and visualization
All data and statistical analyses were performed if not otherwise stated according to
(Sokal 1995) and (Legendre 1998) using R 3.0.2 (R Development Core Team, 2013).
Univariate outliers, extreme deviations from the center, were detected by (i) boxplot
statistics and (ii) Tukey's biweight. The boxplot statistics was performed with a
coefficient of 1.5 and values which lie beyond the extremes of the whiskers were
considered as outliers (cf. (Steinhauser et al 2011)). The Tukey's biweight algorithm was
performed with a tuning constant of 5 (Affymetrix, 2002) and observations with a weight
of 0.0 were considered as outliers. Both approach were executed either in one step or
iteratively with n-steps, i.e. repeated until no outliers were detectable anymore.
Multivariate outliers were detected by calculating the robust Mahalanobis distance based
on a robust estimate of the center and the covariance with the minimum covariance
determinant (MCD) estimator (Rousseeuw and Van Driessen 1999). Outliers were
detected by using the 97.5% quantile of a chi-square distribution with p degrees of
freedom (χ2p), as the observed distances are approximately chi-square distributed.
Coefficients of variation (CV), the ratio of the standard deviation to the mean, were
expressed as percentages. The uniqueness of peaks was estimated using a time similarity clustering approach (see above) with varying time window and similarity
cutoffs. The uniqueness was computed as the fraction of clusters with one member to the
total of estimated clusters and expressed as percentage.
Euclidean distances were computed either on the log2-transformed datasets or on the
estimated component scores from principal component analyses and subjected to various
clustering and visualization approaches. Cluster trees were drawn on the basis of
hierarchical cluster analysis (HCA) using average linkage clustering. Partitioning around
medoids (PAM, k-medoids), a more robust version of k-means clustering, was used for
clustering sample profiles (Kaufman 2005). K-means clustering was performed for
finding peaks revealing similar abundance patterns using initialization with cluster
centers derived from HCA analysis. Gap statistic, a goodness of clustering measure, was
performed to estimate the number of supported clusters (Tibshirani et al 2001). Euclidean
distance matrices were converted into principal coordinates space using classical
multidimensional scaling (CMD; (Cox 2000)).
Non-parametric analysis of variance by means of Mantels test was performed as
Pearson’s matrix correlation (rm) with 9999 bootstrap samples between the Euclidean
distance matrix and a design matrix, a binary (0, 1) matrix representing cluster
assignments. The silhouette information (SI), a combined measure of the separation
among and cohesion within cluster / cluster members, was expressed as mean silhouette
width (Rousseeuw 1987). Both cluster validity indices yield values in the interval of [-1,
1], in which larger positive values reflect more favorable cluster solutions. The variation
of information (VI) index was used to evaluate the similarity between observed and
expected clustering’s (Meila 2007) with VI values closer to 0 revealing a better
agreement. Principal component analysis (PCA) was performed on the log2-transformed
and mean-centered complete dataset using singular value decomposition (Venables 2002).
The number of optimal principal components (PC’s) were estimated using parallel
analysis and optimal coordinates approach (cf. (Cangelosi and Goriely 2007)).
Confidence ellipses were drawn for a 95% region using the correlation, mean and
standard deviation of data points.
Two-way factorial analysis of variance (ANOVA) was performed with genotype,
treatment (time), and genotype × treatment interaction as factors. Tukey's ‘Honest
Significant Difference’ (HSD) method was used as post-hoc test to estimate the
differences between the means of the levels of factors. If not otherwise stated all p-values
(p) were corrected by Benjamini – Yekutieli correction to control the false discovery rate
in multiple testing (Benjamini and Yekutieli 2001).