Alignment based similarity scoring methods distinguish positional isomers

The first step was to establish a template-based method to generate SMILES strings for lipids. We were able to write SMILES in a consistent and predictable manner using template-based structure drawing tools [23,24] and the Open Babel default SMILES algorithm (S1 Protocol). Given these strings, we then tested alignment methods and distance metrics, analogous to those used for protein or nucleotide sequences. Our quality criterion was based on the methods' sensitivity to detect small structural differences commonly found in lipids. The first test dataset consisted of a set of 17 ceramide molecules with the chemical composition C₃₄H₆₈O₄N₁. The position of the hydroxyl group was successively changed from position 2 to 18 at the fatty acid moiety, resulting in 17 isomeric molecules (Fig 1A and 1B). The shift of the hydroxyl group can be easily recognized in the SMILES strings. We then tested six similarity scoring methods (Fig 1C–1H, S1 Dataset). Three from the literature were used as described under Methods: FP2 Fingerprint [16] LINGO [15] and Bioisosteric similarity [17]. Three methods were introduced here: the SMILIGN, Smith and Waterman [18] and Levenshtein distance [19,20].

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Fig 1. Alignment-based distance calculation algorithms can distinguish isomeric lipid molecules.

(A) Structure of 17 ceramide molecules consisting of a C-16 sphingoid base (light green) and an amide-linked hydroxy fatty acid. The carbon atom number of the hydroxyl group position at the fatty acid chain (red) is used for naming individual molecules. (B) SMILES representation of first and last molecules. Colour coding of atoms is identical in SMILES- and structure- representations. (C-H) Heat map of pairwise distances calculated using Open Babel’s FP2 Fingerprint (C) LINGO (D) Bioisosteric (E) SMILIGN (F) Smith-Waterman (G) and Levenshtein distance (H) algorithms. Bioisosteric method uses CACTVS canonical SMILES, whereas for all other methods template-based SMILES were used. Colour bars in each panel indicate range of distances values of the particular method. Black pixels denote a distance of zero, indicating identical molecules. Numbers in rows and columns represent 1) the molecule name and 2) the position of hydroxyl group in fatty acid moiety.

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The first clear result is that a large subset of isomeric structures cannot be distinguished by either Open Babel FP2 Fingerprint or LINGO (Fig 1C and 1D). The FP2 Fingerprint algorithm computed a distance of zero for 78 pairs of ceramide isomers (Fig 1C–black pixels). LINGO gave a zero distance for 91 pairs of isomers (Fig 1D). This would only be correct if the molecules were identical. Both methods segment SMILES into shorter sub-strings (1–7 characters in the Path-length Fingerprint and 4 characters by LINGO) and apply the Tanimoto coefficient for determining distances. This segmentation loses the information on the position of the hydroxyl group. In contrast, the Bioisosteric algorithm distinguished all 17 isomeric structures, even though it uses CACTVS Canonical SMILES. There are no zero distances off the diagonal (Fig 1E). The Bioisosteric method also segments SMILES into sub-strings, but in a hierarchical manner, preserving information on the position of the hydroxyl group [17]. There is a distinct pattern in the heat map of the Bioisosteric method characterized by a gradual increase in distance values for isomers having the hydroxyl group closer to the terminal methyl carbon. The Bioisosteric method returns a distance of 0.13 units for the shift of the hydroxyl group from position 5 to 7 (Fig 1E–yellow pixel), but returns 0.26 units for position 10 to 12 and for positions 16 to 18, a distance of 0.41 was calculated (Fig 1E—blue pixel). This dependence of the distance values on the position of the hydroxyl group leads to an unwanted weighting, which is a clear problem with the approach.

In the SMILIGN algorithm, SMILES strings are treated as if they were amino acid sequences and a multiple sequence alignment was calculated with MUSCLE [25]. Similarity within pairs of lipids was calculated using an identity matrix. The SMILIGN method distinguished all 17 ceramide isomers (Fig 1F), but we noticed an irregular distribution of distance values. For example, comparing molecule pairs where the hydroxyl group was shifted by one position 11–12, 12–13, 13–14 and 14–15 resulted in four different distance values of 0.03, 0.13, 0.25 and 0.06 units respectively. In this regard, we identified two problems with the algorithm. First, there were several misalignments that lead to incorrect distances (S1 Dataset, worksheet 5). Second, one needs 35 characters to represent all the structural details of all lipid molecules of the LMSD, but the software is limited to only 20 characters and too much information is lost. To overcome these two limitations of SMILIGN, we tested two pair-wise alignment methods that do not require conversion to amino acid sequences.

With the Smith-Waterman method, pair-wise alignments are carried out directly with the SMILES strings. All ceramide isomers were distinguished, but we noticed an anomaly in distance values for molecules 17 and 18 (Fig 1G). A closer examination of the pair-wise alignments revealed an inherent issue when applying local alignment procedure to lipids. In the aligned SMILES pairs 2–17 and 2–18, the hydroxyl groups in the fatty acid were ignored, while for the pairs 2–15 and 2–16 the characters were retained (S1 Dataset, worksheet 6). The Smith-Waterman algorithm is designed to find high scoring regions in strings, so differing ends are ignored by design and not by accident. This means that functional groups at the omega position are ignored, despite their role in biology [26]. Although one could try to adjust parameters, the Smith-Waterman method is fundamentally not appropriate for this kind of comparison.

Finally, we tested the Levenshtein distance for measuring similarities between lipid molecules (Fig 1H). Unlike Smith-Waterman, the Levenshtein approach always aligns all characters for a given pair of SMILES. This method was the most successful. It distinguished all ceramide molecules and for each molecule, it correctly scored and ranked distances up to the molecule’s third closest isomers. From the fourth closest isomer onwards, a fixed distance of 0.12 was determined. Unlike other methods, it guarantees a symmetric distance matrix with no unwanted weighting of groups due to their positions. These tests of structural similarity measures led to two conclusions. First, the alignment step is necessary. Second, the Levenshtein distance was most likely to be generally applicable for all molecules in a lipidome.

From structural similarity to chemical space

A set of distances between n molecules defines an (n − 1) dimensional space. The coordinates of molecule i are simply the distances to all members of the set (including the zero distance to molecule i itself). This is formally a vector space, in which similar molecules will have similar coordinates. It is, however, not very compact and because of structural similarities, coordinates in some dimensions would be highly correlated with others. Principal component analysis (PCA) was then used to reduce the dimensionality and see how much information would be lost. The first test was performed on a set of 16 phosphatidylinositol molecules (S1 Protocol).

Considering just the first two principal components was sufficient to highlight problems with some of the distance measures. For example, the map in Fig 2A shows a clear weakness with the Bioisosteric method. The extension of the fatty acid chain at the sn2 position and degree of unsaturation are not accurately represented (Fig 2A, scatter plot). We also computed the Euclidian distance between molecules in the plane of the first two components. This showed an inconsistent trend in the distance increase with each structural alteration (Fig 2A, bar graph). Principal components can often be interpreted in terms of the original descriptors and in the case of SMILIGN, the first two components are dominated by the extension of the acyl chain at the sn2 position (Fig 2B). For SMILIGN, the first two principal components are not sufficient to distinguish molecules that differ only in the presence of a double bond, but the third principal component does capture it (S1 Fig).

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Fig 2. The relationship between phosphatidylinositol (PI) molecules is retained in a two dimensional structural space.

Pairwise distances between 16 PI’s were calculated with Bioisosteric, SMILIGN, Smith-Waterman and Levenshtein methods (A-D). PCA was carried out on the distance matrices to generate two- and three- dimensional maps. The contribution of each principal component to the total variance is shown in brackets. Molecules with double bonds are in grey and without double bonds are in black. Euclidian distances between the first PI molecule and all others in the PC1-PC2 plane are shown as bar graphs on the right side of panels. Molecules were numbered according to the length of the sn2 acyl chain length, wherein an underlined number xx indicate the presence of the double bond.

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In contrast, distances based on Smith-Waterman and Levenshtein algorithms reflected all gradual structural changes in the molecules (Fig 2C and 2D). In both cases, the projection leads to a set of points in a U shape and, if we take molecule 10 as a reference, stepwise changes to the chemistry are reflected in distinct shifts in the principal coordinates. We further recognized that the changes in coordinates, when the acyl chain is extended by two methylene groups (molecules 15–17, 17–19) are about twice as large as the difference between pairs differing by a single methylene group (Fig 2C and 2D). The first two principal components combined, accounted for 95% of the variability in the underlying data set for Smith-Waterman and Levenshtein. Summarizing the results, we see the Levenshtein method coupled with template-based SMILES as the best approach for calculating structural differences in small molecule sets. PCA is an appropriate way to reduce dimensionality and the relation between molecules can be depicted in a PCA map, which we treat as chemical space.

The set of 16 phosphatidylinositol molecules is useful for highlighting details, but one is interested in using the method on much larger molecule sets. To this end, we used the 3510 sphingolipids (SP) from LMSD as a test dataset [22]. All lipid structures were converted into template-based SMILES and pair-wise distances were computed using the Levenshtein method. Fig 3A shows the position of all molecules in terms of the first three principal components. There are two clear observations. First, three principal components account for 99% of the total variance (Fig 3A) and no two SP's have the same coordinates (S2 Dataset, worksheet 1). Second, there was no biochemical knowledge put into the procedure, but the molecules naturally cluster into chemically similar groups (Fig 3A). Sphingosines, ceramides and phosphosphingolipids were clustered separately from the complex glycosphingolipids (GSL). Furthermore, the acidic and neutral GSL where placed in different clusters. Looking at the globo, lacto, neolacto and isoglobo series of neutral GSL, one can see changes in the sugar moiety and a clear separation from the simple Glc series (Fig 3B). This observation fits the intuitive expectation that the Glc series with simple sugar moieties (glucose, galactose or lactose) should be farther from lipids with complex sugars. We noted that changes in the sugar moiety of neutral GSL, which have a strong impact on biochemical behaviour, were separated by a larger distance compared to changes in the ceramide backbone (Fig 3B). In addition, we were intrigued by the recurring appearance of geometric patterns in the form of I, C and L shapes and investigated the structure within these clusters. Within each cluster, lipids were organized based on changes in the ceramide moiety (Fig 3C) so that, for example, eight molecules of the isoglobo series formed a twisted L shape with each successive lipid carrying a gradual change in the ceramide backbone (Fig 3C–light brown coloured points). Analogous geometric arrangements were observed for the globo, lacto and neolacto series (Fig 3C–red, violet and light-blue points). Next, we tested how all 30 150 lipids of the LMSD would be organized in a chemical space based on only structural similarity. All lipid molecules had unique coordinates in this space (S2 Dataset, worksheet 2), indicating that our approach can distinguish between all lipid structures within known, natural lipidomes. With no additional input, the method grouped lipids into clusters that correspond to the popular lipid classification of LIPIDMAPS (Fig 4A) [27].

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Fig 3. The structural space model clusters thousands of sphingolipids (SP) according to their chemical relationship.

(A) Three-dimensional map of 30 510 SP obtained by PCA from a pair wise distance matrix calculated with Levenshtein distance. (B) Plot of all neutral SP within the same coordinate system as (A) indicating several associated glycosphingolipid series. (C) Complex glycosphingolipids are highlighted showing the influence of structural changes in the ceramide backbone and sugar moiety.

https://doi.org/10.1371/journal.pcbi.1004511.g003

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Fig 4. Spatial distribution of related phosphatidylcholines (PC) molecules remains stable in the background of large structure data sets.

(A) Lipid map of 30 150 lipid molecules obtained from LMSD. Pairwise distances were calculated using the Levenshtein method of template-based SMILES. (B) Structures of the 14 PC molecules. Molecules are named based on the number of carbon atoms of the sn2 acyl chain. (C) Two-dimensional map of the selected PC molecules displaying their chemical relation to each other. Euclidian distances in PC1-PC2 plane between the smallest molecule (name 12) and all others are shown in the bar graph. (D) Spatial distribution of 14 PC in the background of 30 136 lipids determined from three principal components and projected on the PC1-PC2 plane. Euclidian distances between first molecule (name 12) and all others were determined from the first two principal components and its trend is shown as bar graph.

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Fatty acyls, glycerophospholipids (GPL), sphingolipids (SP) and polyketides occupied opposite ends of the chemical space (Fig 4A). In contrast, glycerolipids and GPL shared a common region because of their head group similarity. Sterol lipids formed a distinct cluster due to their unique four-ringed core structure. Prenol lipids were widely distributed in the chemical space reflecting their varying chemical composition. For GPL, we observed several distinct clusters, which on closer examination, could be recognized as spatially separated lipid classes like phosphatidylcholine (PC), phosphatidylserine (PS) and phosphatidylinositol (PI) (S2 Fig).

The spatial organization of lipids is robust to changes in background molecule ensemble

As with the set of PI molecules described above (Fig 2D), the PC molecules in the two-dimensional representation form an inverted U pattern (Fig 4C). However, the PC molecules formed a flipped L pattern if all other 30 136 lipids of the LMSD were present (Fig 4D). In both cases (Fig 4C and 4D), the sequential arrangement of the PC molecules in the two-dimensional chemical space accurately represents the gradual increase in acyl chain length. We also observed a gradual increase of the Euclidian distance from the first PC molecule to the last (Fig 4C and 4D, bar graphs). When we gradually increased the complexity of the set of lipid molecules, we noticed that the PCA approach could disturb relationships between structurally similar molecules. In the case of a set consisting of only GPLs and only GPLs and SPs (S3 Fig), we noticed that the distances between molecule 12 and molecules 21–26 did not reflect the sn2 chain length increase anymore. Interestingly, one can observe that the gradual addition of more diverse lipid structures spanning a broader chemical variety compensates for this bias. At the same time we recognized that for other lipid classes like cholesteryl esters and triacylglycerols (TAG) incremental changes in the acyl chains cluster together (S4 Fig). In case of TAG molecular species, a homologues series can be recognised due to the difference of one double bond on the sn3-linked fatty acid (S4C Fig). It seems that the Levenshtein distances and the projection to a chemical space automatically reconstructs conventional lipid class definitions while also clustering closely related molecules in accordance to chemical rules. The next natural step is to test these lipid coordinates, computed from template based SMILES and Levenshtein distances, for their suitability for analysing and comparing complete lipidomes.

The Lipidome jUXtaposition (LUX) score, a single metric for calculating the similarity between lipidomes

The approach to lipidome comparison was then tested on real data. All lipids from four yeast strains BY474, Elo1, Elo2 and Elo3 [6] were combined, yielding a reference lipidome with 248 members, each with unique coordinates (S3 Dataset, worksheet 3). For clarity, this is shown in a 2D map (Fig 5A), which is the basis of comparisons of the four strains and two culturing temperatures (24°C and 37°C). Triacylglycerols (TAG) occupy the largest area on the map in terms of the number and variety of structures. Mannose-bis(InositolPhospho)Ceramides [M(IP)₂C] form a distinct cluster located in the top-left quadrant of the reference map. In the top right quadrant of the reference map, there is a cluster of GPLs consisting of phosphatidic acid (PA), phosphatidylethanolamines (PE), phosphatidylcholines (PC) and TAG. The reference lipidome map clearly shows temperature- and strain-specific changes. The lipidomes of the wild type yeast strains BY4741 and Elo1 grown at 24°C showed only minor differences (Fig 5B). In contrast, the lipidome of the Elo2 mutant is very different to the wild type strain BY4741 (Fig 5C). The mutation has led to dramatic changes amongst the inositol phosphorylceramides (IPC) seen in the top-left quadrant and the appearance of new species not present in the wild type. Using this well-defined lipidome map, one can determine the closest related lipid in the wild type strain. If one calculates the distances that lipids would have to move to make the members of each pair overlap, one can use the Hausdorff distance to compare lipidomes (Fig 5C and 5D, arrow marked lipids). For that, we chose the coordinates of all lipids in the two dimensional coordinate system of the first lipidome and determined the Euclidean distance to its closest structural neighbour in the second. Subsequently, the average of all distances was determined, including all distance values of zero for identical molecular species. Because the Hausdorff distance depends on the direction of the comparison, we used the maximum of the two values (max(d_AB, d_BA)). We named this measure as the ‘Lipidome jUXtaposition (LUX) score’. This score is a distance, so larger values indicate more dissimilarity and identity results in a LUX score of zero. From that perspective, one can see that the LUX score between BY4741 and the Elo2 strain is three-fold larger than the distance between BY4741 and Elo1 (Fig 5B and 5C).

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Fig 5. Lipidome maps highlight relationships between yeast strains.

(A) All lipids from yeast strains, BY4741, Elo1, Elo2 and Elo3 cultured at 24°C and 37°C are combined to create a reference map of the yeast lipidome. Each coloured circle corresponds to a unique lipid. (B) Comparison of lipidomes from strains BY4741 and Elo1 (cultured at 24°C). Arrows in first plot indicate lipids that are present in Elo1, but not in BY4741 and vice versa in the second plot. (C) Comparison of BY4741 and Elo2 lipidomes. A two dimensional Lipidome jUXtaposition (LUX) score is calculated for a pair of lipidomes using reference-map coordinates (S3 Dataset, worksheet 3).

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Next we evaluated the LUX score by computing a hierarchical clustered tree of all eight reported lipidomes of yeast (Fig 6A) and compared it to dendrograms based on the lipid concentrations (Fig 6B), and by simply counting common lipids (Fig 6C). This allowed us to test if our approach can correctly depict the genetic and phenotypic relationship between the yeast strains reported earlier [6]. A dendrogram based purely on correlation of lipid abundances would neglect the structural changes in the lipidome. This approach implies that the largest difference can be found between BY4741 and Elo1 mutants grown at 24°C and 37°C (Fig 6B). Alteration in lipid class profile as well as increased fatty acid length and less double bond content was reported in response to increased growth temperatures [9]. This response however, is well captured in a solely quantity-based lipidome comparison (Fig 6B) because most of the molecular species are present at different temperatures. The tree computed from the LUX score as well as common lipid count indicates that mutation of the Elo1 gene had less influence on the composition of the lipidome than the temperature shift. Both strains, BY4741 and Elo1 were closest neighbours to each other at the culturing temperature of 24°C and 37°C. The lipidomes from mutant strains Elo2 and Elo3 were clustered together using the LUX score (Fig 6A) but in counting common lipids, Elo2 clustered with BY4741 and Elo1 (Fig 6C). This marks the major difference between both metrics. It was reported that no aberrant phenotype for Elo1 was observed and that Elo2 and Elo3 had distinct alterations in their intracellular organization [6,28], which seems better represented with the LUX score. However, we verified this finding with an error model that modify only the presence and quantity for low abundant lipids to estimate a robustness for the observed clustering. One can recognize that the LUX score (Fig 6A) as well as the common lipid count (Fig 6C) comprise a sufficiently robust tree topology and groups Elo2 systematically different. We concluded from this experiment that compositional differences itself are useful to assign a phenotype while comparison purely based on quantities are dominated by changes of abundant lipids (Fig 6B). We also note that just counting of lipids is a simplistic, binary measure of compositional differences. In contrast, the LUX score provides a refined measure of lipidome structural diversity, which we recognize as an advantage.

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Fig 6. The LUX score accounts for genetic alteration of yeast strains.

For the yeast strains, BY4741 (wild type), Elo1, Elo2 and Elo3 (Elongase mutants) cultured at 24°C and 37°C, dendrograms were computed from two-dimensional LUX scores (A) Comparing concentrations of common lipids (B) and counting the percentage of common lipids in a pair of lipidomes (C). All dendograms are based on complete linkage using Euclidean distance as the similarity metric (a.u—arbitrary units). The number of occurrences for each branch in 100 iterations is indicated with coloured numerals that correspond to the utilized parameter set for detection threshold t_detect and standard deviation s applied in the error model (see methods).

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The complexity of the yeast lipidome comparison is relatively small compared to higher organisms. Nevertheless, the two-dimensional structural space reflecting 63% of the overall variability of the dataset (Fig 5A) is sufficient to determine lipidome similarities based upon the LUX score. We also note that the tree topology does not change whether one uses just three principal components (covering 83% of the variability) or the original pairwise distance matrix (S4 Dataset).

The LUX score enables tissue lipidome comparison

Next, we tested the LUX score on the more complex tissue lipidome of Drosophila [8]. In this experiment the lipidome composition of six different larval tissues (gut, lipoprotein, fat body, salivary gland, wing, disc, and brain) were determined in conjunction with two nutrition regimens (yeast food and plant food). In contrast to the yeast dataset, the fatty acid composition and sphingosine structures were not defined, so lipid structures were compiled based on prior knowledge detailed in S3 Protocol. In our analysis, we included 346 lipids structures of 12 classes, which corresponds to 97.2% coverage of the reported lipidome. The structural repertoire of the larval tissue lipidomes is shown in Fig 7A and 7B. For visualization purposes, one is obviously bound to two and three dimensional representation, but because of the set's complexity, we prefer the LUX score based on the original high-dimensional distances for biological interpretation. As one would expect, the dendrogram topology is somewhat sensitive to the dimensionality of the LUX score (Fig 7C–7E). Nevertheless, interesting properties of the larval tissue lipidome are recognizable in all dendrograms. The fat body shows the strongest influence regarding the nutrition regimen of all tissues (Fig 7C–7E). This is consistent with the expectation that the primary storage organ of the larvae reflects the nutritional differences more strongly than other tissues. All other tissues exhibit a systematic compositional shift, but with less than half the LUX score value. Interestingly, the gut lipidome was the least affected by the nutrition, which points to its function as barrier organ, where the lipid composition is tightly controlled to maintain cell membrane integrity. We further recognize that the salivary glands and wing discs lipidomes are clustered together. Using the complete distance matrix, these are the only tissue where the compositional shift induced by the nutrition is scored slightly higher than tissue lipidome similarity (Fig 7E). That might point to the lower structural specificity of the LUX score, that has to be expected because fatty acid composition of the phospholipids and sphingolipids were not experimentally defined. However, even with this limitation, one can cluster lipidomes in a manner similar to gene expression analysis.

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Fig 7. Hierarchical clustering of Drosophila tissue lipidomes based on the LUX score.

(A) Two dimensional reference lipidome map of 6 Drosophila larval tissues (gut, brain, wing disc, salivary glands, fat bodies and lipoprotein) grown on Yeast Food (YF) and Protein Food (PF). (B) The same reference lipidome depicted in the three dimensions. The PC1/PC2 plane is situated on the bottom of the three dimensional representation. Dendrogram were computed on the basis of the pairwise LUX derived from the two dimensional (C) and three dimensional chemical space model (D). (E) Hierarchical cluster tree based on the matrix of pairwise Levenshtein distances of all 346 lipid molecular species. All dendrograms are based on complete linkage using Euclidean distance as the similarity metric (a.u—arbitrary units).

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Lipid structure datasets

Lipid structures for Figs 1 and 2 were drawn and SDF files were generated using PubChem Sketcher [34]. The complete LIPIDMAPS Structure Database (LMSD) in SDF format was downloaded on Nov 9, 2011 from www.lipidmaps.org (LMSDFDownload9Nov11.zip) [22].

Lipidome data of yeast mutants was taken from Ejsing et.al. [6]. LIPIDMAPS structure drawing tools were customized to draw all required lipid structures for yeast. For ergosterol and ergosta-5,7-dien-3β-ol, SDF files were obtained from the LMSD. SMILES for phytosphingosine 1-phosphate was made by hand from the corresponding phytosphingosine. For some molecules, the number of hydroxylations and double bonds was known, but their position was not. In these cases, a list of possible isomers was generated. The position of double bonds and hydroxylations in yeast fatty acids were taken from previous studies [35]. Pairwise distances between all isomers were calculated using the Levenshtein distance method [19,20]. The isomer with smallest average distance to other isomers was chosen as representative molecule (S2 Protocol).

Lipidome data for Drosophila is based on Carvahlo et al. [8] described in detail in S3 Protocol.

Template-based SMILES

LIPIDMAPS perl scripts were modified to generate a wider spectrum of lipid structures [23,24]. These scripts are provided in supplementary information (S5 Dataset) and also available at http://lux.fz-borstel.de. Molecular structures in SDF format were converted to SMILES using the OpenBabel molecular conversion tool with the default algorithm [16]. Characters indicating chirality, cis–trans isomerism and charges were removed automatically for the yeast lipidome analysis.

Structural similarity scoring methods

Six similarity scoring methods were tested 1) OpenBabel FP2 Fingerprint 2) LINGO 3) Bioisosteric similarity 4) SMILIGN 5) Smith Waterman Local Alignment 6) Levenshtein distance. Details are given in supplementary methods (S1 Methods). The Levenshtein method was applied for analysing the LMSD, yeast and Drosphila lipidome (Figs 4–7). This algorithm was originally designed for correcting spelling errors, but the principle can be applied to compare any pair of strings including SMILES [19,20]. The source code used in this study is provided in supplementary information (S5 Dataset) and also at the website http://lux.fz-borstel.de.

Lipidome Juxtaposition Score (LUX) calculation

The LUX score is based on the Hausdorff distance [36] and summarizes the similarity between lipidomes. In pseudocode, the distance from lipidome A to B is calculated from:

for each lipid in A

 find distance d to most similar lipid in B

 d_sum ∶ = d_sum + d

 n = n +1

return d_sum/n

This yields the average shortest distance d_AB from A to B. The larger of d_AB and d_BA was used as the lipidome homology score (AB).

Hierarchical cluster analysis

Complete linkage clustering was performed with R, version 2.14.1, library–‘stats’ and function ‘hclust’ using the LUX score, Pearson and common lipid count as similarity metrics. An error model for the yeast lipidome analysis was computed by iterating all lipid quantities x of the original data set according to:

for each lipid with abundance x

 x' = x + rnorm(1,0,s)

 if x' > t_detect

return x'

The detection limit t_detect and standard deviation s were defined so that only low abundant lipids were significantly affected. We chose the following three parameter sets: 1) t_detect = 0.003 mol %- 4.3% of all reported quantities, s = 0.001mol %- 11.4% of all reported standard deviations 2) t_detect = 0.003 mol %, s = 0.002 mol%- 20.3% of all reported standard deviations and 3) t_detect = 0.006 mol%- 8.7% of all reported quantities, s = 0.004 mol%- 34.7% of all reported standard deviations. The number of occurrences for each branch was counted after 100 iterations using the R library, ape::boot.phylo::prop.part.