EXPLORATION OF REACTANT-PRODUCT LIPID PAIRS IN MUTANT-WILD TYPE LIPIDOMICS EXPERIMENTS

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1 Kasas State Uiversity Libraries Aual Coferece o Applied Statistics i Agriculture - 4th Aual Coferece Proceedigs EXPLORATION OF REACTANT-PRODUCT LIPID PAIRS IN MUTANT-WILD TYPE LIPIDOMICS EXPERIMENTS Liaqig Zheg Gary L. Gadbury Jyoti Shah Ruth Welti Follow this ad additioal works at: Part of the Agriculture Commos, ad the Applied Statistics Commos This work is licesed uder a Creative Commos Attributio-Nocommercial-No Derivative Works 4. Licese. Recommeded Citatio Zheg, Liaqig; Gadbury, Gary L.; Shah, Jyoti; ad Welti, Ruth. "EXPLORATION OF REACTANT-PRODUCT LIPID PAIRS IN MUTANT-WILD TYPE LIPIDOMICS EXPERIMENTS," Aual Coferece o Applied Statistics i Agriculture. This is brought to you for free ad ope access by the Cofereces at. It has bee accepted for iclusio i Aual Coferece o Applied Statistics i Agriculture by a authoried admiistrator of. For more iformatio, please cotact cads@k-state.edu.

2 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity EXPLORATION OF REACTANT-PRODUCT LIPID PAIRS IN MUTANT-WILD TYPE LIPIDOMICS EXPERIMENTS Liaqig Zheg, Gary L. Gadbury *, Jyoti Shah, Ruth Welti 3 Departmet of Statistics, Kasas State Uiversity, Mahatta, KS 6656, Departmet of Biological Scieces, Uiversity of North Teas, Deto, TX Divisio of Biology, Kasas State Uiversity, Mahatta, KS 6656 *Correspodig Author: Gary L. Gadbury, Departmet of Statistics Kasas State Uiversity Mahatta, KS 6656 phoe: , gadbury@ksu.edu Abstract: High-throughput metabolite aalysis is very importat for biologists to idetify the fuctios of gees. A mutatio i a gee ecodig a eyme is epected to alter the level of the metabolites which serve as the eyme s reactats also kow as substrate ad products. To fid the fuctio of a mutated gee, metabolite data from a wild-type orgaism ad a mutat are compared ad cadidate reactats ad products are idetified. The screeig priciple is that the cocetratio of reactats will be higher ad the cocetratio of products will be lower i the mutat tha i wild type. This is because the mutatio reduces the reactio betwee the reactat ad the product i the mutat orgaism. Based upo this priciple, we suggest a method to scree metabolite pairs for cadidate reactat-product pairs. Metrics are defied that quatify the effect of a mutatio o each potetial reactio, represeted by a metabolite pair. For reactios catalyed by well-characteried eymes, oe or more biologically fuctioig reactat-product pairs are kow. Kowledge of the fuctioal reactat-product pairs iforms the developmet of the metrics. The goal is for rakig of the metrics for all possible pairs to reflect the likelihood that a particular metabolite pair is a fuctioal reactat-product pair. Key words: Lipid eperimet; Pathway aalysis; Reactat-product lipid pairs; Metabolome; Statistic distributio;. Itroductio The metabolome is the total collectio of the set of small molecule metabolites Oliver et al. 998; Oliver ; Griffi ad Vidal-Puig 8; Du et al. 5. The metabolome icludes metabolic itermediates, hormoes, ad other products ad itermediates of metabolism. Ulike the geome ad the proteome whose elemets are composed of similar buildig blocks, the metabolome is a group of dyamic molecules with varied structures. Biologists use metabolic profilig to get a sapshot of the compositio of metabolites to uderstad biomolecular fuctios withi orgaisms. Sice metabolites are products of gee ad protei fuctio, it ca be argued that they provide the most complete descriptio of cellular fuctio Wu et al. 5; Raamsdok et al.. Metabolic studies ca be used to address the questio of how a gee s 78

3 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity mutatio affects pheotypes of the orgaism. May biologists advocate metabolic profilig i a fuctioal geomics study Dio et al. 6. Oe subset of the metabolome, the lipidome, plays a importat role i the biochemical processes i the cell. Lipids are compouds of biological origi that are poorly soluble i water but are soluble i opolar solvets Blei ad Odia 6. They iclude well-kow compouds, such as triglycerides, phospholipids, sterols, fat-soluble vitamis, fatty acids, ad may others. May lipids are structural compoets of cell membraes. The cocetratio of lipid metabolites i the cell may chage due to both iteral ad eteral factors Welti ad Wag 4. Cocetratios of lipids reflect eymatic activities which make ad degrade them. The actio of eymes ivolved i lipid formatio ad break-dow is depedet o the presece of gees ecodig the eymes. If a lipid-metaboliig gee is mutated ad its eyme is o loger made, the levels of the gee product s reactats ad products will be altered. Biological reactios may be part of a log chai of reactio paths or reactio etworks. I this paper, we coduct a eploratory aalysis of mutatio effects o reactat-product pathways i the plat Arabidopsis thaliaa, a model plat with may available mutats. Usig kowledge of certai kow pairs whose reactio is modified by the mutatio, we defie metrics that quatify the effect of the mutatio o the reactio. A optimal metric will allow oe to rak all possible metabolite pairs i order of the likelihood that the mutatio modified the pathway betwee them. We use eperimetal data derived from aalysis of wild-type plats ad those defective i a eyme ivolved i the additio of double bods to fatty acid groups i membrae lipids. The defective eymes are kow as a desaturases. Table lists abbreviatios that are used. For eample, DGDG34:6 represets a lipid that has 34 acyl carbos ad 6 carbo-carbo double bods, with a head group DGDG digalactosyldiacylglycerol. To develop the scheme used to idetify a reactat-product pair whose reactio is reduced by a mutatio, amog all lipid pairs, the otatio i table is used, where = wild type ad = mutat. Figure illustrates the scheme used to fid a reactat ad product lipid pair i a metabolic pathway. I Figure, a A B is a geeral otatio for a arbitrary reactat ad product pair if A is a reactat ad B is its product i the pathway. b Aw Bw is a otatio to show that Aw ca geerate Bw. I the wild type coditio, this reactio leads to decreased cocetratio i Aw ad icreased cocetratio i Bw. I step b, Am Bm is the otatio that idicates that the geeratio of Bm from Am is reduced if there is a mutatio that affects the pathway betwee reactat ad product i the mutat. A decrease i the reactio occurs because the mutatio lowers the level of the eyme that is used to catalye the reactio. As a result, the cocetratio of the reactat Am icreases, ad the level of Bm decreases. I geeral, if Aw Bw ad Am Bm i Figure b, the reactat A should have higher cocetratio i the group tha i the group, ad the product B should have lower cocetratio i the group tha i the group. This leads to the two relatios show i c, i.e., Aw < Am ad Bw > Bm. A reactat product pair adherig to the scheme i Figure will be deoted a A-B pair i tet that follows. The scheme illustrated i Figure may seem overly simplistic. However, the usefuless of the scheme is ehaced by employig mutat ad wildtype samples i the eperimet. I a chemical reactio, o matter what the etwork, reactats substrates of a blocked reactio will be icreased ad products decreased. Other compouds may be affected also, but the substrate ad 79

4 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity products should be amog the affected compoud group, provided they are measured. Here we are oly iterested i those poits i the etwork that are altered by the mutatio. Table : Abbreviatios used i this paper DGDG digalactosyldiacylglycerol fad fatty acid desaturase deficiecy LysoPC lysophosphatidylcholie LysoPG lysophosphatidylglycerol MGDG moogalactosyldiacylglycerol PA phosphatidic acid PC phosphatidylcholie PE phosphatidylethaolamie PG phosphatidylglycerol PI phosphatidyliositol PS phosphatidylglycerol Table : The reactat-product otatio i the wild type ad mutat groups A Reactat i the pathway B Product i the pathway A w Reactat cocetratio i A m Reactat cocetratio i B w Product cocetratio i Product cocetratio i B m Figure : The priciple used to fid reactat ad product A-B lipid pairs If A is the reactat ad B is the product i the pathway i a, the reactat A ca geerate B i the, i.e., Aw Bw, but A caot geerate B i the group, i.e., Am Bm i b. As a result, Aw < Am ad Bw > Bm as show i c Fa. Data from si lipidomic eperimets see the detailed eperimetal iformatio i Fa were collected o mutat plats with mutatios i gees with kow fuctios. These mutatios were fad Okuley et al. 994, fad3 Arodel et al. 99, fad4 Gao et al. 9, fad5 Mekhedov et al., fad6 Falcoe et al. 994, ad fad7 Iba et al. 993 ad Gibso et al A total of 974 lipid pairs from the 4 lipids were cosidered i each of the si 8

5 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity differet lipidomic eperimets. There were 5 samples i the group ad 5 samples i the group. To discrimiate the possible reactat-product pairs i the 974 arbitrary lipid pairs, a list of kow reactat-product pairs were used as a criterio for developig a method to idetify A-B pairs whose reactio is blocked by the mutatio. These biologically fuctioal lipid pairs have attributes that were eplaied i Fa. These criteria, combied with kowledge of the particular mutatio, assist the biologist i providig cadidate biologically fuctioal pairs that ca be used to establish statistical metrics that quatify characteristics of these pairs. The goal herei is to use patters that are apparet i the data for kow biologically fuctioal pairs to propose a eploratory method ad metrics to idetify cadidate pairs i future eperimets where the fuctio of the mutatio i the lipid pathway is ukow. Other approaches have bee proposed for eplorig ad idetifyig metabolite etworks. The mai priciple i may methods seekig to detect oe metabolite i the pathway of aother metabolite is to measure ad aalye the chage of cocetratio of the metabolites. Raamsdok et al. itroduced a techique to fid the fuctio of "silet" gees usig metabolite level chages i a sigle-celled orgaism, Saccharomyces cerevisiae, a species of yeast. The researchers epected to reveal the role of ukow gees by comparig the metabolite profile of yeast with mutatios i those gees to those of mutats i gees of kow fuctio usig a corespose coefficiet i a approach they called FANCY Fuctioal Aalysis by Co-resposes i Yeast. The method i Raamsdok et al. is closest to the approach proposed herei; however, their method cosidered cocetratio chages i si metabolites with respect to a sigle referece metabolite ad used a subset of the iformatio that is used here whe defiig metrics. Aother method that has bee used i metabolic pathway aalysis is correlatio aalysis Weckwerth et al. 4; Fukushima et. al. ; Steuer 6. Correlatio aalysis emphasies that the metabolic fluctuatio might have a liear associatio betwee the metabolite cocetratios of a metabolite pair i the ad i the groups. Fukushima et al. used Spearma's correlatio to fid correlatios betwee pairs of metabolites that were sigificatly differet from ero i two parts of a plat, the aerial ad roots. They also tested for correlatios betwee the pairs that were sigificatly differet betwee aerial ad root parts of the plat. Local False Discovery Rate lfdr was used for multiple testig cotrol. We used Spearma's correlatio aalysis as reported i Fukushima et al. to determie if the techique was effective i idetifyig the biologically fuctioal pairs i our lipid data sets. The tests of correlatios did ot detect ay biologically fuctioal pairs that were statistically differet betwee the ad the groups, so the use of correlatio aalysis does ot appear useful for the problem cosidered here. New metrics are eeded for quatifyig A-B pairs whose reactio is blocked by the mutatio.. Data Eploratio ad Defiitio of Metrics Here, we refie the supportig evidece for a mutatio effect as show i Figure ito a statistics. The method is eploratory ad does ot rely o distributioal assumptios ad accommodates potetial oliear relatios ad ero values that are preset i the data sets. Aother limitatio for developig statistical methods with these data is small sample sies. Small sample sies are ot ucommo i metabolomics, ad they preset difficulties for usig 8

6 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity assumptios of ormality or applicatio to cetral limit theorem ad for use of correlatio for quatifyig relatioships. Raamsdok et al. aalyed their metabolomic data with 3 samples i each treatmet. I this eperimet, 5 samples are take for each treatmet. Aother challege with metabolite data is a likely high-dimesioal depedece structure amog lipids ad their cocetratios. If there is a log chai of reactat ad product pathways, oe lipid's cocetratio chage may be associated with all other lipids o the pathway. Therefore, oe chage i cocetratio of a lipid i the etwork might cause a sequece of chages i the pathway or the pathway etworks Steuer et al. 3. However, as oted earlier substrates of a blocked eyme will be icreased ad products decreased ad this priciple is used here i defiig metrics to rak cadidate lipid pairs whose reactio is blocked by the mutatio. We do assume that the samples themselves are idepedet of each other. I the followig part of this aalysis, data from the fad eperimet are used as a illustratio. The other five data sets have similar properties. The uit of the data is mol per mg dry weight. The first 5 samples are from the group ad the last 5 samples are from the group. Table 3 lists all the otatios for the samples before scalig. Table 3: Notatios used for oe reactat A ad product B i a lipid pair : The sample sie i each group. i : Subscript i =, to deote the treatmet, = ad =. : Subscript =,,, deotes sample withi treatmet. Before scalig: i : The cocetratio for the th sample i the i th treatmet for oe lipid. i : The group mea i the i th treatmet for oe lipid. : The overall mea across two treatmet groups for oe lipid, i. s : Stadard deviatio for oe lipid across two treatmets, s Ai : The cocetratio of th sample for lipid A i the i th treatmet. : The cocetratio of th sample for B i the i th treatmet. Bi A : The mea cocetratio of A across two treatmets. B : The mea cocetratio of B across two treatmets. Ai : The mea cocetratio of A i the i th treatmet. : The mea cocetratio of B i the i th treatmet. Bi i i i Differet lipids are foud at varyig cocetratios i biological samples, with some havig substatially greater abudace tha others. This presets challeges to evaluate reactatproduct pairs i a pathway. Thus a first step is to scale lipid cocetratios so that differet pairs are comparable usig a sigle metric. This scalig should ot alter the relative positioig of lipids with respect to oe aother ad, thus, alter the ature of the mutatio s effect o the. 8

7 reactio. Lipid ccocetratios are cetered ad scaled by usig the stadardiatio formula, i, give below. After scalig: Let s i i. The all quatities above that are defied before scalig have correspodig quatities after scalig, ad are deoted by the variable istead of. Propositio : Cosider a sigle lipid ad deote the cocetratio by i for the th sample i the i th treatmet, where i =,, ad =,,,. The, i for i =, ad. Proof: It is clear that i i ad equal samples i each group implies. So if we focus o, we have s s. The umerator of ca be calculated as. The, s i i 83 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity

8 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity Usig ad results i, For oe lipid, let SSW. s, ad SSW, the. 4 SSW SSW SSW SSW For the reciprocal of, 4, 4 SSW SSW i.e.,. 3 Let 4 SSW SSW, the. So. The ma should occur whe which begis to happe whe ad the two withi sums of squares, SSW ad SSW, are close to ero. So Similarly,. Therefore, boud is close to. or. holds. Whe becomes large, this upper After data are cetered ad scaled, Propositio gives the followig results.. For the data described here with = 5, i As gets large, ma i goes to.. For a lipid pair, A ad B, with two dimesioal meas give by A, B ad A, B for the wild type ad mutat groups, respectively, the maimum Euclidia distace betwee them is.684 for = 5 ad approaches as sample sie icreases. 84

9 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity 3. Defiig SS betwee SSD A A B B SSbetwee, A SSbetwee, B ad 5 Ai Ai Bi Bi SS withi, A SS withi B SS, withi, i SS betwee implies that the lipid meas a. for each lipid. b. If SS withi SS, both group ceters are close to the origi,. betwee Figure shows the relative positio i the ad groups for the same lipid pair before ad after scalig. The relative positios of the ad groups remai the same i the two plots. Aother result worth otig is that Pearso s sample correlatio coefficiet betwee a pair of lipids is uchaged after scalig the data as described above. Before Scalig After Scalig B: PC34_ 3 4 B: PC34_ A: PC34_ A: PC34_ Figure : Eample scatter plots of oe lipid pair before ad after scalig Lipid PC34_ A, PC34:, putative reactat ad lipid PC34_ B, PC34:, putative product, which form a lipid pair, are plotted before left pael ad after scalig right pael. After ceterig ad scalig, a total 974 lipids are paired to determie whether or ot the cocetratio chage i the pair follows the scheme show i Figure ad give here by A < A ad B > B. Note that each lipid is allowed to be a cadidate product or reactat prior to the below screeig procedure. For coveiece ad to quatify the scheme i Figure, defie a variable y, where y I{ } A I A { B B }. 4 Whe both A < A ad B B hold, A ad B are a lipid pair that satisfy the screeig procedure for a reactat-product pair, ad y =. The arbitrary lipid pairs that satisfy the coditios y = will be used to prescree the sample of all lipid pairs whe defiig metrics i the sectio that follows. Note that y = reflects the same pair but with product ad reactat roles reversed, ad that y = implies that both lipids are either reactats or products but the two together are ot a reactat-product pair. 85

10 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity 3. Eample The biologically fuctioal reactat-product pairs are used as a stadard to compare with all other arbitrary lipid pairs. Figure 3 shows the scatter plot characteristics of ie biologically fuctioal reactat-product pairs i the data set fad. There are i total 8 biologically fuctioal pairs i the fad data set. The remaiig scatter plots from the biologically fuctioal pairs are all similar to those i Figure 3. All have similar patters: is i the upper left corer, is i the lower right corer. Their cocetratio relatioships satisfy the screeig scheme i Figure which is A < A ad B > B with mea differeces betwee ad ear the maimum derived i the Propositio. I fact, i all other mutat data sets that we have evaluated, the same patters as show i Figure 3 are apparet for ay kow biologically fuctioal substrate-product pairs. Bio_ Bio_ Bio_3 B: PC34_ B: PC34_ B: PC36_ A: PC34_ A: PC36_ A: PC34_ B: PC38_ Bio_ B: PC4_ Bio_ B: PC36_ Bio_ B: PC38_ A: PC34_ Bio_7 B: PC38_ A: PC34_ Bio_8 B: PC4_ A: PC36_ Bio_ A: PC36 A: PC36 A: PC36 Figure 3: Scatter plots of ie biologically fuctioal pairs i Fad I each pael, the 5 blue circles represet the group with coordiates A, B ad the 5 red triagles stad for the group with coordiates A, B. The -ais is the cocetratio of the reactat A ad the y-ais is the cocetratio of the product B. 86

11 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity Three Summary Statistics: Three summary test statistics are developed accordig to patters see i eploratory data aalysis. These three are deoted tg, SSD, ad logr statistics. The distributios of these statistics from the fad data are show i Figure 4. The statistics are computed from each cadidate lipid reactat-product pair i the scaled data i.e., those pairs satisfyig the y = screeig criteria. a. tg b. SSD Distace c. -logr statistic tg i fad SSD i fad logr i fad Figure 4: The distributios of the three test statistics. The red dashed vertical lies show the statistics for the biologically fuctioal lipid pairs i data set fad. Statistic : tg This tg is the ratio of a lipid product B group mea differece to a reactat A group mea differece, ad is defied as B B tg, 5 where the meas Ai ad Bi A A were defied earlier. Accordig to eploratory data aalyses, the positios for the two dimesioal groups ad most represetative of biologically fuctioal pairs is a 35 degree agle with the -ais, which leads to tg =. The red lies i the tg distributio i Figure 4a show the biologically fuctioal pairs with tg values that are all close to. Raamsdok et al. used a measuremet based o tg actually a arctaget trasformatio of it i defiig the co-respose coefficiet Ω which was a ratio of the log cocetratio chage i their FANCY approach. Statistic : SSD SSD is a squared distace betwee the two group ceters ad give by SSD SSbetwee A A B B. 6 Large SSD, or iter-group distace, correspods to biologically fuctioal pairs. These results are show i Figure 4b. 87

12 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity Statistic 3: R Whe used aloe, the tg statistic does ot capture all characteristics of potetial reactatproduct pairs. Similarly, the SSD statistic also has a disadvatage. If the iter-group distace is very large, but the agle betwee the groups is very differet from 35º, the the result usig ust SSD may ot select the true cadidate reactat-product pairs. That is, usig SSD aloe may lead to false discoveries. I Figure 5, the data poits bio.tg, bio.ssd from the 8 differet biologically fuctioal pairs show them to be close to the top peak with coordiates,.684. Therefore, a statistic combiig both tg ad SSD at the same time is proposed. This combied statistic, called R, ca elimiate the respective limitatios of tg ad SSD while keepig their advatages. The statistic R is defied as R tg SSD massd. 7 The value ma SSD is set to.684 from the theoretical maimum SSD from the propositio for our samples of sie 5 i each group. The value of R should ot ever be eactly ero. The lipid pairs that are of iterest will have values of R ear ero. For improved iterpretability ad separatio of small values of R, the R statistics are trasformed by logr so that large values of logr are those of iterest. Figure 4c shows the distributio of the trasformed R statistic, logr. The biologically fuctioal pair's logr statistics red lies show that the larger values of logr reflect results that are of iterest. tg ad SSD i fad Referece lie tg =, SSD =.3 SSD distace tg, SSD bio.tg, bio.ssd tg ratio Figure 5: Illustratio of the iformatio for the R statistic, usig the scatter plot of tg versus SSD i the data set ivolvig the ad the fad mutat The vertical red lie shows tg =. The horiotal red lie shows a arbitrary cutoff poit at SSD =.3. The black poits are the tg, SSD coordiates for each lipid pair. The red poits at the peak are the biologically fuctioal pairs. The peak area cotais the most iterestig lipid pairs with large SSD values ad tg close to. 88

13 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity Note that i Figure 5, the scatter plot of tg ad SSD shows curved patters because tg ad SSD are both fuctios of the meas, Ai ad Bi as show previously. 4. Discussio ad Future Work I coclusio, the three statistics derived i sectio 3 were based o the eploratio of data accordig to the screeig priciple illustrated i Figure. From the above aalysis, we ca see that the three statistics reflect the data characteristics for lipid pairs that are biologically fuctioal reactat-product pairs whose reactio is modified by the mutatio i the orgaism. They ca be employed separately or combied as a whole. So as metrics themselves, they are useful quatities for rakig reactat-product pairs as potetially affected by a mutatio i cases where the role of the mutatio is ukow. Aalysis of other mutat data sets i which biologically fuctioal pairs were kow revealed the same patter for the defied metrics as see above i Figures 4 ad 5. As such, we propose these metrics for idetifyig reactios that are modified by mutatios of ukow fuctio. Work is i curretly i progress ad plaed to do this with ew data sets. There are still improvemets that ca be made to a statistical method for detectig such pairs. After the three statistics are foud from the above eample, the empirical distributios of the three statistics ca be preseted as show i Figure 4. To assess statistical sigificace, this empirical distributio could be compared with a distributio of the statistics uder some ull hypothesis. Null distributios of statistics ca ofte be geerated by bootstrap resamplig methods, uder a coditio for which the ull hypothesis is true. A challege that arises is how to specify a appropriate ull hypothesis. Oe ull hypothesis is : H F = G, where F is a multivariate distributio of lipid cocetratios for the group ad G is the distributio for the group. This ull hypothesis is easy to accommodate i a bootstrap procedure ad some iitial work has bee doe. However, this ull hypothesis may be too restrictive i situatios where a mutatio substatially modifies cocetratios i the etire lipidome. We have see that i some data sets, the bootstrap ull distributios of the test statistics, SSD ad logr, deviate quite far from the empirical distributios. The results suggest strog mutatio effects i the data sets. A less restrictive ull hypothesis would be the followig itersectio-uio hypotheses, H A H : Aw Am or Bw Bm : Aw Am ad Bw Bm. Bootstrap samplig uder these hypotheses may be more reasoable for the applicatio cosidered here. Whe coductig the eploratory aalysis, the prescreeig of cadidate pairs was doe with the y statistic as defied i equatio 4. If attemptig to derive a probabilistic certaity to a list of fidigs, the samplig variability of this prescreeig step may also eed to be icorporated. Also, the metrics that were defied were largely based o differeces i meas. Oe might also woder if differeces i sample variaces might also be used to evaluate cadidate pairs. It is uclear at this poit to what etet or how the sample stadard deviatios may be altered by the mutatio. Oe eceptio would be if the mutatio completely blocked the 89

14 Aual Coferece o Applied Statistics i Agriculture Kasas State Uiversity reactio ad the formatio of the lipid product. I such a case, oe might epect the cadidate product would be positive i the wildtype orgaism ad eactly ero i all samples i the mutat. This has bee rarely see ad it is ot always clear whether ero cocetratios are real eros or simply below the limit of detectio for the istrumet. As developmet of methods for the aalysis of gee epressio data progressed over the past years, attetio tured to methods for simulatig realistic high-dimesioal data. Previously, data were ofte simulated ad still are from multivariate ormal distributios with restrictive depedece structures. Simulatig more realistic gee epressio data was cosidered i Gadbury et al. 8. Simulatig realistic lipidomic data is likely to be challegig. Still it will be ecessary i order to evaluate the performace of ew statistical methods for aalyig lipidomic data. This is aother area of research to be eplored. Ackowledgemets The authors ackowledge Liia Fa, George Millike, Haiyag Wag, Lili Cheg, Richard Jeaotte, ad Ashis Nadi for earlier work leadig to that reported herei. Refereces Arodel, V., Lemieu, B., Hwag, I., Gibso, S., Goodma, H.M. ad Somerville, C.R. 99. Map-based cloig of a gee cotrollig omega-3 fatty acid desaturatio i Arabidopsis. Sciece, 58, Blei, I., Odia G. 6. Geeral, orgaic, ad biochemistry. Secod editio, New York: W.H. Freema ad Compay. Dio, R. A., Gag, D. R., Charlto, A. J., Fieh, O., Kuiper, H. A., Reyolds, T. L., Teerdema, R. S., Jeffery, E. H., Germa, J. B., Ridley, W. P. ad Seiber, J. N. 6. Applicatios of Metabolomics i Agriculture. Joural of Agricultural ad Food Chemistry, 54, Du, W. B., Ellis, D. I. 5. Metabolomics: Curret aalytical platforms ad methodologies. Treds i aalytical chemistry, 4, Falcoe, D.L., Gibso, S., Lemieu, B. ad Somerville, C Idetificatio of a gee that complemets a Arabidopsis mutat deficiet i chloroplast omega 6 desaturase activity. Plat Physiology, 6, Fa, L.. A eploratory method for idetifyig reactat-product lipid pairs from lipidomic profiles of wild-type ad mutat leaves of Arabidopsis thaliaa. Master report. Kasas State Uiversity. Fukushima, A., Kusao, M., Redestig H., Arita, M., Saito, K.. Metabolomic correlatioetwork modules i Arabidopsis based o a graph-clusterig approach. BMC Systems Biology, 5, -. Gadbury, G. L., Xiag, Q., Yag, L., Bares, S., Page, G. P., Alliso, D. B. 8. Evaluatig statistical methods usig plasmode data sets i the age of massive public databases: A illustratio usig False Discovery Rates. PLos Geetics, 46. Gao, J., Aawi, I., Maoli, A., Sawi, A., Xu, C., Froehlich, J. E., Last, R. L. Beig, C. 9. FATTY ACID DESATURASE4 of Arabidopsis ecodes a protei distict from characteried fatty acid desaturases. The Plat Joural, 6,

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