A minimal model for hepatic fatty acid balance during fasting: Application to PPAR alpha-deficient mice

Transcription

1 A mnmal model for hepatc fatty acd balance durng fastng: Applcaton to PPAR alpha-defcent mce Perre Blavy, F. Gondret, Hervé Gullou, S. Lagarrgue, P.G.P. Martn, J. Van Mlgen, Ovdu Radulescu, A. Segel To cte ths verson: Perre Blavy, F. Gondret, Hervé Gullou, S. Lagarrgue, P.G.P. Martn, et al.. A mnmal model for hepatc fatty acd balance durng fastng: Applcaton to PPAR alpha-defcent mce. Journal of Theoretcal Bology, Elsever, 2009, 261 (2), pp.266. < /j.jtb >. <hal > HAL Id: hal Submtted on 25 Jan 2011 HAL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. L archve ouverte plurdscplnare HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés.

2 Author s Accepted Manuscrpt A mnmal model for hepatc fatty acd balance durng fastng: Applcaton to PPAR alpha-defcent mce* P. Blavy, F. Gondret, H. Gullou, S. Lagarrgue, P.G.P. Martn, J. van Mlgen, O. Radulescu, A. Segel PII: S (09) DOI: do: /j.jtb Reference: YJTBI To appear n: Journal of Theoretcal Bology Receved date: 21 March 2009 Revsed date: 25 June 2009 Accepted date: 16 July 2009 Cte ths artcle as: P. Blavy, F. Gondret, H. Gullou, S. Lagarrgue, P.G.P. Martn, J. van Mlgen, O. Radulescu and A. Segel, A mnmal model for hepatc fatty acd balance durng fastng: Applcaton to PPAR alpha-defcent mce*, Journal of Theoretcal Bology, do: /j.jtb Ths s a PDF fle of an unedted manuscrpt that has been accepted for publcaton. As a servce to our customers we are provdng ths early verson of the manuscrpt. The manuscrpt wll undergo copyedtng, typesettng, and revew of the resultng galley proof before t s publshed n ts fnal ctable form. Please note that durng the producton process errors may be dscovered whch could affect the content, and all legal dsclamers that apply to the journal pertan.

3 A mnmal model for hepatc fatty acd balance durng fastng: applcaton to PPAR alpha-defcent mce* P. Blavy a,g,f.gondret a, H. Gullou b, S. Lagarrgue c,d,e,p.g.p.martn b, J. van Mlgen a, O. Radulescu h,g,a.segel f,g a INRA, UMR1079 Systèmes d Elevage, Nutrton Anmale et Humane (SENAH), F Sant Glles, France b INRA, UR66 Laboratore de Pharmacologe et Toxcologe, 180 Chemn de Tournefeulle, BP3, F Toulouse cedex 9, France c Agrocampus Ouest, UMR 598 Génétque Anmale, F Rennes, France d INRA, UMR 598 Génétque Anmale, F Rennes, France e IFR 140, GFAS, F Rennes, France f CNRS, UMR 6074 IRISA, Campus de Beauleu, F Rennes, France g INRIA Rennes Bretagne Atlantque, Symbose-project, Campus de Beauleu, F Rennes, France h Unversté de Rennes 1, UMR 6625 IRMAR, Campus de Beauleu, F Rennes, France Abstract The purpose of ths study s to dentfy the herarchy of mportance amongst pathways nvolved n fatty acd (FA) metabolsm and ther regulators n the control of hepatc FA composton. A modelng approach was appled to expermental data obtaned durng fastng n PPARα-knockout (KO) mce and wld-type mce. A step-by-step procedure was used n whch a very smple model was completed by addtonal pathways untl the model ftted correctly the measured quanttes of FA n the lver. The resultng model ncluded FA uptake by the lver, FA oxdaton, elongaton and elongaton and desaturaton of FA, whch were found actve n both genotypes durng fastng. From the model analyss we concluded that PPARα had a strong effect on FA oxdaton. There were no ndcatons that ths effect changes durng the fastng perod, and t was thus consdered to be constant. In PPARα KO mce, FA uptake was dentfed as the man pathway responsble for FA varaton n the lver. The models showed that FA were oxdzed Emal addresses: perre.blavy@rsa.fr (P. Blavy), florence.gondret@rennes.nra.fr (F. Gondret), Herve.Gullou@toulouse.nra.fr (H. Gullou), Sandrne.Lagarrgue@agrocampus-ouest.fr (S. Lagarrgue), Pascal.Martn@toulouse.nra.fr (P.G.P.Martn),jaap.vanmlgen@rennes.nra.fr (J. van Mlgen), ovdu.radulescu@nra.fr (O. Radulescu ), anne.segel@rsa.fr (A. Segel) * Results were partally presented at the JOBIM-2008 meetng held n Llle, France. ** Correspondng Author : IRISA, Campus de Beauleu. F Rennes Cedex FRANCE. Tel.: ; fax: Preprnt submtted to Elsever June 25, 2009

4 at a constant and small rate, whereas elongaton and desaturaton of FA also occurred durng fastng. The latter observaton was rather unexpected, but was confrmed expermentally by the measurement of delta-6-desaturase mrna usng real-tme quanttatve PCR (QPCR). These results confrm that mathematcal models can be a useful tool n dentfyng new bologcal hypotheses and nutrtonal routes n metabolsm. Key words: fatty acd metabolsm, systems bology, fastng, knockout mce, modellng. 1. Introducton Fatty acds (FA) are the man consttuents of lpds n the body and are buldng blocks for glyco- and phospholpds of cell membranes. FA also play an mportant role n energy metabolsm, allowng the storage of energy n a very dense form as trglycerdes, whch can be oxdzed later when energy s needed. The FA can also act as sgnalng molecules and behave as regulators of several transcrpton factors (Duplus et al., 2000). Therefore, they play crucal roles n normal growth and development (e.g., (Uauy et al., 2007)) but also n coronary artery dsease (Sedeln, 1995; Shra, 2004), dyslpdema, hepatc steatoss and other pathologes (Sedeln, 1995; Smopoulos, 1991). The balance between synthess and degradaton of FA s regulated by nutrent supply and the energy needs of the organsm. In humans and mce, the lver plays a central role n the endogenous synthess of FA (Murur and Levelle, 1970). Durng fastng, FA are released from adpose tssue (AT) by lpolyss, and serve as sources of energy n other organs. Crculatng free FA are extensvely taken up by the lver n fastng rodents (Remesy and Demgne, 1983). In the lver, FA can be a source of substrates for the synthess of ketone bodes ketone, whch can be used as fuel by extrahepatc tssues. The synthess, degradaton, and transformaton of FA n hepatc cells are catalyzed by over 300 enzymatc reactons (Kanehsa et al., 2008) nvolved n dstnct pathways (e.g., FA oxdaton and elongaton). These reactons are regulated at the metabolc and genetc levels by varous hormones (e.g., nsuln (Campbell et al., 1992), leptn (Unger et al., 1999)) and nutrents (e.g., poly unsaturated FA (Sessler and Ntamb, 1998)). However, the smple aggregaton of abundant lterature data cannot account for all underlyng nteractons responsble for both FA metabolsm and lpd phenotype. A better and more comprehensve understandng of FA metabolsm s needed to dentfy routes that wll allow for the nutrtonal modulaton of lpd deposton that may help preventng or curng lpd-related dsorders. Therefore, t s crtcal to dentfy the man pathways and regulators nvolved n the control of FA metabolsm. To acheve ths goal, we used a modellng approach. Mathematcal models are powerful tools to combne nformaton usng a common formalsm. Models are frequently used to descrbe, predct and test hypotheses. Dependng on the objectve, models can have dfferent levels of detal, 2

5 rangng from very basc molecular mechansms (e.g., (Fattal and Ben-Shaul, 1993)) to an emprcal black box approach (e.g., (Forns et al., 2002)). Models can be useful to explore and better understand FA metabolsm and ts regulaton wthn a cell, as well as between organs nvolved n lpd metabolsm. To provde a full descrpton of the dynamcs of the system consdered as a homogeneous organ (e.g., (Calvett et al., 2008)) or ncludng the heterogeneous nature of the organ (e.g., spatal models (Chalhoub et al., 2007b)), metabolc reactons are modeled as dfferental equatons or analyzed by convex optmzaton technques such as flux balance analyss. Spatal models typcally use partal dfferental equatons. A contrasted stuaton s necessary to dentfy the key mechansms nvolved n the regulaton of FA metabolsm. In the present study, we consdered the knetcs of FA metabolsm durng fastng n both wld-type and peroxsome prolferator-actvated receptor alpha (PPARα) knockout (KO) mce. Fastng trggers complex adaptve metabolc responses, ncludng a swtch to rely on FA and ketone bodes for ATP synthess ((Leone et al., 1999)) and an ncreased capacty for mtochondral FA oxdaton n tssues wth hgh energy demands (Hashmoto et al., 2000; Leone et al., 1999). The PPARα s consdered as the master regulator of FA homeostass (Desvergne and Wahl, 1999; Leone et al., 1999). A genome-wde transcrptomc approach n mce has recently ponted out the role of PPARα n the lver n the regulaton of FA oxdaton and ketone body producton durng fastng (Sokolovć et al., 2008). Anmals lackng PPARα appear to be unable to ncrease the capacty for cellular FA utlzaton (Leone et al., 1999). Montorng the varaton n FA composton n tssues of wld-type and PPARα KO mce durng fastng provdes a useful expermental data set to understand the regulaton of FA metabolsm and to develop computatonal models descrbng ths metabolsm. To our knowledge, there s only one model (Chalhoub et al., 2007a) focused on lpd metabolsm n the lver durng fastng condtons. Ths detaled mathematcal model was based on dfferental equatons and smulated gluconeogeness durng a 24-h fastng perod n the perfused rat lver. Ths model ncluded key reactons for FA metabolsm such as FA uptake, synthess of trglycerdes, and FA oxdaton. Because of the large number of reactons nvolved, many of these were aggregated n seres. Moreover, ths model dd not ntend to predct the varaton n FA composton n the lver and dd not nclude the genetc regulaton of FA metabolsm. It ntended to predct concentratons and fluxes of ntermedate metaboltes nvolved n FA metabolsm and gluconeogeness n response to changes n varous substrate concentratons n the perfused lver. The am of the present study was to dentfy the most relevant pathways and ther regulators nvolved n hepatc FA metabolsm. Based on expermental data and nformaton from the lterature, a model (based on dfferental equatons) was developed that allows to explan the varaton n FA composton of the mouse lver durng a fed-to-fastng transton. Addtonal expermental measurements (mrna expresson of delta-6-desaturase, a key enzyme of polyunsaturated FA synthess) were carred out to evaluate hypotheses that were formulated followng model analyses. 3

6 2. Materals and methods 2.1. Bologcal experments Expermental data Expermental data were obtaned n 8 week-old male wld-type C57BL/6J (WT) and PPARα KO mce (Lee et al., 1995; Costet et al., 1998) over a 72 h fastng perod. Three to 6 mce for each genotype were sacrfced at dfferent tmes ponts (0, 3, 6, 9, 12, 18, 24, 36, 48, 60, 72 h) after the last meal. Before fastng, all anmals were fed ad lbtum a rodent det 2018 from Harlan Teklad (Gannat, France). At each tme pont, anmal body weght was recorded and lver and epddymal Whte Adpose tssue (AT) were dssected, weghed, frozen n lqud ntrogen mmedately after dssecton, and stored at -80 Cuntl analyss. Total lpd content was determned n lver and AT as descrbed prevously (Martn et al., 2007). Proportons of ndvdual FA were determned by gas chromatography analyss of FA methyl esters. The quanttes of each FA (C14:0, C16:0, C16:1ω9, C16:1ω7, C18:0, C18:1ω9, C18:1ω7, C18:2ω6, C18:3ω3, C20:1ω9, C20:3ω6, C20:4ω6, C20:5ω3, C22:6ω3) n the lver and AT were calculated consderng the relatve proportons of FA n total lpds and the mass of lver and AT. Tme-related varatons n FA quantty were analyzed usng the lm() lnear regresson mplemented n R ( Gene expresson Hepatc total RNA was extracted usng Trzol reagent (Invtrogen) accordng to the manufacturer s nstructon. Complementary cdna was syntheszed from 2 μg of total RNA usng random prmers and Superscrpt II (Invtrogen) reverse transcrptase accordng to the manufacturer s nstructons. The mrna levels of Delta6 desaturase (D6D) were measuredby quanttatve real-tme PCR (QPCR) after 0, 24, 48, and 72 h of fastng usng 3 -TCCAGTACCAGATCATCATGA- CAA-5 as forward prmer and 3 -GGTGTAGAAGAAACGCATATAGTAGCTG-5 as reverse prmer. Amplfcatons were performed on an ABI Prsm 7000 Sequence Detecton System (Appled Bosystems, Courtaboeuf, France). The QPCR data were normalzed by TATA-box bndng proten (TBP) expresson levels (TBP-F: ACTTCGTGCAAGAAATGCTGAA, TBP-R: GCAGTTGTC- CGTGGCTCTCT) and analyzed usng the DART-PCR software (Person et al., 2003) Prncples of model development A step-by-step procedure was appled to nclude dfferent metabolc pathways and regulators untl the model ftted the data well and no reasonable mprovement could be obtaned. Due to the absence of at least one complex regulatory system, the PPARα KO mce can be consdered as a relatvely smpler model compared to wldtype mce. Therefore we frst ftted the successve models on data obtaned n PPARα KO mce. In order to allow comparsons between genotypes wthn the same model (or modelng framework), we then extrapolated to wld-type mce 4

7 the values of the parameters that should be common to both genotypes. We consder that the KO mce s just a smpler and easer to study submodel of the wld type model. Ths resulted n a mnmal model of a set of ordnary dfferental equatons descrbng FA metabolsm n the lver(table 1). The man pathways used n our model of FA metabolsm are consstent wth common bochemstry knowledge (Kanehsa et al., 2008; Murray et al., 2006), and nclude (Fg. 1) FA uptake, FA oxdaton n mtochondra and peroxsomes, ketogeness, the trcarboxylc acd cycle (where ATP s produced from acetyl-coa), synthess of malonyl-coa from acetyl-coa, synthess of palmtc acd (C16:0) from malonyl-coa and acetyl-coa, glycolyss to produce acetylcoa from glucose, and elongaton and desaturaton of polyunsaturated FA. Several key regulators of FA metabolsm have been descrbed n the lterature. They nclude PPARα, whch s a transcrpton factor that actvates FA oxdaton (Leone et al., 1999; Desvergne and Wahl, 1999; Lee et al., 1995) and FA elongaton and desaturaton (Wang et al., 2006; Gullou et al., 2002). Other regulators are SREBP1, whch s a transcrpton factor that actvates FA synthess (Horton et al., 2002; Jakobsson et al., 2006) as well as FA elongaton and desaturaton (Matsuzaka et al., 2002) and malonylcoa, whch nhbts FA oxdaton. Because of the expermental condtons and the resultng data n the present study, a decson was made as to whch varables should be ncluded n the model. Metabolc pathways and regulators that were supposed to be nactve or constant durng fastng were not consdered (Fg. 1). Durng the early hours of fastng (3 to 6 h), the level of SREBP1 markedly decreases n the lver (Horton et al., 1998), whch results n a fastng-medated transcrptonal downregulaton of the gene encodng FA synthase (.e., the key enzyme of de novo FA synthess (Shmano et al., 1999; Horton et al., 2002; Km et al., 1998)). Therefore, SREBP1 was assumed to be neglgble n our expermental condtons, and de novo FA synthess was supposed not to occur n our expermental condtons. Hence, the nfluence of SREBP1 on elongaton and desaturaton was not consdered. Moreover, snce malonylcoa s an ntermedate n de novo FA synthess, the malonylcoa-dependent nhbton of mtochondral FA uptake was not consdered. Acetyl-coA s a pvot n ntermedary metabolsm between catabolc and anabolc processes (van Mlgen, 2002). However, because the quantty of acetyl-coa has no drect effect on the FA composton n the lver, there was no need to consder the 3 pathways affectng acetyl-coa (.e., glycolyss, ketogeness and the trcarboxylc acd cycle) Model descrpton Choce of varables In the varous models we consdered, we ncluded all measured metaboltes, except those nvolved n ntermedate metabolsm (.e. molecules partcpatng n a consdered reacton that are nether a product nor a substrate). Therefore, when the elongaton and desaturaton pathway was added, we ncluded the sum of Sω3 = C20:5ω3 + C22:6ω3 andsω6 = C20:3ω6 + C20:4ω6 and not 5

8 the ndvdual quanttes of C20:5ω3 and C20:3ω6, whch were consdered as ntermedates. Indvdual quanttes of other FA were ncluded n the model. The quantty of PPARα was not explctly ncluded as a varable n the model. However, the dfference n numercal values of model parameters between wld-type and PPARα mce represent the effect of PPARα Fluxes Lver uptake. Uptake of FA n the lver from the blood was dffcult to assess n the experments. Durng fastng, free FA are released from AT by lpolyss and serve as energy sources for other organs ncludng the lver. We consdered that the observed varaton n FA composton n AT would reflect the FA uptake by the lver. Input fluxes of ndvdual FA n lver (Φ n )werethusconsderedtobe proportonal to FA released from AT by lpolyss durng fastng. The parameter K In represents the proportonalty factor relatng FA release from AT to FA uptake by the lver. The K In was supposed to be the same for all FA. Durng fastng, FA are released at a tme-constant rate from AT that dffers between FA. To evaluate ths rate, a lnear regresson for each FA n AT (X AT )was performed as X AT = a tme + ntercept.theslope(a ) of ths relaton was then used to estmate FA uptake by the lver: Φ n = K In a. (1) Oxdaton. The reacton flux for total oxdaton (Φ Ox )oftheth FA n the lver (X L ) durng fed-to-fast transton was expressed as a Mchaels-Menten equaton n smplfed form, usng a constant parameter representng the oxdaton rate (k ox ) and a relatve affnty parameter for each FA (b ): X L = k b ox Φ Ox j XL j b j wth b =1. (2) We hypotheszed that the quanttes of FA were not lmtng for the reacton. Ths assumpton was supported by the fact that the sum of FA n the lver ncreased from 0 to 72 h snce the onset of fastng (Table 2). The FA do not always undergo complete oxdaton resultng n acetyl-coa and ATP. Consequently, shorter-chan FA ntermedates may be generated, whch can accumulate n the lver. We consdered ncomplete oxdaton of a FA as the reacton producng a FA that s two carbons shorter than the orgnal FA. Therefore, the total oxdaton flux Φ Ox was separated nto 2 fluxes representng ether complete (Φ CompleteOx ) or ncomplete (Φ IncompleteOx )oxdaton fluxes: = s Φ Ox (3) Φ CompleteOx Φ IncompleteOx =(1 s ) Φ Ox, (4) where s represents the proporton of complete oxdaton of the total oxdaton. In the models consdered (Table 1), we had to choose between three hypotheses : the th FA s only oxdzed completely (s = 1), the th FA s only partally 6

9 oxdzed leadng to the generaton of a two carbons shorter FA (s = 0), or the th FA s both partally and totally oxdzed (s ]0; 1[). These hypotheses wll be tested gong from the smplest (s = 1) to the most complcated hypothess (s ]0; 1[) n a step-by-step procedure (secton 2.3.3). As wll be shown later, the thrd hypothess was not necessary to obtan a correct ft of the model to the data. Elongaton and desaturaton. Unsaturated FA consst of monounsaturated and polyunsaturated FA. Based on the locaton of the last double bound, polyunsaturated FA are classfed as ω3 orω6. Wthn each class, FA can be transformed through elongaton and desaturaton reactons (Fg. 2). The enzyme D6D has been consdered a rate-lmtng enzyme (Cho et al., 1999) of the FA elongaton/desaturaton pathway, whch concde wth the observaton that hepatc quanttes of C18:2ω6 and C18:3ω3 ncreased from 0 to 72 h of fastng (Table 2). Because D6D s common to ω3 andω6 desaturaton pathways, C18:2ω6 and C18:3ω3 are n competton for ths enzyme. Elongaton and desaturaton fluxes (Φ Desat C18:2ω6 and ΦDesat C18:3ω3 ) of C18:2ω6 and C18:3ω3 were ncluded n the rate of elongaton and desaturaton (k desat ), and the relatve affnty of D6D for the th FA (d ) can be gven as: C18 : 3ω3 d C18:3ω3 C18:3ω3 = k desat (5) C18 : 3ω3 d C18:3ω3 + C18 : 2ω6 d C18:2ω6 Φ Desat Φ Desat C18:2ω6 d C18:2ω6 C18:2ω6 = k desat C18:3ω3 d C18:3ω3+C18:2ω6 d C18:2ω6 wth d =1. (6) Choosng the optmal level of detal by a step-by-step procedure A step-by-step procedure was appled untl the model ncluded just enough detal to ft the change n FA quanttes over tme. Step 1: We started wth a model ncludng only one flux (.e., uptake of FA from AT by the lver). Step 2: We estmated model parameters from the expermental data (see the parameter estmaton method below). Step 3: If a parameter set was found allowng a close ft of model predctons to the observed data, the model (and ts parameters) was accepted and the procedure ended (see the fttng crteron below). If not, model output was analyzed, and addtonal pathways and regulators were ncluded. The selecton of pathways and regulatons was based on model behavor and bologcal knowledge. We then went back to step 2. Parameters estmaton. An ntal guess of parameter estmates was found by a lnear approxmaton of the model under the assumpton that j FA XL j b j s constant. Ths sum was evaluated by replacng X L j by the mean of observed value for the jth FA. Parameters were then estmated usng the Nelder 7

10 and Mead optmsaton (Nelder and Mead, 1965) mplemented n R optm procedure, by mnmzng the sum of squared devatons between observed data and predcted values. Goodness of ft. Fttng qualty was estmated usng the coeffcent of varaton of the mean squared predcton error (cvmspe) (Tedesch, 2006; Bbby, 1977). The mean squared predcton error measures the dstance between observed and predcted values, and can be decomposed n central error (CE), regresson error (RE), and dsturbance error (DE). The CE descrbes the contrbuton of dstance between mean values of observed and predcted data. The RE descrbes how the slope of the lnear regresson between predcted and observed data dffers from one. The DE s the remanng error. The cvmspe was used to standardze the results, so that dfferent FA could be compared. Models resultng n a low cvmspe combned wth an mportant contrbuton of DE are preferred and we consdered results acceptable f DE > 25% (an arbtrarly chosen value). 3. Results and dscusson In both mouse genotypes, FA quanttes n the lver were generally greater after a 72 h fastng perod compared wth the fed state (Table 2). For only three FA, there was no dfference n the quantty of FA between 0 and 72 h. Ths concerned C20:4ω6 n wld-type mce and C20:4ω6 and C20:5ω3 npparα KO mce. There are ndcatons n the lterature showng that FA can accumulate n the lver durng fastng n both PPARα KO and wld-type mce usng Sudan Black stanng of lpds (Lee et al., 2004) or Ol Red O stanng of neutral lpds (Hashmoto et al., 2000). The ampltudes of fastng-nduced FA accumulatons observed n the present study are consstent wth a prevous study of wld-type and PPARalpha knockout mce under the fed and starved (72h) condtons (see (Lee et al., 2004)). Ths lkely reflects the major role played by the lver durng fastng to cope wth the metabolsm of FA comng from adpose tssue lpolyss. The quanttes of most FA ncreased more markedely n PPARα KO lvers compared to wld-type controls (Table 2). As shown below, ths lkely results from the mpared hepatc FA beta-oxdaton n PPARα KO mce. Saturated and especally monounsaturated FA were most strongly ncreased than polyunsaturated FA n both genotypes. Only C20:5w3 and C22:6w3 ncreased more strongly n wld-typethannpparα KO lvers durng fastng (Table 2) Model structure Accordng to the step-by-step procedure, three successve models were bult, dfferng n degree of complexty. Model 1 ncluded only FA uptake, whereas model 2 ncluded both FA uptake and FA oxdaton. Model 3 was smlar to model 2 but also ncluded elongaton and desaturaton of FA. The equatons used for these models are gven n Table 1. These models are shown n Fgure 3. 8

11 For each model, the values of the parameters were frst estmated n the smpler PPARα KO mce model. The parameter values were then extrapolated to wld-type mce. When the model wth extrapolated parameter values dd not ft to the data for wld-type mce, then new parameter values were estmated from wld-type data (Table 3) Model 1: accumulaton of FA by the lver Ths model ncluded uptake of FA by the lver proportonal to AT efflux. The proportonalty constant was assumed to be the same for all FA. Ths constant was evaluated n PPARα KO mce and then extrapolated to wld-type mce Durng fastng, FA release from AT dffers between genotypes Fatty acd composton n mouse lver (Table 2) and AT (Table 4) n the fed state was dfferent n PPARα KO mce than n wld-type mce. The FA quanttes (except for C20:5ω3 and C22:6ω3) were generaly greater n the lver and lower (except for C18:2ω6 and C18:3ω3) n AT of KO mce compared wth the wld-type mce. The varaton n FA quanttes n AT durng fastng could be descrbed by lnear functons of tme, as shown by the hgh correlaton coeffcents n Table 4. The regresson slopes (Table 4) were lower n PPARα KO mce than n WT anmals, suggestng that lpolyss from AT was less actve durng fastng n the absence of PPARα. A lesser reducton n epddymal fat pad weghts n KO mce compared wth wld-type has been observed by others (Lee et al., 2004), suggestng that moblzaton of fat depots s delayed durng starvaton n mce that lack PPARα. Ths potental effect of PPARα on adpose tssue lpolyss durng fastng contrasts wth ts low expresson n ths tssue (Bookout et al., 2006). However, t has been shown that despte a low expresson level PPARα regulates glycerol knase (GyK) n whte adpose tssue (Mazzucotell et al., 2007). Interestngly, PPARα KO mce exhbt a hgher basal AT Gyk expresson compared to wld-type mce (Mazzucotell et al., 2007). Snce GyK s nvolved n FA recyclng, ts actvty may contrbute to counteract the effect of lpolyss n PPARα KO AT. On the other hand, PPARα-dependent regulatons n other tssues expressng PPARα could have ndrect effects on AT through nterorgan communcatons. For example, t has been proposed that PPARα may regulate specfc genes n the bran whch could could result n ncreased Glut4 expresson n the AT (Knauf et al., 2006). In ths study, hgh Glut4 expresson was proposed to ncrease glucose clearance n the adpose tssue of PPARα KO mce thus contrbutng to ther hypoglycema durng fastng. Increased glucose nput n adpose tssue of fasted PPARα KO mce may also contrbute to counteract the effects of lpolyss on AT lpd content by stmulatng napproprately FA synthess. 9

12 Durng fastng, FA hepatc nput flux s assumed to be proportonal to the FA release from AT Durng fastng, FA released by lpolyss n AT serve as an energy source for other organs, ncludng the lver. The free FA uptake by the lver has been descrbed by others as a lnear functon of the total free FA concentraton n blood (Berk and Stump, 1999), untl saturaton of the uptake system (Sorrentno and Berk, 1993). In the absence of nformaton n our experments on the free FA flux n blood (.e., FA concencentratons and blood flow), we assumed that hepatc nput flux of FA was proportonal to the FA release from AT durng fastng, usng a same K In proportonalty constant for all FA and both genotypes FA uptake s the major phenomenon nvolved n the varaton of FA n PPARα KO mce, but not n wld-type mce where oxdaton s mportant too The cvmspe estmates (Table 5) showed that the sum of all FA and all ndvdual FA quanttes except C16:1ω7, C16:1ω9, C22:6ω3, and C18:3ω3were correctly ftted n PPARα KO mce. By contrast, n wld-type mce nether the sum nor the ndvdual FA are correctly ftted. Ths result was antcpated for wld-type mce, as durng fastng, lver FA oxdaton s known to be more actve n wld-type mce than n PPARα ones (Le May et al., 2000). Therefore, uptake of FA was the major phenomenon nvolved n the varaton of hepatc FA durng fastng n PPARα KO mce, but not n wld-type mce Hepatc FA nput can be modeled as a smple proportonal functon of FA varaton n AT The good fttng of most FA n PPARα KO mce confrmed that hepatc FA nput can be modeled as a smple proportonal functon of FA varaton n AT. Ths also suggests that FA uptake s the man pathway responsble for varaton n hepatc FA composton n PPARα KO mce durng the fed-to-fastng transton. It also suggests that selectve mportaton of FA was neglgble C16:1ω7 has a specfc two tmes dynamc. The quantty of C16:1ω7 was poorly ftted n PPARα KO mce and was overestmated from 50 to 72 h (Fg. 5).The knetcs of C16:1w7 hepatc accumulaton seems to follow a specfc tme pattern wth accumulaton from 0 to 50 h, to reman constant thereafter. Ths pattern cannot be explaned by mportaton or specfc oxdaton, whch should have occurred at a constant rate durng the fed-to-fastng transton. Recently, t was shown that C16:1ω7can act as an AT-derved sgnal and has, unlke other FA, a systemc metabolc effect (Cao et al., 2008). It s possble that C16:1ω7 has a very specfc metabolc fate and not only targets the lver but also other tssues such as muscle. Ths hypothess remans to be explored further expermentally, and the lack-of-ft for C16:1ω7 was therefore not further addressed n our model. 10

13 The bad fttng of C16:1ω9 and C22:6ω3 n PPARα KO mce s unlkely to be explaned by a specfc FA uptake The poor fttng of the quanttes of C16:1ω9 and C22:6ω3 n the lver of PPARα KO mce can be explaned by specfc hgher rates of uptake or by reactons that produce these FA from other FA. Cellular uptake of FA as well as ntracellular transport of FA s medated through smple dffuson, facltated dffuson, or carrer-medated transport (Berk and Stump, 1999). It has been shown (Okar et al., 2008) that cytosolc acyl-carrer bndng proten (ACBP) has a hgher affnty for C14-C22 FA than for medum chan FA (C8-C12). To our knowledge, selectve regulaton of long-chan FA uptake has not yet been descrbed. When we calculate the selectve uptake for C16:1ω9, and C22:6ω3 requred to ft the data, t appears that these values should have been 2 to 12 tmes greater than the common rate determned for the other FA. Therefore, we assumed that transformatons between FA leadng to the producton of C16:1ω9 and C22:6ω3 would be a more lkely scenaro to explan the accumulaton of these FA n the lver, rather than the selectve uptake The bad fttng of C16:1ω9 npparα KO mce s lkely explaned by ncomplete oxdaton of C18:1ω9 C16:1ω9 can be produced by oxdaton from C18:1ω9 (Fg.2). InPPARα KO mce, the proporton of C16:1ω9 n the lver s very small (1.7% of total lver FA at 72 h of fastng), compared wth that of C18:1ω9 (26% of total hepatc FA at 72 h). Therefore, ncluson of the ncomplete oxdaton of C18:1ω9 nto C16:1ω9 mght ft the latter FA, wthout reducng the qualty of ft for C18:1ω9 (ths reacton wll be ncluded n model 2) The bad fttng of C22:6ω3 npparα KO mce s lkely explaned by elongaton/desaturaton of C18:3ω3 C22:6ω3 was underestmated n PPARα KO mce and can only be produced by elongaton and desaturaton (Fg. 2) from C18:3ω3, whch was overestmated. Therefore, t seems plausble that the absence of the elongaton/desaturaton pathway n model 1 s the cause of the observed lacks-of-ft. These reactons wll be added n model 3 (secton 3.4) Buldng the next model Model 2 wll nclude ncomplete oxdaton of C18:1ω9 to C16:1ω9nPPARα KO mce, and complete oxdaton of all FA n wld-type mce Model 2: accumulaton and (complete or partal) oxdaton of FA by the lver Ths model ncluded both FA uptake (see model 1 n secton 3.2) and FA oxdaton n the lver of both genotypes. 11

14 Both PPARα KO and wld-type mce have an actve oxdaton durng fastng but wth much hgher rates n wld-type mce In PPARα KO mce, only the partal oxdaton of C18:1ω9 was consdered (b C18:1ω9 = 1 whereas b = 0 for the other FA). Ths oxdaton was consdered to be ncomplete, and produced C16:1ω9, whch was modeled as s C18:1ω9 =0. As antcpated, the Dsturbance error (DE) of C16:1ω9 was greater for model 2 (87%, Table 6) than from model 1 (8%, Table 5).Comparatvely, the DE for C18:1ω9 dd not decrease notably (from 44 to 36%, Tables 5 and 6). In wld-type mce, the complete oxdaton of all FA was requred to obtan a better ft of the model, as shown by the ncrease of the DE for most of the FA (Tables 5 and 6). The estmated rate of oxdaton of C18:1ω9 npparα KO mce was only 1% of that estmated n wld-type mce durng a 72 h fastng perod, confrmng that wld-type mce had a much hgher hepatc FA oxdaton compared to PPARα KO mce. Fastng s thought to nduce a rse of hepatc lpds sensed by PPARα that, n turn, stmulates the expresson of oxdatve genes (Kersten et al., 1999). Studes usng PPARα KO mce have provded evdence that the absence of functonal PPARα decreases basal levels of β-oxdaton of C16:0 n PPARα KO mce, but nduces no dfference n the metabolsm of C24:0 compared wth wld-type mce (Aoyama et al., 1998). The hepatc expresson of most oxdatve genes was not nduced by fastng n PPARα KO mce (Leone et al., 1999). Fnally, betahydroxybutyrate (.e., an mportant ketone product of lver FA oxdaton) n PPARα KO mce s 14% of that n wld-type mce fasted for 24 h (Kersten et al., 1999). Consdered together, the ntroducton of a small oxdaton rate for PPARα KO mce durng fastng s not nconsstent wth the lterature results ndcated above. It should be kept n mnd that ths opton wll lkely underestmate the oxdaton rate, because a model wth a hgher FA uptake rate and a hgher oxdaton rate would produce smlar results. Furthermore, t s possble that oxdaton of FA other than C18:1ω9 also occurred n PPARα KO mce durng fastng. However, ths was not consdered because results from model 1 suggested that these oxdaton rates are small. Introducng addtonal oxdaton reactons was not necessary to obtan reasonable model predctons (Table 2). In wld-type mce, the smplest hypothess of complete oxdaton (s = 1) of FA was suffcent to model the FA content n the lver. Therefore, a step-bystep procedure dd not nclude the use of more refned hypotheses by combnng complete and ncomplete oxdaton. The calculated affnty coeffcents for the varous FA regardng oxdaton are gven n Table 3 and the cvmspe values are n Table 6. The accuracy of the model was generally good, except for C20:5ω3 and C22:6ω3, whch have DE proportons smaller than 25%. It s known that FA are oxdzed n peroxsomes or mtochondra at dfferent rates accordng to chan length and degree of unsaturaton (Mahler et al., 1953; Frtz, 1959; Shndo and Hashmoto, 1978; Mannaerts et al., 1979; Hltunen et al., 1986). To our knowledge, the relatve rates of oxdaton of FA are unknown. Even though FA may be oxdzed at dfferent rates, the model ftted the expermental data 12

15 well wthout the need for a tme-dependent regulaton of oxdaton durng the fed-to-fastng transton. Ths suggests that the PPARα-dependent nducton of FA oxdaton durng fastng s ether small compared to ts consttutve effect, or that t saturates relatvely quckly durng fastng. The saturaton hypothess may be tested n a specfc study focusng on the frst 10 to 20 h of fastng by evaluatng the expresson of genes and enzymes nvolved n the oxdaton of FA Buldng the next model Model 2 only ncluded FA uptake and oxdaton n the lver, but many of the short-comngs of model 1 could be resolved by ncludng the oxdaton of FA. As dscussed for model 1, the poor qualty of ft for C22:6ω3 cannot be resolved by oxdaton and the results for ths FA were not better n model 2 than they were n model 1 (Table 6). As ndcated above, C22:6ω3 can only be produced by elongaton and desaturaton (Fg. 2) from C18:3ω3.Thus, to buld model 3 we added the elongaton and desaturaton pathway to model 2. In wld-type mce, the oxdaton rate had to be estmated agan to account for the use of C18:3ω3 by both oxdaton and elongaton and desaturaton Model 3: accumulaton, oxdaton, and desaturaton and elongaton of FA by the lver Essental FA metabolsm nvolves the desaturaton and elongaton to synthesze very long-chan polyunsaturated FA from C18:3ω3 and C18:2ω6. Because delta-6 desaturase (D6D) s common to ω3 andω6 desaturaton pathways, C18:2ω6 and C18:3ω3 are n competton for ths rate-lmtng enzyme (Fg. 2) Elongaton and desaturaton process s actve durng fastng n both genotypes For both genotypes model 3 (FA uptake, oxdaton and elongaton/desaturaton) ftted the observed accumulaton of C22:6ω3 better (Table 7) than model 2 (Table 6). Ths suggests that elongaton and desaturaton of C18:3ω3 to C22:6ω3 are actve n both genotypes durng fastng. The need to nclude an actve elongaton and desaturaton pathway n the lver of mce under fastng condtons n PPARα KO mce s surprsng. The rate of desaturaton and elongaton s generally consdered to be lmted by D6D (Cho et al., 1999), whch s transcrptonally-actvated by SREBP1 (Matsuzaka et al., 2002). The nuclear form of SREBP-1 n the lver of mce has a very low, barely detectable level after 6 h of fastng (Horton et al., 1998). A second transcrptonal actvator of D6D s PPARα (Matsuzaka et al., 2002). Consderng that PPARα was nvaldated n PPARα KO mce, and that SREBP- 1 s nhbted by fastng (Horton et al., 1998), transcrpton and actvty of D6D should have rapdly decreased durng the frst hours of fastng n PPARα KO lvers. 13

16 Expermental valdaton: mrna expresson of D6D s stable durng the frst 24h of fastng To support at least n part the results of our model, mrna levels of D6D were montored by real-tme quanttatve PCR n the lver of mce after 0, 24, 48, and 72 h of fastng. As shown n Fg. 4, D6D mrna levels remaned constant durng the frst 24 h of fastng n the two genotypes. D6D mrna levels sgnfcantly decreased at 72h and 48h n wld-type and PPARα KO lvers respectvely. Therefore, D6D expresson seems to be regulated n a tme-dependent manner durng fastng and ts regulaton partally depends on PPARα expresson only after 24h. Ths result s consstent wth the need to ncorporate the desaturaton/elongaton pathway n our model for both genotypes to correctly ft the FA data. Addtonally, these data suggest that the mechansms by whch D6D mrna expresson s regulated durng fastng nvolve other molecular players than the known major regulators PPARα and SREBP1. These unknown regulators reman to be dentfed but could respond to several hormonal or metabolc sgnals that are modulated durng fastng, possbly dfferentally between wld-type and PPARα KO mce. Several hormones have been shown to reduce D6D expresson or actvty n the lver (for a revew see (Brenner, 2003)) ncludng glucagon and glucocortcods whch are ncreased durng fastng. However, to our knowledge, the accurate knetcs of these hormonal changes have not yet been descrbed n wld-type and PPARα knockout mce. Hence, t s dffcult to predct whether such hormonal sgnal may dfferentally nfluence D6D expresson between these two genotypes. On the other hand, several metabolc parameters dffer between fasted wld-type and PPARα KO mce. For nstance, the latter exhbt hypoglycema and reduced metabolc rates durng fastng (Kersten et al., 1999) n addton to mpared FA oxdaton (Le May et al., 2000). In the lver, glucose and FA (Gullou et al., 2008) may nfluence the transcrpton of enzymes nvolved n FA metabolsm. Changes n glucose, FA or other metaboltes that may nfluence the dfferental expresson of D6D reported here remans to be nvestgated. 4. Concluson A smple model ncludng fatty acds uptake, oxdaton and elongaton/desaturaton was able to predct correctly the varaton of most fatty acds n the lver of both PPARα KO and wld-type mce. Ths model ncluded parameter estmates n adpose tssue and lver to explan the change n fatty acd content n the lver durng fastng. Expermental measurements n dfferent organs obtaned n the same anmals and under the same expermental condtons are strongly needed n the future to predct the dynamcs of fatty acds n a gven organ. The presence of a basal oxdaton n both PPARα KO and wld-type mce wth a rate that depended on the genotype but not on the tme of fastng shows that PPARα has a consttutonal effect on oxdaton but lttle or no tme-dependent effects. The presence of an actve elongaton and desaturaton n both genotypes was surprsng n the lver of fastng mce. It confrms and strengthens earler results 14

17 (Nakamura and Nara, 2003) suggestng that the unsaturated fatty acds content n tssues s mantaned wthn physologcal ranges by feedback regulaton of synthetc pathways. The regulaton of desaturases by PPARα s dfferent from the man role of PPARα n nducng oxdaton (Nakamura and Nara, 2003) and cannot be explaned by the dfferental behavor of varous desaturases such as delta-6- desaturase and stearoyl-coenzyme A desaturase (Radulescu et al., 2006). Our results suggest that mechansms other than PPARα actvaton are lkely to contrbute to the regulaton of delta-6-desaturase actvty durng fastng. In the future, the model could be used to desgn specfc experments amng at a better understandng of lpd metabolsm as regulated by the nutrtonal status. The same set of equatons could be used n other tssues such as muscle, n other anmal speces, to predct nter-speces varablty n lpd metabolsm or n anmals fed dets wth dfferent FA compostons. 15

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