CONFORMATIONOFLIQUIDN-ALKANESF.GOODSAID-ZALDUONDOANDD.M.ENGELMAN,DepartmentofMolecularBiophysicsandBiochemistry,YaleUniversity,NewHaven,Connecticut06511ABSTRACrTheconformationsofliquidn-alkaneshavebeenstudiedusingneutronscatteringtechniquestobetterunderstandtheconformationalforcespresentinmembranelipidinteriors.Wehavestudiedhydrocarbonchainshavinglengthscomparabletothosefoundforesterifiedmembranelipidfattyacids,andfindthatthestericconstraintsofpackingintheliquidstatedonotchangetheconformationaldistributionsofhydrocarbonchainsfromthoseimposedbytheintrachainforcespresentinthegasphase.Itfollowsthatthecentralregionofmembranescontaininglipidsinthedisorderedstateshouldcontainhydrocarbonchainconformationsdeterminedprimarilybyintrachainforces.INTRODUCTIONBiologicalmembranescontaininglipidsinthedisordered(liquidcrystalline)statescatterx-raysandneutronsinabroadbandofintensitycenterednear4.6A-'(1,2).Thescatteringfromalkanesintheliquidstateisverysimilarinthisregion(3),andhassuggestedtosomeaclosesimilarityofpropertieswithmembraneinteriors(4).Observationsofmembraneviscositiessupportsuchacontention.Whileitwouldbedesirabletostudytherelativerolesofstericinteractions,bondrotationpotentialsandanisotropicoriginconstraintsinnaturalmembranes,ithasfrequentlyprovedusefultoexploresimplersystemswhichpermitamoreprecisecharacterization.Itis,therefore,ofsomeinteresttoexplorethepropertiesofliquidalkaneshavingchainlengthscomparabletothoseofmembranefattyacidstoimproveourunderstandingoftheconforma-tionspresentinmembranelipidinteriorsandtheforcesgivingrisetothoseconformations.Inthisstudyweaskwhetherthestericconstraintsofpackingintheliquidstatechangetheconformationaldistributionsofhydrocarbonchainsfromthoseimposedbytheintrachainforcespresentinthegasphase(5).Wefocusourattentiononnormalalkanechainsbetween8and16carbonslong,sincethisisthechainlengthrangeforesterifiedmembranelipidfattyacidsinwhichstablebilayerscanbeformed(6)andwhichdonotviolatethebiologicalrequirementforafluidmembrane(7).Saturatedchainslongerthan16carbonsarenotusuallyfoundinlargeamountsinbiomembranes,althoughlongermono-andpolyunsaturatedchainsarecommon.NeutronscatteringcanprovideinformationabouttheconformationofindividualmoleculesinliquidalkanesthroughtheuseofDeuteriumlabeling.Sinceneutronsscatterdifferentlyfrom'Hand2H,alkanechainsinachemicallyhomogeneousliquidcanbemadetocontrastwit&theirnenvironmentbydeuteration.ThispermitsmeasurementoftheradiusofgyrationofDr.Goodsaid-Zalduondo'spresentaddressistheDepartmentofBiologicalChemistry,WashingtonUniversitySchoolofMedicine,St.Louis,Mo.63110.BIOPHYS.J.©BiophysicalSociety*0006-3495/81/09/587/08$1.00587Volume35September1981587-594theaverageconformationforanalkane,andideasabouttheinfluenceoftheenvironmentonconformationcanbetestedusingchangesinameasuredparameter.THEORETICALRESULTSAsinglehydrocarbonchaincanbecharacterizedbyitsneutronscatteringlengthdensity,p=2bi/VwherebisthescatteringlengthoftheithatomicnucleusandVisthevolumeoccupiedbythemolecule.Ifweusethereciprocalspacecoordinatek=2wrs=4wxsin0/Xwhere20isthescatteringangleandXistheneutronwavelength,aninterpretationofthescatteringofmixturesofdeuteratedandhydrogenatedalkanescanbe basedontheexpression(8-10)ITOT(k)=S(k)CHCH(PH-PD)(1)whereITOT(k)isthetotalcoherentlyscatteredintensity,S(k)istheFouriertransformofthemolecularformfactor,CHandCDarethefractionalcompositionofnaturalandperdeuteratedhydrocarbons,andPHandPDarethefractionalcompositionlengthdensities.Eq.1wasoriginallyderivedfromsimilarstudiesontheconformationofpoymersinthemelt.Inthatwork(8)ontheconformationoflargeHandDpolymersinthemeltorbulk,itwasfoundtopredictaccuratelytheHandDfractionalcompositiondependenceofITOT(k),withouttheinclusionofcrossterms,indicatingnegligibleinterferenceeffectsatallfractionalHandDcompositions.Theabsenceofaninterferenceeffectcanbeascribedtothemultipleconforma-tionsandorientationsavailabletothepolymersinthemeltorbulk.Intheabsenceofsignificantintermolecularinterferenceeffects,theradiusofgyrationofamoleculemaybemeasuredfromthelow-anglescatteringcurve.Ingeneral,theradiusofgyrationRg,isthesecondmomentofthescatteringlengthdensity,p(r)withrespecttothecenterofscatteringmass,orR=fr2p(r)dv/fp(r)dv.Theradiusofgyrationofahomogeneousparticledependsontheshapeoftheparticle.Forexample,forellipsoidsofrevolutionofsemi-axesa,a,andwa,(10)Rg=a[(2+w2)/5]'12(2)RgcanbemeasuredforparticlesofanyshapefromtheGaussianregionofthecurvebytheuseofaGuinierplot(9)oftheln[I(k)]asafunctionofk2.Theslope,a,ofthelinearregionofthisplotisrelatedtoRgby(11)Rg=3a'1/2.(3)Intheregionofk-spacewherek<1/Rg,I(k)scatteredbyaflexiblepolymerchainisproportionalto(12)1-k2R2/3.(4)Thefactthatsegmentsinachainareconnectedinarandomcoilyieldsacharacteristicscatteringlaw.Intheabsenceofexcludedvolumeeffects(asisthecaseforthepolymerbulkphase(8]),Debye(13)hasshownthatI(k)fork>1/Rgisproportionalto(2/x)[x-1+exp(-x)],wherex=k2R.BIOPHYSICALJOURNALVOLUME351981588MATERIALSANDMETHODSNeutronDiffractionfromLiquidn-AlkanesSpectrograden-alkaneswerepurchasedfromAldrichChemicalCo.Inc.(Milwaukee,Wis.).Perdeuter-atedn-alkaneswerefromMerckIsotopes.Samplesfortheexperimentsweremixedtoafinalvolumeof300yl,loadedintoneutrondiffractioncells(14)withaPasteurpipette,andsealedwithasampleholderarrangementwhichpreventstheformationofairbubblesbymaintainingasealonthe80-glsamplethroughan0-ring.Low-andhigh-angleneutrondiffractionexperimentsanddatanormalizationprocedureshavebeendescribed(14).RESULTSNeutronDiffractionfromLiquidn-AlkanesFig.1showsthelow-angleneutrondiffractionfromamixtureof8mol%D(mol/100mol)and92mol%Hdodecaneintheliquidphase(450C),andthecorrespondingGuinierplotforthisdata.Modelcalculationsfortheall-transconformationofn-alkanechainsfrom8through32carbonsindicatethatthegaussianapproximation(15)usedbyGuiniershouldbevalidfortherangeofreciprocalspacesampledintheseexperiments,eveniftheconformationintheliquidstateshouldapproachthelimitingcaseoftheall-transmodel.TheresultsofthesecalculationsarepresentedinFig.3intheformofaplotofthemoleculartransformsquaredobtainedfromEq.2andtheGaussianfunctionexpectedfromtheradiusofgyrationforthe4Ik'¶.il4C4!56.0;.-.',..;v,;t-;,*00-.ocwo>A.-.T.-com-4offi