J. Am. Chem. Soc. 1997, 119, 169-174

J.Am.Chem.Soc.1997,119,169-174169

InternuclearDistanceMeasurementsupto0.44nmforRetinalsintheSolidStatewith1-DRotationalResonance13CMASNMRSpectroscopy

P.J.E.Verdegem,M.Helmle,J.Lugtenburg,andH.J.M.deGroot*

ContributionfromGorlaeusLaboratories,LeidenInstituteofChemistry,LeidenUniVersity,P.O.Box9502,2300RALeiden,TheNetherlandsReceiVedMay3,1996X

Abstract:Theresultspresentedinthispapershowthataccuratethrough-spaceinternucleardistancemeasurementscanbeperformedondoublylabeledretinalsusingtheone-dimensionalapproachtothesolidstatemagicanglespinning(MAS)rotationalresonanceNMRtechnique.Theapparentsplitting?ω1oftheresonancesatn)1rotationalresonanceforthelabeledvinylicpositionsof(all-E)-[10,20-13C2]retinal,(all-E)-[11,20-13C2]retinal,and(all-E)-[12,20-13C2]retinalcanbesimulatedwithacoherentsetofparameters.FromaseriesofsimulationswithdifferentdipolarcouplingconstantbIS,itappearsthatbIS/2π??8)1.15(?ω1/2π)+7(Hz)http://wendang.chazidian.comingthisrelationshipasacalibration,itisdemonstratedwithasetofmodelcompoundsthatstraightforwardLorentzianfittingtomeasure?ω1canbeusedtodetermineinternucleardistancesupto0.44nmindoublylabeledretinalsinthesolidstate.

Rotationalresonanceisahigh-resolutionsolidstatemagicanglespinning(MAS)NMRtechniqueinwhichtheinterferenceoftheMASwiththehomonucleardipoleinteractionswithinapairofequalspinsIandSgivesrisetodipolarrecoupling.1,2Thisphenomenoncanbeexploitedtomeasuretheinternucleardistance.Therotationfrequencyofthesampleωrisadjustedtomatcharotationalresonanceconditionnωr)?ωISwith?ωIS)ωI-ωS,thedifferencebetweentheisotropicshifts.Withnasmallintegerandahomonucleardipolarcoupling

µ0γ2BIS)-4πr3

IS

|()(1)

sufficientlystrongcomparedtotheaveragelinewidthsΓ,thelineshapeschangeatorclosetoarotationalresonanceconditionandadditionalfinestructureorbroadeningcanbeobserved.Ineq1µ0isthemagneticpermeabilityinvacuum,γisthegyromagneticratioofthenuclei,andrISrepresentstheinter-nucleardistance.Toafirst-orderapproximation,neglectingtheinfluenceofanisotropyandrelaxationeffects,anapparentsplitting?ωnofeachresonanceisexpected.1Atorcloseton)1rotationalresonancethespectrumofadoublylabeledsamplecanbedescribedby

S(ω))

1

16πbISM)1

∑Y

8

(1)

(

?M(ω)

bIS/(2??8)

]

1/2

(2)

with?M(ω)thesetoffrequencyoffsetfunctionsfortheeightspectralcomponentsand

Y(1)(x))

[

1

+1

(1-x2)1/2

][

1/2

+

1

-1

(1-x2)1/2

(3)

1.Theextremaofthespectrumcanbefoundatthepositionswherex)1orx)-1;inthesecasesthelineshapefunctiongoestoinfinity.IntheabsenceofJ-couplingthesesingularitiescanbefoundatω)ωI(bIS/2??8andω)ωS(bIS/2??8,predictinga“splitting”inthelineshapebIS/??8.1

Inanestablishedapproachtomeasuredistancesbetweenapairof13Catoms,oneofthespinsisselectivelyinvertedandtherotor-drivenexchangeofmagnetizationisfollowedintimebycollectingaseriesof1-Ddatasets.3ThetrajectoryofthedifferenceZeemanpolarization?Iz-Sz?(t)maythenbesimulatedtoyieldtheinternucleardistance.1-3Theinherentlytwo-dimensionalZeemanpolarizationexchangeNMRtechniquehasalready,atanearlystage,beensuccesfullyappliedtospecificallydoubly13C-labeledretinalinthelight-drivenionpumpbacteriorhodopsin,4whichcontainsaretinoidphotochemi-calenergyconverter.5Forthebacteriorhodopsintherotationalresonancetechniquehasbeenusedtodiscriminatebetweens-cisands-transconformations,providingforthefirsttimegenuinestructureinformationtoatomicresolutionforanintrinsicmembraneprotein.4,6Thebacteriorhodopsinmembraneproteinisamemberofanimportantclassofbiologicalphotoreceptors.Anothermemberoftheclass,rhodopsin,7isaG-protein-coupledreceptorandresponsibleforthephotochemicalenergyconver-sionandtheprimarystepsinvisualsignaltransductioninvertebrates.

Theaimofthisinvestigationistoexplorethepossibilityformeasuringthrough-spaceinternucleardistancesupto0.44nmwithhighaccuracyfromtheanalysisoftherotationalresonancelineshape,obtainedthroughasingleone-dimensionalexperi-mentonadi-labeledretinal.Theone-dimensionalapproachtotherotationalresonancedistancemeasurementsisillustratedandcalibratedonasetofdoublylabeledcompounds,(all-E)-[10,20-(3)RaleighD.P.;Levitt,M.H.;Griffin,R.G.Chem.Phys.Lett.1988,146,71.

(4)Creuzet,F.;McDermott,A.;Gebhard,R.;vanderHoef,K.;Spijker-Assink,M.B.;Herzfeld,J.;Lugtenburg,J.;Levitt,M.H.;Griffin,R.G.Science1991,251,783.

(5)Oesterhelt,D.;Stoeckenius,W.NatureNewBiol.1971,233,149.(6)Thompson,L.K.;McDermott,A.E.;Raap,J.;vanderWielen,C.M.;Lugtenburg,J.;Herzfeld,J.;Griffin,R.G.Biochemistry1992,31,7931.(7)Hargrave,P.A.;McDowell,J.H.FASEBJ.1992,6,2323.

thelineshapefunction,1whichisonlyevaluatedfor0<|x|<

AbstractpublishedinAdVanceACSAbstracts,December1,1996.(1)Levitt,M.H.;Raleigh,D.P.;Creuzet,F.;Griffin,R.G.J.Chem.Phys.1990,92,6347.

(2)Nielsen,N.C.;Creuzet,F.;Levitt,M.H.;Griffin,R.G.J.Chem.Phys.1992,96,5668.

X

S0002-7863(96)01475-8CCC:$14.00©1997AmericanChemicalSociety

170J.Am.Chem.Soc.,Vol.119,No.1,1997Figure1.(a)Molecularstructureof(all-E)-retinal,showingthepositionslabeledforthisstudy.(b)Antiparallelarrangementof(all-E)-retinal.Theshortintermoleculardistancer10,20′)0.367nmisindicatedwithadottedline.8Theiononeringisnotcompletelyresolved.

13C2

]-,(all-E)-[11,20-13C2]-,and(all-E)-[12,20-13C2]retinal.Aswillbeexplainedbelow,thesecompoundsprovidemodeldistancesof0.253,0.295,0.367,and0.440nmthatarealsowell-determinedbyX-raydiffractionstructuraldataofthecrystalline(all-E)-retinal.8Inaddition,theyalreadyprovideacoherentsetofmodelsforonespecificbiophysicalproblem,thecharacterizationoftheconformationaroundthe11-(Z)bondoftheretinylidenechromophoreinthevisualsignaltransductionpigmentrhodopsin.7

Figure1ashowsthemolecularstructureof(all-E)-retinal,indicatingthepositionslabeledforthisstudy.InFigure1b,arepresentationoftherelativeorientationoftworetinalmoleculesinthecrystallinesolidstateof(all-E)-retinalisshown.Inthisfiguretheiononeringisnotdrawncompletely,sincestructuraldisorderpreventedthedeterminationofallatompositionswithX-raystructuredetermination.8Becauseoftheantiparallelspatialordering,theshortestintermolecularinternucleardistancebetweenthe10and20′positionsintwodifferentmoleculesr10,20′)0.367nm(indicatedwithadottedline)isshorterthantheintramolecularr10,20)0.440nm.Hence,forasamplecontainingdilutehighlyenrichedpairs,theintramolecularcouplingwilldominate,whilethestrongestdipolarinteractioninauniform[10,20-13C2]-labeledsampleisassociatedwiththeintermolecularcoupling.

Inordertomeasuredistancesbetweenthelabeledpositionsinthesemodelcompounds,wecarefullyanalyzedresonancelineshapesusingsimulationsandfitprocedures.Toachievethis,high-resolutionCP/MASNMRspectrawererecordedforpure[12,20-13C2]-,pure[11,20-13C2]-,pure[10,20-13C2]-,and[10,20-13C2]retinaldilutedto15%innaturalabundanceretinalatdifferentrotationfrequenciesofthesamples.Itisshownthattheobservedsplittingforthen)1rotationalresonance?ω1ofthevinylicpositioncanbeusedforallfourmodelcompoundstodeterminerISusingeq1.Finally,wecomparethedistancesobtainedfromourMASNMRinvestigationswiththeX-raystructuraldata.8MaterialsandMethods

Synthesisof(all-E)-[10,20-13C2]retinal,(all-E)-[11,20-13C2]retinal,and(all-E)-[12,20-13C2]retinalwasperformedwithproceduresoriginallydevelopedbyGroesbeeketal.,9startingfromcommerciallyavailable

(8)Hamanaka,T.;Mitsui,T.Acta.Crystallogr.1972,B28,214.

(9)Groesbeek,M.;Lugtenburg,J.Photochem.Photobiol.1992,56,903.

Verdegemetal.

Table1.IsotropicChemicalShifts(σi),Anisotropies(δ),

AsymmetryParameters(η),andPseudotransverseRelaxationTimes(T2′)for-[11,20-theLabeled13CPositionsof(all-E)-[10,20-13C2]Retinaland(all-E)2]Retinallabelσi(ppm)δ(kHz)ηT2′(ms)10130.1(0.1)8.1(0.3)1.0(0.1)8.3(0.1)11134.1(0.1)-11.3(0.3)0.7(0.1)7.5(0.1)12133.8(0.1)8.0(0.3)1.0(0.1)7.2(0.1)20

12.9(0.1)

-1.6(0.3)

1.0(0.1)

10.6(0.1)

Table2.ObservedSplitting(?ω1/2π),LineWidthofthe

Second-DerivativeSignaloftheωr/2π)10.0kHzSpectrum(Γ),bIS/2π??8CalculatedfromtheNMRData,andInteratomicDistance(rIS)AsDeducedfromNMRfor(all-E)-[10,20-13C2]Retinal,(all-E)-[11,20-13C2]Retinal,and(all-E)-[12,20-13C2]Retinala?ω1/2πΓbIS/2πrIS(NMR)rIS(X-ray)compound(Hz)(Hz)(Hz)??8(nm)(nm)10,20(15%)124120.80.5050.44010,20(100%)354547.30.3830.36711,20784796.70.3020.29612,20

141

55

169.2

0.250

0.253

a

ForcomparisontheX-raydistancesarealsolisted.

[1-13C]acetonitrile,[2-13C]acetonitrile,[2-13C]aceticacid,and[13C]-methyliodide(CambridgeIsotopeLaboratories,MA).Aftersilicagel

columnchromatographypurificationoftheretinalisomermixture,the(all-E)-retinalswerecrystallizedfromn-pentaneat-20oC.Thepurityofthelabeledretinalswasconfirmedwith300MHz1HNMR(CDCl3),75.4MHz1H-noise-decoupled13CNMR(CDCl3),andmassspectrom-etry,andtheisotopeincorporationis>99%atbothpositions.Subsequentlyfivesampleswereprepared:pure(all-E)-[10,20-13C2]-retinal,pure(all-E)-[11,20-13C2]retinal,pure(all-E)-[12,20-13C2]retinal,(all-E)-[10,20-13C2]retinaldilutedto15%innaturalabundance(all-E)-retinal,and(all-E)-[11,20-13C2]retinaldilutedto15%innaturalabundance(all-E)-retinal.Thedilutesampleswerepreparedfromasolutionof15%labeled(all-E)-retinaland85%naturalabundance(all-E)-retinal(FlukaSwitzerland),inn-pentanewithsubsequentrecrys-tallizationat-20°C.Allmanipulationswithisomericallypureretinalswereperformedindimredlight(λ>700nm)orinthedark.Theretinalswerestoredinanargonatmosphereat-80°C.CrystallinesampleswerepackedintozirconiumoxiderotorswithKEL-Fcaps.CP/MASNMRexperimentswereperformedwithaBrukerMSL400spectrometeroperatingata13Cfrequencyof100.6MHz,usinga4mmMASprobewithinfraredspinningspeeddetection.Thespinningspeedwaskeptstablewithin3Hz.RAMPcrosspolarization10andcontinuouswavedecouplingwithatypicalnutationfrequencyof80kHzintheprotonchannelwereused.Thespectraofthecrystallizedretinalswereobtainedbyaccumulatingapproximately1000transientswitharecycledelayof1.75s.Thedatawerecollectedin8192pointswithadigitalresolutionof6Hz.Inoneexperimenttheisotropicchemicalshiftσi)12.9ppmfortheC-20methylpositionwasreferencedtothe1-13Cofexternalsinglylabeledglycine,whichresonatesat176.04ppmdownfieldfromTMS.OtherdataareinternallyreferencedtotheC-20shift.Then)1rotationalresonanceconditionsweredeterminedbyfittingthelinesofthelabeledpositionsintheωr/2π)10.0kHzspectrawithLorentziansandbytakingthedifferencebetweenthefittedresonancefrequencies.Simulationsofrotationalresonancespectrawereperformedusingthenumericalproceduresdescribedinref1and11.Fullpowderaveragesweresimulatedusingatleast2000crystalliteorientations.ForthecomparisoninFigure7,zerofillingupto32kwasappliedpriortoFouriertransformationofthesimulatedsignals.TheinputparametersarelistedinTables1and2.

ResultsandDiscussion

Figure2showsthe100.6MHzCP/MASNMRspectraof(all-E)-[10,20-13C2]retinal(a,b),(all-E)-[11,20-13C2]retinal(c,

(10)Peersen,O.B.;Wu,X.;Kustanovich,I.;Smith,S.O.J.Magn.Reson.1993,104,334.

(11)Weintraub,O.;Vega,S.;Hoelger,Ch.;Limbach,H.H.J.Magn.Reson.1994,109A,

14.

http://wendang.chazidian.comparisonof13CCP/MASdataatn)1rotationalresonance(solidlines)withdataatωr/2π)10.0kHz(dottedlines):welloffrotationalresonanceforpure(all-E)-[10,20-13C2]retinal,99%labeledatbothpositions(a),(all-E)-[10,20-13C2]retinaldilutedto15%innaturalabundance(all-E)-retinal(b),pure(all-E)-[11,20-13C2]retinal99%dilabeled(c),(all-E)-[11,20-13C2]retinaldilutedto15%innaturalabundance(all-E)-retinal(d),and(all-E)-[12,20-13C2]retinal

(e).

d),and(all-E)-[12,20-13C2]retinal(e).Forallfivesamplesspectrawereaccumulatedwithωr/2π)10.0kHz(dottedlines)andattherespectiven)1rotationalresonanceconditions(solidlines).Forthe[10,20-13C2]samplesωr/2π)11.794(2)kHz,forthe[11,20-13C2]samplesωr/2π)12.198(2)kHz,andforthe[12,20-13C2]sampleωr/2π)12.180(2)kHzatthen)1rotationalresonancecondition.ThedatainFigure2arescaledinordertokeeptheintegratedintensitiesofthesignalsapproximatelyequalatthedifferentspinningspeeds.Theeffectoftherotor-drivendipolarrecouplingonthen)1lineshapeisnowevident.Theresonancesofthen)1spectraarebroadenedcomparedtothe10.0kHzspectra,andadditionalfinestructureisobservedforthe[11,20-13C2]and[12,20-13C2]compounds.Then)1spectraofthe[10,20-13C2]sampleshowabroadeningofthesignals,butnoadditionalfinestructure.Thedipolarrecouplingeffectsaremorepronouncedfor(all-E)-[11,20-13C2]-and-[12,20-13C2]retinalsincether11,20)0.296nmandther12,20)0.253nmareconsiderablysmallerthanr10,20)0.440nm.

Ifthespinpairinvolvesamethylandavinyliccarbon,?ωshiftanisotropies.+|δISJ|δI|S|,thesumTofirstoftheorderabsoluteasplittingvaluesoftheoftheresonancechemicalatthen)1rotationalresonanceconditionisexpectedforthestrongerdipolarcouplings.Sincethedipolarinteractionissymmetricinthetwospins,asimilarrotationalresonancelineshapeforbothlabelsignals,forn)1,isinprincipleexpectedinthecaseofsmallshiftanisotropy.1

InFigure2c,dtheC-11resonanceisapparentlyadoublet,buttheC-20lineshapeismorecomplicated.Itisimmediatelyobviousthatforthe[11,20-13C2]compoundonlytheresponsefromthevinylicC-11resonanceisinlinewiththegenerallyacceptedtheory,whichpredictsaneatsplittingofbothlines.1Forthe[12,20-13C2]compoundbothlabeledsidesofthen)1rotationalresonancegiverisetoadoublettypecontributiontothespectrum,althoughtheC-20responseappearsdistorted.Then)1experimentaldatacanbecomparedwiththeoreticalpredictionsindetailtoaddresstheapplicabilityofthetheoretical

J.Am.Chem.Soc.,Vol.119,No.1,1997171

Figure3.ApproximateorientationofthereducedCSAtensorsfortheC-10,C-11,C-12,andC-20positionsandthedipolarcouplingtensorsinthelabeled(all-E)-retinals.

approachesandtocalibrateamethodformeasuringdistances.Itshouldbestressedherethattheparametersusedforthesesimulationsarenotfittedtotherotationalresonancedata,butarefromindependentsources.AllparametersusedforthesimulationsarefromX-rayandseparateMASexperimentsandarelistedinTables1and2.TheisotropicchemicalshiftsσiweremeasuredbyfittingtheMAScenterbandsfortheωr/2π)10.0kHzdatasetswithLorentzians.Theanisotropyparam-etersδandηwereobtainedbyaHerzfeld-Bergeranalysis12ofdatasetscollectedwithωr/2π)2.149kHz,ωr/2π)1.564kHz,andωr/2π)1.937kHzforthe[10,20-13C2],[11,20-13C2],and[12,20-13C2]compounds,respectively(datanotshown).PseudotransverserelaxationtimesT2′usedforthesimulationswereestimatedfromtheLorentzianlinewidthsΓatωr/2π)10.0kHzaccordingtoT2′)(πΓ)-1.Forallthecompoundsusedinourstudy,theJcouplingsareverysmallandcanbeneglected.Intherotationalresonancesimulations,thedipolarcouplingbISiscalculatedfromtheinternucleardistanceusingeq1.Aright-handedprincipalaxisframeforthedipolarcouplingtensorwastakenastheframeofreferencewiththepositivezaxisalongthevectorconnectingthevinylicandC-20atomsandtheyaxisperpendiculartothexaxisintheconjugatedplane(Figure3).Theorientationsoftheprincipalaxisframesofthechemicalshifttensorswithrespecttothemolecularframearenotknownexactly.Foravinyliccarbon,theσ11axis,correspondingtothemostupfieldprincipalcomponent,isalmostperpendiculartotheplaneofconjugation.Theσ33axis,forthemostdownfieldcomponent,isapproximatelyintheconju-gatedplaneperpendiculartothedoublebond,andfinallytheσ22axisisalongthisbond(see,e.g.,Veeman13).Toobtainthereducedtensorelementsforthesimulations,σxx,σyy,andσzz,with|σzzwassubtracted|gand|σxx|thegprincipal|σyy|,theaxisisotropiccomponentschemicalwereshiftre-σiarranged.

TheresultingorientationsoftheprincipalaxesforC-12,C-11,andC-10arealsodepictedinFigure3.Theeffectofthemethylanisotropyonthelineshapeisnegligablesince?ωISismuchlargerthanthemethylanisotropyδS.Anapproximateorienta-tionoftheprincipalaxisframeforthe20-methylwasinferredfromthevariouscompilationsofchemicalshiftanisotropydatapresentedintheliterature,13,14indicatingthattheσ11axisshouldberoughlyalongthechemicalbond,whiletheσ33axisismostlikelyperpendiculartothebondintheplaneofthemolecule.Thischoiceparallelsearlierrotationalresonanceinvestigations.4Aftersubtractionofσiandrearrangementoftheprincipalcomponents,theprincipalaxisframeorientationdepictedinFigure3results.

(12)deGroot,H.J.M.;Smith,S.O.;Kolbert,A.C.;Courtin,J.M.L.;Winkel,C.;Lugtenburg,J.;Herzfeld,J.;Griffin,R.G.J.Magn.Res.1991,91,30.Herzfeld,J.;Berger,A.E.J.Chem.Phys.1980,73,6021.(13)Veeman,W.S.Prog.NMRSpectrosc.1984,16,193.

(14)Mehring,M.PrinciplesofHighResolutionNMRinSolids,2nded.;Berlin,

1983.

172J.Am.Chem.Soc.,Vol.119,No.1,1997Figure4.StepwisederivationoftheEulerangles(R,??,γ)forthevinyliccarbonsillustratingthetransformationoftheprincipalaxisframe(xp,yp,zp)intothedipolarreferenceframe(xd,yd,zd

).

Figure4illustratesthestepwisederivationoftheEuleranglesforthevinyliccarbonsthatarerequiredtotransformthechemicalshifttensorframesintothedipolarreferenceframe.Followingstandardconventions,15whereforasetofEulerangles(R,??,γ)theR(R,??,γ))Rz′′(γ)Ry′(??)Rz(R),itiseasilyseenfromFigure4thatR(-30,90,180)http://wendang.chazidian.comingasimilarprocedure,itcanbededucedthatR(0,-60,-90)representstherotationneededtotransformthemethylprincipalaxisframeintothedipolarreferenceframe.Forthe[12,20-13C2]labelsitisR(0,90,180)andR(0,-30,-90)thattransformtheshiftframesofC-12andC-20intothedipolarframe.Finally,forthepure[10,20-13C2]retinal,inwhichtheintermolecularcouplingdominates,theorientationofthedipolartensorandthereforethereferenceframeisdifferentfromthatinthecaseofdilute[10,20-13C2]retinal.ThedeviationofthevectorconnectingC-10andC-20′andthezpaxisforC-10iswithintheerrorofdeterminingtheEuleranglesassociatedwiththeuncertaintiesintheshifttensororientations,andthedipolarreferenceframewaschosentocoincidewiththeprincipalaxisframeoftheC-10vinyliccarbon.Inthatcase,theorientationoftheprincipalaxisframeforC-10isthesameasforthedipolarreferenceframe,whileR(-90,90,-30)transformstheprincipalaxisframeofC-20′intothereferenceframe.

Forthevinyliccarbons,deviationsupto?15°fromthereferenceframesindicatedinFigure3mayoccur,whileforthe20-methyl,thedeviationmaystillbelarger.However,since?ωISresonanceJ|δI|line+|δSshapes|,theeffectisonlyoftheminor.anisotropyThiswasontheverifiedrotationalbycalculatingtheoreticalpredictionsforthelineshapesusingdifferentvaluesfortheparameters.Inparticular,simulationswithdifferentsetsofEuleranglesweregenerated,givingalmostnegligabledifferencesinthespectra.

Forinstance,acomparisonbetweenexperimentaldatafortheC-11positionandsimulationsisillustratedinFigure5.In

(15)Spiess,H.W.InNMRBasicPrinciplesandProgress;Diehl,P.,Fluck,E.,Kosfeld,R.,Eds.;Springer-Verlag:Berlin,1978;Part15.

Verdegemetal.

Figure5.13CCP/MASNMRdata(solidlines)andsimulations(dottedlines)forpure(all-E)-[11,20-13C2]retinalatωr/2π)10.0kHzandωr/2π)12.198kHz,then)1rotationalresonance:(a)spectrum,(b)firstderivative,and(c)secondderivative.

thisfigure,thesignalsofthevinylicandmethyllabelsareshown,withωr/2π)10kHzandatn)1rotationalresonance.Inaddition,thefirstandsecondderivativesofthesignalsareplotted.AllresonancesarescaledsothattheamplitudesoftheC-11resonancescoincide.ForthevinylicC-11theagreementbetweenthedataandsimulationsisquantitativewithrespecttothepositionsofthemaximaandqualitativewithrespecttotheoveralllineshape.

FromthecomparisonoftheexperimentalresultswiththesimulateddatainFigure5,itisevidentthatitisimpossibletosimulatetheexperimentallyobservedlineshapesofbothspinsindetailforinternucleardistancesinthe0.3nmrangewiththerotationalresonancetheorythatwasoriginallydevelopedforthedescriptionofthisphenomenonwithinadilutespinpair,forshortinternucleardistancesandcorrespondinglystrongdipolarcouplings,asforadjacentcarbonsinonemolecule.1AsimilarconclusionwasreachedindependentlybyPeersenetal.16whostudiedtherotationalresonanceeffectsforpairsofnucleiinasmallpeptide.

Then)1second-derivativelineshapeforthemethylsideapparentlycontainsanoffrotationalresonancetypesingleline,superimposedonthen)1rotationalresonance“doublet”.Thediscrepanciesbetweenexperimentandisolatedspin-pairtheoryforthemethylresponseoriginatefromadditionalfield-dependentinteractionsinterferingwiththeveryweakhomonucleardipolarcouplings.Forinstance,thelinewidthsforthetwolabelsaredifferent,andfortheωr/2π)10kHzdatathevinylicresonancehasextendedwingsatitsbottom,whicharenotreproducedbythetheory.Incontrast,themethylsideofthespinpairresponseismuchnarrower.Interestingly,theseparationbetweenthetwoouterlinesinthesecond-derivativemethylresponseatrotationalresonancematchesthesimulationsandthecharacteristicsplittingofthevinylpart(Figure5c).Inthisinvestigationwefocusontheextremaand?ω1.Adiscussionofthedetailsofthelineshapeisbeyondthescopeofthepresentstudy,andwillbereportedelsewhere.

Interestingly,despitetheobviousdifferencesbetweentheexperimentaldataandthetheoreticalpredictionswithrespecttotheoveralllineshape,the?ω1matchesthesimulationsquitewell.Toenhancetheextremaforfurtheranalysis,wenowoften

(16)Peersen,O.;Groesbeek,M.;Aimoto,S.;Smith,S.O.J.Am.Chem.Soc.1995,117,

7228.

http://wendang.chazidian.comparisonofsecondderivativesofexperimentaldata(solidlines)andsimulations(dottedlines)forpure(all-E)-[10,20-13C2]retinalandpure(all-E)-[11,20-13C2]retinalwithωr/2π)10.0kHz(a),atn)1rotationalresonance(rr),+25Hzoffrr(c),+100Hzoffrr(d),-25Hzoffrr(e),and-100Hzoffrr

(f).

usesecondderivativesofthedataandthecorrespondingsimulations.ThisisillustratedinFigure6,whichshowsthesecondderivativesoftheexperimentaldata(solidlines)andsimulations(dottedlines)forpure(all-E)-[10,20-13C2]retinalandpure(all-E)-[11,20-13C2]retinalatsixdifferentrotationfrequen-cies(ωr/2π)10.0kHz,then)1rotationalresonancecondition,25and100Hzabovethen)1rotationalresonanceconditionand25and100Hzbelowthen)1rotationalresonancecondition).Itisclearthattheminimainallsixsecondderivativedatasetsaresatisfactorilyreproducedbythesimula-tions.InFigure6b,forthen)1rotationalresonancecondition,thesplittingsinthesecondderivativeofthedataareinfactremarkablywellreproducedbythesimulations.

Atn)1rotationalresonance,forpure(all-E)-[10,20-13C2]-retinalthechangeinlineshapeoftheC-10signalisnowalsoduetoacombinationofintramolecularandintermolecularcouplings,sincer10,20′<r10,20.Theminimaintheexperimentaldataareaccuratelyrepresentedbytheminimaofthetheoreticallinecalculatedfortheintermoleculardistance,inagreementwithexpectations.

Itisthusconcludedthattheapparentsplittinginthevinylicresonancesisduetodipolarrecouplingattherotationalresonancecondition.Thisinformationmaybeusedtodeterminedistancesbetweentwospins.Formodelcompoundslike(all-E)-retinaltheanalysisofexperimentaldatawiththehelpofsimulationsisdefinitelythemostelegantandprobablythemostaccuratewayofmeasuringtheinternucleardistancedirectlyfromthesecond-derivativedata.However,whenthemethodisappliedtosystemswherethespinpairsareverydilute,like,forinstance,inmembraneproteins,therelevantinformationneedstobeextractedfromanoisybackgroundcontainingcontributionsfromnaturalabundancesignalsthatmaybeseveraltimesstrongerthanthesignalsfromthelabels.Thenextstepinouranalysisprocedureisthereforetoinvestigateifitispossibletoextractthesplitting?ω1fromthesecond-derivativedatausingstraightforwarditerativefittingwiththesecondderivativeofapairofLorentzianlinesandtoverifyifthesplittingsmeasuredinthiswaystillreproducethe?ω1predictedbythefullcomputersimulations.First,σiandΓfortheωr/2π

J.Am.Chem.Soc.,Vol.119,No.1,1997173

Figure7.bIS/2π??8fromX-raydeterminationversus?ω1/2πofthevinylicresonancesmeasuredfromtheNMRspectraofthefourmodelcompounds(9).Thesizeofthesquaresrepresentstheestimateofthestatisticalerrorsforbothexperimentalprocedures.Thesolidlinerepresentsalinearfittothesimulatedpoints(O)andcorrespondstobIS/2π??8)1.15(?ω1/2π)+7(Hz).

)10.0kHzresonanceweredeterminedbyfittingthesecondderivativesofthesignalsusingLorentzianlines.Then,forpure[12,20-13C2]-,[11,20-13C2]-,and[10,20-13C2]retinal,fittingthetwomaximainthesecondderivativeofthen)1lineshapeswhilekeepingΓconstantyields?ω1withanaccuracyofatleastthedigitalresolution.Thisprocedureensuresanoptimalaccuracyforthemeasurementof?ω1forthesemodelcom-pounds(Table2).Theexperimentalerrorassociatedwiththedatapointsisestimatedas?4Hz.Obviously,theaccuracyisimprovedbytheinterpolationfromthefittingprocedure,relativetosimplydeterminingthepositionsoftheminimabyreadingofftheextremawiththeabsoluteaccuracyofthedigitalresolutioninthespectra.

Fordilute[10,20-13C2]retinaltheeffectofthedipolarre-couplingduetotherelativelylargeinternucleardistancer10,20′)0.440nmissosmallthataccurateanalysisinthepreviouslydescribedwayisnotpossible.Moreover,therelativelylargenaturalabundancebackgroundsignalcomprisesanimportantpartofthetotalresponse.Inthiscase?ω1couldbedeterminedbyanalyzingtheresonancelineshapeinsteadofitssecondderivative.First,aspectrumcollectedwithaspinningspeed100Hzlessthanthen)1rotationalresonanceconditionwascarefullyfittedwithasuperpositionofLorentzianlines.Fordilute[10,20-13C2]retinalatleastfourLorentziansarerequired,onestrongcomponentforthecontributionfromthelabelandthreeweakercomponentstogeneratethenaturalabundancebackgroundinthespectralregionof10-13C.Subsequently,adatasetwiththespinningspeedexactlyatrotationalresonanceisanalyzedwhileallowingforadditionalbroadeningoftheLorentzianrepresentingthelabelresponseslightlyoffrotationalresonance.TheparametersdescribingtheotherLorentziansinthefitarekeptidenticaltothevaluesdeterminedforthedataoffrotationalresonance.Hence,theonlyfreeparameterinthissecondfittingprocedureisthelinewidthofthecontributionfromthelabel.BothfittingproceduresareillustratedintheSupportingInformation.Theincreaseofthelinewidth,withrespecttotheresponseoffrotationalresonance,providesafairestimateofthe?ω1duetotherotationalresonancedipolarrecoupling.

Finally,inFigure7agraphofthebIS/??8inthecompoundsversusthe?ω1ispresented.Tocomparethesedatawiththerotationalresonancetheory,aseriesofn)1rotationalresonancesecond-derivativesimulationswasperformed,with10Hz<bIS/2π??8<190Hz(seetheSupportingInformation).Itappearsthat?ω1inthesimulationsvarieslinearlywithbthesolidlineinFigure7,andcanbe

described

IS/??8,accordingto