Electron Paramagnetic Resonance at 94 GHz: Methodological...

Electron ParamagneticResonanceat 94 GHz:MethodologicalDevelopmentsand Studiesof

PhotosyntheticReactionCenters

vorgelegt von

Diplom-PhysikerWulf TobiasHofbauer

ausStuttgart

von derFakultätII– MathematikundNaturwissenschaften–

derTechnischenUniversitätBerlinzurErlangungdesakademischenGrades

DoktorderNaturwissenschaften– Dr. rer. nat.–

genehmigteDissertation

Promotionsausschuß:Vorsitzender:Prof.Dr. rer. nat.ChristophvanWüllen,TU BerlinBerichter:Prof.Dr. rer. nat.WolfgangLubitz, TU BerlinBerichter:Prof.Dr. rer. nat.KlausMöbius,FU BerlinTagdermündlichenPrüfung:20.Juli 2001

Berlin 2001

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c

Copyright 2001Wulf Hofbauer. Alle Rechtevorbehalten.

WarennamenundBezeichnungenwerdenohneGewährleistungderfreienVerwendbarkeit be-nutzt. AngegebeneSchaltungen,Programmeoder Methodensind möglicherweiserechtlichgeschützt.Für fehlerhafteAngabenbzw. derenFolgenwird keineHaftungübernommen.

1. Auflage(22.August2001)Gesetztin LATEX 2ε.

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ZusammenfassungHofbauer, Wulf:Electron ParamagneticResonanceat 94GHz: MethodologicalDevelopmentsand Studiesof PhotosyntheticReactionCentersDieseArbeit befaßtsichmit derAnwendungvon Elektronenspinresonanz(EPR)bei 94 GHzzur Untersuchungvon radikalischenZuständenin Reaktionszentrendespflanzlichenundbak-teriellenPhotosyntheseapparates.

Die Lichtanregungin situbereitetbeiderHochfrequenz-EPRSchwierigkeiten,daeinopti-scherZugangzumResonatormit deutlichentechnischenKompromissenerkauftwerdenmuß.In dieserArbeit wird deshalbzunächsteineMethodezur Lichtanregungin geschlossenenRe-sonatorstrukturenvorgestelltundcharakterisiert.

Ein weiteresProblemliegt in derhohenEmpfindlichkeit derHochfrequenz-EPRauf Un-tergrundsignale,dievonVerunreinigungenderProbenausgehen.UnterscheidensichdieÜber-gangsdipolmatrixelementevon Probeund Kontamination,könnendie Signalemit gepulsterEPRgetrenntwerden. Eine neueMethodehierzuwird in dieserArbeit vorgestellt. Im Ge-gensatzzu denüblichenVerfahrenerfordertdasneueingeführteExperimentdeutlichwenigerMeßzeitundkleinereMikrowellenleistungen.

Die Leistungsfähigkeit von94GHz-EPRzurUntersuchungvonReaktionszentrenderPho-tosynthesewird andrei Beispielendemonstriert:DasKationenradikaldesprimärenDonatorsin Photosystem(PS)I, P 700, weisteinegeringeg-AnisotropieundeinehoheEPR-Linienbreiteauf. Um aussagekräftigeSpektrenzu erhalten,warenbislangäußersthoheFrequenzenerfor-derlich. Die Verwendungvon Protein-Einkristallenin dieserArbeit erlaubtedie genaueBe-stimmungdesg-Tensorsausden94GHz-Spektren.DurchdenVergleichmit derausderRönt-genstrukturanalysebekanntenOrientierungder entsprechendenChlorophyllmoleküle konntedie in früherenArbeitenvorhergesagteasymmetrischeVerteilungderSpindichtebestätigtwer-den.

Die Kristallisation von PhotosystemII ist erst seit kurzemmöglich. Die in den wahr-scheinlichweltweit erstenEPR-ExperimentenanPSII-Einkristallenerhaltenenorientierungs-abhängigenSpektrendesstabilenTyrosinradikalsY D sind, bedingtdurcheineVielzahl vonHyperfeinkopplungenund8 kristallographischinäquivalenteEinbaupositionen,äußerstkom-pliziert. In Verbindungmit gepulstenENDOR-ExperimentenangefrorenerLösunggelangdievollständigeAnalysederSpektren.Die mit hoherGenauigkeit erhalteneOrientierungdesg-Tensorsergänztdasbislangnoch in weitenTeilen unvollständigeStrukturmodellvon PSII.Aus dengefundeneng-HauptwertenunddenHyperfeinkopplungenlassensichRückschlüsseauf die BindungssituationdesTyrosinradikalsziehen. Insbesonderekonnteder EinflußeinerWasserstoffbrücke im Detail erfaßtwerden.

UntersuchungenandenradikalischenZuständenderAkzeptormoleküleQA undQB im Re-aktionszentrumdesPurpurbakteriumsRhodobactersphaeroidesbeschließendie Arbeit. AusdenSpektrenim biradikalischenZustandQ A Q B konnte– überdie Richtungsabhängigkeitder dipolarenKopplung– die relative Anordnungder Radikaleim Proteinermittelt werden.Dieseunterscheidetsich im Rahmender Meßgenauigkeit nicht von der bekanntenStrukturim monoradikalischenZustandQ B . Die für denElektronentransferbedeutsameStärke derAustauschkopplungzwischendenRadikalenkonntehingegennur näherungsweisebestimmtwerden. Es wird gezeigt,daßsich hier eineGrenzeder EPRbei 94 GHz offenbart,die nurdurchVerwendungnochhöhererMikrowellenfrequenzenüberwundenwerdenkann.

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TeiledervorliegendenArbeit wurdenbereitspubliziert:

[1] HofbauerW. & Bittl R., EPRat 94 GHz of laser-inducedspeciesin anELEXSYSE680spectrometer, Bruker Report145, 38–39(1998).

[2] HofbauerW., SchäferK.O., & Bittl R., Discriminationof S 12 andS 5

2 statesin highfield EPRby field-sweptESE,in MagneticResonanceandRelatedPhenomena(ZiessowD., Lubitz W., & LendzianF., eds.),volumeII, pp.851–852(1998).

[3] Bittl R.,HofbauerW., ZechS.G.,Kamlowski A., FrommeP., & Lubitz W., Time-resolvedandcw-EPRat94GHzonphotoystemI, in MagneticResonanceandRelatedPhenomena(Ziessow D., Lubitz W., & LendzianF., eds.),volumeI, pp.262–263(1998).

[4] SchäferK.O., HofbauerW., Bittl R., & Lubitz W., W-band(94 GHz) EPRinvestigationof anexchangecoupledMnIII MnIV complex, in MagneticResonanceandRelatedPhe-nomena(Ziessow D., Lubitz W., & LendzianF., eds.),volumeII, pp.863–864(1998).

[5] Kammel M., HofbauerW., Zouni A., FrommeP., Bittl R., LendzianF., Witt H.T., &Lubitz W., High field EPR studiesof the tyrosyl radical Y D in photosystemII singlecrystalsof synechococcuselongatus,in XIth InternationalCongresson Photosynthesis,Budapest, Int. Soc.of Photosynth.Res.(1998).

[6] Calvo R., HofbauerW., LendzianF., Lubitz W., PaddockM.L., AbreschE.C., IsaacsonR.A., OkamuraM.Y., & FeherG.,MagneticcouplingbetweenQA andQB in RCsof Rb.sphaeroidesdeterminedby EPRspectroscopy at95GHz,Biophys.J. 76, A392 (1999).

[7] Calvo R., AbreschE.C., Bittl R., FeherG., HofbauerW., IsaacsonR.A., Lubitz W.,OkamuraM.Y., & PaddockM.L., EPRstudyof themolecularandelectronicstructureofthesemiquinonebiradicalQ A Q B in photosyntheticreactioncentersfrom Rhodobactersphaeroides,J. Am.Chem.Soc.122, 7327–7341(2000).

[8] ZechS.G.,HofbauerW., Kamlowski A., FrommeP., StehlikD., Lubitz W., & Bittl R.,A structuralmodel for the charge separatedstateP 700A 1 in photosystemI from theorientationof themagneticinteractiontensors,J. Phys.Chem.B104, 9728–9739(2000).

[9] HofbauerW. & Bittl R., A novel approachto separatingEPRlinesarisingfrom specieswith differenttransitionmoments,J. Magn.Reson.179, 226–231(2000).

[10] HofbauerW., Zouni A., Bittl R., KernJ.,Orth P., LendzianF., FrommeP., Witt H.T., &Lubitz W., PhotosystemII singlecrystalsstudiedby EPRspectroscopy at 94 GHz: ThetyrosineradicalY D, Proc.Natl. Acad.Sci.USA98, 6623–6628(2001).

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WeitereVeröffentlichungenundKonferenzbeiträge:

[1] Bleifuß G., PötschS.,HofbauerW., GräslundA., Lubitz W., LassmannG., & LendzianF., High field EPRat 94 GHz of aminoacidradicalsin ribonucleotidereductase,in Ma-gneticResonanceandRelatedPhenomena(Ziessow D., Lubitz W., & LendzianF., eds.),volumeII, pp.879–880(1998).

[2] TrofanchukO., M. S., BrechtM., HofbauerW., LendzianF., Higuchi Y., & Lubitz W.,Catalyticcenterof [NiFe]-hydrogenases:X- andW-bandEPRstudies,in 31st EPRAn-nual InternationalMeeting, Manchester, RSC(1998).

[3] Ihlo L., StösserR., Hofbauer W., Böttcher R., & Kirmse R., S, X, Q and Wband powder-EPR investigations on tetra-n-butylammonium-bis(1,2-dicyanoethylene-1,2-dithiolato)aurate(II),Z. Naturforsch. B54, 597–602(1999).

[4] LaßmannG., LendzianF., PötschS., Bleifuß G., HofbauerW., Kolberg M., ThelanderL., GräslundA., & Lubitz W., Structureof tryptophanradicalsin mutantsof proteinR2of ribonucleotidereductasestudiedby X-BandEPR,ENDOR,andby high-fieldEPR,J.Inorg. Biochem.74, 201(1999).

[5] LaßmannG., LendzianF., PötschS., Bleifuß G., HofbauerW., Kolberg M., ThelanderL., GräslundA., & Lubitz W., Structureof tryptophanradicalsin mutantsof R2 of ribo-nucleotidereductasestudiedby X-bandEPR/ENDORandby high-field EPR,J. Inorg.Biochem.74, 201(1999).

[6] HofbauerW., Zouni A., Bittl R., KammelM., FrommeP., LendzianF., Witt H.T., Lu-bitz W., KraussN., & Orth P., EPRcharacterizationof the tyrosyl radicalY D in activephotosystemII singlecrystalsat 94 GHz, in High FrequencyElectron ParamagneticRe-sonance, Amsterdam, Royal NetherlandsAcademyof Arts andSciences(2000).

[7] HofbauerW., Zouni A., Bittl R., KernJ.,Orth P., LendzianF., FrommeP., Witt H.T., &Lubitz W., HF-EPRon a tyrosineradical in singlecrystalsof photosystemII, in Rund-gespräch “Anwendungen der MagnetischenResonanzin der Bio- und Materialwissen-schaft”, Riezlern, DFG (2000).

[8] HofbauerW. & Bittl R., A novel approachto separatingEPRlinesarisingfrom specieswith different transitionmoments,in Rundgespräch “Anwendungen der MagnetischenResonanzin der Bio- undMaterialwissenschaft”, Riezlern, DFG (2000).

[9] HofbauerW., Zouni A., Bittl R., KernJ.,Orth P., LendzianF., FrommeP., Witt H.T., &Lubitz W., HF-EPRon a tyrosineradical in singlecrystalsof photosystemII, in Struc-tureandFunctionin OxygenicPhotosynthesis,Roscoff, CentreNationaldela RechercheScientifique(2000).

[10] BleifußG.,Kolberg M., PötschS.,HofbauerW., Lubitz W., GräslundA., LaßmannG.,&LendzianF., Tryptophanandtyrosineradicalsin ribonucleotidereductase:A comparativehigh-fieldEPRstudyat94 GHz,Biochemistry(submitted).

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[11] RudolfT., PöpplA., HofbauerW., & Michel D., X, Q andW bandelectronparamagneticresonancestudyof the sorptionof NO in Na-A andNa-ZSM-5zeolites,Phys.Chem.Chem.Phys.3, 2167–2173(2001).

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Contents

Intr oduction 1

I Theoretical and Experimental Background 5

1 Principles of EPR 71.1 SpinHamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.1.1 ZeemanInteraction. . . . . . . . . . . . . . . . . . . . . . . 81.1.2 ElectronExchangeInteraction . . . . . . . . . . . . . . . . . 91.1.3 ElectronicDipolar Interaction . . . . . . . . . . . . . . . . . 91.1.4 HyperfineInteraction. . . . . . . . . . . . . . . . . . . . . . 11

1.2 SpectroscopicAspects . . . . . . . . . . . . . . . . . . . . . . . . . 111.2.1 Line Broadening . . . . . . . . . . . . . . . . . . . . . . . . 111.2.2 SampleOrientation. . . . . . . . . . . . . . . . . . . . . . . 121.2.3 TransitionStrength . . . . . . . . . . . . . . . . . . . . . . . 141.2.4 Saturation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.3 Classificationof EPRExperiments. . . . . . . . . . . . . . . . . . . 161.3.1 ContinuousWave EPR . . . . . . . . . . . . . . . . . . . . . 161.3.2 TransientEPR . . . . . . . . . . . . . . . . . . . . . . . . . 161.3.3 PulsedEPR . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.4 Multiple ResonanceExperiments. . . . . . . . . . . . . . . . . . . . 181.4.1 ContinuousWave ENDOR . . . . . . . . . . . . . . . . . . . 181.4.2 PulsedENDOR . . . . . . . . . . . . . . . . . . . . . . . . . 18

2 Experimental Setup 252.1 Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.1.1 FieldCalibration . . . . . . . . . . . . . . . . . . . . . . . . 262.2 Resonator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.2.1 SampleMounting . . . . . . . . . . . . . . . . . . . . . . . . 292.3 Microwave Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

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II MethodologicalDevelopmentsfor High Field EPR 33

3 Optical Excitation and Transient EPR 353.1 ExperimentalSetup . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.1 Light Accessto theResonator . . . . . . . . . . . . . . . . . 353.1.2 Light SourceandTransport. . . . . . . . . . . . . . . . . . . 363.1.3 TriggerControl . . . . . . . . . . . . . . . . . . . . . . . . . 383.1.4 BandwidthandDetectionMode . . . . . . . . . . . . . . . . 38

3.2 TransientEPRon theTriplet Stateof Pentacene. . . . . . . . . . . . 393.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4 Soft PulseElectron Spin Echoes 434.1 StandardMethodsto DisentangleSpectra . . . . . . . . . . . . . . . 434.2 TheoreticalDescription . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2.1 ShortPulses. . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2.2 SpinDynamicsSimulation . . . . . . . . . . . . . . . . . . . 464.2.3 FID afteraLongPulse . . . . . . . . . . . . . . . . . . . . . 474.2.4 LongPulseEchoes . . . . . . . . . . . . . . . . . . . . . . . 474.2.5 Flip AngleSelectiveSignalSuppression. . . . . . . . . . . . 51

4.3 ExperimentalDemonstration. . . . . . . . . . . . . . . . . . . . . . 514.3.1 Mn2 andCr3 in CaO. . . . . . . . . . . . . . . . . . . . . 514.3.2 DTNE Complex . . . . . . . . . . . . . . . . . . . . . . . . 534.3.3 Mn-Catalase . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

III Application of High Field EPR to Biological Systems 59

5 Overview of PhotosyntheticReactionCenters 615.1 Photosynthesisin PlantsandCyanobacteria. . . . . . . . . . . . . . 61

5.1.1 PhotosystemI . . . . . . . . . . . . . . . . . . . . . . . . . . 625.1.2 PhotosystemII . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.2 Photosynthesisin PurpleBacteria . . . . . . . . . . . . . . . . . . . 685.2.1 SubunitsL andM . . . . . . . . . . . . . . . . . . . . . . . . 70

5.3 EPRonFrozenSolutionsandSingleCrystals . . . . . . . . . . . . . 70

6 P 700 in SingleCrystals of PhotosystemI 75

6.1 MaterialsandMethods . . . . . . . . . . . . . . . . . . . . . . . . . 756.1.1 PSI CoreComplexes . . . . . . . . . . . . . . . . . . . . . . 756.1.2 PSI SingleCrystals . . . . . . . . . . . . . . . . . . . . . . 766.1.3 cw EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.2 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776.2.1 P

700 in FrozenPSI Solution . . . . . . . . . . . . . . . . . . 77

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6.2.2 P 700 in SingleCrystalsof PSI . . . . . . . . . . . . . . . . . 77

6.3 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

7 Y D in SingleCrystals of PhotosystemII 89

7.1 MaterialsandMethods . . . . . . . . . . . . . . . . . . . . . . . . . 897.1.1 PSII CoreComplexes . . . . . . . . . . . . . . . . . . . . . 897.1.2 PSII SingleCrystals . . . . . . . . . . . . . . . . . . . . . . 907.1.3 cw EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.1.4 PulsedENDOR . . . . . . . . . . . . . . . . . . . . . . . . . 91

7.2 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.2.1 cw EPRof FrozenSolution . . . . . . . . . . . . . . . . . . 927.2.2 PulsedENDORon FrozenSolution . . . . . . . . . . . . . . 927.2.3 cw EPRon SingleCrystals. . . . . . . . . . . . . . . . . . . 957.2.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.3 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1077.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

8 Q A and Q

B in Bacterial Photosystem 1178.1 Simulationof RadicalPair Spectra . . . . . . . . . . . . . . . . . . . 118

8.1.1 SpinHamiltonianfor a SpinCoupledRadicalPair . . . . . . 1188.2 MaterialsandMethods . . . . . . . . . . . . . . . . . . . . . . . . . 121

8.2.1 SamplePreparations. . . . . . . . . . . . . . . . . . . . . . 1218.2.2 cw andPulsedEPR . . . . . . . . . . . . . . . . . . . . . . . 122

8.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1228.3.1 Analysisof BiradicalSpectra. . . . . . . . . . . . . . . . . . 128

8.4 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1308.4.1 Influenceof Fitting MethodsandReliability of Parameters. . 1308.4.2 Implicationsof J for theElectronTransferProcess . . . . . . 133

8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Summary and Outlook 137

Zusammenfassungund Ausblick 141

Appendix 145

A Spin Dynamics 145A.1 DensityMatrix Formalism . . . . . . . . . . . . . . . . . . . . . . . 145A.2 RotatingFrameApproximation. . . . . . . . . . . . . . . . . . . . . 146A.3 Bloch Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

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B Analysis of EPR Spectra 149B.1 OrientationDependentSpinHamiltonian . . . . . . . . . . . . . . . 149B.2 Definitionof EulerAngles . . . . . . . . . . . . . . . . . . . . . . . 150B.3 Simulationof Spectra. . . . . . . . . . . . . . . . . . . . . . . . . . 151B.4 Calculationof theResonanceField Strength. . . . . . . . . . . . . . 152

C Spin DynamicsSimulation Program 153

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Intr oduction

Sinceits inceptionin 1944by E. K. Zavoisky [1], electronparamagneticresonance(EPR)hasbecomea widely usedspectroscopictechniquefor theinvestigationof rad-icalsandotherspeciesexhibiting electronicparamagnetism.Applicationsrangefromchemistry(e.g.identificationof intermediateradicalsin a reaction)to physics(e.g.in-vestigation of the bandstructureof semiconductors)andincludeeven lessacademictopicslike radiationdosimetryor quality controlin beerbrewing [2].

EPRhastraditionally playeda minor role in comparisonto NMR (nuclearmag-netic resonance).Onereasonfor this is that only a relatively small classof speciesexhibit electronicparamagnetismexploitable by EPR.A more importantreasonis,however, thatEPRis muchcloserto thetechnologicaledgein high speedelectronicsandmicrowave technology.

Only in recentyearshasmicrowave technologyadvancedto a statewhich allowsstandardNMR methodologyto be transferredto EPR.EPRhastraditionally beenacontinuouswave (cw) technique.Pulsedandtime-resolvedEPRspectroscopy arestillconsideredto be advancedmethods,available to only a minority of EPR facilities.Concurrentlywith themove to moreadvancedexperiments,it hasbecomepossibletoconsiderablyextendthe frequency range,allowing the useof highermagneticfieldsandyielding highersensitivity andbetterspectralresolution.At the time of writing,therehasbeenacontinuoustrendfor severalyearsto pushthefrequency limits further(seee.g.[3–5]).

Theadvancesin highfield EPRareof particularimportanceto thestudyof biolog-ical systems.In many of thesesystems,organicradicalsplay animportantfunctionalrole. Theseradicalsrequireincreasedspectralresolutionto accessthe rathersmallg anisotropy. Similarly, the isolationandpurificationof biological compoundslikeenzymesis tedious,oftenlimiting thesamplequantityavailable.Theincreasedsensi-tivity of highfield EPRmakesthestudyof suchsamplesmucheasier. Combinedwithotherhigh-resolutionmagneticresonancetechniqueslikeENDOR[6], thepossibilitiesin biologicalresearcharedramaticallyextended.

In 1996, Bruker introducedthe first commercialEPR spectrometeroperatinginthe W-bandfrequency range(94 GHz) [7]. The commercialavailability meansthatthis kind of advancedspectroscopy is now available to researchgroupswithout theresourcesto developaspectrometerof their own.

At theMax-Volmer-Institutefor BiophysicalChemistryattheTechnicalUniversity

1

2 INTRODUCTION

Berlin, biologists,physicists,andchemistswork togetherto manipulate,isolate,andinvestigateprotein-cofactorcomplexes.Thegroupof Prof.Lubitz at theTU Berlin hasa particularlystrongfoothold in EPRandENDOR spectroscopy. The installationofthe94GHzBrukerspectrometerin 1997wasthebasisfor new originalwork, someofwhich is reportedin this thesis.

Thisthesisisdividedinto threeparts.A shortoverview of EPRfoundationsisgivenfirst. The secondpart concentrateson apparative andmethodologicaldevelopmentsthat extendedthe applicationrangeof this high field EPRspectrometer. Finally, thethird partpresentsstudieson threedifferentphotosyntheticreactioncenters.

Thephotosyntheticapparatusof plants,algaeandbacteriahaslong beena field ofintenseresearch.Many detailsof its workingcouldbeelucidatedin thelastyears.It is,however, still unclearhow theprotein/cofactorcomplexesin thethylakoid membraneimplementthis process.An understandingof how the proteinmatrix custom-tailorsboundcofactorsinto a fine tunedelectrontransferchainwill yield many insightsthatwill hopefully be transferableto otherbiological systems.It might even be possiblein thefutureto mimic thephotosyntheticprocessfor theindustrialconversionof solarenergy into chemicalenergy carriers.

EPRandENDORareexcellenttoolsto probetheelectronicstructureof thecofac-tors in theelectrontransferchainin thesereactioncenters[8–10]. Thelocal structureof paramagneticcofactorstatescanbeaccessedby theg andhyperfineinteractionten-sorswhile dipolarandexchangecouplingparametersprovide informationabouthowtheseindividual cofactorsareturnedinto achain.

Besidestherelevanceof theseexperimentsfor biophysics,they presenta demon-strationof the possibilitiesas well as limitations of 94 GHz EPR.The orientation-dependentspectraof the primary donorin photosystemI exhibit a broad,poorly re-solved EPRline. Still, it is possibleto analyzethesespectraandobtainorientationdatafor theg tensorwith remarkableaccuracy. In contrast,the tyrosineD radicalinsinglecrystalsof photosystemII yieldswell resolvedspectra.High field EPRservesherefor separatingtheZeemananisotropy from thecomplex hyperfinestructure,thusenablingan accurateanalysisof the orientationof the radicalsin the crystal. Lastly,theexperimentson frozensolutionsof coupledquinoneradicalsin bacterialreactioncentersshow thatthanksto theexcellentspectralresolutionof highfield EPR,detailedgeometricinformationcanbe obtainedeven from disorderedsamples.However, thestrengthof theexchangeinteractionbetweenthequinoneradicalsturnsout to be justbeyondthecapabilitiesof 94 GHz EPR.Findingssuchasthis motivatethedesireforEPRexperimentsatevenhigherfrequencies.

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[4] Earle K.A., Tipikin D.S., & FreedJ.H., Far-infrared electron-paramagnetic-resonancespectrometerutilizing a quasiopticalreflectionbridge,Rev. Sci.Instrum.67, 2502–2513(1996).

[5] Fuchs M.R., Prisner T.F., & Möbius K., A high-field/high-frequency heterodyneinduction-modeelectronparamagneticresonancespectrometeroperatingat 360 GHz,Rev. Sci.Instrum.70, 3681–3683(1999).

[6] FeherG., Observation of nuclearmagneticresonancesvia the electronspin resonanceline, Phys.Rev. 103, 834–835(1956).

[7] SchmalbeinD., MareschG.G.,Kamlowski A., & Höfer P., TheBruker high-frequency-EPRsystem,Appl.Magn.Reson.16, 185–205(1999).

[8] MöbiusK., High-field high-frequency EPR/ENDOR– a powerful new tool in photosyn-thesisresearch,Appl.Magn.Reson.9, 389–407(1995).

[9] LevanonH. & Möbius K., AdvancedEPRspectroscopy on electrontransferprocessesin photosynthesisandbiomimeticmodelsystems,Ann.Rev. Biophys.Biomol.Struct.26,495–540(1997).

[10] MöbiusK., Primaryprocessesin photosynthesis:Whatdo we learnfrom high-fieldEPRspectroscopy?,Chem.Soc.Rev. 29, 129–139(2000).

4 INTRODUCTION

Part I

Theoretical and ExperimentalBackground

5

Chapter 1

Principles of Electron ParamagneticResonance

1.1 Spin Hamiltonian

Magneticresonanceexperimentsobserve transitionsbetweenquantumstatesassoci-atedwith a magneticdipole moment. Magnetismat the atomic level is tied to thespinsof theelectronsandnucleonsaswell asorbital angularmomentum.Usually, anexternalstaticmagneticfield is appliedto the systemunderinvestigation in ordertolift degeneraciesof themagneticenergy levels. Thequantumenergiesof therelevantmagnetictransitionsaretypically small comparedto electronicor nucleartransitionenergies. Therefore,it is possibleto treatmagneticresonanceexperimentsby pertur-bationtheory. Using this approachsimplifiestheorybecauseit canbe confinedto aHilbert spacewith only spin andangularmomentumcomponents.The effect of theneglecteddegreesof freedomis includedin theform of parametersto thismodel.

Thisverysuccessfulmethodfor thedescriptionof magneticresonanceexperimentsis theso-calledspinHamiltonianformalism.TheHamiltonianmodelsthesystemby apower seriesexpansionin angularmomentumoperatorsj i commonlydenotedasspinoperators,eventhoughthey mayhaveorbitalmomentumcontributions:

H ∑i

c1

i j i ∑i j

c2

i j j i j j ∑i j kc

3

i jk j i j j jk (1.1)

Then-th ordercouplingconstantscn reflecttheeffect of theneglectedelectronic

statesandthestrengthof theappliedmagneticfield B. In mostcases,therapidconver-genceof theseriesallows to restrictthespinHamiltonianto only very few low-orderterms.TheHamiltonianis furthersimplifiedby thefactthatmany couplingconstantshave to vanishfor symmetryreasons.It is alsoconvenientthat thespinHamiltoniandescribesasystemin aHilbert spaceof finite (andusuallyverylow) dimension,easingalgebraicor numericaltreatments.

In thefollowing, themostimportantlow-ordertermsof thespinHamiltonianwill

7

8 CHAPTER1. PRINCIPLESOFEPR

beintroduced.

1.1.1 ZeemanInteraction

Themagneticcouplingof anappliedhomogeneousmagneticfield andanelectronspinSresp.anuclearspinI is calledZeemaninteraction.Thecouplingis describedin unitsof the Bohr magnetonandnuclearmagneton,respectively, anda couplingmatrix gcommonlyreferredto astheg tensor.

HZ e µB

BT gS

S (1.2)

HZ n µn

BT gI

I (1.3)

Thecouplingmatrix g for a restingfreeelectronis isotropicandcanthereforebegivenby a scalarfactorge 2 0023193043737 38 [1]1.

The local field at the positionof the electroncanhowever be different from theexternally appliedmagneticfield. In particular, the interactionof the electronspinwith orbital magnetism(spin-orbit coupling) leadsto admixtureof other electronicstateswith orbital momentum(seee.g. [3]). Therefore,the “effective spin” is not apurespin stateany longer, but also includesorbital components,andthe effective gvalueis changed.Whentheorbital structureof theconsideredsystemis anisotropic,the spin-orbit coupling reflectsthe orientationdependence,therebygiving rise to atensorialg. Everysystemmorecomplex thanasingleatomis anisotropic;anisotropicg canhowever occuralsoin systemswith reduced,i.e. cubic,symmetry.

The“quantizationdirection”, i.e. thedirectionof theexpectationvalueof thespinin aneigenstate,is determinedby theeffective field

Beff gT

B. Themagneticdipole

momentof thespinis thereforealwaysparallelto theeffectivefield:BT

eff µ

BTeff

Beff

BT ggT B (1.4)

Consequently, only the symmetrictensorggT is accessibleto spectroscopy. Thistensorcanbegivenby its principalvaluesandtheorientationof theorthogonaleigen-systemrelative to a referenceframe. Sinceasymmetriesof g arenot observable,it iscustomaryto describeg itself in termsof principal valuesandanorientationrelativeto a referenceframe.

Similar theory appliesfor nuclearspins. The nuclearg factorsfor protonsandneutronsaregp 5 585694675 57 andgn 3 82608545 90 , respectively [1]. Theg factorsof compoundnuclei can thereforevary over a large range. Sincenuclearspin-orbitcouplingis severalordersof magnitudestrongerthanthe interactionof thenucleonswith theelectronshell or anappliedmagneticfield, thenucleareigenstatesarenotnoticeablydisturbedandthenuclearg factorcanbeconsideredisotropic.

1The g factorof a free electronis definedpositive herefor historicalreasonsonly. For a detaileddiscussionof thesignof g factors,referto [2].

1.1. SPINHAMILTONIAN 9

1.1.2 Electron ExchangeInteraction

In thespinHamiltonian,spatialcoordinatesarecompletelyeliminated.This is a validapproachif thespatialcomponentof thewavefunctionis not correlatedwith thespincomponent.ThePauli principlehowever establishesa very strict correlation:thetotalwavefunctionof amulti-electronsystemhasto beantisymmetric.A transitionbetweentwo spin statescan thereforelead to energy shifts of the spatialcomponentof thewavefunction.This energy shift hasto bereproducedin thespinHamiltonian.

The energy associatedwith the changeof the spatialwavefunctioncomponentisprimarily causedby Coulombinteractionbetweenelectrons

Eee e2

4πε0r (1.5)

This leadsto a couplingconstantbetweenthespin-carryingelectronsthat is givenbytheexchangeintegral

J ψ1 e2

4πε0r ψ2 (1.6)

whereψ1 2 refer to the spatialwavefunctionsof the uncoupledelectrons.Using thisconstant,theinteractioncanbewritten as

Hex 2J S1

T S2 (1.7)

TheCoulombinteractionpotentialcanbecrudelyapproximatedby a Dirac δ dis-tribution. In this light, it is easyto recognizethat J is relatedto the overlapintegral ψ1 ψ2 . In weaklyexchangecoupledsystems,J canthereforeprovide insightabouttunnelingprobabilitiesinvolvedin electrontransferprocesses.

Exchangeinteractioncanalsobe mediatedvia excited electronicstates(“kineticexchange”).Smallercontributionsaredueto changesin spin-orbitcoupling,confor-mationalchanges,etc. Theresultingexchangeinteractionis thereforenot necessarilyisotropic. In commonuse,the term “exchangeinteraction”is, however, usedfor theisotropicpart of spin-spininteractionswhile anisotropiccomponentsareincludedindipolarcouplingterms(seebelow).

1.1.3 Electronic Dipolar Interaction

Two magneticdipolemomentsµ1 and

µ2 separatedby adistancevector

r interactwith

anenergy

Edd µ0

4π

µT

1 µ2

r3 3 µT

1 r

µT2

r

r5 (1.8)

The dipolar interactionbetweentwo electronspinsS1 andS2 canbe rewritten intermsof spin operatorsS1 andS2. It is, however, not trivial what magneticmomenthasto beassociatedwith them.For largedistances,thedipolemomentis givenby the


momentof theelectronandits environmentasa whole, i.e. µ1 2 g1 2 S1 2 . When

theelectronsarecloseto eachother, they seeeachother“naked” andthege valueof afreeelectronhasto beused.Thiscomplicationis oftenneglectedasin many casestheg factorsdiffer only slightly from ge.

Substitutingge for g, onearrivesat

Hdd g2eµ2

Bµ0

4π S1

T S2

r3 3 S1

T r

S2T

r r5

S1T D

S2 (1.9)

wherethecouplingtensorD hastheelements

Dxx g2eµ2

Bµ0

4πr2 3x2

r5 (1.10) Dxy g2

eµ2Bµ0

4π3xyr5 (1.11)

For tightly coupledelectrons,the Hamiltonianis usuallywritten in termsofS

S1 S2. Thedipolarcouplingis thenwrittenas

Hdd S

T D S (1.12)

where

D 12

D (1.13)

ThecouplingtensorD is symmetricandcanbediagonalizedby choosingasuitableorthogonalreferencesystem:

D D xx 0 00 D yy 00 0 D zz

(1.14)

Thedipolarcouplingtensoris usuallyconsideredto betraceless.Thedipolarcou-pling tensorcan,however, containan isotropiccontribution causedby the neglectedg anisotropy. In practice,it is however often includedinto thescalarJ couplingtermdiscussedabove. Therefore,it is sufficient to definetwo parametersD andE suchthat

D xx 13

D E (1.15)

D yy 13

D E (1.16)

D zz 23

D (1.17)

It shouldbenotedthatthedipolarcouplingcanbewrittenasa symmetricaltensorevenif theapproximationof usingge is not valid any more.However, thegeometricalinterpretationof thecouplingparametersis lessclearin thosecases.

1.2. SPECTROSCOPICASPECTS 11

Figure 1.1: Lorentzian(left) andGaussian(right) line shapes.Note that the Lorentzianis given infrequency spacedue to its relation to a relaxationratek. The Gaussiandistribution of the effectivemagneticfield B is characterizedby thestandarddeviation σB.

1.1.4 Hyperfine Interaction

Themagneticinteractionbetweenelectronicandnuclearmagneticmomentsis calledhyperfineinteraction:

Ehfc µ0

4π

µT

e µn

r3 3 µT

e r

µTn

r

r5 2µ0

3 ψ 0 2 µT

e µn (1.18)

In contrastto the purely dipolar electron-electroninteractiondiscussedin sec-tion 1.1.3,eqn.1.18containsan additionalisotropicterm. This term, called“Fermicontactinteraction”,reflectstheoverlapof theelectronicandnuclearwavefunctions2.Usually, the electronicwavefunctionshows structureon a much larger lengthscalethenthe sizeof a nucleus,andit is sufficient to resortto a 0th orderapproximation(henceψ 0 , where0 representsthelocationof thenucleus).Therefore,theisotropicpartof thehyperfineinteractioncanbeusedto probetheelectronicspindensity.

The spin Hamiltonianfor the hyperfineinteractioncanbe written in analogytoeqn.1.9as

Hhf S

T A I (1.19)

wherethehyperfineinteractiontensorA is symmetricandgivenin termsof its princi-pal valuesAx, Ay, Az, andits orientation.

1.2 SpectroscopicAspects

1.2.1 Line Broadening

HomogeneousBroadening

Decoherencein the dynamicsof the systemcan leadto broadeningof the observedtransition.In thesimplestmodel,coherencedecaysexponentiallyover time with a re-

2A properderivationof this termis ratherinvolved. For somebasicargumentson theorigin of thecontactinteractionseee.g.[4].


laxationrate3 k. Theexponentialdecayin time is equivalentto aLorentzianlineshapein thefrequency domain:

L ν ν0 πkk2 4π2 ν ν0 2 (1.20)

To simulatea spectrumwith Lorentzianline broadening,the convolution hastotake placein thefrequency domain.EPRspectraaretypically obtainedasa functionof themagneticfield B. ThenonlineartransformationbetweenspectradependingonνandB mustthereforebetakeninto account.Only for narrow spectra,i.e. ∆B

B 1, thenonlineartransformationcanbeneglected.

InhomogeneousBroadening

Often,whatappearsto beoneline in EPRspectroscopy is really theunresolvedsuper-positionof multiple spectrallines. This canbecausedby inhomogeneoussamplesorby theinhomogeneityof theappliedmagneticfield B. Therefore,thiseffect is referredto as“inhomogeneousbroadening”.Anotherandoftenmoreimportantcontribution toinhomogeneousbroadeningis unresolvedhyperfinesplitting.

While sampleheterogeneitycanleadto peculiarlineshapesreflectingthestatisticaldistributionof microstatesof individualspecimen(oftenreferredtoas“g strain”),othermechanismsusuallyresult in a Gaussianlineshape.This is easyto seefor hyperfinecouplingsthat lead– in goodapproximation– to symmetricalsplitting of theoriginalline. An ensembleof hyperfine-splitlines thereforeresultsin a multinomialdistribu-tion of resonancefrequencieswhich, in the limit of a large ensemble,approachesaGaussian,i.e.

G B B0 12πσB

e B ! B0 " 22σ2

B (1.21)

It is alsoevident that the inhomogeneouslinewidth is in generalanisotropic. In thecaseof a Gaussianlineshape,the linewidth parameterσB appearsin quadraticformonly. Therefore,theanisotropiclinewidth tensorσ 1

B is symmetricandcanbegivenintermsof its principalvaluesandorientation.

1.2.2 SampleOrientation

EPRspectraaredependenton theorientationof theappliedfieldsrelative to thesam-ple. Whenlookingatanensemble,theobservedspectrumis asuperpositionof spectraof individual specimen:

I B # # # dψdφsinθdθp φ $ θ $ ψ Iφθψ B (1.22)

3For aslightly morerealisticdescription,seeappendixA.


Figure 1.2: Derivative spectraof a crystallinesamplewith four sitesperunit cell andananisotropicgtensorfor differentturninganglesaboutanaxis.

Figure 1.3: Integral (left) andderivative (right) EPRspectrumof a powder or solutionsamplewithanisotropicg tensorandnohyperfinecouplings.


whereφ, θ, ψ areEulerangles,p φ $ θ $ ψ is theprobabilitydensityfor finding a spec-imenof thatorientation,andIφθ B thecorrespondingspectrum.Iφθψ B canbecon-structedby adjustingthespatialcouplingparameters(tensors)accordingto

Ci Ri jCj

Ci j RikRj lCkl (1.23) whereR R φ $ θ $ ψ is a rotationmatrix.

In thecaseof crystals,eqn.1.22is reducedto asumover thedifferentorientationsof the sitesin the crystalstructure. The resultingspectradependon the orientationof thecrystalin theexternalfield (Fig. 1.2). For solutionsor sufficiently fine-grainedpowders,and in the absenceof interactionscausingpartial orientation,an isotropicdistribution pφθψ constcanbe assumed.Neglectingline broadening,this leadstosingularitiesin thederivative spectrum.In thepresenceof line broadening,thesesin-gularitiesleadto significantfeaturesin thespectrumthattypically exhibit theprincipalvaluesof involvedcouplingtensors(Fig. 1.3).A detaileddiscussionof orientationde-pendentEPRspectrafor thecasesrelevantto this thesisis givenin appendixB.

1.2.3 Transition Strength

The transitionprobability betweentwo states i and f is given by Fermi’s goldenrule as

pi % f 2πh && f H1 i && 2δ hν ∆E (1.24)

whereH1 is the perturbingHamiltonian. In the caseof EPR, i and f arethe ini-tial andfinal statesof the spin systemin the externally appliedstaticfield

B0. The

perturbingHamiltonianrepresentstheinteractionwith themagneticcomponentof theappliedmicrowave field. Thedelta termresultsfrom theconservationof energy andrepresentstheresonancecondition.

When the Zeemaninteractionwith the static field is isotropic and thereare nocompetingotherinteractions,the eigenstatesof the spin systemarecharacterizedbythemagneticquantumnumberm. In thiscase,only m ' m ( 1 transitionsarepossible.Theassociateddipolemomentsareperpendicularto thestaticmagneticfield andscalewith m 1 Sx m ) S S 1 m m 1 (1.25)

WhentheZeemaninteractionbecomesanisotropic,or whenotherinteractionsper-turb theeigenstatesof thesystem,othertransitionsmaybecomepossible.Theseso-called“forbidden transitions”increasethe complexity of the observed EPRspectra.Sincethetransitiondipolemomentsmayhavedifferentorientations,theobtainedspec-traalsodependon thepolarizationof theappliedmicrowavefield.


Figure1.4: Saturationbehavior for varyingmicrowavepower.

1.2.4 Saturation

In many experiments,it is assumedthat the systemunder investigation is closetothermalequilibrium.Thisis only trueif theappliedelectromagneticfield is sufficientlyweaksincethatfield inducestransitionsbetweenthe involvedstates.For a two-levelsystemwith incoherentdynamics(due to coupling to the environment)this can bewrittenasa setof rateequations[5]

dn1

dt B N n1 n2 (1.26)

dn2

dt B N n2 n1 (1.27)

wheren1, n2 denotethepopulationof therespectivestate,N is thenumberof photons,andB theEinsteincoefficient. For thepopulationdifferencen n2 n1, this resultsin

dndt

2 B N n (1.28)

On the other hand,relaxationeffects drive the systemtowardsthermalequilibrium(denotedby apopulationdifferencen0) with aratek. Therefore,thetotal rateequationis

dndt

2 B N n k n n0 (1.29)

Thegeneralsolutionto thisequationis anexponentialdecaytowardsastationarypop-ulationdifference

n n0

1 2BNk

(1.30)

which leadsto astationaryphotonabsorptionrateof

wN 2 B N n n01

2BN 1k

(1.31)


Figure 1.5: Left: Monitoring a decayingparamagneticspecieswith transientEPRat low microwavepower levels. Right: Rabi oscillationson a quasi-stationaryparamagneticspeciesat high microwavepower levels.

Therefore,theEPRabsorptionsignalis proportionalto the intensityof the irradiatedelectromagneticfield at low intensities,but is limited by the relaxationratek at highintensities. This effect is calledsaturationandcanbe usedto probek. More oftenthough,saturationeffectsareundesirablebecausethey canleadto severedistortionofthespectra.

1.3 Classificationof EPR Experiments

1.3.1 ContinuousWaveEPR

Continuouswave(cw) EPRis experimentallytheeasiestEPRtechnique.Thoughtech-nically not entirelycorrect(seesection1.3.2),the termusuallyimpliesacquiringthestationaryabsorbanceof an incidentelectromagneticfield asa functionof frequency,appliedmagneticfield, temperature,etc.,ignoringkineticor dynamiceffects.

The stationarynatureof the cw experimentmeansthat spin dynamicsare inco-herent.Usually, the interactionwith the apparatusis kept weak(non-saturatingcon-ditions) so that the samplecan be consideredto be infinitesimally closeto thermalequilibrium.

In somespecialapplications(like zerofield magneticresonanceexperiments),thefrequency of theappliedelectromagneticfield is sweptto obtainaspectrum.For tech-nical reasons,theusualway to performcw EPRexperimentsis to keepthetransitionfrequency constantand sweepthe appliedmagneticfield B0 instead. For sensitiv-ity reasons,virtually all spectrometersuseeffect modulationtechniquesto detectthesignal. Cw EPRspectraarethereforeuniversallygiven asthe derivativesof the truespectra.

1.3.2 Transient EPR

TransientEPRis closelyrelatedto the cw EPRexperiment.The major differenceisthatthesystemis not stationaryany more,andits kineticsaremonitoredby accessingtheEPRspectrain a time-resolvedway.

1.3. CLASSIFICATION OFEPREXPERIMENTS 17

Thenon-stationarystateof thesystemis generatedby a nonadiabaticprocess.Ex-amplesincludelight flashexcitation,startinga chemicalreaction,steppingthe staticmagneticfield or themicrowavepower level, etc.

At low microwave power levels, i.e. undernonsaturatingconditions,the time re-solvedcw experimentmonitorsthebuildup and/ordecayof paramagneticspecies.Athigherpowers,themicrowaveirradiationitself beginsto steerthedynamicsof thesys-tem,andcoherentRabioscillationsbecomeobservable.Fromtheseoscillations,bothpropertiesof thespectrometerandof thesamplecanbederived(Fig. 1.5).

To improvetimeresolutionof transientexperiments,theEPRsignalis usuallymea-sureddirectly, without thehelpof effectmodulationtechniques.Thelossof sensitivityis often compensatedby large spin polarizationsobtainedin preparingthe transientstate.

1.3.3 PulsedEPR

PulsedEPRexperimentsusemicrowave pulsesto preparethe spin systemunderex-aminationinto anon-equilibriumstate.Afterwards,thefreemagneticinductionof thesampleis measured,withoutapplyingamicrowavefield.

Due to the direct interactionof the appliedmicrowave pulseswith the magneticmomentassociatedwith spins,the pulsescanbe representedby rathersimpleoper-atorsactingon the spin system. This allows to establisha ratherintuitive algebraicformalism for the descriptionof the spin dynamicsand, consequently, enablesthecreationof custompulsesequencesto generatealmostany conceivablequantumco-herency. Thesecoherencescanbeusedin turn to probespecificpropertiesof thespinsystem. Recently, pulsedmagneticresonancemethodshave alsocomeinto usefornon-spectroscopicpurposeslike “quantumcomputing”[6]. Here,only the two mostbasicpulseexperimentsareintroduced.For anoverview of pulsedEPRmethods,seee.g.[7].

In the rotating frameapproximation(seeappendixA), the effect of appliedmi-crowave pulseson the spin systemcanbe describedasan additionalstaticmagneticfield, giving rise to Larmorprecession.By adjustingthestrengthandthedurationofthe pulse,different“flip angles”,i.e. partial precessionperiods,canbe achieved. Inmostexperiments,pulsesareusedto switchthepolarizationof thespinensemblebe-tweenlongitudinal(alongthestaticmagneticfield) andtransversal(perpendiculartothestaticfield).

FID Spectroscopy

FID (freeinductiondecay)spectroscopy accessesthemagneticinductionafterprepa-ration of the systemby a microwave pulse. The initial pulseturns longitudinalpo-larizationinto a transversaldirection;thetransversalmagnetizationis thenmeasured.As subensemblesof the spin systemexhibit differentLarmor frequencies(reflecting


theEPRspectrum),thespectrumcanberecoveredby a Fourier transformof theFIDsignal.

Spin Echo Spectroscopy

Spinechospectroscopy extendsFID spectroscopy by addingoneor more“refocusingpulse(s)”. The spectraldistribution of Larmor frequenciescausesthe free inductionto decay. A refocusingpulseeffectively changesthesignof thestaticmagneticfieldasseenby thespinensemble,therebycausinga pseudotime reversalof thesystem’sevolution. The reverseof the inductiondecayleadsto an “echo” of the initial FIDwhich is thenmeasured(Fig. 1.6).

1.4 Multiple ResonanceExperiments

Driving a transitionbetweentwo eigenstateseffectively couplesthesestates,therebyestablishinga correlationbetweenthem. By driving multiple transitionsthatshareatleastonestatecorrelationsbetweenmorethantwo statesareestablished.Multiple res-onancemethodsusethesecorrelationsto identify transitionswith sharedeigenstates.In a multi-level system,transitionsdo not necessarilysharecommonstates.Experi-mentsthataresensitiveonly to correlatedtransitionsthereforeyield simplifiedspectra.

Thebestknown of theseexperimentsis calledENDOR(ElectronNuclearDouble-Resonance)[8]. In ENDOR, the spin systemunder investigation is comprisedofweaklyinteractingelectronicandnuclearspins.For suchasystem,theallowedtransi-tionsaffecteitherthenuclearor theelectronicspincomponentsonly (hencethename).Theelectronicspin transitionis thenusedto probethenuclearspin transition.Com-paredto aNMR experiment,ENDORis selectiveto nucleicoupledto anelectronspin.Comparedto EPR,theNMR transitionsyield a muchhigherspectralresolution.Thisallows to accessthehyperfineinteractionwith high accuracy.

1.4.1 ContinuousWaveENDOR

In thecw ENDORexperiment,cw NMR andcw EPRarecombined.TheEPRtran-sition is usuallydrivenundersaturationconditions.Whena nuclearresonanceis hit,thenuclearsublevelsarecoupled,therebyproviding analternaterelaxationpath.Thisleadsto adecreaseof saturation,andtherforeto anincreasedEPRsignal(Fig. 1.7).

1.4.2 PulsedENDOR

In contrastto cw ENDOR,pulsedENDORexperimentscanutilize coherentspindy-namicsandneednot necessarilyrely on relaxationeffects. The two mostcommonmethodswereintroducedby Mims andDavies. A goodoverview of pulsedENDORmethodologycanbefoundin [9].

1.4. MULTIPLE RESONANCE EXPERIMENTS 19

B

a b c

d

e f g

Figure 1.6: Evolution of a spin echoin the rotating frame: Magnetizationis turnedaway from thedirectionof thestaticmagneticfield *B by aπ + 2 pulse(a). Inhomogeneousbroadeningleadsto diffusionof the magnetizationin a planeperpendicularto *B (b, c). A π pulseflips the magnetizationover (d).Inhomogeneousbroadeningnow reversesthedephasingprocess(e, f), leadingto anechoof the initialmagnetization(g).


mS

mI

+½

−½

+½

−½

−½

+½

a

b

b

2

4

1

3

c

c

c

c

Figure 1.7: Left: energy level splittingsof a weaklycoupledelectron/nuclearspinsystem(S , I , 12)

in anexternalmagneticfield. Energy contributions:a) electronZeemanterm,b) nuclearZeemanterm,c) hyperfineinteraction.Allowedtransitionsflip only eithertheelectronspinor thenuclearspin.Right:relaxationpathwaysin the four-level system(dotted). Saturationof the 1 - 3 EPRtransitioncanbereducedby driving anNMR transition.i.e. 1 - 2, thatenhancesrelaxation.

1.4. MULTIPLE RESONANCE EXPERIMENTS 21

Mims ENDOR

TheENDORexperimentintroducedby Mims [10] is basedon anstimulatedelectronspinechoexperiment.By irradiatinga π RF pulsebeforethefinal pulse,theresonantnuclearspinsareflipped.Thecorrelationbetweentheelectronicspinstateswithin onesubsystemof samemI is thereforedestroyed,preventinganecho(Fig.1.8). It shouldbenotedthatthetiming of thepulsesequencecanleadto additionalcorrelationsbetweenthesubensembles,resultingin “blind spots”,i.e. NMR frequencieswhereno ENDOReffect is observed.

DaviesENDOR

Davies’ ENDORmethod[11] is basedon anelectronspin inversionrecovery experi-ment. The selective initial inversionpulsecausesa spectralhole in theelectronspinpopulation(Fig. 1.9). Again,a resonantπ RF pulseflips nuclearspins,therebyswap-pingthespectralpositionof spinsubensembleswith differentpolarizationand“filling”thespectralhole. Thespectralholeis thenprobedby a two pulseechosequence.Forsmall NMR transitionfrequencies,the correspondingspin subsystemare spectrallyvery closeandshareaboutthesamespinpolarization.Therefore,DaviesENDORisinsensitive towardsNMR transitionfrequenciessmallerthanthewidth of thespectralholecreatedby themicrowave inversionpulse.


mw

RF

echo

π/2 π/2 π/2

π

Figure 1.8: Mims ENDORpulsesequenceandevolution of spin level populationin an S , 12, I , 1

2system. The first two microwave pulsesgeneratea coherentsuperpositionof spin stateswithin eachsubsystemof thesamenuclearspin state.TheRF pulsetransferscoherencebetweenthesubsystems,destroying coherencewithin eachsubsystemand suppressingthe echo. Correlatedpopulationsareindicatedby thesamefill pattern.

ν ν ν ν

mw

RF

echo

ππ/2π

π

Figure1.9: DaviesENDORpulsesequenceandcorrespondingevolutionof thespinpolarizationwithinan inhomogeneouslybroadenedline. The first microwave pulseburnsa spectralhole that is filled bypopulationtransferbetweenNMR sublevelsduringtheRF pulse.

REFERENCES 23

REFERENCES

[1] Mohr P.J. & Taylor B.N., CODATA recommendedvaluesof the fundamentalphysicalconstants:1998,Rev. ModernPhys.72, 351–495(2000).

[2] Brown J.M.,Buenker R.J.,CarringtonA., Di LauroC., Dixon R.N.,Field R.W., HougenJ.T., HuttnerW., KuchitskuK., MehringM., MererA.J.,Miller T.A., QuackM., RamsayD.A., VesethL., & ZareR.N.,Remarkson thesignsof g factorsin atomicandmolecularZeemanspectroscopy, Mol. Phys.98, 1597–1601(2000).

[3] CarringtonA. & McLachlanA.D., Introductionto MagneticResonancewith Applicationsto ChemistryandChemicalPhysics, chapter9, Harper& Row (1967).

[4] SlichterC.P., Principlesof MagneticResonance, chapter4.6,SpringerVerlag,3rdedition(1989).

[5] SlichterC.P., Principlesof MagneticResonance, chapter1.3,SpringerVerlag,3rdedition(1989).

[6] Mehring M., Conceptsof spin quantumcomputing,Appl. Magn. Reson.17, 141–172(1999).

[7] SchweigerA., Puls-Elektronenspinresonanz-Spektroskopie: Grundlagen,VerfahrenundAnwendungsbeispiele,Angew. Chem.103, 223–250(1991).

[8] FeherG., Observation of nuclearmagneticresonancesvia the electronspin resonanceline, Phys.Rev. 103, 834–835(1956).

[9] GemperleC. & SchweigerA., Pulsedelectron-nucleardoubleresonancemethodology,Chem.Rev. 91, 1481–1505(1991).

[10] Mims W.B., PulsedENDORexperiments,Proc.R.Soc.A283, 452–457(1965).

[11] DaviesE.R.,A new pulseENDORtechnique,Phys.Lett.47A, 1–2(1974).

Chapter 2

Experimental Setup

Thehigh field EPRexperimentsdescribedin this thesiswereperformedwith a com-mercial Bruker ElexsysE680 94 GHz cw/pulsedEPR spectrometer[1]. The spec-trometerconcepthassomenotabledifferencesfrom most conventionalEPR spec-trometersthat have to be consideredfor successfulexperiments. This chapteraimsto describesomeunusualconceptsusedin thespectrometeranddiscussexperimentalconsequences.

Fig. 2.1 shows a simplifiedblock diagramincluding themostprominentsubunitsof the spectrometer. Most spectrometeroperationsare controlledfrom an externalworkstation(not shown) runninga front-enduserinterfaceto the real time capable

Magnet Power

Supply and Control

9.5 GHz Pulsed IF BridgeMixers

84.5 GHz L.O.

Lock−InModulation Control Transient

Averager

Programmable

GeneratorPulse Pattern

6T Wide Bore Hybrid Magnet

Resonator

Acquisition

Server to Workstation

Oversized Waveguide

Coaxial Line

Digital Signal Line

Analog Signal Line

Digital Network

Other

Figure2.1: Simplifiedblockdiagramof theBrukerE68094GHz spectrometer.

25

26 CHAPTER2. EXPERIMENTAL SETUP

acquisitionserver.

2.1 Magnet

The magnetusedto createthe strongmagneticfield neededfor 94 GHz EPR(about3350mT atg 2) followsaratherunusualdesignconcept.Theabsolutefield inhomo-geneityover thesampleregionhasto bekeptsmallto profit from thepotentialspectralresolutionof HFEPRwhile the absolutefield is muchhigherthanwith conventionalspectrometers.Theserequirementsresultin theneedfor a ratherbulky magnet.As allpracticalferromagneticmaterialsaresaturatedat therequiredfields,thefield strengthH hasto bevery large,calling for high currentsanda lot of turnsof thefield inducingcoil. To avoid the high energy consumptionandheatdissipationof sucha magnet,a superconductingcoil is used. The coil is split into two halvesin a Helmholtz-likearrangement,resultingin easyaccessto theregionof highestfield andbesthomogene-ity. To avoid unnecessaryboil-off of the cryogen(liquid helium) dueto dissipationin the connectionto an externalpower supply, the magnetcanbe put into persistentfield modevia a superconductingshort. To changethe field, the coil still hasto beconnectedto anexternalpower supplyandtheshorthasto beremoved. This is doneby heatingthesuperconductingshortover its critical temperature(“heaterswitch”).

In many experiments,only smallvariationsof thestaticmagneticfield arerequired.Therefore,the superconductingcoil is complementedby a pair of resistive auxiliarycoils that superimposean additionalmagneticfield of 40 40 mT. Using thesecoils greatlyreducestheliquid heliumconsumptionof thesystemandallows for sig-nificantly fastersweeps.

The magnetis specifiedfor staticfields of up to 6 T. The relative field inhomo-geneityover thesamplevolumecanbe estimatedto be smallerthan10 5. The fieldis orientedhorizontally. Sincetheprobeheadallows to turn samplesabouttheverticalaxis,it is possibleto measureEPRspectraasa functionof thesampleorientationwithrespectto themagneticfield.

2.1.1 Field Calibration

Oneconsequenceof themagnetdesignis theparticularwaythemagneticfield is deter-mined.In mostEPRspectrometers,themagneticfield is measuredby a Hall effect orNMR probeandcorrectedin a feedbackloop. Thehybrid magnetusedin the94 GHzspectrometer, however, superimposestwo fields with differentgeometry. Therefore,it is in generalimpossibleto probethe field in oneplaceanddeducethe field at thesamplepositionfrom thatvalue. Theonly known quantitiesarethecurrentsthroughthe superconductingand resistive coils. The magneticfield is thus calculatedas alinear function of thesecurrents. The constantsinvolved in this calculationhave tobe determinedempirically by taking EPRspectraof standardsampleswith known gfactors.

2.1. MAGNET 27

= I0 = IH L

R

H = I0 L

Figure2.2: Schematicof thesuperconducting(left) andauxiliarycoil (right) system.TheheaterswitchresistanceRactsasabypassto thesuperconductingcoil.

Throughoutthis work, Li:LiF hasbeenusedas g standardfor the rangeaboutg 2. This sampleis preparedfrom a LiF crystalby heavy neutronirradiationandthermaltreatment;asa resultmicroscopicmetallicLi clustersareformed.Sincetheseclustersareprotectedby therigid LiF latticearoundthem,they areverystable,andtheyhave a definedchemicalenvironment.TheEPRline is very narrow (linewidth below30 µT at 94 GHz for the sampleused). Due to the cubic crystal lattice, the g factoris independentof thecrystalorientation.In addition,sincethemetalclustersexhibitPauli paramagnetism,g is virtually independentof thetemperature(seee.g.[2]). In ahigh precisionexperiment[3], it hasbeendeterminedasgLi:LiF 2 002293 2 .

If nonlinearmagneticsaturationeffectsof thespectrometerconstructionmaterialareneglected,themagneticfield dependson thecurrentthroughtheauxiliary coil ac-cordingto B aI b. As bothconstantsa andb haveto bedetermined,it is necessaryto measurethe EPR line of the Li:LiF sampleat two different microwave frequen-cies, thusyielding two referencesfor the magneticfield. Throughoutthis work, nosignificantdeviationsfrom theassumedlinearitycouldbeobserved.

This approachis complicatedby the fact that the superconductingcoils, afterswitchingto persistentmode,tendto losesomecurrentdueto relaxationof the fluxlattice1.

Therefore,it is necessaryto performcalibrationmeasurementsimmediatelybeforeor aftereveryEPRexperimentwhenhigh precisionis desired.

A muchmoreseriousproblemfor accuratemeasurementsoccurswhenlargefieldsweepsarerequiredandthe currentthroughthe superconductingcoils hasto be ad-justed. The “open” heaterswitch still hasa ratherlow resistance( . 5 Ω) andactsthereforeasa currentbypasswhenever thereis somevoltagepresentacrossthe coil(Fig. 2.2). Thebehavior of thesystemis governedby thedifferentialequation

I0 IL LR

dILdt (2.1)

1Abovesomecritical appliedmagneticfield B / T 0 , superconductivity breaksdown. In typeII super-conductors,superconductingandnon-superconductingphasescoexist, forminga2D currentvortex/fluxlattice(seee.g.[4]).


For L 92H andR 5 Ω, thecurrentthroughthesuperconductingcoil thereforelagswith a time constantL 1 R . 18 s behindthe known injectedcurrent. To compensatefor this lag, the operatingsoftware tries to inject an additional“jump current” IJ L 1 R dIL

dt . This methodis limited thoughbecauseR andL aredifficult to accesswiththerequiredprecision.Evenworse,R is not constant,but varieswith thetemperatureof the heaterswitch. This temperaturemay dependon parameterslike the appliedvoltageor the filling level of the helium reservoir. It alsodependson the conditionsbefore theexperimentdueto theheatcapacityof thesystem.

Consequently, theonly wayto arriveat linear, reproduciblesweepsof themagneticfieldusingthesuperconductingcoilsis tokeeptheinductionvoltageaslow aspossible.This in turn requiresextremelyslow sweepswhicharenot alwayspractical.

2.2 Resonator

The microwave resonatorin any EPRspectrometerhasto satisfy two contradictorygoals: it hasto maximizethe interactionof thesamplewith themagneticcomponentof the microwave field while simultaneouslyminimizing dielectric lossesdueto thesample.Thefirst propertyis characterizedby theconversionfactor κ whichdescribesthe relationbetweentheappliedmicrowave power andthemagneticfield strengthatthesamplelocation:

B1 κ ) Pmw (2.2)

Theconversionfactoritself is closelytied to thequality factorQ which is definedas

Q Eνmw

Pmw(2.3)

whereE is the steady-statemicrowave energy in the resonator, νmw the microwavefrequency, and Pmw the appliedmicrowave power. It immediatelyfollows that themicrowave energy density, andthereforethemagneticfield strengthin thecavity, in-creaseswith Q.

Apart from the sample,the main sourceof dissipationis the materialof the res-onatoritself. For a cavity, most lossesaredue to resistive dissipationat the cavitywalls. Thesurfacescalesquadraticwith thelinearscaleof thecavity. Themicrowaveenergy, however, is distributedover the cavity volumewhich scalescubic relative tothe linear size. As the cavity size is determinedby the wavelengthλ c1 νmw, Qgenerallyvariesas Q λ ν 1

mw. The constructionof good microwave cavities isthereforegettingincreasinglydifficult with themove to higherfrequencies.Onepos-sibility to overcomethisproblemis to useaharmonicmodeof anoversizedresonator.This is theapproachfollowedin Fabry-Perotresonatorswhicharewidely usedin highfrequency EPR.This decreaseshowever the conversionfactorof the resonatorsincethemicrowave energy is distributedover a largervolume. Theratherlow microwavepower availablefrom theBruker microwave bridge(seesection2.3)prohibitstheuse

2.3. MICROWAVE BRIDGE 29

of sucha resonatorwhentheability to performpulsedexperimentsis required.Con-sequently, theBruker spectrometerusesa cylindrical cavity operatingin TE011 mode.To compensateshiftsof theresonancefrequency inducedby thesample,theresonatorvolumeis adjustable.Theresonatoris coupledto thewaveguideusingasmallantenna(fig. 2.3). Critical couplingis achievedby animpedancetransformerimplementedasamovableshortat theendof thewaveguide(not shown).

2.2.1 SampleMounting

The samplesare insertedinto the resonatoralong the cylindrical axis from the top.To reducemicrowave leakage,thehole is implementedasa metalpipewith lessthan1 mm in diameteranda lengthof several mm. The samplecapillariesarethereforelimited to an outerdiameterof 0 9 mm. The capillariesprovided by Bruker have anouterdiameterof 0 9 mm andaninnerdiameterof 0 5 mm. For mostexperimentsinthis work, however, clearfusedquartzcapillarieswith anouterdiameterof 0 87 mmandaninnerdiameterof 0 70mmwereused(Vitrocom#CV7087Q).Thelargerinnerdiameterincreasestheeffective samplevolume. In additionit allows to mountlargercrystalsandeasesfilling thetubewith viscoussolutions.

The samplecapillary dips into the resonatorfor at most 3 mm (fig. 2.3). Thislimit is givenfor oneby theheightof theresonator, but moreoftenby theamountofdielectriclossescausedby thesamplethatcanbetolerated.Theactivesamplevolumeis thereforerestrictedto about3 mm; with theCV7087Qcapillaries,this correspondsto about1 µl.

2.3 Micr owaveBridge

Themicrowave bridgeof thespectrometeris designedfor bothcw andpulsedacqui-sition modes.It is a superheterodynedesignwith an intermediaryfrequency (I.F.) of. 9 5 GHz, i.e. X bandfrequency. All signalforming andprocessingis doneat theI.F. level (Fig. 2.4). Conversionto/from 94 GHz is doneby anadditionallocal oscil-lator andmixersthatarephysically separatedfrom thebridge,allowing to placethemcloserto theprobeheadandtherebyto reducelossesin thewaveguides(Fig. 2.5). TheconvertersandtheI.F. bridgeareconnectedvia semirigidcoaxiallines.

In the I.F. bridge,a Gunnoscillatoris usedasa low-noisemicrowave source.Incw mode,themicrowave power is passedthroughanattenuatorto theconverterunit.In pulsedmode,microwave pulsesareformedby pin diode“pulseshapers”.For eachpulsechannel,thephaseandattenuationcanbesetindividually.

The I.F. bridge employs two detectors.For cw and other low-bandwidthappli-cations(e.g. many transientEPR experiments)the I.F. signal is superimposedto areferencesignalderived from the Gunnoscillator. The diodeeffectively works asamixer, convertingtheI.F. signalto DC. TherecoveredDC signalis fed througha lowbandwidth,low noiseamplifier.


antenna

waveguide

sample holder

adjustable plunger

cavity

Figure 2.3: Diagramof the 94 GHz microwave resonator. The resonatorvolumecanbe adjustedtocompensatefrequency shifts inducedby the sample. Coupling to the waveguide is achieved usingawire antenna.Themagneticfield distributionof thefundamentalresonatormodeis indicatedby dashedlines.

2.3. MICROWAVE BRIDGE 31

A

A P

pin

A P

A P

Pulse Forming Unit (4 times)

Delay Line

cw

pulse

pulse

cw

Gunn MW Source

Diode Detecion

Mixer Detection

MW PreAmp

MW Diode

Quad Mixer

Video Amps

Diode Out

Quad Out

cw Branch

Low Bandwidth Amp Attenuator Phase Shifter

9.5 GHz IF in

from Pulse Generator

9.5 GHz IF out

Figure2.4: Block Diagramof the9 2 5 GHz I.F. pulsedandcw bridge.

84.5 GHzGunn Source

9.5 GHz IF in

9.5 GHz IF out

Diode Mixer

Diode Mixer

94 GHz

to/from Resonator

Figure 2.5: Simplified schematicof the mixer stageusedto convert signalsbetween9 2 5 GHz and94 GHz.


For pulsedandhighspeedapplications,abalancedquadraturemixer is used.Bothphasesignalsof thequadratureoutputarefedthroughhighbandwidth(upto 250MHz)videoamplifiers.

The I.F. bridgeis equippedwith AFC (automaticfrequency control) circuitry. Inmostcases,however, theoscillatorhasto beusedin freerunningmodesincetheAFCis unableto lock to theresonatordip at low microwavepowers.Frequency drifts in thefreerunningmodeareon theorderof only a few kHz which makesthis anacceptablelimitation.

Themixer/converterunit providesanotherGunnoscillatorandthemixersfor con-versionbetween9 5 GHz and94 GHz. TheGunnoscillatoris phase-lockedto a pre-cision quartzreferenceoscillator. The converter block also provides the circulatorneededfor insulationof thetransmitandreceivechannels.Thereis nomicrowaveam-plification at 94 GHz. Themaximumavailablemicrowave power is thereforelimitedto only . 5 mW whichplacessomerestrictionsonpulsedexperiments.

The I.F. bridgefeaturesan internal frequency counter. Togetherwith the knownoscillatorfrequency of the converterblock, it is thereforepossibleto derive the finalmicrowave frequency with anaccuracy of about1 kHz.

REFERENCES

[1] SchmalbeinD., MareschG.G., Kamlowski A., & Höfer P., The Bruker high-frequency-EPRsystem,Appl.Magn.Reson.16, 185–205(1999).

[2] ZimanJ.M.,Principlesof theTheoryof Solids, chapter10.2,UniversityPress,Cambridge,2ndedition(1972).

[3] StesmansA. & vanGorpG., Novel methodfor accurateg measurementsin electron-spinresonance,Rev. Sci.Instrum.60, 2949–2952(1989).

[4] Ziman J.M., Principles of the Theoryof Solids, chapter11.11,University Press,Cam-bridge,2ndedition(1972).

Part II

MethodologicalDevelopmentsforHigh Field EPR

33

Chapter 3

Optical Excitation and Transient EPR

TransientEPRaddstime asan additionalparameterto the observed EPRspectrum.To observe a meaningfultime dependenceof theEPRsignal,thesystemunderexam-ination hasto be preparedto a statefar from thermodynamicequilibrium beforethemeasurementtakesplace.This preparationcanbeachievedby a nonadiabaticchangein theHamiltoniangoverningthedynamicsof thesystem.

Thesimplestway to achieve this is to turn on themicrowave irradiationin a nona-diabaticway, i.e. instantlyascomparedto thetimescaleof therelevantspindynamics.Anotherwaywouldbeto changethemagneticfield atthebeginningof theexperiment.With thesemethods,however, thespinpolarizationthatcanbeachievedis still rathersmallandmostlydeterminedby thesmallBoltzmannpopulationdifference.

By far moreintensesignalscanbe obtainedwith larger thanthermalspin polar-ization. Oneway to achieve this is via optical excitation of the sample. Obviously,time-resolved EPRon light inducedparamagneticintermediatesis an importanttoolfor investigationsof photophysical andphotochemicalprocesses.A review of timeresolvedEPRtechniquesandtheir applicationon thestudyof photoprocessesis givenin [2].

While theseexperimentsarewell establishedat lower frequencies,only few exper-imentsof thistypehavebeenreportedatW band(e.g.[3–6]). TheBrukerspectrometerusedthroughoutthis work wasnot originally designedto performthis typeof experi-mentandneededto beextendedfor time-resolvedEPRon photoinducedstates.

3.1 Experimental Setup

3.1.1 Light Accessto the Resonator

Light accessis straightforward to implementif eitheran openresonatorstructureisused(i.e.Fabry-Perottype),or if theresonatorcanbemadetransparentfor light. Nei-therappliesto thecylindrical cavity of the94GHzspectrometerusedhere.Thesingleaccessibleopeningof the resonatoris the hole usedto insert the sample.The entire

35

36 CHAPTER3. OPTICAL EXCITATION AND TRANSIENTEPR

Figure3.1: Positioningof theopticalfiber in theresonator.

diameterof thisopeningis usuallyblockedby thesamplecapillary. Theonly possibil-ity for light accessis thereforethroughthesamplecapillary itself. This wasachievedby feedinganoptic fiber throughthesampleholderrod thatdipsinto thesamplecap-illary (Fig. 3.1). Specialcarehasto be taken however to not disturbthe microwavecharacteristicsof theresonator.

Theprototypesampleholderrod providedby Bruker allows to adjusthow far thefiber extendsinto thecapillary. This featureallows to optimizetheillumination of thesamplewhile minimizing dielectriclossesdueto thefiber enteringtheresonator. Theotherendof thefiber is fitted to amaleFSMA 905connector.

3.1.2 Light Sourceand Transport

A Q-switched1 Nd:YAG laser(SpectraPhysicsQuantaRayDCR-2(10))wasusedtogenerateshort(5 ns),repetitive (10 Hz) light pulsesat a basewavelengthof 1064nmwith a multimodalbeam(about15 mm diameter).A harmonicsgeneratorallows todouble,triple, or quadruplethe light frequency. For mostexperimentson photosyn-thetic reactioncenters,the doubled(λ 532 nm) settingprovidessuitablequantumenergy of the photons(hν 2 3 eV). For the experimentson pentacenedescribedhere,thesamesettingwasused.

Thelight energy is transferedto thesamplerod via severalmetersof a silica mul-timode optical fiber (SpecTran HCG-M0365T, Fig. 3.2) that is fitted with a FSMAsocket on oneend. Thedimensionsof the laserbeamhave to bereducedto thecorediameterof this fiber (365 µm). This is doneusinga f 50 mm silica lens. Sincethesmallercrosssectiongreatlyincreasesthelight intensity, thelaserbeamhasto beattenuatedusinga grayfilter (6% transmission)in orderto not exceedthedestructionthresholdof the fiber (Fig. 3.3). This thresholdis easilyreached,even at ratherlownominal intensities,due to the multimodestructureof the beamand corresponding“hot spots”.

Theoverall transmissionfrom thelensto thesamplelocationwasdeterminedto beabout50%atλ 532nmby comparinglaserpulseenergiesafterthegrayfilter andatthesamplelocationasmeasuredwith apyroelectricprobehead.Thelaserpulseenergy

1Q refersin this context to thequality factorof thelaserresonatorandnot to thatof themicrowavecavity.

3.1. EXPERIMENTAL SETUP 37at

tenu

atio

n (d

B/k

m)

wavelength (nm)

Figure3.2: Attenuationcharacteristicsof theSpecTranHCG-M0365Tsilicafiberusedfor light accessto thesample[7].

6% gray filter

f=50 mm lens

adjustable fiber holder

fiber

Figure3.3: Setupfor couplinga laserbeaminto asilicafiber.


waslimited by thedestructionthresholdof thefiberat theinsertionpoint. Up to 1 5 mJper pulseat the samplelocationcould be achieved with this setup,correspondingtoabout4 1015 photons. This allows up to 6 5 nmol of samplecentersto be excited,correspondingto a sampleconcentrationof 130 mM at a typical samplevolumeofabout500nl.

3.1.3 Trigger Control

Dataacquisitionhasto besynchronizedwith theexcitationof thesampleby thelaser.In the setupused,the laseris runningfreely andtriggersthe transientrecorder. It isdesirableto be ableto useboth positive andnegative delaysof the trigger signalforthetransientrecorderrelative to thelaserpulse.Negative delaysallow to includepre-excitationsignalcomponentsin the acquiredtransientandusethemfor studyingthekineticsof the rising transientsignalor to eliminatebaselinedrifts by deriving dif-ferencespectra.Positive delaysallow to observe the transientsignal in a small timewindow a considerabletime after excitation. This is useful for studyingsecondarytransientspeciesthataregeneratedindirectly, e.g.by electronor energy transferpro-cesses.

Thelaserprovidesasynchronizationsignaltiedto thefiring of theflashlampsusedfor excitationof theNd:YAG rods. Theactuallaserflashoccurssynchronouslywiththe operationof the Q switch andis deferredby about210 µs to allow for inversionbuildup in thelaserrods[8].

The flashlamp synchronizationsignal is usedto trigger the programmablepulsepatterngeneratorof the spectrometerwhich in turn generatesa trigger pulsefor thetransientrecorder. By reprogrammingthepulsegenerator, arbitrarydelayscanbegen-erated.Therefore,the transientacquisitiontriggercanbechosenfrom 210µs beforethelaserflashto 100msthereafter2.

3.1.4 Bandwidth and DetectionMode

Transientspectraare typically measuredwithout modulationof the static field B0.Modulationcomplicatesthespectralcomponentsof theobservedsignalin anonlinearway, makingit impracticalto observe kineticson a timescaleshorterthantheperiodof the modulationsignal. The unmodulatedacquisitionmethodthereforepotentiallyallows for largerdetectionbandwidth.

The bandwidthlimiting elementsin the setupareeither the resonatoror the mi-crowavedetectorandsignalamplifiersused.At a resonancefrequency of 94GHzanda typical resonatorquality of Q . 2000, the resonatorbandwidthis about50 MHz.Thefrequency responseof thequadraturemixeroutputof theI.F. bridgeis determinedby theconfigurablebandwidthof thevideoamplifiersandcanrangeup to 200MHz.In order to reducewhite noise,it is advisableto matchthe bandwidthto that of the

2The100mslimit is givenby the10 Hz repetitionrateof thelaser.

3.2. TRANSIENT EPRON THE TRIPLETSTATE OFPENTACENE 39

Figure3.4: Pentacene(left) andp-terphenyl (right).

Figure3.5: Rabioscillationsof thepentacenetriplet statevs.B0.

resonator. Thediodedetectionoutputhasa muchsmallerbandwidth(0 4 MHz) andcannotbeusedto analyzefastkinetic components.It is still usefulhowever to obtainpseudo-stationaryspectraof short-livedparamagneticspecies.

3.2 Transient EPR on the Triplet Stateof Pentacene

To examinetheperformanceof thesetup,transientEPRexperimentswereperformedon thelight-inducedtriplet statesof pentacenein ap-terphenyl hostcrystal(Fig. 3.4).

After laserexcitation, pentacenemay undergo selective intersystemcrossing,re-sultingin a spinpolarizedtriplet state.A representative two dimensionalspectrumofthisstateis shown in fig. 3.5.

As thetriplet stateis populatedfrom asingletstate,theinitial totalmagnetizationiszero.Emissive andabsorptive componentsof thespectrummustthereforebeof equalintensity. They are split, however, by the coupling betweenthe unpairedelectronscomprisingthe triplet (Fig. 3.6). The crystallinestructureof the sampleimplies anorientationdependenceof thespectra.Thisorientationdependenceisbeyondthescopeof this chapterandhasnotbeenexaminedfurther.

Timeresolvedspectrashow thedecaycausedby relaxationat low microwavepow-ers.At high microwave powers,themicrowave radiationitself beginsto dominatethedynamicsof thesystem,leadingto Rabioscillations(Fig. 3.7).Thefrequency of theseoscillationis givenby theamplitudeof themagneticcomponentof themicrowavefieldin therotatingframeasωR

8πγeB1. Therefore,it is straightforward to determinethe rotatingframefield B1 from suchmeasurements.B1 itself is proportionalto the


Figure 3.6: Spinpolarizedtriplet spectrumobtainedimmediatelyafter light excitationof pentaceneinp-terphenyl.

Figure3.7: Rabinutationsof thepentacenetriplet signalat differentmicrowavepower levels.

3.2. TRANSIENT EPRON THE TRIPLETSTATE OFPENTACENE 41

Figure3.8: TransientEPRsignalof thepentacenetriplet state(B0 , 3328mT) obtainedby usingdiodedetection,mixerdetection,andnumericallybandwidth-limitedmixerdetection.

microwave energy storedin the resonatorwhich dependson the incidentmicrowavepowerPmw andthequality factorQ asB1 κ

PmwQ. Theconversionfactorκ canbe

estimatedfrom theobservedRabifrequenciesandthespectrometerparametersQ andPmw asκ . 0 014mT1

W.

Theeffectof differentdetectionbandwidthsis demonstratedin Fig. 3.8.Thesametransientsignalwasacquiredthroughthelow-bandwidthdiodedetectionchannelandthe high-bandwidthquadraturemixer channel.The low bandwidthof thediodepathcausesartefactsmostnoticeableat theinitial riseof thetransientwhich in factreflectstherisetimeof thedetectionamplifier. AlthoughtheRabioscillationfrequency, ωR, isstill within thefrequency rangecoveredby thediodedetectionpath,significantphaseshifts areobserved that could leadto a wrong interpretationof the acquireddataascomparedwith thesignalacquiredvia themixer detectionpath.

Theapparentincreasednoiselevel of the mixer-detectedsignalin fig. 3.8 canbemostlyattributedto thehigherbandwidthof thesystemandincreasedwhite noiseasa result.After limiting thebandwidthof themixer-detectedsignalnumericallyto thatof thediodedetectionpath,thesignal/noiseperformancesof bothdetectionchannelsturn out to be similar. Therefore,thereis no particularadvantagein usingthe diodedetectionpathfor transientEPR.


3.3 Conclusion

Usingpentacenein p-terphenyl asa modelsystem,it wasshown thattransientexperi-mentsonlight-inducedspeciesarepossiblewith theBruker94GHzEPRspectrometer,despitetheclosedresonatorstructureandthelackof a dedicatedlight accesspath.Asa sideeffect, theeffective B1 field strengthin theresonatorandtheconversionfactorcouldbedetermined.

Similar experimentson light-inducedspeciescan be performedin pulsedEPRmode. It is alsopossibleto usethe installedlight accesspathfor in situ irradiationof samplesprior to EPRexperiments.

REFERENCES

[1] HofbauerW. & Bittl R., EPRat 94 GHz of laser-inducedspeciesin anELEXSYSE680spectrometer, Bruker Report145, 38–39(1998).

[2] StehlikD. & MöbiusK., New EPRmethodsfor investigatingphotoprocesseswith param-agneticintermediates,Ann.Rev. Phys.Chem.48, 745–784(1997).

[3] GroenenE.J.J.,Poluektov O.G.,MatsushitaM., SchmidtJ.,vanderWaalsJ.H.,& MeijerG., Triplet excitation of C60 andthe structureof the crystalat 1 3 2 K, Chem.Phys.Lett.197, 314–318(1992).

[4] PrisnerT.F., RohrerM., & Möbius K., Pulsed95 GHz high-field EPRheterodynespec-trometerwith highspectralandtime resolution,Appl.Magn.Reson.7, 167–183(1994).

[5] PrisnerT., van der Est A., Bittl R., FrommeP., Lubitz W., Möbius K., & Stehlik D.,Time-resolvedW-band(95 GHz) EPRspectroscopy of Zn-substitutedreactioncentersofRhodobactersphaeroidesR-26,Chem.Phys.194, 361–370(1995).

[6] van der Est A., PrisnerT., Bittl R., Lubitz W., Stehlik D., & Möbius K., Time-resolvedX-, K-, andW-bandEPRof theradicalpairstateP 700A 1 of photosystemI in comparisonwith P 865Q A in bacterialreactioncenters,J. Phys.Chem.B101, 1437–1443(1997).

[7] SpecTranSpecialtyOpticsCompany, HCG-M0365TDataSheet.

[8] SpectraPhysics,Inc.,QuantaRayDCR2(10)Nd:YAG LaserManual.

Chapter 4

Soft PulseElectron Spin Echoes

With mostpulsedEPRspectrometers,availablemicrowave power is not muchof aconcernandpulsescanbe kept very short. Consequently, the detailedspin dynam-ics during themicrowave pulsesareoftenneglected.Themixer designof theBrukerE680 W bandspectrometerusedthroughoutthis work severely limits the availablemicrowave power. This meansthat ratherlong microwave pulseshave to be usedtoachievea givenflip angle.Theresultingnarrow excitationbandwidthimposesrestric-tionsonmany standardexperiments.

A commonproblemof EPRspectroscopy is thesensitivity towardsunwantedpara-magneticimpurities. Often, suchimpuritiescannotbe avoidedin the preparationofthesample.Theresultingcontaminationsignalscanaffectaspectrumto anextentthatmakesit virtually useless.This is especiallytrue for high field/high frequency EPR.A very commoncontaminationseenin high field/high frequency EPRspectrais freeMn2 .

A closerinvestigationof pulsedEPRexperimentsrevealsthat long pulsescanbeexploitedto disentanglespectraassociatedwith differenttransitionmomentsin a sur-prisingly simpleandfastelectronspin echoexperiment. In particular, the proposedmethodhasprovento beusefulto eliminateMn2 contaminationsignals.

4.1 Standard Methods to DisentangleSpectra

Thegeneralapproachto disentangleEPRspectrais to associatethespectralcontribu-tionswith distinctiveparametersandvaryexperimentalconditionsto mapout thecor-respondingparameterspace.Themostobviousspectralcharacteristiconecouldthinkof is the g factorwhich allows to separatespectraon the magneticfield axis. Otherpossible“tags” includesampleorientation,temperature,longitudinalandtransversalrelaxationtimes,spinmultiplicities,hyperfineinteractions,g anisotropy, andtransitionprobabilities.

In standardcw experiments,only someof thoselabelsareaccessibleby theavail-ableexperimentalparameters.Orientationor temperaturedependenciesareeasyto

43

44 CHAPTER4. SOFTPULSEELECTRON SPINECHOES4 5−5/2

+5/2

−1/2

+1/2

+3/2

−3/2

6

Figure 4.1: Splitting of Kramersdoubletsof a S , 52 systemin a magneticfield. Theenergiesof the

∆mS , 7 1 transitionsdiffer dueto thezerofield splitting,separatingthemin a resonanceexperiment.

accesswhile measuringspectraat saturatingmicrowavepower levelsor varyingmod-ulation frequenciescanseparatespecieswith different longitudinalrelaxationtimes.In ENDOR experiments,it is possibleto addressspeciesby their hyperfineinterac-tion. While virtually every conceivable label affects cw spectrain someway (e.g.linewidths,relativeintensities,or saturationcharacteristics),theeffectsareoftenrathersmall,makingit difficult to exploit themfor separatingdifferentspecies.

Time resolved experimentsexhibit a much larger experimentalparameterspace.Adding a singletime axisasin transientEPRexperimentsallows to observe Rabios-cillationswhichreflectthedipolematrixelementof thecorrespondingEPRtransition.In pulsedEPR,eachpulseaddstwo moredimensions,pulsedurationandseparation,to theparameterspace.In mostpulsedEPRexperimentsthepulsesequencehasto bevariedto mapout theparameterspaceandto accesstheRabinutations.Someexper-imentsof this kind canbefoundin [1–7]. This approachis however usuallycostly intermsof acquisitiontime.

The basicidea behindthe experimentintroducedhereis to spreadout the EPRsignal over the time axis with one fixed pulsesequence.This makes it possibletomeasurethetime-dependentinformationin onesingleshot. Therefore,this approachyieldstherequiredinformationwithoutanincreasein acquisitiontime.

4.2. THEORETICAL DESCRIPTION 45

Figure 4.2: A 908 – τ – 1808 pulsesequencefor onespeciesis a 2708 – τ – 5408 sequencefor anotherspecieswith a threetimeslarger transitionmoment.For shortpulses,theFIDs andechoesdiffer onlyin sign. Therefore,the correspondingsignalsare linearly dependentand a superpositioncannotbedecomposed.

4.2 Theoretical Description

4.2.1 Short Pulses

In the following, an isolatedeffective Kramersdoubletwithin a spin stateof multi-plicity 2S 1 is considered.Thereductionto this two-level systemis a goodapprox-imation if transitionsbetweenotherstatesareoff-resonantandthereforenot coupledto the transitionbetweenthe doubletlevels, i.e. dueto zerofield splitting (spin-spincoupling)(fig. 4.1).

Uponirradiationof a microwave field resonantwith them 9 m 1 transition,thesystemoscillatesbetweenthestates m and m 1 with theRabifrequency

ω1 γB1 ) S S 1 m m 1 (4.1)

whereγ is thegyromagneticratio andB1 is theamplitudeof themagneticmicrowavecomponentin the rotating frame. The Rabi frequency and thereforethe flip angleassociatedwith amicrowavepulseof givenlengthis thustied to theSandm quantumnumbersof therespective transitions.This meansthat thesamemicrowave pulsecancausedifferentflip anglesfor differentspecies.

For illustrationalpurposes,two systemsareassumedwhoseRabifrequenciesdifferby a factor of 3. A 90: pulsefor one specieswould occur as a 270: pulseto theotherspecies.For shortpulses,the resultingFIDs differ in sign. Anotherrefocusingpulsegeneratesspin echoes(fig. 4.2). Apart from the changein sign, no noticeabledifferenceis observablefor both FIDs or echoes.Therefore,a superpositionof bothsignalscannotbedecomposedinto separatesignals.

46 CHAPTER4. SOFTPULSEELECTRON SPINECHOES

The effect of long pulses,however, cannotbe adequatelydescribedby just oneparametersuchasaflip angle.This is becauseothercontributionsto thespindynamicsarenolongernegligible comparedto theinteractionof thespinsystemwith theappliedmicrowave field. In orderto examinetheeffectsof long pulsesfor a largesetof casesandaspartof this thesis,asimulationprogramwaswritten.

4.2.2 Spin DynamicsSimulation

Thesimulationprogramdescribedhereandlistedin appendixC waswritten with theintent of providing a tool to numericallysolve the Liouville-von Neumannequation(seeappendixA.1) for avarietyof pulseexperiments.Theprogramshouldbe; genericenoughto simulatetheeffectof longpulsesfor avarietyof experiments,

and; specificenoughto allow fast,efficientexecution.

Tosatisfybothrequirements,it wasdecidedtosimulatethedynamicsof anisotropic,inhomogeneouslybroadened,two-level spinsystem.Relaxationeffectswereneglected.The allowed experimentsinclude arbitrary pulse sequencesbuilt from rectangularpulseswith ( x and ( y phase.This choiceallows to utilize straightforward analyt-ical solutionsthroughoutthe program. Only inhomogeneousbroadeningrequiresanumericalintegration. The program,written in C++, simulateseven complex pulsesequencesin only a few secondson a (at the time of this writing) reasonablymodernPCor workstation.

Theinput parametersto thesimulationprogramare; a resonancefrequency offsetto simulateoff-resonantexperiments,; a linewidth parameterdescribingtheinhomogeneous(Gaussian)broadening,; a “pulselist” describingthepulsesequence,; andparametersfor settingthe requiredobservation time window andtemporalresolution.

The“pulselist” is a sequenceof microwavepulsesor delays.Eachpulsecanhavearbitraryparameterssuchas; phase( x, x, y, y),; duration,; andRabifrequency.


Figure 4.3: y componentof the transientnutationduringandtheFID after time-extendedmicrowavepulseswith nominalflip anglesof 908 and2708 < x pulses,respectively.

4.2.3 FID after a Long Pulse

The simulationprogramdescribedabove was usedto investigate the effect of longmicrowavepulseson theobservedFID. Fig. 4.3shows theobservedmagnetizationfornominal90: and270: pulses.TheFID afterthe90: pulseis rathersimilar to theFIDafterashortpulse.Themaindifferenceis aslight “wobble”sothatthetrail of theFIDchangessign. For the270: pulse,this “wobble” becomesthedominantfeatureof theFID. TheFID is nolongerapuredecayof thetransversemagnetizationafterthepulse.Rather, transversemagnetizationbuildsupandreachesits maximumafteranoticeabledelayaftertheendof themicrowavepulse.

To understandthisbehavior, it is illustrativeto decomposethelongΦ 270: pulseinto a Φ1 90: – Φ2 180: sequence.Temporarilyneglecting the effect of thelong pulseduration,an “equivalent” pulsesequencecanbe constructedby replacingthe long Φ1 andΦ2 pulseswith short Φ 1 90: and Φ 2 180: pulses(fig. 4.4).This substitutionleadsto a delayτ betweenthepulses,therebyarriving at a 90: –τ—180: two pulseechosequence.

Dividing the long 270: pulse into a 90: and a 180: pulse is only one possiblepartitioning of the pulse. Furthermore,the long pulsecould also be divided into 3or even morepulses.The FID observed after a long microwave pulsecanthereforebe consideredasthe superpositionof “true” FIDs andmulti-pulseechoesof varyingorder. In this light, thedeviationof theapparentFID from a truedecayis obvious.

4.2.4 Long PulseEchoes

As shown above, theshapeof anFID aftera long pulsedependson thenominalflipangle.Therefore,it is in principlepossibleto separatesignalcontributionsfrom tran-sitionswith differentRabinutations.In practice,this is problematicbecausethedeadtime of thespectrometerafterthepulsepreventstheacquisitionof theentireFID. Re-focusingtheFID in anechoexperimentfor remotedetectionallowsto circumventthis


Figure 4.4: A long 2708 pulsecanbe split into a 908 anda 1808 pulse. Replacingthesewith shortpulsesof equivalentflip angleresultsin a two-pulseechosequence.Therefore,theFID after the long2708 pulsecanbeconsideredto beto someextenta “one-pulseecho”.

problem.Ideally, therefocusingpulsein atwo-pulseechoexperimentwouldhaveaflip angle

of 180: . Thedependenceof theflip angleontheRabinutationfrequency applieshere,however, aswell. It is notcleara priori thata two-pulseechosequencewouldwork inpracticefor thepurposeof separatingthedifferentsignalcontributions.

Thefeasibility of sucha two-pulseechoexperimenthadto beelucidatedby moresimulations.Two identicalpulseswerechosenfor theechosequencein orderto obtainuniformexcitationbandwidthandthereforeavoid additionalcomplications.

Thesimulationsshown in fig. 4.5exhibit severalproperties:; Echoesof considerablestrengthariseevenfor ratheruntypicalnominalflip an-glesof thepulses;; for not too largeflip angles,theechosignalbeginswith a negative contributionandendswith a positivecontribution;; the“centerof gravity” of theechosignalshiftsalongthetimeaxis.

A more quantitative analysisof the echoshapeswas performedby plotting thetimesof theechominimum,theechomaximum,andthezerocrossingbetweenthem(fig. 4.6). Theminimumof theechoshifts in time by aboutthepulselengthwhile thepositionof theechomaximumis lesssensitive to theflip angle.Thezerocrossingoftheechosignal,however, variesmuchmore.This is dueto changingrelativecontribu-tionsof positiveandnegativecomponentsto thetotalechosignal.Theshapeof afieldsweptechospectrumdependsthereforeconsiderablyon thedetectiontime chosen.


Figure 4.5: Simulatedevolution of they magnetizationin a two-pulseechoexperimentwith < x phasepulses. The timing of the sequenceis fixed while the nominal flip angleof the pulsesis changed.Dependingon theflip angle,theshapeandpositionof theechosignalis changed.Fig. 4.6shows somecharacteristicsof theobservedechoesin moredetail.


Figure 4.6: Temporalcharacteristicsof a two pulseechoas in fig. 4.5 asa function of the nominalflip angle.Shown arethepositionsof theechominimum(∇), themaximum(∆), andthezerocrossingbetweenthem( < ). Flip angleswith a3:2:1ratio,correspondingto theRabifrequenciesfor mS , = 1

2 -< 12 transitionsin S , 5

2, S , 32, andS , 1

2 systems,havebeenmarked.Theverticaldottedlinesindicatezerocrossingtimesfor therespectivesignal.

4.3. EXPERIMENTAL DEMONSTRATION 51

4.2.5 Flip Angle Selective SignalSuppression

Thetemporalcharacteristicsof anechoderiving from two longpulsesdescribedabovecanbe utilized to selectively suppresssignalcontributionsassociatedwith a specificflip angle. This is doneby placing the detectingwindow aroundthe zero crossingof the echocomponentto be suppressed.Due to the strongdependenceof the zerocrossingtimeon theflip angle,othersignalswill still bemaintained.

As anexample,we considerthemS 12 9 1

2 transitionof specieswith S 52,

S 32, andS 1

2. Accordingto eqn.4.1, the correspondingRabi frequenciesresp.thenominalflip anglesfor thesamepulsesequencehave a ratio of 3:2:1. Horizontaldottedlinesin fig. 4.6indicateflip anglesof 216: , 144: , and72: , correspondingto theconsideredtransitions.To suppressthesignalcomponentfrom theS 5

2 component,thedetectionwindow is placedat thezerocrossingtime of the216: signal(indicatedby a dottedvertical line at 11 7 time units). This time coincides,however, with themaximumof the144: signal(S 3

2), andit is closeto themaximumof the72: (S 12)

component,maintainingcontributionsarising from suchspecies.Placingthe detec-tion window at theotherindicatedtime would eliminatetheS 3

2 componentwhilemaintainingtheothers,etc.

4.3 Experimental Demonstration

The describedexperimentwas performedand testedwith three different systems.Mn2 (S 5

2) andCr3 (S 32) centersin a CaOmatrix give rise to EPRlines that

arespectrallyseparated,thereforemakingit easyto verify theoreticalpredictions.Ex-perimentson an exchangecoupledmetallorganic manganesecomplex (S 1

2) withMn2 impuritiesdemonstratestheapplicabilityof themethodto eliminatecontamina-tion signalsthatoverlapwith thedesiredspectrum.Finally, Mn-catalasefrom Thermusthermophilus, a metalloenzyme,exemplifiesthe potentialof thesuggestedtechniquefor biologicalsystems.

All experimentswereperformedwith theBrukerE680W bandspectrometer. Pulsegeneration,the acquisitionof the echoshapewith a transientrecorder, andmagneticfield sweepwerecontrolledby Bruker Xepr softwarecombinedwith a customPuls-eSpeLprogram.

4.3.1 Mn2> and Cr3> in CaO

CalciumoxideusuallycontainsbothMn2 (S 52) andCr3 (S 3

2) centers.Duetothecubicsymmetryof thehostcrystallattice,theg tensoris isotropic,andverynarrowEPRlinesresult.Thezerofield splitting for bothionsis largeenoughthat transitionsbetweenthe 1

2 and 12 statesaresufficiently decoupledfrom othermS transitions.

Manganeseoccursas55Mn (I 52) with 100%naturalabundance.Therefore,hy-

perfinesplitting givesriseto 6 EPRlines. Chromiumis presentin theform of several


Figure 4.7: 94 GHz cw EPRspectrumof powderedCaOat roomtemperature.Themarkedlinesarisefrom Mn2? andCr3? centersin theCaOlattice. Otherspectralfeaturesaredueto impuritiesthatarenot consideredhere.

Figure4.8: Simulated(left) andexperimental(right) echoshapesfor flip anglesof 1448 and2168 resp.a Mn2? and the centralCr3? line. The 3:2 ratio of flip anglesin the simulationcorrespondsto thetransitionmomentsfor theEPRlines.


Figure4.9: Field-sweptESEspectraof theCaOsamplewith two differentintegrationwindows. For the“early” window, theMn2? line is maintainedwhile theCr3? contributionsaresuppressed.For “late”detection,theMn2? signalis suppressedwhile theCr3? line (includingsatellites)becomesvisible.

isotopes.52Cr, 50Cr, and54Cr have nuclearspin I 0 andaccountfor about90 5%naturalabundance.53Cr hasa nuclearspinof I 3

2 at 9 5% naturalabundance.Thiscombinationof isotopesgives rise to a single strongline surroundedby four weaksatellitelinesin theEPRspectrum.Fig. 4.7shows a cw spectrumof CaOpowderat amicrowave frequency of 94GHz.

Field-swepttwo-pulseelectronspinechoexperimentswereperformedoverafieldrangethat includesthehighest-fieldMn2 line andtheCr3 lines. Fig. 4.8 comparesexperimentalechoshapes,obtainedat the resonancepositionsof Mn2 andthe cen-tral Cr3 line, with simulationdata. The predictedeffect of the different transitionmomentson theechoshapesis clearlyreproducedin theexperiment.

Time-integratedfield sweptechospectraareshown in fig. 4.9 for two choicesofthe integrationwindow. Virtually completeseparationof theMn2 andCr3 spectracouldbeachieved.

4.3.2 DTNE Complex

DTNE1 (Mn III µ OAc µ O 2Mn VI @ 2 ) (fig. 4.10)is anexchangecoupledbinu-clearmanganesecomplex. Themanganesecentersareantiferromagneticallycoupled,giving riseto anS 1

2 groundstate.DTNE samplesareusuallycontaminatedby freeMn2 thatis generatedduringsynthesisanddecayof theratherunstablecomplex andcanberemovedonly by extensivepurificationprocedures.

TheEPRspectrumof DTNE is very complex andspreadout over A 100mT dueto hyperfineinteractions. The centralpart of the spectrumis severely impairedbyintenselines arisingfrom Mn2 contamination(fig. 4.11,top). Attemptsto separateDTNE andcontaminationsignalsby analyzingT1 andT2 decayfailed at T 20 K

1TheDTNE samplesweremadeavailableby Dr. K. Wieghardt,MPI für Strahlenphysik, MülheimandK.-O. Schäfer, TU Berlin.


MnMn

N

N

N N

N

N

O

O

O O

Figure 4.10: Structureof the exchanged-coupleddimanganese-DTNEcomplex (picture courtesyofK.-O. Schäfer).

Figure4.11: Top: Centralregion of the94 GHz cw EPRspectrumof DTNE. Thespectrumis severelyimpairedby six lines arising from contaminationwith Mn2? . Bottom: Derivative field-sweptESEspectrumof thesamesamplefor anoptimizeddetectionwindow.


Figure4.12: Field-sweptESEspectraof DTNE at 94 GHz for two differentintegrationwindows.

sincerelaxationratesweretoohigh to allow asignificanttiming variationof thepulsesequence.

The different spin statesof the complex and the Mn2 contaminationlead to aflip angleratio of 3:1 for thespecies.Fig. 4.12shows field-sweptESEspectraof thecontaminatedcomplex with two differentintegrationtimewindows. By carefulchoiceof anoptimumdetectionwindow, theMn2 signalscouldbesuccessfullyeliminated.

4.3.3 Mn-Catalase

Mn-catalase2 is anenzymethatsplitshydrogenperoxideinto waterandoxygen:

2H2O2MnCat ' 2H2O O2 (4.2)

At the catalytic centerof the protein is an exchangecoupledbinuclearmanganesecomplex. In thecatalyticprocess,themanganeseatomsproceedthroughseveraloxi-dationstates.For thenon-physiologicalsuperoxidizedstate,theindividualmanganeseatomsarein theformaloxidationstatesMnIII (SIII 2) andMnIV (SIV 3

2), couplingantiferromagneticallyto agroundstateof S 1

2.Thecw EPRspectrumof Mn-Catalasein thesuperoxidizedstateis similar to the

DTNE complex spectradiscussedin section4.3.2andequallyimpairedby Mn2 con-tamination(fig. 4.13, top). A field-sweptESEexperimentallows to decomposethesignal into contributionswith differenttransitionprobabilities(fig. 4.13,middle andbottom). BesideseliminatingtheMn2 contaminationsignal,theseparationalsore-vealsanadditionalsignalwith ahighertransitionprobabilityandthereforeaspinstate

2Thecatalase(Thermusthermophilus) samplewaskindly providedby Dr. V.V. Barynin,U Sheffield.


Figure 4.13: 94 GHz EPRspectraof Mn-catalasefrom Thermusthermophilusat T , 20 K. Top: cwspectrumwith Mn2? contaminationsignals.Middle: Derivativeof anESEspectrumwith thedetectionwindow chosento suppressMn2? signals. Bottom: Derivative of an ESEspectrumwith suppressedS , 1

2 signals. The latter spectrumrevealsan additionalsignal of unknown origin (marked *) withhigherspinmultiplicity thatis not readilyapparentin thecw spectrum.

4.4. CONCLUSION 57

S A 12. While this signal is also visible in cw EPR, it is not obvious from the cw

spectrumthatit doesnotarisefrom theS 12 groundstateof thedimanganesecenter.

4.4 Conclusion

In thischapter, it wasshown thatspectracanbeseparatedbasedontransitionprobabil-ity in a simpletwo-pulseESEexperiment,usinglow microwave power andthereforelong pulses.EPRmeasurementson severalsystemsdemonstratetheapplicabilityandpracticalvalueof this technique.Themethodis particularlyusefulfor high frequencyEPR spectroscopy which is very sensitive to contaminationsignalswhile sufferingfrom relatively low availablemicrowavepowers.

The introducedexperimentis alsoremarkablyeasyto implement. A fixed pulsesequenceis used. In conjunctionwith the useof a transientrecorderto recordthetime-resolvedechosignal,aseparationof spectracanbeachievedwithoutany increasein acquisitiontime ascomparedto a non-selective field-sweptESEexperiment. Anadditionaladvantageis that thecritical part of theprocess– choosinganappropriateintegrationwindow to obtainthedesiredspectrum– canbedoneafterdataacquisition,requiringno trial anderrorprocedureduringtheexperiment.

As demonstratedin section4.3.3,theuseof transitionprobabilityselective meth-odscanalsoidentify superimposedsignalswhoseexistenceis difficult to beseenfromcw EPRspectra.Since2D experimentsareratherexpensive in acquisitiontime, theyareusuallynot employed routinely. Thesimplifiedexperimentdescribedhereis fastenoughto beperformedon a wider scaleandmaythereforerevealsuchsignalcontri-butionsthatmightotherwisego unnoticed.

REFERENCES

[1] Isoya J., Kanda H., Norris J.R., Tang J., & Bowman M.K., Fourier-transform andcontinuous-wave EPRstudiesof nickel in syntheticdiamond:Site andspin multiplicity,Phys.Rev. B41, 3905–3913(1990).

[2] SchweigerA., Puls-Elektronenspinresonanz-Spektroskopie: Grundlagen,VerfahrenundAnwendungsbeispiele,Angew. Chem.103, 223–250(1991).

[3] BowmanM.K., in ModernPulsedandContinuous-WaveElectronSpinResonance(KevanL. & BowmanM.K., eds.),Wiley (1990).

[4] AstashkinA.V. & SchweigerA., Electron-spintransientnutation:A new approachto sim-plify theinerpretationof ESRspectra,Chem.Phys.Lett.174, 595–602(1990).

[5] Torrey H.C.,Transientnutationsin nuclearmagneticresonance,Phys.Rev. 76, 1059–1068(1949).


[6] Takui T., SatoK., ShiomiD., Itoh K., Kaneko T., TsuchidaE., & NishideH., FT pulsedESR/electronspintransientnutation(ESTN)spectroscopy appliedto high-spinsystemsinsolids;directevidenceof a topologicallycontrolledhigh-spinpolymerasmodelsfor quasi1D organicferro-andsuperpara-magnets,Mol. Cryst.Liq. Cryst.279, 155–176(1996).

[7] Stoll S.,JeschkeG.,Willer M., & SchweigerA., Nutation-frequency correlatedEPRspec-troscopy: ThePEANUTexperiment,J. Magn.Reson.130, 86–96(1998).

Part III

Application of High Field EPR toBiological Systems

59

Chapter 5

Overview of PhotosyntheticReactionCenters

Thischaptergivesanoverview of thevariousphotosyntheticreactioncentersexaminedby EPRin laterchapters.In addition,themethodusedfor analyzingEPRspectraofradicalsin frozensolutionsandsinglecrystalsof thesereactioncentersis discussed.

5.1 Overview of the PhotosynthesicProcessin Plantsand Cyanobacteria

Photosyntheticorganismsconvert light into chemicallyboundenergy which is thenusedby themetabolism.Speciesdiffer in thesubstratesusedfor this process.Greenplantsandcyanobacteriaperformoxygenicphotosynthesis,which is characterizedbythereductionof carbondioxideto sugarssuchasglucose:

6CO2 6H2Olight ' C6H12O6 6O2 B (5.1)

As a by-productof this process,molecularoxygenis released.During evolution, ithasaccumulatedfrom negligible amountsto about20% in theatmosphere,paving theway for thedevelopmentof oxygendependentorganismsand,ultimately, mankind.

Thephotosyntheticprocesscanbebrokenup into two majorsteps:light reactionswhich,asthenamesuggests,aredrivenby absorptionof light, anddarkreactionsthatcompletethephotosyntheticprocess,usingtheproductsof thelight reactions.In plantsand cyanobacteria,the photosyntheticapparatusconsistsof several protein/cofactorcomplexesthatarelocatedin thethylakoid membrane.

In thelight reactions,wateris oxidizedandNADP (nicotineamideadeninedinu-cleoutidephosphate)is reducedto NADPH,anenergy carrierin thecell. Theoxidationof wateralsoreleasesprotonsonthelumenalsideof themembrane,therebycreatingacross-membraneprotongradientwhichis thedriving forcebehindthephosphorylation

61

62 CHAPTER5. OVERVIEW OF PHOTOSYNTHETICREACTION CENTERS

of ADP (adenosinediphosphate)to ATP (adenosinetriphosphate),

2H2O 2NADP 6hν ' 2NADPH 2H O2 (5.2)

ADP Pi∆pH ' ATP (5.3)

Two protein-cofactorcomplexes,photosystemI (PSI) andphotosystemII (PSII),serve asthe centralhubsfor the light reactions.Upon light excitation,eachof thesecomplexesperformsacross-membraneelectrontransfer, therebystoringenergy in theform of redoxequivalents. PSI andPSII work in seriesto achieve a higher redoxpotentialdifferencethaneitheronecouldindividually (fig. 5.1).

5.1.1 PhotosystemI

PSI consistsof 11–13proteinsubunits, dependingon species.Upon excitation byabsorptionof a photon,PSI reducesferredoxin(FD) on thestromalsideof themem-brane.Ferredoxinactsasan intermediatechargecarrier, reducingin turn NADP toNADPH. To replacethe electron,PS I oxidizesplastocyanine(PC) on the lumenalside.PSI canthusbeconsidereda light-driventransmembraneelectronpump:

PCred FDox hν PSI ' PCox FDred (5.4)

2FDred NADP H ' 2FDox NADPH (5.5)

Fig. 5.2shows aschematicoverview of thePSI reactioncenter.

Subunits PsaAand PsaB

The two proteinsubunits PsaA(mass. 83 2 kDa) andPsaB(mass. 82 5 kDa) atthereactioncentercoreshow stronghomologyandarearrangedapproximatelysym-metrically, eachbindingsimilar cofactors[4]. Thesignificanceof thedeviation fromsymmetryis still subjectof activeresearch.At thetimeof thiswriting, it is still unclearwhetherthelight inducedelectrontransferoccursvia thecofactorsin bothsubunitsornot and,if theelectrontransferis asymmetric,whichsubunit is theactiveone.Aminosequencehomologiesandsimilar cofactorssuggestthatPSI is closelyrelatedto thereactioncentersof greensulphurbacteriaandheliobacteria.Thesebacterialreactioncentersexhibit a homodimerin placeof subunitsPsaAandPsaB,suggestingthat theelectrontransfermight indeedoccuralongbothsubunits[5, 6].

P700. Photochemistryin thePSI reactioncenterstartswith theprimarydonor, P700

(namedafter a correspondingoptical absorptionbandat λ 700 nm). P700 consistsof two chlorophyll a moleculesboundto subunitsPsaAandPsaB,respectively. Whileit hasbeena subjectof discussionwhetherP700 is a truedimeror whetherthechloro-phylls areelectronicallydecoupled,newer researchindicatesthat P

700 hasa highly

5.1. PHOTOSYNTHESISIN PLANTS AND CYANOBACTERIA 63

Cν

Cν

2H O

ZY

680P

P680*

AQ

BQ

700*P

0A

1A

XF

FA

BF

700P

−1

0

0.5

−0.5

1

E [V]

WOC

Pheo

Cytb6

PC

NADP

PS I

PS II

FD

Figure 5.1: Electrontransferpathway andassociatedredoxpotentialduring the photosyntheticlightreactionsin plantsandcyanobacteria.


A 0

A 1

P700

FX

FA

FB

PsaF

PsaEPsaD

PsaA

PsaB

A

PsaC stroma

lumen

Figure 5.2: Overview of thephotosystemI reactioncentercoreandtheelectrontransferchain(for adetailedmodel,see[1–3]).


asymmetricelectronicstructure[4, 7, 8]. After theabsorptionof a photonor indirectexcitationvia anexciton transferfrom peripheralantennachlorophylls, PD700 actsasanelectrondonor:

P700 hν ' PD700 ' P 700 e (5.6)

The redoxpotentialof theexcitedPD700 amountsto approximately 1 2 V, makingitoneof the strongestreductantsknown in biological systems.P

700 in turn oxidizesaplastocyanineat thelumenalsideof PSI.

A0 and A1. A chlorophyll a cofactordenotedasA0 is coupledvia an “accessorychlorophyll” A to P700andservesastheprimaryacceptorin theelectrontransferchain.A

0 is stablefor about30ps[4] afterwhich theelectronis passedon to thesecondaryacceptorA1, a phylloquinone.A

1 is morestablethanA 0 , but still hasa lifetime of

only about15 200ns[4]. BothA0 andA1 areboundto oneof thesubunitsPsaAorPsaB;therespectiveothersubunit bindssimilar cofactorsA 0 andA 1.

FX. FX is the lastelectronacceptorwithin subunitsPsaAandPsaB.It is a [4Fe4S]cluster that is boundin betweensubunits A and B. Both possibleelectrontransferpathways,alongsubunitsPsaAandPsaB,join atFX.

Subunit PsaC

The proteinsubunit PsaC(mass . 8 9 kDa) is adjacentto subunits PsaAandPsaBon the stromalsideof the membrane.It binds the remainingcofactorsforming theelectrontransferchainin PSI.

FA/FB. Subunit PsaCbinds two [4Fe4S]clusters,referredto as FA and FB. Thearrangementof bothclustershasalocalC2 symmetry, but is asymmetricrelativeto theaxisdefinedby thePsaA/PsaBpseudodimer. Oneof theseiron-sulphurclustersservesastheterminalelectronacceptorin PSI (beforesubsequentreductionof ferredoxin).Only recently, this terminal[4Fe4S]clusterhasbeenidentifiedasFB, while FA servesasanintermediateacceptor[9] (seealso[10, 11]).

5.1.2 PhotosystemII

PSII usesthephotonenergy of incidentlight to abstractelectronsfrom water, releas-ing protonsandmolecularoxygenon the lumenalside. The electronsaretransferedacrossthe membraneby the PS II reactioncenter, reducingplastoquinone(PQ) tohydroplastoquinone(H2PQ):

2H2O 4hν ' 4H O2 4e (5.7)

PQ 2H 2e ' H2PQ (5.8)


Mn22 H O

O2 4H+

WOCMn

MnMn

Y

D1D2

QAQ B

PheoPheo

P680

Chl Chl

DZ Y

Fe

Cytb559

Cytc550

stroma

lumen

Figure 5.3: Simplified modelof the photosystemII corecomplex in the photosyntheticmembrane,includingsubunitsD1, D2, andthewateroxidizing complex (WOC).For a detailedstructure,see[12,13].


The protonreleasesin eqn.5.7 occuron the lumenalsideof the reactioncenterwhile protonsareconsumedaccordingto eqn.5.8 on thestromalside. Theresultingtransmembraneproteingradientis usedfor theproductionof ATP (seee.g.[14, 15]).

PSII consistsof several proteinsubunits that serve, in conjunctionwith their re-spectivecofactors,aslight harvestingantennasystems,energy transferpaths,electrontransferpaths,catalyticsites,andprotective groups,amongothers.Themostpromi-nentconstituentsof thereactioncentercorearetheproteinsubunitsD1 andD2 andthewateroxidizingcomplex (WOC).D1 andD2 hostanumberof cofactorsthatcomprisetheelectrontransferpathafterphotoexcitationof thecomplex. TheWOC contains4manganeseatomsthatform thecatalyticcenterfor thewatersplittingprocess(fig. 5.3).

Subunits D1 and D2

The polypeptidesD1 andD2 (massE 30 kDa each)arelargely homologousto eachotherandform anapproximatelysymmetricalproteinheterodimer. This is similar tothe subunits L andM in bacterial“type II” photosyntheticreactioncenters,as wassuggestedbasedonaminoacidsequencehomologies[16–18] andcomputermodeling[19]. This finding is useful becausethe structureof thesebacterialphotosyntheticreactioncentersis known (e.g.[20]). Thestructuralsimilarity hasbeenconfirmedbyelectron[21] andrecentlyX-ray [12] diffractionstudiesontwo- andthree-dimensionalcrystalsof PSII.

D1 andD2 serveasahostmatrixfor theembeddedcofactorsthatmarktheelectrontransferpath. Thesecofactorsare two chlorophyll a species,pheophytin a, and aplastoquinonefor eachsubunit. Thoughsimilar cofactorsappearin both subunits,their functionalrole is different,andelectrontransferis confinedto the D1 subunit,with theexceptionof theintermediateacceptorQA which is boundto D2.

P680. The primary electrondonor P680 (namedafter a correspondingoptical ab-sorbancebandat λ F 680 nm) is an aggregate of two chlorophyll a speciesboundto subunits D1 andD2. The functionalrole of P680 canbe comparedto the primarydonorsin photosystemI andbacterialreactioncenters.After excitation,eitherby di-rect absorptionof a photonor by an energy transferfrom light harvestingantennacomplexesoutsidethecorecomplex, PG680 actsasanelectrondonor, initiating theelec-tron transferprocesswithin thereactioncenter:

P680 H hν I PG680 I PJ K680 H eL (5.9)

PJ K680 is characterizedby an unusuallyhigh redox potentialof E H 1 M 1 V whichallowssubsequentsplittingof waterin theWOC.

Pheo a. The pheophytin a cofactor in the D1 subunit serves, via an intermediary“accessory”chlorophyll, asthe first electronacceptorafter excitation of the primarydonor. Chargeseparationtakesplaceon a timescaleof lessthan25 ps. In contrastto


PSI, the asymmetryof the electrontransferalongthe subunits is firmly established.Thepheophytin residuein theD2 subunit doesnot takepartin directedelectrontrans-fer.

QA and QB. TheplastoquinonesQA (D2 subunit) andQB (D1 subunit) arecoupledby a non-hemeFe2J ion andact asintermediateandterminalelectronacceptors,re-spectively. In contrastto QA, the terminalacceptorQB is only weakly boundto thecorecomplex. After two reductionandconcomitantprotonationsteps,H2QB leavestheprotein,actingasacharge/protoncarrier, andis replacedby aplastoquinonefrom aplastoquinone“pool” in themembrane.Theredoxpotentialcarriedby thehydroplas-toquinoneis laterutilizedby photosystemI.

YZ andYD. ThetyrosinesYZ (Tyr161residueonD1)andYD (Tyr160/161in cyanobac-terial and spinachD2, respectively) act as secondaryelectrondonors,reducingthephotooxidizedPJ K680 andbeingoxidizedto neutralaminoacidradicals:

PJ K680 H Y LZ N D I P680 H Y KZ N D (5.10)

YD seemsto beadeadendin theelectrontransferchain.Its functionalimportanceis not yet understood,thoughthereare hints that it may play an significantrole inpreventingphotoinhibitionduring activationof photosystemII [22]. Recently, it hasalsobeensuggestedthattheYD neutralradicalmayenhancechargeseparationvia YZ

by electrostaticinteractions[23]. After generationby a photoinducedhole transferfrom PJ K680, the Y KD radical is stablein the dark. In contrast,Y KZ abstractsan electronfrom theWOC ona sub-millisecondtimescale.

Water Oxidizing Complex

Watersplitting takesplacein themembrane-extrinsic WOC. It is known to containatetranuclearmanganesecluster, acalciumatom,andpossiblyachlorideion. Catalyticactivity is most likely tied to the manganesecluster, and several modelshave beenproposedfor thewatersplitting mechanism.Watersplitting occursin a cyclic processwith four consecutiveoxidationsof theWOC(for recentreviews,seee.g.[24, 25]).

5.2 Photosynthesisin Purple Bacteria

In contrastto plantsor cyanobacteria,purplebacteriahave only onekind of photo-syntheticreactioncenter, locatedin the intracytoplasmiccell membrane.The redoxpotentialdifferencegeneratedby theelectrontransferfrom theperiplasmto thecyto-plasmaticsideof themembraneis notsufficient for thereductionof NAD J to NADH.Therefore,theprimarypurposeof thephotosyntheticprocessin thebacterialreaction

5.2. PHOTOSYNTHESISIN PURPLEBACTERIA 69

P865

Q BQ A

φB

φA

Fe

H

C

M L

Figure5.4: Overview of thephotosyntheticreactioncentercorein purplebacteria.


centerseemsto be the creationof a transmembraneprotongradientfor driving ATPsynthesis.

Fig. 5.4 shows a schematicrepresentationof the bacterialreactioncenter(bRC)found in purplebacteria. The mostobvious differenceto PS II is the absenceof aWOC. The boundcofactorsdiffer only slightly from PSII, e.g.bacteriochlorophyllinsteadof chlorophyll pigments. All the cofactorscomprisingthe electrontransferpathwayareboundto two proteinsubunitscalledL andM.

5.2.1 Subunits L and M

The subunits L andM of the bRC found in purplebacteriacanbe comparedto theD1/D2subunitsin PSII. They form anequallypseudo-symmetricalarrangement(withtheC2 symmetryaxisperpendicularto themembrane).As in PSII, thephotoinducedelectrontransferis asymmetric.

P865. Photochemistryin bRC startsat P865, comprisedof two bacteriochlorophyllmoleculesboundto the L and M subunits, respectively. After excitation, either byabsorptionof a photonor by exciton transferfrom peripherallight harvestingantennacomplexes(LHC), PG865 actsasanelectrondonor, analogouslyto theprimarydonorinPSII.

ΦA and ΦB. ΦA andΦB aresymmetry-relatedbacteriopheophytin b speciesboundto theM andL subunit, respectively. They arecoupledto P865 by accessorybacteri-ochlorophylls, makingthempossibleelectronacceptors.Only ΦA on the M subunittakespartin directedelectrontransfer, however.

QA and QB. As in PSII, two quinonespeciesserve asfurther intermediateandter-minal acceptors,respectively. QA is boundto theM subunit andtheterminalacceptorQB is boundto subunit L. A non-hemeFe2J centerlocatedbetweenthequinonescou-plesQA andQB. After two reductionandconcomitantprotonationsteps,H2QB leavesthebacterialreactioncenterandis replacedby anotherubiquinonefrom thequinonepool. It is known that the QB binding site undergoesstructuralchangesduring re-ductionsteps,breakinghydrogenbondsandleadingto a differentorientationof thereducedquinone[26]. Therefore,theredoxstateof thereactioncentermustbeknownin orderto interpretstructuraldata.

5.3 EPR on Frozen Solutions and Single Crystals ofReactionCenters

Thefunctionalstateof photosyntheticreactioncentersis characterizedby radicalstatesalongtheelectrontransferchain.Onshorttimescales,theelectrontransferprocesscan

REFERENCES 71

beobservedafterphotoexcitationin theform of radicalpairs(seee.g.[27]). Somerad-icalsmayalsobetrapped,eitherby loweringthetemperatureandinhibiting thermallyactivatedtransfersteps,or by chemicalinhibition. EPRis an ideal tool to investigatetheseparamagneticstates.

With few exceptions(e.g. the iron-sulphurclustersin PSI), the electrontransferpathway consistsof organic radicalsthat usuallyexhibit rathersmall g anisotropies.The increasedZeemanresolutionof high field EPRis thereforeextremelyuseful intheanalysisandinterpretationof therespective EPRspectra.The increasedsensitiv-ity of high field EPRalsoallows oneto obtaingoodspectrafrom very small samplequantities.This is helpful becausethe isolationandpurificationof membraneboundproteinsis a complex task,yielding only smallquantities.In particularhowever, thisallows the studysinglecrystalsof thesemembraneproteinswhich aretypically sub-millimeter sized.

Crystalstructuresarecharacterizedby asetof symmetries.A crystalis definedbyaunit cell thatis repeatedperiodicallythroughspace.If thereareseveralsiteswithin aunit cell, thesearerelatedto eachotherby acombinationof translationsandrotations.The spin Hamiltonianusedto describeEPRdoesnot containspatialcoordinatesasparameters.EPRis thereforeinsensitive towardstranslationalsymmetries,andcrystalsymmetriesarereducedto orientationalsymmetriesassociatedwith thetruecrystallo-graphicspacegroup.

Realcrystalsarenotperfect.Asidefrom impurities,theprevalentproblemis struc-tural disorder, i.e. mosaicity. Mosaicity createsseriousproblemsfor investigationtechniquesthat rely on theperiodicityof thecrystallattice, like X-ray diffractionex-periments.While smallmosaicanglesgreatlydisturbthelatticeperiodicity, they haveonly a slight effect on the orientationof the individual sites. EPR spectraare thusvirtually unaffectedby small mosaicities,andEPRexperimentscanthereforederivestructuralinformationfrom crystalsthatarenot suitablefor X-ray diffractionstudies.

REFERENCES

[1] Klukas O., SchubertW.D., JordanP., KraussN., FrommeP., Witt H.T., & SaengerW.,PhotosystemI, an improvedmodelof thestromalsubunitsPsac,PsadandPsae,J. Biol.Chem.274, 7351–7360(1999).

[2] Klukas O., SchubertW.D., JordanP., KraussN., FrommeP., Witt H.T., & SaengerW.,Localizationof two phylloquinones,Q(K) andQ(K)’, in an improved electrondensitymapof photosystemI at4 angstromresolution(1999).

[3] Klukas O., SchubertW.D., JordanP., KraussN., FrommeP., Witt H.T., & SaengerW.,Proteindatabank,accesscode1C51: Photosyntheticreactioncenterandcoreantennasystem(trimeric),α carbononly, http://www.rcsb.org/pdb.


[4] Brettel K., Electrontransferandarrangementof the redoxcofactorsin photosystemI,Biochim.Biophys.Acta1318, 322–373(1997).

[5] BüttnerM., Xie D.L., NelsonH., PintherW., HauskaG., & NelsonN., Photosyntheticreactioncentergenesin greensulfurbacteriaandin photosystem1 arerelated,Proc.Natl.Acad.Sci.USA89, 8135–8139(1992).

[6] Liebl U., Mockensturm-Wilson M., Trost J.T., Brune D.C., BlankenshipR.E., & Ver-maasW., Singlecorepolypeptidein thereactioncenterof thephotosyntheticbacteriumHeliobacillusmobilis: Structuralimplicationsandrelationsto otherphotosystems,Proc.Natl. Acad.Sci.USA90, 7124–7128(1993).

[7] KäßH., Die StrukturdesprimärenDonatorsP700 in PhotosystemI: UntersuchungenmitMethodender stationären und gepulstenElektronenspinresonanz, Ph.D.thesis,Techni-scheUniversitätBerlin (1995).

[8] KäßH., FrommeP., Witt H.T., & Lubitz W., Orientationandelectronicstructureor theprimary donorradicalcationPO P700 in photosystemI: A singlecrystalEPRandENDORstudy, J. Phys.Chem.B 105, 1225–1239(2001).

[9] JordanP., FrommeP., Witt H.T., KlukasO.,SaengerW., & KraussN., Three-dimensionalstructureof cyanobacterialphotosystemI at 2 Q 5 Å resolution,Nature 411, 909–917(2001).

[10] GolbeckJ.H.,A comparative analysisof thespinstatedistribution of in vitro andin vivomutantsof PsaC,Photosynth.Res.61, 107–144(1999).

[11] ZhaoJ.,Li N., WarrenP.V., GolbeckJ.H.,& BryantD.A., Site-directedconversionof acysteineto aspartateleadsto theassemblyof a[3Fe-4S]clusterin PsaCof photosystemI.Thephotoreductionof FA is independentof FB, Biochemistry31, 5093–5099(1992).

[12] Zouni A., Witt H.T., Kern J., FrommeP., KraussN., SaengerW., & Orth P., Crystalstructureof photosystemII from Synechococcuselongatusat 3 Q 8 Å resolution,Nature409, 739–743(2001).

[13] Zouni A., Witt H.T., KernJ.,FrommeP., KraussN., SaengerW., & Orth P., Proteindatabank,accesscode1FE1:Crystalstructureof photosystemII, http://www.rcsb.org/pdb.

[14] Boyer P.D., TheATP synthase– a splendidmolecularmachine,Ann.Rev. Biochem.66,717–749(1997).

[15] JungeW., ATP synthaseandothermotorproteins,Proc.Natl. Acad.Sci.USA96, 4735–4737(1999).

[16] TrebstA., The topologyof the plastoquinoneandherbicidebinding peptidesof photo-systemII in thethylakoid membrane,Z. Naturforsch. C41, 240–245(1986).

[17] Michel H. & DeisenhoferJ.,Relevanceof thephotosyntheticreactioncenterfrom purplebacteriato thestructureof photoystemII, Biochemistry27, 1–7(1988).

REFERENCES 73

[18] TangX.S.,FushimiK., & SatohK., D1-D2complex of thephotosystemII reactioncenterfrom spinach– isolationandpartialcharacterization,FEBSLett.273, 257–260(1990).

[19] Ruffle S.V., DonnellyD., BlundellT.L., & NugentJ.H.A.,A 3-dimensionalmodelof thephotosystemII reactioncenterof Pisumsativum,Photosynth.Res.34, 287–300(1992).

[20] Ermler U., FritzschG., BuchananS.K., & Michel H., Structureof the photosyntheticreactioncenterfrom Rhodobactersphaeroidesat 2 Q 65 Ångstrømresolution– cofactorsandprotein-cofactorinteractions,Structure 2, 925–936(1994).

[21] RheeK.H., Morris E.P., BarberJ.,& KühlbrandtW., Three-dimensionalstructureof theplantphotosystemII reactioncentreat8 Å resolution,Nature 396, 283–286(1998).

[22] MagnusonA., Rova M., Mamedov F., FredrikssonP.O., & Styring S., The role of cy-tochromeb559 andtyrosineD in protectionagainstphotoinhibitionduring in vivo pho-toactivationof photosystemII, Biochim.Biophys.Acta1411, 180–191(1999).

[23] RutherfordW., Tyrosineredoxreactionsin PSII (2001),DFG Sonderforschungsbereich498seminartalk, 17.April 2001.

[24] MessingerJ.,Towardsunderstandingthechemistryof photosyntheticoxygenevolution:Dynamicstructuralchanges,redoxstatesandsubstratewaterbindingof theMn clusterin photosystemII, Biochim.Biophys.Acta1459, 481–488(2000).

[25] RengerG., Photosyntheticwateroxidationto molecularoxygen:Apparatusandmecha-nism,Biochim.Biophys.Acta1503, 210–228(2001).

[26] Stowell M.H.B., McPhillipsT.M., ReesD.C.,SoltisS.M.,AbreschE.,& FeherG.,Light-inducedstructuralchangesin photosyntheticreactioncenter:Implicationsfor mechanismof electron-protontransfer, Science276, 812–816(1997).

[27] Zech S.G., Lubitz W., & Bittl R., PulsedEPR experimentson radical pairs in photo-synthesis:Comparisonof the donor-acceptordistancesin photosystemI andbacterialreactioncenters,Ber. Bunsenges.Phys.Chem.100, 2041–2044(1996).

Chapter 6

High Field EPR on the Primary DonorPR S700 Radical in SingleCrystals ofPhotosystemI

Thephotoinducedelectrontransferin photosystemI asdescribedin chapter5 beginsat the primary donorP700. While P700 consistsof two chlorophyll a molecules,itselectronicstructurestill is onlypartiallyunderstood,thoughtherearerecentresultsthatmaysolve thisquestion[1, 2]. In particular, it hasbeenamatterof discussionwhetherP700 is a truedimeror if photophysicsis mostlyconfinedto oneof thechlorophylls.

High field EPRexperimentson PJ K700 in singlecrystalsof PSI canprovide detailedinformationaboutthe magnitudeand the orientationof its g tensor, reflectingelec-tronic structure. This can be comparedto the spatialstructurederived from X-raydiffraction data. In addition,the experimentson singlecrystalsof PSI demonstratethe benefitsof high field EPRfor the investigation of organic radicalsin biologicalsamples.

6.1 Materials and Methods

6.1.1 PSI Core Complexes

PSI corecomplexespreparationsweremadeavailableby Dr. P. Frommeandcowork-ers.Thecellsweregrown from Synechococcuselongatusasdescribedin [3]. Sampleswerefrozenunderillumination in orderto photoaccumulatePJ K700. Partial orientationasreportedin [4] wasavoidedby performingthe freezeprocessin the absenceof amagneticfield.

75

76 CHAPTER6. PJ K700 IN SINGLECRYSTALS OF PHOTOSYSTEMI

b

c a

Figure 6.1: Layout of the unit cell (a T b T 288 Å, c T 167 Å) in singlecrystalsof photosystemIreactioncenters.The centersappearastrimerswith a threefoldsymmetryaxis parallel to the c axis.Thetrimersin theunit cell arerelatedby theP63 spacegroup.Theapproximateorientationsof theP700

chlorophyll ring planesareindicated.

6.1.2 PSI SingleCrystals

Singlecrystalsof PSI corecomplexesweregrown by Dr. P. Frommeandcoworkersfrom the preparationsdescribedabove. The crystalsarehexagonal(a F b F 288 Å,c F 167 Å). The unit cell contains6 PSI reactioncenters,arrangedin two trimers(fig. 6.1). The correspondingspacegroupis P63. In EPRexperimentsthe effectivesymmetryis D6 sinceEPRspectraareinvariantundera 180U rotationof thesample.The crystalsappearasneedleswith a hexagonalbaseplatethat is parallel to the abplane.

The crystalsweremountedin the W-bandEPRtubesby immersingthemin tinyamountsof motherliquor andsubsequentfreezingin liquid nitrogen,again underil-luminationin orderto generatePJ K700. Themountingorientationsweredefinedby thecrystal morphology. In one case,the needleaxis of the crystals(c direction) wasalignedwith thecapillaryaxis;anothercrystalwasmountedwith theneedleaxisper-pendicularto thecapillaryaxis.

6.1.3 cw EPR

All cw spectrawereobtainedwith amicrowavepowerof E 150nW and0 M 2 mT peak-to-peakmodulationamplitude(100kHz) atT F 80K. Typicalacquisitiontimefor onetracewas40s. Themagneticfield wascalibratedwith Li:LiF asag standardusingthe

6.2. RESULTS 77

proceduredescribedin section2.1.1.Themicrowave frequency wasslightly differentfor eachorientationof thesingle

crystal samplesbecausethe resonatorfrequency reactsvery sensitive to the samplegeometry. For easiercomparison,all spectrawerescaledto a hypotheticfrequency of94M 000GHzby theformula

BV F B W 94GHzν

M (6.1)

Therequiredadjustmentswereverysmall(lessthan0 M 1 %) andthereforedonotaffectthe interpretationof the spectra. In particular, this transformationhasno effect onderivedg values.

6.2 Results

6.2.1 PX Y700 in FrozenPSI Solution

A spectrumof PJ K700 in frozensolutionatT F 80K is shown in fig. 6.2.Thespectrumischaracterizedby a considerableinhomogeneouslinewidth. Despitethehigh magneticfieldandaresultingincreasedZeemansplitting,theg anisotropy is toosmallin relationto thelinewidth to resolve theprincipalvalues.It thusseemsasif 94GHzEPRwouldnot suffice to accesstheg tensoror PJ K700.

6.2.2 PX Y700 in SingleCrystals of PSI

Orientationdependentspectraof thePJ K700 radicalin two differentlymountedcrystalsareshown in fig. 6.4 andfig. 6.6. In contrastto the frozensolutionspectra(includedat the top), the apparentlinewidth is significantlyreduced,andthe crystallinenatureis reflectedby a cleardependenceof the spectraon the turning angle. The reducedapparentlinewidth clearlyshows that thebroadeningof the frozensolutionspectrumis causedby bothunresolvedhyperfineinteractionsandg anisotropy.

In fig. 6.4 a splitting in two lines is readily apparent.The line intensitiesdiffer,however, considerably, suggestingthattheseapparentlinesarestill comprisedof sev-eralunresolvedEPRlinesfrom differentsitesin thecrystal.This is in accordancewiththecrystalstructurethat, in thegeneralcase,predictssix EPRlines in a crystalspec-trum. For rotationanglesof 0U resp.90U , the line separationdisappears.This agreeswith themountingorientationof thecrystal(c axisperpendicularto therotationaxis,seefig. 6.3)whichimpliesthatthemagneticfield is parallelto c for two turningangles,leadingto completedegeneracy of all sites.

By comparison,fig. 6.6 exhibits a moreregular structure. Here, the crystalwasrotatedapproximatelyaboutits c axis(seefig. 6.3); themagneticfield is thereforeal-waysin theab plane.For this orientation,thesix EPRlinesdegeneratein pairs. The


Figure 6.2: 94 GHz cw EPRspectrumof photoaccumulatedPZ [700 in frozensolutionof protonatedPSIat T T 80 K (solid) andsimulation(dotted). Even at W-bandfrequencies,theg anisotropy cannotberesolveddueto thelargeinhomogeneouslinewidth.

6.2. RESULTS 79

\] ^

Figure 6.3: Appearanceof the PS I cc singlecrystals,orientationof the crystallographicaxes, androtationaxesfor thecrystalspectra(schematic).

effective D6 symmetryleadsto threeequallyintenselineswith sinusoidaldependen-ciesof g on the rotationangle. The sixfold symmetryis alsoconfirmedby the 60Uperiodicityof thespectra.

Consideringthe degeneraciesandthe moderateresolution,a numericalfit of sixindependentEPRlines to thespectrais questionable.However, taking thestrict cor-relationbetweenthe line positionsinducedby thecrystalsymmetryinto account,thenumberof independentparametersis reducedto anextent thatmakesa fit stableand,within theconstraintsimposedby thesymmetry, unambiguous.

A simultaneoussimulationof all spectra,including the frozensolutionspectrum,allowedthereforeto derive almostfull g tensorinformation,i.e. bothprincipalvaluesandtheorientation,with theexceptionof oneof theEulerangles(seebelow, tab. 6.1).Theresultingsetsof simulatedspectraareshown in fig. 6.5andfig. 6.7. Theeffectiveg valuesresp.resonancepositionsascalculatedfrom the simulationparametersaremarkedfor all six sites.The imperfectdegeneracy of line positionsreflectssmallde-viationsfrom thenominalmountingorientations:Thec axisof thecrystalsis inclinedby 88U (90U nominal)and3U (0U nominal)relative to therotationaxis,respectively.

Theorientationof theg tensorcanonly bepartially derived.This is not aproblemof themeasurementsor thesimulation,but reflectsthespecialcrystalsymmetry:theP63 symmetryaxismarksthec directionof thecrystalaxissystem,but is independentof theorientationof thea andb axes.Thisproblemarisesin generalwhenthereis onlyonesymmetryaxis.Therefore,only theorientationof thec directionin thelaboratorysystemcanbedeterminedfrom theEPRspectrawhile thea andb axisdirectionsarenot accessible.To obtain the full information, the orientationof the mountedcrys-


Figure 6.4: 94 GHz cw EPRspectraof PZ [700 in a singlecrystalof PSI (T T 80 K). The rotationaxisis approximatelyperpendicularto the c axis of the crystal; at the rotation angles0_ resp.180_ , themagneticfield is parallelto thec axis.

6.2. RESULTS 81

Figure6.5: Simulationof thespectrain fig. 6.4.Thedottedlinesrepresenttheeffectiveg valuesfor thesix inequivalentsitesin thecrystal.Whenthemagneticfield is parallelto thec axis(0_ and180_ ), theEPRlinesarecompletelydegenerate.


Figure6.6: 94GHzcw EPRspectraof PZ [700 in asinglecrystalof PSI atT T 80K. Therotationaxisisapproximatelyparallelto thec axisof thecrystal;themagneticfield is in theab plane.Sincethec axisis parallelto theC3 symmetryaxis,a120_ periodicityin thespectraresults.

6.2. RESULTS 83

Figure6.7: Simulationof thespectrain fig. 6.6.Thedottedlinesrepresenttheeffectiveg valuesfor thesix inequivalentsitesin thecrystal.Themagneticfield is approximatelyperpendicularto thec axisforall orientations,leadingto pairwisedegenerayof theEPRlines.


x y z accuracy (est.)g 2 M 00309 2 M 00260 2 M 00223 2 W 10L 5`c 68U 38U 61U 2U

Table 6.1: g tensordeterminedfrom simulationsof orientation-dependentEPRspectraof PZ [700. Theorientationof thetensoris givenastheinclinationof theprincipaldirectionswith respectto thec axis.

gx gy gz reference2 M 00309 2 M 00260 2 M 00223 this work, [7]1

2 M 00308 2 M 00264 2 M 00226 [7]2

2 M 00317 2 M 00264 2 M 00226 [5]3

2 M 00307 2 M 00260 2 M 00226 [5]4

2 M 00304 2 M 00262 2 M 00232 [8]5

194GHz EPRat T T 80K on singlecrystals294 GHz EPRon deuteratedfrozensolution

3325GHz EPRat T T 40 K on frozensolution4325GHz EPRat T T 200K on frozensolution

5140GHz EPRondeuteratedfrozensolution

Table 6.2: Comparisonof principal g valuesfor the PZ [700 radicalobtainedin this work with literaturedata.Notethatexperimentson frozensolutioneitherrequireddeuterationof thesampleor significantlyhighermicrowave frequencies.

tal could be determinedby X-ray diffraction experimentsprior to or after the EPRmeasurements.This requireshowever a very preciseandreproduciblemountingori-entationof thecrystal in both the EPRspectrometerandthe X-ray-diffraction setup:Sincethe EPRexperimentdoesnot yield any informationaboutthe orientationof aandb within theab plane,thereis no way to correctsmalldeviationsin themountingorientationbetweenbothsetups,andratherlargesystematicerrorsmayarise.

6.3 Discussion

Principal Valuesof g. Theprincipalvaluesasobtainedfrom thesinglecrystalspec-traarein goodagreementwith otherworks(seetab. 6.2). It is known thattheg tensorof P700 exhibits a slight temperaturedependence,indicative of a redistribution of thespin densityacrossthe chlorophyll molecules(e.g. [5, 6]). The valuesobtainedinthis work at T F 80 K arevery closeto thevaluesreportedfor T F 200K in [5], incontrastto T F 40K datafrom thesamereference.ThissuggeststhatthePJ K700 stateatT F 80K shouldbeverysimilarto thatat200K, andpossiblyevento thephysiologicalPJ K700 state.

Orientation of g. Almost completeorientationinformationon theg tensorof PJ K700could be derived from the singlecrystalEPRspectra.The only missingorientation

6.3. DISCUSSION 85

parametercannotbeobtainedfrom EPRexperimentsalonedueto thespecialsymme-try propertiesof thePSI singlecrystals.It is however known that thePSI enzymeisorientedin thecrystalsin suchawaythatthecrystallographicc axiscorrespondsto thenormalof the thylakoid membrane.Therefore,the obtainedorientationinformation,while incomplete,canbedirectly comparedto otherexperiments(tab. 6.3).

Structuralmodelsfrom X-ray diffractionindicatethat thechlorophyll heterocycleplanesof the Chla comprisingP700 areapproximatelyparallel to the c axis [2, 10].Fig. 6.8showssuchamodelfor P700 andtheobtainedorientationof theg tensoraxes.Onewould expect,i.e. basedon [11], that thegz directionshouldbeperpendiculartothatplane,i.e. beapproximatelyperpendicularto thec directionin thecrystals.Fromtheseexperimentsandin accordancewith [12, 13], this is obviouslynot thecase.Thiskind of tilt of the g tensorwith respectto the chlorophyll planeis known from theprimarydonorPJ K865 in bacterialreactioncenters.For bacteriochlorophyll, this devia-tion canbeexplainedby theorientationof theacetylgroups[14]. Suchgroupsarenotpresentin chlorophyll a, however, andthetilt of theg tensormustbeattributedto theinfluenceof theproteinenvironment,or to theelectroniccouplingbetweenthechloro-phylls comrisingP700, or both.Very recently, it hasbeenrevealedthatthetwo chloro-phylls comprisingP700 arenot completelyidentical [2], but areepimersChla/ChlaV .Therefore,the interactionwith theproteinmatrix maybedifferentfor bothhalvesoftheP700 “dimer”. Similarly, anasymmetricspindensitydistributionover bothchloro-phylls would breakthesymmetrydefinedby theheterocycle ring planesandgive riseto theobserved tilt of theg tensor. Suchanasymmetricspindensitydistribution hasalreadybeenreportedin otherworks,e.g.[12, 13].

The orientationof the g tensorcould in principle be an independentargumenttodecidewhetherthe main part of the spin densityof PJ K700 is always localizedon thesamechlorophyll or not. If thestatecouldbe localizedon eitherof thechlorophylls,two differentg tensororientationswould beobserved in thesample.TheChla/ChlaVmoleculesarehowever relatedto eachotherby an approximateC2 symmetryaboutthemembranenormal.SinceC2 is a subgroupof D6, thedifferencesof theeffectivegfactorsshouldbeverysmall.Thisdegeneracy couldbealleviatedby thedifferencebe-tweenChla and ChlaV . It seemshowever still unlikely that sucha splitting wouldbe noticeablein the single crystal spectraat 94 GHz, unlessthe relation betweenthe molecularaxesandg principal axeswould be very different for the Chla/ChlaVmolecules.

However, theobtainedg tensororientationcanbeusedin conjunctionwith struc-tural modelsfrom X-ray diffraction experimentsto shedmorelight on the natureofP700. Theorientationof g canalsoserveasareferencefor otherparamagneticinterme-diatesthatarecoupledto PJ K700. Thisallows to derive informationabouttheorientationof theseintermediatesrelative to the membranenormal, even from experimentsonfrozensolutions(i.e. [7]).


a bc d

Figure6.8: Structureof theP700 Chla/Chlae supermolecule[9]. Thepossibleg tensoraxesorientationsarerepresentedby coneswith avariousopeninganglearoundthemembranenormal fn (which is parallelto thecrystallographicc axis). In particular, no g axisis perpendicularto thechlorophyll ring planes.

x y z method reference68U 38U 61U singlecrystalEPR this work, [7]69U 36U 62U radicalpair EPR+ X-ray diffraction [7]48U 44U 81U EPRon partiallyorientedcells [4]

Table 6.3: Comparisonof thePZ [700 g tensororientationobtainedfrom high field EPRon singlecrystalsof PS I with other experiments. Given are the anglesbetweenthe principal directionsof g and thethylakoid membranenormal(= crystallographicc axis).

REFERENCES 87

High Field EPR of SingleCrystals. Thecw EPRexperimentson PJ K700 demonstratethebenefitsof highfield EPRonsinglecrystalsfor theinvestigationof biologicalsam-pleswith organicradicals.Theshortacquisitiontimesneededto achieve anexcellentsignalto noiseratio underlinethe high sensitivity of high field EPR.The benefitsofthe increasedresolutionseemlessclearat thefirst glance.Evenat 94 GHz, theZee-mansplitting anisotropy is rathersmall in relation to the inhomogeneouslinewidth.As a consequence,theg anisotropy is not resolved in the frozensolutionspectra.Inthe literature,eitherdeuteratedsampleswereusedto decreasethehyperfinecouplingconstantscausingthe inhomogeneousbroadening(i.e. [7, 8]), or significantlyhighermicrowave frequencieswereutilized (i.e. 325 GHz, [5]). The singlecrystalspectrahowever exhibit a pronouncedstructure. By taking the constraintsarising from thecrystal symmetryinto account,it is possibleto derive accuratespectralparametersfrom protonatedsamplesat94 GHz.

REFERENCES

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[3] RögnerM., Nixon P.J.,& Diner B.A., Purificationandcharacterizationof photosystemIandphotosystemII corecomplexesfrom wild-type andphycocyanin-deficientstrainsofthecyanobacteriumsynechocystisPCC6803,J. Biol. Chem.265, 6189–6196(1990).

[4] BertholdT., BechtholdM., HeinenU., Link G., Poluektov O., UtschigL., TangJ.,Thur-nauerM., & KotheG.,Magnetic-field-inducedorientationof photosyntheticreactioncen-tersasrevealedby time-resolved W-bandEPRof spin-correlatedradicalpairs,J. Phys.Chem.B 103, 10733–10736(1999).

[5] BrattP.J.,RohrerM., KrzystekJ.,EvansM.C.W., BrunelL.C.B.,& AngerhoferA., Sub-millimeterhigh-fieldEPRstudiesof theprimarydonorin plantphotosystemI P700P O , J.Phys.Chem.B 101, 9686–9689(1997).

[6] Bratt P.J.,Poluektov O.G.,ThurnauerM.C., KrzystekJ., BrunelL.C., SchrierJ., HsiaoY.W., ZernerM., & AngerhoferA., The g-factoranisotropy of plant chlorophyll aP , J.Phys.Chem.B 104, 6973–6977(2000).

[7] ZechS.G.,HofbauerW., Kamlowski A., FrommeP., StehlikD., Lubitz W., & Bittl R.,A structuralmodel for the charge separatedstatePP O700A P g1 in photosystemI from theorientationof themagneticinteractiontensors,J. Phys.Chem.B104, 9728–9739(2000).


[8] PrisnerT.F., McDermottA.E., Un S.,NorrisJ.R.,ThurnauerM.C., & Griffin R.G.,Mea-surementof theg-tensorof theP700O P signalfrom deuteratedcyanobacterialphotosys-temI particles,Proc.Natl. Acad.Sci.USA90, 9485–9488(1993).

[9] KraussN., personalcommunication(2001).

[10] Klukas O., SchubertW.D., JordanP., KraussN., FrommeP., Witt H.T., & SaengerW.,Localizationof two phylloquinones,Qk andQhk, in animprovedelectrondensitymapofphotosystemI at4 Å resolution,J. Biol. Chem.274, 7361–7367(1999).

[11] StoneA.J.,Gaugeinvarianceof theg tensor, Proc.R.Soc.A 271, 424–434(1963).

[12] KäßH., Die StrukturdesprimärenDonatorsP700 in PhotosystemI: UntersuchungenmitMethodender stationären und gepulstenElektronenspinresonanz, Ph.D.thesis,Techni-scheUniversitätBerlin (1995).

[13] KäßH., FrommeP., Witt H.T., & Lubitz W., Orientationandelectronicstructureor theprimary donorradicalcationPO P700 in photosystemI: A singlecrystalEPRandENDORstudy, J. Phys.Chem.B 105, 1225–1239(2001).

[14] PlatoM. & MöbiusK., Structuralcharacterizationof theprimarydonorin photosyntheticbacteriaby its electronicg-tensor, Chem.Phys.197, 289–295(1995).

Chapter 7

High Field EPR on the TyrosineRadical Y SD in SingleCrystals ofPhotosystemII

Crystallizationof the intactphotosystemII reactioncenterhasonly becomepossiblevery recently[1]. A first structuralmodel for PS II basedon X-ray diffraction (at3 M 8 Å resolution)hasbeendevelopedconcurrentlyto this work andhasmeanwhilebeenpublished[2]. While this structureconfirmstheoverall modelof PSII asgivenin chapter5, many structuraldetailsarestill lacking.High field EPRonsinglecrystalshasthe potentialto fill in informationaboutthe detailedgeometricaland electronicstructureof theparamagneticintermediatesin PSII which is notavailablefrom X-raydiffractionexperimentsalone.

The investigation of the dark stabletyrosineradicalY KD is an importantfirst stepin this direction. Y KD is easilygeneratedwithout chemicaltreatment,eliminatingthepotentialof artifacts.It combinesasmallg anisotropy with acomplex hyperfinestruc-ture. This makes it an interestingbenchmarkfor the analysisof radical speciesinsinglecrystalsusinghigh field EPRin general.


The PSII preparationsusedin this work werekindly provided by Dr. Athina Zouniandcoworkersin anin-housecollaborationproject.

7.1.1 PSII CoreComplexes

PS II core complexes (cc) were isolatedfrom Synechococcuselongatusand puri-fied accordingto a protocol describedby Dekker et al. [3]. According to SDS1-

1SodiumDodecyl Sulfate

89

90 CHAPTER7. Y KD IN SINGLE CRYSTALS OFPHOTOSYSTEMII

a

b

c

Figure 7.1: Non-trivial symmetryoperationsof theP212121 spacegroupin anorthorhombicunit cell.SincetheanglesbetweentheC2 symmetryaxesareequal,it is generallynot possibleto distinguishthea, b, andc directionsin EPRexperiments.

polyacrylamidegel electrophoresisandMALDI-T OF2 massspectrometry, the PSIIcorecomplexesarecomposedof at least17subunits[4].

For frozensolutionEPRandENDOR,glycerolwasusedasa cryoprotectant,andthePSII ccsolutionswerefrozenin liquid nitrogen.

7.1.2 PSII SingleCrystals

From the above preparations,three-dimensionalsinglecrystalscould be grown [1].ThePSII corecomplexesin thesecrystalsretainfull wateroxidationactivity, ashasbeenshown by measuringthe oxygenevolution activity of core complex solutionsobtainedby dissolvingcrystals[5]. Thegeometricalstructureof thecrystalshasbeencharacterizedby X-ray diffractionexperiments.Thecrystalsexhibit anorthorhombicunit cell of dimensionsa F 130Å, b F 227Å, andc F 308Å. Theunit cell includes4sitesrelatedby theP212121 spacegroup(seefig. 7.1).Eachsiteis occupiedby adimerof PSII corecomplexes.Theindividualcorecomplexesin thedimerarerelatedto eachotherby anon-crystallographicC2 (180U rotation)symmetryaxisthatis parallelto themembranenormal.

As in the frozensolutioncase,thecrystalsweresoaked in glycerolasa cryopro-tectantbeforefreezingthemin liquid nitrogen.

7.1.3 cw EPR

Continuouswave EPRexperimentswereperformedat 94 GHz anda temperatureofT F 80 K. Frozensolutionsampleswerehandledasdescribedin chapter2. For thesinglecrystals,threemountingvariantswereused(fig. 7.2):

2Matrix AssistedLaserDesorptionIonization-TimeOf Flight

7.1. MATERIALS AND METHODS 91

Figure7.2: Severalvariantsof mountingsmallPSII singlecrystalsin capillariesfor 94GHz EPR.

1. Crystalswere placedinside the sampletube (0 M 7 mm inner diameter)with asmallamountof motherliquor andfrozenin this position. In this arrangement,morphologicalplanesof thecrystalstendto bealignedto thewall of thecapil-lary.

2. Crystalswereplacedon the endof a capillary, coveredby a small amountofmotherliquor, andfixedin thispositionby freezing.With thismountingvariant,crystalsreston largemorphologicalplanes,thereforethenormalof therespec-tiveplaneis alignedwith thecapillaryaxis.

3. Crystalsweremountedin a loop protrudingfrom a capillary and frozenwithsomemotherliquor in that position. Sincethe loop canbe tilted with respectto thecapillaryaxisandthecrystalis floating freely in a membraneof motherliquor prior to freezing,thereis noinherentpreferentialorientationof thecrystal.

Option3allowstoperformadditionalX-raydiffractionexperimentsonthemountedcrystals.Thesecanbeusefulto obtainindependentinformationabouttheorientationof thecrystalaxeswith respectto the laboratoryaxissystem,therebysupplementingor corroboratingEPRresults.

7.1.4 PulsedENDOR

PulsedENDORexperimentswereperformedon frozencorecomplex solutions(T F5 K) at X band(9 M 5 GHz) microwave frequencies.A Bruker ESP380Espectrometer,equippedwith anESP360D-PpulsedENDORaccessoryandanENI A-500 RF am-plifier wasused.Davies’ pulsesequence[6] with a tRF F 8 µs RF pulsewasapplied(seesection1.4.2).


7.2 Results

7.2.1 cw EPR of FrozenSolution

A 94 GHz cw EPRspectrumof Y KD in frozenPSII cc solutionis shown in fig. 7.3.The spectrumwasobtainedat a sampletemperatureof T F 80 K anda microwavepower level of Pmw E 500nW. A distinctandwell-resolvedhyperfinestructurereflectsa narrow EPRlinewidth and,therefore,a homogeneoussample.At thegx F 2 M 00767andgz F 2 M 00219edges,a fourfold hyperfinesplitting with an intensityratio patternof 1:3:3:1is apparent.This intensityratio correspondsto a binomial distribution forN F 3, suggestingthatthestructureis causedby threeI F 1

2 nuclearspinswith similareffective hyperfinecoupling constantsfor orientationsalong the molecularx and zaxes. On the gy F 2 M 00438edge,only a twofold splitting is resolved. Therefore,atleastsomeof thehyperfinecouplingtensorshave to beratheranisotropic,resultingina small effective hyperfinecouplingconstantfor thegy orientation.Basedon earlierEPRwork on similar phenoxyl-typeradicals(e.g. [7]) andtheoreticalstudies[8, 9],the hyperfinestructureis assignedto threeprotonsin position3, 5, and7a (refer tofig. 7.4).

7.2.2 PulsedENDOR on FrozenSolution

Thereis considerablevariationin the hyperfinedatafor Y KD in the literature(see[7,11–15]). It canalsonot beexcludedthatthehyperfinecouplingsmaybedifferentforPSII preparationsfrom differentspecies.ThesinglecrystalY KD spectraare,aswill beseenlater, dominatedby thecomplex hyperfinestructure.Thereproducibilityof thisstructureis an importantcriterion for thequality of simulationsof thesespectra.Forthispurpose,accuratehyperfinecouplingconstantsareessential.

Fig.7.5showstheDaviesENDORspectrumobtainedfrom frozensolutionof PSIIcc at T F 5 K at X band. The g anisotropy of the Y KD radical is too small to leadtopronouncedorientationselectioneffectsin X bandENDOR.Therefore,the ENDORspectrumshown exhibits thefull hyperfinecouplingtensors.For a giveneffective hy-perfinecouplingconstantaandanuclearZeemanfrequency νn, theENDORresonanceconditionis ν iENDOR F jj νn k a

2 jj . Here,theprotonZeemanfrequency is νn F 14M 8 MHz.Thespectralfeaturescorrespondingto protonhyperfinecouplings l a l m 2νn arethere-fore groupedsymmetricallyaboutthis frequency. Thelargesthyperfinecouplingsarecloseto 2νn in magnitude,andcorrespondingfeaturescanbeseenonly on thehigh-frequency sideof thespectrum.

Thehigh-frequency endof theENDORspectrum(νRF F 27 M M M 32 MHz) is domi-natedby anaxial hyperfinetensor. Themoderaterelative anisotropy

a n L ao13 p a n J 2ao q shows

thatdipolarcontributionsto this couplingaresmallascomparedto thecontactinter-actionwith thelocal electronspindensitymediatedfrom thephenoxylring by hyper-conjugation(seee.g.[16]). In accordancewith theliterature,this tensorwasassigned

7.2. RESULTS 93

Figure 7.3: 94 GHz cw EPR spectrumof the Y [D radical in frozen solutionof photosystemII corecomplexesat T T 80 K (solid) andsimulation(dotted). The narrow linewidth reflectsthe excellenthomogeneityof thesampleandallowsacomplex hyperfinestructureto beresolved.

C O

H

H H

HH

R

H

H

6 5

4

32

17a

7b

r s tFigure 7.4: Hydrogen-bondedY [D radicalwith protonnumberingscheme.Themolecularaxescorre-spondto theprincipalaxesof theg tensor[10].


Figure 7.5: Davies ENDOR spectrumof Y [D in frozensolutionof photosystemII corecomplexesatT T 5 K. B0 T 346u 7 mT, νMW T 9 u 73 GHz. The upperfrequency axis givesthe magnitude(but notthesign) of theobservedhyperfinecouplings.Dottedlines representthe assignedhyperfineprincipalvalues.

7.2. RESULTS 95

to a β proton in position7a and the sign of the hyperfinecouplingsassumedto bepositive. The mirror imageof this structureon the low-frequency sidewould fall intheνRF m 1 M 5 MHz rangewhich is outsideof theusefulspectralrangeof theENDORsetupused.

At νRF E 24 MHz on the high frequency sideand5 MHz on the low frequencysideof thespectrum,a split peakis observed. On bothsidesof this split peak,thereare broadslopesthat extend into the matrix region (νRF F 10 M M M 20 MHz) and intothe rangeof the axial β proton tensorassignedabove. This suggeststhe split peakto representthemiddlecomponentsof two highly anisotropic,rhombichyperfineten-sors. Basedon the stronganisotropy and the splitting of the lines, thesecouplingswereassignedto approximatelysymmetry-equivalentα protonsof thephenoxylring.Theoretical[8, 9] studiesindicatethat thespindensityhasa local maximumneartheβ protonsin positions3 and5 andthat the correspondinghyperfinecouplingshavenegative sign. The correspondinglargestcouplingcomponentsderiving from theseprotonsshow up assmall shouldersat aboutνRF E 26 MHz with a similar splitting.Thesmallestcouplingsof theseprotonscouldnot beunambiguouslyidentifiedin thematrixsignalregion. Thesplittingof thetwo observedprincipalvaluesis comparable,suggestingthattheinequivalenceis mostlycausedby adifferentspindensity. A likelycausefor suchadeviationfrom symmetrywouldbetheinfluenceof anasymmetricallyorientedhydrogenbondto thephenoxyloxygen(seee.g.fig. 7.4).

7.2.3 cw EPR on SingleCrystals

Severalsetsof cw EPRspectrawereobtainedfor differentlymountedsinglecrystalsof PSII cc (fig. 7.6,7.8,7.10,and7.12).Within eachset,thesamplewasturnedaboutthecapillaryaxiswhich is perpendicularto theappliedmagneticfield vB0.

The combinationof 8 magneticallyinequivalentY KD sitesand the superimposedhyperfinestructuremakesthespectravery complex. Takingonly thethreeprotonhy-perfinecouplingsresolved in thefrozensolutionspectrainto account,8 w 8 F 64 po-tentially resolvablelinescontributeto everytrace.It is thereforenotgenerallypossibleto tracetheangulardependenceof theeffectiveg valuefor thedifferentsites.Also, thehyperfinestructureis very pronouncedfor someorientationsbut completelysmearedout for others.This again illustratestheneedfor spectralsimulationsasdiscussedinappendixB in orderto obtaininformationabouttheorientationof theg tensor.

7.2.4 Analysis

Parameter estimation. The only parametersthat canbe derived from the spectraindependentlyfrom otherparametersaretheprincipalvaluesof theaccessedhyperfinetensors.This is dueto the absenceof orientationselectivity in the X-bandENDORexperimentswhich in turn is aresultfrom thesmallg anisotropy. Theprincipalhyper-fine valueshave beendeterminedby picking thepositionof peaksor othersignificantfeaturesin theENDORspectrummanually(dottedlinesin fig. 7.5). Thestructuresin


Figure 7.6: Orientation-dependent94 GHz cw EPRspectraof the Y [D radical in a singlecrystal ofphotosystemII corecomplexesfrom SynechococcuselongatusT T 80 K and500 nW of microwavepower. Thespectrumof PSII cc in frozensolutionhasbeenincludedat thetop.

7.2. RESULTS 97

Figure 7.7: Simulationof the spectrain fig. 7.6. Effective g valuesarisingfrom the 8 magneticallyinequivalentY [D sitesaremarked by coloredlines. Identicalcolors representsitesrelatedby theC2

dimersymmetry. Therotationaxiscorrespondsto thecrystallographica direction(tilted by 3_ ), leadingto pairwisedegeneracy of the g factors. As a consequence,a comparablesimulationyielding wrongresultscanbeobtainedtakingonly four Y [D sitesinto account.Seetab. 7.1 for thedetailedorientationof thecrystal.


Figure 7.8: 94 GHz cw EPRspectraof theY [D radicalin singlecrystalsof PSII cc asin fig. 7.6 for adifferentmountingorientation.

7.2. RESULTS 99

Figure 7.9: Simulationof the EPRspectrain fig. 7.8. For this crystal,the b axis is approximatelyintheplaneof themagneticfield. Again, theeffective g valuesof theY [D sitesappeargroupedtogether,makingit difficult to recognizethe truenumberof sites. Referto tab. 7.1 for detailson themountingorientationof thecrystal.


Figure7.10: 94 GHz EPRspectraof aPSII ccsinglecrystalwith a third mountingorientation.

7.2. RESULTS 101

Figure 7.11: Simulationof thespectrain fig. 7.10. For this orientation,thea axis is approximatelyinthe planeof the magneticfield, leadingagain to degeneracy at the 0_ /180_ and90_ orientations.Forother rotationangles,the g valuesexhibit again somegrouping,making it difficult to recognizethenumberof magneticallyinequivalentsites.Seetab. 7.1for detailson thecrystalorientation.


Figure7.12: Orientation-dependent94GHzcw EPRspectraof theY [D radicalin singlecrystalsof PSIIcc for anarbitrarymountingorientationof thecrystalwhich largelyavoidsdegeneracies.

7.2. RESULTS 103

Figure 7.13: Simulationof thespectrain fig. 7.12. Theeffective g valuesof differentsitesarespreadout,andnoclusteringappears.Thissetof spectraunambiguouslyprovesthatmorethanoneY [D radicalbelongsto eachof the four crystallographicsites. The mountingorientationof the crystal is given intab. 7.1.


thespectrumarenarrow andtheir spectralpositionsarewell-defined.This allows toestimatetheuncertaintyof theobtainedvaluesas∆A m 0 M 2 MHz.

In contrast,anaccuratedeterminationof g principalvaluesfrom thecw EPRspec-tra is not completelyindependentfrom other parametersin the spin Hamiltonian.Therefore,an iterative estimationprocedurewas usedto arrive at a self-consistentparameterset.

Basedon initial guessesabouttheorientationof thehyperfinetensorswith respectto theg tensor, theprincipalvaluesof g couldbedeterminedfrom a simulationof thefrozensolutioncw EPRspectrum.Both g andhyperfineprincipal valueswerethenusedin turn to simulatethe orientation-dependentsingle crystal spectraand obtainorientationinformationfor theindividual tensors.this procedurewasrepeatedseveraltimes.

A completeparametersetconsistsofx 3 principalvaluesfor g,x 3 principalvaluesfor eachhyperfinetensorincludedin theHamiltonian,x 3Euleranglesperhyperfinecoupling,giving theorientationof thetensorrelativeto g,x 3 principal valuesof a Gaussianlinewidth tensor(representingthe unresolvedhyperfineinteractions),x and3 Euleranglesdescribingtheorientationof thelinewidth tensor.

In addition,thesimulationof singlecrystalspectrarequiresx 3 Euleranglesfor theorientationof theg tensorfor eachmagneticallyinequiv-alentsitein theunit cell,x and3 Euleranglesdescribingthecrystalorientationwith respectto the labora-tory axissystem.

To increaseboththenumericalstability of thefitting procedureandthestatisticalsig-nificanceof the obtainedparameters,the numberof parameterswasreducedasfol-lows:x In the crystals,theorientationof all magneticallyinequivalentsitescanbe de-

rivedfrom theorientationsof theY KD radicalsin asinglephotosystemII ccdimerby usingthesymmetryoperationsof theP212121 spacegroup.x From X-ray diffraction experiments,theC2 symmetryaxis relatingboth PSIIspecimenwithin a dimer is known with high accuracy. Therefore,only onesetof Euleranglesis neededto describetheorientationof bothY KD radicalsin eachdimer.

7.2. RESULTS 105x The small inequivalencein the hyperfinecouplingconstantsfor the protonsinpositions3 and5 wasneglectedandtherespective tensorswereassumedto beorientedsymmetricalto eachotherwith respectto themolecularaxissystem.x An isotropicGaussianlinewidth wasassumed.

The smallestcomponentof the α protonhyperfinetensorscould not be assignedin theENDORspectrum.This valuewasusedasa freeparameterin thesimulations.It shouldbenoted,however, thatthevalueobtainedfrom thesimulationsis alsoinflu-encedby linewidth contributionsfrom unresolved hyperfinecouplingsandis at besta crudeapproximation.Tab. 7.2 shows thefinal parametersetobtained,with theex-ceptionof theorientationof thecrystalin thelaboratorysystemwhichdiffersfor eachspectrum.

Quality of simulations. Thesimulatedfrozensolutionandcrystalspectraareshownin fig. 7.7,7.9,7.11,and7.13,next to therespective experimentalspectra.While thefrozensolutionspectrumis reproducedwith excellentaccuracy, the hyperfinestruc-turesof the experimentalandsimulatedsinglecrystalspectralook somewhat differ-ent for many orientations.Closeinspectionof the spectrarevealshowever that onlythe amplitudeof the hyperfinestructurediffers significantly. Thesedifferencesarethe resultof an assumedisotropiclinewidth usedin thesimulations:for orientationswheretheassumedlinewidth is too large,hyperfinestructureis lostdueto thereducedresolutionof the simulatedspectrum.Similarly, for orientationswherethe assumedlinewidth is too small, thehyperfinestructureappearsmorepronouncedin thesimu-lations.Thespectralpositionsof thehyperfinefeatures,however, arewell reproducedby thesimulations,corroboratingtheparametersused.

PhotosystemII dimers. For specialorientationsof thecrystalswith respectto themagneticfield, degeneracy occurs.Sincemostmountingvariantsinduceapreferentialorientationof thecrystalsthat is relatedto their morphologicalstructure,suchspecialorientationsareobtainedratheroften. A goodexamplecanbe seenin fig. 7.6/7.7.Here,the rotationaxis is very closeto the crystallographica axis, andthe magneticfield is thereforealmostexactly in the bc planefor all rotationangles. For suchanorientation,a pairwisedegeneracy occurs,reducingtheapparentnumberof inequiva-lent tyrosineradicalsin theunit cell to 4. It is indeedpossibleto obtaina rathergoodsimulationof thespectrain fig. 7.6with amodelthatassumes4 monomericPSII sites.Furthermore,atearlystagesof theanalysisof singlecrystalspectra,thedimericnatureof thesitesin thecrystalswasnot known yet, leadingto a wronginitial interpretationof thespectra.Only laterexperimentsinvolvedsufficiently “arbitrary” orientationsofthe crystals(i.e. fig. 7.12) to clearly resolve more than4 inequivalentY KD radicals,therebyconfirmingthedimericnatureof PSII at thecrystallographicsites.


φ θ ψ figures93U 90U 87U 7.6,7.762U 64U 92U 7.8,7.91U 73U y 1U 7.10,7.1141U y 49U 41U 7.12,7.13

Table 7.1: Orientationof thePSII cc crystalsfor a rotationangleof 0_ (determinedfrom simulationsof theEPRspectra).TheEuleranglesrelatethecrystallographicabcaxesto thelaboratoryaxissystemxyz; themagneticfield B0 is parallelto thex axis. Thecrystalrotationaroundthez axiscorrespondstoanincreaseof φ. For thedefinitionof Euleranglesusedhere,referto appendixB.2.

x y zg 2 M 00767 2 M 00438 2 M 00219

A3 z 5 [MHz] y 26M 1 E y 8 y 19M 5A7a [MHz] H 32M 8 H 27M 2 H 27M 2

Table 7.2: Simplifiedparametersetusedfor simulationof spectra.Referto tab. 7.3 for theorientationof theg tensorin thecrystal.Thehyperfinetensorsfor theα protons(3,5)arerotatedby 20_ aboutzwith respectto theg tensor. TheA7a tensoris collinearwith g.

cos x1 y1 z1 x2 y2 z2 C2

a y 0 M 681 y 0 M 201 y 0 M 704 H 0 M 177 H 0 M 257 H 0 M 950 H 0 M 282b y 0 M 440 H 0 M 881 H 0 M 174 y 0 M 557 y 0 M 769 H 0 M 312 H 0 M 558c H 0 M 585 H 0 M 428 y 0 M 688 H 0 M 811 y 0 M 585 H 0 M 007 y 0 M 781

Table7.3: Orientationof theY [D g tensoraxesin thecrystalsitedefinedby thegivenC2 axisorientation.Givenarethedirectionalcosineswith respectto thecrystallographicabcsystem.Orientationsfor othersitescanbe obtainedusingthe symmetryoperationsof the P212121 spacegroup. Subscripts1 and2referto thetwo halvesof thePSII cchomodimer.

7.3. DISCUSSION 107

Assignmentof axes. The symmetryoperationsof the P212121 spacegrouparein-variantunderpermutationsof thecrystallographicaxes.For thisreason,anassignmentof thecrystallographicaxesis notpossiblebasedontheanalysisof orientationsymme-triesin thesinglecrystalspectra.Moreprecisely, EPRallowsto identify theorientationof asetof threesymmetryaxeswhichcorrespondsto thecrystallographicaxissystem,but not to assignindividual symmetryaxesto thecrystallographica, b, andc axes.Acommonway to resolve this sixfold ambiguity is to determinethe orientationof thecrystalusedin theEPRexperimentby X-ray diffraction.

The crystalsusedherehave an additionalsymmetry, however. For eachsite inthecrystal,thereis a localC2 axis that relatesbothhalvesof thePSII homodimertoeachother. This additionalsymmetryaffects the EPRspectraandcanbe analyzed.Whenthe inclination anglesof theC2 axis with respectto the crystallographicaxesaredifferent,theseanglescanbeusedto labelthesymmetryaxesandunambiguouslyassignthem to the crystallographicaxes system(fig. 7.14). This still requirestheorientationof theC2 axis with respectto the crystalaxis systemto be known fromotherexperimentslike X-ray crystallography. It is however not necessaryany moretoperformX-ray diffractionexperimentson thecrystalsusedfor EPR.

Theorientationof thelocalC2 dimeraxesin thesinglecrystalsof PSII ccusedherefulfills therequirementsstatedabove. Theorientationof theC2 axis for onearbitrarysitein thecrystal(right columnin tab. 7.3)wasobtainedfrom X-ray diffractionstudiesandkindly providedby Dr. PeterOrth (FU Berlin).

Assignmentof sites. Furthermore,thedimersymmetryis non-crystallographic,i.e.eachsitein theunit cell hasadifferentlyorientedlocalC2 axis.Thismakesit possibleto labelpairsof Y KD signalsderiving from thesamedimerin theunit cell with thecor-respondingorientationof the localC2 axis (seefig. 7.15for anexample). Therefore,orientationinformationabouttheY KD radicalscanbegivenfor aspecificsitethatcanbeunambiguouslyidentifiedby otherstructuralinvestigationmethods(i.e.X-ray diffrac-tion). This is of particularhelpwhencombiningresultsfrom differenttechniques.

7.3 Discussion

The94GHzcw EPRspectraof frozensolutionof PSII ccexhibit excellentresolutionas evident by the well-resolved hyperfinestructure. On the instrumentalside, thisreflectsthegoodhomogeneityof themagneticfield. Moreimportantly, however, it canbeattributedto a small inherentlinewidth of thesamplethat indicatesa well-defined,homogeneousenvironmentof theY KD radicalin theprotein.

g tensor. The good resolutionof the spectraallowed to determinethe principal gvalueswith high accuracy (∆g F 2 W 10L 5). The obtainedvaluesaresimilar to thosefoundin otherworks(seetab. 7.4),althoughthey do not agreewithin their errormar-ginsin every case.It cannotberuledout that thevaluesmaydependon theorganism

108 CHAPTER7. Y KD IN SINGLE CRYSTALS OFPHOTOSYSTEMII|

~

Figure 7.14: Orientationof a non-crystallographicC2 symmetryaxis with respectto the crystalaxissystem.Thecrystallographica, b, andc axescanbeidentifiedby themagnitudeof thedirectioncosines(bold)which areknown from X-ray diffraction.

Figure 7.15: 2D exampleon how crystallographicsitescanbedistinguishedbasedon a noncrystallo-graphicsymmetry. Thesameinitial tensororientation(boldellipsis)is assumedfor differentsites.Sincethecrystallographic(solid)andthenoncrystallographic(dashed)symmetryoperationsdonotcommute,differentsetsof orientationsresult.

7.3. DISCUSSION 109

gx gy gz ∆g organism reference2 M 00767 2 M 00438 2 M 00219 2 W 10L 5 S.elongatus this work2 M 0074 2 M 0044 2 M 0023 notgiven spinach [7]2 M 0075 2 M 0045 2 M 0021 1 W 10L 4 spinach [17]2 M 00756 2 M 00432 2 M 00215 1 W 10L 4 spinach [11]2 M 00740 2 M 00425 2 M 00205 notgiven Synechocystis6803 [18]2 M 00737 2 M 00420 2 M 00208 notgiven spinach [18]2 M 00745 2 M 00422 2 M 00212 2 W 10L 4 spinach [19]2 M 00782 2 M 00450 2 M 00232 notgiven spinach [12]2 M 00752 2 M 00426 2 M 00212 7 W 10L 5 spinach [20]

Table 7.4: Comparisonof principal valuesof theg tensorfor theY [D radicalin PSII. ∆g denotestheaccuracy of thegivendata.

from which PSII wasprepared,or from artifactsof the preparationprocedure.Thelatterpossibilityis, however, unlikely, consideringthatthePSII corecomplexesin thecrystalsusedheremaintainedtheir catalyticactivity [5]. It seemsmostplausibletoattributeminor differencesin g to differentfield calibrationproceduresor g referencesamples.Theg valuesobtainedin this work aretied to theg factorof theLi:LiF sam-ple which is known to a high degreeof accuracy [21] while Mn2J centersareanotherpopularreferencesampleusedfor calibrationin high field EPR.

Hyperfine couplings. Reliabledataon the hyperfineinteractionsis importantforthe simulationof the EPRspectra,especiallyfor singlecrystal spectra.The resultsobtainedby DaviesENDORarecomparedwith thosefrom othersourcesin tab. 7.5.It canbeseenthatthereis a ratherlargevariationof hyperfinedatafor theY KD radicalin the literature. The accuracy of the hyperfinedatataken from the ENDOR spec-trum in this work is estimatedas∆A F 0 M 2 MHz, basedon thewidth of thefeaturesin

A3 5x A5 3

x A3 5y A5 3

y A3 5z A5 3

z A7a A7a organism reference 25u 5 26u 8 8 19u 0 20u 1 27u 2 32u 8 S.elongatus this work 29u 4 9 u 0 19u 6 21u 6 23u 2 spinach [7]24 3 19 27 28 31 spinach [11]

14u 8 18u 8 20u 3 23u 0 27u 0 30u 5 spinach [12]12u 3 18u 8 20u 3 23u 0 27u 0 30u 5 spinach [13] 25u 6 27u 5 8 u 0 19u 1 20u 5 27u 2 31u 5 spinach [14] 25u 6 27u 5 8 u 0 19u 1 20u 5 28u 5 33u 0 C. reinhardtii [14] 25u 6 27u 5 8 u 0 19u 1 20u 5 24u 5 29u 0 P. laminosum [14] 25u 4 7 u 2 19u 5 20u 2 29u 3 Synechocystis6803 [15]

Table 7.5: Hyperfinecoupling principal valuesfor the Y [D radical as determinedin this work andcomparisonwith literaturedata. All valuesare given in MHz. (Somedatagiven in magneticfieldunitsin theliteraturehave beenconverted.)


gx gy gz radical2 M 00767 2 M 00438 2 M 00219 Y KD2 M 0076 2 M 0046 2 M 0021 Y1772 M 0092 2 M 0046 2 M 0021 Y122

Table 7.6: Comparisonof g valuesfor Y [D andtyrosineradicalsY122 (E. coli) resp.Y177 (mouse)inthe R2 subunit of ribonucleotidereductase.Comparedto Y177, Y122 is missinga hydrogenbondtothephenoxyloxygen,causingashift of gx to a largervalue[22].

theENDORspectra.ThegivenA3N 5y couplingsareanestimatebasedon EPRspectra

simulations;the obtainedvaluesarevery likely influencedby the neglectedsmallercouplingsandno errorcanbegiven. Theasymmetryof thehyperfinetensorsfor pro-tonsin positions3 and5 hasbeenobservedby otherauthorsaswell andis attributedto ahydrogenbondfrom thephenoxylgroupto ahistidineresidue(His189)in thepro-tein backbone[23]. The lengthandorientationof this bondnot only affectsthespindensitydistribution within the phenoxylring (and thus the hyperfinecoupling con-stants),but alsohasaneffectontheg tensor. Particularlythegx componentis sensitivetowardssucha hydrogenbond,aswasshown by calculationsandEPRexperimentson tyrosineradicalsin othersystems[18, 22, 24, 25] (seealsotab. 7.6). The largesthyperfinecouplingderivesfrom theprotonin position7a(seefig. 7.4),while thecor-respondingcouplingfrom theprotonin position7b is not resolvedin theEPRspectraandwasnot identifiedin the ENDOR spectrum.The couplingfor suchβ protonsisratherisotropicanddominatedby the Fermi contactinteractionterm. The spin den-sity in thephenoxylring hasa π orbital-likedistributionwith anodein thering plane.Consequently, for varyingorientationof thephenoxylring with respectto theaminoacid headgroup(denoted‘R’ in fig. 7.4), the β protonsin positions7a and7b mayexperienceratherdifferentspindensities.Sincethe7b protonhyperfineinteractionissmall,it is concludedthatthis protonlies in or closeto thering plane.

Small protein crystals. Thesinglecrystalspectrademonstratethathigh-fieldEPRexperimentsonorganicradicalsin thesesmallcrystalsarefeasibleanddeliverspectrawith an excellent signal to noiseratio. The typical crystal size in the experimentsshown herewasabout35 nl, correspondingto about1013 spins(assumingthe upperlimit of 100% for the yield of Y KD). Typical acquisitiontimes for one traceof thecrystalspectrawereabout3 minutes;thereforethesensitivity is sufficientto investigateconsiderablysmallercrystalsat still practicalacquisitiontimes. As an example,30minutesof dataacquisitionwith a1 nl crystal(correspondingto about3 W 1011 unpairedspins)wouldyield aspectrumwith atenthof thesignal/noiseratio. Thequalityof sucha spectrumwould still beusablefor ananalysis,andit couldbe further increasedbyresortingto lessconservativefiltering/modulationparametersthanwereusedhere.

Theexcellentagreementof thespectralfeaturesof thehyperfinestructurebetweenthe experimentalsinglecrystalspectraandthe simulationscorroboratethe obtained

7.3. DISCUSSION 111

Oαβ

R

O

R

Figure 7.16: Schematicrepresentationof theY [D orientationin PSII cc with respectto the thylakoidmembraneasdeterminedin thiswork (solid)andin [11] (slashed).Bothviewsarealongthemembraneplane.α is theanglebetweenthemoleculary directionandthemembranenormal fn; β is thetilt of thephenoxylring planewith respectto fn.

hyperfinevalues.More important,however, is theorientationinformationgainedfromthesespectra(tab. 7.3). The orientationof the g tensorcould be determinedwithan estimatedaccuracy of 3U . Sincethe g tensororientationis tied to the molecularsymmetryaxesof thephenoxylradical,theorientationof thetyrosyl in thecrystalsisalsoobtained.Thisknowledgepotentiallyhelpsin thecreationof adetailedstructuralmodel. To derive the sameinformation from X-ray diffraction analysis,very highresolutionis required,placingextremelyhigh demandson thequality of thecrystals.

Comparisonwith oriented membranedata. DimericPSII hasalsobeenobservedin 2D crystalsandnative membranefragments[26–28]. It seemslikely that thePSIIdimersin thesinglecrystalsareidentical.Underthis assumption,theC2 axisof eachPSII homodimercorrespondsto themembranenormalof nativePSII. Theorientationof the Y KD radicalwith respectto the membranecan thus be derived andcomparedto EPR work on Y KD in orientedmembranefragments[11]. Sucha comparisonisshown in fig. 7.16. The discrepancy in orientationsbetweenthis work and [11] ismoderate,but still significant.In singlecrystals,theorientationof thetyrosinesitesisverywell definedwhereastheremightbeaconsiderabledistributionof orientationsinimperfectlyorientedmembranes.For this reason,theresultsobtainedfrom thesinglecrystalstudiesshown herearebelieved to be muchmorereliable. Also, the spectrain this work show significantlymoredetail thanthosein [11], therebyincreasingtherobustnessof thefit.


Comparison with structural model. The obtainedorientationof Y KD canalsobecomparedto therecentlypublishedPSII structure.However, the3 M 8 Å resolutionofthe diffraction dataon which that structureis basedis not really sufficient to obtainsuchinformationfor moleculargroupsthesizeof a phenoxylring, evenif anorienta-tion of thetyrosyl radicalsis suggestedin [2]. A tentative identificationof Y KD1 (indexreferringto tab. 7.3)with TYR94(nomenclatureusedin in [29]) andY KD2 with TYR92yieldsadeviationof themolecularx axesof about15U ; they andzaxesdirectionsdif-fer by about60U . Theratherlargedeviationsarenotsurprisingconsideringthepresentresolutionof X-ray diffractiondata.

7.4 Conclusion

Using the PSII cc singlecrystals,it wasshown that high-field EPRyields the sen-sitivity andthespectralresolutionto analyzesmall proteinsinglecrystalscontainingorganicradicals.Consideringtheexcellentqualityof theobtainedspectra,it shouldbepossibleto performexperimentswith singlecrystalsassmall as1 nl (3 W 1011 spins).Also, thanksto theexcellentresolution,verydetailedspectracanbeobtainedthatallowthe investigationof crystalswith a considerablenumberof magneticallyinequivalentradicals(8 in thisspecificcase).

The g tensorand the dominanthyperfineinteractiontensorsfor the Y KD radicalcouldbedeterminedwith very goodaccuracy from combinedhigh field EPRandX-bandENDORexperiments.Thehighaccuracy allowedusto derivepreciseorientationinformationaboutthe g tensorfrom singlecrystalEPRspectraand,thereby, theori-entationof theradicalitself. This detailedinformationaboutpotentiallyfunctionallyrelevantradicalscanbeevenobtainedfrom singlecrystalswhosequality is insufficientfor X-ray diffractionstructuralanalysissinceEPRexperimentsaremuchlessaffectedby mosaicityof the crystals. The knowledgeobtainedfrom theseEPRexperimentscanbederivedfrom X-ray structuralanalysisonly atveryhighresolutions.Thus,highfield EPRexperimentscomplementX-ray diffractionasa tool for theinvestigationofproteinstructure.

ThedarkstableY KD radicaltargetedin thiswork providesagoodtestcasefor EPRonorganicradicalsin thePSII ccsinglecrystals.With theseexperimentsandthesub-sequentsuccessfulanalysis,a foundationfor theinvestigationof furtherparamagneticspeciesin thesecrystalshasbeenlaid.

REFERENCES

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[3] DekkerJ.P., BoekemaE.J.,Witt H.T., & RögnerM., Refinedpurificationandfurtherchar-acterizationof oxygen-evolving andtris-treatedphotosystemII particlesfrom the ther-mophilic cyanobacteriumSynechococcuselongatus,Biochim. Biophys.Acta 936, 307–318(1988).

[4] Barry B.A., BoerusR.J.,& dePaulaL.C., Theuseof cyanobacteriain thestudyof thestructureand function of photosystemII, in The Molecular Biology of Cyanobacteria(BryantD.A., ed.),pp.217–257,Kluwer AcademicPublishers(1994).

[5] ZouniA., JordanR.,SchlodderE.,FrommeP., & Witt H.T., FirstphotosystemII crystalscapableof wateroxidation,Biochim.Biophys.Acta1457, 103–105(2000).

[6] DaviesE.R.,A new pulseENDORtechnique,Phys.Lett.47A, 1–2(1974).

[7] HogansonC.W. & BabcockG.T., Protein-tyrosylinteractionsin photosystemII studiedby electronspinresonanceandelectronnucleardoubleresonancespectroscopy: Compar-isonwith ribonucleotidereductaseandin vitro tyrosine,Biochemistry31, 11874–11880(1992).

[8] O’Malley P.J.& EllsonD., 1H, 13C and17O isotropicandanisotropichyperfinecouplingpredictionfor thetyrosyl radicalusinghybrid densityfunctionalmethods,Biochim.Bio-phys.Acta1320, 65–72(1997).

[9] Himo F., GräslundA., & ErikssonL.A., Densityfunctionalcalculationsonmodeltyrosinradicals,Biophys.J. 72, 1556–1567(1997).

[10] FasanellaE.L. & Gordy W., Electronspin resonanceof an irradiatedsinglecrystal ofL-tyrosine-HCl,Proc.Natl. Acad.Sci.USA62, 299–301(1969).

[11] DorletP., RutherfordA.W., & Un S.,Orientationof thetyrosylD, pheophytin anion,andsemiquinoneQP gA radicalsin photosystemII determinedby high-fieldelectronparamag-neticresonance,Biochemistry39, 7826–7834(2000).

[12] Farrar C.T., GerfenG.J., Griffin R.G., Force D.A., & Britt R.D., Electronicstructureof the YD tyrosyl radical in photosystemII: A high-frequency electronparamagneticresonancespectroscopicanddensityfunctionaltheoreticalstudy, J. Phys.Chem.B101,6634–6641(1997).

[13] GilchristM.L., Ball J.A.,RandallD.W., & Britt R.D.,Proximityof themanganeseclusterof photosystemII to theredox-active tyrosineYZ, Proc.Natl. Acad.Sci.USA92, 9545–9549(1995).

[14] RigbyS.E.J.,NugentJ.H.A.,& O’Malley P.J.O.,Thedarkstabletyrosineradicalof pho-tosystem2 studiedin threespeciesusingENDORandEPRspectroscopies,Biochemistry33, 1734–1742(1994).


[15] Warncke K., BabcockG.T., & McCracken J., Structureof the YD tyrosineradical inphotosystemII asrevealedby 2H electronspinechomodulation(ESEEM)spectroscopicanalysisof hydrogenhyperfineinteractions,J. Am.Chem.Soc.116, 7332–7340(1994).

[16] CarringtonA. & McLachlanA.D., Introductionto MagneticResonancewith Applicationsto ChemistryandChemicalPhysics, chapter6.4,Harper& Row (1967).

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[20] Gulin V.I., Dikanov S.A., Tsvetkov Y.D., Evelo R.G., & Hoff A.J., Very high fre-quency (135 GHz) EPR of the oxidized primary donor of the photosyntheticbacteriaRb. sphaeroidesR-26andRps.viridis andof Y PD (signalII) of plantphotosystemII, PureAppl.Chem.64, 903–906(1992).

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[23] TangX.S.,ChisholmD.A., DismukesG.C.,BrudvigG.W., & Diner B.A., Spectroscopicevidencefrom site-directedmutantsof synechocystisPCC6803in favor of a closeinter-actionbetweenhistidine189andredox-active tyrosine160,bothpolypeptideD2 of thephotosystemII reactioncenter, Biochemistry32, 13742–13748(1993).

[24] EngströmM., Hime F., GräslundA., Minaev B., VahtrasO., & Agren H., Hydrogenbondingto tyrosyl radical analyzedby ab initio g-tensorcalculations,J. Phys.Chem.A104, 5149–5153(2000).

[25] StoneA.J.,Gaugeinvarianceof theg tensor, Proc.R.Soc.A 271, 424–434(1963).

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[28] BoekemaE.J.,van BreemenJ.F.L., van RoonH., & Dekker J.P., Arrangementof pho-tosystemII supercomplexesin crystallinemacrodomainswithin thethylakoid membraneof greenplantchloroplasts,J. Mol. Biol. 301, 1123–1133(2000).

[29] Zouni A., Witt H.T., KernJ.,FrommeP., KraussN., SaengerW., & Orth P., Proteindatabank,accesscode1FE1:Crystalstructureof photosystemII, http://www.rcsb.org/pdb.

Chapter 8

High Field EPR on the QuinoneAcceptor RadicalsQ SA and Q SB inReactionCentersfr om Rhodobactersphaeroides R26

In thephotosyntheticreactioncenterof purplebacteria,photoinducedelectrontrans-fersproceedalonga seriesof cofactorsasdescribedin chapter5. Thefinal cofactorsalongthischainarethequinonesQA andQB. InvestigatingthecorrespondingradicalsQ L KA andQ L KB by EPRandENDORhelpsto understandtheir electronicstructure.Foran understandingof the electrontransferprocessitself, however, an analysisof theelectronicinteraction,namelytheexchangeinteraction,betweenthe two quinonesisessential.

In thenormalreactioncycleof thebRC,QB is reducedby two consecutiveelectrontransfersthatproceedvia QA. Therefore,a biradicalstateQ L KA QL KB appearsasa func-tional intermediatein theenzyme.Whenthis intermediatestateis trapped,EPRcanaccessthe spin-spininteractionsbetweenthe individual radicalsandprovide insightinto theelectroniccouplingbetweenthecofactors.

Thequinoneradicalsin bacterialreactioncentersarenormallycoupledto a para-magnetichigh-spiniron ion. This presentsa major difficulty for EPRexperiments,sincethemagneticcouplingleadsto greatlyincreasedspinrelaxationratesand,con-sequently, severehomogeneousbroadeningof the EPRspectra. It has,however, bedemonstratedthat the iron canbeexchangedby severalotherionswhile maintainingtheactivity of thereactioncenters[1, 2]. In particular, theiron canbesubstitutedby adiamagneticZn2J ion. This substitutiongreatlydecreasesthelinewidth andallows toobtainEPRspectrawith excellentresolution.

117

118 CHAPTER8. QL KA AND Q L KB IN BACTERIAL PHOTOSYSTEM

8.1 Simulation of Radical Pair Spectra

In thepreviouschapters,isolatedS F 12 radicalshavebeeninvestigated.A coupledrad-

ical systemis morecomplex andconsequentlyrequiresmoresophisticatedtechniquesfor theanalysisandinterpretationof theEPRspectra.

8.1.1 Spin Hamiltonian for a Spin CoupledRadical Pair

The spin coupledradicalpair underconsiderationcanbe describedby the g tensorsof theindividual spinsS1 F 1

2 andS2 F 12 anda couplingtensorD that includesdipo-

lar andexchangeinteraction. Neglectingunresolved hyperfineinteractions,the spinHamiltonianis thus

H F µB vBT0 W g1 W vS1 H g2 W vS2 H vST

1 W D W vS2 M (8.1)

This Hamiltonianis formally similar to a single radicalwith hyperfineinteractions.However, severalcomplicationsmayarise:x SincetheelectronicZeemanenergiesof theuncoupledspinsaresimilar, rather

small inter-electroncouplingscanbridge this energy difference. Under theseconditions,the propereigenstatesof the systemchangesignificantly from theuncoupledcase.As a consequence,the probabilitiesfor the variousEPRtran-sitionsaremodified,enabling“forbidden” transitions.For a correctsimulation,therelative intensitiesof all EPRtransitionshasto betakeninto account.x Thetransitionintensitiesalsodependon thepopulationof theenergy levels.Athigh temperatures,theBoltzmannfactordescribingthelevel populationscanbe

linearized,i.e. eL EkBT E 1 y E

kBT . The populationdifferencefor pairsof energylevelswith thesameenergy differenceis thusconstant.Thisapproximationis nolongerapplicablewhentheconditionE kBT doesnot hold. At 94 GHz, thetransitionenergy correspondsto a temperatureof T F hν

kBE 4 M 5 K. Therefore,a

ratherpronouncedtemperaturedependenceof thespectracanbeexpected,evenatmodestcryogenictemperatures.

Fig. 8.1 illustratesthefour level spinsystemin thelimits of weakandstrongspin-spin coupling, respectively. Whenthe coupling is very anisotropic,both casesmayapply, dependingon theorientationof thesamplewith respectto theappliedmagneticfield. Thegeneralorientationdependenceof thedipolarinteractionis givenin fig. 8.2.

Simulation Program

An analyticaltreatmentof theradicalpair problemis ratherstraightforwardwhenthecoupling tensorsg1, g2, and D are isotropic (seee.g. [3]). This conditiondoesnotapply here,however. This makes it necessaryto resortto perturbative approaches.

8.1. SIMULATION OFRADICAL PAIR SPECTRA 119

T+=

T−=

2

1T0 = ( + ) 2

1−S= ( )

I

II III

IV

II

I IV

III

Figure8.1: Energy levelsandallowedEPRtransitionsfor a radicalpairwith isotropiccouplings.Left:Weakcouplinglimit: transitionsI–IV areallowed.Theeigenstatesaredominatedby theZeemanenergydifferencebetweenboth radicalswhile the smallerspin-spininteractionactsasa small perturbation,shifting energies. Right: Strongcoupling limit: The systemseparatesinto a singletandthreetripletstates.Intersystemcrossing(transitionsIII andIV) is forbidden.TheZeemanenergydifferencebetweentheradicalsactsasasmallperturbation.

Higherorderperturbationtheoryleadsto ratherlengthy expressions,however. Sincein practicecomputersareusedanyway for the simulationof the spectra,it wasde-cidedto employ a full numericaldiagonalizationof theHamiltonianfor determiningeigenvalues,eigenstates,andtransitionmatrixelements.

To accomplishthis, a new C++ program(not given here)waswritten within thecontext of this thesis. The basicprocessingstepsperformedfor the simulationofradicalpair spectraareasfollows:x A setof isotropicallydistributedorientationsis generatedto simulatetheensem-

ble in frozensolution.x For eachorientation,thefield strengthindependentpartof thespinHamiltonianis calculatedfrom theinput parameters.x For eachorientationandfield strength,thetotal Hamiltonianis calculatedfromthe field dependentand field independentcontributions. This Hamiltonianisthendiagonalized.x Thedipolematrixelementsfor transitionsbetweenall levelsarecalculated.x TheBoltzmannpopulationof theenergy levelsis calculated.x The EPRsignalcontribution for the chosenorientationandfield is calculatedfrom thepopulationdifference,dipolematrix element,andthedeviation of thetransitionenergy from the microwave frequency (usinga Lorentzianlineshapefunction).


Figure 8.2: Angulardependenceof theinteractionbetweentwo paralleldipoles( cos2 θ 13). When

thedistancevectoris at the“magic angle”of 54u 7_ relative to thedirectionof thedipolemoments,theinteractionvanishes.

8.2. MATERIALS AND METHODS 121x The spectrumis convoluted with a Gaussianto accountfor inhomogeneousbroadening.

Thesimulationthusmimicsthequantummechanicsof thesystemwithout resort-ing to possiblyunjustifiedapproximations.

In many otherprograms,thespectrumis calculatedin thefrequency domain,anda nonlineartransformationis usedfor conversionto field-sweptspectra.As explainedabove, the propereigenstatesof the systemmay dependto a much larger extent ontheappliedfield thanin simplersystems.A conversionof spectrafrom thefrequencydomainto amagneticfield axisdoesnotreflectthisdependency andis thereforepoten-tially inaccurate.Theseproblemsarecompletelyavoidedby diagonalizingtheHamil-tonian separatelyfor eachfield strengthB0. By using an interative diagonalizationmethod(complex Jacobirotations,seee.g.[4]) andusingthesetof calculatedeigen-vectorsasthe initial transformationmatrix for thenext diagonalization,thecomputa-tion timepenaltyfor thiscanbekeptmoderate.


Thebacterialreactioncentersamplesdescribedwerepreparedby E. Abresch,andtheradical stateswere generatedby E. Abreschand M. Paddockin the group of Prof.G. Feher(UCSD,La Jolla).

8.2.1 SamplePreparations

Reactioncenterswereisolatedfrom RhodobactersphaeroidesR26. To decreasetheEPRlinewidth andincreasespectralresolution,the non-heme,high-spinFe(II) cou-pled to thequinoneacceptorradicalsQL KA andQL KB wassubstitutedwith diamagneticZn(II) following theproceduresdescribedin [1, 2]. In orderto reduceinhomogeneousbroadeningdueto unresolvedhyperfineinteractions,QA andQB wereexchangedwithdeuteratedubiquinone-10.The reactioncenterswereincubatedfor 24 hoursin D2Oto remove otherexchangeableprotons.All sampleswerefilled in CV7087Ssuprasilcapillaries(seechapter2).

Q L KA and Q L KB radicals. Quinoneradicalsweregeneratedby illuminationwith asin-gle,saturationlaserflash.Excesscytochromec wasaddedto reducetheprimarydonorradicalafterphotooxidation.Dueto theshortdurationof theflash(400nsFWHM atλ F 590 nm), multiple electrontransferswithin the sameRC aresuppressedas thereductionof the donor radical PJ K865, a preconditionto the secondelectrontransfer,occurson a muchslower time scale. SinceQA is an intermediaryacceptor, Q L KA istransientandonly Q L KB is obtained.In orderto trapQL KA , thesamplesweretreatedwithstigmatellin,an inhibitor blocking the QB site andtherebydisablingfurther electrontransfer. After this treatment,thesampleswerefrozenin liquid nitrogen.Specialcare


radical gx gy gz

Q L KA 2 M 00647 3 2 M 00532 3 2 M 00215 3Q L KB 2 M 00628 3 2 M 00530 3 2 M 00217 3

Table8.1: Principalg valuesof theQ [A andQ [B statesin bRCobtainedfrom simulationsof the94GHzEPRspectra.

wastakenduring thehandlingof thesamplesto avoid light exposurethatwould leadto additionalphotochemistry.

Q L KA Q L KB biradical. Two methodswereusedto obtainthe QL KA Q L KB biradicalstate.(i) Q L KB samplespreparedasdescribedabove wereilluminatedat T F 190 K. SincetheelectrontransferQ L KA H Q L KB I QA H QB

2 L is thermallyactivated,theQ L KA QL KB stateis trappedandstabilizedby further cooling down underillumination to 77 K in liq-uid nitrogen. (ii) Reactioncentersweredoubly reducedto the QB

2 L stateby addingNaBH4. Sincethedoublereductiongoesalongwith protonationof QB, increasingthepH valueof thesamples,by withdrawing protonsfrom QB, shiftstheequilibriumfromtheQAQB

2 L statetowardsQ L KA QL KB . A pH of 10M 5 wasusedin thesamples.

8.2.2 cw and PulsedEPR

Cw EPRexperimentswereperformedusingtheproceduresin chapter2. Specialcarewastakento avoid light exposureto thesamples.At low temperatures( m 20 K), spinrelaxationratesin the Q L KA Q L KB biradicalsamplewereso low that no undistortedcwspectracould be obtained,even at the lowestmicrowave power settingof the spec-trometer(5 nW). Field-sweptelectronspinechoexperimentswith low repetitionrates(down to 5 sL 1) wereusedto accessspectraat theselow temperatures.For easiercom-parisonwith thefield-modulatedcw spectra,thefirst derivativeof theESEspectrawascalculated.

8.3 Results

Fig. 8.3 shows cw EPR spectrafor the three radical statesof bRC investigatedatT F 100K. All spectraarewell resolved with linewidthsbelow 1 mT. The Q L KA andQL KB statespectraarewell reproducedby simulations(dotted).Theprincipalg valuesresultingfrom thesesimulationsaregivenin tab. 8.1.Only thegx valuedifferssignifi-cantlyfor thesestates.This maybeattributedto differencesin thehydrogenbondstobothquinones,similar to thegx shift in thecaseof tyrosinesdiscussedin chapter7.

Thegx andgy edgesin theQ L KA Q L KB biradicalspectrumaresplit asa consequenceof thecouplingbetweenspinson bothradicalswhile no splitting is resolvedon thegz

component.Thesefeaturesarealsosignificantlyshiftedrelative to thesingleradical

8.3. RESULTS 123

Figure8.3: Comparisonof cwEPRspectra(94GHz)of theradicalstatesQ [A andQ [B andthebiradicalstateQ [A Q [B in bRC(T T 100K). TheQ [A andQ [B singleradicalspectradiffer mainlyin thegx value.Thebiradicalspectrumexhibits line splittingsdueto theinteractionof thespins.It is notasuperpositionof theQ [A andQ [B spectra.Thedottedspectraaresimulationsof thesingleradicalspectra.Theverticallinesindicatetheprincipalg valuesof thesingleradicals.


Figure 8.4: Cw EPR(94 GHz) spectraof the Q [A radical in frozensolutionat varioustemperatures.Theshapeof thespectrumis temperatureindependent(arrows).

8.3. RESULTS 125

Figure 8.5: Cw EPR(94 GHz) spectraof the Q [B radical in frozensolutionat varioustemperatures.Theshapeof thespectrumis temperatureindependent.


Figure8.6: Cw EPR(94GHz)spectraof thecoupledQ [A andQ [B radicalsin frozensolutionatvarioustemperatures.Thetemperaturedependentpopulationsof thefour spinlevelsstronglyaffect therelativeEPRline intensities.Thespectrafor T T 10 K andT T 5 K arederivativesof field-sweptelectronspinechospectrasinceit wasnotpossibleto obtaincw EPRspectraat thesetemperatureswithoutsaturationartifacts.

8.3. RESULTS 127

Figure8.7: Simulationsof thespectrain fig. 8.6usingtheparametersin tab. 8.2.


spectra.It canthereforebe ruled out that the biradicalspectrumarisesmerelyfroma superpositionof thesingleradicalspectra.Theabsenceof splitting on thegz com-ponentcanbe explainedby the anisotropy of the dipolar interactionterm. Sincethedipolarinteractioncanbebothpositiveor negative,dependingonorientation(fig. 8.2),it cancancelsmalldifferencesof theeffectiveg valuesof bothradicalsfor specialori-entations.

Thelinewidth of thebiradicalspectrumis slightly smallerthanin thesingleradicalspectraof Q L KA andQ L KB . This narrowing is a hint towardsthe presenceof exchangeinteractionbetweenthe quinones.The exchangetendsto delocalizethe spin densityover both radicals. This increasesthe numberof unresolved hyperfineinteractionswhile decreasingthe magnitudeof eachindividual hyperfinecoupling. As a conse-quence,thestatisticalvariationof resonancepositionsis lowered,andthelinewidth isreduced.

Fig. 8.4andfig. 8.5show thesingleradicalcw EPRspectrameasuredover a tem-peraturerangefrom 5 to 100K. No significantchangesareobserved. In contrast,fora four-level systemlike the coupledbiradical, the relative energy level populationsandthusintensitiesof spectralfeaturesdependon thetemperature.This is indeedthecase,ascanbe seenin fig. 8.6. This temperaturedependenceultimately provesthatthespectraaredueto a coupledradicalpair andrulesout thepossibility that theQ L KAandQL KB quinoneradicalsareuncoupled.Otherwise,onemightarguethatthebiradicalspectrumcouldalsobeasuperpositionof Q L KA andQL KB spectrawith changedg tensorsresultingfrom structuralchangesin thebiradicalstate.

8.3.1 Analysisof Biradical Spectra

Theanalysisof the radicalpair spectrais difficult sincethenumberof parametersinthespinHamiltonianof a coupledradicalpair is muchlargerthanfor a singleradical;simultaneously, a lot of detailis obscuredin thefrozensolutionspectra.A full param-etersetis comprisedof theprincipalg valuesfor bothspincarryingsites,therelativeorientationof the g tensors,andthe principal valuesandorientationof the couplingtensorD, amountingto 15 parametersin total.

In thebiradicalspectra,only 5 pronouncedfeaturesarepresent,andthe tempera-turedependenceof thefeatureintensitiesis known. A fit of morethansix independentparametershasthereforeto rely on rathersubtledetailsin thespectra.Thestatisticalmeaningof a fit of 15 independentparametershasthereforeto be takenwith a grainof salt: It canbeexpectedthattheχ2 minimumin theparameterspaceis shallow andthatstrongcorrelationsbetweendifferentparametersexist. As anadditionalcomplica-tion, it is difficult to find theglobal minimumof χ2 asthecomputationaleffort growsexponentiallywith thenumberof parameters.

Theonly remediesto thisproblemareeitherto obtainspectrawith muchlessnoiseanddistortion,or to reducethe dimensionof the parameterspace.Only gradualim-provementswould be feasibleregarding the first point with reasonableeffort. Thesecondoptionrelieson thesimplificationof themodel,or theknowledgeof somepa-

8.3. RESULTS 129

parameter this work [5] X-ray structure[7, 8]J [MHz] 50 60 k 20 -D [MHz] 36M 4 k 0 M 4 30M 9 k 0 M 3 -

φg U y 19 k 10 y 21 k 14 y 14 k 7θg U y 152 k 3 y 190 k 16 y 155 k 7ψg U y 180 k 20 y 197 k 20 y 179 k 7φD U y 93 k 10 y 88 k 6 y 81 k 7θD U y 59 k 3 y 65M 6 k 3 M 5 y 60 k 7d [Å] 16M 3 k 0 M 1 17M 2 k 0 M 2 17M 3/16M 3

Table 8.2: Parametersdeterminedfrom the94 GHz Q [A Q [B biradicalspectrain thefitting proceduresdescribedhereandin [5]. X-ray diffractionexperiments[7, 8] yield only dataof thegeometricalstruc-ture.Thedistanced givenfor theEPRresultsis calculatedfrom D usingthepointdipoleapproximation.For theX-ray structuraldata,d is takenasthedistancebetweenthering centersof Q [A andQ [B (17u 3Å)or asaweighteddistanceof thespincarryingoxygenatoms(16u 3 Å, seetext). TheEuleranglesspecifythe orientationof the Q [B g tensorand the axis of the dipolar coupling tensorrelative to the Q [A gtensor, respectively, accordingto thedefinitionin appendixB.2.

rametersfrom othersources.Onesimplificationis to neglectthedeviation of thecou-pling tensorD from uniaxiality, i.e. E F 0. This alleviatestheproblemonly slightly,however.

In thefollowing analysis,two differentapproacheshavebeenpursued:x Within the collaborationproject, R. Calvo (UniversidadNacionaldel Litoral,Argentina)employed a global fit1 [5] of the 14 remainingparameters,usingarefined,but computationallyveryexpensivefitting method(simulatedannealing,seee.g.[6]) thatis suitedto findingtheglobalminimumof χ2. Thismethoddoesnot improve on thestatisticalsignificanceof thefit, however.x For this thesis,it wasassumedthat the g tensorsof Q L KA andQ L KB radicalsareidentical in the biradical QL KA Q L KB and single radical QL KA /Q L KB states,respec-tively. Thisassumptionis purelytentativeandcanonly bejustifieda posteriori.The principal valuesof the Q L KA andQ L KB g tensorswere taken from tab. 8.1.This reducestheparameterspaceto 8 dimensions(relative orientationof thegtensors,orientationof the spin-spincouplingtensor, J, andD) which is muchmorefavorablein relationto theamountof detailvisible in thespectra.

The resultingparametersetsfor bothanalysismethodsareshown in tab. 8.2; thesimulatedspectraareshown next to theexperimentalonesin fig. 8.7. Theestimateduncertaintiesfor theparametersdiffer greatly, reflectingtheirsignificancefor thespec-trum. It is noteworthy, however, thattwo Eulerangles,θg andθD, seemto beremark-ably well definedanduncorrelatedto otherparametersfor thesimulationusingfixed

1Some34GHz EPRspectratakenat theFehergroupin La Jollawerealsousedin theanalysis.


g principalvalues.In particular, theobtainedvaluesarevery closeto thegeometricalstructureobtainedfrom X-ray diffractiondata[7, 8]. Only a mimimumvaluefor theexchangecouplingparameterJ could be given using the analysismethodassumingfixed g values: For larger couplings,the forbiddentransitionsIII and IV in fig. 8.1becometooweakto noticeablyaffect thespectra.SinceJ is thereforeeffectively elim-inatedasa parameter, thefit is likely to becomelessambiguous,andthereliability oftheobtainedotherparametersis in turn increased.

8.4 Discussion

8.4.1 Influenceof Fitting Methodsand Reliability of Parameters

The94 GHz cw EPRspectraobtainedfrom frozensolutionsof deuteratedbRCin themono-andbiradicalstatesQ L KA , Q L KB , andQL KA Q L KB have excellentspectralresolutionand a good signal to noiseratio. No resolved hyperfinestructureis observed. Inaddition,thebiradicalspectrashow a distincttemperaturedependence.

From thesecharacteristics,onewould expect that an analysisof the spectraandthederivationof theparametersin thespinHamiltonianis rathereasy. This is indeedthe casefor the single radical (QL KA andQL KB ) spectrawhich are fully characterizedby the principal valuesof g. The Q L KA Q L KB biradical is, however, characterizedby amuchlargernumberof parameters.Sincethegeometryof QA andQB is fixedrelativeto eachother in the protein, orientationparametersdo not averageout in a frozensolutionspectrum.Thisaccountsfor 6 additionalparameters,on topof the6 principalg valuesand3 principal valuesof the spin-spincouplingtensor. Sincethe biradicalspectrado not exhibit nearlyasmany characteristicfeatures,theanalysisis, contraryto whatintuition might suggest,ratherdifficult.

Both analysismethodsusedyield comparablevalues(seetab. 8.2) that arecloseto what thestructuralmodelderived from X-ray diffractionexperimentssuggests.Acloserlook revealshowever somesignificantdifferences:x ThedipolarcouplingstrengthsD differssignificantlyfor bothanalysismethods.

Thederivedradicaldistancesreflectthis mismatch.x Theanglesθg describingtherelative orientationof thequinoneradicalsdiffersby considerablemorethanthe error margin. It is alsonoteworthy that the as-sumptionof identicalg valuesfor thesingleandbiradicalstatesleadsto amuchdecreasederrormargin.x Theanglesψg agreewithin their errormargins. Theerrormarginsarehoweverratherwide,andthestatisticallymostlikely valueis thereforeratherdifferent.x TheanglesθD differ, eventakingerrormarginsinto account.

8.4. DISCUSSION 131

With theexceptionof thedipolarcouplingstrengthD, theanalysisassumingfixedg factorsyieldsconsistentlyvaluesthatarein betteragreementwith thestructuraldatafrom X-ray experiments.This suggeststhat theassumptionof unchangedg valuesisjustifiedandthattherespective resultsmaybemorereliable.

This inrepretationseemshowever to be falsifiedby thedisagreementof thespin-spin couplingstrengthD andthe Q L KA –QL KB distanced calculatedfrom it. Here,theglobal unrestrictedfit yields resultsthat appearto be in muchbetteragreementwiththeX-ray structuralmodel. It mustbeconsidered,however, that thequinoneradicalsarerathercloseto eachotherandthatthespindensityis delocalizedovereachquinoneradical.Undertheseconditions,thepoint dipoleapproximationfor thecalculationofthedipolarcouplingstrengthis notapplicableanymore.

A considerablepartof thespindensityin quinoneanionradicalsis expectedat thefunctionaloxygenatoms.Therefore,two limiting modelcasesfor the calculationofthedipolarinteractioncanbegiven:x Thespindensityis assumedto belocalizedat thecentersof thequinonerings.x 50%of thespindensityareassumedto belocalizedateachoxygenatom.

Using the structuraldatafrom X-ray diffractions[7, 8], oneobtainsa center-to-centerdistanceof 17M 3 Å for thequinones.Using theoxygen-oxygendistancesfromthesamesource(seefig. 8.8),weighedby ther L 3 dependency of thedipolarinteractionstrength,oneobtainsaneffectivedistance

deff F d L 313 H d L 3

14 H d L 323 H d L 3

24

4 L 13

(8.2)

thatamountsto 16M 3 Å. This is in excellentagreementwith thedistancefoundassum-ing unchangedg factors.

The real spin densitydistribution certainly lies betweenthesetwo extremesandshouldleadto a couplingstrengthbetweenthe two valuesgiven in tab. 8.2. A com-promisebetweenbothmodels,assuming25%spindensityon eachoxygenand50%locatedin themiddleof thequinonering, yieldsaneffective distanceof 16M 8 Å. Thissimple model compareswell with the 23% spin densityper oxygendeterminedinvitro [9]. On the other hand,the spin density in the protein-boundquinonesleakssomewhat to the ligandsandhydrogenbonds. This would leadagain to an increaseof thedipolarcoupling,or a decreaseof theeffective distancedeff , favoring again thevaluefoundassumingfixedg values.

In any case,it is clearthattheseeminglybetteragreementof thequinone-quinonedistanceobtainedfrom theglobalfit of all parameterswith theX-ray structuralmodelis coincidental,sincedeff , asdeterminedfrom thedipolarcouplingstrengthD, hastobesmallerthanthegeometricaldistanceof thequinonecenters.

Theresultsdiscussedsofar yield mainly informationaboutthegeometricalstruc-ture of the quinoneradicalsin the reactioncenterand onceagain demonstratethe


1 2

34

Figure 8.8: Geometryof thequinonesin theQAQ [B stateof thebacterialreactioncenter[7, 8], usedasanapproximationfor thebiradicalQ [A Q [B statestructure.Thespindensityof thequinoneradicalsis stronglylocalizedat thebold oxygenatomsandcanbemodeledby point dipoles. Thedottedlinesrepresentthedistancesd13, d14, d23, andd24 usedfor estimatingthestrengthof thedipolar interactionterm.

8.4. DISCUSSION 133

usefulnessof EPRexperimentsfor structuralanalysis.However, themostdesiredin-formationis abouttheelectronic structure,i.e. theexchangeinteractionparameterJ.Unfortunately, neitheranalysismethodis able to yield a reliable value for J. Theforbiddentransitionsaretooweakto affect the94GHzEPRspectranoticeably.

This mayseemlike a contradictionto tab. 8.2,wherea valuefor J is given. Calvoclaimsin [5] to obtaina valueof J F 60 k 20 MHz, but readilyadmitsin thesamearticlethattheerrormargin is thestandarddeviationof theresultsfrom severalrunsofthe fitting procedureusingdifferentsequencesof pseudorandomnumbers(“thermalannealing”is astochasticmethod).Thus,thegivenerrormargin reflectsthereliabilityof the fitting procedure andhasno relationwhatsoever to the statisticalerror of thedata. Theratherlargevariationof J for severalfitting runsitself is just anotherman-ifestationthat the94 GHz EPRspectraarevirtually independentof J. This is furtherillustratedby the dependenceof χ2 on J given in [5]: doublingJ from 60 MHz to120 MHz increasesχ2 from 0 M 023 to only 0 M 024 (figure 8 in [5]). A moredetaileddiscussionconsideringthe statisticalsignificanceof fitted parameterscan be foundin [10].

In contrast,the sign of J is unambiguous.The temperaturedependenceof theintensityof theallowedtransitionsin theEPRspectracorrelatesthesignof J with thesignof D. ThedipolarinteractionstrengthD is however alwayspositive.

Recently, similar EPRexperimentshave beenperformedat microwave frequencyof 326 GHz [11, 12]. At thesehigh frequencies,the forbiddentransitionsbecomeclearly visible. From thesemeasurements,the strengthof the exchangeinteractioncouldbedeterminedasJ F 82 k 3 MHz. Alas,[11, 12] donotgiveotherparametersderived from the 326 GHz spectra.With the uncertaintyof J resolved, it would beinterestinghow the g principal valuesand the relative orientationsof the g tensorscompareto thevaluesobtainedin thiswork.

8.4.2 Implications of J for the Electron Transfer Process

While only a lower limit for J could be deducedfrom the dataandanalysisin thisthesis,it is neverthelesspossibleto give anestimatefor theelectrontransferratekET.Accordingto Fermi’s goldenrule, therateis

kET F 2πh

jj ψtot z f l Htot l ψtot z i jj 2 W ρ (8.3)

whereψtot z i and ψtot z f representthe initial and final total wavefunctionsof the sys-tem,respectively, andρ is thedensityof states.In theBorn-Oppenheimer(adiabatic)approximation,theelectronicandlatticecomponentsof thewavefunctionsaredecou-pled. The latticecontributionscanthereforebedescribedby a Franck-CondonfactorF , arriving at

kET F 2πh

F jj ψ f l H l ψi jj 2 (8.4)

usingonly electronicwavefunctionsandtheelectronicHamiltonianH.


Assumingaharmonicpotentialfor latticevibrationsandthermallypopulated,suf-ficiently densephononlevels,theFranck-Condonfactorcanbederivedas[13]

F F 14πλkBT

exp y ∆E H λ 2

4λkBT (8.5)

where∆E is the changeof the enthalpy and λ is the reorganizationenergy of theenvironment.

In the bacterialreactioncenter, the quinonesare physically well separated,andtheoverlapof theelectronwavefunctionsin theQ L KA QL KB statecanbeexpectedto benegligible. In thiscase,J is dominatedby kineticexchange[14],

J F jj ψ f l H l ψi jj 2U

(8.6)

whereU is the separationof the groundstateandthe “ionic” state,i.e. the stateaf-ter electrontransfer. U canthereforebe approximatedby ∆E H λ [15]. Combiningequations8.4,8.5,and8.6yieldstheelectrontransferrate

kET F J W πλkBT

l ∆E H λ lh

W exp y ∆E H λ 2

4λkBT (8.7)

or, when J is given in frequency units and accountingfor the Pauli principle witha factorof 1

2 (sincethe LUMO of Q L KB is alreadyhalf occupiedbeforethe electrontransfer),

kET F J W π3

λkBTl ∆E H λ l W exp y ∆E H λ 2

4λkBT M (8.8)

For T F 280 K andusing λ F 1 M 2 eV [16, 17], ∆E F y 0 M 25 eV [18], one thusarrivesat

kET F 0 M 013 W J M (8.9)

Thelowerlimit of J 50MHz determinedin thiswork yieldskET 0 M 78 W 106 sL 1.TakingthevalueJ F 82 MHz from recentEPRexperimentsat 326GHz [11, 12], oneobtainskET F 1 M 1 W 106 sL 1 which is in excellentagreementwith the estimateof theintrinsicelectrontransferrateke E 106 sL 1 in [18].

Thisagreementshouldnotbeoverrated,however, asit couldbemostlycoinciden-tal, giventhecrudeapproximationsmadeabove. Ontheotherhand,it doescorroboratethe assumptionsaboutthe mechanismof the quinonereduction/protonationprocessdescribedin [18] which led to thereportedintrinsicelectrontransferrate.

8.5 Conclusion

Using94 GHz EPR,it waspossibleto accessandanalyzethecoupledbiradicalstateQL KA Q L KB in deuterated,zincreconstitutedreactioncentersfromRhodobactersphaeroides.

REFERENCES 135

Theanalysisof thespectrayieldedgeometricalinformationthatagreeswith theX-raystructureof theproteinin theQAQ L KB state.

Only a lower limit for thestrengthof theexchangeinteractionJ 50 MHz couldbedeterminedin theanalysissincethecouplingis toostrongcomparedto theZeemananisotropy at 3 M 35 T andthe forbiddentransitionsaretoo weakto be observed. ThevalueJ F 60 k 20 MHz obtainedby an alternateanalysiswithin the collaborationproject doesagreewith this minimum estimate;the given error margin is howeverarguablytoosmall.

TheQL KA Q L KB stateof thebacterialreactioncenterthusreachesthelimits of 94GHzEPRanddemonstratestheneedfor furtherevolutionof EPRtechnologytowardsevenhighermicrowave frequencies.This is confirmedby recentexperimentsat 326 GHz[11, 12] that clearly detectthe forbidden transitionsneededto determineJ. Theelectrontransferrate kET F 1 M 1 W 106 sL 1 derived from J F 82 GHz is in excellentagreementwith anestimategiven in [18] andcorroboratesthesuggestedQ L KB reduc-tion/protonationmechanism.

REFERENCES

[1] DebusR.J.,FeherG.,& OkamuraM.Y., Iron-depletedreactioncentersfrom Rhodopseu-domonassphaeroidesR-26.1 – characterizationand reconstitutionwith Fe2O , Mn2O ,Co2O , Ni2O , Cu2O , andZn2O , Biochemistry25, 2276–2287(1986).

[2] UtschigL.M., GreenfieldS.R.,TangJ.,LaibleP.D.,& ThurnauerM.C., Influenceof iron-removal procedureson sequentialelectrontransferin photosyntheticbacterialreactioncentersstudiedby transientEPRspectroscopy, Biochemistry36, 8548–8558(1997).

[3] CarringtonA. & McLachlanA.D., Introductionto MagneticResonancewith Applicationsto ChemistryandChemicalPhysics, chapter2.6,Harper& Row (1967).

[4] PressW.H., Teukolsky S.A., VetterlingW.T., & FlanneryB.P., NumericalRecipesin C:TheArt of ScientificComputing, chapter11, CambridgeUniversity Press,2nd edition(1992).

[5] Calvo R., AbreschE.C., Bittl R., FeherG., HofbauerW., IsaacsonR.A., Lubitz W.,OkamuraM.Y., & PaddockM.L., EPRstudyof themolecularandelectronicstructureofthesemiquinonebiradicalQg PA Qg PB in photosyntheticreactioncentersfrom Rhodobactersphaeroides,J. Am.Chem.Soc.122, 7327–7341(2000).


[7] Stowell M.H.B., McPhillipsT.M., ReesD.C.,SoltisS.M.,AbreschE.,& FeherG.,Light-inducedstructuralchangesin photosyntheticreactioncenter:Implicationsfor mechanismof electron-protontransfer, Science276, 812–816(1997).


[8] Stowell M.H.B., McPhillips T.M., ReesD.C., Soltis S.M., AbreschE., & FeherG.,Proteindatabank,accesscode1AIG: Photosyntheticreactioncenterfrom Rhodobactersphaeroidesin theD+QB- chargeseparatedstate,http://www.rcsb.org/pdb.

[9] MacMillan F., Lendzian F., & Lubitz W., EPR and ENDOR characterizationofsemiquinoneanionradicalsrelatedto photosynthesis,Mag. Reson.in Chem.33, 81–93(1995).


[11] Calvo R., IsaacsonR.A., AbreschE.C.,PaddockM.L., ManieroA.L., SaylorC., BrunelL.C., OkamuraM.Y., & FeherG., EPRstudyof the semiquinonebiradicalQg PA Qg PB inphotosyntheticreactioncentersof Rb. sphaeroidesat326GHz,Biophys.Journal80, 122(2001).

[12] Calvo R., IsaacsonR.A., PaddockM.L., AbreschE.C., OkamuraM.Y., ManieroA.L.,Brunel L.C., OkamuraM.Y., & FeherG., EPR study of the semiquinonebiradicalQg PA Qg PB in photosyntheticreactioncentersof Rb. sphaeroidesat 326 GHz: Determi-nationof theexchangeinteractionJ0, J. Phys.Chem.B 105, 4053–4057(2001).

[13] MarcusR.A. & SutinN., Electrontransfersin chemistryandbiology, Biochim.Biophys.Acta811, 265–322(1985).

[14] Bencini A. & GatteschiD., EPRof Exchange CoupledSystems, chapter1.2, Springer-Verlag(1990).

[15] OkamuraM.Y., Fredkin D.R., IsaacsonR.A., & FeherG., in Tunnelingin BiologicalSystems(ChanceB., DeVaultD.C.,FrauenfelderH., MarcusR.A.,SchrieferJ.R.,& SutinN., eds.),pp.729–743,AcademicPress(1979).

[16] LabahnA., BruceJ.M., OkamuraM.Y., & FeherG., Direct charge recombinationfromD O QAQgB to DQAQB in bacterialreactioncentersfrom Rhodobactersphaeroidescontain-ing low potentialquinonein theQA site,Chem.Phys.197, 355–366(1995).

[17] Allen J.P., Williams J.C., GraigeM.S., PaddockM.L., LabahnA., & FeherG., Freeenergy dependenceof the direct charge recombinationfrom the primaryandsecondaryquinonesin reactioncentersfrom Rhodobactersphaeroides,Photosynth.Res.55, 227–233(1998).

[18] OkamuraM.Y., PaddockM.L., GraigeM.S.,& FeherG., Protonandelectrontransferinbacterialreactioncenters,Biochim.Biophys.Acta1458, 148–163(2000).

Summary and Outlook

The main focusof this thesisis the applicationof EPRat high magneticfields andmicrowavefrequencies(94GHz)onbiologicalsamples.Fromaninstrumentalpointofview, highfield/highfrequency EPRis morechallenginganddependingonthespecificspectrometerimplementationthanEPRat conventionalfrequencies.The limitationsandpeculiaritiesof thespectrometerusedthroughoutthiswork havebeendescribedinthis thesisto establishacontext for thefollowing methodologicalwork.

In situ optical excitation: Originally, the Bruker spectrometerdid not provide alight accesspath,which is requiredfor time-resolvedmeasurementsof photoinducedprocesses.This spectroscopictechniqueis of particularinterestfor the researchonphotoenzymessuchasphotosyntheticreactioncenters.In orderto enablesuchmea-surements,the sampleholderof the spectrometerhadto be modifiedin cooperationwith themanufacturerby feedinganopticalfiber throughit. A lasersetupwasimple-mentedfor opticalexcitationvia thisaccesspath.Theperformanceof thisarrangementwasdemonstratedby transientEPRexperimentson thetriplet stateof pentacene.

Transition strengthselectivespectroscopy: A commonproblemof high field EPRis theextraordinarysensitivity to contaminationsof thesampleor the resonator. Of-ten,therespectivesignalscanbedistinguishedfrom thedesiredspectrumby theirEPRtransitionmoments.Several experimentsto achieve sucha separationhave beende-scribedin the literature. Thesepulsedexperimentsgenerallyvary the timing of themicrowave pulsesto achieve the desiredseparation.To obtaina spectrum,the mag-netic field strengthB0 hasto be variedaswell. Theseexperimentsneedthereforetomapout a two-dimensionalparameterspaceandareconsequentlycostly in termsofacquisitiontime.

In thisthesis,anovel methodto achievethedesiredseparationhasbeenintroduced.By usingafixed,“soft” microwavepulsesequence,componentsof theEPRsignalthatareassociatedwith differenttransitionmomentsarespreadoutonthetimeaxis.Usinga transientrecorder, onedimensionof theparameterspacecanbescannedin a single“shot”. Only themagneticfield B0 hasto besweptto recorda full spectrum,andtherequiredacquisitiontime is therebyreducedto thatof a one-dimensionalexperiment.In addition,sincethemethodis basedontheuseof low-powermicrowavepulses,it si-multaneouslycircumventsthepower limitationsof thespectrometerusedin thiswork.

137

138 SUMMARY AND OUTLOOK

The viability of the methodhasbeendemonstratedusingdifferentmodelsystemsaswell asorganicandbiologicalsamplesfrom currentresearch.

Themainpartof this thesisdescribesEPRexperimentson radicalstatesin threedif-ferentphotosyntheticreactioncenters.While the samplesarecloselyrelatedandallexperimentsincreasetheknowledgeaboutthephotosyntheticapparatusof plantsandbacteria,eachalsoservesto demonstrateadifferentaspectof 94 GHzEPR.

PhotosystemI: Thecation,radicalstateof theprimarydonorin photosystemI, PJ K700,is characterizedby a small g anisotropy anda large inhomogeneouslinewidth. It isthereforedifficult to resolve the g tensorusingconventionalEPR.In earlierwork, itwas necessaryto deuteratethe frozen solution sampleseven for 140 GHz EPR,orto utilize microwave frequenciesashigh as325GHz in orderto resolve theg tensorprincipalvalues.

In this thesis,PJ K700 hasbeenexaminedusing 94 GHz EPR in single crystalsofprotonatedphotosystemI. Theseexperimentsallowedto deriveboththeprincipalval-uesandtheorientationof theg tensorwith respectto thecrystalaxessystemat veryhighprecision.Sincethis informationcanbecomparedwith thegeometricorientationof P700 obtainedfrom x-ray structuralanalysis,it is of particularimportancefor anunderstandingof theelectronicnatureof thepair of chlorophylls thatformsP700.

PhotosystemII: The crystallizationof photosystemII of oxygenicphotosynthesishasonly recentlybeenaccomplished.This thesisreports,to my knowledge,thefirstsuccessfulEPR experimentson a radical statein single crystalsof photosystemII.Theorientation-dependent94 GHz EPRspectracouldbefully analyzedwith thehelpof hyperfinecouplingdataobtainedfrom frozensolutionENDORexperiments.Thegtensor(bothprincipalvaluesandorientation)couldbedeterminedwith veryhighaccu-racy. Dueto a non-crystallographicsymmetryin thesinglecrystals,it waspossibletogivetheorientationof g with respectto adefinedsite,removing otherwiseunavoidableambiguitiesin correlatingEPRandx-ray diffractionresults.Theverygoodresolutionof theY KD spectraandtheabsenceof noticeableg strainis attributedto a well-definedbindingsituationin the protein. In particular, a hydrogenbondbetweenthe tyrosineandtheproteinbackbonecouldbeobservedby its effecton theg tensorandasplittingof otherwisesymmetryrelatedhyperfinecouplings.

Bacterial reaction center: Finally, the radical statesQ L KA , Q L KB , and the biradi-cal stateQL KA Q L KB in zinc-reconstitutedbacterialreactioncentersfrom Rhodobactersphaeroideswereinvestigatedby 94 GHz EPR.Usingtheprincipalvaluesof theQ L KAandQ L KB g tensors,thedipolarcouplingof the radicalsin theQ L KA QL KB statecouldbeanalyzed.Theresultinggeometricinformation,relativeorientationanddistanceof theradicals,is in excellentagreementwith the x-ray structureof the bacterialreaction

139

centerin theQL KB state.Theexchangecouplingbetweenthequinonesis however toostrongto bederivedfrom theseexperiments,andonly a lower limit J 60MHz couldbegiven.

It canbe concludedthat,at this time, 94 GHz EPRis still a challenging,but alsoanimmenselypowerful spectroscopictechnique.While commontechniqueslike time-resolvedEPRon light-inducedspeciescanbetransferedto high field/high frequencyEPRwith tricky designconcepts,moregenericproblemslike thesensitivity towardsunwantedcontaminationsignalscanbesolvedby thedevelopmentof new experimen-tal methods.

It is not theapplicationof high frequenciesalonewhich makes94 GHz EPRuse-ful. This is exemplifiedby theexperimentsonthephotoenzymes:Thespectrumof thePJ K700 radicalin frozenphotosystemI solutionis very poorly resolved,evenat consid-erablyhigherfrequencies.However, combinedwith theuseof proteinsinglecrystalsfacilitatedby the high sensitivity of high field EPR,surprisinglypreciseinformationcanbegainedfrom aseemingly“hopeless”system.In contrast,theinvestigationof theY KD radicalin singlecrystalsof photosystemII is challengingnot becauseof a lack ofresolution,but dueto thesheeramountof resolvedfeaturesin theEPRspectra.In con-junctionwith supportingENDORexperimentsand,equallyimportant,theexploitationof thecrystalsymmetriesin theanalysis,it is again possibleto obtainprecisedataontheelectronicandgeometricstructureof thesample.

Thespectraof coupledquinoneradicalsin zinc-reconsitutedbacterialreactioncen-ters exhibit excellent resolutionand a very good signal to noiseratio along with asimplestructure.At first, it comesasa surprisethat thestrengthof theexchangein-teractioncould not be derived undertheseconditions. The analysisrevealsthat themagneticfield usedat 94 GHz is simply not sufficient to breakapartthestrongcou-pling, andessentialtransitionsarenot observable. Findingssuchasthis motivatethedesirefor EPRspectroscopy atevenhigherfrequencies.

It will beinterestingto investigateotherparamagneticstatesin thesephotoenzymeswith 94 GHz EPR.In particular, thecombinationof varioustechniquesshouldproveextremelyuseful. 94 GHz on transient,photoinducedspecieswill allow to obtainin-formationaboutotherwiseinaccessiblestates.Theobservationof radicalpairsyields– via the dipolar interaction– specificgeometricalinformationalreadyin frozenso-lution samples. In combinationwith the useof single crystals,even more detailedinformationcanbeobtained.

Another interestingpossibility will be 94 GHz ENDOR experiments. The in-creasedorientationselectivity shouldallow to obtainboth thestrengthandtheorien-tationof hyperfineinteractionsand,therefore,theelectronicstructureof paramagneticstates.ENDORon singlecrystalsshouldincreasetheprecisionof theseexperimentsevenmore.Finally, ENDORon light-inducedtransientstates,possiblyevenin singlecrystals,would greatlycontributeto anunderstandingof thepreciseworking of these

140 SUMMARY AND OUTLOOK

photoenzymes.

Zusammenfassungund Ausblick

DerSchwerpunktdieserArbeit ist dieAnwendungvonEPRbeihohenMagnetfeldernundMikrowellenfrequenzen(94GHz)aufbiologischeProben.In instrumentellerHin-sicht ist Hochfeld-/Hochfrequenz-EPRim Vergleichzu EPRbei konventionellenFre-quenzenanspruchsvoller undmehrvomjeweilsverwendetenSpektrometerbeeinflußt.Die BeschränkungenundEigenheitendesin dieserArbeit durchgehendverwendetenSpektrometerswurdeneingangsbeschrieben,umdieRahmenbedingungenfür die fol-gendenmethodischenArbeitenfestzulegen.

Optische in situ Anr egung: UrsprünglichsahdasSpektrometerder Firma BrukerkeinenoptischenZugang,wie erfür zeitaufgelösteMessungenanlichtinduziertenPro-zessennötig ist, vor. DiesesSpektroskopieverfahrenist jedochfür die Untersuchungvon Photosytemen,wie z.B. denReaktionszentrender Photosynthese,besondersin-teressant.Um solcheMessungenzu ermöglichen,wurdederProbenhalterdesSpek-trometersin Kooperationmit demHerstellerdurchEinbringeneinesLichtleitersmo-difiziert. Ein Laseraufbauzur optischenAnregungüberdiesenZugangwurdeerstellt.Die Leistungsfähigkeit dieserAnordnungwurdedurchtransienteEPR-MessungenamTriplettzustandvon Pentacenaufgezeigt.

Übergangsstärkenselektive Spektroskopie: Ein häufigesProblemder Hochfeld-EPRliegt in deraußergewöhnlichenEmpfindlichkeit auf VerunreinigungenderProbeoderdesResonators.Oftmalskönnendie entsprechendenSignaleanhandihrer EPR-Übergangsmatrixelementevom erwünschtenSpektrumunterschiedenwerden.In derLiteratur wurdenmehrereMethodenbeschrieben,die solcheineTrennungermögli-chen. DiesegepulstenExperimentevariierengrundsätzlichdie zeitlicheAbfolge derMikrowellenpulse,um die erwünschteTrennungzu erzielen. Um ein Spektrumzuerhalten,mußdie magnetischeFeldstärke B0 ebenfalls variiert werden.DieseExperi-mentemüssendeshalbeinenzweidimensionalenParameterraumerfassenundsind inderFolgesehrzeitaufwendig.

In dieserArbeit wurdeein neuesVerfahrenvorgestelt,mit demdie gewünschteTrennungerzielt werdenkann. Durch die VerwendungeinerfestenFolge “weicher”MikrowellenpulsewerdendiezuverschiedenenÜbergangsstärkengehörendenSignal-anteileauf derZeitachseausgebreitet.Mit einemTransientenrecorderkanneinekom-pletteDimensionin einemeinzigen“Schuß” erfaßtwerden. Nur dasMagnetfeldB0

141

142 ZUSAMMENFASSUNGUND AUSBLICK

mußzurAufnahmeeinesvollständigenSpektrumsnochvariiertwerden.Die erforder-liche Meßzeitreduziertsichdamitauf die eineseindimensionalenExperiments.WeildiesesVerfahrenaußerdemauf der Verwendungvon Mikrowellenpulsenmit kleinerLeistungbasiert,umgehtesgleichzeitigdie Beschränkungendesin dieserArbeit ver-wendetenSpektrometers.Die Praxistauglichkeit dieserMethodewurdeanhandver-schiedenerModellsystemeebensowie an organischenund biologischenProbenausderaktuellenForschungdemonstriert.

Der HauptteildieserArbeit beschreibtEPR-ExperimenteanradikalischenZuständenin drei verschiedenenReaktionszentrender Photosynthese.Obwohl die Probenengverwandtsindundalle ExperimentezumWissenüberdenPhotosyntheseapparatvonPflanzenundBakterienbeitragen,zeigtjedeProbeeinenanderenAspektder94GHz-EPRauf.

PhotosystemI: Der kationische,radikalischeZustanddes primärenDonatorsinPhotosystemI, PJ K700, ist durcheinegeringeg-AnisotropieundeinegroßeinhomogeneLinienbreitegekennzeichnet.Es ist deshalbschwierig,deng-Tensormit konventio-nellerEPRaufzulösen.In früherenArbeitenwar esselbstbei 140GHz nötig, die ge-frorenenLösungsprobenzu deuterierenodersolchhoheMikrowellenfrequenzenwie325GHzzuverwenden,umdie Hauptwertedesg-Tensorsaufzulösen.

In dieserArbeit wurdePJ K700 mit 94 GHz-EPRin Einkristallenvon protoniertemPhotosystemI untersucht.DieseExperimenteerlaubtenes,sowohl die Hauptwertewie auchdie Orientierungdesg-TensorsbezüglichderKristallachsenmit hoherGe-nauigkeit zu bestimmen.Da dieseInformationmit der geometrischenOrientierungvon P700, die ausRöntgenbeugungsexperimentenerhaltenwurde,verglichenwerdenkann,ist sievon besondererBedeutungfür dasVerständnisderelektronischenNaturdesChlorophyllpaares,dasP700 bildet.

PhotosystemII: Die Kristallisationvon PhotosystemII deroxygenenPhotosynthe-seist erstvor kurzemgelungen.DieseArbeit berichtetvon denmeinesWissensnacherstenerfolgreichenEPR-ExperimentenaneinemradikalischenZustandin Einkristal-len von PhotosystemII. Die orientierungsabhängigen94 GHz-EPR-Spektrenkonntenmit Hilfe von Hyperfeinkopplungsdaten,die durchENDOR-Experimenteangefrore-ner Lösunggewonnenwurden,vollständiganalysiertwerden.Der g-Tensor(sowohlHauptwertewie auchOrientierung)konntemit hoherGenauigkeit bestimmtwerden.DurcheinenichtkristallographischeSymmetriein denKristallenwar esmöglich,dieOrientierungvon g bezüglicheinerdefiniertenSite, ohnedie ansonstenunvermeid-barenMehrdeutigkeiten bei der Korrelationvon Ergebnissenausder EPR und derRöntgenbeugung,anzugeben.Die sehrhoheAuflösungderY KD-SpektrenunddasFeh-len einerbeobachtbareng-VerteilungwerdeneinerwohldefiniertenBindungssituationim Proteinzugeschrieben.InsbesonderekonnteeineWasserstoffbrückezwischendem

143

Tyrosin und demProteingerüstüberihre Auswirkungenauf deng-Tensorund durcheineAufspaltungansonstensymmetrieäquivalenterHyperfeinkopplungenbeobachtetwerden.

BakteriellesReaktionszentrum: SchließlichwurdendieradikalischenZuständeQ L KA ,Q L KB undderbiradikalischeZustandQ L KA Q L KB in Zink-rekonstituiertenbakteriellenRe-aktionszentrenvonRhodobactersphaeroidesmit 94GHz-EPRuntersucht.UnterVer-wendungderg-HauptwertevonQL KA undQ L KB konntediedipolareKopplungderRadi-kaleim QL KA Q L KB -Zustandanalysiertwerden.Die sichergebendeGeometrieinformati-on, relative OrientierungundAbstandderRadikale,ist in vorzüglicherÜbereinstim-mungmit der RöntgenstrukturdesbakteriellenReaktionszentrumsim Q L KB -Zustand.Die AustauschkopplungzwischendenChinonenist jedochzustark,umsieausdiesenExperimentenabzuleiten,undeskonntenur eineuntereGrenzevon J 60 MHz an-gegebenwerden.

Eskannzusammenfassendgesagtwerden,daß94 GHz-EPRderzeitnochein heraus-forderndes,aberauchäußerstmächtigesSpektroskopieverfahrenist. Währendver-breiteteTechnikenwie zeitaufgelösteEPRanlichtinduziertenSpeziesdurchtrickrei-cheKonzepteaufdieHochfeld/Hochfrequenz-EPRübertragbarsind,könnengenerelleProblemewie dieEmpfindlichkeit aufVerunreinigungendurchdieEntwicklungneuerexperimentellerMethodengelöstwerden.

Die Nützlichkeit der94GHz-EPRberuhtnichtalleinaufderhohenFrequenz.Dieswird beispielhaftdurchdie ExperimenteandenPhotoenzymenbelegt: DasSpektrumdesPJ K700-Radikalsin gefrorenerLösungvon PhotosystemI ist selbstbei beträchtlichhöherenFrequenzenäußerstschlechtaufgelöst.In Kombinationmit derNutzungvonProtein-Einkristallen,die durchdie hoheEmpfindlichkeit der Hochfeld-EPRermög-licht wird, könnenjedochüberraschendpräziseInformationenüberein “hoffnungs-loses”Systemgewonnenwerden. Im Gegensatzdazuist die UntersuchungdesY KD-Radikalsin PhotosystemII-Einkristallen nicht wegen einer zu geringenAuflösung,sondernaufgrundder UnmengeaufgelösterDetails in den EPR-Spektreneine Her-ausforderung.In Verbindungmit unterstützendenENDOR-Messungenund, ebensobedeutsam,demAusnutzender Kristallsymmetrienbei der Analyseist eswiederummöglich, genaueDatenzur elektronischenund geometrischenStrukturder Probezuerhalten.

Die SpektrengekoppelterChinonradikalein Zink-rekonstituiertenbakeriellenRe-aktionszentrenweiseneineexzellenteAuflösungund ein sehrgutesSignal/Rausch-Verhältnisin Verbindungmit einereinfachenStrukturauf. Zunächstüberraschtes,daßdieStärkederAustauschwechselwirkungunterdiesenVoraussetzungennichtermitteltwerdenkonnte.Die Analyseoffenbartjedoch,daßdie bei 94 GHz-EPRverwendetenmagnetischenFeldstärkenschlichtweg nicht ausreichen,um die starke Kopplungauf-zubrechenundwesentlicheÜbergängenichtbeobachtbarsind.Erkenntnissewie diese

144 ZUSAMMENFASSUNGUND AUSBLICK

motivierendenWunschnachEPR-SpektroskopiebeinochhöherenFrequenzen.Es wird interessantsein,andereparamagnetischeZuständein diesenPhotoenzy-

menmit 94 GHz-EPRzu untersuchen.Insbesonderesolltesichdie Kombinationver-schiedenerMethodenalsäußerstnützlicherweisen.94 GHzEPRantransienten,pho-toinduziertenSpezieswird eserlauben,Informationüberansonstennicht zugänglicheZuständezu erhalten.Die Beobachtungvon Radikalpaarenliefert – überdie dipola-re Kopplung– bereitsin gefrorenerLösungspezifischeGeometrieinformationen.InVerbundmit demEinsatzvon EinkristallenkönnennochdetailliertereInformationenerhaltenwerden.

EineandereinteressanteMöglichkeit werden94 GHz-ENDOR-Experimentedar-stellen. Die verstärkteOrientierungsselektionsollte es erlauben,sowohl GrößealsauchOrientierungvonHyperfeinkopplungen,unddamitInformationüberdieelektro-nischeStrukturparamagnetischerZuständezuerhaltenENDORanEinkristallensolltedieGenauigkeit solcherExperimentenochweitererhöhen.SchließlichwürdeENDORanlichtinduzierten,transientenZuständen,womöglichsogar in Einkristallen,wesent-lich zumVerständnisdergenauenWirkungsweisedieserPhotoenzymebeitragen.

Appendix A

Spin Dynamics

A.1 DensityMatrix Formalism

In theSchrödingerrepresentation,thedynamicsof a quantumsystemin a state l ψ isdescribedby theSchrödingerequation

ddt

l ψ F y ih

H l ψ (A.1)

whereH is theHamiltoniandescribingthesystem.Typical experimentsarehoweverperformedonanentireensembleof similarsystems.A descriptionof suchanensemblein the Schrödingerrepresentationwould have to be donein the productspaceof theindividual systems.This increasesthedimensionalityof theHilbert spaceto anextentthatrendersthis approachimpractical.

A partial solutionto this problemis to employ classicalstatisticsto describetheensembleasa whole. TheSchrödingerrepresentationdoesnot lend itself directly tothismethodsincethewavevectorsaverageoutfor anensemblewith incoherentphases.Anotherequationof motion is neededthatutilizesa representationof quantumstateslendingitself to classicalstatistics.Thedensitymatrix is sucha representation.

Fromeqn.A.1 andits adjunct(notethatH is Hermitian)

ddt ψ l F i

h ψ l H (A.2)

theequationof motionfor thedyadicproduct l ψ ψ l canbederivedas

ddt l ψ ψ l F l ψ d

dt ψ l H ddt

l ψ ψ lF ih

l ψ ψ l H y ih

H l ψ ψ lF y ih ¡ H l ψ ψ l ¢ (A.3)

145

146 APPENDIXA. SPINDYNAMICS

wherethebracketsrepresentthecommutator. Theexpectationvalueof anobservabledescribedby theoperatorO canbederivedfrom thequantity l ψ ψ l as O F ψ l O l ψ F ∑

k ψ l l φk φk l O l ψ F ∑

k φk l O l ψ ψ l l φk F Tr £ O l ψ ψ l ¤ (A.4)

where l φk is acompleteorthonormalbaseof theHilbert space.Thelastexpressionis linearin l ψ ψ l . Therefore,theensembleaverageof anobservablecanbecalculatedfrom theensembleaverageof l ψ ψ l which is calleddensitymatrix ρ: O F Tr ¥ O l ψ ψ l ¦ F Tr £ Oρ ¤ (A.5)

Sinceeqn.A.3 is alsolinearin l ψ ψ l , it appliesfor thedensitymatrix ρ aswell:

ddt

ρ F y ih ¡ H ρ ¢ M (A.6)

This equationof motionis calledtheLiouville-vonNeumannequation.For anensemblein thermalequilibrium,only theaverageenergy level populations

areknown from theBoltzmannlaw while differenteigenstatesof theHamiltonianarecompletelyuncorrelated.In the eigenbaseof the Hamiltonian,suchcorrelationsarerepresentedby the off-diagonalelementsof the densitymatrix ρ. From thesetworequirements,it follows thatthedensitymatrix ρ0 in thermalequilibriumis givenby

ρ0 F exp y HkBT

Tr ¥ exp y HkBT ¦ M (A.7)

A.2 Rotating Frame Approximation

Themostcommonmagneticresonanceexperimentscanbemodeledby a spin j cou-pled to an external static field vB0 F B0 vez which conventionally marks the z direc-tion of the laboratoryframe. Transitionsareinducedby anoscillatingmagneticfieldvB1 W cosωt F B1cosωt W vex alongthex direction. Thesystemis thereforegovernedbytheHamiltonian

H F y γ § B0 jz H B1 W cosωt W jx ¨ M (A.8)

Theoscillatingtermcanbeequallywrittenasthesuperpositionof two magneticfieldsrotatingin thexy plane:

H F y γ B0 jz H B1

2§ 2cosωt W jx H sinωt W jy y sinωt W jy ¨ (A.9)

A.3. BLOCH EQUATIONS 147

This representationsuggeststhat onelooks at the systemfrom a referenceframe xV yV

zV F xcosωt H ysinωtycosωt y xsinωt

z . rotating aroundthe z axis with

frequency ω. Eqn.A.9 is thentransformedto

H V F y γ B0 y ωγ jz© y γ

B1

2jx© y γ

B1

2§ cos2ωt W jx© y sin2ωt W jy© ¨E y γ B0 y ω

γ jz© y γB1

2jx©

(A.10)

neglectingthe termsoscillatingwith 2ω (rotating frameapproximation). This adia-baticapproximationis valid provided2ω is sufficiently far away from any resonancefrequency. In this case,the systemcanbe describedin the rotatingframeasa spin

interactingwith a static magneticfield vBV F B0 y ωγ W vez© H B1

2 vex© , therebygreatly

simplifying theHamiltonian.

A.3 Bloch Equations

The dynamicsof the averagemagnetization vM F γTr ¥ v jρ ¦ of a spin ensemblein a

magneticfield vB canbeeasilyderivedin thedensitymatrix formalismusingthecom-mutators ¡ jk

j l ¢ F ih jmεklm:

ddt

vM F γddt

Tr ¥ v jρ ¦F iγ2

hTr ¥ v j ª vB W v j ρ « ¦F iγ2

hTr ¥ v j vB W v j ρ y v jρ vB W v j ¦F iγ2

hTr ¥ vB w v j w v jρ ¦F iγ2

hvB w Tr ¥ ihv jρ ¦F y γ vB w vM (A.11)

Thus,themagnetizationof theensemblebehaveslikeaclassicalgyroscope,precessingaroundthe appliedmagneticfield vB (Larmor precession) with a frequency ωL F γB

h .Thesetof equationsin eqn.A.11 is calledtheBloch equations.

TheBloch equationscanalsobeusedto introducerelaxationon a phenomenolog-ical level. Assumingthestaticmagneticfield vB0 is orientedalongthez direction,themagnetizationwill relaxtowardsanequilibriummagnetizationvM0 ¬ vez. Sincethex andy componentsof themagnetizationprecessaroundthestaticfield, their “transversal”relaxationratecanbeexpectedto bedifferentthanthe “longitudinal” relaxationrate

148 APPENDIXA. SPINDYNAMICS

for thez magnetization.TheresultingmodifiedBlochequationsarethus

ddt

Mx F γMyB0 y Mx

T2(A.12)

ddt

My F y γMxB0 y My

T2(A.13)

ddt

Mz F y Mz y Mz0

T1(A.14)

whereT1 andT2 representthe longitudinalresp.transversallifetimesof themagneti-zation.

Appendix B

Analysis of EPR Spectrafor SingleCrystals and FrozenSolutions

B.1 Orientation DependentSpin Hamiltonian

Thegenericform of orientationdependentspinHamiltonianshasbeendiscussedin aratherabstractway in section1.2.2.Focusingon organicradicalsoccurringin photo-syntheticreactioncentersallows to considera morespecificspinHamiltonian.In thefollowing, anS F 1

2 systemwith N protonhyperfinecouplings(I F 12) is considered.

ThespinHamiltonianfor sucha radicalis

H F vBT0 W µBg W vS y N

∑k 1

µngpv Ik H N

∑k 1

vST W Ak W v Ik M (B.1)

Theanisotropiccouplingconstantsin this Hamiltonianaretheelectronicg tensorandthehyperfinecouplingtensorsAk. All thesetensorsdependon theorientationof themoleculein thelaboratorysystem.It is usefulto isolatethis dependency in onesinglerotationmatrix R specifyingthe orientationof the g tensorin the laboratorysystem.It also simplifies parameterizationto specify eachhyperfinetensorby its principalvaluesanda rotationmatrix Rk describingits orientationrelative to theg axissystem.Therebyonearrivesat

H F vBT0 W µBRgRT W vSl y N

∑k 1

µngpv Ikl H vST

l W N

∑k 1

RRkAkRTk RT W v Ikl M (B.2)

In frozensolutionswithoutpreferentialorientation,asuperpositionof many orien-tationsis observed.A largenumber(typically severalthousands)of orientationsR hasto beusedto describesucha sampleappropriately.

For a crystal,therearefewer orientations.Given the orientationof onearbitrarysite, theothersitescanbeconstructedfrom theM symmetryelementsof thecrystal.Theseoperationscanagainbedescribedby rotationmatrices.As thesymmetriesarise

149

150 APPENDIXB. ANALYSIS OFEPRSPECTRA

from thecrystalstructure,they arebestdescribedin thecrystallographicaxissystem.This resultsin anotherstepin a sequenceof rotationsgiving the final orientationofthecouplingtensorsin thelaboratoryframe:Rg definestheorientationof theg tensorof onearbitrarysitewith respectto thecrystalframe;theRl (l F 1 M M M M) generatetheorientationsof the othersitesin the crystalsystem;andR is usedto give the orien-tation of the crystalasa whole with respectto the laboratorysystem.The resultingHamiltonian

H F M

∑l 1 ® vBT

0 W µBRRl RggRTgRT

l RT W vS y N

∑k 1

µngpv Ik H vST W N

∑k 1

RRl RgRkAkRTk RT

gRTl RT W v Ik ¯ (B.3)

reflectsthe hierarchicalparameterizationof the coupling tensors.The advantageofthis representationis thecompleteseparationof orientationrelationson themolecularlevel (Rk), crystallinelevel (Rg), crystal symmetry(Rl ), and the orientationin thelaboratorysystem(R). Thisdecomposition,oncedetermined,is easierto interpretthanthe productof the individual rotationmatrices. In addition, the distinctionbetweenexperimentaldetailslike thesampleorientationandintrinsic samplepropertiesmakesnumericalfitting methodsusedto derive thespectroscopicparametersmorerobust.

B.2 Definition of Euler Angles

Any orientationor rotation in 3D spacecanbe describedby threeparameters.Themostcommonway to defineanarbitraryrotationis by replacingit with threeconsec-utive rotationsaboutcanonicalaxesby specifiedangles(Euler angles). Thereexistseveral conventionsfor the choiceof thesecanonicalrotations,makingit difficult tocompareorientationsspecifiedin Euleranglesfrom differentsources.For ageometri-cal interpretationit is thereforebestto considertheindividualelementsof therotationmatrix (directionalcosines).

Euleranglesarehowever still requiredfor a non-redundantandself-consistentpa-rameterizationof the spin Hamiltonian. The conventionusedthroughoutthis thesisis equivalentto that usedin [1]. It is definedby rotationsaroundthe axesof a fixedright-handedCartesianreferenceframein thefollowing order1

1. A rotationaboutthezaxisby anangleψ,

2. a rotationaboutthex axisby anangleθ,

3. anotherrotationaboutthez axisby anangleφ.1In [1], rotationsareappliedin reverseorderand,consequently, intermediateauxiliary axesfor the

rotationshave to beintroduced.

B.3. SIMULATION OFSPECTRA 151

All rotationanglesaredefinedin themathematicallypositivesense.A genericrotationmatrix transformingcoordinatesfrom a local cartesiansystemxV yV zV to thexyzsystemis thereforegivenby2

R φ θ ψ F R φ W R θ W R ψ (B.4)

where

R φ F °± cosφ y sinφ 0sinφ cosφ 0

0 0 1 ²³ (B.5)

R θ F °± 1 0 00 cosθ y sinθ0 sinθ cosθ ²³ (B.6)

R ψ F °± cosψ y sinψ 0sinψ cosψ 0

0 0 1 ²³ M (B.7)

For thecompleterotationmatrix,onearrivesat

R φ θ ψ F °± cosφcosψ L sinφcosθsinψ L cosφsinψ L sinφcosθcosψ sinφsinθsinφcosψ J cosφcosθsinψ L sinφsinψ J cosφcosθcosψ L cosφsinθ

sinθsinψ sinθcosψ cosθ ²³ M(B.8)

B.3 Simulation of Spectra

In general,EPRspectraarisingfrom an orientation-dependentspin Hamiltonianaretoocomplex for ananalyticalevaluation.Thereductionof experimentaldatathereforehasto resortto trial anderrorprocedureslikenonlinearleastsquaresfitting [2]. WhentheexperimentalEPRspectraaresufficiently resolvedto identify andassignindividualresonancelines, the experimentalline positionscanbe comparedto their computedcounterparts.Basedon theobserveddifferences,theparametersetcanbeimproved.

With an increasingnumberof resolved hyperfineinteractionsand,in the caseofcrystals,inequivalentsitesin theunit cell, EPRlinesaremorelikely to overlapanditis no longerfeasibleto pick line positionsfrom thespectra.In thiscase,it is necessaryto simulatecompletespectraandcomparethosewith theexperimentalones.

For thesimulationof frozensolutionandcrystalEPRspectra,aC++ programwaswritten. Theprogramhasto performtwo steps:it hasto useaseriesof transformationsto setup thespinHamiltonianfor a specificsampleorientation,andit hasto calculatethespectrumfrom thatHamiltonian. For thesimulationof frozensolutionspectra,a

2Anothersourceof confusionis thatsomeauthors,including[1], give thematrix for thetransforma-tion from theglobalto thelocal cartesiansystem.

152 APPENDIXB. ANALYSIS OFEPRSPECTRA

largenumberof isotropicallydistributedorientationsis generatedfollowing an algo-rithm describedin [3]. In thecaseof crystalspectra,orientationsaregeneratedfrom auser-suppliedsetof R, Rl , andRg (specifiedasEulerangles).

Calculatingthespectrumfor a givenorientationinvolvesa trade-off betweeneffi-cientcomputationandaccuracy. For organicradicalswith smallg anisotropy andnottoo largehyperfineinteractions,thefollowing approximationcanbeused.

B.4 Calculation of the ResonanceField Strength

For the organic radicalsunder investigation the hyperfinecouplingsand the aniso-tropy of theZeemantermaresmallcomparedto theabsoluteZeemanenergy. This isespeciallytruein highfieldEPR.Therefore,theeigenstatesof theHamiltonianareverycloseto Sz eigenstates(assumingvB0 F B0 W vez), andcanonicalselectionrules∆mS F k 1apply. ThenuclearZeemantermscanthenbeneglected.TheEPRtransitionfieldsforagivenmicrowave frequency νmw resultas

B F hνmw y ∑Nk 1aeff z kmI

µBgeff(B.9)

with theeffectiveg andhyperfineconstants

geff F vnT W RRl RggRTgRT

l RT W vn (B.10)

aeff z k F vnT W RRl RgRkAkRTk RT

gRTl RT W vn (B.11)

where vn is thedirectionof themagneticfield. In anensemble,thecombinationsof NdifferentmI give riseto ∏N

k 1 2Ik H 1 EPRlines.

REFERENCES

[1] GoldsteinH., Klassische Mechanik, chapter4, AkademischeVerlagsgesellschaftWies-baden,7thedition(1983).

[2] PressW.H., Teukolsky S.A., VetterlingW.T., & FlanneryB.P., NumericalRecipesin C:The Art of ScientificComputing, chapter15, CambridgeUniversity Press,2nd edition(1992).

[3] GeßnerC., NiFe-Hydrogenasen:Beiträge der EPR-Spektroskopiezur StrukturaufklärungdesaktivenZentrums, Ph.D.thesis,TechnischeUniversitätBerlin (1996).

Appendix C

Spin DynamicsSimulation Program

Thefollowing C++ programwasusedin chapter4 to numericallysolve theLiouville-von Neumannequationfor a two-level spin systemwith inhomogeneousline broad-ening. It is listed herein the hopethat it may be useful as an educationaltool forunderstandingpulsedEPRexperiments.

/*Simulation von Spindynamik ohne Relaxation(C) 1998-2000 W. Hofbauer

*/

#include <stdio.h>#include <string.h>#include <iostream.h>#include <float.h>#include <math.h>

class cplx public:

cplx(double x=0, double y=0): re(x), im(y) cplx(const cplx &z) re=z.re; im=z.im;cplx &operator=(const cplx &src) re=src.re; im=src.im; return *this;cplx &operator+=(const cplx &src) re+=src.re; im+=src.im; return *this;cplx &operator-=(const cplx &src) re-=src.re; im-=src.im; return *this;cplx &operator*=(const cplx &src)

double x=re, y=im; re=x*src.re-y*src.im;im=x*src.im+y*src.re; return *this;

cplx &operator/=(const cplx &src)

double a=src.re*src.re+src.im*src.im;return *this*=cplx(src.re/a, -src.im/a);

double real(void) return re;double imag(void) return im;

private:friend cplx operator+(const cplx &add1, const cplx &add2)

return cplx(add1.re+add2.re, add1.im+add2.im);friend cplx operator-(const cplx &sub1, const cplx &sub2)

return cplx(sub1.re-sub2.re, sub1.im-sub2.im);friend cplx operator*(const cplx &mul1, const cplx &mul2)

return cplx(mul1.re*mul2.re-mul1.im*mul2.im,mul1.re*mul2.im+mul1.im*mul2.re);

friend cplx operator/(const cplx &div1, const cplx &div2)

double a=div2.re*div2.re+div2.im*div2.im;return cplx((div1.re*div2.re+div1.im*div2.im)/a,

(div1.im*div2.re-div1.re*div2.im)/a);friend cplx operator*(const cplx &src)

return cplx(src.re, -src.im);friend cplx operator-(const cplx &src)

return cplx(-src.re, -src.im);friend cplx operator*(const cplx &z, const double x)

return cplx(z.re*x, z.im*x);

153

154 APPENDIX C. SPINDYNAMICS SIMULATION PROGRAM

friend cplx operator*(const double x, const cplx &z) return z*x;

friend ostream &operator<<(ostream &os, const cplx &z)

return os << "(" << z.re << ", " << z.im << ")";double re;double im;

;

const cplx i(0, 1);

class spinmatrix public:

spinmatrix(const spinmatrix &src): S0(src.S0), S1(src.S1),S2(src.S2), S3(src.S3) ;

spinmatrix(const cplx &s0=0, const cplx &s1=0, const cplx &s2=0,const cplx &s3=0): S0(s0), S1(s1), S2(s2), S3(s3) ;

spinmatrix &operator=(const spinmatrix &src) S0=src.S0; S1=src.S1; S2=src.S2; S3=src.S3;return *this;

spinmatrix &operator+=(const spinmatrix &src)

S0+=src.S0; S1+=src.S1; S2+=src.S2; S3+=src.S3;return *this;

spinmatrix &operator-=(const spinmatrix &src)

S0-=src.S0; S1-=src.S1; S2-=src.S2; S3-=src.S3;return *this;

spinmatrix &operator*=(const spinmatrix &src)

cplx s0(S0), s1(S1), s2(S2), s3(S3);S0=0.5*(s0*src.S0+s1*src.S1+s2*src.S2+s3*src.S3);S1=0.5*(s0*src.S1+s1*src.S0+i*(s2*src.S3-s3*src.S2));S2=0.5*(s0*src.S2+s2*src.S0+i*(s3*src.S1-s1*src.S3));S3=0.5*(s0*src.S3+s3*src.S0+i*(s1*src.S2-s2*src.S1));return *this;

cplx trace() return S0;cplx x() return S1;cplx y() return S2;cplx z() return S3;

private:friend spinmatrix operator*(const spinmatrix &src)

spinmatrix res(src);res.S0=*(res.S0);res.S1=*(res.S1);res.S2=*(res.S2);res.S3=*(res.S3);return res;

friend spinmatrix operator*(const spinmatrix &mul1, const spinmatrix &mul2)

return spinmatrix(0.5*(mul1.S0*mul2.S0+mul1.S1*mul2.S1

+mul1.S2*mul2.S2+mul1.S3*mul2.S3),0.5*(mul1.S0*mul2.S1+mul1.S1*mul2.S0

+i*(mul1.S2*mul2.S3-mul1.S3*mul2.S2)),0.5*(mul1.S0*mul2.S2+mul1.S2*mul2.S0

+i*(mul1.S3*mul2.S1-mul1.S1*mul2.S3)),0.5*(mul1.S0*mul2.S3+mul1.S3*mul2.S0

+i*(mul1.S1*mul2.S2-mul1.S2*mul2.S1)));friend spinmatrix operator+(const spinmatrix &add1, const spinmatrix &add2)

return spinmatrix(add1.S0+add2.S0, add1.S1+add2.S1,add1.S2+add2.S2, add1.S3+add2.S3);

friend spinmatrix operator-(const spinmatrix &sub1, const spinmatrix &sub2)

return spinmatrix(sub1.S0-sub2.S0, sub1.S1-sub2.S1,sub1.S2-sub2.S2, sub1.S3-sub2.S3);

friend spinmatrix operator*(const spinmatrix &mul1, const cplx &mul2)

return spinmatrix(mul1.S0*mul2, mul1.S1*mul2, mul1.S2*mul2,mul1.S3*mul2);

friend spinmatrix operator*(const cplx &mul1, const spinmatrix &mul2)

return mul2*mul1;friend ostream &operator<<(ostream &os, const spinmatrix &src)

os << "[" << src.S0 << ", " << src.S1 << ", "<< src.S2 << ", " << src.S3 << "]";

return os;cplx S0;cplx S1;cplx S2;cplx S3;

;

155

spinmatrix nopulse(double omega0, double t) return spinmatrix(2*cos(omega0*t/2), 0, 0, -2*i*sin(omega0*t/2));

spinmatrix xpulse(double omega0, double omega1, double t) double omega=sqrt(omega0*omega0+omega1*omega1);return spinmatrix(2*cos(omega*t/2),

-i*2*omega1/omega*sin(omega*t/2),0,-i*2*omega0/omega*sin(omega*t/2));

spinmatrix ypulse(double omega0, double omega1, double t) double omega=sqrt(omega0*omega0+omega1*omega1);return spinmatrix(2*cos(omega*t/2),

0,-i*2*omega1/omega*sin(omega*t/2),-i*2*omega0/omega*sin(omega*t/2));

const spinmatrix sigma_0(1, 0, 0, 0);const spinmatrix sigma_x(0, 1, 0, 0);const spinmatrix sigma_y(0, 0, 1, 0);const spinmatrix sigma_z(0, 0, 0, 1);

#define NL "\n"#define TAB "\t"#define PI (3.141592653589793)#define TWO_PI (2*PI)

double f0=0.0; // Frequenz des Uebergangs (rotating frame)double sigma_f=1.0; // Standardabweichung der inhomogenen Gaussliniedouble quality=1.0; // beruecksichtigte Bandbreite in Nyquist-Einheiten

double f1=1.0; // Rabi-Frequenz

double t_start=0.0; // Start des Detektionsfenstersdouble t_end=100.0; // Ende des Detektionsfenstersint t_steps=256; // Anzahl der Zeitschritte

enum kind tau, plusx, plusy, minusx, minusy; // Art des Pulses

class pulse public:

pulse* next; // verkettete lineare Liste der Pulse (zeitgeordnet)kind what; // Art des Pulsesdouble f1; // Rabifrequenzdouble length; // Pulsdauer

;

double* signalx; // Puffer fuer Signaldouble* signaly;double* signalz;pulse* pulselist=NULL;

bool show=false;char *prgname;int ac;char **av;

void usage(void);void parseargs(void);void addtotrace(double weight, double f0);spinmatrix pulsematrix(double f0, double f1, kind what, double length);char* nextarg(void);double getdouble(void);void addpulse(double f1, kind what, double length);void dumppulselist(void);

int main(int argc, char** argv)

try // Optionen einlesen, Aufbau der Pulsliste etc.ac=argc; av=argv; prgname=nextarg();parseargs();

// mit option "sh" war’s das schon...if (show) dumppulselist(); return 0;

// am Ende der Pulsliste "unendlich lange" freie Evolution anhaengen// (spart bei der Berechnung laestige (und ineffiziente) Abfragen)addpulse(f1, tau, DBL_MAX);

// Puffer allozieren und initialisierensignalx=new double[t_steps+1];signaly=new double[t_steps+1];signalz=new double[t_steps+1];if (!(signalx&&signaly&&signalz)) throw "Fehler beim Allozieren der Datenpuffer";


for (int j=0; j<=t_steps; ++j) signalx[j]=signaly[j]=signalz[j]=0;

// Zahl der Abtastschritte im Frequenzraum festlegen// Aequidistante Abtastung -> periodische Fourierreihe der Zeitentwicklung

// Der Frequenzbereich wird durch das Nyquist-Limit festgelegt// (symmetrische Abtastung um f=0).double f_max=0.5*t_steps/(t_end-t_start);f_max*=quality;

// Die Periode soll > Zeitraum der Propagatorberechnung sein,// da sonst Echos "von selbst" auftreten. Dauer des inhomogenen FIDs// muss dazugerechnet werden...

double delta_f=1/(t_end+3/sigma_f);

// Aufsummieren im Frequenzraum.for (double f=-f_max; f<f_max; f+=delta_f)

double factor=delta_f/(sigma_f*sqrt(TWO_PI))*exp(-0.5*(f-f0)*(f-f0)/(sigma_f*sigma_f)); // Gauss-Glocke fuer f0

addtotrace(factor, f);for (int j=0; j<=t_steps; ++j)

double t=(t_end-t_start)/(t_steps)*j+t_start;cout << t << TAB << signalx[j] << TAB << signaly[j]

<< TAB << signalz[j] << NL;

catch (char *msg) cerr << *argv << ": " << msg << NL;exit(1);

cout.flush();return 0;

void usage()

cerr << "Aufruf: " << prgname << " Option|Puls\n";cerr << "Optionen: f0 <freq> zentrale Uebergangsfrequenz (rotating frame)\n";cerr << " s0 <freq> Standardabweichung der f0-Verteilung\n";cerr << " co <fact> Abschneideparameter fuer Apodisierung\n";cerr << " qu <fact> beruecksichtigte Bandbreite in Vielfachen\n";cerr << " der Nyquist-Grenzfrequenz\n";cerr << " f1 <freq> Rabi-Frequenz der nachfolgenden Pulse\n";cerr << " ta <zeit> Anfangszeitpunkt des Signalfensters\n";cerr << " te <zeit> Endzeitpunkt des Signalfensters\n";cerr << " ts <ganz> Aufloesung der Zeitachse (Schritte)\n";cerr << " sh Ausgabe der Pulsliste\n";cerr << "Pulse: +x <zeit> +x-Puls mit Dauer <zeit> und Rabifrequenz f1\n";cerr << " +y, -x, -y entsprechend\n";cerr << " tau <zeit> Evolution ohne Rabi-Nutation\n";

;

void parseargs(void)

char* arg;

while (arg=nextarg()) if (!strcmp(arg, "f0")) f0=getdouble(); continue;if (!strcmp(arg, "s0")) sigma_f=getdouble(); continue;if (!strcmp(arg, "qu")) quality=getdouble(); continue;if (!strcmp(arg, "f1")) f1=getdouble(); continue;if (!strcmp(arg, "ta")) t_start=getdouble(); continue;if (!strcmp(arg, "te")) t_end=getdouble(); continue;if (!strcmp(arg, "ts")) t_steps=(int)getdouble(); continue;if (!strcmp(arg, "sh")) show=true; continue;if (!strcmp(arg, "+x")) addpulse(f1, plusx, getdouble()); continue;if (!strcmp(arg, "+y")) addpulse(f1, plusy, getdouble()); continue;if (!strcmp(arg, "-x")) addpulse(f1, minusx, getdouble()); continue;if (!strcmp(arg, "-y")) addpulse(f1, minusy, getdouble()); continue;if (!strcmp(arg, "tau")) addpulse(f1, tau, getdouble()); continue;usage(); throw "Programm abgebrochen";

if (sigma_f<=0) throw "s0 muss >0 sein.";if (quality<1) throw "qu muss >=1 sein.";if (t_start<0) throw "ta muss >=0 sein.";if (t_end<=t_start) throw "ta muss >te sein.";if (t_steps<1) throw "ts muss >=1 sein.";if (!pulselist) throw "Pulsliste ist leer";

char* nextarg(void)

return (--ac>=0)?*av++:(char*)NULL;

double getdouble(void)

157

char* s=nextarg();double d;char dummy;

if (!s) throw "vorzeitiges Ende der Kommandozeile";if (sscanf(s, "%lf%c", &d, &dummy)!=1) throw "fehlerhafter numerischer Parameter";return d;

void addpulse(double f1, kind what, double length)

pulse **p=&pulselist;while (*p) p=&(*p)->next;pulse *np=new pulse;if (!np) throw "Fehler beim Eintrag in die Pulsliste";np->next=NULL;np->what=what;np->f1=f1;np->length=length;*p=np;

void dumppulselist(void)

pulse *p;cout << "Pulsliste:" << NL;for (p=pulselist; p; p=p->next)

char *name;switch (p->what)

case tau: name="tau"; break;case plusx: name="+x"; break;case plusy: name="+y"; break;case minusx: name="-x"; break;case minusy: name="-y"; break;default: name="?";

cout << TAB << name << "\tt=" << p->length;if (p->what!=tau) cout << "\tf1=" << p->f1;cout << NL;

void addtotrace(double weight, double f0)

double dt=(t_end-t_start)/(t_steps-1); // Zeitinkrementdouble t=t_start; // aktuelle Zeitdouble t0=0; // Beginn des aktuellen Pulsesdouble t_last=0; // letzter Zeitpunktpulse* current=pulselist; // aktueller Pulsspinmatrix U=2*sigma_0; // Identitaet, Ausgangszustandspinmatrix dU=2*sigma_0; // Cache fuer Propagatorbool dUvalid=false; // Flag, ob dU gueltigspinmatrix rho0=sigma_0+sigma_z; // 100% Polarisation, Ausgangszustandspinmatrix rho; // Dichtematrix zum Zeitpunkt t

for (int j=0; j<=t_steps; ++j) while (t_last<t) // Zeitentwicklung fortfuehren

if (t0+current->length<=t) // bis Ende des PulsesU*=pulsematrix(f0, current->f1, current->what,

t0+current->length-t_last);t0=t_last=t0+current->length;current=current->next;dUvalid=false;

else // angeschnittener Pulsif (dUvalid)

U*=dU;t_last=t;

else U*=pulsematrix(f0, current->f1, current->what,

t-t_last);t_last=t;dU=pulsematrix(f0, current->f1, current->what, dt);dUvalid=true;

rho=(*U)*rho0*U;signalx[j]+=weight*(rho.x().real());signaly[j]+=weight*(rho.y().real());signalz[j]+=weight*(rho.z().real());

t+=dt;

spinmatrix pulsematrix(double f0, double f1, kind what, double length)

double t=-TWO_PI*length; // Vorzeichen vertauscht, da adjungierte Matrix benoetigt wird


switch (what) case tau:

return nopulse(f0, t);case plusx:

return xpulse(f0, f1, t);case plusy:

return ypulse(f0, f1, t);case minusx:

return xpulse(f0, -f1, t);case minusy:

return ypulse(f0, -f1, t);default:

throw "Interner Fehler - unbekannter Pulstyp!";

Danksagung

Bei der AnfertigungdieserDissertationerfuhr ich Unterstützungvon vielen Seiten.An ersterStellemöchteich mich bei Prof. Dr. WolfgangLubitz bedanken. NachderAufnahmein seineArbeitsgruppehat er mich, wo er konnte, tatkräftig unterstütztunddenFortgangderArbeit wohlwollendbegleitet. AufgrundmeinergelegentlichenSkepsisgegenüberdenhochkomplexen Probenhattenwir nicht immer die gleichenAnsichten. Trotzdem– odergeradedeshalb– habeich in dendarauserwachsenenDiskussionenviel gelernt.

Prof.Dr. KlausMöbiusdankeich für seinInteresseamFortgangmeinerArbeit unddie spontaneBereitschaftzur ÜbernahmedesMitberichtes.Obwohl „sein“ Institut anderFreienUniversitätBerlin nur wenigeKilometer entferntliegt, war ich leider vielzuseltendort – wofür ich michandieserStelleentschuldige.

Mit HerrnDr. RobertBittl hatteich zahlreiche,oftmalssehrgrundsätzlicheDiskus-sionenüberphysikalischeHintergründe,spektroskopischeTechnikenundmathemati-scheMethodenzur Beschreibungbzw. AnalysederExperimente.Für diesewertvolleHilfestellungmöchteich michganzbesondersbedanken.

Dr. FriedhelmLendzianverdanke ich nichtnurzahlreichelehr- undhilfreicheDis-kussionen,sondernauchden Einblick in einengroßenSchatzan Erfahrungen,dieim Laboralltagund bei der Interpretationder Datenvon unschätzbaremWert waren.Zudemhatmich seintrotz anderslautenderBeteuerungenungebrochenerOptimismusstetsaufsneuemotiviert undwird mir in schwierigenZeitenAnspornsein.

WesentlichenAnteil an dieserArbeit habendie Kooperationspartner, die die un-tersuchtenProbenbeigesteuerthaben.An ersterStelleist hier die AG Fromme/WittamMax-Volmer-Laboratoriumzu nennen.FrauDr. PetraFrommehatdie LösungenundKristallevonPhotosystemI zurVerfügunggestellt,die in dieserArbeit vermessenwurden,wofür ich mich andieserStellebedankenmöchte.Ein besondersherzlicherDank gebührtFrauDr. Athina Zouni und JanKern für die engeund fruchtbareZu-sammenarbeitbei denExperimentenamPhotosystemII. Athina hatnicht nur etlichederwertvollen Kristalle für die EPR-Experimentegeopfert,sondernwar auchbeson-dersan densich ergebendenResultateninteressiert.Die zahlreichenmotivierendenDiskussionen– nicht nur fachlicherNatur– mit ihr habenmir sehrgeholfen.

Röntgenbeugungsexperimentean denKristallen, die direkt und indirekt in dieseArbeit eingeflossensind,wurdenmit der Hilfe von Dr. NorbertKraußund Dr. PeterOrth in derAG SaengeramkristallographischenInstitut derFU Berlin durchgeführt.

159

Die ErfahrungvonPeterundNorbertkammir auchbei vielenDiskussionenüberKri-stallsymmetrien,Koordinatensystemeund Methodik der Röntgenstrukturanalysezu-gute.

Die untersuchtenbakteriellenReaktionszentrenstammenausderGruppevonProf.GeorgeFeher(UCSD,La Jolla).

Im Kapitel 4 fandenProbenvon Prof. Wieghardt(MPI für Strahlenphysik, Mül-heim)undV. Barynin(U Sheffield) Verwendung.

Allen MitarbeiternderAG Lubitz danke ich für dasangenehmeArbeitsklima.KaiSchäferhat nicht nur als mein BürogenossemeineAnwesenheitmehrereJahreohneMurren ertragen,sondernauch„seine“ Mangankomplexe für Messungenzur Verfü-gunggestellt.Mit den„Reduktasen“,GünterBleifuß undMatthiasKolberg, habeichauchaußerhalbdesInstitutsviel Zeit verbracht.Mit MarcBrechthatteich interessanteDiskussionenüberfortgeschrittenePuls-EPR-Techniken.MichaelKammelhalf mir inderAnfangsphasederPhotosystemII-Experimente.RafaelJordanverdankeich einigeIllustrationen,die in modifizierterForm im einführendenKapitel überReaktionszen-trenverwendetwurden. Auch all die anderenwürdeich gernenamentlichwürdigen,wasmir angesichtsderGrößederArbeitsgruppejedochderPlatzunddieBefürchtung,jemandenzuvergessen,verbieten.

In Zeiten knapperKassenist eine leistungsfähigeInfrastrukturan Universitätenkeine Selbstverständlichkeit mehr. Daß trotzdemerfolgreicheForschungbetriebenwerdenkann,verdanktdieTU Berlin – unddamitauchich – demgroßenEngagementeinzelnerMitarbeiter, die bei unvorhergesehenenProblemenauchabseitsdesDienst-wegszu unkomplizierterHilfe bereitsind. Stellvertretendfür alle seiandieserStelleFrauMichaelaSofsky von der „ZentraleinrichtungGasverflüssigungsanlage“(ZGA)genannt,dieoft auchsehrkurzfristigeWünschenachflüssigemStickstoff undHeliumbefriedigenkonnte.

DerEPR-AbteilungderFirmaBrukerAnalytik danke ich für dieguteundunkom-plizierte Zusammenarbeit.Die bereitwilligenAuskünfteübertechnischeDetailsderSpektrometer– oft auchnachderoffiziellen Geschäftszeit– gingendeutlichübereinnormalesGeschäftsverhältnishinausundhalfenmir bei derLösungvon etlichenklei-nerenundgrößerenProblemenim Labor. Darüberhinauswurdenmir MessungenimBruker-Laborermöglicht,alsunsereigenesSpektrometereinmalkränkelte.

Wennauchformal Herr Prof. Lubitz undHerr Dr. Bittl meineArbeitgeberwaren,wardereigentlicheGeldgeberim HintergrunddieDeutscheForschungsgemeinschaft.Deshalbmöchteich michbeiderDFGbedankenunddiesmit demWunschverbinden,daßdie DFG sichauchin Zukunft nicht derkurzsichtigenPolitik derWirtschaftsma-gnatenanschließt,sondernweiterhinGrundlagenforschungzum Wohle aller fördert.AuchunsereZeit wird einesfernenTagesnichtanhandvonKonzernbilanzen,sondernihrerBeiträgezuKultur undWissenschaftbeurteiltwerden.

MeinenElterndanke ich für ihre fortwährendeUnterstützungundEileenfür ihreGeduld.

Lebenslauf

Name Wulf TobiasHofbauerAkademischeGrade Diplom-Physiker (Dipl.-Phys.)Geburtsdatum 29. März 1969Geburtsort Stuttgart-BadCannstattFamilienstand ledig

Ausbildung

1975–1979 Herbert-Hoover-Grundschule,Stuttgart1979 GrundschuleHohenstange,Tamm(Württ.)1979–1988 Friedrich-List-Gymnasium,Asperg (Württ.)Mai 1988 Abitur1989–1996 StudiumderPhysik anderUniversitätStuttgartOktober1991 Vordiplom(„sehrgut“)1995–1996 Diplomarbeit auf dem Gebiet der transientenoptischen

Spektroskopieam2. PhysikalischenInstitut derUniversitätStuttgart bei Prof.Dr. M. Mehring

Januar1996 Hauptdiplom(„sehrgut“)seit1996 Anfertigung der Dissertationauf dem Gebiet der Elek-

tronenspinresonanz-SpektroskopieamMax-Volmer-Institut(seit April 2001: Max-Volmer-Laboratorium)der Techni-schenUniversitätBerlin bei Prof.Dr. W. Lubitz

Tätigkeiten

1988–1989 Grundwehrdienst1992–1996 Lehrtätigkeit als wissenschaftlicherMitarbeiteram Physi-

kalischenInstitut derUniversitätStuttgart1996–2000 WissenschaftlicherMitarbeiter bei PD Dr. R. Bittl an der

TechnischenUniversitätBerlinseit2000 WissenschaftlicherMitarbeiterbei Prof. Dr. W. Lubitz an

derTechnischenUniversitätBerlin

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