Electron Paramagnetic Resonance at 94 Ghz: Methodological Developments and Studies of Photosynthetic Reaction Centers

Electron Paramagnetic Resonance at 94 GHz: Methodological Developments and Studies of Photosynthetic Reaction Centers

vorgelegt von Diplom-Physiker Wulf Tobias Hofbauer aus Stuttgart

von der Fakultät II – Mathematik und Naturwissenschaften – der Technischen Universität Berlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften – Dr. rer. nat. – genehmigte Dissertation

Promotionsausschuß: Vorsitzender: Prof. Dr. rer. nat. Christoph van Wüllen, TU Berlin Berichter: Prof. Dr. rer. nat. Wolfgang Lubitz, TU Berlin Berichter: Prof. Dr. rer. nat. Klaus Möbius, FU Berlin Tag der mündlichen Prüfung: 20. Juli 2001

Berlin 2001

Warennamen und Bezeichnungen werden ohne Gewährleistung der freien Verwendbarkeit be- nutzt. Angegebene Schaltungen, Programme oder Methoden sind möglicherweise rechtlich geschützt. Für fehlerhafte Angaben bzw. deren Folgen wird keine Haftung übernommen.

1. Auﬂage (22. August 2001) Gesetzt in LATEX 2ε.

ii Zusammenfassung Hofbauer, Wulf: Electron Paramagnetic Resonance at 94 GHz: Methodological Developments and Studies of Photosynthetic Reaction Centers Diese Arbeit befaßt sich mit der Anwendung von Elektronenspinresonanz (EPR) bei 94 GHz zur Untersuchung von radikalischen Zuständen in Reaktionszentren des pﬂanzlichen und bakteriellen Photosyntheseapparates. Die Lichtanregung in situ bereitet bei der Hochfrequenz-EPR Schwierigkeiten, da ein opti- scher Zugang zum Resonator mit deutlichen technischen Kompromissen erkauft werden muß. In dieser Arbeit wird deshalb zunächst eine Methode zur Lichtanregung in geschlossenen Re- sonatorstrukturen vorgestellt und charakterisiert. Ein weiteres Problem liegt in der hohen Empﬁndlichkeit der Hochfrequenz-EPR auf Un- tergrundsignale, die von Verunreinigungen der Proben ausgehen. Unterscheiden sich die Über- gangsdipolmatrixelemente von Probe und Kontamination, können die Signale mit gepulster EPR getrennt werden. Eine neue Methode hierzu wird in dieser Arbeit vorgestellt. Im Ge- gensatz zu den üblichen Verfahren erfordert das neu eingeführte Experiment deutlich weniger Meßzeit und kleinere Mikrowellenleistungen. Die Leistungsfähigkeit von 94 GHz-EPR zur Untersuchung von Reaktionszentren der Pho-

tosynthese wird an drei Beispielen demonstriert: Das Kationenradikal des primären Donators ¢ in Photosystem (PS) I, P700¡ , weist eine geringe g-Anisotropie und eine hohe EPR-Linienbreite auf. Um aussagekräftige Spektren zu erhalten, waren bislang äußerst hohe Frequenzen erfor- derlich. Die Verwendung von Protein-Einkristallen in dieser Arbeit erlaubte die genaue Be- stimmung des g-Tensors aus den 94 GHz-Spektren. Durch den Vergleich mit der aus der Rönt- genstrukturanalyse bekannten Orientierung der entsprechenden Chlorophyllmoleküle konnte die in früheren Arbeiten vorhergesagte asymmetrische Verteilung der Spindichte bestätigt werden. Die Kristallisation von Photosystem II ist erst seit kurzem möglich. Die in den wahr- scheinlich weltweit ersten EPR-Experimenten an PS II-Einkristallen erhaltenen orientierungs- abhängigen Spektren des stabilen Tyrosinradikals YD¢ sind, bedingt durch eine Vielzahl von Hyperfeinkopplungen und 8 kristallographisch inäquivalente Einbaupositionen, äußerst kom- pliziert. In Verbindung mit gepulsten ENDOR-Experimenten an gefrorener Lösung gelang die vollständige Analyse der Spektren. Die mit hoher Genauigkeit erhaltene Orientierung des g- Tensors ergänzt das bislang noch in weiten Teilen unvollständige Strukturmodell von PS II. Aus den gefundenen g-Hauptwerten und den Hyperfeinkopplungen lassen sich Rückschlüsse auf die Bindungssituation des Tyrosinradikals ziehen. Insbesondere konnte der Einﬂuß einer Wasserstoffbrücke im Detail erfaßt werden. Untersuchungen an den radikalischen Zuständen der Akzeptormoleküle QA und QB im Re-

aktionszentrum des Purpurbakteriums Rhodobacter sphaeroides beschließen die Arbeit. Aus

¢ £ ¢ den Spektren im biradikalischen Zustand QA£ QB konnte – über die Richtungsabhängigkeit der dipolaren Kopplung – die relative Anordnung der Radikale im Protein ermittelt werden.

Diese unterscheidet sich im Rahmen der Meßgenauigkeit nicht von der bekannten Struktur ¢ im monoradikalischen Zustand QB£ . Die für den Elektronentransfer bedeutsame Stärke der Austauschkopplung zwischen den Radikalen konnte hingegen nur näherungsweise bestimmt werden. Es wird gezeigt, daß sich hier eine Grenze der EPR bei 94 GHz offenbart, die nur durch Verwendung noch höherer Mikrowellenfrequenzen überwunden werden kann.

iii iv Teile der vorliegenden Arbeit wurden bereits publiziert:

[1] Hofbauer W. & Bittl R., EPR at 94 GHz of laser-induced species in an ELEXSYS E680 spectrometer, Bruker Report 145, 38–39 (1998).

1 5 ¤ [2] Hofbauer W., Schäfer K.O., & Bittl R., Discrimination of S ¤ 2 and S 2 states in high ﬁeld EPR by ﬁeld-swept ESE, in Magnetic Resonance and Related Phenomena (Ziessow D., Lubitz W., & Lendzian F., eds.), volume II, pp. 851–852 (1998).

[3] Bittl R., Hofbauer W., Zech S.G., Kamlowski A., Fromme P., & Lubitz W., Time-resolved and cw-EPR at 94 GHz on photoystem I, in Magnetic Resonance and Related Phenomena (Ziessow D., Lubitz W., & Lendzian F., eds.), volume I, pp. 262–263 (1998).

[4] Schäfer K.O., Hofbauer W., Bittl R., & Lubitz W., W-band (94 GHz) EPR investigation of an exchange coupled MnIIIMnIV complex, in Magnetic Resonance and Related Phe- nomena (Ziessow D., Lubitz W., & Lendzian F., eds.), volume II, pp. 863–864 (1998).

[5] Kammel M., Hofbauer W., Zouni A., Fromme P., Bittl R., Lendzian F., Witt H.T., &

Lubitz W., High ﬁeld EPR studies of the tyrosyl radical YD¢ in photosystem II single crystals of synechococcus elongatus, in XIth International Congress on Photosynthesis, Budapest, Int. Soc. of Photosynth. Res. (1998).

[6] Calvo R., Hofbauer W., Lendzian F., Lubitz W., Paddock M.L., Abresch E.C., Isaacson £ R.A., Okamura M.Y., & Feher G., Magnetic coupling between QA£ and QB in RCs of Rb. sphaeroides determined by EPR spectroscopy at 95 GHz, Biophys. J. 76, A392 (1999).

[7] Calvo R., Abresch E.C., Bittl R., Feher G., Hofbauer W., Isaacson R.A., Lubitz W.,

Okamura M.Y., & Paddock M.L., EPR study of the molecular and electronic structure of

¢ £ ¢ the semiquinone biradical QA£ QB in photosynthetic reaction centers from Rhodobacter sphaeroides, J. Am. Chem. Soc. 122, 7327–7341 (2000).

[8] Zech S.G., Hofbauer W., Kamlowski A., Fromme P., Stehlik D., Lubitz W., & Bittl R.,

¡ ¢ £ A structural model for the charge separated state P700¢ A1 in photosystem I from the orientation of the magnetic interaction tensors, J. Phys. Chem. B104, 9728–9739 (2000).

[9] Hofbauer W. & Bittl R., A novel approach to separating EPR lines arising from species with different transition moments, J. Magn. Reson. 179, 226–231 (2000).

[10] Hofbauer W., Zouni A., Bittl R., Kern J., Orth P., Lendzian F., Fromme P., Witt H.T., & Lubitz W., Photosystem II single crystals studied by EPR spectroscopy at 94 GHz: The

tyrosine radical YD¢ , Proc. Natl. Acad. Sci. USA 98, 6623–6628 (2001).

v Weitere Veröffentlichungen und Konferenzbeiträge:

[1] Bleifuß G., Pötsch S., Hofbauer W., Gräslund A., Lubitz W., Lassmann G., & Lendzian F., High ﬁeld EPR at 94 GHz of amino acid radicals in ribonucleotide reductase, in Ma- gnetic Resonance and Related Phenomena (Ziessow D., Lubitz W., & Lendzian F., eds.), volume II, pp. 879–880 (1998).

[2] Trofanchuk O., M. S., Brecht M., Hofbauer W., Lendzian F., Higuchi Y., & Lubitz W., Catalytic center of [NiFe]-hydrogenases: X- and W-band EPR studies, in 31st EPR An- nual International Meeting, Manchester, RSC (1998).

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

[4] Laßmann G., Lendzian F., Pötsch S., Bleifuß G., Hofbauer W., Kolberg M., Thelander L., Gräslund A., & Lubitz W., Structure of tryptophan radicals in mutants of protein R2 of ribonucleotide reductase studied by X-Band EPR, ENDOR, and by high-ﬁeld EPR, J. Inorg. Biochem. 74, 201 (1999).

[5] Laßmann G., Lendzian F., Pötsch S., Bleifuß G., Hofbauer W., Kolberg M., Thelander L., Gräslund A., & Lubitz W., Structure of tryptophan radicals in mutants of R2 of ribonucleotide reductase studied by X-band EPR/ENDOR and by high-ﬁeld EPR, J. Inorg. Biochem. 74, 201 (1999).

[6] Hofbauer W., Zouni A., Bittl R., Kammel M., Fromme P., Lendzian F., Witt H.T., Lu-

bitz W., Krauss N., & Orth P., EPR characterization of the tyrosyl radical YD¢ in active photosystem II single crystals at 94 GHz, in High Frequency Electron Paramagnetic Re- sonance, Amsterdam, Royal Netherlands Academy of Arts and Sciences (2000).

[7] Hofbauer W., Zouni A., Bittl R., Kern J., Orth P., Lendzian F., Fromme P., Witt H.T., & Lubitz W., HF-EPR on a tyrosine radical in single crystals of photosystem II, in Rund- gespräch “Anwendungen der Magnetischen Resonanz in der Bio- und Materialwissen- schaft”, Riezlern, DFG (2000).

[8] Hofbauer W. & Bittl R., A novel approach to separating EPR lines arising from species with different transition moments, in Rundgespräch “Anwendungen der Magnetischen Resonanz in der Bio- und Materialwissenschaft”, Riezlern, DFG (2000).

[9] Hofbauer W., Zouni A., Bittl R., Kern J., Orth P., Lendzian F., Fromme P., Witt H.T., & Lubitz W., HF-EPR on a tyrosine radical in single crystals of photosystem II, in Struc- ture and Function in Oxygenic Photosynthesis, Roscoff, Centre National de la Recherche Scientiﬁque (2000).

[10] Bleifuß G., Kolberg M., Pötsch S., Hofbauer W., Lubitz W., Gräslund A., Laßmann G., & Lendzian F., Tryptophan and tyrosine radicals in ribonucleotide reductase: A comparative high-ﬁeld EPR study at 94 GHz, Biochemistry (submitted).

vi [11] Rudolf T., Pöppl A., Hofbauer W., & Michel D., X, Q and W band electron paramagnetic resonance study of the sorption of NO in Na-A and Na-ZSM-5 zeolites, Phys. Chem. Chem. Phys. 3, 2167–2173 (2001).

vii viii Contents

Introduction 1

I Theoretical and Experimental Background 5

1 Principles of EPR 7 1.1 Spin Hamiltonian ...... 7 1.1.1 Zeeman Interaction ...... 8 1.1.2 Electron Exchange Interaction ...... 9 1.1.3 Electronic Dipolar Interaction ...... 9 1.1.4 Hyperﬁne Interaction ...... 11 1.2 Spectroscopic Aspects ...... 11 1.2.1 Line Broadening ...... 11 1.2.2 Sample Orientation ...... 12 1.2.3 Transition Strength ...... 14 1.2.4 Saturation ...... 15 1.3 Classiﬁcation of EPR Experiments ...... 16 1.3.1 Continuous Wave EPR ...... 16 1.3.2 Transient EPR ...... 16 1.3.3 Pulsed EPR ...... 17 1.4 Multiple Resonance Experiments ...... 18 1.4.1 Continuous Wave ENDOR ...... 18 1.4.2 Pulsed ENDOR ...... 18

2 Experimental Setup 25 2.1 Magnet ...... 26 2.1.1 Field Calibration ...... 26 2.2 Resonator ...... 28 2.2.1 Sample Mounting ...... 29 2.3 Microwave Bridge ...... 29

ix II Methodological Developments for High Field EPR 33

3 Optical Excitation and Transient EPR 35 3.1 Experimental Setup ...... 35 3.1.1 Light Access to the Resonator ...... 35 3.1.2 Light Source and Transport ...... 36 3.1.3 Trigger Control ...... 38 3.1.4 Bandwidth and Detection Mode ...... 38 3.2 Transient EPR on the Triplet State of Pentacene ...... 39 3.3 Conclusion ...... 42

4 Soft Pulse Electron Spin Echoes 43 4.1 Standard Methods to Disentangle Spectra ...... 43 4.2 Theoretical Description ...... 45 4.2.1 Short Pulses ...... 45 4.2.2 Spin Dynamics Simulation ...... 46 4.2.3 FID after a Long Pulse ...... 47 4.2.4 Long Pulse Echoes ...... 47 4.2.5 Flip Angle Selective Signal Suppression ...... 51

4.3 Experimental Demonstration ...... 51 ¥ 4.3.1 Mn2 ¥ and Cr3 in CaO ...... 51 4.3.2 DTNE Complex ...... 53 4.3.3 Mn-Catalase ...... 55 4.4 Conclusion ...... 57

III Application of High Field EPR to Biological Systems 59

5 Overview of Photosynthetic Reaction Centers 61 5.1 Photosynthesis in Plants and Cyanobacteria ...... 61 5.1.1 Photosystem I ...... 62 5.1.2 Photosystem II ...... 65 5.2 Photosynthesis in Purple Bacteria ...... 68 5.2.1 Subunits L and M ...... 70

5.3 EPR on Frozen Solutions and Single Crystals ...... 70

¥ ¦ 6 P700 in Single Crystals of Photosystem I 75 6.1 Materials and Methods ...... 75 6.1.1 PS I Core Complexes ...... 75 6.1.2 PS I Single Crystals ...... 76 6.1.3 cw EPR ...... 76

6.2 Results ...... 77

¥ ¦ 6.2.1 P700 in Frozen PS I Solution ...... 77

¥ ¦ 6.2.2 P700 in Single Crystals of PS I ...... 77

6.3 Discussion ...... 84 ¦ 7 YD in Single Crystals of Photosystem II 89 7.1 Materials and Methods ...... 89 7.1.1 PS II Core Complexes ...... 89 7.1.2 PS II Single Crystals ...... 90 7.1.3 cw EPR ...... 90 7.1.4 Pulsed ENDOR ...... 91 7.2 Results ...... 92 7.2.1 cw EPR of Frozen Solution ...... 92 7.2.2 Pulsed ENDOR on Frozen Solution ...... 92 7.2.3 cw EPR on Single Crystals ...... 95 7.2.4 Analysis ...... 95 7.3 Discussion ...... 107

7.4 Conclusion ...... 112

¦ ¦ § 8 QA§ and QB in Bacterial Photosystem 117 8.1 Simulation of Radical Pair Spectra ...... 118 8.1.1 Spin Hamiltonian for a Spin Coupled Radical Pair ...... 118 8.2 Materials and Methods ...... 121 8.2.1 Sample Preparations ...... 121 8.2.2 cw and Pulsed EPR ...... 122 8.3 Results ...... 122 8.3.1 Analysis of Biradical Spectra ...... 128 8.4 Discussion ...... 130 8.4.1 Inﬂuence of Fitting Methods and Reliability of Parameters . . 130 8.4.2 Implications of J for the Electron Transfer Process ...... 133 8.5 Conclusion ...... 134

Summary and Outlook 137

Zusammenfassung und Ausblick 141

Appendix 145

A Spin Dynamics 145 A.1 Density Matrix Formalism ...... 145 A.2 Rotating Frame Approximation ...... 146 A.3 Bloch Equations ...... 147

xi B Analysis of EPR Spectra 149 B.1 Orientation Dependent Spin Hamiltonian ...... 149 B.2 Deﬁnition of Euler Angles ...... 150 B.3 Simulation of Spectra ...... 151 B.4 Calculation of the Resonance Field Strength ...... 152

C Spin Dynamics Simulation Program 153

xii Introduction

Since its inception in 1944 by E. K. Zavoisky [1], electron paramagnetic resonance (EPR) has become a widely used spectroscopic technique for the investigation of radicals and other species exhibiting electronic paramagnetism. Applications range from chemistry (e.g. identification of intermediate radicals in a reaction) to physics (e.g. investigation of the band structure of semiconductors) and include even less academic topics like radiation dosimetry or quality control in beer brewing [2]. EPR has traditionally played a minor role in comparison to NMR (nuclear magnetic resonance). One reason for this is that only a relatively small class of species exhibit electronic paramagnetism exploitable by EPR. A more important reason is, however, that EPR is much closer to the technological edge in high speed electronics and microwave technology. Only in recent years has microwave technology advanced to a state which allows standard NMR methodology to be transferred to EPR. EPR has traditionally been a continuous wave (cw) technique. Pulsed and time-resolved EPR spectroscopy are still considered to be advanced methods, available to only a minority of EPR facilities. Concurrently with the move to more advanced experiments, it has become possible to considerably extend the frequency range, allowing the use of higher magnetic fields and yielding higher sensitivity and better spectral resolution. At the time of writing, there has been a continuous trend for several years to push the frequency limits further (see e.g. [3–5]). The advances in high field EPR are of particular importance to the study of biological systems. In many of these systems, organic radicals play an important functional role. These radicals require increased spectral resolution to access the rather small g anisotropy. Similarly, the isolation and purification of biological compounds like enzymes is tedious, often limiting the sample quantity available. The increased sensitivity of high field EPR makes the study of such samples much easier. Combined with other high-resolution magnetic resonance techniques like ENDOR [6], the possibilities in biological research are dramatically extended. In 1996, Bruker introduced the first commercial EPR spectrometer operating in the W-band frequency range (94 GHz) [7]. The commercial availability means that this kind of advanced spectroscopy is now available to research groups without the resources to develop a spectrometer of their own. At the Max-Volmer-Institute for Biophysical Chemistry at the Technical University

1 2 INTRODUCTION

Berlin, biologists, physicists, and chemists work together to manipulate, isolate, and investigate protein-cofactor complexes. The group of Prof. Lubitz at the TU Berlin has a particularly strong foothold in EPR and ENDOR spectroscopy. The installation of the 94 GHz Bruker spectrometer in 1997 was the basis for new original work, some of which is reported in this thesis. This thesis is divided into three parts. A short overview of EPR foundations is given first. The second part concentrates on apparative and methodological developments that extended the application range of this high field EPR spectrometer. Finally, the third part presents studies on three different photosynthetic reaction centers. The photosynthetic apparatus of plants, algae and bacteria has long been a field of intense research. Many details of its working could be elucidated in the last years. It is, however, still unclear how the protein/cofactor complexes in the thylakoid membrane implement this process. An understanding of how the protein matrix custom-tailors bound cofactors into a fine tuned electron transfer chain will yield many insights that will hopefully be transferable to other biological systems. It might even be possible in the future to mimic the photosynthetic process for the industrial conversion of solar energy into chemical energy carriers. EPR and ENDOR are excellent tools to probe the electronic structure of the cofactors in the electron transfer chain in these reaction centers [8–10]. The local structure of paramagnetic cofactor states can be accessed by the g and hyperfine interaction tensors while dipolar and exchange coupling parameters provide information about how these individual cofactors are turned into a chain. Besides the relevance of these experiments for biophysics, they present a demonstration of the possibilities as well as limitations of 94 GHz EPR. The orientation- dependent spectra of the primary donor in photosystem I exhibit a broad, poorly resolved EPR line. Still, it is possible to analyze these spectra and obtain orientation data for the g tensor with remarkable accuracy. In contrast, the tyrosine D radical in single crystals of photosystem II yields well resolved spectra. High field EPR serves here for separating the Zeeman anisotropy from the complex hyperfine structure, thus enabling an accurate analysis of the orientation of the radicals in the crystal. Lastly, the experiments on frozen solutions of coupled quinone radicals in bacterial reaction centers show that thanks to the excellent spectral resolution of high field EPR, detailed geometric information can be obtained even from disordered samples. However, the strength of the exchange interaction between the quinone radicals turns out to be just beyond the capabilities of 94 GHz EPR. Findings such as this motivate the desire for EPR experiments at even higher frequencies.

REFERENCES

[1] Zavoisky E.K., Paramagnetic Absorption in Orthogonal and Parallel Fields for Salts, Solutions and Metals, Ph.D. thesis, Kazan University (1944). REFERENCES 3

[2] Barr D., Measuring ﬂavor stability of beer using the Bruker EMX spectrometer, Bruker Analytik EPR application note.

[3] Lebedev Y.S., Very-high-ﬁeld EPR and its applications, Appl. Magn. Reson. 7, 339–362 (1994).

[4] Earle K.A., Tipikin D.S., & Freed J.H., Far-infrared electron-paramagnetic-resonance spectrometer utilizing a quasioptical reﬂection bridge, Rev. Sci. Instrum. 67, 2502–2513 (1996).

[5] Fuchs M.R., Prisner T.F., & Möbius K., A high-ﬁeld/high-frequency heterodyne induction-mode electron paramagnetic resonance spectrometer operating at 360 GHz, Rev. Sci. Instrum. 70, 3681–3683 (1999).

[6] Feher G., Observation of nuclear magnetic resonances via the electron spin resonance line, Phys. Rev. 103, 834–835 (1956).

[7] Schmalbein D., Maresch G.G., Kamlowski A., & Höfer P., The Bruker high-frequency- EPR system, Appl. Magn. Reson. 16, 185–205 (1999).

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

[9] Levanon H. & Möbius K., Advanced EPR spectroscopy on electron transfer processes in photosynthesis and biomimetic model systems, Ann. Rev. Biophys. Biomol. Struct. 26, 495–540 (1997).

[10] Möbius K., Primary processes in photosynthesis: What do we learn from high-ﬁeld EPR spectroscopy?, Chem. Soc. Rev. 29, 129–139 (2000). 4 INTRODUCTION Part I

Theoretical and Experimental Background

Chapter 1

Principles of Electron Paramagnetic Resonance

1.1 Spin Hamiltonian

Magnetic resonance experiments observe transitions between quantum states associated with a magnetic dipole moment. Magnetism at the atomic level is tied to the spins of the electrons and nucleons as well as orbital angular momentum. Usually, an external static magnetic field is applied to the system under investigation in order to lift degeneracies of the magnetic energy levels. The quantum energies of the relevant magnetic transitions are typically small compared to electronic or nuclear transition energies. Therefore, it is possible to treat magnetic resonance experiments by perturbation theory. Using this approach simplifies theory because it can be confined to a Hilbert space with only spin and angular momentum components. The effect of the neglected degrees of freedom is included in the form of parameters to this model. This very successful method for the description of magnetic resonance experiments is the so-called spin Hamiltonian formalism. The Hamiltonian models the system by a power series expansion in angular momentum operators jî commonly denoted as spin

operators, even though they may have orbital momentum contributions:

1 2 3

ˆ ¨ ˆ ˆ ˆ ˆ ˆ ˆ

H ∑ci ji ∑ci j ji j j ∑ ci jk ji j j jk (1.1)

i i j i j k ©

The n-th order coupling constants c n reflect the effect of the neglected electronic states and the strength of the applied magnetic field B. In most cases, the rapid conver- gence of the series allows to restrict the spin Hamiltonian to only very few low-order terms. The Hamiltonian is further simplified by the fact that many coupling constants have to vanish for symmetry reasons. It is also convenient that the spin Hamiltonian describes a system in a Hilbert space of finite (and usually very low) dimension, easing algebraic or numerical treatments. In the following, the most important low-order terms of the spin Hamiltonian will

7 8 CHAPTER 1. PRINCIPLES OF EPR be introduced.

1.1.1 Zeeman Interaction The magnetic coupling of an applied homogeneous magnetic ﬁeld and an electron spin S resp. a nuclear spin I is called Zeeman interaction. The coupling is described in units of the Bohr magneton and nuclear magneton, respectively, and a coupling matrix g

commonly referred to as the g tensor.

T ˆ

ˆ ¨

HZ e µBB gS S (1.2)

ˆ ¨ ˆ HZ n µnB gI I (1.3)

The coupling matrix g for a resting free electron is isotropic and can therefore be

¨ given by a scalar factor ge 2 0023193043737 38 [1] . The local field at the position of the electron can however be different from the externally applied magnetic field. In particular, the interaction of the electron spin with orbital magnetism (spin-orbit coupling) leads to admixture of other electronic states with orbital momentum (see e.g. [3]). Therefore, the “effective spin” is not a pure spin state any longer, but also includes orbital components, and the effective g value is changed. When the orbital structure of the considered system is anisotropic, the spin-orbit coupling reflects the orientation dependence, thereby giving rise to a tensorial g. Every system more complex than a single atom is anisotropic; an isotropic g can however occur also in systems with reduced, i.e. cubic, symmetry.

The “quantization direction”, i.e. the direction of the expectation value of the spin T in an eigenstate, is determined by the effective ﬁeld Beff ¨ g B. The magnetic dipole

moment of the spin is therefore always parallel to the effective ﬁeld:

T T T T ¨ Beff µ Beff Beff B gg B (1.4)

Consequently, only the symmetric tensor ggT is accessible to spectroscopy. This tensor can be given by its principal values and the orientation of the orthogonal eigen- system relative to a reference frame. Since asymmetries of g are not observable, it is customary to describe g itself in terms of principal values and an orientation relative to a reference frame.

Similar theory applies for nuclear spins. The nuclear g factors for protons and

¨ ¨ neutrons are gp 5 585694675 57 and gn 3 82608545 90 , respectively [1]. The g factors of compound nuclei can therefore vary over a large range. Since nuclear spin-orbit coupling is several orders of magnitude stronger than the interaction of the nucleons with the electron shell or an applied magnetic ﬁeld, the nuclear eigenstates are not noticeably disturbed and the nuclear g factor can be considered isotropic.

1The g factor of a free electron is deﬁned positive here for historical reasons only. For a detailed discussion of the sign of g factors, refer to [2]. 1.1. SPIN HAMILTONIAN 9

1.1.2 Electron Exchange Interaction In the spin Hamiltonian, spatial coordinates are completely eliminated. This is a valid approach if the spatial component of the wavefunction is not correlated with the spin component. The Pauli principle however establishes a very strict correlation: the total wavefunction of a multi-electron system has to be antisymmetric. A transition between two spin states can therefore lead to energy shifts of the spatial component of the wavefunction. This energy shift has to be reproduced in the spin Hamiltonian. The energy associated with the change of the spatial wavefunction component is primarily caused by Coulomb interaction between electrons

e2 ¨

Eee (1.5) 4πε0r This leads to a coupling constant between the spin-carrying electrons that is given by the exchange integral

¨ ψ ψ

J 1 2 (1.6) 4πε0r ψ where 1 2 refer to the spatial wavefunctions of the uncoupled electrons. Using this

constant, the interaction can be written as

ˆ ˆ

ˆ ¨

Hex 2J S1 S2 (1.7)

The Coulomb interaction potential can be crudely approximated by a Dirac δ dis-

tribution. In this light, it is easy to recognize that J is related to the overlap integral

ψ ψ 1 2 . In weakly exchange coupled systems, J can therefore provide insight about tunneling probabilities involved in electron transfer processes. Exchange interaction can also be mediated via excited electronic states (“kinetic exchange”). Smaller contributions are due to changes in spin-orbit coupling, confor- mational changes, etc. The resulting exchange interaction is therefore not necessarily isotropic. In common use, the term “exchange interaction” is, however, used for the isotropic part of spin-spin interactions while anisotropic components are included in dipolar coupling terms (see below).

1.1.3 Electronic Dipolar Interaction

Two magnetic dipole moments µ1 and µ2 separated by a distance vector r interact with

an energy

T T T

µ0 µ1 µ2 3 µ1 r µ2 r Edd ¨ (1.8) 4π r3 r5

The dipolar interaction between two electron spins S1 and S2 can be rewritten in terms of spin operators Sˆ1 and Sˆ2. It is, however, not trivial what magnetic moment has to be associated with them. For large distances, the dipole moment is given by the

10 CHAPTER 1. PRINCIPLES OF EPR

moment of the electron and its environment as a whole, i.e. µ1 2 g1 2S1 2 . When the electrons are close to each other, they see each other “naked” and the ge value of a free electron has to be used. This complication is often neglected as in many cases the g factors differ only slightly from ge.

Substituting ge for g, one arrives at

T T T

2 2 T

g µ µ Sˆ Sˆ Sˆ r Sˆ r

e B 0 1 2 1 2 ˆ ˜ ˆ

Hˆdd ¨ 3 S1 D S2 (1.9)

π 3 5 4 r r where the coupling tensor D˜ has the elements 2 2 2 2 geµBµ0 r 3x

D˜ ¨ (1.10)

xx 4π r5

2 2

geµBµ0 3xy D˜ ¨ (1.11)

xy 4π r5

For tightly coupled electrons, the Hamiltonian is usually written in terms of S ¨

ˆ ˆ

S1 S2. The dipolar coupling is then written as

T ˆ ˆ Hˆdd ¨ S D S (1.12) where

1 ˜ ¨

D D (1.13) 2 The coupling tensor D is symmetric and can be diagonalized by choosing a suitable orthogonal reference system:

Dxx 0 0

D 0 Dyy 0 (1.14)

0 0 Dzz The dipolar coupling tensor is usually considered to be traceless. The dipolar coupling tensor can, however, contain an isotropic contribution caused by the neglected g anisotropy. In practice, it is however often included into the scalar J coupling term discussed above. Therefore, it is sufﬁcient to deﬁne two parameters D and E such that

D D E (1.15) xx 3

D D E (1.16) yy 3

D D (1.17) zz 3 It should be noted that the dipolar coupling can be written as a symmetrical tensor even if the approximation of using ge is not valid any more. However, the geometrical interpretation of the coupling parameters is less clear in those cases. 1.2. SPECTROSCOPIC ASPECTS 11

Figure 1.1: Lorentzian (left) and Gaussian (right) line shapes. Note that the Lorentzian is given in frequency space due to its relation to a relaxation rate k. The Gaussian distribution of the effective magnetic ﬁeld B is characterized by the standard deviation σB.

1.1.4 Hyperﬁne Interaction The magnetic interaction between electronic and nuclear magnetic moments is called

hyperﬁne interaction:

T T T

µ µ µ 3 µ r µ r 2µ

0 e n e n 0 ψ 2 T ¨

Ehfc 0 µ µn (1.18) 4π r3 r5 3 e In contrast to the purely dipolar electron-electron interaction discussed in section 1.1.3, eqn. 1.18 contains an additional isotropic term. This term, called “Fermi contact interaction”, reﬂects the overlap of the electronic and nuclear wavefunctions2. Usually, the electronic wavefunction shows structure on a much larger length scale

then the size of a nucleus, and it is sufficient to resort to a 0th order approximation (hence ψ 0 , where 0 represents the location of the nucleus). Therefore, the isotropic part of the hyperfine interaction can be used to probe the electronic spin density. The spin Hamiltonian for the hyperfine interaction can be written in analogy to

eqn. 1.9 as

T ˆ Hˆhf ¨ S A Iˆ (1.19) where the hyperﬁne interaction tensor A is symmetric and given in terms of its principal values Ax, Ay, Az, and its orientation.

1.2 Spectroscopic Aspects

1.2.1 Line Broadening Homogeneous Broadening Decoherence in the dynamics of the system can lead to broadening of the observed transition. In the simplest model, coherence decays exponentially over time with a re- 2A proper derivation of this term is rather involved. For some basic arguments on the origin of the contact interaction see e.g. [4]. 12 CHAPTER 1. PRINCIPLES OF EPR laxation rate3 k. The exponential decay in time is equivalent to a Lorentzian lineshape in the frequency domain:

πk

¨ ν ν

L 0 2 2 2 (1.20)

π ν ν

k 4 0

To simulate a spectrum with Lorentzian line broadening, the convolution has to take place in the frequency domain. EPR spectra are typically obtained as a function of the magnetic ﬁeld B. The nonlinear transformation between spectra depending on ν and B must therefore be taken into account. Only for narrow spectra, i.e. ∆B 1, the B nonlinear transformation can be neglected.

Inhomogeneous Broadening Often, what appears to be one line in EPR spectroscopy is really the unresolved superposition of multiple spectral lines. This can be caused by inhomogeneous samples or by the inhomogeneity of the applied magnetic field B. Therefore, this effect is referred to as “inhomogeneous broadening”. Another and often more important contribution to inhomogeneous broadening is unresolved hyperfine splitting. While sample heterogeneity can lead to peculiar lineshapes reflecting the statistical distribution of microstates of individual specimen (often referred to as “g strain”), other mechanisms usually result in a Gaussian lineshape. This is easy to see for hyperfine couplings that lead – in good approximation – to symmetrical splitting of the original line. An ensemble of hyperfine-split lines therefore results in a multinomial distribution of resonance frequencies which, in the limit of a large ensemble, approaches a Gaussian, i.e. 2 B ! B 0 "

1 2

§ 2σ

¨ B

G B B0 e (1.21) 2πσB It is also evident that the inhomogeneous linewidth is in general anisotropic. In the case of a Gaussian lineshape, the linewidth parameter σB appears in quadratic form

1 σ § only. Therefore, the anisotropic linewidth tensor B is symmetric and can be given in terms of its principal values and orientation.

1.2.2 Sample Orientation EPR spectra are dependent on the orientation of the applied ﬁelds relative to the sample. When looking at an ensemble, the observed spectrum is a superposition of spectra

of individual specimen:

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

3For a slightly more realistic description, see appendix A. 1.2. SPECTROSCOPIC ASPECTS 13

Figure 1.2: Derivative spectra of a crystalline sample with four sites per unit cell and an anisotropic g tensor for different turning angles about an axis.

Figure 1.3: Integral (left) and derivative (right) EPR spectrum of a powder or solution sample with anisotropic g tensor and no hyperﬁne couplings. 14 CHAPTER 1. PRINCIPLES OF EPR

φ θ ψ φ θ ψ $ $

where , , are Euler angles, p is the probability density for ﬁnding a spec-

imen of that orientation, and Iφθ B the corresponding spectrum. Iφθψ B can be con-

structed by adjusting the spatial coupling parameters (tensors) according to ¨

Ci Ri jCj ¨

Ci j RikR jlCkl (1.23)

$ $ where R ¨ R φ θ ψ is a rotation matrix. In the case of crystals, eqn. 1.22 is reduced to a sum over the different orientations of the sites in the crystal structure. The resulting spectra depend on the orientation of the crystal in the external field (Fig. 1.2). For solutions or sufficiently fine-grained powders, and in the absence of interactions causing partial orientation, an isotropic

distribution pφθψ ¨ const can be assumed. Neglecting line broadening, this leads to singularities in the derivative spectrum. In the presence of line broadening, these singularities lead to signiﬁcant features in the spectrum that typically exhibit the principal values of involved coupling tensors (Fig. 1.3). A detailed discussion of orientation dependent EPR spectra for the cases relevant to this thesis is given in appendix B.

1.2.3 Transition Strength

The transition probability between two states i and f is given by Fermi’s golden rule as

2π 2

¨ ˆ δ ν ∆

pi % f f H1 i h E (1.24) &

h¯ &

& &

where H is the perturbing Hamiltonian. In the case of EPR, i and f are the ini-

1 tial and final states of the spin system in the externally applied static field B0. The perturbing Hamiltonian represents the interaction with the magnetic component of the applied microwave field. The delta term results from the conservation of energy and represents the resonance condition. When the Zeeman interaction with the static field is isotropic and there are no

competing other interactions, the eigenstates of the spin system are characterized by ( the magnetic quantum number m. In this case, only m ' m 1 transitions are possible. The associated dipole moments are perpendicular to the static magnetic ﬁeld and scale with

ˆ )

m 1 Sx m S S 1 m m 1 (1.25) When the Zeeman interaction becomes anisotropic, or when other interactions per- turb the eigenstates of the system, other transitions may become possible. These so- called “forbidden transitions” increase the complexity of the observed EPR spectra. Since the transition dipole moments may have different orientations, the obtained spectra also depend on the polarization of the applied microwave ﬁeld. 1.2. SPECTROSCOPIC ASPECTS 15

Figure 1.4: Saturation behavior for varying microwave power.

1.2.4 Saturation In many experiments, it is assumed that the system under investigation is close to thermal equilibrium. This is only true if the applied electromagnetic field is sufficiently weak since that field induces transitions between the involved states. For a two-level system with incoherent dynamics (due to coupling to the environment) this can be written as a set of rate equations [5]

¨ B N n n (1.26) dt 1 2

¨ B N n n (1.27) dt 2 1

where n1, n2 denote the population of the respective state, N is the number of photons, and B the Einstein coefﬁcient. For the population difference n ¨ n2 n1, this results in

2 B N n (1.28) dt On the other hand, relaxation effects drive the system towards thermal equilibrium (denoted by a population difference n0) with a rate k. Therefore, the total rate equation is

2 B N n k n n (1.29) dt 0 The general solution to this equation is an exponential decay towards a stationary population difference

n0 ¨ n 2BN (1.30)

1 k which leads to a stationary photon absorption rate of

¨ ¨ wN 2 B N n 1 1 (1.31)

2BN k 16 CHAPTER 1. PRINCIPLES OF EPR

Figure 1.5: Left: Monitoring a decaying paramagnetic species with transient EPR at low microwave power levels. Right: Rabi oscillations on a quasi-stationary paramagnetic species at high microwave power levels.

Therefore, the EPR absorption signal is proportional to the intensity of the irradiated electromagnetic ﬁeld at low intensities, but is limited by the relaxation rate k at high intensities. This effect is called saturation and can be used to probe k. More often though, saturation effects are undesirable because they can lead to severe distortion of the spectra.

1.3 Classiﬁcation of EPR Experiments

1.3.1 Continuous Wave EPR Continuous wave (cw) EPR is experimentally the easiest EPR technique. Though tech- nically not entirely correct (see section 1.3.2), the term usually implies acquiring the stationary absorbance of an incident electromagnetic field as a function of frequency, applied magnetic field, temperature, etc., ignoring kinetic or dynamic effects. The stationary nature of the cw experiment means that spin dynamics are incoherent. Usually, the interaction with the apparatus is kept weak (non-saturating conditions) so that the sample can be considered to be infinitesimally close to thermal equilibrium. In some special applications (like zero field magnetic resonance experiments), the frequency of the applied electromagnetic field is swept to obtain a spectrum. For technical reasons, the usual way to perform cw EPR experiments is to keep the transition frequency constant and sweep the applied magnetic field B0 instead. For sensitivity reasons, virtually all spectrometers use effect modulation techniques to detect the signal. Cw EPR spectra are therefore universally given as the derivatives of the true spectra.

1.3.2 Transient EPR Transient EPR is closely related to the cw EPR experiment. The major difference is that the system is not stationary any more, and its kinetics are monitored by accessing the EPR spectra in a time-resolved way. 1.3. CLASSIFICATION OF EPR EXPERIMENTS 17

The non-stationary state of the system is generated by a nonadiabatic process. Ex- amples include light ﬂash excitation, starting a chemical reaction, stepping the static magnetic ﬁeld or the microwave power level, etc. At low microwave power levels, i.e. under nonsaturating conditions, the time resolved cw experiment monitors the buildup and/or decay of paramagnetic species. At higher powers, the microwave irradiation itself begins to steer the dynamics of the system, and coherent Rabi oscillations become observable. From these oscillations, both properties of the spectrometer and of the sample can be derived (Fig. 1.5). To improve time resolution of transient experiments, the EPR signal is usually measured directly, without the help of effect modulation techniques. The loss of sensitivity is often compensated by large spin polarizations obtained in preparing the transient state.

1.3.3 Pulsed EPR Pulsed EPR experiments use microwave pulses to prepare the spin system under ex- amination into a non-equilibrium state. Afterwards, the free magnetic induction of the sample is measured, without applying a microwave field. Due to the direct interaction of the applied microwave pulses with the magnetic moment associated with spins, the pulses can be represented by rather simple operators acting on the spin system. This allows to establish a rather intuitive algebraic formalism for the description of the spin dynamics and, consequently, enables the creation of custom pulse sequences to generate almost any conceivable quantum co- herency. These coherences can be used in turn to probe specific properties of the spin system. Recently, pulsed magnetic resonance methods have also come into use for non-spectroscopic purposes like “quantum computing” [6]. Here, only the two most basic pulse experiments are introduced. For an overview of pulsed EPR methods, see e.g. [7]. In the rotating frame approximation (see appendix A), the effect of applied microwave pulses on the spin system can be described as an additional static magnetic field, giving rise to Larmor precession. By adjusting the strength and the duration of the pulse, different “flip angles”, i.e. partial precession periods, can be achieved. In most experiments, pulses are used to switch the polarization of the spin ensemble between longitudinal (along the static magnetic field) and transversal (perpendicular to the static field).

FID Spectroscopy

FID (free induction decay) spectroscopy accesses the magnetic induction after preparation of the system by a microwave pulse. The initial pulse turns longitudinal polarization into a transversal direction; the transversal magnetization is then measured. As subensembles of the spin system exhibit different Larmor frequencies (reﬂecting 18 CHAPTER 1. PRINCIPLES OF EPR the EPR spectrum), the spectrum can be recovered by a Fourier transform of the FID signal.

Spin Echo Spectroscopy Spin echo spectroscopy extends FID spectroscopy by adding one or more “refocusing pulse(s)”. The spectral distribution of Larmor frequencies causes the free induction to decay. A refocusing pulse effectively changes the sign of the static magnetic ﬁeld as seen by the spin ensemble, thereby causing a pseudo time reversal of the system’s evolution. The reverse of the induction decay leads to an “echo” of the initial FID which is then measured (Fig. 1.6).

1.4 Multiple Resonance Experiments

Driving a transition between two eigenstates effectively couples these states, thereby establishing a correlation between them. By driving multiple transitions that share at least one state correlations between more than two states are established. Multiple resonance methods use these correlations to identify transitions with shared eigenstates. In a multi-level system, transitions do not necessarily share common states. Experi- ments that are sensitive only to correlated transitions therefore yield simpliﬁed spectra. The best known of these experiments is called ENDOR (Electron Nuclear Double- Resonance) [8]. In ENDOR, the spin system under investigation is comprised of weakly interacting electronic and nuclear spins. For such a system, the allowed transitions affect either the nuclear or the electronic spin components only (hence the name). The electronic spin transition is then used to probe the nuclear spin transition. Com- pared to a NMR experiment, ENDOR is selective to nuclei coupled to an electron spin. Compared to EPR, the NMR transitions yield a much higher spectral resolution. This allows to access the hyperﬁne interaction with high accuracy.

1.4.1 Continuous Wave ENDOR In the cw ENDOR experiment, cw NMR and cw EPR are combined. The EPR transition is usually driven under saturation conditions. When a nuclear resonance is hit, the nuclear sublevels are coupled, thereby providing an alternate relaxation path. This leads to a decrease of saturation, and therfore to an increased EPR signal (Fig. 1.7).

1.4.2 Pulsed ENDOR In contrast to cw ENDOR, pulsed ENDOR experiments can utilize coherent spin dynamics and need not necessarily rely on relaxation effects. The two most common methods were introduced by Mims and Davies. A good overview of pulsed ENDOR methodology can be found in [9]. 1.4. MULTIPLE RESONANCE EXPERIMENTS 19

a b c

e f g

Figure 1.6: Evolution of a spin echo in the rotating frame: Magnetization is turned away from the

π + direction of the static magnetic ﬁeld B* by a 2 pulse (a). Inhomogeneous broadening leads to diffusion π of the magnetization in a plane perpendicular to B* (b, c). A pulse ﬂips the magnetization over (d). Inhomogeneous broadening now reverses the dephasing process (e, f), leading to an echo of the initial magnetization (g). 20 CHAPTER 1. PRINCIPLES OF EPR

m m S I −½ 1 +½ c b c +½ 2

−½ c 3 b −½ c 4 +½

1 , Figure 1.7: Left: energy level splittings of a weakly coupled electron/nuclear spin system (S , I 2 ) in an external magnetic field. Energy contributions: a) electron Zeeman term, b) nuclear Zeeman term, c) hyperfine interaction. Allowed transitions flip only either the electron spin or the nuclear spin. Right:

relaxation pathways in the four-level system (dotted). Saturation of the 1 - 3 EPR transition can be

reduced by driving an NMR transition. i.e. 1 - 2, that enhances relaxation. 1.4. MULTIPLE RESONANCE EXPERIMENTS 21

Mims ENDOR The ENDOR experiment introduced by Mims [10] is based on an stimulated electron spin echo experiment. By irradiating a π RF pulse before the ﬁnal pulse, the resonant nuclear spins are ﬂipped. The correlation between the electronic spin states within one subsystem of same mI is therefore destroyed, preventing an echo (Fig. 1.8). It should be noted that the timing of the pulse sequence can lead to additional correlations between the subensembles, resulting in “blind spots”, i.e. NMR frequencies where no ENDOR effect is observed.

Davies ENDOR Davies’ ENDOR method [11] is based on an electron spin inversion recovery experiment. The selective initial inversion pulse causes a spectral hole in the electron spin population (Fig. 1.9). Again, a resonant π RF pulse ﬂips nuclear spins, thereby swap- ping the spectral position of spin subensembles with different polarization and “ﬁlling” the spectral hole. The spectral hole is then probed by a two pulse echo sequence. For small NMR transition frequencies, the corresponding spin subsystem are spectrally very close and share about the same spin polarization. Therefore, Davies ENDOR is insensitive towards NMR transition frequencies smaller than the width of the spectral hole created by the microwave inversion pulse. 22 CHAPTER 1. PRINCIPLES OF EPR

π/2 π/2 π/2

mw echo

RF π

1 1 , Figure 1.8: Mims ENDOR pulse sequence and evolution of spin level population in an S , 2 , I 2 system. The ﬁrst two microwave pulses generate a coherent superposition of spin states within each subsystem of the same nuclear spin state. The RF pulse transfers coherence between the subsystems, destroying coherence within each subsystem and suppressing the echo. Correlated populations are indicated by the same ﬁll pattern. π π/2 π

mw echo

RF π

ν ν ν ν

Figure 1.9: Davies ENDOR pulse sequence and corresponding evolution of the spin polarization within an inhomogeneously broadened line. The ﬁrst microwave pulse burns a spectral hole that is ﬁlled by population transfer between NMR sublevels during the RF pulse. REFERENCES 23

REFERENCES [1] Mohr P.J. & Taylor B.N., CODATA recommended values of the fundamental physical constants: 1998, Rev. Modern Phys. 72, 351–495 (2000).

[2] Brown J.M., Buenker R.J., Carrington A., Di Lauro C., Dixon R.N., Field R.W., Hougen J.T., Huttner W., Kuchitsku K., Mehring M., Merer A.J., Miller T.A., Quack M., Ramsay D.A., Veseth L., & Zare R.N., Remarks on the signs of g factors in atomic and molecular Zeeman spectroscopy, Mol. Phys. 98, 1597–1601 (2000).

[3] Carrington A. & McLachlan A.D., Introduction to Magnetic Resonance with Applications to Chemistry and Chemical Physics, chapter 9, Harper & Row (1967).

[4] Slichter C.P., Principles of Magnetic Resonance, chapter 4.6, Springer Verlag, 3rd edition (1989).

[5] Slichter C.P., Principles of Magnetic Resonance, chapter 1.3, Springer Verlag, 3rd edition (1989).

[6] Mehring M., Concepts of spin quantum computing, Appl. Magn. Reson. 17, 141–172 (1999).

[7] Schweiger A., Puls-Elektronenspinresonanz-Spektroskopie: Grundlagen, Verfahren und Anwendungsbeispiele, Angew. Chem. 103, 223–250 (1991).

[8] Feher G., Observation of nuclear magnetic resonances via the electron spin resonance line, Phys. Rev. 103, 834–835 (1956).

[9] Gemperle C. & Schweiger A., Pulsed electron-nuclear double resonance methodology, Chem. Rev. 91, 1481–1505 (1991).

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

[11] Davies E.R., A new pulse ENDOR technique, Phys. Lett. 47A, 1–2 (1974). 24 CHAPTER 1. PRINCIPLES OF EPR Chapter 2

Experimental Setup

The high ﬁeld EPR experiments described in this thesis were performed with a commercial Bruker Elexsys E680 94 GHz cw/pulsed EPR spectrometer [1]. The spectrometer concept has some notable differences from most conventional EPR spectrometers that have to be considered for successful experiments. This chapter aims to describe some unusual concepts used in the spectrometer and discuss experimental consequences. Fig. 2.1 shows a simpliﬁed block diagram including the most prominent subunits of the spectrometer. Most spectrometer operations are controlled from an external workstation (not shown) running a front-end user interface to the real time capable

84.5 GHz L.O. 9.5 GHz Pulsed IF Bridge Mixers

Transient Programmable Modulation Control Pulse Pattern Lock−In Averager Generator

Resonator

Magnet Power Acquisition Supply and Control Server to Workstation 6T Wide Bore Hybrid Magnet

Oversized Waveguide Digital Signal Line Digital Network Coaxial Line Analog Signal Line Other

Figure 2.1: Simpliﬁed block diagram of the Bruker E680 94 GHz spectrometer.

25 26 CHAPTER 2. EXPERIMENTAL SETUP acquisition server.

2.1 Magnet

The magnet used to create the strong magnetic ﬁeld needed for 94 GHz EPR (about

3350 mT at g ¨ 2) follows a rather unusual design concept. The absolute field inhomogeneity over the sample region has to be kept small to profit from the potential spectral resolution of HFEPR while the absolute field is much higher than with conventional spectrometers. These requirements result in the need for a rather bulky magnet. As all practical ferromagnetic materials are saturated at the required fields, the field strength H has to be very large, calling for high currents and a lot of turns of the field inducing coil. To avoid the high energy consumption and heat dissipation of such a magnet, a superconducting coil is used. The coil is split into two halves in a Helmholtz-like arrangement, resulting in easy access to the region of highest field and best homogeneity. To avoid unnecessary boil-off of the cryogen (liquid helium) due to dissipation in the connection to an external power supply, the magnet can be put into persistent field mode via a superconducting short. To change the field, the coil still has to be connected to an external power supply and the short has to be removed. This is done by heating the superconducting short over its critical temperature (“heater switch”). In many experiments, only small variations of the static magnetic field are required.

Therefore, the superconducting coil is complemented by a pair of resistive auxiliary

coils that superimpose an additional magnetic field of 40 40 mT. Using these coils greatly reduces the liquid helium consumption of the system and allows for significantly faster sweeps. The magnet is specified for static fields of up to 6 T. The relative field inhomo- 5 geneity over the sample volume can be estimated to be smaller than 10 § . The field is oriented horizontally. Since the probehead allows to turn samples about the vertical axis, it is possible to measure EPR spectra as a function of the sample orientation with respect to the magnetic field.

2.1.1 Field Calibration One consequence of the magnet design is the particular way the magnetic field is determined. In most EPR spectrometers, the magnetic field is measured by a Hall effect or NMR probe and corrected in a feedback loop. The hybrid magnet used in the 94 GHz spectrometer, however, superimposes two fields with different geometry. Therefore, it is in general impossible to probe the field in one place and deduce the field at the sample position from that value. The only known quantities are the currents through the superconducting and resistive coils. The magnetic field is thus calculated as a linear function of these currents. The constants involved in this calculation have to be determined empirically by taking EPR spectra of standard samples with known g factors. 2.1. MAGNET 27

= I0 = IH H L = I0 L

Figure 2.2: Schematic of the superconducting (left) and auxiliary coil (right) system. The heater switch resistance R acts as a bypass to the superconducting coil.

Throughout this work, Li:LiF has been used as g standard for the range about

g ¨ 2. This sample is prepared from a LiF crystal by heavy neutron irradiation and thermal treatment; as a result microscopic metallic Li clusters are formed. Since these clusters are protected by the rigid LiF lattice around them, they are very stable, and they have a deﬁned chemical environment. The EPR line is very narrow (linewidth below 30 µT at 94 GHz for the sample used). Due to the cubic crystal lattice, the g factor is independent of the crystal orientation. In addition, since the metal clusters exhibit

Pauli paramagnetism, g is virtually independent of the temperature (see e.g. [2]). In a

¨ high precision experiment [3], it has been determined as gLi:LiF 2 002293 2 . If nonlinear magnetic saturation effects of the spectrometer construction material

are neglected, the magnetic ﬁeld depends on the current through the auxiliary coil ac- ¨

cording to B aI b. As both constants a and b have to be determined, it is necessary to measure the EPR line of the Li:LiF sample at two different microwave frequencies, thus yielding two references for the magnetic field. Throughout this work, no significant deviations from the assumed linearity could be observed. This approach is complicated by the fact that the superconducting coils, after switching to persistent mode, tend to lose some current due to relaxation of the flux lattice1. Therefore, it is necessary to perform calibration measurements immediately before or after every EPR experiment when high precision is desired. A much more serious problem for accurate measurements occurs when large field sweeps are required and the current through the superconducting coils has to be ad-

justed. The “open” heater switch still has a rather low resistance ( . 5 Ω) and acts therefore as a current bypass whenever there is some voltage present across the coil (Fig. 2.2). The behavior of the system is governed by the differential equation

L dIL

I I (2.1) 0 L R dt

1 0 Above some critical applied magnetic ﬁeld B / T , superconductivity breaks down. In type II super- conductors, superconducting and non-superconducting phases coexist, forming a 2D current vortex/ﬂux lattice (see e.g. [4]). 28 CHAPTER 2. EXPERIMENTAL SETUP

Ω ¨

For L ¨ 92 H and R 5 , the current through the superconducting coil therefore lags . with a time constant L 1 R 18 s behind the known injected current. To compensate

for this lag, the operating software tries to inject an additional “jump current” IJ ¨

dIL L 1 R dt . This method is limited though because R and L are difficult to access with the required precision. Even worse, R is not constant, but varies with the temperature of the heater switch. This temperature may depend on parameters like the applied voltage or the filling level of the helium reservoir. It also depends on the conditions before the experiment due to the heat capacity of the system. Consequently, the only way to arrive at linear, reproducible sweeps of the magnetic field using the superconducting coils is to keep the induction voltage as low as possible. This in turn requires extremely slow sweeps which are not always practical.

2.2 Resonator

The microwave resonator in any EPR spectrometer has to satisfy two contradictory goals: it has to maximize the interaction of the sample with the magnetic component of the microwave field while simultaneously minimizing dielectric losses due to the sample. The first property is characterized by the conversion factor κ which describes the relation between the applied microwave power and the magnetic field strength at the sample location:

κ ) B1 ¨ Pmw (2.2) The conversion factor itself is closely tied to the quality factor Q which is deﬁned as

Eνmw

Q ¨ (2.3) Pmw where E is the steady-state microwave energy in the resonator, νmw the microwave frequency, and Pmw the applied microwave power. It immediately follows that the microwave energy density, and therefore the magnetic ﬁeld strength in the cavity, increases with Q. Apart from the sample, the main source of dissipation is the material of the resonator itself. For a cavity, most losses are due to resistive dissipation at the cavity walls. The surface scales quadratic with the linear scale of the cavity. The microwave energy, however, is distributed over the cavity volume which scales cubic relative to

λ ν 1 the linear size. As the cavity size is determined by the wavelength ¨ c mw, Q

λ ν 1 generally varies as Q mw§ . The construction of good microwave cavities is therefore getting increasingly difﬁcult with the move to higher frequencies. One possibility to overcome this problem is to use a harmonic mode of an oversized resonator. This is the approach followed in Fabry-Perot resonators which are widely used in high frequency EPR. This decreases however the conversion factor of the resonator since the microwave energy is distributed over a larger volume. The rather low microwave power available from the Bruker microwave bridge (see section 2.3) prohibits the use 2.3. MICROWAVE BRIDGE 29 of such a resonator when the ability to perform pulsed experiments is required. Con- sequently, the Bruker spectrometer uses a cylindrical cavity operating in TE011 mode. To compensate shifts of the resonance frequency induced by the sample, the resonator volume is adjustable. The resonator is coupled to the waveguide using a small antenna (ﬁg. 2.3). Critical coupling is achieved by an impedance transformer implemented as a movable short at the end of the waveguide (not shown).

2.2.1 Sample Mounting The samples are inserted into the resonator along the cylindrical axis from the top. To reduce microwave leakage, the hole is implemented as a metal pipe with less than 1 mm in diameter and a length of several mm. The sample capillaries are therefore

limited to an outer diameter of 0 9 mm. The capillaries provided by Bruker have an outer diameter of 0 9 mm and an inner diameter of 0 5 mm. For most experiments in

this work, however, clear fused quartz capillaries with an outer diameter of 0 87 mm

and an inner diameter of 0 70 mm were used (Vitrocom #CV7087Q). The larger inner diameter increases the effective sample volume. In addition it allows to mount larger crystals and eases ﬁlling the tube with viscous solutions. The sample capillary dips into the resonator for at most 3 mm (ﬁg. 2.3). This limit is given for one by the height of the resonator, but more often by the amount of dielectric losses caused by the sample that can be tolerated. The active sample volume is therefore restricted to about 3 mm; with the CV7087Q capillaries, this corresponds to about 1 µl.

2.3 Microwave Bridge

The microwave bridge of the spectrometer is designed for both cw and pulsed acqui-

sition modes. It is a superheterodyne design with an intermediary frequency (I.F.) of .

9 5 GHz, i.e. X band frequency. All signal forming and processing is done at the I.F. level (Fig. 2.4). Conversion to/from 94 GHz is done by an additional local oscillator and mixers that are physically separated from the bridge, allowing to place them closer to the probehead and thereby to reduce losses in the waveguides (Fig. 2.5). The converters and the I.F. bridge are connected via semirigid coaxial lines. In the I.F. bridge, a Gunn oscillator is used as a low-noise microwave source. In cw mode, the microwave power is passed through an attenuator to the converter unit. In pulsed mode, microwave pulses are formed by pin diode “pulse shapers”. For each pulse channel, the phase and attenuation can be set individually. The I.F. bridge employs two detectors. For cw and other low-bandwidth applications (e.g. many transient EPR experiments) the I.F. signal is superimposed to a reference signal derived from the Gunn oscillator. The diode effectively works as a mixer, converting the I.F. signal to DC. The recovered DC signal is fed through a low bandwidth, low noise ampliﬁer. 30 CHAPTER 2. EXPERIMENTAL SETUP

sample holder

adjustable plunger

cavity

antenna

waveguide

Figure 2.3: Diagram of the 94 GHz microwave resonator. The resonator volume can be adjusted to compensate frequency shifts induced by the sample. Coupling to the waveguide is achieved using a wire antenna. The magnetic ﬁeld distribution of the fundamental resonator mode is indicated by dashed lines. 2.3. MICROWAVE BRIDGE 31

Gunn MW Source

cw cw Branch cw A 9.5 GHz IF out

Pulse Forming Unit (4 times) pulse pin pulse

A P

from Pulse Generator

Delay Line MW Diode Diode Detecion

A P 9.5 GHz IF in Quad Mixer Mixer Detection

MW PreAmp Quad Out Video Amps

A P

Diode Out Low Bandwidth Amp Attenuator Phase Shifter

Figure 2.4: Block Diagram of the 9 2 5 GHz I.F. pulsed and cw bridge.

Diode Mixer

9.5 GHz IF in

84.5 GHz 94 GHz Gunn Source to/from Resonator

9.5 GHz IF out

Diode Mixer

Figure 2.5: Simpliﬁed schematic of the mixer stage used to convert signals between 9 2 5 GHz and 94 GHz. 32 CHAPTER 2. EXPERIMENTAL SETUP

For pulsed and high speed applications, a balanced quadrature mixer is used. Both phase signals of the quadrature output are fed through high bandwidth (up to 250 MHz) video ampliﬁers. The I.F. bridge is equipped with AFC (automatic frequency control) circuitry. In most cases, however, the oscillator has to be used in free running mode since the AFC is unable to lock to the resonator dip at low microwave powers. Frequency drifts in the free running mode are on the order of only a few kHz which makes this an acceptable limitation. The mixer/converter unit provides another Gunn oscillator and the mixers for con-

version between 9 5 GHz and 94 GHz. The Gunn oscillator is phase-locked to a precision quartz reference oscillator. The converter block also provides the circulator needed for insulation of the transmit and receive channels. There is no microwave am- pliﬁcation at 94 GHz. The maximum available microwave power is therefore limited

to only . 5 mW which places some restrictions on pulsed experiments. The I.F. bridge features an internal frequency counter. Together with the known oscillator frequency of the converter block, it is therefore possible to derive the ﬁnal microwave frequency with an accuracy of about 1 kHz.

REFERENCES [1] Schmalbein D., Maresch G.G., Kamlowski A., & Höfer P., The Bruker high-frequency- EPR system, Appl. Magn. Reson. 16, 185–205 (1999).

[2] Ziman J.M., Principles of the Theory of Solids, chapter 10.2, University Press, Cambridge, 2nd edition (1972).

[3] Stesmans A. & van Gorp G., Novel method for accurate g measurements in electron-spin resonance, Rev. Sci. Instrum. 60, 2949–2952 (1989).

[4] Ziman J.M., Principles of the Theory of Solids, chapter 11.11, University Press, Cam- bridge, 2nd edition (1972). Part II

Methodological Developments for High Field EPR

Chapter 3

Optical Excitation and Transient EPR

Transient EPR adds time as an additional parameter to the observed EPR spectrum. To observe a meaningful time dependence of the EPR signal, the system under exam- ination has to be prepared to a state far from thermodynamic equilibrium before the measurement takes place. This preparation can be achieved by a nonadiabatic change in the Hamiltonian governing the dynamics of the system. The simplest way to achieve this is to turn on the microwave irradiation in a nonadiabatic way, i.e. instantly as compared to the timescale of the relevant spin dynamics. Another way would be to change the magnetic ﬁeld at the beginning of the experiment. With these methods, however, the spin polarization that can be achieved is still rather small and mostly determined by the small Boltzmann population difference. By far more intense signals can be obtained with larger than thermal spin polarization. One way to achieve this is via optical excitation of the sample. Obviously, time-resolved EPR on light induced paramagnetic intermediates is an important tool for investigations of photophysical and photochemical processes. A review of time resolved EPR techniques and their application on the study of photoprocesses is given in [2]. While these experiments are well established at lower frequencies, only few experiments of this type have been reported at W band (e.g. [3–6]). The Bruker spectrometer used throughout this work was not originally designed to perform this type of experiment and needed to be extended for time-resolved EPR on photoinduced states.

3.1 Experimental Setup

3.1.1 Light Access to the Resonator Light access is straightforward to implement if either an open resonator structure is used (i.e. Fabry-Perot type), or if the resonator can be made transparent for light. Nei- ther applies to the cylindrical cavity of the 94 GHz spectrometer used here. The single accessible opening of the resonator is the hole used to insert the sample. The entire

35 36 CHAPTER 3. OPTICAL EXCITATION AND TRANSIENT EPR

Figure 3.1: Positioning of the optical fiber in the resonator. diameter of this opening is usually blocked by the sample capillary. The only possibility for light access is therefore through the sample capillary itself. This was achieved by feeding an optic fiber through the sample holder rod that dips into the sample capillary (Fig. 3.1). Special care has to be taken however to not disturb the microwave characteristics of the resonator. The prototype sample holder rod provided by Bruker allows to adjust how far the fiber extends into the capillary. This feature allows to optimize the illumination of the sample while minimizing dielectric losses due to the fiber entering the resonator. The other end of the fiber is fitted to a male FSMA 905 connector.

3.1.2 Light Source and Transport A Q-switched1 Nd:YAG laser (Spectra Physics Quanta Ray DCR-2(10)) was used to generate short (5 ns), repetitive (10 Hz) light pulses at a base wavelength of 1064 nm with a multimodal beam (about 15 mm diameter). A harmonics generator allows to double, triple, or quadruple the light frequency. For most experiments on photosyn- λ thetic reaction centers, the doubled ( ¨ 532 nm) setting provides suitable quantum

ν ¨

energy of the photons (h 2 3 eV). For the experiments on pentacene described here, the same setting was used. The light energy is transfered to the sample rod via several meters of a silica multimode optical ﬁber (SpecTran HCG-M0365T, Fig. 3.2) that is ﬁtted with a FSMA socket on one end. The dimensions of the laser beam have to be reduced to the core

diameter of this fiber (365 µm). This is done using a f ¨ 50 mm silica lens. Since the smaller cross section greatly increases the light intensity, the laser beam has to be attenuated using a gray filter (6% transmission) in order to not exceed the destruction threshold of the fiber (Fig. 3.3). This threshold is easily reached, even at rather low nominal intensities, due to the multimode structure of the beam and corresponding “hot spots”. The overall transmission from the lens to the sample location was determined to be λ about 50% at ¨ 532 nm by comparing laser pulse energies after the gray filter and at the sample location as measured with a pyroelectric probehead. The laser pulse energy 1Q refers in this context to the quality factor of the laser resonator and not to that of the microwave cavity. 3.1. EXPERIMENTAL SETUP 37 attenuation (dB/km)

wavelength (nm)

Figure 3.2: Attenuation characteristics of the SpecTran HCG-M0365T silica ﬁber used for light access to the sample [7].

f=50 mm lens

fiber

6% gray filter adjustable fiber holder

Figure 3.3: Setup for coupling a laser beam into a silica ﬁber. 38 CHAPTER 3. OPTICAL EXCITATION AND TRANSIENT EPR

was limited by the destruction threshold of the ﬁber at the insertion point. Up to 1 5 mJ per pulse at the sample location could be achieved with this setup, corresponding to

about 4 10 photons. This allows up to 6 5 nmol of sample centers to be excited, corresponding to a sample concentration of 130 mM at a typical sample volume of about 500 nl.

3.1.3 Trigger Control Data acquisition has to be synchronized with the excitation of the sample by the laser. In the setup used, the laser is running freely and triggers the transient recorder. It is desirable to be able to use both positive and negative delays of the trigger signal for the transient recorder relative to the laser pulse. Negative delays allow to include pre- excitation signal components in the acquired transient and use them for studying the kinetics of the rising transient signal or to eliminate baseline drifts by deriving difference spectra. Positive delays allow to observe the transient signal in a small time window a considerable time after excitation. This is useful for studying secondary transient species that are generated indirectly, e.g. by electron or energy transfer processes. The laser provides a synchronization signal tied to the firing of the flash lamps used for excitation of the Nd:YAG rods. The actual laser flash occurs synchronously with the operation of the Q switch and is deferred by about 210 µs to allow for inversion buildup in the laser rods [8]. The flash lamp synchronization signal is used to trigger the programmable pulse pattern generator of the spectrometer which in turn generates a trigger pulse for the transient recorder. By reprogramming the pulse generator, arbitrary delays can be generated. Therefore, the transient acquisition trigger can be chosen from 210 µs before the laser flash to 100 ms thereafter2.

3.1.4 Bandwidth and Detection Mode

Transient spectra are typically measured without modulation of the static ﬁeld B0. Modulation complicates the spectral components of the observed signal in a nonlinear way, making it impractical to observe kinetics on a timescale shorter than the period of the modulation signal. The unmodulated acquisition method therefore potentially allows for larger detection bandwidth. The bandwidth limiting elements in the setup are either the resonator or the microwave detector and signal ampliﬁers used. At a resonance frequency of 94 GHz and

a typical resonator quality of Q . 2000, the resonator bandwidth is about 50 MHz. The frequency response of the quadrature mixer output of the I.F. bridge is determined by the conﬁgurable bandwidth of the video ampliﬁers and can range up to 200 MHz. In order to reduce white noise, it is advisable to match the bandwidth to that of the

2The 100 ms limit is given by the 10 Hz repetition rate of the laser. 3.2. TRANSIENT EPR ON THE TRIPLET STATE OF PENTACENE 39

Figure 3.4: Pentacene (left) and p-terphenyl (right).

Figure 3.5: Rabi oscillations of the pentacene triplet state vs. B0.

resonator. The diode detection output has a much smaller bandwidth (0 4 MHz) and cannot be used to analyze fast kinetic components. It is still useful however to obtain pseudo-stationary spectra of short-lived paramagnetic species.

3.2 Transient EPR on the Triplet State of Pentacene

To examine the performance of the setup, transient EPR experiments were performed on the light-induced triplet states of pentacene in a p-terphenyl host crystal (Fig. 3.4). After laser excitation, pentacene may undergo selective intersystem crossing, resulting in a spin polarized triplet state. A representative two dimensional spectrum of this state is shown in ﬁg. 3.5. As the triplet state is populated from a singlet state, the initial total magnetization is zero. Emissive and absorptive components of the spectrum must therefore be of equal intensity. They are split, however, by the coupling between the unpaired electrons comprising the triplet (Fig. 3.6). The crystalline structure of the sample implies an orientation dependence of the spectra. This orientation dependence is beyond the scope of this chapter and has not been examined further. Time resolved spectra show the decay caused by relaxation at low microwave powers. At high microwave powers, the microwave radiation itself begins to dominate the dynamics of the system, leading to Rabi oscillations (Fig. 3.7). The frequency of these

oscillation is given by the amplitude of the magnetic component of the microwave ﬁeld in the rotating frame as ωR ¨ 8πγeB1. Therefore, it is straightforward to determine the rotating frame ﬁeld B1 from such measurements. B1 itself is proportional to the 40 CHAPTER 3. OPTICAL EXCITATION AND TRANSIENT EPR

Figure 3.6: Spin polarized triplet spectrum obtained immediately after light excitation of pentacene in p-terphenyl.

Figure 3.7: Rabi nutations of the pentacene triplet signal at different microwave power levels. 3.2. TRANSIENT EPR ON THE TRIPLET STATE OF PENTACENE 41

Figure 3.8: Transient EPR signal of the pentacene triplet state (B0 , 3328 mT) obtained by using diode detection, mixer detection, and numerically bandwidth-limited mixer detection.

microwave energy stored in the resonator which depends on the incident microwave power Pmw and the quality factor Q as B1 ¨ κ PmwQ. The conversion factor κ can be

estimated from the observed Rabi frequencies and the spectrometer parameters Q and

1 κ .

Pmw as 0 014 mT W.

The effect of different detection bandwidths is demonstrated in Fig. 3.8. The same transient signal was acquired through the low-bandwidth diode detection channel and the high-bandwidth quadrature mixer channel. The low bandwidth of the diode path causes artefacts most noticeable at the initial rise of the transient which in fact reflects the rise time of the detection amplifier. Although the Rabi oscillation frequency, ωR, is still within the frequency range covered by the diode detection path, significant phase shifts are observed that could lead to a wrong interpretation of the acquired data as compared with the signal acquired via the mixer detection path.

The apparent increased noise level of the mixer-detected signal in ﬁg. 3.8 can be mostly attributed to the higher bandwidth of the system and increased white noise as a result. After limiting the bandwidth of the mixer-detected signal numerically to that of the diode detection path, the signal/noise performances of both detection channels turn out to be similar. Therefore, there is no particular advantage in using the diode detection path for transient EPR. 42 CHAPTER 3. OPTICAL EXCITATION AND TRANSIENT EPR 3.3 Conclusion

Using pentacene in p-terphenyl as a model system, it was shown that transient experiments on light-induced species are possible with the Bruker 94 GHz EPR spectrometer, despite the closed resonator structure and the lack of a dedicated light access path. As a side effect, the effective B1 ﬁeld strength in the resonator and the conversion factor could be determined. Similar experiments on light-induced species can be performed in pulsed EPR mode. It is also possible to use the installed light access path for in situ irradiation of samples prior to EPR experiments.

REFERENCES [1] Hofbauer W. & Bittl R., EPR at 94 GHz of laser-induced species in an ELEXSYS E680 spectrometer, Bruker Report 145, 38–39 (1998).

[2] Stehlik D. & Möbius K., New EPR methods for investigating photoprocesses with paramagnetic intermediates, Ann. Rev. Phys. Chem. 48, 745–784 (1997).

[3] Groenen E.J.J., Poluektov O.G., Matsushita M., Schmidt J., van der Waals J.H., & Meijer

G., Triplet excitation of C60 and the structure of the crystal at 1 3 2 K, Chem. Phys. Lett. 197, 314–318 (1992).

[4] Prisner T.F., Rohrer M., & Möbius K., Pulsed 95 GHz high-ﬁeld EPR heterodyne spectrometer with high spectral and time resolution, Appl. Magn. Reson. 7, 167–183 (1994).

[5] Prisner T., van der Est A., Bittl R., Fromme P., Lubitz W., Möbius K., & Stehlik D., Time-resolved W-band (95 GHz) EPR spectroscopy of Zn-substituted reaction centers of Rhodobacter sphaeroides R-26, Chem. Phys. 194, 361–370 (1995).

[6] van der Est A., Prisner T., Bittl R., Lubitz W., Stehlik D., & Möbius K., Time-resolved

¢ £ ¡

X-, K-, and W-band EPR of the radical pair state P700¢ A1 of photosystem I in comparison

¡ ¢ £ with P865¢ QA in bacterial reaction centers, J. Phys. Chem. B101, 1437–1443 (1997). [7] SpecTran Specialty Optics Company, HCG-M0365T Data Sheet.

[8] Spectra Physics, Inc., Quanta Ray DCR 2(10) Nd:YAG Laser Manual. Chapter 4

Soft Pulse Electron Spin Echoes

With most pulsed EPR spectrometers, available microwave power is not much of a concern and pulses can be kept very short. Consequently, the detailed spin dynamics during the microwave pulses are often neglected. The mixer design of the Bruker E680 W band spectrometer used throughout this work severely limits the available microwave power. This means that rather long microwave pulses have to be used to achieve a given flip angle. The resulting narrow excitation bandwidth imposes restrictions on many standard experiments. A common problem of EPR spectroscopy is the sensitivity towards unwanted paramagnetic impurities. Often, such impurities cannot be avoided in the preparation of the sample. The resulting contamination signals can affect a spectrum to an extent that makes it virtually useless. This is especially true for high field/high frequency EPR. A very common contamination seen in high field/high frequency EPR spectra is free

Mn2 ¥ . A closer investigation of pulsed EPR experiments reveals that long pulses can be exploited to disentangle spectra associated with different transition moments in a surprisingly simple and fast electron spin echo experiment. In particular, the proposed method has proven to be useful to eliminate Mn2 ¥ contamination signals.

4.1 Standard Methods to Disentangle Spectra

The general approach to disentangle EPR spectra is to associate the spectral contributions with distinctive parameters and vary experimental conditions to map out the corresponding parameter space. The most obvious spectral characteristic one could think of is the g factor which allows to separate spectra on the magnetic ﬁeld axis. Other possible “tags” include sample orientation, temperature, longitudinal and transversal relaxation times, spin multiplicities, hyperﬁne interactions, g anisotropy, and transition probabilities. In standard cw experiments, only some of those labels are accessible by the available experimental parameters. Orientation or temperature dependencies are easy to

44 CHAPTER 4. SOFT PULSE ELECTRON SPIN ECHOES

4 5

+5/2

−5/2

+3/2

−3/2

+1/2 −1/2

Figure 4.1: Splitting of Kramers doublets of a S , 2 system in a magnetic ﬁeld. The energies of the 7 ∆mS , 1 transitions differ due to the zero ﬁeld splitting, separating them in a resonance experiment.

access while measuring spectra at saturating microwave power levels or varying modulation frequencies can separate species with different longitudinal relaxation times. In ENDOR experiments, it is possible to address species by their hyperﬁne interaction. While virtually every conceivable label affects cw spectra in some way (e.g. linewidths, relative intensities, or saturation characteristics), the effects are often rather small, making it difﬁcult to exploit them for separating different species.

Time resolved experiments exhibit a much larger experimental parameter space. Adding a single time axis as in transient EPR experiments allows to observe Rabi oscillations which reﬂect the dipole matrix element of the corresponding EPR transition. In pulsed EPR, each pulse adds two more dimensions, pulse duration and separation, to the parameter space. In most pulsed EPR experiments the pulse sequence has to be varied to map out the parameter space and to access the Rabi nutations. Some experiments of this kind can be found in [1–7]. This approach is however usually costly in terms of acquisition time.

The basic idea behind the experiment introduced here is to spread out the EPR signal over the time axis with one ﬁxed pulse sequence. This makes it possible to measure the time-dependent information in one single shot. Therefore, this approach yields the required information without an increase in acquisition time.

4.2. THEORETICAL DESCRIPTION 45

8 8 8 Figure 4.2: A 90 8 – τ – 180 pulse sequence for one species is a 270 – τ – 540 sequence for another species with a three times larger transition moment. For short pulses, the FIDs and echoes differ only in sign. Therefore, the corresponding signals are linearly dependent and a superposition cannot be decomposed.

4.2 Theoretical Description

4.2.1 Short Pulses In the following, an isolated effective Kramers doublet within a spin state of multi-

plicity 2S 1 is considered. The reduction to this two-level system is a good approximation if transitions between other states are off-resonant and therefore not coupled to the transition between the doublet levels, i.e. due to zero ﬁeld splitting (spin-spin

coupling) (ﬁg. 4.1). 9

Upon irradiation of a microwave ﬁeld resonant with the m m 1 transition, the

system oscillates between the states m and m 1 with the Rabi frequency

ω γ ) ¨

1 B1 S S 1 m m 1 (4.1) γ where is the gyromagnetic ratio and B1 is the amplitude of the magnetic microwave component in the rotating frame. The Rabi frequency and therefore the ﬂip angle associated with a microwave pulse of given length is thus tied to the S and m quantum numbers of the respective transitions. This means that the same microwave pulse can cause different ﬂip angles for different species.

For illustrational purposes, two systems are assumed whose Rabi frequencies differ : by a factor of 3. A 90 : pulse for one species would occur as a 270 pulse to the other species. For short pulses, the resulting FIDs differ in sign. Another refocusing pulse generates spin echoes (ﬁg. 4.2). Apart from the change in sign, no noticeable difference is observable for both FIDs or echoes. Therefore, a superposition of both signals cannot be decomposed into separate signals. 46 CHAPTER 4. SOFT PULSE ELECTRON SPIN ECHOES

The effect of long pulses, however, cannot be adequately described by just one parameter such as a ﬂip angle. This is because other contributions to the spin dynamics are no longer negligible compared to the interaction of the spin system with the applied microwave ﬁeld. In order to examine the effects of long pulses for a large set of cases and as part of this thesis, a simulation program was written.

4.2.2 Spin Dynamics Simulation The simulation program described here and listed in appendix C was written with the intent of providing a tool to numerically solve the Liouville-von Neumann equation (see appendix A.1) for a variety of pulse experiments. The program should be

; generic enough to simulate the effect of long pulses for a variety of experiments, and

; speciﬁc enough to allow fast, efﬁcient execution.

To satisfy both requirements, it was decided to simulate the dynamics of an isotropic, inhomogeneously broadened, two-level spin system. Relaxation effects were neglected.

The allowed experiments include arbitrary pulse sequences built from rectangular ( pulses with ( x and y phase. This choice allows to utilize straightforward analytical solutions throughout the program. Only inhomogeneous broadening requires a numerical integration. The program, written in C++, simulates even complex pulse sequences in only a few seconds on a (at the time of this writing) reasonably modern PC or workstation. The input parameters to the simulation program are

; a resonance frequency offset to simulate off-resonant experiments,

; a linewidth parameter describing the inhomogeneous (Gaussian) broadening,

; a “pulse list” describing the pulse sequence,

; and parameters for setting the required observation time window and temporal resolution.

The “pulse list” is a sequence of microwave pulses or delays. Each pulse can have

arbitrary parameters such as

;

phase ( x, x, y, y),

; duration,

; and Rabi frequency. 4.2. THEORETICAL DESCRIPTION 47

Figure 4.3: y component of the transient nutation during and the FID after time-extended microwave

8 < pulses with nominal ﬂip angles of 90 8 and 270 x pulses, respectively.

4.2.3 FID after a Long Pulse The simulation program described above was used to investigate the effect of long

microwave pulses on the observed FID. Fig. 4.3 shows the observed magnetization for

: : nominal 90 : and 270 pulses. The FID after the 90 pulse is rather similar to the FID after a short pulse. The main difference is a slight “wobble” so that the trail of the FID

changes sign. For the 270 : pulse, this “wobble” becomes the dominant feature of the FID. The FID is no longer a pure decay of the transverse magnetization after the pulse. Rather, transverse magnetization builds up and reaches its maximum after a noticeable delay after the end of the microwave pulse.

Φ : To understand this behavior, it is illustrative to decompose the long ¨ 270 pulse

Φ Φ ¨ : ¨ : into a 1 90 – 2 180 sequence. Temporarily neglecting the effect of the long pulse duration, an “equivalent” pulse sequence can be constructed by replacing

Φ Φ Φ Φ ¨ : ¨ : the long 1 and 2 pulses with short 1 90 and 2 180 pulses (ﬁg. 4.4). τ τ This substitution leads to a delay between the pulses, thereby arriving at a 90 : – —

180 : two pulse echo sequence.

: : Dividing the long 270 : pulse into a 90 and a 180 pulse is only one possible partitioning of the pulse. Furthermore, the long pulse could also be divided into 3 or even more pulses. The FID observed after a long microwave pulse can therefore be considered as the superposition of “true” FIDs and multi-pulse echoes of varying order. In this light, the deviation of the apparent FID from a true decay is obvious.

4.2.4 Long Pulse Echoes As shown above, the shape of an FID after a long pulse depends on the nominal ﬂip angle. Therefore, it is in principle possible to separate signal contributions from transitions with different Rabi nutations. In practice, this is problematic because the dead time of the spectrometer after the pulse prevents the acquisition of the entire FID. Re- focusing the FID in an echo experiment for remote detection allows to circumvent this

48 CHAPTER 4. SOFT PULSE ELECTRON SPIN ECHOES

8 8 Figure 4.4: A long 270 8 pulse can be split into a 90 and a 180 pulse. Replacing these with short pulses of equivalent ﬂip angle results in a two-pulse echo sequence. Therefore, the FID after the long

270 8 pulse can be considered to be to some extent a “one-pulse echo”. problem. Ideally, the refocusing pulse in a two-pulse echo experiment would have a ﬂip angle

of 180 : . The dependence of the ﬂip angle on the Rabi nutation frequency applies here, however, as well. It is not clear a priori that a two-pulse echo sequence would work in practice for the purpose of separating the different signal contributions. The feasibility of such a two-pulse echo experiment had to be elucidated by more simulations. Two identical pulses were chosen for the echo sequence in order to obtain uniform excitation bandwidth and therefore avoid additional complications. The simulations shown in ﬁg. 4.5 exhibit several properties:

; Echoes of considerable strength arise even for rather untypical nominal ﬂip angles of the pulses;

; for not too large ﬂip angles, the echo signal begins with a negative contribution and ends with a positive contribution;

; the “center of gravity” of the echo signal shifts along the time axis.

A more quantitative analysis of the echo shapes was performed by plotting the times of the echo minimum, the echo maximum, and the zero crossing between them (fig. 4.6). The minimum of the echo shifts in time by about the pulse length while the position of the echo maximum is less sensitive to the flip angle. The zero crossing of the echo signal, however, varies much more. This is due to changing relative contributions of positive and negative components to the total echo signal. The shape of a field swept echo spectrum depends therefore considerably on the detection time chosen. 4.2. THEORETICAL DESCRIPTION 49

Figure 4.5: Simulated evolution of the y magnetization in a two-pulse echo experiment with < x phase pulses. The timing of the sequence is fixed while the nominal flip angle of the pulses is changed. Depending on the flip angle, the shape and position of the echo signal is changed. Fig. 4.6 shows some characteristics of the observed echoes in more detail. 50 CHAPTER 4. SOFT PULSE ELECTRON SPIN ECHOES

Figure 4.6: Temporal characteristics of a two pulse echo as in ﬁg. 4.5 as a function of the nominal ﬂip angle. Shown are the positions of the echo minimum (∇), the maximum (∆), and the zero crossing

, = - between them ( < ). Flip angles with a 3:2:1 ratio, corresponding to the Rabi frequencies for mS 2

1 5 3 1

, , , < 2 transitions in S 2 , S 2 , and S 2 systems, have been marked. The vertical dotted lines indicate zero crossing times for the respective signal. 4.3. EXPERIMENTAL DEMONSTRATION 51

4.2.5 Flip Angle Selective Signal Suppression The temporal characteristics of an echo deriving from two long pulses described above can be utilized to selectively suppress signal contributions associated with a specific flip angle. This is done by placing the detecting window around the zero crossing of the echo component to be suppressed. Due to the strong dependence of the zero crossing time on the flip angle, other signals will still be maintained.

1 1 5

¨ 9 ¨ As an example, we consider the mS 2 2 transition of species with S 2 ,

3 1 ¨ S ¨ 2 , and S 2 . According to eqn. 4.1, the corresponding Rabi frequencies resp.

the nominal ﬂip angles for the same pulse sequence have a ratio of 3:2:1. Horizontal

: : dotted lines in ﬁg. 4.6 indicate ﬂip angles of 216 : , 144 , and 72 , corresponding to the 5 considered transitions. To suppress the signal component from the S ¨ 2 component,

the detection window is placed at the zero crossing time of the 216 : signal (indicated

by a dotted vertical line at 11 7 time units). This time coincides, however, with the

3 1

¨ ¨ : maximum of the 144 : signal (S 2 ), and it is close to the maximum of the 72 (S 2 ) component, maintaining contributions arising from such species. Placing the detec- 3 tion window at the other indicated time would eliminate the S ¨ 2 component while maintaining the others, etc.

4.3 Experimental Demonstration

The described experiment was performed and tested with three different systems. ¥

2 ¥ 5 3 3 ¨ Mn (S ¨ 2 ) and Cr (S 2 ) centers in a CaO matrix give rise to EPR lines that are spectrally separated, therefore making it easy to verify theoretical predictions. Ex- 1 periments on an exchange coupled metallorganic manganese complex (S ¨ 2 ) with Mn2 ¥ impurities demonstrates the applicability of the method to eliminate contamination signals that overlap with the desired spectrum. Finally, Mn-catalase from Thermus thermophilus, a metalloenzyme, exempliﬁes the potential of the suggested technique for biological systems. All experiments were performed with the Bruker E680 W band spectrometer. Pulse generation, the acquisition of the echo shape with a transient recorder, and magnetic ﬁeld sweep were controlled by Bruker Xepr software combined with a custom Puls-

eSpeL program. >

4.3.1 Mn2 > and Cr3 in CaO ¥

2 ¥ 5 3 3 ¨ Calcium oxide usually contains both Mn (S ¨ 2 ) and Cr (S 2 ) centers. Due to the cubic symmetry of the host crystal lattice, the g tensor is isotropic, and very narrow EPR lines result. The zero ﬁeld splitting for both ions is large enough that transitions

1 1

between the 2 and 2 states are sufﬁciently decoupled from other mS transitions. 55 5 Manganese occurs as Mn (I ¨ 2 ) with 100% natural abundance. Therefore, hy- perﬁne splitting gives rise to 6 EPR lines. Chromium is present in the form of several 52 CHAPTER 4. SOFT PULSE ELECTRON SPIN ECHOES

Figure 4.7: 94 GHz cw EPR spectrum of powdered CaO at room temperature. The marked lines arise ? from Mn2 ? and Cr3 centers in the CaO lattice. Other spectral features are due to impurities that are

not considered here. 8

Figure 4.8: Simulated (left) and experimental (right) echo shapes for ﬂip angles of 144 8 and 216 resp. ? a Mn2 ? and the central Cr3 line. The 3:2 ratio of ﬂip angles in the simulation corresponds to the transition moments for the EPR lines. 4.3. EXPERIMENTAL DEMONSTRATION 53

Figure 4.9: Field-swept ESE spectra of the CaO sample with two different integration windows. For the ?

“early” window, the Mn2 ? line is maintained while the Cr3 contributions are suppressed. For “late” ? detection, the Mn2 ? signal is suppressed while the Cr3 line (including satellites) becomes visible.

52 50 54 ¨

isotopes. Cr, Cr, and Cr have nuclear spin I 0 and account for about 90 5%

53 3 ¨ natural abundance. Cr has a nuclear spin of I 2 at 9 5% natural abundance. This combination of isotopes gives rise to a single strong line surrounded by four weak satellite lines in the EPR spectrum. Fig. 4.7 shows a cw spectrum of CaO powder at a microwave frequency of 94 GHz.

Field-swept two-pulse electron spin echo experiments were performed over a ﬁeld ¥ range that includes the highest-ﬁeld Mn2 ¥ line and the Cr3 lines. Fig. 4.8 compares experimental echo shapes, obtained at the resonance positions of Mn2 ¥ and the central Cr3 ¥ line, with simulation data. The predicted effect of the different transition moments on the echo shapes is clearly reproduced in the experiment.

Time-integrated ﬁeld swept echo spectra are shown in ﬁg. 4.9 for two choices of ¥ the integration window. Virtually complete separation of the Mn2 ¥ and Cr3 spectra could be achieved.

4.3.2 DTNE Complex

1 2 ¥

@ DTNE (Mn III µ OAc µ O 2Mn VI ) (ﬁg. 4.10) is an exchange coupled binuclear manganese complex. The manganese centers are antiferromagnetically coupled, 1 giving rise to an S ¨ 2 ground state. DTNE samples are usually contaminated by free Mn2 ¥ that is generated during synthesis and decay of the rather unstable complex and can be removed only by extensive puriﬁcation procedures.

The EPR spectrum of DTNE is very complex and spread out over A 100 mT due to hyperﬁne interactions. The central part of the spectrum is severely impaired by intense lines arising from Mn2 ¥ contamination (ﬁg. 4.11, top). Attempts to separate

DTNE and contamination signals by analyzing T1 and T2 decay failed at T ¨ 20 K 1The DTNE samples were made available by Dr. K. Wieghardt, MPI für Strahlenphysik, Mülheim and K.-O. Schäfer, TU Berlin. 54 CHAPTER 4. SOFT PULSE ELECTRON SPIN ECHOES

O O N O Mn N Mn N

N O

N N

Figure 4.10: Structure of the exchanged-coupled dimanganese-DTNE complex (picture courtesy of K.-O. Schäfer).

Figure 4.11: Top: Central region of the 94 GHz cw EPR spectrum of DTNE. The spectrum is severely impaired by six lines arising from contamination with Mn2 ? . Bottom: Derivative ﬁeld-swept ESE spectrum of the same sample for an optimized detection window. 4.3. EXPERIMENTAL DEMONSTRATION 55

Figure 4.12: Field-swept ESE spectra of DTNE at 94 GHz for two different integration windows. since relaxation rates were too high to allow a signiﬁcant timing variation of the pulse sequence.

The different spin states of the complex and the Mn2 ¥ contamination lead to a ﬂip angle ratio of 3:1 for the species. Fig. 4.12 shows ﬁeld-swept ESE spectra of the contaminated complex with two different integration time windows. By careful choice of an optimum detection window, the Mn2 ¥ signals could be successfully eliminated.

4.3.3 Mn-Catalase Mn-catalase2 is an enzyme that splits hydrogen peroxide into water and oxygen:

MnCat

2H2O2 2H2O O2 (4.2)

At the catalytic center of the protein is an exchange coupled binuclear manganese complex. In the catalytic process, the manganese atoms proceed through several oxidation states. For the non-physiological superoxidized state, the individual manganese

III III IV IV 3 ¨ atoms are in the formal oxidation states Mn (S ¨ 2) and Mn (S 2 ), coupling 1 antiferromagnetically to a ground state of S ¨ 2 . The cw EPR spectrum of Mn-Catalase in the superoxidized state is similar to the

DTNE complex spectra discussed in section 4.3.2 and equally impaired by Mn2 ¥ contamination (fig. 4.13, top). A field-swept ESE experiment allows to decompose the signal into contributions with different transition probabilities (fig. 4.13, middle and bottom). Besides eliminating the Mn2 ¥ contamination signal, the separation also reveals an additional signal with a higher transition probability and therefore a spin state 2The catalase (Thermus thermophilus) sample was kindly provided by Dr. V.V. Barynin, U Sheffield. 56 CHAPTER 4. SOFT PULSE ELECTRON SPIN ECHOES

Figure 4.13: 94 GHz EPR spectra of Mn-catalase from Thermus thermophilus at T , 20 K. Top: cw spectrum with Mn2 ? contamination signals. Middle: Derivative of an ESE spectrum with the detection window chosen to suppress Mn2 ? signals. Bottom: Derivative of an ESE spectrum with suppressed 1 S , 2 signals. The latter spectrum reveals an additional signal of unknown origin (marked *) with higher spin multiplicity that is not readily apparent in the cw spectrum. 4.4. CONCLUSION 57

1 S A 2 . While this signal is also visible in cw EPR, it is not obvious from the cw 1 spectrum that it does not arise from the S ¨ 2 ground state of the dimanganese center.

4.4 Conclusion

In this chapter, it was shown that spectra can be separated based on transition probability in a simple two-pulse ESE experiment, using low microwave power and therefore long pulses. EPR measurements on several systems demonstrate the applicability and practical value of this technique. The method is particularly useful for high frequency EPR spectroscopy which is very sensitive to contamination signals while suffering from relatively low available microwave powers. The introduced experiment is also remarkably easy to implement. A fixed pulse sequence is used. In conjunction with the use of a transient recorder to record the time-resolved echo signal, a separation of spectra can be achieved without any increase in acquisition time as compared to a non-selective field-swept ESE experiment. An additional advantage is that the critical part of the process – choosing an appropriate integration window to obtain the desired spectrum – can be done after data acquisition, requiring no trial and error procedure during the experiment. As demonstrated in section 4.3.3, the use of transition probability selective methods can also identify superimposed signals whose existence is difficult to be seen from cw EPR spectra. Since 2D experiments are rather expensive in acquisition time, they are usually not employed routinely. The simplified experiment described here is fast enough to be performed on a wider scale and may therefore reveal such signal contributions that might otherwise go unnoticed.

REFERENCES

[1] Isoya J., Kanda H., Norris J.R., Tang J., & Bowman M.K., Fourier-transform and continuous-wave EPR studies of nickel in synthetic diamond: Site and spin multiplicity, Phys. Rev. B41, 3905–3913 (1990).

[2] Schweiger A., Puls-Elektronenspinresonanz-Spektroskopie: Grundlagen, Verfahren und Anwendungsbeispiele, Angew. Chem. 103, 223–250 (1991).

[3] Bowman M.K., in Modern Pulsed and Continuous-Wave Electron Spin Resonance (Kevan L. & Bowman M.K., eds.), Wiley (1990).

[4] Astashkin A.V. & Schweiger A., Electron-spin transient nutation: A new approach to sim- plify the inerpretation of ESR spectra, Chem. Phys. Lett. 174, 595–602 (1990).

[5] Torrey H.C., Transient nutations in nuclear magnetic resonance, Phys. Rev. 76, 1059–1068 (1949). 58 CHAPTER 4. SOFT PULSE ELECTRON SPIN ECHOES

[6] Takui T., Sato K., Shiomi D., Itoh K., Kaneko T., Tsuchida E., & Nishide H., FT pulsed ESR/electron spin transient nutation (ESTN) spectroscopy applied to high-spin systems in solids; direct evidence of a topologically controlled high-spin polymer as models for quasi 1D organic ferro- and superpara-magnets, Mol. Cryst. Liq. Cryst. 279, 155–176 (1996).

[7] Stoll S., Jeschke G., Willer M., & Schweiger A., Nutation-frequency correlated EPR spectroscopy: The PEANUT experiment, J. Magn. Reson. 130, 86–96 (1998). Part III

Application of High Field EPR to Biological Systems

Chapter 5

Overview of Photosynthetic Reaction Centers

This chapter gives an overview of the various photosynthetic reaction centers examined by EPR in later chapters. In addition, the method used for analyzing EPR spectra of radicals in frozen solutions and single crystals of these reaction centers is discussed.

5.1 Overview of the Photosynthesic Process in Plants and Cyanobacteria

Photosynthetic organisms convert light into chemically bound energy which is then used by the metabolism. Species differ in the substrates used for this process. Green plants and cyanobacteria perform oxygenic photosynthesis, which is characterized by the reduction of carbon dioxide to sugars such as glucose:

light

6CO2 6H2O C6H12O6 6O2 (5.1)

As a by-product of this process, molecular oxygen is released. During evolution, it has accumulated from negligible amounts to about 20 % in the atmosphere, paving the way for the development of oxygen dependent organisms and, ultimately, mankind. The photosynthetic process can be broken up into two major steps: light reactions which, as the name suggests, are driven by absorption of light, and dark reactions that complete the photosynthetic process, using the products of the light reactions. In plants and cyanobacteria, the photosynthetic apparatus consists of several protein/cofactor complexes that are located in the thylakoid membrane.

In the light reactions, water is oxidized and NADP ¥ (nicotineamide adenine dinu- cleoutide phosphate) is reduced to NADPH, an energy carrier in the cell. The oxidation of water also releases protons on the lumenal side of the membrane, thereby creating a cross-membrane proton gradient which is the driving force behind the phosphorylation

61 62 CHAPTER 5. OVERVIEW OF PHOTOSYNTHETIC REACTION CENTERS

of ADP (adenosine diphosphate) to ATP (adenosine triphosphate),

¥ ¥

' ν

2H2O 2NADP 6h 2NADPH 2H O2 (5.2)

∆pH

ADP Pi ATP (5.3)

Two protein-cofactor complexes, photosystem I (PS I) and photosystem II (PS II), serve as the central hubs for the light reactions. Upon light excitation, each of these complexes performs a cross-membrane electron transfer, thereby storing energy in the form of redox equivalents. PS I and PS II work in series to achieve a higher redox potential difference than either one could individually (ﬁg. 5.1).

5.1.1 Photosystem I PS I consists of 11–13 protein subunits, depending on species. Upon excitation by absorption of a photon, PS I reduces ferredoxin (FD) on the stromal side of the membrane. Ferredoxin acts as an intermediate charge carrier, reducing in turn NADP ¥ to NADPH. To replace the electron, PS I oxidizes plastocyanine (PC) on the lumenal side. PS I can thus be considered a light-driven transmembrane electron pump:

PS I

PCred FDox h PCox FDred (5.4)

¥ ¥

2FDred NADP H 2FDox NADPH (5.5)

Fig. 5.2 shows a schematic overview of the PS I reaction center.

Subunits PsaA and PsaB

. .

The two protein subunits PsaA (mass 83 2 kDa) and PsaB (mass 82 5 kDa) at the reaction center core show strong homology and are arranged approximately symmetrically, each binding similar cofactors [4]. The signiﬁcance of the deviation from symmetry is still subject of active research. At the time of this writing, it is still unclear whether the light induced electron transfer occurs via the cofactors in both subunits or not and, if the electron transfer is asymmetric, which subunit is the active one. Amino sequence homologies and similar cofactors suggest that PS I is closely related to the reaction centers of green sulphur bacteria and heliobacteria. These bacterial reaction centers exhibit a homodimer in place of subunits PsaA and PsaB, suggesting that the electron transfer might indeed occur along both subunits [5, 6].

P700. Photochemistry in the PS I reaction center starts with the primary donor, P700

(named after a corresponding optical absorption band at λ ¨ 700 nm). P700 consists of two chlorophyll a molecules bound to subunits PsaA and PsaB, respectively. While

it has been a subject of discussion whether P700 is a true dimer or whether the chloro-

¥ ¦ phylls are electronically decoupled, newer research indicates that P700 has a highly 5.1. PHOTOSYNTHESIS IN PLANTS AND CYANOBACTERIA 63

P* E [V] 700

A1 −1 P* 680 FX

FA Pheo FB

−0.5 C ν FD

QA NADP

QB PS I

0 C ν PS II Cytb6

P700 0.5

H 2 O WOC 1 YZ P 680

Figure 5.1: Electron transfer pathway and associated redox potential during the photosynthetic light reactions in plants and cyanobacteria. 64 CHAPTER 5. OVERVIEW OF PHOTOSYNTHETIC REACTION CENTERS

F PsaD B PsaE PsaC stroma

F X PsaB

A 1

A 0 PsaA A

P700

PsaF lumen

Figure 5.2: Overview of the photosystem I reaction center core and the electron transfer chain (for a detailed model, see [1–3]). 5.1. PHOTOSYNTHESIS IN PLANTS AND CYANOBACTERIA 65 asymmetric electronic structure [4, 7, 8]. After the absorption of a photon or indirect excitation via an exciton transfer from peripheral antenna chlorophylls, P700D acts as an

electron donor:

¥ ¦

ν D

' ' §

P700 h P700 P700 e (5.6)

The redox potential of the excited P700 amounts to approximately 1 2 V, making it

¥ ¦ one of the strongest reductants known in biological systems. P700 in turn oxidizes a plastocyanine at the lumenal side of PS I.

A0 and A1. A chlorophyll a cofactor denoted as A0 is coupled via an “accessory

chlorophyll” A to P700 and serves as the primary acceptor in the electron transfer chain. ¦

A0§ is stable for about 30 ps [4] after which the electron is passed on to the secondary

¦ ¦ §

acceptor A1, a phylloquinone. A1§ is more stable than A0 , but still has a lifetime of

only about 15 200 ns [4]. Both A0 and A1 are bound to one of the subunits PsaA or PsaB; the respective other subunit binds similar cofactors A0 and A1.

FX. FX is the last electron acceptor within subunits PsaA and PsaB. It is a [4Fe4S] cluster that is bound in between subunits A and B. Both possible electron transfer pathways, along subunits PsaA and PsaB, join at FX.

Subunit PsaC .

The protein subunit PsaC (mass 8 9 kDa) is adjacent to subunits PsaA and PsaB on the stromal side of the membrane. It binds the remaining cofactors forming the electron transfer chain in PS I.

FA/FB. Subunit PsaC binds two [4Fe4S] clusters, referred to as FA and FB. The arrangement of both clusters has a local C2 symmetry, but is asymmetric relative to the axis deﬁned by the PsaA/PsaB pseudodimer. One of these iron-sulphur clusters serves as the terminal electron acceptor in PS I (before subsequent reduction of ferredoxin). Only recently, this terminal [4Fe4S] cluster has been identiﬁed as FB, while FA serves as an intermediate acceptor [9] (see also [10, 11]).

5.1.2 Photosystem II PS II uses the photon energy of incident light to abstract electrons from water, releas- ing protons and molecular oxygen on the lumenal side. The electrons are transfered across the membrane by the PS II reaction center, reducing plastoquinone (PQ) to hydroplastoquinone (H2PQ):

ν ¥ ' §

2H2O 4h 4H O2 4e (5.7)

§ '

PQ 2H 2e H2PQ (5.8) 66 CHAPTER 5. OVERVIEW OF PHOTOSYNTHETIC REACTION CENTERS

stroma

Q Q A Fe B

D2 D1

Pheo Pheo Cytb559

Chl Chl

P680 Y Z YD

2 H2 O Mn MnMn WOC Mn

Cytc550 + lumen O2 4H

Figure 5.3: Simpliﬁed model of the photosystem II core complex in the photosynthetic membrane, including subunits D1, D2, and the water oxidizing complex (WOC). For a detailed structure, see [12, 13]. 5.1. PHOTOSYNTHESIS IN PLANTS AND CYANOBACTERIA 67

The proton releases in eqn. 5.7 occur on the lumenal side of the reaction center while protons are consumed according to eqn. 5.8 on the stromal side. The resulting transmembrane protein gradient is used for the production of ATP (see e.g. [14, 15]). PS II consists of several protein subunits that serve, in conjunction with their respective cofactors, as light harvesting antenna systems, energy transfer paths, electron transfer paths, catalytic sites, and protective groups, among others. The most prominent constituents of the reaction center core are the protein subunits D1 and D2 and the water oxidizing complex (WOC). D1 and D2 host a number of cofactors that comprise the electron transfer path after photoexcitation of the complex. The WOC contains 4 manganese atoms that form the catalytic center for the water splitting process (ﬁg. 5.3).

Subunits D1 and D2

The polypeptides D1 and D2 (mass E 30 kDa each) are largely homologous to each other and form an approximately symmetrical protein heterodimer. This is similar to the subunits L and M in bacterial “type II” photosynthetic reaction centers, as was suggested based on amino acid sequence homologies [16–18] and computer modeling [19]. This finding is useful because the structure of these bacterial photosynthetic reaction centers is known (e.g. [20]). The structural similarity has been confirmed by electron [21] and recently X-ray [12] diffraction studies on two- and three-dimensional crystals of PS II. D1 and D2 serve as a host matrix for the embedded cofactors that mark the electron transfer path. These cofactors are two chlorophyll a species, pheophytin a, and a plastoquinone for each subunit. Though similar cofactors appear in both subunits, their functional role is different, and electron transfer is confined to the D1 subunit, with the exception of the intermediate acceptor QA which is bound to D2.

P680. The primary electron donor P680 (named after a corresponding optical ab- λ sorbance band at F 680 nm) is an aggregate of two chlorophyll a species bound to subunits D1 and D2. The functional role of P680 can be compared to the primary donors in photosystem I and bacterial reaction centers. After excitation, either by direct absorption of a photon or by an energy transfer from light harvesting antenna complexes outside the core complex, P680G acts as an electron donor, initiating the elec-

tron transfer process within the reaction center:

I J K L

ν I H

P680 H h P680 P680 e (5.9)

J K

E M P680 is characterized by an unusually high redox potential of H 1 1 V which allows subsequent splitting of water in the WOC.

Pheo a. The pheophytin a cofactor in the D1 subunit serves, via an intermediary “accessory” chlorophyll, as the ﬁrst electron acceptor after excitation of the primary donor. Charge separation takes place on a timescale of less than 25 ps. In contrast to 68 CHAPTER 5. OVERVIEW OF PHOTOSYNTHETIC REACTION CENTERS

PS I, the asymmetry of the electron transfer along the subunits is ﬁrmly established. The pheophytin residue in the D2 subunit does not take part in directed electron transfer.

QA and QB. The plastoquinones QA (D2 subunit) and QB (D1 subunit) are coupled 2 by a non-heme Fe J ion and act as intermediate and terminal electron acceptors, respectively. In contrast to QA, the terminal acceptor QB is only weakly bound to the core complex. After two reduction and concomitant protonation steps, H2QB leaves the protein, acting as a charge/proton carrier, and is replaced by a plastoquinone from a plastoquinone “pool” in the membrane. The redox potential carried by the hydroplastoquinone is later utilized by photosystem I.

YZ and YD. The tyrosines YZ (Tyr161 residue on D1) and YD (Tyr160/161 in cyanobac-

terial and spinach D2, respectively) act as secondary electron donors, reducing the K

photooxidized P680J and being oxidized to neutral amino acid radicals:

J K L K

I H P H Y P Y (5.10)

680 N 680 Z N D Z D

YD seems to be a dead end in the electron transfer chain. Its functional importance is not yet understood, though there are hints that it may play an signiﬁcant role in preventing photoinhibition during activation of photosystem II [22]. Recently, it has also been suggested that the YD neutral radical may enhance charge separation via YZ

by electrostatic interactions [23]. After generation by a photoinduced hole transfer

J K K from P680, the YDK radical is stable in the dark. In contrast, YZ abstracts an electron from the WOC on a sub-millisecond timescale.

Water Oxidizing Complex Water splitting takes place in the membrane-extrinsic WOC. It is known to contain a tetranuclear manganese cluster, a calcium atom, and possibly a chloride ion. Catalytic activity is most likely tied to the manganese cluster, and several models have been proposed for the water splitting mechanism. Water splitting occurs in a cyclic process with four consecutive oxidations of the WOC (for recent reviews, see e.g. [24, 25]).

5.2 Photosynthesis in Purple Bacteria

In contrast to plants or cyanobacteria, purple bacteria have only one kind of photosynthetic reaction center, located in the intracytoplasmic cell membrane. The redox potential difference generated by the electron transfer from the periplasm to the cyto-

plasmatic side of the membrane is not sufﬁcient for the reduction of NAD J to NADH. Therefore, the primary purpose of the photosynthetic process in the bacterial reaction 5.2. PHOTOSYNTHESIS IN PURPLE BACTERIA 69

Q A Fe Q B

φ B φ M A L

P865

Figure 5.4: Overview of the photosynthetic reaction center core in purple bacteria. 70 CHAPTER 5. OVERVIEW OF PHOTOSYNTHETIC REACTION CENTERS center seems to be the creation of a transmembrane proton gradient for driving ATP synthesis. Fig. 5.4 shows a schematic representation of the bacterial reaction center (bRC) found in purple bacteria. The most obvious difference to PS II is the absence of a WOC. The bound cofactors differ only slightly from PS II, e.g. bacteriochlorophyll instead of chlorophyll pigments. All the cofactors comprising the electron transfer pathway are bound to two protein subunits called L and M.

5.2.1 Subunits L and M The subunits L and M of the bRC found in purple bacteria can be compared to the D1/D2 subunits in PS II. They form an equally pseudo-symmetrical arrangement (with the C2 symmetry axis perpendicular to the membrane). As in PS II, the photoinduced electron transfer is asymmetric.

P865. Photochemistry in bRC starts at P865, comprised of two bacteriochlorophyll molecules bound to the L and M subunits, respectively. After excitation, either by absorption of a photon or by exciton transfer from peripheral light harvesting antenna complexes (LHC), P865G acts as an electron donor, analogously to the primary donor in PS II.

ΦA and ΦB. ΦA and ΦB are symmetry-related bacteriopheophytin b species bound to the M and L subunit, respectively. They are coupled to P865 by accessory bacteri- ochlorophylls, making them possible electron acceptors. Only ΦA on the M subunit takes part in directed electron transfer, however.

QA and QB. As in PS II, two quinone species serve as further intermediate and terminal acceptors, respectively. QA is bound to the M subunit and the terminal acceptor 2 QB is bound to subunit L. A non-heme Fe J center located between the quinones couples QA and QB. After two reduction and concomitant protonation steps, H2QB leaves the bacterial reaction center and is replaced by another ubiquinone from the quinone pool. It is known that the QB binding site undergoes structural changes during reduction steps, breaking hydrogen bonds and leading to a different orientation of the reduced quinone [26]. Therefore, the redox state of the reaction center must be known in order to interpret structural data.

5.3 EPR on Frozen Solutions and Single Crystals of Reaction Centers

The functional state of photosynthetic reaction centers is characterized by radical states along the electron transfer chain. On short time scales, the electron transfer process can REFERENCES 71 be observed after photoexcitation in the form of radical pairs (see e.g. [27]). Some radicals may also be trapped, either by lowering the temperature and inhibiting thermally activated transfer steps, or by chemical inhibition. EPR is an ideal tool to investigate these paramagnetic states. With few exceptions (e.g. the iron-sulphur clusters in PS I), the electron transfer pathway consists of organic radicals that usually exhibit rather small g anisotropies. The increased Zeeman resolution of high field EPR is therefore extremely useful in the analysis and interpretation of the respective EPR spectra. The increased sensitivity of high field EPR also allows one to obtain good spectra from very small sample quantities. This is helpful because the isolation and purification of membrane bound proteins is a complex task, yielding only small quantities. In particular however, this allows the study single crystals of these membrane proteins which are typically sub- millimeter sized. Crystal structures are characterized by a set of symmetries. A crystal is defined by a unit cell that is repeated periodically through space. If there are several sites within a unit cell, these are related to each other by a combination of translations and rotations. The spin Hamiltonian used to describe EPR does not contain spatial coordinates as parameters. EPR is therefore insensitive towards translational symmetries, and crystal symmetries are reduced to orientational symmetries associated with the true crystallographic space group. Real crystals are not perfect. Aside from impurities, the prevalent problem is structural disorder, i.e. mosaicity. Mosaicity creates serious problems for investigation techniques that rely on the periodicity of the crystal lattice, like X-ray diffraction experiments. While small mosaic angles greatly disturb the lattice periodicity, they have only a slight effect on the orientation of the individual sites. EPR spectra are thus virtually unaffected by small mosaicities, and EPR experiments can therefore derive structural information from crystals that are not suitable for X-ray diffraction studies.

REFERENCES

[1] Klukas O., Schubert W.D., Jordan P., Krauss N., Fromme P., Witt H.T., & Saenger W., Photosystem I, an improved model of the stromal subunits Psac, Psad and Psae, J. Biol. Chem. 274, 7351–7360 (1999).

[2] Klukas O., Schubert W.D., Jordan P., Krauss N., Fromme P., Witt H.T., & Saenger W., Localization of two phylloquinones, Q(K) and Q(K)’, in an improved electron density map of photosystem I at 4 angstrom resolution (1999).

[3] Klukas O., Schubert W.D., Jordan P., Krauss N., Fromme P., Witt H.T., & Saenger W., Protein data bank, access code 1C51: Photosynthetic reaction center and core antenna system (trimeric), α carbon only, http://www.rcsb.org/pdb. 72 CHAPTER 5. OVERVIEW OF PHOTOSYNTHETIC REACTION CENTERS

[4] Brettel K., Electron transfer and arrangement of the redox cofactors in photosystem I, Biochim. Biophys. Acta 1318, 322–373 (1997).

[5] Büttner M., Xie D.L., Nelson H., Pinther W., Hauska G., & Nelson N., Photosynthetic reaction center genes in green sulfur bacteria and in photosystem 1 are related, Proc. Natl. Acad. Sci. USA 89, 8135–8139 (1992).

[6] Liebl U., Mockensturm-Wilson M., Trost J.T., Brune D.C., Blankenship R.E., & Ver- maas W., Single core polypeptide in the reaction center of the photosynthetic bacterium Heliobacillus mobilis: Structural implications and relations to other photosystems, Proc. Natl. Acad. Sci. USA 90, 7124–7128 (1993).

[7] Käß H., Die Struktur des primären Donators P700 in Photosystem I: Untersuchungen mit Methoden der stationären und gepulsten Elektronenspinresonanz, Ph.D. thesis, Techni- sche Universität Berlin (1995).

[8] Käß H., Fromme P., Witt H.T., & Lubitz W., Orientation and electronic structure or the P primary donor radical cation P700O in photosystem I: A single crystal EPR and ENDOR study, J. Phys. Chem. B 105, 1225–1239 (2001).

[9] Jordan P., Fromme P., Witt H.T., Klukas O., Saenger W., & Krauss N., Three-dimensional

structure of cyanobacterial photosystem I at 2 Q 5 Å resolution, Nature 411, 909–917 (2001).

[10] Golbeck J.H., A comparative analysis of the spin state distribution of in vitro and in vivo mutants of PsaC, Photosynth. Res. 61, 107–144 (1999).

[11] Zhao J., Li N., Warren P.V., Golbeck J.H., & Bryant D.A., Site-directed conversion of a cysteine to aspartate leads to the assembly of a [3Fe-4S] cluster in PsaC of photosystem I. The photoreduction of FA is independent of FB, Biochemistry 31, 5093–5099 (1992).

[12] Zouni A., Witt H.T., Kern J., Fromme P., Krauss N., Saenger W., & Orth P., Crystal

structure of photosystem II from Synechococcus elongatus at 3 Q 8 Å resolution, Nature 409, 739–743 (2001).

[13] Zouni A., Witt H.T., Kern J., Fromme P., Krauss N., Saenger W., & Orth P., Protein data bank, access code 1FE1: Crystal structure of photosystem II, http://www.rcsb.org/pdb.

[14] Boyer P.D., The ATP synthase – a splendid molecular machine, Ann. Rev. Biochem. 66, 717–749 (1997).

[15] Junge W., ATP synthase and other motor proteins, Proc. Natl. Acad. Sci. USA 96, 4735– 4737 (1999).

[16] Trebst A., The topology of the plastoquinone and herbicide binding peptides of photosystem II in the thylakoid membrane, Z. Naturforsch. C41, 240–245 (1986).

[17] Michel H. & Deisenhofer J., Relevance of the photosynthetic reaction center from purple bacteria to the structure of photoystem II, Biochemistry 27, 1–7 (1988). REFERENCES 73

[18] Tang X.S., Fushimi K., & Satoh K., D1-D2 complex of the photosystem II reaction center from spinach – isolation and partial characterization, FEBS Lett. 273, 257–260 (1990).

[19] Rufﬂe S.V., Donnelly D., Blundell T.L., & Nugent J.H.A., A 3-dimensional model of the photosystem II reaction center of Pisum sativum, Photosynth. Res. 34, 287–300 (1992).

[20] Ermler U., Fritzsch G., Buchanan S.K., & Michel H., Structure of the photosynthetic

reaction center from Rhodobacter sphaeroides at 2 Q 65 Ångstrøm resolution – cofactors and protein-cofactor interactions, Structure 2, 925–936 (1994).

[21] Rhee K.H., Morris E.P., Barber J., & Kühlbrandt W., Three-dimensional structure of the plant photosystem II reaction centre at 8 Å resolution, Nature 396, 283–286 (1998).

[22] Magnuson A., Rova M., Mamedov F., Fredriksson P.O., & Styring S., The role of cytochrome b559 and tyrosine D in protection against photoinhibition during in vivo pho- toactivation of photosystem II, Biochim. Biophys. Acta 1411, 180–191 (1999).

[23] Rutherford W., Tyrosine redox reactions in PS II (2001), DFG Sonderforschungsbereich 498 seminar talk, 17. April 2001.

[24] Messinger J., Towards understanding the chemistry of photosynthetic oxygen evolution: Dynamic structural changes, redox states and substrate water binding of the Mn cluster in photosystem II, Biochim. Biophys. Acta 1459, 481–488 (2000).

[25] Renger G., Photosynthetic water oxidation to molecular oxygen: Apparatus and mechanism, Biochim. Biophys. Acta 1503, 210–228 (2001).

[26] Stowell M.H.B., McPhillips T.M., Rees D.C., Soltis S.M., Abresch E., & Feher G., Light- induced structural changes in photosynthetic reaction center: Implications for mechanism of electron-proton transfer, Science 276, 812–816 (1997).

[27] Zech S.G., Lubitz W., & Bittl R., Pulsed EPR experiments on radical pairs in photosynthesis: Comparison of the donor-acceptor distances in photosystem I and bacterial reaction centers, Ber. Bunsenges. Phys. Chem. 100, 2041–2044 (1996). 74 CHAPTER 5. OVERVIEW OF PHOTOSYNTHETIC REACTION CENTERS Chapter 6

High Field EPR on the Primary Donor S P700R Radical in Single Crystals of Photosystem I

The photoinduced electron transfer in photosystem I as described in chapter 5 begins at the primary donor P700. While P700 consists of two chlorophyll a molecules, its electronic structure still is only partially understood, though there are recent results that may solve this question [1, 2]. In particular, it has been a matter of discussion whether

P700 is a true dimer or if photophysics is mostly confined to one of the chlorophylls. K High field EPR experiments on P700J in single crystals of PS I can provide detailed information about the magnitude and the orientation of its g tensor, reflecting electronic structure. This can be compared to the spatial structure derived from X-ray diffraction data. In addition, the experiments on single crystals of PS I demonstrate the benefits of high field EPR for the investigation of organic radicals in biological samples.

6.1 Materials and Methods

6.1.1 PS I Core Complexes

PS I core complexes preparations were made available by Dr. P. Fromme and cowork-

ers. The cells were grown from Synechococcus elongatus as described in [3]. Samples K were frozen under illumination in order to photoaccumulate P700J . Partial orientation as reported in [4] was avoided by performing the freeze process in the absence of a magnetic ﬁeld.

75 K 76 CHAPTER 6. P700J IN SINGLE CRYSTALS OF PHOTOSYSTEM I

c a

T T Figure 6.1: Layout of the unit cell (a T b 288 Å, c 167 Å) in single crystals of photosystem I reaction centers. The centers appear as trimers with a threefold symmetry axis parallel to the c axis. The trimers in the unit cell are related by the P63 space group. The approximate orientations of the P700 chlorophyll ring planes are indicated.

6.1.2 PS I Single Crystals

Single crystals of PS I core complexes were grown by Dr. P. Fromme and coworkers F from the preparations described above. The crystals are hexagonal (a F b 288 Å,

c F 167 Å). The unit cell contains 6 PS I reaction centers, arranged in two trimers (ﬁg. 6.1). The corresponding space group is P63. In EPR experiments the effective symmetry is D6 since EPR spectra are invariant under a 180 U rotation of the sample. The crystals appear as needles with a hexagonal base plate that is parallel to the ab plane. The crystals were mounted in the W-band EPR tubes by immersing them in tiny

amounts of mother liquor and subsequent freezing in liquid nitrogen, again under il- K lumination in order to generate P700J . The mounting orientations were deﬁned by the crystal morphology. In one case, the needle axis of the crystals (c direction) was aligned with the capillary axis; another crystal was mounted with the needle axis perpendicular to the capillary axis.

6.1.3 cw EPR M All cw spectra were obtained with a microwave power of E 150 nW and 0 2 mT peak-

to-peak modulation amplitude (100 kHz) at T F 80 K. Typical acquisition time for one trace was 40 s. The magnetic ﬁeld was calibrated with Li:LiF as a g standard using the 6.2. RESULTS 77 procedure described in section 2.1.1. The microwave frequency was slightly different for each orientation of the single crystal samples because the resonator frequency reacts very sensitive to the sample geometry. For easier comparison, all spectra were scaled to a hypothetic frequency of

94 M 000 GHz by the formula

94 GHz

F W M B V B ν (6.1)

The required adjustments were very small (less than 0 M 1 %) and therefore do not affect the interpretation of the spectra. In particular, this transformation has no effect on derived g values.

6.2 Results Y

6.2.1 P700X in Frozen PS I Solution

J K A spectrum of P700 in frozen solution at T F 80 K is shown in ﬁg. 6.2. The spectrum is characterized by a considerable inhomogeneous linewidth. Despite the high magnetic ﬁeld and a resulting increased Zeeman splitting, the g anisotropy is too small in relation

to the linewidth to resolve the principal values. It thus seems as if 94 GHz EPR would K

not sufﬁce to access the g tensor or P700J . Y

6.2.2 P700X in Single Crystals of PS I K Orientation dependent spectra of the P700J radical in two differently mounted crystals are shown in fig. 6.4 and fig. 6.6. In contrast to the frozen solution spectra (included at the top), the apparent linewidth is significantly reduced, and the crystalline nature is reflected by a clear dependence of the spectra on the turning angle. The reduced apparent linewidth clearly shows that the broadening of the frozen solution spectrum is caused by both unresolved hyperfine interactions and g anisotropy. In fig. 6.4 a splitting in two lines is readily apparent. The line intensities differ, however, considerably, suggesting that these apparent lines are still comprised of several unresolved EPR lines from different sites in the crystal. This is in accordance with

the crystal structure that, in the general case, predicts six EPR lines in a crystal spec- U trum. For rotation angles of 0 U resp. 90 , the line separation disappears. This agrees with the mounting orientation of the crystal (c axis perpendicular to the rotation axis, see fig. 6.3) which implies that the magnetic field is parallel to c for two turning angles, leading to complete degeneracy of all sites. By comparison, fig. 6.6 exhibits a more regular structure. Here, the crystal was rotated approximately about its c axis (see fig. 6.3); the magnetic field is therefore always in the ab plane. For this orientation, the six EPR lines degenerate in pairs. The K

78 CHAPTER 6. P700J IN SINGLE CRYSTALS OF PHOTOSYSTEM I [ Figure 6.2: 94 GHz cw EPR spectrum of photoaccumulated P700Z in frozen solution of protonated PS I

at T T 80 K (solid) and simulation (dotted). Even at W-band frequencies, the g anisotropy cannot be resolved due to the large inhomogeneous linewidth.

6.2. RESULTS 79

] ^

Figure 6.3: Appearance of the PS I cc single crystals, orientation of the crystallographic axes, and rotation axes for the crystal spectra (schematic).

effective D6 symmetry leads to three equally intense lines with sinusoidal dependen-

cies of g on the rotation angle. The sixfold symmetry is also confirmed by the 60 U periodicity of the spectra. Considering the degeneracies and the moderate resolution, a numerical fit of six independent EPR lines to the spectra is questionable. However, taking the strict correlation between the line positions induced by the crystal symmetry into account, the number of independent parameters is reduced to an extent that makes a fit stable and, within the constraints imposed by the symmetry, unambiguous. A simultaneous simulation of all spectra, including the frozen solution spectrum, allowed therefore to derive almost full g tensor information, i.e. both principal values and the orientation, with the exception of one of the Euler angles (see below, tab. 6.1). The resulting sets of simulated spectra are shown in fig. 6.5 and fig. 6.7. The effective g values resp. resonance positions as calculated from the simulation parameters are marked for all six sites. The imperfect degeneracy of line positions reflects small de-

viations from the nominal mounting orientations: The c axis of the crystals is inclined

U U U by 88 U (90 nominal) and 3 (0 nominal) relative to the rotation axis, respectively. The orientation of the g tensor can only be partially derived. This is not a problem of the measurements or the simulation, but reﬂects the special crystal symmetry: the P63 symmetry axis marks the c direction of the crystal axis system, but is independent of the orientation of the a and b axes. This problem arises in general when there is only one symmetry axis. Therefore, only the orientation of the c direction in the laboratory system can be determined from the EPR spectra while the a and b axis directions are not accessible. To obtain the full information, the orientation of the mounted crys- K

80 CHAPTER 6. P700J IN SINGLE CRYSTALS OF PHOTOSYSTEM I

T [

Figure 6.4: 94 GHz cw EPR spectra of P700Z in a single crystal of PS I (T 80 K). The rotation axis _ is approximately perpendicular to the c axis of the crystal; at the rotation angles 0 _ resp. 180 , the magnetic ﬁeld is parallel to the c axis. 6.2. RESULTS 81

Figure 6.5: Simulation of the spectra in ﬁg. 6.4. The dotted lines represent the effective g values for the _ six inequivalent sites in the crystal. When the magnetic ﬁeld is parallel to the c axis (0 _ and 180 ), the EPR lines are completely degenerate. K

82 CHAPTER 6. P700J IN SINGLE CRYSTALS OF PHOTOSYSTEM I

T [ Figure 6.6: 94 GHz cw EPR spectra of P700Z in a single crystal of PS I at T 80 K. The rotation axis is approximately parallel to the c axis of the crystal; the magnetic ﬁeld is in the ab plane. Since the c axis

is parallel to the C3 symmetry axis, a 120 _ periodicity in the spectra results. 6.2. RESULTS 83

Figure 6.7: Simulation of the spectra in ﬁg. 6.6. The dotted lines represent the effective g values for the six inequivalent sites in the crystal. The magnetic ﬁeld is approximately perpendicular to the c axis for all orientations, leading to pairwise degeneray of the EPR lines. K 84 CHAPTER 6. P700J IN SINGLE CRYSTALS OF PHOTOSYSTEM I

x y z accuracy (est.)

M M M W

g 2 00309 2 00260 2 00223 2 10 L

U U U

c 68 U 38 61 2 [ Table 6.1: g tensor determined from simulations of orientation-dependent EPR spectra of P700Z . The orientation of the tensor is given as the inclination of the principal directions with respect to the c axis.

gx gy gz reference

M M 2 M 00309 2 00260 2 00223 this work, [7]

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

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

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

M M 2 M 00304 2 00262 2 00232 [8] 1

94 GHz EPR at T T 80 K on single crystals 294 GHz EPR on deuterated frozen solution 3

325 GHz EPR at T T 40 K on frozen solution 4

325 GHz EPR at T T 200 K on frozen solution

5140 GHz EPR on deuterated frozen solution [ Table 6.2: Comparison of principal g values for the P700Z radical obtained in this work with literature data. Note that experiments on frozen solution either required deuteration of the sample or signiﬁcantly higher microwave frequencies. tal could be determined by X-ray diffraction experiments prior to or after the EPR measurements. This requires however a very precise and reproducible mounting orientation of the crystal in both the EPR spectrometer and the X-ray-diffraction setup: Since the EPR experiment does not yield any information about the orientation of a and b within the ab plane, there is no way to correct small deviations in the mounting orientation between both setups, and rather large systematic errors may arise.

6.3 Discussion

Principal Values of g. The principal values as obtained from the single crystal spectra are in good agreement with other works (see tab. 6.2). It is known that the g tensor of P700 exhibits a slight temperature dependence, indicative of a redistribution of the

spin density across the chlorophyll molecules (e.g. [5, 6]). The values obtained in F

this work at T F 80 K are very close to the values reported for T 200 K in [5], in

J K contrast to T F 40 K data from the same reference. This suggests that the P700 state at

T F 80 K should be very similar to that at 200 K, and possibly even to the physiological K

P700J state. K Orientation of g. Almost complete orientation information on the g tensor of P700J could be derived from the single crystal EPR spectra. The only missing orientation 6.3. DISCUSSION 85 parameter cannot be obtained from EPR experiments alone due to the special symmetry properties of the PS I single crystals. It is however known that the PS I enzyme is oriented in the crystals in such a way that the crystallographic c axis corresponds to the normal of the thylakoid membrane. Therefore, the obtained orientation information, while incomplete, can be directly compared to other experiments (tab. 6.3).

Structural models from X-ray diffraction indicate that the chlorophyll heterocycle planes of the Chla comprising P700 are approximately parallel to the c axis [2, 10]. Fig. 6.8 shows such a model for P700 and the obtained orientation of the g tensor axes. One would expect, i.e. based on [11], that the gz direction should be perpendicular to that plane, i.e. be approximately perpendicular to the c direction in the crystals. From these experiments and in accordance with [12, 13], this is obviously not the case. This

kind of tilt of the g tensor with respect to the chlorophyll plane is known from the K primary donor P865J in bacterial reaction centers. For bacteriochlorophyll, this deviation can be explained by the orientation of the acetyl groups [14]. Such groups are not present in chlorophyll a, however, and the tilt of the g tensor must be attributed to the inﬂuence of the protein environment, or to the electronic coupling between the chlorophylls comrising P700, or both. Very recently, it has been revealed that the two chloro-

phylls comprising P700 are not completely identical [2], but are epimers Chla/Chla V . Therefore, the interaction with the protein matrix may be different for both halves of the P700 “dimer”. Similarly, an asymmetric spin density distribution over both chlorophylls would break the symmetry deﬁned by the heterocycle ring planes and give rise to the observed tilt of the g tensor. Such an asymmetric spin density distribution has already been reported in other works, e.g. [12, 13].

The orientation of the g tensor could in principle be an independent argument to K decide whether the main part of the spin density of P700J is always localized on the same chlorophyll or not. If the state could be localized on either of the chlorophylls,

two different g tensor orientations would be observed in the sample. The Chla/Chla V molecules are however related to each other by an approximate C2 symmetry about the membrane normal. Since C2 is a subgroup of D6, the differences of the effective g factors should be very small. This degeneracy could be alleviated by the difference be-

tween Chla and Chla V . It seems however still unlikely that such a splitting would be noticeable in the single crystal spectra at 94 GHz, unless the relation between

the molecular axes and g principal axes would be very different for the Chla/Chla V molecules.

However, the obtained g tensor orientation can be used in conjunction with structural models from X-ray diffraction experiments to shed more light on the nature of

P700. The orientation of g can also serve as a reference for other paramagnetic interme- K diates that are coupled to P700J . This allows to derive information about the orientation of these intermediates relative to the membrane normal, even from experiments on frozen solutions (i.e. [7]). K

86 CHAPTER 6. P700J IN SINGLE CRYSTALS OF PHOTOSYSTEM I

c d

a b

Figure 6.8: Structure of the P700 Chla/Chla e supermolecule [9]. The possible g tensor axes orientations

are represented by cones with a various opening angle around the membrane normal nf (which is parallel to the crystallographic c axis). In particular, no g axis is perpendicular to the chlorophyll ring planes.

x y z method reference

U U

68 U 38 61 single crystal EPR this work, [7]

U U

69 U 36 62 radical pair EPR + X-ray diffraction [7]

U U

48 U 44 81 EPR on partially oriented cells [4] [ Table 6.3: Comparison of the P700Z g tensor orientation obtained from high ﬁeld EPR on single crystals of PS I with other experiments. Given are the angles between the principal directions of g and the thylakoid membrane normal (= crystallographic c axis).

REFERENCES 87 K High Field EPR of Single Crystals. The cw EPR experiments on P700J demonstrate the benefits of high field EPR on single crystals for the investigation of biological samples with organic radicals. The short acquisition times needed to achieve an excellent signal to noise ratio underline the high sensitivity of high field EPR. The benefits of the increased resolution seem less clear at the first glance. Even at 94 GHz, the Zee- man splitting anisotropy is rather small in relation to the inhomogeneous linewidth. As a consequence, the g anisotropy is not resolved in the frozen solution spectra. In the literature, either deuterated samples were used to decrease the hyperfine coupling constants causing the inhomogeneous broadening (i.e. [7, 8]), or significantly higher microwave frequencies were utilized (i.e. 325 GHz, [5]). The single crystal spectra however exhibit a pronounced structure. By taking the constraints arising from the crystal symmetry into account, it is possible to derive accurate spectral parameters from protonated samples at 94 GHz.

REFERENCES

[1] Webber A.N. & Lubitz W., P700: The primary electron donor of photosystem I, Biochim. Biophys. Acta (in press).

[2] Jordan P., Fromme P., Witt H.T., Klukas O., Saenger W., & Krauss N., Three-dimensional

structure of cyanobacterial photosystem I at 2 Q 5 Å resolution, Nature 411, 909–917 (2001).

[3] Rögner M., Nixon P.J., & Diner B.A., Puriﬁcation and characterization of photosystem I and photosystem II core complexes from wild-type and phycocyanin-deﬁcient strains of the cyanobacterium synechocystis PCC 6803, J. Biol. Chem. 265, 6189–6196 (1990).

[4] Berthold T., Bechthold M., Heinen U., Link G., Poluektov O., Utschig L., Tang J., Thur- nauer M., & Kothe G., Magnetic-ﬁeld-induced orientation of photosynthetic reaction centers as revealed by time-resolved W-band EPR of spin-correlated radical pairs, J. Phys. Chem. B 103, 10733–10736 (1999).

[5] Bratt P.J., Rohrer M., Krzystek J., Evans M.C.W., Brunel L.C.B., & Angerhofer A., Sub- O millimeter high-ﬁeld EPR studies of the primary donor in plant photosystem I P700 P , J. Phys. Chem. B 101, 9686–9689 (1997).

[6] Bratt P.J., Poluektov O.G., Thurnauer M.C., Krzystek J., Brunel L.C., Schrier J., Hsiao

Y.W., Zerner M., & Angerhofer A., The g-factor anisotropy of plant chlorophyll a P , J. Phys. Chem. B 104, 6973–6977 (2000).

[7] Zech S.G., Hofbauer W., Kamlowski A., Fromme P., Stehlik D., Lubitz W., & Bittl R.,

O P g A structural model for the charge separated state P700P A1 in photosystem I from the orientation of the magnetic interaction tensors, J. Phys. Chem. B104, 9728–9739 (2000). K 88 CHAPTER 6. P700J IN SINGLE CRYSTALS OF PHOTOSYSTEM I

[8] Prisner T.F., McDermott A.E., Un S., Norris J.R., Thurnauer M.C., & Grifﬁn R.G., Mea- P surement of the g-tensor of the P700 O signal from deuterated cyanobacterial photosystem I particles, Proc. Natl. Acad. Sci. USA 90, 9485–9488 (1993).

[9] Krauss N., personal communication (2001).

[10] Klukas O., Schubert W.D., Jordan P., Krauss N., Fromme P., Witt H.T., & Saenger W.,

Localization of two phylloquinones, Qk and Qkh , in an improved electron density map of photosystem I at 4 Å resolution, J. Biol. Chem. 274, 7361–7367 (1999).

[11] Stone A.J., Gauge invariance of the g tensor, Proc. R. Soc. A 271, 424–434 (1963).

[12] Käß H., Die Struktur des primären Donators P700 in Photosystem I: Untersuchungen mit Methoden der stationären und gepulsten Elektronenspinresonanz, Ph.D. thesis, Techni- sche Universität Berlin (1995).

[13] Käß H., Fromme P., Witt H.T., & Lubitz W., Orientation and electronic structure or the P primary donor radical cation P700O in photosystem I: A single crystal EPR and ENDOR study, J. Phys. Chem. B 105, 1225–1239 (2001).

[14] Plato M. & Möbius K., Structural characterization of the primary donor in photosynthetic bacteria by its electronic g-tensor, Chem. Phys. 197, 289–295 (1995). Chapter 7

High Field EPR on the Tyrosine

Radical YDS in Single Crystals of Photosystem II

Crystallization of the intact photosystem II reaction center has only become possible very recently [1]. A ﬁrst structural model for PS II based on X-ray diffraction (at

3 M 8 Å resolution) has been developed concurrently to this work and has meanwhile been published [2]. While this structure confirms the overall model of PS II as given in chapter 5, many structural details are still lacking. High field EPR on single crystals has the potential to fill in information about the detailed geometrical and electronic structure of the paramagnetic intermediates in PS II which is not available from X-ray diffraction experiments alone.

The investigation of the dark stable tyrosine radical YDK is an important first step in this direction. YDK is easily generated without chemical treatment, eliminating the potential of artifacts. It combines a small g anisotropy with a complex hyperfine structure. This makes it an interesting benchmark for the analysis of radical species in single crystals using high field EPR in general.

7.1 Materials and Methods

The PS II preparations used in this work were kindly provided by Dr. Athina Zouni and coworkers in an in-house collaboration project.

7.1.1 PS II Core Complexes PS II core complexes (cc) were isolated from Synechococcus elongatus and puri- ﬁed according to a protocol described by Dekker et al. [3]. According to SDS1-

1Sodium Dodecyl Sulfate

89 90 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

Figure 7.1: Non-trivial symmetry operations of the P212121 space group in an orthorhombic unit cell. Since the angles between the C2 symmetry axes are equal, it is generally not possible to distinguish the a, b, and c directions in EPR experiments.

polyacrylamide gel electrophoresis and MALDI-TOF2 mass spectrometry, the PS II core complexes are composed of at least 17 subunits [4]. For frozen solution EPR and ENDOR, glycerol was used as a cryoprotectant, and the PS II cc solutions were frozen in liquid nitrogen.

7.1.2 PS II Single Crystals

From the above preparations, three-dimensional single crystals could be grown [1]. The PS II core complexes in these crystals retain full water oxidation activity, as has been shown by measuring the oxygen evolution activity of core complex solutions obtained by dissolving crystals [5]. The geometrical structure of the crystals has been

characterized by X-ray diffraction experiments. The crystals exhibit an orthorhombic

F F unit cell of dimensions a F 130 Å, b 227 Å, and c 308 Å. The unit cell includes 4 sites related by the P212121 space group (see ﬁg. 7.1). Each site is occupied by a dimer of PS II core complexes. The individual core complexes in the dimer are related to each

other by a non-crystallographic C2 (180 U rotation) symmetry axis that is parallel to the membrane normal. As in the frozen solution case, the crystals were soaked in glycerol as a cryoprotectant before freezing them in liquid nitrogen.

7.1.3 cw EPR

Continuous wave EPR experiments were performed at 94 GHz and a temperature of

T F 80 K. Frozen solution samples were handled as described in chapter 2. For the single crystals, three mounting variants were used (ﬁg. 7.2):

2Matrix Assisted Laser Desorption Ionization-Time Of Flight 7.1. MATERIALS AND METHODS 91

Figure 7.2: Several variants of mounting small PS II single crystals in capillaries for 94 GHz EPR.

1. Crystals were placed inside the sample tube (0 M 7 mm inner diameter) with a small amount of mother liquor and frozen in this position. In this arrangement, morphological planes of the crystals tend to be aligned to the wall of the capillary.

2. Crystals were placed on the end of a capillary, covered by a small amount of mother liquor, and ﬁxed in this position by freezing. With this mounting variant, crystals rest on large morphological planes, therefore the normal of the respective plane is aligned with the capillary axis.

3. Crystals were mounted in a loop protruding from a capillary and frozen with some mother liquor in that position. Since the loop can be tilted with respect to the capillary axis and the crystal is ﬂoating freely in a membrane of mother liquor prior to freezing, there is no inherent preferential orientation of the crystal.

Option 3 allows to perform additional X-ray diffraction experiments on the mounted crystals. These can be useful to obtain independent information about the orientation of the crystal axes with respect to the laboratory axis system, thereby supplementing or corroborating EPR results.

7.1.4 Pulsed ENDOR

Pulsed ENDOR experiments were performed on frozen core complex solutions (T F

5 K) at X band (9 M 5 GHz) microwave frequencies. A Bruker ESP 380E spectrometer, equipped with an ESP 360D-P pulsed ENDOR accessory and an ENI A-500 RF am-

pliﬁer was used. Davies’ pulse sequence [6] with a tRF F 8 µs RF pulse was applied (see section 1.4.2). 92 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II 7.2 Results

7.2.1 cw EPR of Frozen Solution

A 94 GHz cw EPR spectrum of YDK in frozen PS II cc solution is shown in ﬁg. 7.3.

The spectrum was obtained at a sample temperature of T F 80 K and a microwave

power level of Pmw E 500 nW. A distinct and well-resolved hyperﬁne structure reﬂects M

a narrow EPR linewidth and, therefore, a homogeneous sample. At the gx F 2 00767 M and gz F 2 00219 edges, a fourfold hyperﬁne splitting with an intensity ratio pattern of 1:3:3:1 is apparent. This intensity ratio corresponds to a binomial distribution for

1 F N F 3, suggesting that the structure is caused by three I 2 nuclear spins with similar

effective hyperfine coupling constants for orientations along the molecular x and z M axes. On the gy F 2 00438 edge, only a twofold splitting is resolved. Therefore, at least some of the hyperfine coupling tensors have to be rather anisotropic, resulting in a small effective hyperfine coupling constant for the gy orientation. Based on earlier EPR work on similar phenoxyl-type radicals (e.g. [7]) and theoretical studies [8, 9], the hyperfine structure is assigned to three protons in position 3, 5, and 7a (refer to fig. 7.4).

7.2.2 Pulsed ENDOR on Frozen Solution

There is considerable variation in the hyperﬁne data for YDK in the literature (see [7, 11–15]). It can also not be excluded that the hyperﬁne couplings may be different for

PS II preparations from different species. The single crystal YDK spectra are, as will be seen later, dominated by the complex hyperﬁne structure. The reproducibility of this structure is an important criterion for the quality of simulations of these spectra. For this purpose, accurate hyperﬁne coupling constants are essential.

Fig. 7.5 shows the Davies ENDOR spectrum obtained from frozen solution of PS II F cc at T 5 K at X band. The g anisotropy of the YDK radical is too small to lead to pronounced orientation selection effects in X band ENDOR. Therefore, the ENDOR spectrum shown exhibits the full hyperﬁne coupling tensors. For a given effective hy- perﬁne coupling constant a and a nuclear Zeeman frequency νn, the ENDOR resonance

F j j F M ν i ν ν

condition is ENDOR n k 2 . Here, the proton Zeeman frequency is n 14 8 MHz.

j j

l m The spectral features corresponding to proton hyperﬁne couplings l a 2νn are therefore grouped symmetrically about this frequency. The largest hyperﬁne couplings are close to 2νn in magnitude, and corresponding features can be seen only on the high- frequency side of the spectrum.

M M M

The high-frequency end of the ENDOR spectrum ( RF F 27 32 MHz) is domi- o a n a

nated by an axial hyperﬁne tensor. The moderate relative anisotropy 1 L shows

o q a n 2a 3 p that dipolar contributions to this coupling are small as compared to the contactJ interaction with the local electron spin density mediated from the phenoxyl ring by hyper- conjugation (see e.g. [16]). In accordance with the literature, this tensor was assigned 7.2. RESULTS 93

Figure 7.3: 94 GHz cw EPR spectrum of the YD[ radical in frozen solution of photosystem II core

complexes at T T 80 K (solid) and simulation (dotted). The narrow linewidth reﬂects the excellent

homogeneity of the sample and allows a complex hyperﬁne structure to be resolved.

r s H H H 2 3 7a H 1 t R C O 7b 4 H 6 5 H H

Figure 7.4: Hydrogen-bonded YD[ radical with proton numbering scheme. The molecular axes corre- spond to the principal axes of the g tensor [10]. 94 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

Figure 7.5: Davies ENDOR spectrum of YD[ in frozen solution of photosystem II core complexes at

ν T u T u T T 5 K. B0 346 7 mT, MW 9 73 GHz. The upper frequency axis gives the magnitude (but not the sign) of the observed hyperfine couplings. Dotted lines represent the assigned hyperfine principal values. 7.2. RESULTS 95 to a β proton in position 7a and the sign of the hyperfine couplings assumed to be

positive. The mirror image of this structure on the low-frequency side would fall in M the νRF m 1 5 MHz range which is outside of the useful spectral range of the ENDOR setup used.

At νRF E 24 MHz on the high frequency side and 5 MHz on the low frequency

side of the spectrum, a split peak is observed. On both sides of this split peak, there

M M M are broad slopes that extend into the matrix region (νRF F 10 20 MHz) and into the range of the axial β proton tensor assigned above. This suggests the split peak to represent the middle components of two highly anisotropic, rhombic hyperfine tensors. Based on the strong anisotropy and the splitting of the lines, these couplings were assigned to approximately symmetry-equivalent α protons of the phenoxyl ring. Theoretical [8, 9] studies indicate that the spin density has a local maximum near the β protons in positions 3 and 5 and that the corresponding hyperfine couplings have negative sign. The corresponding largest coupling components deriving from these ν protons show up as small shoulders at about RF E 26 MHz with a similar splitting. The smallest couplings of these protons could not be unambiguously identified in the matrix signal region. The splitting of the two observed principal values is comparable, suggesting that the inequivalence is mostly caused by a different spin density. A likely cause for such a deviation from symmetry would be the influence of an asymmetrically oriented hydrogen bond to the phenoxyl oxygen (see e.g. fig. 7.4).

7.2.3 cw EPR on Single Crystals Several sets of cw EPR spectra were obtained for differently mounted single crystals of PS II cc (ﬁg. 7.6, 7.8, 7.10, and 7.12). Within each set, the sample was turned about

the capillary axis which is perpendicular to the applied magnetic ﬁeld Bv 0.

The combination of 8 magnetically inequivalent YDK sites and the superimposed

hyperfine structure makes the spectra very complex. Taking only the three proton hy- F perfine couplings resolved in the frozen solution spectra into account, 8 w 8 64 potentially resolvable lines contribute to every trace. It is therefore not generally possible to trace the angular dependence of the effective g value for the different sites. Also, the hyperfine structure is very pronounced for some orientations but completely smeared out for others. This again illustrates the need for spectral simulations as discussed in appendix B in order to obtain information about the orientation of the g tensor.

7.2.4 Analysis Parameter estimation. The only parameters that can be derived from the spectra independently from other parameters are the principal values of the accessed hyperfine tensors. This is due to the absence of orientation selectivity in the X-band ENDOR experiments which in turn is a result from the small g anisotropy. The principal hyperfine values have been determined by picking the position of peaks or other significant features in the ENDOR spectrum manually (dotted lines in fig. 7.5). The structures in 96 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

Figure 7.6: Orientation-dependent 94 GHz cw EPR spectra of the YD[ radical in a single crystal of

photosystem II core complexes from Synechococcus elongatus T T 80 K and 500 nW of microwave power. The spectrum of PS II cc in frozen solution has been included at the top. 7.2. RESULTS 97

Figure 7.7: Simulation of the spectra in ﬁg. 7.6. Effective g values arising from the 8 magnetically inequivalent YD[ sites are marked by colored lines. Identical colors represent sites related by the C2

dimer symmetry. The rotation axis corresponds to the crystallographic a direction (tilted by 3 _ ), leading to pairwise degeneracy of the g factors. As a consequence, a comparable simulation yielding wrong results can be obtained taking only four YD[ sites into account. See tab. 7.1 for the detailed orientation of the crystal. 98 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

Figure 7.8: 94 GHz cw EPR spectra of the YD[ radical in single crystals of PS II cc as in ﬁg. 7.6 for a different mounting orientation. 7.2. RESULTS 99

Figure 7.9: Simulation of the EPR spectra in fig. 7.8. For this crystal, the b axis is approximately in the plane of the magnetic field. Again, the effective g values of the YD[ sites appear grouped together, making it difficult to recognize the true number of sites. Refer to tab. 7.1 for details on the mounting orientation of the crystal. 100 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

Figure 7.10: 94 GHz EPR spectra of a PS II cc single crystal with a third mounting orientation. 7.2. RESULTS 101

Figure 7.11: Simulation of the spectra in ﬁg. 7.10. For this orientation, the a axis is approximately in

_ _ the plane of the magnetic ﬁeld, leading again to degeneracy at the 0 _ /180 and 90 orientations. For other rotation angles, the g values exhibit again some grouping, making it difﬁcult to recognize the number of magnetically inequivalent sites. See tab. 7.1 for details on the crystal orientation. 102 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

Figure 7.12: Orientation-dependent 94 GHz cw EPR spectra of the YD[ radical in single crystals of PS II cc for an arbitrary mounting orientation of the crystal which largely avoids degeneracies. 7.2. RESULTS 103

Figure 7.13: Simulation of the spectra in ﬁg. 7.12. The effective g values of different sites are spread out, and no clustering appears. This set of spectra unambiguously proves that more than one YD[ radical belongs to each of the four crystallographic sites. The mounting orientation of the crystal is given in tab. 7.1. 104 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

the spectrum are narrow and their spectral positions are well-defined. This allows to M estimate the uncertainty of the obtained values as ∆A m 0 2 MHz. In contrast, an accurate determination of g principal values from the cw EPR spectra is not completely independent from other parameters in the spin Hamiltonian. Therefore, an iterative estimation procedure was used to arrive at a self-consistent parameter set. Based on initial guesses about the orientation of the hyperfine tensors with respect to the g tensor, the principal values of g could be determined from a simulation of the frozen solution cw EPR spectrum. Both g and hyperfine principal values were then used in turn to simulate the orientation-dependent single crystal spectra and obtain orientation information for the individual tensors. this procedure was repeated several times. A complete parameter set consists of

x 3 principal values for g,

x 3 principal values for each hyperﬁne tensor included in the Hamiltonian,

x 3 Euler angles per hyperﬁne coupling, giving the orientation of the tensor relative to g,

x 3 principal values of a Gaussian linewidth tensor (representing the unresolved hyperﬁne interactions),

x and 3 Euler angles describing the orientation of the linewidth tensor.

In addition, the simulation of single crystal spectra requires

x 3 Euler angles for the orientation of the g tensor for each magnetically inequivalent site in the unit cell,

x and 3 Euler angles describing the crystal orientation with respect to the laboratory axis system.

To increase both the numerical stability of the ﬁtting procedure and the statistical sig- niﬁcance of the obtained parameters, the number of parameters was reduced as follows:

x In the crystals, the orientation of all magnetically inequivalent sites can be de-

rived from the orientations of the YDK radicals in a single photosystem II cc dimer

by using the symmetry operations of the P212121 space group. x From X-ray diffraction experiments, the C2 symmetry axis relating both PS II specimen within a dimer is known with high accuracy. Therefore, only one set

of Euler angles is needed to describe the orientation of both YDK radicals in each dimer. 7.2. RESULTS 105

x The small inequivalence in the hyperﬁne coupling constants for the protons in positions 3 and 5 was neglected and the respective tensors were assumed to be oriented symmetrical to each other with respect to the molecular axis system.

x An isotropic Gaussian linewidth was assumed.

The smallest component of the α proton hyperfine tensors could not be assigned in the ENDOR spectrum. This value was used as a free parameter in the simulations. It should be noted, however, that the value obtained from the simulations is also influenced by linewidth contributions from unresolved hyperfine couplings and is at best a crude approximation. Tab. 7.2 shows the final parameter set obtained, with the exception of the orientation of the crystal in the laboratory system which differs for each spectrum.

Quality of simulations. The simulated frozen solution and crystal spectra are shown in fig. 7.7, 7.9, 7.11, and 7.13, next to the respective experimental spectra. While the frozen solution spectrum is reproduced with excellent accuracy, the hyperfine structures of the experimental and simulated single crystal spectra look somewhat different for many orientations. Close inspection of the spectra reveals however that only the amplitude of the hyperfine structure differs significantly. These differences are the result of an assumed isotropic linewidth used in the simulations: for orientations where the assumed linewidth is too large, hyperfine structure is lost due to the reduced resolution of the simulated spectrum. Similarly, for orientations where the assumed linewidth is too small, the hyperfine structure appears more pronounced in the simulations. The spectral positions of the hyperfine features, however, are well reproduced by the simulations, corroborating the parameters used.

Photosystem II dimers. For special orientations of the crystals with respect to the magnetic field, degeneracy occurs. Since most mounting variants induce a preferential orientation of the crystals that is related to their morphological structure, such special orientations are obtained rather often. A good example can be seen in fig. 7.6/7.7. Here, the rotation axis is very close to the crystallographic a axis, and the magnetic field is therefore almost exactly in the bc plane for all rotation angles. For such an orientation, a pairwise degeneracy occurs, reducing the apparent number of inequivalent tyrosine radicals in the unit cell to 4. It is indeed possible to obtain a rather good simulation of the spectra in fig. 7.6 with a model that assumes 4 monomeric PS II sites. Furthermore, at early stages of the analysis of single crystal spectra, the dimeric nature of the sites in the crystals was not known yet, leading to a wrong initial interpretation of the spectra. Only later experiments involved sufficiently “arbitrary” orientations of the crystals (i.e. fig. 7.12) to clearly resolve more than 4 inequivalent YDK radicals, thereby confirming the dimeric nature of PS II at the crystallographic sites. 106 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

φ θ ψ ﬁgures

U U

93 U 90 87 7.6, 7.7

U U

62 U 64 92 7.8, 7.9

U y U

1 U 73 1 7.10, 7.11

U U 41 U 49 41 7.12, 7.13

Table 7.1: Orientation of the PS II cc crystals for a rotation angle of 0 _ (determined from simulations of the EPR spectra). The Euler angles relate the crystallographic abc axes to the laboratory axis system xyz; the magnetic ﬁeld B0 is parallel to the x axis. The crystal rotation around the z axis corresponds to an increase of φ. For the deﬁnition of Euler angles used here, refer to appendix B.2.

x y z

M M g 2 M 00767 2 00438 2 00219

3 z 5

y y y

E M A [MHz] 26 M 1 8 19 5

M M M

H H A [MHz] H 32 8 27 2 27 2

Table 7.2: Simpliﬁed parameter set used for simulation of spectra. Refer to tab. 7.3 for the orientation

α _ of the g tensor in the crystal. The hyperﬁne tensors for the protons (3,5) are rotated by { 20 about z

with respect to the g tensor. The A7a tensor is collinear with g. `

cos x1 y1 z1 x2 y2 z2 C2

y y y

M M M M M M M

H H H

a 0 681 0 201 0 704 H 0 177 0 257 0 950 0 282

y y y

M M M M M M M

H H H

b 0 440 H 0 881 0 174 0 557 0 769 0 312 0 558

y y y

M M M M M M M

H H H c H 0 585 0 428 0 688 0 811 0 585 0 007 0 781

Table 7.3: Orientation of the YD[ g tensor axes in the crystal site deﬁned by the given C2 axis orientation. Given are the directional cosines with respect to the crystallographic abc system. Orientations for other sites can be obtained using the symmetry operations of the P212121 space group. Subscripts 1 and 2 refer to the two halves of the PS II cc homodimer. 7.3. DISCUSSION 107

Assignment of axes. The symmetry operations of the P212121 space group are invariant under permutations of the crystallographic axes. For this reason, an assignment of the crystallographic axes is not possible based on the analysis of orientation symmetries in the single crystal spectra. More precisely, EPR allows to identify the orientation of a set of three symmetry axes which corresponds to the crystallographic axis system, but not to assign individual symmetry axes to the crystallographic a, b, and c axes. A common way to resolve this sixfold ambiguity is to determine the orientation of the crystal used in the EPR experiment by X-ray diffraction. The crystals used here have an additional symmetry, however. For each site in the crystal, there is a local C2 axis that relates both halves of the PS II homodimer to each other. This additional symmetry affects the EPR spectra and can be analyzed. When the inclination angles of the C2 axis with respect to the crystallographic axes are different, these angles can be used to label the symmetry axes and unambiguously assign them to the crystallographic axes system (ﬁg. 7.14). This still requires the orientation of the C2 axis with respect to the crystal axis system to be known from other experiments like X-ray crystallography. It is however not necessary any more to perform X-ray diffraction experiments on the crystals used for EPR. The orientation of the local C2 dimer axes in the single crystals of PS II cc used here fulﬁlls the requirements stated above. The orientation of the C2 axis for one arbitrary site in the crystal (right column in tab. 7.3) was obtained from X-ray diffraction studies and kindly provided by Dr. Peter Orth (FU Berlin).

Assignment of sites. Furthermore, the dimer symmetry is non-crystallographic, i.e. each site in the unit cell has a differently oriented local C2 axis. This makes it possible to label pairs of YDK signals deriving from the same dimer in the unit cell with the corresponding orientation of the local C2 axis (see fig. 7.15 for an example). Therefore, orientation information about the YDK radicals can be given for a specific site that can be unambiguously identified by other structural investigation methods (i.e. X-ray diffraction). This is of particular help when combining results from different techniques.

7.3 Discussion

The 94 GHz cw EPR spectra of frozen solution of PS II cc exhibit excellent resolution as evident by the well-resolved hyperfine structure. On the instrumental side, this reflects the good homogeneity of the magnetic field. More importantly, however, it can be attributed to a small inherent linewidth of the sample that indicates a well-defined, homogeneous environment of the YDK radical in the protein. g tensor. The good resolution of the spectra allowed to determine the principal g

W ∆ F values with high accuracy ( g 2 10 L ). The obtained values are similar to those found in other works (see tab. 7.4), although they do not agree within their error margins in every case. It cannot be ruled out that the values may depend on the organism

108 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

} ~

Figure 7.14: Orientation of a non-crystallographic C2 symmetry axis with respect to the crystal axis system. The crystallographic a, b, and c axes can be identiﬁed by the magnitude of the direction cosines (bold) which are known from X-ray diffraction.

Figure 7.15: 2D example on how crystallographic sites can be distinguished based on a noncrystallographic symmetry. The same initial tensor orientation (bold ellipsis) is assumed for different sites. Since the crystallographic (solid) and the noncrystallographic (dashed) symmetry operations do not commute, different sets of orientations result. 7.3. DISCUSSION 109

gx gy gz ∆g organism reference

M M M W

2 00767 2 00438 2 00219 2 10 L S. elongatus this work

M M 2 M 0074 2 0044 2 0023 not given spinach [7]

M M M W 2 0075 2 0045 2 0021 1 10 L spinach [17]

M M M W

2 00756 2 00432 2 00215 1 10 L spinach [11]

M M

2 M 00740 2 00425 2 00205 not given Synechocystis 6803 [18]

M M 2 M 00737 2 00420 2 00208 not given spinach [18]

M M M W

2 00745 2 00422 2 00212 2 10 L spinach [19]

M M 2 M 00782 2 00450 2 00232 not given spinach [12]

M M M W 2 00752 2 00426 2 00212 7 10 L spinach [20]

∆ Table 7.4: Comparison of principal values of the g tensor for the YD[ radical in PS II. g denotes the accuracy of the given data. from which PS II was prepared, or from artifacts of the preparation procedure. The latter possibility is, however, unlikely, considering that the PS II core complexes in the crystals used here maintained their catalytic activity [5]. It seems most plausible to attribute minor differences in g to different ﬁeld calibration procedures or g reference samples. The g values obtained in this work are tied to the g factor of the Li:LiF sam- 2 ple which is known to a high degree of accuracy [21] while Mn J centers are another popular reference sample used for calibration in high ﬁeld EPR.

Hyperﬁne couplings. Reliable data on the hyperﬁne interactions is important for the simulation of the EPR spectra, especially for single crystal spectra. The results obtained by Davies ENDOR are compared with those from other sources in tab. 7.5.

It can be seen that there is a rather large variation of hyperﬁne data for the YDK radical

in the literature. The accuracy of the hyperﬁne data taken from the ENDOR spec- M

trum in this work is estimated as ∆A F 0 2 MHz, based on the width of the features in

3 5 5 3 3 5 5 3 3 5 5 3 7a 7a

Ax Ax Ay Ay Az Az A A organism reference

u u u u u

25 u 5 26 8 8 19 0 20 1 27 2 32 8 S. elongatus this work

u u u u 29 u 4 9 0 19 6 21 6 23 2 spinach [7]

24 3 19 27 28 31 spinach [11]

u u u u u

14 u 8 18 8 20 3 23 0 27 0 30 5 spinach [12]

u u u u u

12 u 3 18 8 20 3 23 0 27 0 30 5 spinach [13]

u u u u u u

25 u 6 27 5 8 0 19 1 20 5 27 2 31 5 spinach [14]

u u u u u u

25 u 6 27 5 8 0 19 1 20 5 28 5 33 0 C. reinhardtii [14]

u u u u u u

25 u 6 27 5 8 0 19 1 20 5 24 5 29 0 P. laminosum [14]

u u u u 25 u 4 7 2 19 5 20 2 29 3 Synechocystis 6803 [15]

Table 7.5: Hyperﬁne coupling principal values for the YD[ radical as determined in this work and comparison with literature data. All values are given in MHz. (Some data given in magnetic ﬁeld units in the literature have been converted.) 110 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

gx gy gz radical

M M M

2 00767 2 00438 2 00219 YDK

M M

2 M 0076 2 0046 2 0021 Y177

M M 2 M 0092 2 0046 2 0021 Y122

Table 7.6: Comparison of g values for YD[ and tyrosine radicals Y122 (E. coli) resp. Y177 (mouse) in the R2 subunit of ribonucleotide reductase. Compared to Y177, Y122 is missing a hydrogen bond to the phenoxyl oxygen, causing a shift of gx to a larger value [22].

3 N 5 the ENDOR spectra. The given Ay couplings are an estimate based on EPR spectra simulations; the obtained values are very likely influenced by the neglected smaller couplings and no error can be given. The asymmetry of the hyperfine tensors for protons in positions 3 and 5 has been observed by other authors as well and is attributed to a hydrogen bond from the phenoxyl group to a histidine residue (His189) in the protein backbone [23]. The length and orientation of this bond not only affects the spin density distribution within the phenoxyl ring (and thus the hyperfine coupling constants), but also has an effect on the g tensor. Particularly the gx component is sensitive towards such a hydrogen bond, as was shown by calculations and EPR experiments on tyrosine radicals in other systems [18, 22, 24, 25] (see also tab. 7.6). The largest hyperfine coupling derives from the proton in position 7a (see fig. 7.4), while the corresponding coupling from the proton in position 7b is not resolved in the EPR spectra and was not identified in the ENDOR spectrum. The coupling for such β protons is rather isotropic and dominated by the Fermi contact interaction term. The spin density in the phenoxyl ring has a π orbital-like distribution with a node in the ring plane. Consequently, for varying orientation of the phenoxyl ring with respect to the amino acid head group (denoted ‘R’ in fig. 7.4), the β protons in positions 7a and 7b may experience rather different spin densities. Since the 7b proton hyperfine interaction is small, it is concluded that this proton lies in or close to the ring plane.

Small protein crystals. The single crystal spectra demonstrate that high-field EPR experiments on organic radicals in these small crystals are feasible and deliver spectra with an excellent signal to noise ratio. The typical crystal size in the experiments shown here was about 35 nl, corresponding to about 1013 spins (assuming the upper limit of 100% for the yield of YDK ). Typical acquisition times for one trace of the crystal spectra were about 3 minutes; therefore the sensitivity is sufficient to investigate considerably smaller crystals at still practical acquisition times. As an example, 30 11 minutes of data acquisition with a 1 nl crystal (corresponding to about 3 W 10 unpaired spins) would yield a spectrum with a tenth of the signal/noise ratio. The quality of such a spectrum would still be usable for an analysis, and it could be further increased by resorting to less conservative filtering/modulation parameters than were used here. The excellent agreement of the spectral features of the hyperfine structure between the experimental single crystal spectra and the simulations corroborate the obtained

7.3. DISCUSSION 111

O α O β

R R

Figure 7.16: Schematic representation of the YD[ orientation in PS II cc with respect to the thylakoid membrane as determined in this work (solid) and in [11] (slashed). Both views are along the membrane

plane. α is the angle between the molecular y direction and the membrane normal nf ; β is the tilt of the

phenoxyl ring plane with respect to nf .

hyperﬁne values. More important, however, is the orientation information gained from these spectra (tab. 7.3). The orientation of the g tensor could be determined with

an estimated accuracy of 3 U . Since the g tensor orientation is tied to the molecular symmetry axes of the phenoxyl radical, the orientation of the tyrosyl in the crystals is also obtained. This knowledge potentially helps in the creation of a detailed structural model. To derive the same information from X-ray diffraction analysis, very high resolution is required, placing extremely high demands on the quality of the crystals.

Comparison with oriented membrane data. Dimeric PS II has also been observed in 2D crystals and native membrane fragments [26–28]. It seems likely that the PS II dimers in the single crystals are identical. Under this assumption, the C2 axis of each PS II homodimer corresponds to the membrane normal of native PS II. The orientation of the YDK radical with respect to the membrane can thus be derived and compared to EPR work on YDK in oriented membrane fragments [11]. Such a comparison is shown in fig. 7.16. The discrepancy in orientations between this work and [11] is moderate, but still significant. In single crystals, the orientation of the tyrosine sites is very well defined whereas there might be a considerable distribution of orientations in imperfectly oriented membranes. For this reason, the results obtained from the single crystal studies shown here are believed to be much more reliable. Also, the spectra in this work show significantly more detail than those in [11], thereby increasing the robustness of the fit. 112 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

Comparison with structural model. The obtained orientation of YDK can also be

compared to the recently published PS II structure. However, the 3 M 8 Å resolution of the diffraction data on which that structure is based is not really sufﬁcient to obtain such information for molecular groups the size of a phenoxyl ring, even if an orientation of the tyrosyl radicals is suggested in [2]. A tentative identiﬁcation of YDK 1 (index referring to tab. 7.3) with TYR94 (nomenclature used in in [29]) and YDK 2 with TYR92

yields a deviation of the molecular x axes of about 15 U ; the y and z axes directions dif-

fer by about 60 U . The rather large deviations are not surprising considering the present resolution of X-ray diffraction data.

7.4 Conclusion

Using the PS II cc single crystals, it was shown that high-ﬁeld EPR yields the sensitivity and the spectral resolution to analyze small protein single crystals containing organic radicals. Considering the excellent quality of the obtained spectra, it should be 11 possible to perform experiments with single crystals as small as 1 nl (3 W 10 spins). Also, thanks to the excellent resolution, very detailed spectra can be obtained that allow the investigation of crystals with a considerable number of magnetically inequivalent radicals (8 in this speciﬁc case).

The g tensor and the dominant hyperfine interaction tensors for the YDK radical could be determined with very good accuracy from combined high field EPR and X- band ENDOR experiments. The high accuracy allowed us to derive precise orientation information about the g tensor from single crystal EPR spectra and, thereby, the orientation of the radical itself. This detailed information about potentially functionally relevant radicals can be even obtained from single crystals whose quality is insufficient for X-ray diffraction structural analysis since EPR experiments are much less affected by mosaicity of the crystals. The knowledge obtained from these EPR experiments can be derived from X-ray structural analysis only at very high resolutions. Thus, high field EPR experiments complement X-ray diffraction as a tool for the investigation of protein structure.

The dark stable YDK radical targeted in this work provides a good test case for EPR on organic radicals in the PS II cc single crystals. With these experiments and the subsequent successful analysis, a foundation for the investigation of further paramagnetic species in these crystals has been laid.

REFERENCES [1] Zouni A., Lüneberg C., Fromme P., Schubert W.D., Saenger W., & Witt H.T., Char- acterization of single crystals of photosystem II from the thermophilic cyanobacterium Synechococcus elongatus, in Photosynthesis: Mechanisms and Effects (Garab G., ed.), volume 2, pp. 925–928, Kluwer Academic Publishers (1998). REFERENCES 113

[2] Zouni A., Witt H.T., Kern J., Fromme P., Krauss N., Saenger W., & Orth P., Crystal

structure of photosystem II from Synechococcus elongatus at 3 Q 8 Å resolution, Nature 409, 739–743 (2001).

[3] Dekker J.P., Boekema E.J., Witt H.T., & Rögner M., Reﬁned puriﬁcation and further characterization of oxygen-evolving and tris-treated photosystem II particles from the thermophilic cyanobacterium Synechococcus elongatus, Biochim. Biophys. Acta 936, 307– 318 (1988).

[4] Barry B.A., Boerus R.J., & de Paula L.C., The use of cyanobacteria in the study of the structure and function of photosystem II, in The Molecular Biology of Cyanobacteria (Bryant D.A., ed.), pp. 217–257, Kluwer Academic Publishers (1994).

[5] Zouni A., Jordan R., Schlodder E., Fromme P., & Witt H.T., First photosystem II crystals capable of water oxidation, Biochim. Biophys. Acta 1457, 103–105 (2000).

[6] Davies E.R., A new pulse ENDOR technique, Phys. Lett. 47A, 1–2 (1974).

[7] Hoganson C.W. & Babcock G.T., Protein-tyrosyl interactions in photosystem II studied by electron spin resonance and electron nuclear double resonance spectroscopy: Compar- ison with ribonucleotide reductase and in vitro tyrosine, Biochemistry 31, 11874–11880 (1992).

[8] O’Malley P.J. & Ellson D., 1H, 13C and 17O isotropic and anisotropic hyperﬁne coupling prediction for the tyrosyl radical using hybrid density functional methods, Biochim. Bio- phys. Acta 1320, 65–72 (1997).

[9] Himo F., Gräslund A., & Eriksson L.A., Density functional calculations on model tyrosin radicals, Biophys. J. 72, 1556–1567 (1997).

[10] Fasanella E.L. & Gordy W., Electron spin resonance of an irradiated single crystal of L-tyrosine-HCl, Proc. Natl. Acad. Sci. USA 62, 299–301 (1969).

[11] Dorlet P., Rutherford A.W., & Un S., Orientation of the tyrosyl D, pheophytin anion, and g semiquinone QAP radicals in photosystem II determined by high-ﬁeld electron paramagnetic resonance, Biochemistry 39, 7826–7834 (2000).

[12] Farrar C.T., Gerfen G.J., Grifﬁn R.G., Force D.A., & Britt R.D., Electronic structure of the YD tyrosyl radical in photosystem II: A high-frequency electron paramagnetic resonance spectroscopic and density functional theoretical study, J. Phys. Chem. B101, 6634–6641 (1997).

[13] Gilchrist M.L., Ball J.A., Randall D.W., & Britt R.D., Proximity of the manganese cluster of photosystem II to the redox-active tyrosine YZ, Proc. Natl. Acad. Sci. USA 92, 9545– 9549 (1995).

[14] Rigby S.E.J., Nugent J.H.A., & O’Malley P.J.O., The dark stable tyrosine radical of photosystem 2 studied in three species using ENDOR and EPR spectroscopies, Biochemistry 33, 1734–1742 (1994). 114 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II

[15] Warncke K., Babcock G.T., & McCracken J., Structure of the YD tyrosine radical in photosystem II as revealed by 2H electron spin echo modulation (ESEEM) spectroscopic analysis of hydrogen hyperﬁne interactions, J. Am. Chem. Soc. 116, 7332–7340 (1994).

[16] Carrington A. & McLachlan A.D., Introduction to Magnetic Resonance with Applications to Chemistry and Chemical Physics, chapter 6.4, Harper & Row (1967).

[17] Dorlet P., Hanley J., Rutherford A.W., & Un S., Orientation study on the stable tyrosyl radical in photosystem II by high ﬁeld EPR, in Photosynthesis: Mechanisms and Effects (Garab G., ed.), volume 2, pp. 1395–1398, Kluwer Academic Publishers (1998).

[18] Un S., Tang X.S., & Diner B.A., 245 GHz high-ﬁeld EPR study of tyrosine-D and

tyrosine-Z in mutants of photosystem II, Biochemistry 35, 679–684 (1996).

[19] Un S., Brunel L.C., Brill T.M., & Zimmermann J.L., Angular orientation of the stable tyrosyl radical within photosystem II by high-ﬁeld 245-GHz electron paramagnetic resonance, Proc. Natl. Acad. Sci. USA 91, 5262–5266 (1994).

[20] Gulin V.I., Dikanov S.A., Tsvetkov Y.D., Evelo R.G., & Hoff A.J., Very high frequency (135 GHz) EPR of the oxidized primary donor of the photosynthetic bacteria

Rb. sphaeroides R-26 and Rps. viridis and of YDP (signal II) of plant photosystem II, Pure Appl. Chem. 64, 903–906 (1992).

[21] Stesmans A. & van Gorp G., Novel method for accurate g measurements in electron-spin resonance, Rev. Sci. Instrum. 60, 2949–2952 (1989).

[22] Bleifuß G., Pötsch S., Hofbauer W., Gräslund A., Lubitz W., Lassmann G., & Lendzian F., High ﬁeld EPR at 94 GHz of amino acid radicals in ribonucleotide reductase, in Mag- netic Resonance and Related Phenomena (Ziessow D., Lubitz W., & Lendzian F., eds.), volume II, pp. 879–880 (1998).

[23] Tang X.S., Chisholm D.A., Dismukes G.C., Brudvig G.W., & Diner B.A., Spectroscopic evidence from site-directed mutants of synechocystis PCC6803 in favor of a close interaction between histidine 189 and redox-active tyrosine 160, both polypeptide D2 of the photosystem II reaction center, Biochemistry 32, 13742–13748 (1993).

[24] Engström M., Hime F., Gräslund A., Minaev B., Vahtras O., & Agren H., Hydrogen bonding to tyrosyl radical analyzed by ab initio g-tensor calculations, J. Phys. Chem. A104, 5149–5153 (2000).

[25] Stone A.J., Gauge invariance of the g tensor, Proc. R. Soc. A 271, 424–434 (1963).

[26] Rhee K.H., Morris E.P., Zheleva D., Hankamer B., Kühlbrandt W., & Barber J., Two- dimensional structure of plant photosystem II at 8-Å resolution, Nature 389, 522–526 (1997).

[27] Rhee K.H., Morris E.P., Barber J., & Kühlbrandt W., Three-dimensional structure of the plant photosystem II reaction centre at 8 Å resolution, Nature 396, 283–286 (1998). REFERENCES 115

[28] Boekema E.J., van Breemen J.F.L., van Roon H., & Dekker J.P., Arrangement of photosystem II supercomplexes in crystalline macrodomains within the thylakoid membrane of green plant chloroplasts, J. Mol. Biol. 301, 1123–1133 (2000).

[29] Zouni A., Witt H.T., Kern J., Fromme P., Krauss N., Saenger W., & Orth P., Protein data bank, access code 1FE1: Crystal structure of photosystem II, http://www.rcsb.org/pdb. 116 CHAPTER 7. YDK IN SINGLE CRYSTALS OF PHOTOSYSTEM II Chapter 8

High Field EPR on the Quinone

S Acceptor Radicals QA S and QB in Reaction Centers from Rhodobacter sphaeroides R26

In the photosynthetic reaction center of purple bacteria, photoinduced electron transfers proceed along a series of cofactors as described in chapter 5. The ﬁnal cofactors

along this chain are the quinones QA and QB. Investigating the corresponding radicals

K L K QAL and QB by EPR and ENDOR helps to understand their electronic structure. For an understanding of the electron transfer process itself, however, an analysis of the electronic interaction, namely the exchange interaction, between the two quinones is essential.

In the normal reaction cycle of the bRC, QB is reduced by two consecutive electron

K L K transfers that proceed via QA. Therefore, a biradical state QAL QB appears as a functional intermediate in the enzyme. When this intermediate state is trapped, EPR can access the spin-spin interactions between the individual radicals and provide insight into the electronic coupling between the cofactors.

The quinone radicals in bacterial reaction centers are normally coupled to a paramagnetic high-spin iron ion. This presents a major difﬁculty for EPR experiments, since the magnetic coupling leads to greatly increased spin relaxation rates and, consequently, severe homogeneous broadening of the EPR spectra. It has, however, be demonstrated that the iron can be exchanged by several other ions while maintaining the activity of the reaction centers [1, 2]. In particular, the iron can be substituted by a 2 diamagnetic Zn J ion. This substitution greatly decreases the linewidth and allows to obtain EPR spectra with excellent resolution.

117

K L K 118 CHAPTER 8. QAL AND QB IN BACTERIAL PHOTOSYSTEM 8.1 Simulation of Radical Pair Spectra

1 In the previous chapters, isolated S F 2 radicals have been investigated. A coupled radical system is more complex and consequently requires more sophisticated techniques for the analysis and interpretation of the EPR spectra.

8.1.1 Spin Hamiltonian for a Spin Coupled Radical Pair The spin coupled radical pair under consideration can be described by the g tensors

1 1 ˜ F of the individual spins S1 F 2 and S2 2 and a coupling tensor D that includes dipolar and exchange interaction. Neglecting unresolved hyperﬁne interactions, the spin Hamiltonian is thus T

v v v

v ˆ ˆ ˆ ˜ ˆ

v W W W W W M

ˆ F

H H µBB0 g1 S1 H g2 S2 S1 D S2 (8.1)

This Hamiltonian is formally similar to a single radical with hyperﬁne interactions. However, several complications may arise:

x Since the electronic Zeeman energies of the uncoupled spins are similar, rather small inter-electron couplings can bridge this energy difference. Under these conditions, the proper eigenstates of the system change signiﬁcantly from the uncoupled case. As a consequence, the probabilities for the various EPR transitions are modiﬁed, enabling “forbidden” transitions. For a correct simulation, the relative intensities of all EPR transitions has to be taken into account.

x The transition intensities also depend on the population of the energy levels. At high temperatures, the Boltzmann factor describing the level populations can be E

k T E

L y linearized, i.e. e B E 1 . The population difference for pairs of energy kBT levels with the same energy difference is thus constant. This approximation is no

longer applicable when the condition E kBT does not hold. At 94 GHz, the

hν

E M transition energy corresponds to a temperature of T F 4 5 K. Therefore, a kB rather pronounced temperature dependence of the spectra can be expected, even at modest cryogenic temperatures.

Fig. 8.1 illustrates the four level spin system in the limits of weak and strong spin- spin coupling, respectively. When the coupling is very anisotropic, both cases may apply, depending on the orientation of the sample with respect to the applied magnetic ﬁeld. The general orientation dependence of the dipolar interaction is given in ﬁg. 8.2.

Simulation Program An analytical treatment of the radical pair problem is rather straightforward when the coupling tensors g1, g2, and D˜ are isotropic (see e.g. [3]). This condition does not apply here, however. This makes it necessary to resort to perturbative approaches. 8.1. SIMULATION OF RADICAL PAIR SPECTRA 119

T+ =

II III II III

1 S= ( − ) T = 1 2 0 2 ( + )

I IV I IV

T− =

Figure 8.1: Energy levels and allowed EPR transitions for a radical pair with isotropic couplings. Left: Weak coupling limit: transitions I–IV are allowed. The eigenstates are dominated by the Zeeman energy difference between both radicals while the smaller spin-spin interaction acts as a small perturbation, shifting energies. Right: Strong coupling limit: The system separates into a singlet and three triplet states. Intersystem crossing (transitions III and IV) is forbidden. The Zeeman energy difference between the radicals acts as a small perturbation.

Higher order perturbation theory leads to rather lengthy expressions, however. Since in practice computers are used anyway for the simulation of the spectra, it was decided to employ a full numerical diagonalization of the Hamiltonian for determining eigenvalues, eigenstates, and transition matrix elements. To accomplish this, a new C++ program (not given here) was written within the context of this thesis. The basic processing steps performed for the simulation of radical pair spectra are as follows:

x A set of isotropically distributed orientations is generated to simulate the ensemble in frozen solution.

x For each orientation, the ﬁeld strength independent part of the spin Hamiltonian is calculated from the input parameters.

x For each orientation and field strength, the total Hamiltonian is calculated from the field dependent and field independent contributions. This Hamiltonian is then diagonalized.

x The dipole matrix elements for transitions between all levels are calculated.

x The Boltzmann population of the energy levels is calculated.

x The EPR signal contribution for the chosen orientation and ﬁeld is calculated from the population difference, dipole matrix element, and the deviation of the transition energy from the microwave frequency (using a Lorentzian lineshape function).

K L K 120 CHAPTER 8. QAL AND QB IN BACTERIAL PHOTOSYSTEM

2 1 θ

Figure 8.2: Angular dependence of the interaction between two parallel dipoles ( cos 3 ). When _ the distance vector is at the “magic angle” of 54 u 7 relative to the direction of the dipole moments, the interaction vanishes. 8.2. MATERIALS AND METHODS 121

x The spectrum is convoluted with a Gaussian to account for inhomogeneous broadening.

The simulation thus mimics the quantum mechanics of the system without resorting to possibly unjustified approximations. In many other programs, the spectrum is calculated in the frequency domain, and a nonlinear transformation is used for conversion to field-swept spectra. As explained above, the proper eigenstates of the system may depend to a much larger extent on the applied field than in simpler systems. A conversion of spectra from the frequency domain to a magnetic field axis does not reflect this dependency and is therefore potentially inaccurate. These problems are completely avoided by diagonalizing the Hamil- tonian separately for each field strength B0. By using an interative diagonalization method (complex Jacobi rotations, see e.g. [4]) and using the set of calculated eigen- vectors as the initial transformation matrix for the next diagonalization, the computation time penalty for this can be kept moderate.

8.2 Materials and Methods

The bacterial reaction center samples described were prepared by E. Abresch, and the radical states were generated by E. Abresch and M. Paddock in the group of Prof. G. Feher (UCSD, La Jolla).

8.2.1 Sample Preparations Reaction centers were isolated from Rhodobacter sphaeroides R26. To decrease the

EPR linewidth and increase spectral resolution, the non-heme, high-spin Fe(II) cou-

K L K pled to the quinone acceptor radicals QAL and QB was substituted with diamagnetic Zn(II) following the procedures described in [1, 2]. In order to reduce inhomogeneous broadening due to unresolved hyperﬁne interactions, QA and QB were exchanged with deuterated ubiquinone-10. The reaction centers were incubated for 24 hours in D2O to remove other exchangeable protons. All samples were ﬁlled in CV7087S suprasil

capillaries (see chapter 2).

K L K QAL and QB radicals. Quinone radicals were generated by illumination with a single, saturation laser ﬂash. Excess cytochrome c was added to reduce the primary donor radical after photooxidation. Due to the short duration of the ﬂash (400 ns FWHM at λ

F 590 nm), multiple electron transfers within the same RC are suppressed as the K

reduction of the donor radical P865J , a precondition to the second electron transfer, K

occurs on a much slower time scale. Since QA is an intermediary acceptor, QAL is

K L K transient and only QBL is obtained. In order to trap QA , the samples were treated with stigmatellin, an inhibitor blocking the QB site and thereby disabling further electron transfer. After this treatment, the samples were frozen in liquid nitrogen. Special care

K L K 122 CHAPTER 8. QAL AND QB IN BACTERIAL PHOTOSYSTEM

radical gx gy gz

L K

M M

QA 2 M 00647 3 2 00532 3 2 00215 3

L K

M M

QB 2 M 00628 3 2 00530 3 2 00217 3

[ [ Table 8.1: Principal g values of the QA and QB states in bRC obtained from simulations of the 94 GHz EPR spectra. was taken during the handling of the samples to avoid light exposure that would lead

to additional photochemistry.

K L K L K L K

QAL QB biradical. Two methods were used to obtain the QA QB biradical state.

L K (i) QB samples prepared as described above were illuminated at T F 190 K. Since

L K L K L K L K

L H the electron transfer QA H QB QA QB is thermally activated, the QA QB state is trapped and stabilized by further cooling down under illumination to 77 K in liq- 2 uid nitrogen. (ii) Reaction centers were doubly reduced to the QB L state by adding NaBH4. Since the double reduction goes along with protonation of QB, increasing the pH value of the samples, by withdrawing protons from QB, shifts the equilibrium from

L K L K M the QAQB L state towards QA QB . A pH of 10 5 was used in the samples.

8.2.2 cw and Pulsed EPR Cw EPR experiments were performed using the procedures in chapter 2. Special care

was taken to avoid light exposure to the samples. At low temperatures ( m 20 K), spin

K L K relaxation rates in the QAL QB biradical sample were so low that no undistorted cw spectra could be obtained, even at the lowest microwave power setting of the spectrometer (5 nW). Field-swept electron spin echo experiments with low repetition rates 1

(down to 5 s L ) were used to access spectra at these low temperatures. For easier comparison with the ﬁeld-modulated cw spectra, the ﬁrst derivative of the ESE spectra was calculated.

8.3 Results

Fig. 8.3 shows cw EPR spectra for the three radical states of bRC investigated at

L K

T F 100 K. All spectra are well resolved with linewidths below 1 mT. The QA and K QBL state spectra are well reproduced by simulations (dotted). The principal g values resulting from these simulations are given in tab. 8.1. Only the gx value differs signiﬁ- cantly for these states. This may be attributed to differences in the hydrogen bonds to

both quinones, similar to the gx shift in the case of tyrosines discussed in chapter 7.

K L K The gx and gy edges in the QAL QB biradical spectrum are split as a consequence of the coupling between spins on both radicals while no splitting is resolved on the gz component. These features are also signiﬁcantly shifted relative to the single radical

8.3. RESULTS 123

[ [

Figure 8.3: Comparison of cw EPR spectra (94 GHz) of the radical states QA and QB and the biradical

[ [ [ [ state QA QB in bRC (T T 100 K). The QA and QB single radical spectra differ mainly in the gx value.

The biradical spectrum exhibits line splittings due to the interaction of the spins. It is not a superposition

[ [ of the QA and QB spectra. The dotted spectra are simulations of the single radical spectra. The vertical lines indicate the principal g values of the single radicals.

K L K

124 CHAPTER 8. QAL AND QB IN BACTERIAL PHOTOSYSTEM [ Figure 8.4: Cw EPR (94 GHz) spectra of the QA radical in frozen solution at various temperatures. The shape of the spectrum is temperature independent (arrows).

8.3. RESULTS 125 [ Figure 8.5: Cw EPR (94 GHz) spectra of the QB radical in frozen solution at various temperatures. The shape of the spectrum is temperature independent.

K L K

126 CHAPTER 8. QAL AND QB IN BACTERIAL PHOTOSYSTEM

[ [ Figure 8.6: Cw EPR (94 GHz) spectra of the coupled QA and QB radicals in frozen solution at various

temperatures. The temperature dependent populations of the four spin levels strongly affect the relative T EPR line intensities. The spectra for T T 10 K and T 5 K are derivatives of ﬁeld-swept electron spin echo spectra since it was not possible to obtain cw EPR spectra at these temperatures without saturation artifacts. 8.3. RESULTS 127

Figure 8.7: Simulations of the spectra in ﬁg. 8.6 using the parameters in tab. 8.2.

K L K 128 CHAPTER 8. QAL AND QB IN BACTERIAL PHOTOSYSTEM spectra. It can therefore be ruled out that the biradical spectrum arises merely from a superposition of the single radical spectra. The absence of splitting on the gz component can be explained by the anisotropy of the dipolar interaction term. Since the dipolar interaction can be both positive or negative, depending on orientation (ﬁg. 8.2), it can cancel small differences of the effective g values of both radicals for special orientations.

The linewidth of the biradical spectrum is slightly smaller than in the single radical

K L K spectra of QAL and QB . This narrowing is a hint towards the presence of exchange interaction between the quinones. The exchange tends to delocalize the spin density over both radicals. This increases the number of unresolved hyperfine interactions while decreasing the magnitude of each individual hyperfine coupling. As a consequence, the statistical variation of resonance positions is lowered, and the linewidth is reduced. Fig. 8.4 and fig. 8.5 show the single radical cw EPR spectra measured over a temperature range from 5 to 100 K. No significant changes are observed. In contrast, for a four-level system like the coupled biradical, the relative energy level populations and thus intensities of spectral features depend on the temperature. This is indeed the

case, as can be seen in ﬁg. 8.6. This temperature dependence ultimately proves that K

the spectra are due to a coupled radical pair and rules out the possibility that the QAL K

and QBL quinone radicals are uncoupled. Otherwise, one might argue that the biradical

K L K spectrum could also be a superposition of QAL and QB spectra with changed g tensors resulting from structural changes in the biradical state.

8.3.1 Analysis of Biradical Spectra The analysis of the radical pair spectra is difficult since the number of parameters in the spin Hamiltonian of a coupled radical pair is much larger than for a single radical; simultaneously, a lot of detail is obscured in the frozen solution spectra. A full parameter set is comprised of the principal g values for both spin carrying sites, the relative orientation of the g tensors, and the principal values and orientation of the coupling tensor D˜ , amounting to 15 parameters in total. In the biradical spectra, only 5 pronounced features are present, and the temperature dependence of the feature intensities is known. A fit of more than six independent parameters has therefore to rely on rather subtle details in the spectra. The statistical meaning of a fit of 15 independent parameters has therefore to be taken with a grain of salt: It can be expected that the χ2 minimum in the parameter space is shallow and that strong correlations between different parameters exist. As an additional complication, it is difficult to find the global minimum of χ2 as the computational effort grows exponentially with the number of parameters. The only remedies to this problem are either to obtain spectra with much less noise and distortion, or to reduce the dimension of the parameter space. Only gradual im- provements would be feasible regarding the first point with reasonable effort. The second option relies on the simplification of the model, or the knowledge of some pa- 8.3. RESULTS 129

parameter this work [5] X-ray structure [7, 8]

J [MHz] 50 60 k 20 -

M M M

˜ M k

D [MHz] 36 4 k 0 4 30 9 0 3 -

y y y

φ U

k k k

g 19 10 21 14 14 7

y y y

θ U

k k k

g 152 3 190 16 155 7

y y y

ψ U

k k k

g 180 20 197 20 179 7

y y y

φ U

k k k

D 93 10 88 6 81 7

y y y

M M θ U

k k k

D 59 3 65 6 3 5 60 7

M M M M M M k

d [Å] 16 3 k 0 1 17 2 0 2 17 3/16 3

[ [ Table 8.2: Parameters determined from the 94 GHz QA QB biradical spectra in the ﬁtting procedures described here and in [5]. X-ray diffraction experiments [7, 8] yield only data of the geometrical struc-

ture. The distance d given for the EPR results is calculated from D˜ using the point dipole approximation.

[ [ For the X-ray structural data, d is taken as the distance between the ring centers of QA and QB (17 u 3 Å)

or as a weighted distance of the spin carrying oxygen atoms (16 u 3 Å, see text). The Euler angles specify

[ [ the orientation of the QB g tensor and the axis of the dipolar coupling tensor relative to the QA g tensor, respectively, according to the deﬁnition in appendix B.2. rameters from other sources. One simpliﬁcation is to neglect the deviation of the cou- ˜ pling tensor D from uniaxiality, i.e. E F 0. This alleviates the problem only slightly, however. In the following analysis, two different approaches have been pursued:

x Within the collaboration project, R. Calvo (Universidad Nacional del Litoral, Argentina) employed a global fit1 [5] of the 14 remaining parameters, using a refined, but computationally very expensive fitting method (simulated annealing, see e.g. [6]) that is suited to finding the global minimum of χ2. This method does

not improve on the statistical signiﬁcance of the ﬁt, however.

K L K

For this thesis, it was assumed that the g tensors of QAL and QB radicals are

K L K L K L K identical in the biradical QAL QB and single radical QA /QB states, respec-

tively. This assumption is purely tentative and can only be justiﬁed a posteriori.

K L K The principal values of the QAL and QB g tensors were taken from tab. 8.1. This reduces the parameter space to 8 dimensions (relative orientation of the g tensors, orientation of the spin-spin coupling tensor, J, and D) which is much more favorable in relation to the amount of detail visible in the spectra.

The resulting parameter sets for both analysis methods are shown in tab. 8.2; the simulated spectra are shown next to the experimental ones in fig. 8.7. The estimated uncertainties for the parameters differ greatly, reflecting their significance for the spectrum. It is noteworthy, however, that two Euler angles, θg and θD, seem to be remarkably well defined and uncorrelated to other parameters for the simulation using fixed

1Some 34 GHz EPR spectra taken at the Feher group in La Jolla were also used in the analysis.

K L K 130 CHAPTER 8. QAL AND QB IN BACTERIAL PHOTOSYSTEM g principal values. In particular, the obtained values are very close to the geometrical structure obtained from X-ray diffraction data [7, 8]. Only a mimimum value for the exchange coupling parameter J could be given using the analysis method assuming fixed g values: For larger couplings, the forbidden transitions III and IV in fig. 8.1 become too weak to noticeably affect the spectra. Since J is therefore effectively eliminated as a parameter, the fit is likely to become less ambiguous, and the reliability of the obtained other parameters is in turn increased.

8.4 Discussion

8.4.1 Inﬂuence of Fitting Methods and Reliability of Parameters

The 94 GHz cw EPR spectra obtained from frozen solutions of deuterated bRC in the

K L K L K L K mono- and biradical states QAL , QB , and QA QB have excellent spectral resolution and a good signal to noise ratio. No resolved hyperﬁne structure is observed. In addition, the biradical spectra show a distinct temperature dependence. From these characteristics, one would expect that an analysis of the spectra and

the derivation of the parameters in the spin Hamiltonian is rather easy. This is indeed

K L K

the case for the single radical (QAL and QB ) spectra which are fully characterized

K L K by the principal values of g. The QAL QB biradical is, however, characterized by a much larger number of parameters. Since the geometry of QA and QB is fixed relative to each other in the protein, orientation parameters do not average out in a frozen solution spectrum. This accounts for 6 additional parameters, on top of the 6 principal g values and 3 principal values of the spin-spin coupling tensor. Since the biradical spectra do not exhibit nearly as many characteristic features, the analysis is, contrary to what intuition might suggest, rather difficult. Both analysis methods used yield comparable values (see tab. 8.2) that are close to what the structural model derived from X-ray diffraction experiments suggests. A closer look reveals however some significant differences:

x The dipolar coupling strengths D differs signiﬁcantly for both analysis methods.

The derived radical distances reﬂect this mismatch. x The angles θg describing the relative orientation of the quinone radicals differs by considerable more than the error margin. It is also noteworthy that the assumption of identical g values for the single and biradical states leads to a much

decreased error margin. x The angles ψg agree within their error margins. The error margins are however

rather wide, and the statistically most likely value is therefore rather different. x The angles θD differ, even taking error margins into account. 8.4. DISCUSSION 131

With the exception of the dipolar coupling strength D, the analysis assuming ﬁxed g factors yields consistently values that are in better agreement with the structural data from X-ray experiments. This suggests that the assumption of unchanged g values is justiﬁed and that the respective results may be more reliable.

This inrepretation seems however to be falsiﬁed by the disagreement of the spin-

K L K spin coupling strength D and the QAL –QB distance d calculated from it. Here, the global unrestricted ﬁt yields results that appear to be in much better agreement with the X-ray structural model. It must be considered, however, that the quinone radicals are rather close to each other and that the spin density is delocalized over each quinone radical. Under these conditions, the point dipole approximation for the calculation of the dipolar coupling strength is not applicable anymore. A considerable part of the spin density in quinone anion radicals is expected at the functional oxygen atoms. Therefore, two limiting model cases for the calculation of the dipolar interaction can be given:

x The spin density is assumed to be localized at the centers of the quinone rings.

x 50% of the spin density are assumed to be localized at each oxygen atom. Using the structural data from X-ray diffractions [7, 8], one obtains a center-to-

center distance of 17 M 3 Å for the quinones. Using the oxygen-oxygen distances from 3 the same source (see ﬁg. 8.8), weighed by the r L dependency of the dipolar interaction strength, one obtains an effective distance

1 3

3 3 3 3 L

L L L L

H H

d13 H d14 d23 d24 deff F (8.2)

that amounts to 16 M 3 Å. This is in excellent agreement with the distance found assuming unchanged g factors. The real spin density distribution certainly lies between these two extremes and should lead to a coupling strength between the two values given in tab. 8.2. A com- promise between both models, assuming 25% spin density on each oxygen and 50%

located in the middle of the quinone ring, yields an effective distance of 16 M 8 Å. This simple model compares well with the 23% spin density per oxygen determined in vitro [9]. On the other hand, the spin density in the protein-bound quinones leaks somewhat to the ligands and hydrogen bonds. This would lead again to an increase of the dipolar coupling, or a decrease of the effective distance deff, favoring again the value found assuming ﬁxed g values. In any case, it is clear that the seemingly better agreement of the quinone-quinone distance obtained from the global ﬁt of all parameters with the X-ray structural model is coincidental, since deff, as determined from the dipolar coupling strength D, has to be smaller than the geometrical distance of the quinone centers. The results discussed so far yield mainly information about the geometrical structure of the quinone radicals in the reaction center and once again demonstrate the

K L K 132 CHAPTER 8. QAL AND QB IN BACTERIAL PHOTOSYSTEM

3 4

1 2 [

Figure 8.8: Geometry of the quinones in the QAQB state of the bacterial reaction center [7, 8], used

[ [ as an approximation for the biradical QA QB state structure. The spin density of the quinone radicals is strongly localized at the bold oxygen atoms and can be modeled by point dipoles. The dotted lines represent the distances d13, d14, d23, and d24 used for estimating the strength of the dipolar interaction term. 8.4. DISCUSSION 133 usefulness of EPR experiments for structural analysis. However, the most desired information is about the electronic structure, i.e. the exchange interaction parameter J. Unfortunately, neither analysis method is able to yield a reliable value for J. The forbidden transitions are too weak to affect the 94 GHz EPR spectra noticeably.

This may seem like a contradiction to tab. 8.2, where a value for J is given. Calvo

claims in [5] to obtain a value of J 60 k 20 MHz, but readily admits in the same article that the error margin is the standard deviation of the results from several runs of the fitting procedure using different sequences of pseudo random numbers (“thermal annealing” is a stochastic method). Thus, the given error margin reflects the reliability of the fitting procedure and has no relation whatsoever to the statistical error of the data. The rather large variation of J for several fitting runs itself is just another man- ifestation that the 94 GHz EPR spectra are virtually independent of J. This is further illustrated by the dependence of χ2 on J given in [5]: doubling J from 60 MHz to

2 M 120 MHz increases χ from 0 M 023 to only 0 024 (figure 8 in [5]). A more detailed discussion considering the statistical significance of fitted parameters can be found in [10]. In contrast, the sign of J is unambiguous. The temperature dependence of the intensity of the allowed transitions in the EPR spectra correlates the sign of J with the sign of D. The dipolar interaction strength D is however always positive. Recently, similar EPR experiments have been performed at microwave frequency of 326 GHz [11, 12]. At these high frequencies, the forbidden transitions become

clearly visible. From these measurements, the strength of the exchange interaction

could be determined as J 82 k 3 MHz. Alas, [11, 12] do not give other parameters derived from the 326 GHz spectra. With the uncertainty of J resolved, it would be interesting how the g principal values and the relative orientations of the g tensors compare to the values obtained in this work.

8.4.2 Implications of J for the Electron Transfer Process While only a lower limit for J could be deduced from the data and analysis in this thesis, it is nevertheless possible to give an estimate for the electron transfer rate kET. According to Fermi’s golden rule, the rate is

2π 2

j l l j W

F ψ ˆ ψ ρ

kET tot z f Htot tot i (8.3)

j h¯ j

ψ ψ z where tot z i and tot f represent the initial and ﬁnal total wavefunctions of the system, respectively, and ρ is the density of states. In the Born-Oppenheimer (adiabatic) approximation, the electronic and lattice components of the wavefunctions are decoupled. The lattice contributions can therefore be described by a Franck-Condon factor F, arriving at π

2 2

j j

l l

F ψ ˆ ψ

kET F f H i (8.4)

j h¯ j using only electronic wavefunctions and the electronic Hamiltonian Hˆ .

K L K 134 CHAPTER 8. QAL AND QB IN BACTERIAL PHOTOSYSTEM

Assuming a harmonic potential for lattice vibrations and thermally populated, suf- ﬁciently dense phonon levels, the Franck-Condon factor can be derived as [13]

∆ λ

1 E H

y F F exp λ (8.5) 4πλkBT 4 kBT where ∆E is the change of the enthalpy and λ is the reorganization energy of the environment.

In the bacterial reaction center, the quinones are physically well separated, and

K L K the overlap of the electron wavefunctions in the QAL QB state can be expected to be negligible. In this case, J is dominated by kinetic exchange [14],

l l j

j ψ ˆ ψ

f H i

j j J F (8.6) U where U is the separation of the ground state and the “ionic” state, i.e. the state af- ∆ λ

ter electron transfer. U can therefore be approximated by E H [15]. Combining equations 8.4, 8.5, and 8.6 yields the electron transfer rate

π l ∆ λ ∆ λ H

E H E

W W kET F J λ exp λ (8.7) kBT h¯ 4 kBT or, when J is given in frequency units and accounting for the Pauli principle with

1 K a factor of 2 (since the LUMO of QBL is already half occupied before the electron transfer),

π3 ∆ λ 2

E H

W l l W M F ∆ λ kET J λ E H exp λ (8.8)

kBT 4 kBT

F M F M For T F 280 K and using λ 1 2 eV [16, 17], ∆E 0 25 eV [18], one thus

arrives at

M W M kET F 0 013 J (8.9)

6 1

M W The lower limit of J 50 MHz determined in this work yields kET 0 78 10 s L .

Taking the value J F 82 MHz from recent EPR experiments at 326 GHz [11, 12], one

6 1

F M W obtains kET 1 1 10 s L which is in excellent agreement with the estimate of the

6 1 E intrinsic electron transfer rate ke 10 s L in [18]. This agreement should not be overrated, however, as it could be mostly coincidental, given the crude approximations made above. On the other hand, it does corroborate the assumptions about the mechanism of the quinone reduction/protonation process described in [18] which led to the reported intrinsic electron transfer rate.

8.5 Conclusion

Using 94 GHz EPR, it was possible to access and analyze the coupled biradical state

K L K QAL QB in deuterated, zinc reconstituted reaction centers from Rhodobacter sphaeroides. REFERENCES 135

The analysis of the spectra yielded geometrical information that agrees with the X-ray K structure of the protein in the QAQBL state.

Only a lower limit for the strength of the exchange interaction J 50 MHz could be determined in the analysis since the coupling is too strong compared to the Zeeman

anisotropy at 3 M 35 T and the forbidden transitions are too weak to be observed. The

value J 60 k 20 MHz obtained by an alternate analysis within the collaboration project does agree with this minimum estimate; the given error margin is however

arguably too small.

K L K The QAL QB state of the bacterial reaction center thus reaches the limits of 94 GHz EPR and demonstrates the need for further evolution of EPR technology towards even higher microwave frequencies. This is conﬁrmed by recent experiments at 326 GHz [11, 12] that clearly detect the forbidden transitions needed to determine J. The

6 1

F M W F

electron transfer rate kET 1 1 10 s L derived from J 82 GHz is in excellent K agreement with an estimate given in [18] and corroborates the suggested QBL reduction/protonation mechanism.

REFERENCES [1] Debus R.J., Feher G., & Okamura M.Y., Iron-depleted reaction centers from Rhodopseu-

2 2 O domonas sphaeroides R-26.1 – characterization and reconstitution with Fe O , Mn ,

2 2 2 2

O O O Co O , Ni , Cu , and Zn , Biochemistry 25, 2276–2287 (1986).

[2] Utschig L.M., Greenﬁeld S.R., Tang J., Laible P.D., & Thurnauer M.C., Inﬂuence of iron- removal procedures on sequential electron transfer in photosynthetic bacterial reaction centers studied by transient EPR spectroscopy, Biochemistry 36, 8548–8558 (1997).

[3] Carrington A. & McLachlan A.D., Introduction to Magnetic Resonance with Applications to Chemistry and Chemical Physics, chapter 2.6, Harper & Row (1967).

[4] Press W.H., Teukolsky S.A., Vetterling W.T., & Flannery B.P., Numerical Recipes in C: The Art of Scientiﬁc Computing, chapter 11, Cambridge University Press, 2nd edition (1992).

[5] Calvo R., Abresch E.C., Bittl R., Feher G., Hofbauer W., Isaacson R.A., Lubitz W.,

Okamura M.Y., & Paddock M.L., EPR study of the molecular and electronic structure of

P g P the semiquinone biradical QAg QB in photosynthetic reaction centers from Rhodobacter sphaeroides, J. Am. Chem. Soc. 122, 7327–7341 (2000).

[6] Press W.H., Teukolsky S.A., Vetterling W.T., & Flannery B.P., Numerical Recipes in C: The Art of Scientiﬁc Computing, chapter 10, Cambridge University Press, 2nd edition (1992).

[7] Stowell M.H.B., McPhillips T.M., Rees D.C., Soltis S.M., Abresch E., & Feher G., Light- induced structural changes in photosynthetic reaction center: Implications for mechanism of electron-proton transfer, Science 276, 812–816 (1997).

K L K 136 CHAPTER 8. QAL AND QB IN BACTERIAL PHOTOSYSTEM

[8] Stowell M.H.B., McPhillips T.M., Rees D.C., Soltis S.M., Abresch E., & Feher G., Protein data bank, access code 1AIG: Photosynthetic reaction center from Rhodobacter sphaeroides in the D+QB- charge separated state, http://www.rcsb.org/pdb.

[9] MacMillan F., Lendzian F., & Lubitz W., EPR and ENDOR characterization of semiquinone anion radicals related to photosynthesis, Mag. Reson. in Chem. 33, 81–93 (1995).

[10] Press W.H., Teukolsky S.A., Vetterling W.T., & Flannery B.P., Numerical Recipes in C: The Art of Scientiﬁc Computing, chapter 15, Cambridge University Press, 2nd edition (1992).

[11] Calvo R., Isaacson R.A., Abresch E.C., Paddock M.L., Maniero A.L., Saylor C., Brunel

P g P L.C., Okamura M.Y., & Feher G., EPR study of the semiquinone biradical QAg QB in photosynthetic reaction centers of Rb. sphaeroides at 326 GHz, Biophys. Journal 80, 122 (2001).

[12] Calvo R., Isaacson R.A., Paddock M.L., Abresch E.C., Okamura M.Y., Maniero A.L.,

Brunel L.C., Okamura M.Y., & Feher G., EPR study of the semiquinone biradical

P g P QAg QB in photosynthetic reaction centers of Rb. sphaeroides at 326 GHz: Determi- nation of the exchange interaction J0, J. Phys. Chem. B 105, 4053–4057 (2001). [13] Marcus R.A. & Sutin N., Electron transfers in chemistry and biology, Biochim. Biophys. Acta 811, 265–322 (1985).

[14] Bencini A. & Gatteschi D., EPR of Exchange Coupled Systems, chapter 1.2, Springer- Verlag (1990).

[15] Okamura M.Y., Fredkin D.R., Isaacson R.A., & Feher G., in Tunneling in Biological Systems (Chance B., DeVault D.C., Frauenfelder H., Marcus R.A., Schriefer J.R., & Sutin N., eds.), pp. 729–743, Academic Press (1979).

[16] Labahn A., Bruce J.M., Okamura M.Y., & Feher G., Direct charge recombination from g D O QAQB to DQAQB in bacterial reaction centers from Rhodobacter sphaeroides containing low potential quinone in the QA site, Chem. Phys. 197, 355–366 (1995). [17] Allen J.P., Williams J.C., Graige M.S., Paddock M.L., Labahn A., & Feher G., Free energy dependence of the direct charge recombination from the primary and secondary quinones in reaction centers from Rhodobacter sphaeroides, Photosynth. Res. 55, 227– 233 (1998).

[18] Okamura M.Y., Paddock M.L., Graige M.S., & Feher G., Proton and electron transfer in bacterial reaction centers, Biochim. Biophys. Acta 1458, 148–163 (2000). Summary and Outlook

The main focus of this thesis is the application of EPR at high magnetic fields and microwave frequencies (94 GHz) on biological samples. From an instrumental point of view, high field/high frequency EPR is more challenging and depending on the specific spectrometer implementation than EPR at conventional frequencies. The limitations and peculiarities of the spectrometer used throughout this work have been described in this thesis to establish a context for the following methodological work.

In situ optical excitation: Originally, the Bruker spectrometer did not provide a light access path, which is required for time-resolved measurements of photoinduced processes. This spectroscopic technique is of particular interest for the research on photoenzymes such as photosynthetic reaction centers. In order to enable such measurements, the sample holder of the spectrometer had to be modiﬁed in cooperation with the manufacturer by feeding an optical ﬁber through it. A laser setup was implemented for optical excitation via this access path. The performance of this arrangement was demonstrated by transient EPR experiments on the triplet state of pentacene.

Transition strength selective spectroscopy: A common problem of high field EPR is the extraordinary sensitivity to contaminations of the sample or the resonator. Of- ten, the respective signals can be distinguished from the desired spectrum by their EPR transition moments. Several experiments to achieve such a separation have been described in the literature. These pulsed experiments generally vary the timing of the microwave pulses to achieve the desired separation. To obtain a spectrum, the magnetic field strength B0 has to be varied as well. These experiments need therefore to map out a two-dimensional parameter space and are consequently costly in terms of acquisition time. In this thesis, a novel method to achieve the desired separation has been introduced. By using a fixed, “soft” microwave pulse sequence, components of the EPR signal that are associated with different transition moments are spread out on the time axis. Using a transient recorder, one dimension of the parameter space can be scanned in a single “shot”. Only the magnetic field B0 has to be swept to record a full spectrum, and the required acquisition time is thereby reduced to that of a one-dimensional experiment. In addition, since the method is based on the use of low-power microwave pulses, it simultaneously circumvents the power limitations of the spectrometer used in this work.

137 138 SUMMARY AND OUTLOOK

The viability of the method has been demonstrated using different model systems as well as organic and biological samples from current research.

The main part of this thesis describes EPR experiments on radical states in three different photosynthetic reaction centers. While the samples are closely related and all experiments increase the knowledge about the photosynthetic apparatus of plants and

bacteria, each also serves to demonstrate a different aspect of 94 GHz EPR. K Photosystem I: The cation, radical state of the primary donor in photosystem I, P700J , is characterized by a small g anisotropy and a large inhomogeneous linewidth. It is therefore difﬁcult to resolve the g tensor using conventional EPR. In earlier work, it was necessary to deuterate the frozen solution samples even for 140 GHz EPR, or to utilize microwave frequencies as high as 325 GHz in order to resolve the g tensor

principal values. K In this thesis, P700J has been examined using 94 GHz EPR in single crystals of protonated photosystem I. These experiments allowed to derive both the principal values and the orientation of the g tensor with respect to the crystal axes system at very high precision. Since this information can be compared with the geometric orientation of P700 obtained from x-ray structural analysis, it is of particular importance for an understanding of the electronic nature of the pair of chlorophylls that forms P700.

Photosystem II: The crystallization of photosystem II of oxygenic photosynthesis has only recently been accomplished. This thesis reports, to my knowledge, the first successful EPR experiments on a radical state in single crystals of photosystem II. The orientation-dependent 94 GHz EPR spectra could be fully analyzed with the help of hyperfine coupling data obtained from frozen solution ENDOR experiments. The g tensor (both principal values and orientation) could be determined with very high accuracy. Due to a non-crystallographic symmetry in the single crystals, it was possible to give the orientation of g with respect to a defined site, removing otherwise unavoidable ambiguities in correlating EPR and x-ray diffraction results. The very good resolution of the YDK spectra and the absence of noticeable g strain is attributed to a well-defined binding situation in the protein. In particular, a hydrogen bond between the tyrosine and the protein backbone could be observed by its effect on the g tensor and a splitting

of otherwise symmetry related hyperﬁne couplings.

K L K

Bacterial reaction center: Finally, the radical states QAL , QB , and the biradi-

K L K

cal state QAL QB in zinc-reconstituted bacterial reaction centers from Rhodobacter K

sphaeroides were investigated by 94 GHz EPR. Using the principal values of the QAL

K L K L K and QBL g tensors, the dipolar coupling of the radicals in the QA QB state could be analyzed. The resulting geometric information, relative orientation and distance of the radicals, is in excellent agreement with the x-ray structure of the bacterial reaction

139 K center in the QBL state. The exchange coupling between the quinones is however too

strong to be derived from these experiments, and only a lower limit J 60 MHz could be given.

It can be concluded that, at this time, 94 GHz EPR is still a challenging, but also an immensely powerful spectroscopic technique. While common techniques like time- resolved EPR on light-induced species can be transfered to high ﬁeld/high frequency EPR with tricky design concepts, more generic problems like the sensitivity towards unwanted contamination signals can be solved by the development of new experimental methods. It is not the application of high frequencies alone which makes 94 GHz EPR use-

ful. This is exempliﬁed by the experiments on the photoenzymes: The spectrum of the K P700J radical in frozen photosystem I solution is very poorly resolved, even at considerably higher frequencies. However, combined with the use of protein single crystals facilitated by the high sensitivity of high ﬁeld EPR, surprisingly precise information can be gained from a seemingly “hopeless” system. In contrast, the investigation of the

YDK radical in single crystals of photosystem II is challenging not because of a lack of resolution, but due to the sheer amount of resolved features in the EPR spectra. In conjunction with supporting ENDOR experiments and, equally important, the exploitation of the crystal symmetries in the analysis, it is again possible to obtain precise data on the electronic and geometric structure of the sample. The spectra of coupled quinone radicals in zinc-reconsituted bacterial reaction centers exhibit excellent resolution and a very good signal to noise ratio along with a simple structure. At first, it comes as a surprise that the strength of the exchange interaction could not be derived under these conditions. The analysis reveals that the magnetic field used at 94 GHz is simply not sufficient to break apart the strong coupling, and essential transitions are not observable. Findings such as this motivate the desire for EPR spectroscopy at even higher frequencies. It will be interesting to investigate other paramagnetic states in these photoenzymes with 94 GHz EPR. In particular, the combination of various techniques should prove extremely useful. 94 GHz on transient, photoinduced species will allow to obtain information about otherwise inaccessible states. The observation of radical pairs yields – via the dipolar interaction – specific geometrical information already in frozen solution samples. In combination with the use of single crystals, even more detailed information can be obtained. Another interesting possibility will be 94 GHz ENDOR experiments. The increased orientation selectivity should allow to obtain both the strength and the orientation of hyperfine interactions and, therefore, the electronic structure of paramagnetic states. ENDOR on single crystals should increase the precision of these experiments even more. Finally, ENDOR on light-induced transient states, possibly even in single crystals, would greatly contribute to an understanding of the precise working of these 140 SUMMARY AND OUTLOOK photoenzymes. Zusammenfassung und Ausblick

Der Schwerpunkt dieser Arbeit ist die Anwendung von EPR bei hohen Magnetfeldern und Mikrowellenfrequenzen (94 GHz) auf biologische Proben. In instrumenteller Hin- sicht ist Hochfeld-/Hochfrequenz-EPR im Vergleich zu EPR bei konventionellen Fre- quenzen anspruchsvoller und mehr vom jeweils verwendeten Spektrometer beeinﬂußt. Die Beschränkungen und Eigenheiten des in dieser Arbeit durchgehend verwendeten Spektrometers wurden eingangs beschrieben, um die Rahmenbedingungen für die fol- genden methodischen Arbeiten festzulegen.

Optische in situ Anregung: Ursprünglich sah das Spektrometer der Firma Bruker keinen optischen Zugang, wie er für zeitaufgelöste Messungen an lichtinduzierten Pro- zessen nötig ist, vor. Dieses Spektroskopieverfahren ist jedoch für die Untersuchung von Photosytemen, wie z.B. den Reaktionszentren der Photosynthese, besonders interessant. Um solche Messungen zu ermöglichen, wurde der Probenhalter des Spek- trometers in Kooperation mit dem Hersteller durch Einbringen eines Lichtleiters mo- diﬁziert. Ein Laseraufbau zur optischen Anregung über diesen Zugang wurde erstellt. Die Leistungsfähigkeit dieser Anordnung wurde durch transiente EPR-Messungen am Triplettzustand von Pentacen aufgezeigt.

Übergangsstärkenselektive Spektroskopie: Ein häuﬁges Problem der Hochfeld- EPR liegt in der außergewöhnlichen Empﬁndlichkeit auf Verunreinigungen der Probe oder des Resonators. Oftmals können die entsprechenden Signale anhand ihrer EPR- Übergangsmatrixelemente vom erwünschten Spektrum unterschieden werden. In der Literatur wurden mehrere Methoden beschrieben, die solch eine Trennung ermögli- chen. Diese gepulsten Experimente variieren grundsätzlich die zeitliche Abfolge der Mikrowellenpulse, um die erwünschte Trennung zu erzielen. Um ein Spektrum zu erhalten, muß die magnetische Feldstärke B0 ebenfalls variiert werden. Diese Experi- mente müssen deshalb einen zweidimensionalen Parameterraum erfassen und sind in der Folge sehr zeitaufwendig. In dieser Arbeit wurde ein neues Verfahren vorgestelt, mit dem die gewünschte Trennung erzielt werden kann. Durch die Verwendung einer festen Folge “weicher” Mikrowellenpulse werden die zu verschiedenen Übergangsstärken gehörenden Signal- anteile auf der Zeitachse ausgebreitet. Mit einem Transientenrecorder kann eine kom- plette Dimension in einem einzigen “Schuß” erfaßt werden. Nur das Magnetfeld B0

141 142 ZUSAMMENFASSUNG UND AUSBLICK muß zur Aufnahme eines vollständigen Spektrums noch variiert werden. Die erforder- liche Meßzeit reduziert sich damit auf die eines eindimensionalen Experiments. Weil dieses Verfahren außerdem auf der Verwendung von Mikrowellenpulsen mit kleiner Leistung basiert, umgeht es gleichzeitig die Beschränkungen des in dieser Arbeit verwendeten Spektrometers. Die Praxistauglichkeit dieser Methode wurde anhand ver- schiedener Modellsysteme ebenso wie an organischen und biologischen Proben aus der aktuellen Forschung demonstriert.

Der Hauptteil dieser Arbeit beschreibt EPR-Experimente an radikalischen Zuständen in drei verschiedenen Reaktionszentren der Photosynthese. Obwohl die Proben eng verwandt sind und alle Experimente zum Wissen über den Photosyntheseapparat von Pﬂanzen und Bakterien beitragen, zeigt jede Probe einen anderen Aspekt der 94 GHz- EPR auf.

Photosystem I: Der kationische, radikalische Zustand des primären Donators in K Photosystem I, P700J , ist durch eine geringe g-Anisotropie und eine große inhomogene Linienbreite gekennzeichnet. Es ist deshalb schwierig, den g-Tensor mit konventio- neller EPR aufzulösen. In früheren Arbeiten war es selbst bei 140 GHz nötig, die ge- frorenen Lösungsproben zu deuterieren oder solch hohe Mikrowellenfrequenzen wie

325 GHz zu verwenden, um die Hauptwerte des g-Tensors aufzulösen. K In dieser Arbeit wurde P700J mit 94 GHz-EPR in Einkristallen von protoniertem Photosystem I untersucht. Diese Experimente erlaubten es, sowohl die Hauptwerte wie auch die Orientierung des g-Tensors bezüglich der Kristallachsen mit hoher Ge- nauigkeit zu bestimmen. Da diese Information mit der geometrischen Orientierung von P700, die aus Röntgenbeugungsexperimenten erhalten wurde, verglichen werden kann, ist sie von besonderer Bedeutung für das Verständnis der elektronischen Natur des Chlorophyllpaares, das P700 bildet.

Photosystem II: Die Kristallisation von Photosystem II der oxygenen Photosynthe- se ist erst vor kurzem gelungen. Diese Arbeit berichtet von den meines Wissens nach ersten erfolgreichen EPR-Experimenten an einem radikalischen Zustand in Einkristal- len von Photosystem II. Die orientierungsabhängigen 94 GHz-EPR-Spektren konnten mit Hilfe von Hyperfeinkopplungsdaten, die durch ENDOR-Experimente an gefrorener Lösung gewonnen wurden, vollständig analysiert werden. Der g-Tensor (sowohl Hauptwerte wie auch Orientierung) konnte mit hoher Genauigkeit bestimmt werden. Durch eine nichtkristallographische Symmetrie in den Kristallen war es möglich, die Orientierung von g bezüglich einer deﬁnierten Site, ohne die ansonsten unvermeid- baren Mehrdeutigkeiten bei der Korrelation von Ergebnissen aus der EPR und der

Röntgenbeugung, anzugeben. Die sehr hohe Auﬂösung der YDK -Spektren und das Feh- len einer beobachtbaren g-Verteilung werden einer wohldeﬁnierten Bindungssituation im Protein zugeschrieben. Insbesondere konnte eine Wasserstoffbrücke zwischen dem 143

Tyrosin und dem Proteingerüst über ihre Auswirkungen auf den g-Tensor und durch eine Aufspaltung ansonsten symmetrieäquivalenter Hyperfeinkopplungen beobachtet

werden. K

Bakterielles Reaktionszentrum: Schließlich wurden die radikalischen Zustände QAL ,

K L K L K QBL und der biradikalische Zustand QA QB in Zink-rekonstituierten bakteriellen Re-

aktionszentren von Rhodobacter sphaeroides mit 94 GHz-EPR untersucht. Unter Ver-

K L K

wendung der g-Hauptwerte von QAL und QB konnte die dipolare Kopplung der Radi-

K L K kale im QAL QB -Zustand analysiert werden. Die sich ergebende Geometrieinformati-

on, relative Orientierung und Abstand der Radikale, ist in vorzüglicher Übereinstim- K mung mit der Röntgenstruktur des bakteriellen Reaktionszentrums im QBL -Zustand. Die Austauschkopplung zwischen den Chinonen ist jedoch zu stark, um sie aus diesen

Experimenten abzuleiten, und es konnte nur eine untere Grenze von J 60 MHz an- gegeben werden.

Es kann zusammenfassend gesagt werden, daß 94 GHz-EPR derzeit noch ein heraus- forderndes, aber auch äußerst mächtiges Spektroskopieverfahren ist. Während ver- breitete Techniken wie zeitaufgelöste EPR an lichtinduzierten Spezies durch trickrei- che Konzepte auf die Hochfeld/Hochfrequenz-EPR übertragbar sind, können generelle Probleme wie die Empﬁndlichkeit auf Verunreinigungen durch die Entwicklung neuer experimenteller Methoden gelöst werden. Die Nützlichkeit der 94 GHz-EPR beruht nicht allein auf der hohen Frequenz. Dies

wird beispielhaft durch die Experimente an den Photoenzymen belegt: Das Spektrum K des P700J -Radikals in gefrorener Lösung von Photosystem I ist selbst bei beträchtlich höheren Frequenzen äußerst schlecht aufgelöst. In Kombination mit der Nutzung von Protein-Einkristallen, die durch die hohe Empfindlichkeit der Hochfeld-EPR ermög- licht wird, können jedoch überraschend präzise Informationen über ein “hoffnungs- loses” System gewonnen werden. Im Gegensatz dazu ist die Untersuchung des YDK - Radikals in Photosystem II-Einkristallen nicht wegen einer zu geringen Auflösung, sondern aufgrund der Unmenge aufgelöster Details in den EPR-Spektren eine Her- ausforderung. In Verbindung mit unterstützenden ENDOR-Messungen und, ebenso bedeutsam, dem Ausnutzen der Kristallsymmetrien bei der Analyse ist es wiederum möglich, genaue Daten zur elektronischen und geometrischen Struktur der Probe zu erhalten. Die Spektren gekoppelter Chinonradikale in Zink-rekonstituierten bakeriellen Re- aktionszentren weisen eine exzellente Auflösung und ein sehr gutes Signal/Rausch- Verhältnis in Verbindung mit einer einfachen Struktur auf. Zunächst überrascht es, daß die Stärke der Austauschwechselwirkung unter diesen Voraussetzungen nicht ermittelt werden konnte. Die Analyse offenbart jedoch, daß die bei 94 GHz-EPR verwendeten magnetischen Feldstärken schlichtweg nicht ausreichen, um die starke Kopplung auf- zubrechen und wesentliche Übergänge nicht beobachtbar sind. Erkenntnisse wie diese 144 ZUSAMMENFASSUNG UND AUSBLICK motivieren den Wunsch nach EPR-Spektroskopie bei noch höheren Frequenzen. Es wird interessant sein, andere paramagnetische Zustände in diesen Photoenzy- men mit 94 GHz-EPR zu untersuchen. Insbesondere sollte sich die Kombination ver- schiedener Methoden als äußerst nützlich erweisen. 94 GHz EPR an transienten, pho- toinduzierten Spezies wird es erlauben, Information über ansonsten nicht zugängliche Zustände zu erhalten. Die Beobachtung von Radikalpaaren liefert – über die dipolare Kopplung – bereits in gefrorener Lösung spezifische Geometrieinformationen. In Verbund mit dem Einsatz von Einkristallen können noch detailliertere Informationen erhalten werden. Eine andere interessante Möglichkeit werden 94 GHz-ENDOR-Experimente dar- stellen. Die verstärkte Orientierungsselektion sollte es erlauben, sowohl Größe als auch Orientierung von Hyperfeinkopplungen, und damit Information über die elektro- nische Struktur paramagnetischer Zustände zu erhalten ENDOR an Einkristallen sollte die Genauigkeit solcher Experimente noch weiter erhöhen. Schließlich würde ENDOR an lichtinduzierten, transienten Zuständen, womöglich sogar in Einkristallen, wesent- lich zum Verständnis der genauen Wirkungsweise dieser Photoenzyme beitragen. Appendix A

Spin Dynamics

A.1 Density Matrix Formalism l ψ

In the Schrödinger representation, the dynamics of a quantum system in a state is described by the Schrödinger equation

d i

F l

l ψ ˆ ψ H (A.1) dt h¯ where Hˆ is the Hamiltonian describing the system. Typical experiments are however performed on an entire ensemble of similar systems. A description of such an ensemble in the Schrödinger representation would have to be done in the product space of the individual systems. This increases the dimensionality of the Hilbert space to an extent that renders this approach impractical. A partial solution to this problem is to employ classical statistics to describe the ensemble as a whole. The Schrödinger representation does not lend itself directly to this method since the wave vectors average out for an ensemble with incoherent phases. Another equation of motion is needed that utilizes a representation of quantum states lending itself to classical statistics. The density matrix is such a representation. From eqn. A.1 and its adjunct (note that Hˆ is Hermitian)

d ψ i ψ F l

l Hˆ (A.2)

dt h¯

l l ψ ψ

the equation of motion for the dyadic product can be derived as

d d d

l F l l l l l ψ ψ ψ ψ ψ ψ

dt dt dt

i i

ψ ψ y ψ ψ l l l l

F ˆ ˆ

H H h¯ h¯

l l ¢ F ˆ ψ ψ

H (A.3) h¯ ¡

145 146 APPENDIX A. SPIN DYNAMICS where the brackets represent the commutator. The expectation value of an observable

l l ψ ψ

described by the operator O can be derived from the quantity as

l l ˆ F ψ ˆ ψ

O O

ˆ l l l l

F ψ φ φ ψ

∑ k k O k

F φ l l ψ ψ l l φ

∑ k O k k

ˆ ψ ψ

F £ l l ¤

Tr O (A.4)

φ l where k is a complete orthonormal base of the Hilbert space. The last expression

ψ ψ l l

is linear in . Therefore, the ensemble average of an observable can be calculated

ψ ψ ρ l l

from the ensemble average of which is called density matrix ˆ:

ˆ ˆ ˆ

¥ l l ¦ F F ψ ψ ρ

£ ¤

O Tr O Tr Oˆ (A.5)

l l ψ ψ ρ

Since eqn. A.3 is also linear in , it applies for the density matrix ˆ as well:

d i

¢ M ρˆ F Hˆ ρˆ (A.6)

dt h¯ ¡ This equation of motion is called the Liouville-von Neumann equation. For an ensemble in thermal equilibrium, only the average energy level populations are known from the Boltzmann law while different eigenstates of the Hamiltonian are completely uncorrelated. In the eigenbase of the Hamiltonian, such correlations are represented by the off-diagonal elements of the density matrix ρˆ. From these two requirements, it follows that the density matrix ρˆ 0 in thermal equilibrium is given by

Hˆ

exp

kBT M ρˆ 0 F (A.7)

Hˆ

¥ ¦

Tr exp kBT

A.2 Rotating Frame Approximation

The most common magnetic resonance experiments can be modeled by a spin j cou-

F v pled to an external static ﬁeld B0 B0ev z which conventionally marks the z direction of the laboratory frame. Transitions are induced by an oscillating magnetic ﬁeld

ω ω

W F W Bv cos t B cos t e along the x direction. The system is therefore governed by 1 1 v x

the Hamiltonian

y γ ω

§ W W M

ˆ F ˆ ˆ ¨ H B0 jz H B1 cos t jx (A.8) The oscillating term can be equally written as the superposition of two magnetic ﬁelds rotating in the xy plane:

y y

W W W F γ ω ω ω

ˆ ˆ ˆ ˆ ˆ

¨ H H B0 jz H 2cos t jx sin t jy sin t jy (A.9)

2 A.3. BLOCH EQUATIONS 147

This representation suggests that one looks at the system from a reference frame

F ω ω ω ω

V V V

x y z xcos t H ysin t ycos t xsin t z . rotating around the z axis with frequency ω. Eqn. A.9 is then transformed to

ω B1 B1

y y y y y

F W W V γ γ γ ω ω

ˆ ˆ ˆ ˆ ˆ

y y

y γ γ E

ˆ ˆ © B0 γ jz © jx (A.10) 2 neglecting the terms oscillating with 2ω (rotating frame approximation). This adiabatic approximation is valid provided 2ω is sufﬁciently far away from any resonance frequency. In this case, the system can be described in the rotating frame as a spin

ω B1

v F W

H ©

A.3 Bloch Equations

¥ ¦ F γ ρ The dynamics of the average magnetization Mv Tr jˆ of a spin ensemble in a

magnetic ﬁeld Bv can be easily derived in the density matrix formalism using the com-

mutators jˆk jˆl ¢ ih¯ jˆmεklm: ¡ d d

γ v ρ F ¥ ¦ Mv Tr jˆˆ dt dt γ2

v v

ª W « F ρ

v ¦ Tr ¥ jˆ B jˆ ˆ h¯

iγ2

v v v v

W W

F ρ ρ

v v ¦

¥ ˆ ˆ ˆ ˆ Tr j B j ˆ jˆ B j h¯

iγ2 v

v ρ

¥ v w w ¦

F ˆ ˆ Tr B j j ˆ h¯

iγ2

v w ¥ ¦ F B Tr ih¯ jˆρˆ

h¯

v w v F γB M (A.11)

Thus, the magnetization of the ensemble behaves like a classical gyroscope, precessing

ω γB F around the applied magnetic ﬁeld Bv (Larmor precession) with a frequency L h¯ . The set of equations in eqn. A.11 is called the Bloch equations. The Bloch equations can also be used to introduce relaxation on a phenomenolog-

ical level. Assuming the static magnetic ﬁeld Bv 0 is oriented along the z direction, the

v ¬ magnetization will relax towards an equilibrium magnetization M0 ev z. Since the x and y components of the magnetization precess around the static ﬁeld, their “transversal” relaxation rate can be expected to be different than the “longitudinal” relaxation rate 148 APPENDIX A. SPIN DYNAMICS for the z magnetization. The resulting modiﬁed Bloch equations are thus

d Mx γ y Mx F MyB0 (A.12) dt T2

d My

y y γ My F MxB0 (A.13) dt T2

d Mz y Mz0 y Mz F (A.14) dt T1 where T1 and T2 represent the longitudinal resp. transversal lifetimes of the magnetization. Appendix B

Analysis of EPR Spectra for Single Crystals and Frozen Solutions

B.1 Orientation Dependent Spin Hamiltonian

The generic form of orientation dependent spin Hamiltonians has been discussed in a rather abstract way in section 1.2.2. Focusing on organic radicals occurring in photosynthetic reaction centers allows to consider a more speciﬁc spin Hamiltonian. In the

1 1 F following, an S F 2 system with N proton hyperﬁne couplings (I 2 ) is considered. The spin Hamiltonian for such a radical is

N N T

v v

ˆ y ˆ F W W W W M

ˆ v ˆ ˆ

H B0 µBg S ∑ µngpIk H ∑ S Ak Ik (B.1)

k 1 k 1 The anisotropic coupling constants in this Hamiltonian are the electronic g tensor and the hyperfine coupling tensors Ak. All these tensors depend on the orientation of the molecule in the laboratory system. It is useful to isolate this dependency in one single rotation matrix R specifying the orientation of the g tensor in the laboratory system. It also simplifies parameterization to specify each hyperfine tensor by its principal values and a rotation matrix Rk describing its orientation relative to the g axis system. Thereby one arrives at

N T N

T T T T

v v

ˆ y ˆ

v W W W W M

ˆ F ˆ ˆ

H B0 µBRgR Sl ∑ µngpIkl H Sl ∑ RRkAkRk R Ikl (B.2)

k 1 k 1 In frozen solutions without preferential orientation, a superposition of many orientations is observed. A large number (typically several thousands) of orientations R has to be used to describe such a sample appropriately. For a crystal, there are fewer orientations. Given the orientation of one arbitrary site, the other sites can be constructed from the M symmetry elements of the crystal. These operations can again be described by rotation matrices. As the symmetries arise

149 150 APPENDIX B. ANALYSIS OF EPR SPECTRA from the crystal structure, they are best described in the crystallographic axis system. This results in another step in a sequence of rotations giving the ﬁnal orientation of

the coupling tensors in the laboratory frame: Rg deﬁnes the orientation of the g tensor

M M M of one arbitrary site with respect to the crystal frame; the Rl (l F 1 M) generate the orientations of the other sites in the crystal system; and R is used to give the orientation of the crystal as a whole with respect to the laboratory system. The resulting Hamiltonian

M N

T T T T

ˆ y

v W W

ˆ F ˆ

H ∑ B0 µBRRlRggRg Rl R S ∑ µngpIk

® l 1 k 1 T N

T T T T v

ˆ v W

W ˆ ¯ H S ∑ RRlRgRkAkRk Rg Rl R Ik (B.3)

k 1 reﬂects the hierarchical parameterization of the coupling tensors. The advantage of this representation is the complete separation of orientation relations on the molecular level (Rk), crystalline level (Rg), crystal symmetry (Rl), and the orientation in the laboratory system (R). This decomposition, once determined, is easier to interpret than the product of the individual rotation matrices. In addition, the distinction between experimental details like the sample orientation and intrinsic sample properties makes numerical ﬁtting methods used to derive the spectroscopic parameters more robust.

B.2 Deﬁnition of Euler Angles

Any orientation or rotation in 3D space can be described by three parameters. The most common way to define an arbitrary rotation is by replacing it with three consecutive rotations about canonical axes by specified angles (Euler angles). There exist several conventions for the choice of these canonical rotations, making it difficult to compare orientations specified in Euler angles from different sources. For a geometrical interpretation it is therefore best to consider the individual elements of the rotation matrix (directional cosines). Euler angles are however still required for a non-redundant and self-consistent parameterization of the spin Hamiltonian. The convention used throughout this thesis is equivalent to that used in [1]. It is defined by rotations around the axes of a fixed right-handed Cartesian reference frame in the following order1

1. A rotation about the z axis by an angle ψ,

2. a rotation about the x axis by an angle θ,

3. another rotation about the z axis by an angle φ. 1In [1], rotations are applied in reverse order and, consequently, intermediate auxiliary axes for the rotations have to be introduced. B.3. SIMULATION OF SPECTRA 151

All rotation angles are deﬁned in the mathematically positive sense. A generic rotation

V V matrix transforming coordinates from a local cartesian system x V y z to the xyz system

is therefore given by2

F W W R φ θ ψ R φ R θ R ψ (B.4) where

cosφ y sinφ 0

φ φ φ F °±

R sin cos 0 (B.5) ³ 0 0 1 ²

1 0 0

θ θ y θ F °±

R 0 cos sin (B.6) ³ 0 sinθ cosθ ²

cosψ y sinψ 0

ψ ψ

F M

ψ ±

R ° sin cos 0 (B.7) ³ 0 0 1 ²

For the complete rotation matrix, one arrives at

cosφcosψ sinφcosθsinψ cosφsinψ sinφcosθcosψ sinφsinθ

L L L

φ ψ F φ θ ψ φ ψ φ θ ψ φ θ M

φ θ ψ ±

R ° sin cos cos cos sin sin sin cos cos cos cos sin

J L J L

θ ψ θ ψ θ ³ sin sin sin cos cos ² (B.8)

B.3 Simulation of Spectra

In general, EPR spectra arising from an orientation-dependent spin Hamiltonian are too complex for an analytical evaluation. The reduction of experimental data therefore has to resort to trial and error procedures like nonlinear least squares fitting [2]. When the experimental EPR spectra are sufficiently resolved to identify and assign individual resonance lines, the experimental line positions can be compared to their computed counterparts. Based on the observed differences, the parameter set can be improved. With an increasing number of resolved hyperfine interactions and, in the case of crystals, inequivalent sites in the unit cell, EPR lines are more likely to overlap and it is no longer feasible to pick line positions from the spectra. In this case, it is necessary to simulate complete spectra and compare those with the experimental ones. For the simulation of frozen solution and crystal EPR spectra, a C++ program was written. The program has to perform two steps: it has to use a series of transformations to set up the spin Hamiltonian for a specific sample orientation, and it has to calculate the spectrum from that Hamiltonian. For the simulation of frozen solution spectra, a

2Another source of confusion is that some authors, including [1], give the matrix for the transformation from the global to the local cartesian system. 152 APPENDIX B. ANALYSIS OF EPR SPECTRA large number of isotropically distributed orientations is generated following an algo- rithm described in [3]. In the case of crystal spectra, orientations are generated from a user-supplied set of R, Rl, and Rg (specified as Euler angles). Calculating the spectrum for a given orientation involves a trade-off between effi- cient computation and accuracy. For organic radicals with small g anisotropy and not too large hyperfine interactions, the following approximation can be used.

B.4 Calculation of the Resonance Field Strength

For the organic radicals under investigation the hyperﬁne couplings and the anisotropy of the Zeeman term are small compared to the absolute Zeeman energy. This is especially true in high ﬁeld EPR. Therefore, the eigenstates of the Hamiltonian are very

ˆ ∆ v F W F k close to Sz eigenstates (assuming B0 B0 v ez), and canonical selection rules mS 1 apply. The nuclear Zeeman terms can then be neglected. The EPR transition ﬁelds for a given microwave frequency νmw result as

ν y ∑

h a z m mw k 1 eff k I

B F (B.9) µBgeff with the effective g and hyperﬁne constants

T T T T

F W W v geff nv RRlRggRg Rl R n (B.10)

T T T T T

F W W

z v

aeff k nv RRlRgRkAkRk Rg Rl R n (B.11) where nv is the direction of the magnetic ﬁeld. In an ensemble, the combinations of N

N ∏ different m give rise to 2I H 1 EPR lines. I k 1 k

REFERENCES [1] Goldstein H., Klassische Mechanik, chapter 4, Akademische Verlagsgesellschaft Wies- baden, 7th edition (1983).

[2] Press W.H., Teukolsky S.A., Vetterling W.T., & Flannery B.P., Numerical Recipes in C: The Art of Scientiﬁc Computing, chapter 15, Cambridge University Press, 2nd edition (1992).

[3] Geßner C., NiFe-Hydrogenasen: Beiträge der EPR-Spektroskopie zur Strukturaufklärung des aktiven Zentrums, Ph.D. thesis, Technische Universität Berlin (1996). Appendix C

Spin Dynamics Simulation Program

The following C++ program was used in chapter 4 to numerically solve the Liouville- von Neumann equation for a two-level spin system with inhomogeneous line broadening. It is listed here in the hope that it may be useful as an educational tool for understanding pulsed EPR experiments.

#include #include #include #include #include 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. SPIN DYNAMICS 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 Gausslinie double quality=1.0; // beruecksichtigte Bandbreite in Nyquist-Einheiten double f1=1.0; // Rabi-Frequenz double t_start=0.0; // Start des Detektionsfensters double t_end=100.0; // Ende des Detektionsfensters int 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 Pulses double f1; // Rabifrequenz double length; // Pulsdauer }; double* signalx; // Puffer fuer Signal double* 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 initialisieren signalx=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"; 156 APPENDIX C. SPIN DYNAMICS SIMULATION PROGRAM

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 zentrale Uebergangsfrequenz (rotating frame)\n"; cerr << " s0 Standardabweichung der f0-Verteilung\n"; cerr << " co Abschneideparameter fuer Apodisierung\n"; cerr << " qu beruecksichtigte Bandbreite in Vielfachen\n"; cerr << " der Nyquist-Grenzfrequenz\n"; cerr << " f1 Rabi-Frequenz der nachfolgenden Pulse\n"; cerr << " ta Anfangszeitpunkt des Signalfensters\n"; cerr << " te Endzeitpunkt des Signalfensters\n"; cerr << " ts Aufloesung der Zeitachse (Schritte)\n"; cerr << " sh Ausgabe der Pulsliste\n"; cerr << "Pulse: +x +x-Puls mit Dauer und Rabifrequenz f1\n"; cerr << " +y, -x, -y entsprechend\n"; cerr << " tau 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); // Zeitinkrement double t=t_start; // aktuelle Zeit double t0=0; // Beginn des aktuellen Pulses double t_last=0; // letzter Zeitpunkt pulse* current=pulselist; // aktueller Puls spinmatrix U=2*sigma_0; // Identitaet, Ausgangszustand spinmatrix dU=2*sigma_0; // Cache fuer Propagator bool dUvalid=false; // Flag, ob dU gueltig spinmatrix rho0=sigma_0+sigma_z; // 100% Polarisation, Ausgangszustand spinmatrix rho; // Dichtematrix zum Zeitpunkt t

for (int j=0; j<=t_steps; ++j) { while (t_lastlength<=t) { // bis Ende des Pulses U*=pulsematrix(f0, current->f1, current->what, t0+current->length-t_last); t0=t_last=t0+current->length; current=current->next; dUvalid=false; } else { // angeschnittener Puls if (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 158 APPENDIX C. SPIN DYNAMICS SIMULATION PROGRAM

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 Anfertigung dieser Dissertation erfuhr ich Unterstützung von vielen Seiten. An erster Stelle möchte ich mich bei Prof. Dr. Wolfgang Lubitz bedanken. Nach der Aufnahme in seine Arbeitsgruppe hat er mich, wo er konnte, tatkräftig unterstützt und den Fortgang der Arbeit wohlwollend begleitet. Aufgrund meiner gelegentlichen Skepsis gegenüber den hochkomplexen Proben hatten wir nicht immer die gleichen Ansichten. Trotzdem – oder gerade deshalb – habe ich in den daraus erwachsenen Diskussionen viel gelernt. Prof. Dr. Klaus Möbius danke ich für sein Interesse am Fortgang meiner Arbeit und die spontane Bereitschaft zur Übernahme des Mitberichtes. Obwohl „sein“ Institut an der Freien Universität Berlin nur wenige Kilometer entfernt liegt, war ich leider viel zu selten dort – wofür ich mich an dieser Stelle entschuldige. Mit Herrn Dr. Robert Bittl hatte ich zahlreiche, oftmals sehr grundsätzliche Diskus- sionen über physikalische Hintergründe, spektroskopische Techniken und mathemati- sche Methoden zur Beschreibung bzw. Analyse der Experimente. Für diese wertvolle Hilfestellung möchte ich mich ganz besonders bedanken. Dr. Friedhelm Lendzian verdanke ich nicht nur zahlreiche lehr- und hilfreiche Dis- kussionen, sondern auch den Einblick in einen großen Schatz an Erfahrungen, die im Laboralltag und bei der Interpretation der Daten von unschätzbarem Wert waren. Zudem hat mich sein trotz anderslautender Beteuerungen ungebrochener Optimismus stets aufs neue motiviert und wird mir in schwierigen Zeiten Ansporn sein. Wesentlichen Anteil an dieser Arbeit haben die Kooperationspartner, die die untersuchten Proben beigesteuert haben. An erster Stelle ist hier die AG Fromme/Witt am Max-Volmer-Laboratorium zu nennen. Frau Dr. Petra Fromme hat die Lösungen und Kristalle von Photosystem I zur Verfügung gestellt, die in dieser Arbeit vermessen wurden, wofür ich mich an dieser Stelle bedanken möchte. Ein besonders herzlicher Dank gebührt Frau Dr. Athina Zouni und Jan Kern für die enge und fruchtbare Zu- sammenarbeit bei den Experimenten am Photosystem II. Athina hat nicht nur etliche der wertvollen Kristalle für die EPR-Experimente geopfert, sondern war auch besonders an den sich ergebenden Resultaten interessiert. Die zahlreichen motivierenden Diskussionen – nicht nur fachlicher Natur – mit ihr haben mir sehr geholfen. Röntgenbeugungsexperimente an den Kristallen, die direkt und indirekt in diese Arbeit eingeﬂossen sind, wurden mit der Hilfe von Dr. Norbert Krauß und Dr. Peter Orth in der AG Saenger am kristallographischen Institut der FU Berlin durchgeführt.

159 Die Erfahrung von Peter und Norbert kam mir auch bei vielen Diskussionen über Kri- stallsymmetrien, Koordinatensysteme und Methodik der Röntgenstrukturanalyse zu- gute. Die untersuchten bakteriellen Reaktionszentren stammen aus der Gruppe von Prof. George Feher (UCSD, La Jolla). Im Kapitel 4 fanden Proben von Prof. Wieghardt (MPI für Strahlenphysik, Mül- heim) und V. Barynin (U Sheffield) Verwendung. Allen Mitarbeitern der AG Lubitz danke ich für das angenehme Arbeitsklima. Kai Schäfer hat nicht nur als mein Bürogenosse meine Anwesenheit mehrere Jahre ohne Murren ertragen, sondern auch „seine“ Mangankomplexe für Messungen zur Verfü- gung gestellt. Mit den „Reduktasen“, Günter Bleifuß und Matthias Kolberg, habe ich auch außerhalb des Instituts viel Zeit verbracht. Mit Marc Brecht hatte ich interessante Diskussionen über fortgeschrittene Puls-EPR-Techniken. Michael Kammel half mir in der Anfangsphase der Photosystem II-Experimente. Rafael Jordan verdanke ich einige Illustrationen, die in modifizierter Form im einführenden Kapitel über Reaktionszen- tren verwendet wurden. Auch all die anderen würde ich gerne namentlich würdigen, was mir angesichts der Größe der Arbeitsgruppe jedoch der Platz und die Befürchtung, jemanden zu vergessen, verbieten. In Zeiten knapper Kassen ist eine leistungsfähige Infrastruktur an Universitäten keine Selbstverständlichkeit mehr. Daß trotzdem erfolgreiche Forschung betrieben werden kann, verdankt die TU Berlin – und damit auch ich – dem großen Engagement einzelner Mitarbeiter, die bei unvorhergesehenen Problemen auch abseits des Dienst- wegs zu unkomplizierter Hilfe bereit sind. Stellvertretend für alle sei an dieser Stelle Frau Michaela Sofsky von der „Zentraleinrichtung Gasverflüssigungsanlage“ (ZGA) genannt, die oft auch sehr kurzfristige Wünsche nach flüssigem Stickstoff und Helium befriedigen konnte. Der EPR-Abteilung der Firma Bruker Analytik danke ich für die gute und unkom- plizierte Zusammenarbeit. Die bereitwilligen Auskünfte über technische Details der Spektrometer – oft auch nach der offiziellen Geschäftszeit – gingen deutlich über ein normales Geschäftsverhältnis hinaus und halfen mir bei der Lösung von etlichen klei- neren und größeren Problemen im Labor. Darüber hinaus wurden mir Messungen im Bruker-Labor ermöglicht, als unser eigenes Spektrometer einmal kränkelte. Wenn auch formal Herr Prof. Lubitz und Herr Dr. Bittl meine Arbeitgeber waren, war der eigentliche Geldgeber im Hintergrund die Deutsche Forschungsgemeinschaft. Deshalb möchte ich mich bei der DFG bedanken und dies mit dem Wunsch verbinden, daß die DFG sich auch in Zukunft nicht der kurzsichtigen Politik der Wirtschaftsma- gnaten anschließt, sondern weiterhin Grundlagenforschung zum Wohle aller fördert. Auch unsere Zeit wird eines fernen Tages nicht anhand von Konzernbilanzen, sondern ihrer Beiträge zu Kultur und Wissenschaft beurteilt werden. Meinen Eltern danke ich für ihre fortwährende Unterstützung und Eileen für ihre Geduld. Lebenslauf

Name Wulf Tobias Hofbauer Akademische Grade Diplom-Physiker (Dipl.-Phys.) Geburtsdatum 29. März 1969 Geburtsort Stuttgart-Bad Cannstatt Familienstand ledig

Ausbildung

1975–1979 Herbert-Hoover-Grundschule, Stuttgart 1979 Grundschule Hohenstange, Tamm (Württ.) 1979–1988 Friedrich-List-Gymnasium, Asperg (Württ.) Mai 1988 Abitur 1989–1996 Studium der Physik an der Universität Stuttgart Oktober 1991 Vordiplom („sehr gut“) 1995–1996 Diplomarbeit auf dem Gebiet der transienten optischen Spektroskopie am 2. Physikalischen Institut der Universität Stuttgart bei Prof. Dr. M. Mehring Januar 1996 Hauptdiplom („sehr gut“) seit 1996 Anfertigung der Dissertation auf dem Gebiet der Elek- tronenspinresonanz-Spektroskopie am Max-Volmer-Institut (seit April 2001: Max-Volmer-Laboratorium) der Techni- schen Universität Berlin bei Prof. Dr. W. Lubitz

Tätigkeiten

1988–1989 Grundwehrdienst 1992–1996 Lehrtätigkeit als wissenschaftlicher Mitarbeiter am Physi- kalischen Institut der Universität Stuttgart 1996–2000 Wissenschaftlicher Mitarbeiter bei PD Dr. R. Bittl an der Technischen Universität Berlin seit 2000 Wissenschaftlicher Mitarbeiter bei Prof. Dr. W. Lubitz an der Technischen Universität Berlin