Biological Magnetic Resonance Volume 19

Distance Measurements in Biological Systems by EPR

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Biological Magnetic Resonance Volume 19

Distance Measurements in Biological Systems by EPR

Edited by

Lawrence J. Berliner Ohio State University Columbus, Ohio

Gareth R. Eaton and

Sandra S. Eaton University of Denver Denver, Colorado

KLUWER ACADEMIC/PLENUM PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

ISBN 978-1-4757-0575-1 ISBN 978-0-306-47109-4 (eBook) DO 10.1007/978-0-306-47109-4 I

© 2000 Kluwer Academic/Plenum Publishers, New York Softcover reprint of the hardcover 1 st edition 2000

233 Spring Street, New York, New York 10013

http://www.wkap/nl

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A c.I.P. record for this book is available from the Library of Congress

All rights reserved

No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher

To Pier Luigi Nordio

CONTRIBUTORS

Albert H. Beth. Department of Molecular Physiology and Biophysics, Vanderbilt University, Nashville, Tennessee 37232

Petr P. Borbat. Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853

Gary W. Brudvig. Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107

Sergei A. Dzuba • Institute of Chemical Kinetics and Combustion, Russian Academy of Sciences, Novosibirsk, Russia

Gareth R. Eaton. Department of Chemistry and Biochemistry, University of Denver, Denver, Colorado 80208

Sandra S. Eaton. Department of Chemistry and Biochemistry, University of Denver, Denver, Colorado 80208

Jack H. Freed. Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853

Arnold J. Hoff. Department of Biophysics, Leiden University, Leiden, the Netherlands

Eric J. Hustedt • Department of Molecular Physiology and Biophysics, Vanderbilt University, Nashville, Tennessee 37232

Gunnar Jeschke. Max-Planck-Institute for Polymer Research, Postfach 3148, D-55021 Mainz, Germany

K. V. Lakshmi. Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107

Gertz I. Likhtenshtein • Department of Chemistry, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 84105, Israel

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viii Contributors

Hassane S. Mchaourab • Department of Molecular Physiology and Biophysics, Vanderbilt University School of Medicine, Nashville, Tennessee 37232

Joseph C. McNulty. Department of Chemistry and Biochemistry, University of California, Santa Cruz, California 95064

Glenn L. Millhauser • Department of Chemistry and Biochemistry, University of California, Santa Cruz, California 95064

Eduardo Perozo. Department of Molecular Physiology and Biological Physics, University of Virginia Health Science Center, Charlottesville, VA 22906

Martin Pannier. Max-Planck-Institute for Polymer Research, Postfach 3148, D-55021 Mainz, Germany

Arnold Raitsimring. Department of Chemistry, University of Arizona, Tucson, Arizona 85721

Yeon-Kyun Shin. Department of Biochemistry and Biophysics, Iowa State University, Ames, Iowa 50011

Hans W. Spiess. Max-Planck-Institute for Polymer Research, Postfach 3148, D-55021 Mainz, Germany

Wenzhong Xiao. Department of Chemistry, University of California, Berkeley, California 94270

Preface

Distance measurements in biological systems by EPR

The foundation for understanding function and dynamics of biological systems is knowledge of their structure. Many experimental methodologies are used for determination of structure, each with special utility. Volumes in this series on Biological Magnetic Resonance emphasize the methods that involve magnetic resonance. This volume seeks to provide a critical evaluation of EPR methods for determining the distances between two unpaired electrons.

The editors invited the authors to make this a very practical book, with specific numerical examples of how experimental data is worked up to produce a distance estimate, and realistic assessments of uncertainties and of the range of applicability, along with examples of the power of the technique to answer biological problems.

The first chapter is an overview, by two of the editors, of EPR methods to determine distances, with a focus on the range of applicability. The next chapter, also by the Eatons, reviews what is known about electron spin relaxation times that are needed in estimating distances between spins or in selecting appropriate temperatures for particular experiments. Albert Beth and Eric Hustedt describe the information about spin-spin interaction that one can obtain by simulating CW EPR line shapes of nitroxyl radicals. The information in fluid solution CW EPR spectra of dual-spin labeled proteins is illustrated by Hassane Mchaourab and Eduardo Perozo. Wenzhoug Xiao and Yeon-Kyun Shin show a way to determine dipolar interactions by Fourier deconvolution of nitroxyl CW EPR spectra. Glenn Millhauser describes the use of the rigid spin label abbreviated TOAC. The broadening of CW EPR of spin labels caused by paramagnetic metals reveals depth of the radical beneath the surface and the electrostatic environment, as described by Gertz Likhtenshtein. The use of T I and T m effects to determine distances is described by the Eatons. Arnold Raitsimring shows how to apply the "2+ 1" pulse sequence for distance and spatial distribution measurements of paramagnetic centers. Double-Quantum ESR is applied to distance measurements by Petr Borbat and Jack Freed. Pulsed double

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x Preface

electron-electron methods, sometimes called PELDOR or DEER are described by Gunnar Jeschke, Martin Pannier and Hans Spiess. K. V. Lakshmi and Gary Brudvig discuss spin-spin interactions in the photosynthetic reaction center revealed by CW EPR spectra. The distance information that is obtainable from out-of-phase electron spin echoes of photo-induced radical pairs is explained by Sergei Dzuba and Arnold Hoff.

Some related topics have been discussed in other volumes of Biological Magnetic Resonance and consequently are not included in the present volume. In particular, we call the reader's attention to the Mims and Peisach review of ESEEM in Volume 3, the review of biological applications of time domain EPR by Thomann, Dalton, and Dalton in Volume 6, the four reviews of ENDOR by Hoffman and coworkers, Hiittermann, Mobius, and Thomann and Bernardo in Volume 13, progressive saturation and saturation transfer EPR by Marsh, Pali, and Horvath in Volume 14, and of ENDOR by Makinen, Mustafi and Kasa in Volume 14. Other reviews are cited in the appropriate chapters.

Site-directed spin labeling and time-domain EPR are enabling technologies for using spin-spin interactions to estimate distances. Now that commercial pulsed EPR spectrometers are available, both the CW and pulsed EPR the techniques that are described in this volume can be applied by many researchers. We hope that this volume guides users to the technique(s) most suitable for the problem to be solved.

Sandra S. Eaton Gareth R. Eaton Denver, Colorado

Lawrence J. Berliner Columbus, Ohio

Contents

Section I. Introduction

Chapter 1 Distance Measure,ments by CW and Pulsed EPR

Sandra S. Eaton and Gareth R. Eaton

1. Structural Studies of Biomolecules .......................... , .................. , ............... 2 1.1. Structure and Dynamics .................. , ...... , ............................. , .......... ,.... 3 1.2. Rationale for Distance Measurements by EPR .......... ,......................... 4

2. Dipolar Interactions .................................................................................... 6 3. Exchange Interaction .................................................................................. 9 4. Determination of Electron-Electron Distances from Dipolar Interaction

Measured by EPR ...................................................................................... 10 4.1. Pairwise Interaction Between Two Slowly-Relaxing Spins in an

Immobilized Sample ......................................................................... 12 4.2. Pairwise Interaction Between Two Slowly-Relaxing Spins in a Siowly-

Tumbling Macromolecule in Fluid Solution ..................................... 17 4.3. Pairwise Interaction Between a Slowly-Relaxing Spin and a More

Rapidly-Relaxing Spin in an Immobilized Sample ................ ........... 18 4.4. Out-of-Phase Echo for Spin-Polarized Radical Pairs .... , .................... 20 4.5. Collisions Between Slowly-Relaxing Label and More Rapidly-

Relaxing Spin in Fluid Solution ............................................ , ........... 20 5. Distributions of Distances ................ , ..................... , ................................... 21 6. Accuracy and Precision of Distances Measured .......................... , ............. 21

References ......................... , ............................ , .. , ........................................ 21

Chapter 2 Relaxation Times of Organic Radicals and Transition Metal Ions

Sandra S. Eaton and Gareth R. Eaton 1. Introduction ................................................... ,............................................ 29

1.1. Scope of this Chapter .................................................. ,....................... 29 1.2, Why You Should Care about Relaxation Times ................................. 31

2. Terminology ...................................................................................... , ... , .... 32 3. Experimental Measurements of Relaxation Times .................................... 36

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3.1. Which Spins are Observed? ................................................................ 38 3.2. Spin-Lattice Relaxation, T j ••.••..••.••••••••..•••••••••••••••••••••••••.••••••••.••••.•.•. 39 3.3. Spin Echo Dephasing, Tm ................................................................... 49 3.4. Spin-Spin Relaxation, T 2 .................................................................... 50

4. Processes that Contribute to T j in Immobilized Samples .......................... 51 4.1. Debye Temperature ............................................................................ 52 4.2. Direct Process..................................................................................... 54 4.3. Raman Process .................................................................................... 54 4.4. Orbach Process ................................................................................... 55 4.5. Local Modes ....................................................................................... 55 4.6. Spectral Density Functions ................................................................. 55 4.7. Fitting Experimental T j Data .............................................................. 56 4.8. Modulation of Spin-orbit Coupling .................................................... 58 4.9. Tunnelling ........................................................................................... 59 4.10. Fractal Relaxation............................................................................. 60 4.11. Field/frequency Dependence of Relaxation ...................................... 61 4.12. Effect of Pairs and Clusters ............................................................... 62

5. Processes that Contribute to T m in Immobilized Samples.......................... 63 5.1. The Shape of the Echo Decay Curve .................................................. 63 5.2. Instantaneous Diffusion ....................................................................... 64 5.3. Nuclear Spin Diffusion ....................................................................... 65 5.4. Dephasing by Methyl Groups in the Solvent/Surroundings ............... 68 5.5. Averaging of Electron-nuclear Couplings due to Rotation of Methyl

Groups Within the Radical or Transition Metal Complex ................. 69 5.6. Collapse of Electron-Electron Spin-Spin Coupling to a More Rapidly

Relaxing Partner................................................................................ 70 5.7. Librational Motion .............................................................................. 71 5.8. Molecular Tumbling ........................................................................... 71 5.9. Oxygen .............................................................................................. 71

6. Processes that Contribute to T j and T2 in Fluid Solution ........................... 72 6.1. Small Molecules................................................................................. 72 6.2. Macromolecules .................................................................................. 74 6.3. Oxygen ............................................................................................... 75 6.4. The Ultimate Limit on Relaxation ...................................................... 75

7. Experimental Data ..................................................................................... 76 7.1. Nitroxyls ............................................................................................. 83 7.2. Other Organic Radicals ....................................................................... 93 7.3. Radicals Produced by Irradiation ........................................................ 96 7.4. Radicals in Polymers......... ............................................................. .... 97 7.5. Triplets ................................................................................................ 98 7.6. Transition metals with S = h .............................................................. 98 7.7. Transition metals with S > h ............................................................. 109 7.8. Lanthanides and Actinides ................................................................. 112 7.9. Frequency Dependence of Relaxation ............................................... 113

8. Implications for Recording CW spectra of Nitroxyls at -100 K .............. 116 9. Summary of Trends in T m and T j from Experimental Data ...................... 118

Contents xiii

9.l. Spin Echo Dephasing and T2 for S = Yl ............................................. 118 9.2. Spin-lattice Relaxation for S = Yl ....................................................... 119 9.3. Spin-lattice Relaxation for S > Yl ....................................................... 124 9.4. Summary of Relaxation Mechanisms ................................................ 126 9.5. Estimating Relaxation Times of Species or Environments for Which

Experimental Values are Not Available ........................................... 128 References ................................................................................................. 129

Section II. CW Measurements

Chapter 3 Structural Information from CW-EPR Spectra of Dipolar Coupled Nitroxide Spin Labels

Eric J. Hustedt and Albert H. Beth

l. Overview of Site Directed Spin Labeling ................................................. 155 2. The Three Cases ........................................................................................ 158

2.l. Distinguishing Between the Three Cases .......................................... 161 3. Theoretical Basis ...................................................................................... 162 4. Analysis of Experimental Data for Case 1 ................................................ 169

4.l. Factors Influencing the Precision of the Determined Parameters ...... 172 5. Analysis of Experimental Data for Case 2 ................................................ 174 6. Analysis of Experimental Data for Case 3 ................................................ 178 7. Conclusions ............................................................................................... 179 8. Availability of Computer Programs .......................................................... 180

References ................................................................................................. 180

Chapter 4 Determination of Protein Folds and Conformational Dynamics using Spin­Labeling EPR Spectroscopy

Hassane S. Mchaourab and Eduardo Peraza

1. Introduction ............................................................................................... 185 2. Spatial Restraints and Protein Conformational Space ............................... 188 3. Experimental Strategies in Protein Fold Determination ........................... 190

3.1. Structural Information Derived from EPR Analysis of Spin Labeled Proteins ............................................................................................. 190

3.2. Methods for Secondary Structure Assignment .................................. 192 3.3. Methods for the Analysis of Inter-Nitroxide Proximities .................. 197

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3.4. Quaternary Structure Packing and Symmetry from Inter-Subunit Spin Coupling ........................................................................................... 199

4. Determination of Protein Folding Patterns and Quaternary Structure Packing ..................................................................................................... 200 4.1. a-Crystallin as an Example of Water Soluble Proteins ..................... 200 4.2. Membrane Proteins ........................................................................... 212

5. Detection of Conformational Dynamics in Spin-Labeled Proteins ........... 221 5.1. Conformation Dynamics in Proteins .................................................. 221 5.2. Triggered Structural Transitions ........................................................ 230

6. Critical Perspective ........................................................ '" ........................ 237 References ................................................................................................. 238

Chapter 5 EPR Spectroscopic Ruler: the Deconvolution Method and its Applications

Wenzhong Xiao and Yeon-Kyun Shin

1. Introduction .............................................................................................. 249 1.1. Review of the Theory for Dipolar Interactions Between Two

Nitroxides ......................................................................................... 252 1.2. Fourier Deconvolution ....................................................................... 253 1.3. Spectral Analysis ............................................................................... 254 1.4. Model Systems: a Spectroscopic Ruler. ............................................. 257 1.5. Monoradical Impurities ..................................................................... 258

2. Structural Modeling Using EPR-Determined Distances ........................... 259 3. Investigating Membrane Protein Dynamics using Dipolar and

Time-Resolved EPR ................................................................................. 266 References ................................................................................................. 273

Chapter 6 TOAC: The Rigid Nitroxide Side Chain

Joseph C. McNulty and Glenn L. Millhauser

1. Introduction: Incorporating TOAC into Polypeptides .............................. 277 2. Evaluating the Structure of Short Helical Peptides ................................... 283 3. Structure of the a-Helix ............................................................................ 289 4. The Trichogin GA IV Peptide: Resolving Multiple Conformations ......... 296 5. Summary and Outlook .............................................................................. 304

References ................................................................................................. 305

Contents

Chapter 7 Depth of Immersion of Paramagnetic Centers in Biological Systems

Gertz I. Likhtenshtein

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1. Introduction ............................................................................................... 309 2. Spin-Spin Metal-Radical Interaction ........................................................ 311

2.1. Distances Between Isolated Pairs ...................................................... 311 2.2. Distance of Closest Approach ............................................................ 317

3. Investigation of Electrostatic Effects in Molecules in Solutions .............. 324 3.1. Effect of Charge on Dipolar Interactions Between Protons and a

Paramagnetic Species ....................................................................... 324 3.2. Impact of Charge on Spin Exchange Interactions between Radicals

and Paramagnetic Complexes .......................................................... 328 4. Experimental Data on Biological Systems ................................................ 331

4.1. Photosynthetic Reaction Centers ....................................................... 331 4.2. Cytochrome P450 .............................................................................. 333 4.3. Flavin-Dependent Alcohol Oxidase ................................................... 335 4.4. Determination of Electrostatic Potential Around Molecules of

Biological Importance ...................................................................... 336 5. Conclusions ............................................................................................... 339

References ................................................................................................. 341

Section III. Pulsed EPR Measurements of Electron-Electron Interactions

Chapter 8 Determination of Distances Based on T 1 and T m Effects

Sandra S. Eaton and Gareth R. Eaton

1. Effect of Rapidly-Relaxing Metal on TI for Slowly-Relaxing Spin ......... 348 1.1. Application of Bloembergen Equation Based on an Average Value

of Tis"""""""""""""""""""""""'" ................................................ 351 1.2. Application of Bloembergen Equation Based on Analysis of

Saturation Recovery Curves without Knowledge of T If and T 2f ...... 351 1.3. Application of Bloembergen Equation Based on Analysis of the

Saturation Recovery Curve with Knowledge of T If and T 2f .•....•...•.• 352 1.4. Application to Slowly-Tumbling Macromolecules in Fluid Solution 353 1.5. Modification to Explicitly Treat S=5/2 .............................................. 354 1.6. Predicted Frequency Dependence ...................................................... 355

2. Distance Determination Based on T I Effects - Experimental Data .......... 356 2.1. High-spin Fe(II) ................................................................................. 356 2.2. Low-spin Heme Fe(III) ...................................................................... 357

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2.3. High-spin Heme Fe(III) with Zero-Field Splitting Greater than the X-band EPR Quantum ...................................................................... 361

3. Effect of Rapidly-Relaxing Metal on Spin Echo Dephasing, T m' for Slowly-Relaxing Spin ............................................................................... 365

4. Distance Determination Based on T m Effects - Experimental Data ......... 372 4.1. Effect of Low-Spin Fe(III) ................................................................. 372 4.2. Effect of High-spin Fe(III) on Echo Dephasing ................................. 375

5. Summary and Guide to Application of These Techniques ....................... 376 References ................................................................................................. 378

Chapter 9 Double-Quantum ESR and Distance Measurements

Petr P. Barbat and Jack H. Freed

1. Introduction ............................................................................................... 383 2. Theory of Double Quantum Coherence .................................................... 385

2.1. Multiple Quantum Coherences in ESR .............................................. 385 2.2. Product Operator Analysis for Arbitrary Pulses ................................ 396 2.3. Approach for General Analysis ......................................................... 404 2.4. Relation to Other ESR Techniques .................................................... 404

3. Instrumentation ......................................................................................... 405 3.1. 2D-FT Pulse ESR Spectrometer ........................................................ 405

4. Examples ................................................................................................... 413 4.1. Random Radicals (E' Centers in Fused Silica) .................................. 413 4.2. Bilabeled Organic Molecules ............................................................. 417 4.3. Bilabeled Peptides ............................................................................. 430 4.4. "Forbidden" Coherences .................................................................... 433

5. Discussion ................................................................................................. 434 5.1. Comparison with Other Pulsed ESR Techniques .............................. 436 5.2. Improvements in the Future ............................................................... 440

6. Appendices ............................................................................................... 441 A. Effects of the Pseudo-Secular Terms .................................................. 441 B. Sensitivity and the Upper Range of Measurable Distances ................. 445 C. 5-Pulse SQ Sequence .......................................................................... 449 D. Phase Cycles ....................................................................................... 451 References ................................................................................................. 456

Contents

Chapter 10 "2+1" Pulse Sequence as Applied for Distance and Spatial Distribution Measurements of Paramagnetic Centers

A. Raitsimring

xvii

1. Introduction ............................................................................................... 461 2. Theory ....................................................................................................... 463 3. Experiment. ............................................................................................... 476 4. Conclusion ................................................................................................ 489

References ................................................................................................. 490

Chapter 11 Double Electron-Electron Resonance

Gunnar Jeschke, Martin Pannier, and Hans W. Spiess

1. Introduction ............................................................................................... 493 2. Three-Pulse DEER .................................................................................... 495 3. Four-Pulse DEER ..................................................................................... 499 4. Technical Requirements ............................................................................ 502 5. Limitations and Comparisons with Other Methods .................................. 504 6. DEER on Nitroxides ................................................................................. 506 7. Cluster Size and Intercluster Distances in Ionomers ................................. 508 8. Conclusions ............................................................................................... 510

References ................................................................................................. 511

Section IV. Applications to Photosynthesis

Chapter 12 Electron Paramagnetic Resonance Distance Measurements in Photosynthetic Reaction Centers

K. V. Lakshmi and Gary W. Brudvig

1. Introduction ............................................................................................... 513 1.1. Photosynthetic Reaction Centers ....................................................... 514

2. EPR Distance Measurements .................................................................... 522 2.1. Theory ................................................................................................ 522

3. Distance Measurements in Photosynthetic Reaction Centers ................... 526 3.1. Lineshape Analysis in the Static Limit.. ............................................ 526 3.2. Spin-Lattice Relaxation Enhancement Measurements ....................... 537 .

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3.3. Pulsed Electron-Electron Double-Resonance Distance Measurements .................................................................................. 557

4. Summary ................................................................................................... 559 References ................................................................................................. 562

Chapter 13 Photo-Induced Radical Pairs Investigated using Out-of-Phase Electron Spin Echo

Sergei A. Dzuba and Arnold J. Hoff

1. Introduction ............................................................................................... 569 2. Electron Spin Echo Envelope Modulation of a Photoinduced Radical

Pair ........................................................................................................... 571 2.1. Energy Levels of the Interacting Radical Pair ................................... 571 2.2. Electron Spin Echo Formation ........................................................... 573 2.3. Echo Amplitudes and Pulse Angle Dependence ................................ 576 2.4. Zero-Quantum and Double Quantum Coherences ............................. 578 2.5. Fourier Transformation and Distance Determination ........................ 580 2.6. Sequential Electron Transfer ............................................................. 583 2.7. Contributions to Nuclear ESEEM ...................................................... 584

3. Structural Investigations in Photosynthetic Reaction Centers .................. 586 3.1. Bacterial Reaction Centers ................................................................. 586 3.2. Photosystem I Reaction Centers ........................................................ 587 3.3. Photosystem II Reaction Centers ....................................................... 588 3.4. The Energy Landscape of a Reaction Center Protein ........................ 589 3.5. Kleinfeld Effect ................................................................................. 591

4. Conclusion ................................................................................................ 592 References ................................................................................................. 593

Contents of Prior Related Volumes .............................................................. 597

Index ........................................................................................................... 605