enzyme-catalyzed electron and radical transfer

Chapman Department of Chemistry, University of burgh, Edinburgh EH9 3JJ, Scotland, United Kingdom Edin-Xiaoxi Chen Johnson Research Foundation, Department of istry and Biophysics, Univer

Electron and

Radical Transfer Subcellular Biochemistry

Volume 35

SUBCELLULAR BIOCHEMISTRY

SERIES EDITOR

J ROBIN HARRIS, Institute of Zoology, University of Mainz, Mainz, GermanyASSISTANT EDITORS

H J HILDERSON, University of Antwerp, Antwerp, Belgium

B B BISWAS, University of Calcutta, Calcutta, India

Recent Volumes in This Series

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Transduction

Edited by B B Biswas and Susweta Biswas

Biology of the Lysosome

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Cholesterol: Its Functions and Metabolism in Biology and Medicine

Edited by Robert Bittman

Edited by Harald Herrmann and J Robin Harris

α -Gal and Anti-Gal: α1,3-Galactosyltransferase,α-Gal Epitopes, and the Natural Anti-Gal Antibody

Edited by Uri Galili and JosÈ Luis Avila

Bacterial Invasion into Eukaryotic Cells

Edited by Tobias A Oelschlaeger and Jˆrg Hacker

Fusion of Biological Membranes and Related Problems

Edited by Herwig Hilderson and Stephen Fuller

Enzyme-Catalyzed Electron and Radical Transfer

Edited by Andreas Holzenburg and Nigel S Scrutton

Enzyme-Catalyzed Electron and

Texas A&M University

College Station, Texas

(formerly of University of Leeds

Leeds, United Kingdom)

and

Nigel S Scrutton

University of Leicester

Leicester, United Kingdom

Kluwer Academic Publishers

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©2002 Kluwer Academic / Plenum Publishers, New York

233 Spring Street, New York, N Y 10013

Prin t © 2000 KluwerAcademic / Plenum Publishers, New York

R BITTMAN, City University of New York, New York, USA

N BORGESE, CNR Center for Cytopharmacology, University of Milan, Milan, Italy

D DASGUPTA, Saha Institute of Nuclear Physics, Calcutta, India

H ENGELHARDT, Max-Planck-Institute for Biochemistry, Martinsried, GermanyA.-H ETEMADI, University of Paris VI, Paris France

S FULLER, University of Oxford, Oxford, UK

J HACKER, University of W¸rzburg, W¸rzburg, Germany

H HERRMANN, German Cancer Research Center, Heidelberg, Germany

A HOLZENBURG, Texas A&M University, College Station, Texas, USA

J B LLOYD, University of Sunderland, Sunderland, England, UK

P QUINN, Kingís College London, London, England, UK

S ROTTEM, The Hebrew University, Jerusalem, Israel

Christopher Anthony Division of Biochemistry and Molecular Biology, School of Biological Sciences, University of Southampton, Southamp- ton, SO16 7PX, United Kingdom

Edward A Berry E.O Lawrence Berkeley National Laboratory, versity of California, Berkeley, California 94720

Uni-Brian J Brazeau Department of Biochemistry, Molecular Biology, and Biophysics, University of Minnesota, Minneapolis, Minnesota 55455

Marion E van Brederode Faculty of Sciences, Division of Physics and Astronomy, Department of Biophysics and Physics of Complex Systems, Free University of Amsterdam, 1081 HV Amsterdam, The Netherlands

Stephen K Chapman Department of Chemistry, University of burgh, Edinburgh EH9 3JJ, Scotland, United Kingdom

Edin-Xiaoxi Chen Johnson Research Foundation, Department of istry and Biophysics, University of Pennsylvania, Philadelphia, Penn- sylvania 19104

Biochem-Louise Cunane Department of Biochemistry and Molecular physics, Washington University School of Medicine, St Louis, Missouri 63110

Bio-Victor L Davidson Department of Biochemistry, University of sippi Medical Center, Jackson, Mississippi 39214-4505

Missis-Rosemary C E Durley Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St Louis, Missouri 63110

ix

P Leslie Dutton Johnson Research Foundation, Department of chemistry and Biophysics, University of Pennsylvania, Philadelphia, Pennsylvania 19104

Bio-Stuart J Ferguson Department of Biochemistry and Oxford Centre for Molecular Sciences, University of Oxford, Oxford OX1 3QU, United Kingdom

Vilmos F¸lˆp Department of Biological Sciences, University of Warwick, Coventry CV4 7AL, United Kingdom

Amanda J Green Department of Chemistry, University of Edinburgh, Edinburgh EH9 3JJ, Scotland, United Kingdom

Malcolm Halcrow Department of Chemistry, University of Leeds, Leeds, LS2 9JT, United Kingdom

Russ Hille Department of Medical Biochemistry, Ohio State sity, Columbus, Ohio 43210-1218

Univer-Daniel E Holloway Department of Biology and Biochemistry, sity of Bath, Bath BA2 7AY, United Kingdom

Univer-Li-Shar Huang E.O Lawrence Berkeley National Laboratory and Department of Chemistry, University of California, Berkeley, California 94720

Michael R Jones Department of Biochemistry, School of Medical ences, University of Bristol, Bristol BS8 1TD, United Kingdom

Sci-Sung-Hou Kim E.O Lawrence Berkeley National Laboratory and Department of Chemistry, University of California, Berkeley, California 94720

Peter Knowles School of Biochemistry and Molecular Biology, versity of Leeds, Leeds, LS2 9JT, United Kingdom

Uni-John D Lipscomb Department of Biochemistry, Molecular Biology, and Biophysics, University of Minnesota, Minneapolis, Minnesota 55455

Kirsty McLean Department of Pure and Applied Chemistry, University

of Strathclyde, Glasgow G1 1XL, Scotland, United Kingdom

E Neil G Marsh Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109

F Scott Mathews Department of Biochemistry and Molecular physics, Washington University School of Medicine, St Louis, Missouri 63110

Bio-Caroline S Miles Department of Chemistry, University of Edinburgh, Edinburgh EH9 3JJ, Scotland, United Kingdom

Christopher C Moser Johnson Research Foundation, Department of Biochemistry and Biophysics, University of Pennsylvania, Philadel- phia, Pennsylvania 19104

Christopher G Mowat Department of Chemistry, University of burgh, Edinburgh EH9 3JJ, Scotland, United Kingdom

Edin-Andrew W Munro Department of Pure and Applied Chemistry, versity of Strathclyde, Glasgow G1 1XL, Scotland, United Kingdom

Uni-Jane Murdoch Department of Chemistry, University of Edinburgh, Edinburgh EH9 3JJ, Scotland, United Kingdom

Michael A Noble Department of Chemistry, University of Edinburgh, Edinburgh EH9 3JJ, Scotland, United Kingdom

Tobias W B Ost Department of Chemistry, University of Edinburgh, Edinburgh EH9 3JJ, Scotland, United Kingdom

Christopher C Page Johnson Research Foundation, Department of Biochemistry and Biophysics, University of Pennsylvania, Philadel- phia, Pennsylvania 19104

Simon Phillips School of Biochemistry and Molecular Biology, sity of Leeds, Leeds, LS2 9JT, United Kingdom

Univer-Stephen Ragsdale Department of Biochemistry, Beadle Center, versity of Nebraska, Lincoln, Nebraska 68588-0664

Uni-Emma Lloyd Raven Department of Chemistry, University of Leicester, Leicester LE1 7RH, United Kingdom

Laura Robledo Department of Chemistry, University of Edinburgh, Edinburgh EH9 3JJ, Scotland, United Kingdom

Margareta Sahlin Department of Molecular Biology, Stockholm versity, SE-10691 Stockholm, Sweden

Uni-Nigel S Scrutton Department of Biochemistry, University of Leicester, Leicester, LE1 7RH, United Kingdom

Britt-Marie Sjˆberg Department of Molecular Biology, Stockholm University, SE-10691 Stockholm, Sweden

Michael J Sutcliffe Department of Chemistry, University of Leicester, Leicester, LE1 7RH, United Kingdom

Shinya Yoshikawa Department of Life Science, Himeji Institute ofTechnology and CREST, Japan Science and Technology CorporationKamigohri, Akoh, Hyogo 678-1297, Japan

ZhaoLei Zhang E.O Lawrence Berkeley National Laboratory, versity of California, Berkeley, California 94720

Major advances have been made in recent years in the field of redox mology In part this has been attributable to the wealth of structural infor-mation acquired for redox systems, principally by X-ray methods Thesuccessful application of electron transfer theory to redox proteins has alsoput the study of biological electron transfer onto a sound theoretical plat-form Coupled with the ability to interrogate mechanism by site-directedmutagenesis, spectroscopic and transient kinetic methods these develop-ments have contributed to the major expansion seen in recent years ofresearch activity in the field of biological electron and radical transfer.The purpose of this book is to bring into a single volume milestonedevelopments in the field The approach is one of systems: all contributionshave been selected carefully to illustrate important aspects of the mecha-nisms of electron and radical transfer in proteins Our aim is to unite theoryand experiment to demonstrate the key principles controlling biologicalredox reactions Detailed understanding of these reactions requires knowl-edge of the role of protein dynamics, chemistries of the redox-active pros-thetic groups, the mechanisms governing the diffusional encounter andassembly of electron transfer complexes and the role of protein structure

enzy-in controllenzy-ing the physical parameters (reorganisational energy and tronic coupling matrix element) that govern the transfer rate Additionally,the role of gating mechanisms, such as rate-limiting conformational change,protonation/deprotonation and ligand binding are addressed Contribu-tions were selected such that each system provides its own unique ìspinî

elec-on some of these important issues We have included those systems forwhich there is high resolution structural information, since detailed inter-pretation of kinetic data and the results of spectroscopic and mutagenesisexperiments is less informative in its absence The recent development of

xiii

computational algorithms to calculate electron transfer rates in structurallydetermined protein molecules has supported, and will continue to support,experimental investigations This aspect alone illustrates the synergy result-ing from a melding of different and complementary techniques in this inter-disciplinary field.

The volume begins with a theoretical treatment of biological electrontransfer and descriptions of new key structures of soluble electron transferproteins Experimental studies of ìsimpleî soluble systems based primarily

on the quinoprotein and flavoprotein enzyme families are then introduced

to illustrate key concepts in the control of electron transfer reactions.Radical chemistry is also discussed in detail in contributions on ribonu-cleotide reductase, vitamin B12-dependent reactions, soluble methanemonooxygenase and peroxidase-catalysed reactions Chapters focused onnickel and molybdenum-containing enzymes discuss the chemistries ofcomplex redox centres and their role in biological redox reactions Finally,the remarkable advances made recently in our understanding of mem-brane electron transfer through structural descriptions of key membrane-embedded proteins are discussed in chapters on bovine heart cytochrome

bc1, cytochrome c oxidase and the reaction centre complex from purple

bac-teria All contributions are from leading scientists in the field, drawn from

a truly international community of redox enzymologists We hope thisvolume will inspire those who are less familiar with the field, but also serve

as a valuable resource to experienced practitioners The Editors found thecompilation of this volume to be a pleasurable and informative experience

We hope this enthusiasm translates faithfully to the reader

Andreas Holzenburg,

Leeds, UK Nigel S Scrutton, Leicester, UK

Chapter 1

Electron Transfer in Natural Proteins: Theory and Design

Christopher C Moser, Christopher C Page, Xiaoxi Chen, and

P Leslie Dutton

1 Introduction

2 Basic Electron Tunneling Theory

2.1 Classical Free Energy and Temperature Dependence of Tunneling

2.2 Quantum Free Energy and Temperature Dependence

2.3 A Generic Protein Tunneling Rate Expression

3 Protein Structural Heterogeneity

3.1 Monitoring Heterogeneity via Packing Density

3 2 Natural Tunneling Distances

4 Chains and Robust Electron Transfer Protein Design

5 Electron Transfer Clusters

5.1 Cluster Examples

5.2 Control of Electron Transfer Through Escapement Mechanisms

6 Caution and Hope

7 References

Chapter 2 Flavin Electron Transfer Proteins F Scott Mathews, Louise Cunane, and Rosemary C E Durley 1 Introduction

2 Background and Structural Properties

1 2 3 7 8 9 10 13 14 17 19 21 23 24

29 32

xv

2.1 NADPH-Cytochrome P450 Reductase (CPR)

2.2 Flavocytochrome P450BM3

2.3 Flavocytochrome b2(FCB2)

2.4 p-Cresol Methylhydroxylase (PCMH)

2.5 Flavocytochrome c Sulfide Dehydrogenase (FCSD)

2.6 Trimethylamine Dehydrogenase (TMADH)

2.7 Phthalate Dioxygenase Reductase (PDR)

2.8 Fumarate Reductase (FUM)

3 Electron Transfer

3.1 General Aspects

3.2 Electronic Coupling

3.2.1 BMP/FMN

3.2.2 FCB2

3.2.3 PCMH

3.2.4 FCSD

3.2.5 FUM

4 Conclusions

4.1 Domain Interactions

4.2 Features of Electron Transfer

5 References

Chapter 3 Methanol Dehydrogenase, a PQQ-Containing Quinoprotein Dehydrogenase Christopher Anthony 1 Introduction

2 General Enzymology

2.1 The Determination of MDH Activity

2.2 The Substrate Specificity of MDH

3 The Kinetics of Methanol Dehydrogenase

3.1 The Reaction Cycle of MDH

3.2 The Activation of MDH by Ammonia and Amines

3.3 The Low in vitro Rate of Cytochrome cLReduction by MDH

4 The Absorption Spectra of Methanol Dehydrogenase

5 Pyrrolo-Quinoline Quinone (PQQ): The Prosthetic Group of Methanol Dehydrogenase

6 The Reaction Mechanism of Methanol Dehydrogenase

6.1 The Reductive Half-Reaction of MDH

6.2 The Role of Ammonia in the Reductive Half-Reaction Mechanism of MDH

32 38 42 45 47 48 50 52 55 55 59 59 61 61 63 65 65 65 67 68

73 75 75 76 77 77 78 80 80 84 88 88 94

6.3 The Oxidative Half-Reaction of MDH

6.3.1 The ìMethanol Oxidaseî Electron Transport Chain

6.3.2 The Interaction of MDH with Cytochrome cL 6.3.3 The Oxidation of Reduced PQQ in MDH

7 The Structure of Methanol Dehydrogenase

7.1 The Structure of the α-Subunit

7.2 The Tryptophan-Docking Interactions in the α-Subunit

7.3 Structure of the β-Subunit

7.4 The Active Site of Methanol Dehydrogenase

7.4.1 The Novel Disulphide Ring Structure in the Active Site

7.4.2 The Bonding of PQQ in the Active Site

7.4.3 The Location of Substrate in the Active Site

8 Processing and Assembly of Methanol Dehydrogenase

9 References

Chapter 4 Methylamine Dehydrogenase: Structure and Function of Electron Transfer Complexes Victor L Davidson 1 Methylamine Dehydrogenase

1.1 Structure and Function

1.2 The TTQ Prosthetic Group

1.3 Catalytic Reaction Mechanism

1.4 Spectral and Redox Properties

2 Amicyanin

2.1 Physical Properties

2.2 Interactions with Methylamine Dehydrogenase

3 Methylamine Dehydrogenase-Amicyanin-Cytochrome c-551i Complex

3.1 Structure of the MADH-Amicyanin-Cytochrome c-551i Complex

3.2 Interactions between Amicyanin and Cytochrome c-551i

3.3 Pathways Analysis of the Electron Transfer Protein C o m p l e x

4 Electron Transfer Reactions in Methylamine Dehydrogenase C o m p l e x e s

94 94 95 97 97 100 102 105 105 105 107 109 110 112

119 120 121 121 124 125 125 126 128 128 128 129 131

4.1 Electron Transfer Theory

4.2 Kinetic Complexity of Protein Electron Transfer Reactions

4.2.1 True Electron Transfer

4.2.2 Coupled Electron Transfer

4.2.3 Gated Electron Transfer

4.3 Electron Transfer from TTQ to Copper

4.3.1 Non-Adiabatic Electron Transfer Reactions

4.3.2 Mutation of Amicyanin Alters the HABf o r Electron Transfer from MADH

4.3.3 Gated Electron Transfer Reactions

4.4 Electron Transfer from Copper to Heme

5 Application of Marcus Theory to other Protein Electron Transfer Reactions

6 Conclusions

7 References

Chapter 5 Trimethylamine Dehydrogenase and Electron Transferring Flavoprotein Nigel S Scrutton and Michael J Sutcliffe 1 Electron Transfer Proteins in Methylotrophic Bacteria

2 Prosthetic Groups and Structure of TMADH

2.1 Identification of the Prosthetic Groups

2.2 Structure of TMADH

2.2.1 Evolution of the Crystal Structure of TMADH

2.2.2 Domain and Quaternary Structure

2.2.3 Large Domain and Active Site Structure

2.2.4 The Medium and Small Domains

3 Electron Flow in TMADHóStatic Titrations, Reduction Potentials and Inactivation Studies

3.1 Static Titrations

3.2 Reduction Potentials and Selective Inactivation

4 Single Turnover Stopped-Flow Studies of Electron Transfer 4.1 Early Stopped-Flow Investigations

4.2 pH-Dependence of the Reductive Half-Reaction with Diethylmethylamine

4.3 pH-Dependence of the Reductive Half-Reaction with Trimethylamine: Native and Mutant Enzyme Studies

4.4 Quantum Tunneling of Hydrogen

131 132 132 133 133 134 134 134 137 138 138 139 140

145 148 148 149 149 150 150 153 154 154 155 156 156 158

159 163

5 Control of Intramolecular Electron Transfer: pH-Jump

Stopped-Flow Studies

6 The Oxidative Half-Reaction and TMADH-ETF Complex Assembly

6.1 Stopped-Flow Studies

6.2 A Model for the Electron Transfer Complex

7 Enzyme Over-Reduction and Substrate Inhibition: Multiple Turnover Studies

8 Cofactor Assembly and the Role of the 6-S-Cysteinyl FMN 9 Summary and Future Prospects

10 References

Chapter 6 Amine Oxidases and Galactose Oxidase Malcolm Halcrow, Simon Phillips, and Peter Knowles 1 Introduction

2 Galactose Oxidase

2.1 Structure

2.1.1 General Structural Properties

2.1.2 Primary Structure

2.1.3 Secondary and Tertiary Structure

2.1.4 Structure of the Active Site

2.2 Catalytic Mechanism

2.2.1 Substrate Binding

2.2.2 Substrate Activation

2.2.3 Hydrogen Abstraction from Substrate

2.2.4 Formation of Ereduced

2.2.5 Reoxidation of Ereduced

2.3 Biogenesis of the Thio-Ether Bond and other Processing Events

2.4 Model Studies

2.5 Biological Role of Galactose Oxidase

3 Amine Oxidases

3.1 Structure

3.1.1 General Structural Properties

3.1.2 Protein Structure

3.1.3 Active Site Structure

3.1.3.1 The Copper Site

3.1.3.2 The TPQ Site

3.1.3.3 Substrate Access Channels to the Active Site of Amine Oxidases

164 167 167 168 170 173 176 177

183 184 185 185 185 186 186 189 191 191 191 192 192 192 193 196 197 199 199 199 205 205 205 207

3.1.3.4 Other Structural Features 207

3.2 Catalytic Mechanism 208

3.2.1 Reductive Half Cycle 208

3.2.1.1 Substrate Binding/Substrate Schiff-Base 209

3.2.1.2 Product Schiff-Base 211

3.2.1.3 Reduced Forms of the Enzyme 213

3.2.2 Oxidative Half Cycle 214

3.3 Biogenesis of TPQ and Related Cofactors 217

3.4 Model Studies 219

3.5 Biological Roles of Amine Oxidases 219

3.5.1 Microorganisms 219

3.5.2 Plants 219

3.5.3 Mammals 220

4 Comparisons between Galactose Oxidase and Amine Oxidases 221

5 Future Directions 222

6 References 223

Chapter 7 Electron Transfer and Radical Forming Reactions in Methane Monooxygenase Brian J Brazeau and John D Lipscomb 1 Introduction 233

2 Components 237

2.1 MMOH 237

2.1.1 X-Ray Crystallography 237

2.1.2 Spectroscopy 241

2.1.2.1 Diferric MMOH 241

2.1.2.2 Mixed Valence MMOH 242

2.1.2.3 Diferrous MMOH 243

2.2 M M O B 243

2.2.1 NMR Solution Structure 244

2.3 M M O R 244

3 Component Complexes 245

4 Oxidation-Reduction Potentials 246

5 Electron Transfer Kinetics 248

6 Turnover Systems 250

7 Reaction Cycle Intermediates 252

7.1 Transient Intermediates of the Reaction Cycle of MMOH 252

7.2 Structures of the Intermediates 2567.3 The Mechanism of Oxygen Cleavage 259

8 Mechanism of CóH Bond Cleavage and Oxygen Insertion 2618.1 Radical Rebound Mechanism 2628.2 Isotope Effects 2628.3 Radical Clock Substrates 2648.4 Modified Radical Rebound Mechanism 2668.5 Concerted Oxygen Insertion Mechanisms 2678.6 Mechanistic Theory based on Calculations 268

2 Flavin Reduction and Substrate Oxidation 282

3 Flavin to Heme Electron Transfer 285

4 The Flavocytochrome b2: Cytochrome c Interaction 286

5 Engineering Substrate Specificity in Flavocytochrome b2 290

6 Conclusions 292

7 References 292

Chapter 9

Flavocytochrome P450 BM3óSubstrate Selectivity and Electron

Transfer in a Model Cytochrome P450

Andrew W Munro, Michael A Noble, Tobias W B Ost,

Amanda J Green, Kirsty J MacLean, Laura Robledo,

Carolyn S Miles, Jane Murdoch, and Stephen K Chapman

1 Introduction 297

2 Bacterial Model P450 Systems 302

3 P450 BM3 Structure and Mechanism 304

4 Electron Transfer and its Control 307

5 Site-Directed Mutagenesis in the Study of Substrate

Selectivity and Electron Transfer 309

6 Conclusions 312

7 References 312

Chapter 10

Peroxidase-Catalysed Oxidation of Ascorbate: Structural,

Spectroscopic and Mechanistic Correlations in

8 Radical Chemistry 332

8.2 Nature of the Intermediates 3338.2.1 Compound I 3338.2.2 Compound II 333

8.2.4 Role of Trp 179 335

9 Substrate Recognition 335

10 Redox Properties 337

11 Inactivation 33911.1 Inactivation by Cyanid 339

1.3 Adenosylcobalamin-Dependent Enzymes 3551.4 Outline Mechanism of Adenosylcobalamin-Dependent

Rearrangements 3571.5 Ribonucleotide Reductase 358

1.7 Longstanding Questions 360

2 Strucural Features of Adenosylcobalamin-Dependent

Enzymes 3612.1 Cobalamin Binding by Enzymes Containing the

D-x-H-x-x-G Motif 3622.2 Substrate Binding and Initiation of Catalysis 3692.3 Structure of Diol Dehydrase 371

3 Mechanistic Aspects of Adenosylcobalamin-Mediated

Catalysis 3753.1 Homolysis of Adenosylcobalamin and the Formation

of Substrate Radicals 3753.1.1 EPR Studies on Adenosylcobalamin Enzymes 3753.1.2 Stopped-Flow Studies of Adenosylcobalamin

Homolysis 3773.1.3 Magnetic Field Effects on Adenosylcobalamin-

Dependent Reactions 3813.1.4 Resonance Raman Experiments 3823.1.5 Role of the Axial Ligand in Catalysis 3843.2 Rearrangement of Substrate Radicals 3863.2.1 Mechanistic Studies on Methylmalonyl-

CoA Mutase 3903.2.2 Mechanistic Studies on Glutamate Mutase 391

4 Perspective 394

5 References 397

Chapter 12

Ribonucleotide Reductaseóa Virtual Playground for

Electron Transfer Reactions

Margareta Sahlin and Britt-Marie Sjˆberg

1 Introduction 405

2 Three Different Ribonucleotide Reductase Classes 406

3 Reaction Mechanism 4103.1 Radical Chemistry at Work 4103.2 Substrate Analogues

412

3.3 Studies in Active Site Mutant Enzymes

4 Class I ribonucleotide ReductaseóThe Radical Transfer

Pathway 4.1 Protein R1 4.2 Protein R2 4.2.1 The Tyrosyl Radical and the Iron Centre 4.2.2 A Hydrogen-Bonded Triad 4.2.3 The Flexible C-Terminal Domain 4.2.4 Is the Tyrosyl Radical H-Bonded to the

Radical Transfer Pathway? 4.3 Theoretical Considerations on Radical Transfer and

Protein Dynamics

5 Generation of the Stable Tyrosyl Radical in Protein R2 .5.1 Radical Generation Involves the Radical Transfer

Pathway 5.2 Interactions between Metal Sites 5.3 Non-Native Radicals and Secondary Radical Transfer

Pathways Observed in Mutant R2 Proteins 5.4 Unexpected Hydroxylation Reactions

6 Stability of the Tyrosyl Radical 6.1 Different Tyrosyl Radical Conformers 6.2 The Tyrosyl Radical Environment 6.3 Radical Stability during Catalysis

7 Radical Transfer Reactions in Class II and III

Ribonucleotide Reductases 7.1 Class II Ribonucleotide Reductases 7.2 Class III Ribonucleotide Reductases

they Catalyse 1.2 Sequence Homologies and Classification of the

Molybdenum Enzymes 1.3 Structural and Catalytic Variations within the Three

Families of Molybdenum Enzymes

2 The Molybdenum Hydroxylases 2.1 Structural Studies

413415418418418420421422422424424428429431431431433433434434434436

445445446451453453

2.2 Mechanistic Aspects 458

3 The Eukaryotic Oxotransferases 4653.1 Structural Studies 4653.2 Mechanistic Aspects 468

4 The Prokaryotic Oxotransferases 4724.1 Structural Studies 4724.2 Mechanistic Aspects 475

Anaerobic Microbes 4871.1.1 Why CO? 4871.1.2 Where Does the CO Come from and Where

Does It Go? 4891.1.3 Why H2? 4891.1.4 Where Does the H2Come from and Where

Does It Go? 4901.1.5 Supercellular Biochemistry: Interspecies H2

Transfer 4901.2 Introduction to the Enzymes 4911.2.1 CO Dehydrogenase and Acetyl-CoA Synthase 4911.2.2 Hydrogenase 491

2 CO Oxidation and CO2 Reduction by CO Dehydrogenase 4932.1 The Catalytic Redox Machine: a NióFeóS Cluster 4932.2 The Intramolecular Wire 4952.3 The Intermolecular Wires: How Electrons Enter and

Exit CO Dehydrogenase 4952.4 By Channel or by Sea? How Carbon Enters and Exits

CO Dehydrogenase 4962.5 Coupling CO2 Reduction and Acetyl-CoA Synthesis 4962.6 Acetyl-CoA Synthase: Another Catalytic NióFeóS

Cluster 497

3 H2Oxidation and Proton Reduction by Hydrogenase 4993.1 The Catalytic Redox Machine: NióFeóS and

FeóFeS Clusters 4993.1.1 The NióFe Hydrogenase 499

3.1.2 The NióFe Regulatory Hydrogenase 5043.1.3 The Fe-Only Hydrogenase 5043.1.4 Models of Hydrogenase 5053.1.5 The Metal-Free Hydrogenase 5053.2 Proton Transfer Pathway 5063.3 The Intramolecular Wire 5083.4 The Intermolecular Wires: How Electrons Enter and

Exit Hydrogenase 5103.5 Tunnel-Diodes and Catalytic Bias 510

Chapter 16

Mitochondrial Cytochrome bc1 Complex

ZhaoLei Zhang, Edward A Berry, Li-Shar Huang, and

Sung-Hou Kim

1 Introduction

2 Crystal Structure of a bc1Complex 5462.1 bc1 Complex is a Homodimer as a Functional Unit 5472.2 Cytochrome b and Two Haems 5492.3 Cytochrome c1 5502.4 Alternative Conformations of Rieske Protein and

Cross-Transfer of Electrons 5532.5 The Two Core Proteins and Subunit 9 5572.6 Other Subunits without Prosthetic Groups 559

3 Quinone Reactions and Electron Transfer by bc1Complex 561

541

3.1 Quinone Reduction at QiSite 5613.2 Quinone Oxidation at QoSite 5663.3 The ìDomain Shuttleî Mechanism 5693.4 Bifurcated Reaction at QoSite 571

5852.4 Subunit Composition and Amino Acid Sequences 589Function of Bovine Heart Cytochrome c Oxidase 5903.1 Enzymic Activity 5903.2 Reduction of O2 592Crystallisation of Bovine Heart Cytochrome c Oxidase 5964.1 Crystallisation of Membrane Proteins 5974.2 Crystallisation of Cytochrome c Oxidase 597X-ray Structure of Bovine Heart Cytochrome c Oxidase 599

Cytochrome c Oxidase 611References 616

Chapter 18

Reaction Centres of Purple Bacteria

Marion E van Brederode and Michael R Jones

1 Introduction 621

2 Structure of the Bacterial Reaction Centre 622

Summary and Perspective

Redox-Active Metal Sites

Three-Dimensional Structure of the Protein Portion

Reduction Mechanism 607

2.1 The Structures of the Rhodopseudomonas viridis and

Rhodobacter sphaeroides Reaction Centres .

2.2 Recent Structural Information Relating to Function 2.3 Structures of Mutant Complexes 2.4 Electronic Structure: The Reaction Centre AbsorbanceSpectrum

3 The Mechanism of Energy Storage by the Bacterial

Reaction Centre 3.1 Primary Photochemistry 3.2 Ubiquinol Formation and Re-Reduction of P+ .3.3 Light-Driven Cyclic Electron Transfer Coupled to

Proton Translocation

4 .4.1 Non-Adiabatic Electron Transfer 4.2 Adiabatic Electron Transfer

5 Studies of Ultrafast Electron Transfer in a Light-Activated

Protein 5.1 The Role of the BAMonomeric BChl 5.2 The Asymmetry of Primary Electron Transfer 5.2.1 Evidence for the Asymmetry of Primary

Electron Transfer 5.2.2 Origins of the Asymmetry of Primary Electron

Transfer 5.2.3 Re-Routing Primary Electron Transfer 5.3 Temperature DependenceóActivationless Reactions 5.4 Dispersive Kinetics: Heterogeneity or Protein

Dynamics? 5.5 Femtosecond Biology: Coherent Nuclear Dynamics

Studied in Populations of Proteins 5.6 Modulation of the Time Constant for Primary

Electron Transfer between 200fs and 500ps through

Site-Directed Mutagenesis 5.6.1 Tyrosine M210 5.6.2 Hydrogen Bond Mutants 5.7 Parallel Pathways for Primary Electron Transfer

6 Summary

7 References

Index

622625626627628631633634634635639640641643643644646650651654

656657658661665665677Biological Electron Transfer

Electron Transfer in Natural Proteins

Theory and Design

Christopher C Moser, Christopher C Page,

Xiaoxi Chen, and P Leslie Dutton

1 INTRODUCTION

Biochemical catalysis and redox energy conversion requires the ing of electron transfer from site to site within proteins Yet, the proteininterior is a good electrical insulator More than 30 years ago, Devault &Chance (Devault and Chance, 1966) made it clear that Nature relies on elec-tron tunneling to move electrons over tens of ≈ngstroms In flash activatedphotosynthetic membranes, visible spectroscopy can monitor heme andchlorophyll oxidation and reduction electron transfer kinetics down toliquid helium temperatures At temperatures below 100K, electron trans-fer kinetics became temperature independent, the hallmark of quantumtunneling reactions While thermal energy may be insufficient to classicallycarry the electron over the insulating barrier, quantum tunneling throughthe energy barrier is still possible Electron tunneling, undeniable in

engineer-CHRISTOPHER C MOSER, engineer-CHRISTOPHER C PAGE, XIAOXI CHEN and P LESLIE DUTTON Johnson Research Foundation, Department of Biochemistry and Biophysics,

University of Pennsylvania, Philadelphia, PA 19104.

Subcellular Biochemistry, Volume 35: Enzyme-Catalyzed Electron and Radical Transfer, edited

by Holzenburg and Scrutton Kluwer Academic / Plenum Publishers, New York, 2000.

1

photosynthetic membranes at low temperatures, was soon seen to be active

in other systems at physiological temperatures as well

An appreciation of the basic parameters of electron tunneling theoryand a survey of the values of these parameters in natural systems allows us

to grasp the natural engineering of electron transfer proteins, what elements

of their design are important for function and which are not, and how theyfail under the influence of disease and mutation Furthermore, this under-standing also provides us with blueprint for the design of novel electrontransfer proteins to exploit natural redox chemistry in desirable, simplified

de novo synthetic proteins (Robertson et al., 1994).

2 BASIC ELECTRON TUNNELING THEORY

A strict quantum mechanical calculation of a tunneling system thesize of a protein quickly becomes intractably complex Fortunately, rela-tively simple theory has been successful at organizing and predictingelectron tunneling rates in proteins When the donor and acceptorredox centers are well separated, non-adiabatic electron transfer theoryapplies Fermiís Golden Rule, in which the rate of electron transfer is pro-portional to two terms, one electronic, H ≤ ab, and the other nuclear, F C

of the barrier height in eV Thus for typical biological redox centers thatmust overcome a barrier of about 8eV to be ionized in a vacuum, we canestimate the β for exponential decay of electron transfer in vacuum to beabout 2.8≈ ñ1 Much less of a barrier is presented by a surrounding organic

medium, where the positively charged nuclei can interact favorably with theelectron Studies of the distance dependence of electron transfer betweendonors and acceptors bridged by rigid covalent linkers and dissolved in anorganic solvent or in monolayers on electrodes (Moser et al., 1992; Smalley

et al., 1995) shows β of 0.7 to 0.9≈ ñ1, the larger β corresponding to a barrier

of about 0.8eV The protein medium presents a barrier between theseextremes In the absence of an intervening structure that is unusually wellbonded or unusually loosely packed, the protein displays an average barrieraround 2eV, with a β usually quite close to 1.4≈ ñ1(Moser et al., 1992) Note

that for redox centers with extremely high midpoint potentials (above 1 e Vrelative to hydrogen electrode, including many radical centers such as thosefound in ribonucleotide reductase or photosystem II) the barrier might beexpected to be smaller However, with the small set of experiments avail-able, there is no clear indication so far that β is different for high potentialradical electron transfer mechanisms

No matter what the value of β , the rate of electron tunneling will

be fastest at short distances There appears to be a practical upper limit

on the rate of electron tunneling at distances that approach van derWaals contact of around 1013sñ1, both in chemical systems and in manyproteins (Moser et al., 1992) This limiting rate may be a reflection of

the characteristic time of vibration and hence nuclear rearrangement thattakes place upon electron transfer With the seemingly reasonable assump-tion that the 1013limit is appropriate for proteins in general, Eq (2) and the

β values described above permit an estimate of the maximal rate ofelectron tunneling in any system at a given distance, or conversely, themaximum distance at which an observed tunneling rate can take place(Figure 1)

2.1 Classical Free Energy and Temperature Dependence of Tunneling

The second term of Fermiís Golden Rule depends on the changingposition of the atomic nuclei upon electron transfer and is abbreviated as

FC, for Franck-Condon The nuclei assume different lowest energy

geome-tries when the electron is on the donor as compared to the acceptor Forexample, polar solvent molecules and protein groups will point in differentdirections, and the lengths of chemical bonds within the redox centers them-selves will change as the centers are oxidized and reduced However, in non-adiabatic electron transfer theory, the electron tunnels from the donor toacceptor only if the nuclear geometry is such that the energies immediatelybefore and after electron transfer are momentarily the same Marcus pro-vided a simple and successful description of this process by introducingthe term reorganization energy λ: the energy required to distort the

FIGURE 1 The maximum electron tunneling rate depends on the distance between donor

and acceptor and the effective height of the tunneling barrier, decaying rapidly with distance (exponential slope β).

equilibrium geometry of the reactant into the equilibrium geometry of theproduct, but without allowing the electron transfer to take place (Marcus,1956; Marcus and Sutin, 1985)

In Figure 2, the reactant and product describe simple harmonic tials as the nuclei are displaced from their equilibrium positions at thebottom of the parabolas If the reaction is exothermic, then the productparabola will be ∆G lower in energy To displace the nuclei of the reactant

poten-to the geometry of the product requires an input of energy λ, the nization energy In this symmetric description, the same reorganizationenergy λ is required to distort product nuclei to resemble the reactantgeometry The crossing point of these surfaces where electron tunneling cantake place, requires the following activation energy:

reorga-(3)Thus, classical Marcus theory predicts an electron transfer rate that has

a Gaussian dependence on the free energy of the reaction (Marcus, 1956;Marcus and Sutin, 1985)

FIGURE 2 The Marcus expression can be understood in terms of reactant and product

potential surfaces approximated as simple harmonic oscillations of the nuclei The equilibrium position of the nuclei at the bottom of the reactant potential well (1) changes to a new equi- librium position in the product potential well (2) releasing free energy ∆G The energy required

to distort the reactant nuclei (1) so that they resemble the product equilibrium geometry, but without allowing electron transfer (3) defines the reorganization energy λ The potential sur-

faces intersect and define an activation energy E Ü

(4)

When the driving force of the reaction matches the reorganizationand the reaction is activationless and free energy optimized Because of theclassical kBT term of the Marcus description, the Gaussian dependence ofthe rate on ∆ G becomes increasingly narrow as the temperature falls, sothat at cryogenic temperatures if the electron transfer is observed at all, ithas an extremely steep free energy dependence

A counter-intuitive prediction of the Marcus theory is that ing the reaction, so that ∆G < ñ λ , causes the activation energy to rise againand the reaction to slow (Figure 3) The Marcus inverted region has beenobserved clearly in a number of synthetic chemical systems in which it ispossible to vary the driving force of the reaction over a range greater than

overdriv-1 e V (Closs et al., 1986; Miller et al., 1984).

The free energy dependence of a number of electron tunneling tions in natural proteins can be approximated by a Gaussian free energydependence (Moser et al., 1992) The free energy can be varied either by

reac-extracting protein redox centers and replacing them with analogous exoticenergy, ∆G = ñ λ , the surfaces intersect at the bottom of the reactant well

energy, ∆G = ñλ.

FIGURE 3 Marcus theory predicts a Gaussian

dependence of the electron transfer rate ket on free energy ∆G, which appears as a parabolic depen-

dence on a log plot The maximum rate is found when the driving force matches the reorganization

centers that have different redox midpoint potentials, or by making tional changes in the medium around the proteins to effect changes inthe redox properties (Gunner et al., 1986; Gunner and Dutton, 1989;

muta-Giangiacomo and Dutton, 1989; Okamura and Feher, 1992; Lin et al., 1994;

Labahn et al., 1994) The photosynthetic reaction center (RC) provides

several examples of both types of changes It is generally difficult to vary thefree energy over so great a range that the inverted region can be clearly exp-lored Although there appear to be some examples of the inverted region inaction in natural redox proteins (Franzen et al., 1992; Dutton and Moser,

1994; Moser et al., 1995), more experiments are needed before the effect is

no longer controversial Somewhat greater freedom to explore the freeenergy dependence of tunneling in proteins can be achieved by modifyingproteins to introduce extra, potentially light-activatable redox centers,usually on the outside of the proteins (Pan et al., 1988; Onuchic et al., 1992).

The reorganization energies experimentally defined for natural tron transfer reactions cover a range depending on the cofactors themselvesand polarity of the cofactor environment Typical reorganization energiesfor redox cofactors buried in a protein are 0.6 to 1eV Reorganization ener-gies will tend to be larger for redox centers that are small (a few atoms)and concentrate the change in charge upon oxidation/reduction and thustend to have large local changes in the electric field Reorganization ener-gies may be as large as 1.4eV for redox centers that are near an aqueoussurface where nearby polar molecules can reorient Reorganization ener-gies will be smaller for redox centers that are large (like chlorophylls) anddistribute charge changes, are buried far from the aqueous phase, or par-ticipate in rapid electron transfers in which there is little time for dramaticreorganization All of these conditions appear to conspire to make the reor-ganization of the initial charge separation in photosynthetic reactioncenters as small as 0.2eV (Parson et al., 1990) or even smaller (Jia et al.,

elec-1993; Parson et al., 1998).

2.2 Quantum Free Energy and Temperature Dependence

Intraprotein electron tunneling studies in which both the free energyand the temperature have been varied over large ranges are rare Excellentexamples are provided by photosynthetic reaction centers in which quinonesubstitution has varied ∆G by more than 0.5eV and temperature has rangedfrom 300 to 10K (Gunner et al., 1986; Gunner and Dutton, 1989) While the

free energy dependence of these reactions is roughly Gaussian, it is clear,especially at lower temperatures, that the Gaussian is considerably broaderthan the classical Marcus expression of Eq (4) Apparently, these electron-tunneling reactions are coupled to nuclear rearrangements or vibrationsthat are larger than the room temperature thermal energy kBT, about

25 meV Thus, the classical Marcus expression should be replaced by a tized version, such as the exact but somewhat complicated quantummechanical harmonic oscillator expression (Levich and Dogonadze, 1959;Jortner, 1976) or the simpler semi-classical expression of Hopfield(Hopfield, 1974), which retains the Gaussian form,

of the difficulties of performing these extensive experiments, there arenot enough comparable studies to determine if this value is essentiallyuniversal for all intraprotein electron transfers Nevertheless, rate calcula-tions using this value are usually quite successful at predicting electrontransfer rates

In principle it should be possible to determine the reorganizationenergy simply by examining the temperature dependence of the reaction

to determine the activation energy, without the need to replace naturalredox centers with exotic cofactors, or mutational changes to modulate mid-point potentials However, this method is fraught with traps for the unwary.First, it may be more appropriate to use the semi-classical version of the

FC in Eq (6) rather than the commonly used Marcus expression of Eq (3).Second, the activation energy measured may instead be of a reactioncoupled to electron transfer, such as proton binding or release or diffusionalmotions of redox centers, rather than the electron tunneling itself Thisshould immediately be suspected if calculated reorganization energies arelarger than 1.5eV (Davidson, 1996) or if the rates seem to be significantlyslower than that predicted by Eq (7) Thus the variation of the free energy

of the reaction by chemical or even applied electric field methods providesthe most secure way to determine if the observed rate is limited by the rate

of electron tunneling It is also the most secure way to find the tion energy and the free energy optimized tunneling rate

reorganiza-Reaction center experiments show that the electron transfer rate is notvery sensitive to the detailed chemical nature of the donor and acceptor.Thus ubiquinone can be replace by naphthoquinones, anthraquinones,fluorenones and even dinitrobenzenes (Warncke and Dutton, 1993; Moser

et al., 1992), yet all these species can still be embraced by a single broad

Gaussian free energy dependence

2.3 A Generic Protein Tunneling Rate Expression

Equations 1,2 and 5 can be combined into an extremely useful ical expression that estimates room temperature electron tunneling ratesfor all proteins to within about an order of magnitude (Moser and Dutton,1992):

empir-(7)where ke t is in units of sñ1, R in ≈ and ∆G and λ in eV In a classical Marcusexpression, the coefficient 3.1 is replaced with 4.2

The variable R, the edge-to-edge distance between cofactors, is clearlythe most important variable in predicting the electron transfer rate A prac-tical definition of R identifies the atoms which make up a biological redoxcofactors to include all atoms making up the aromatic/conjugated systems

of porphyrins, chlorophylls, flavins, pterins, amino acid radicals andquinones, including oxygens attached to the quinone rings, as well as themetal atoms in redox centers and the immediate atoms liganded to thesemetals Thus, a heme will have 27 atoms, a 2Fe2S center 8 atoms and a Cucenter only 5

The explosion in recent years of newly resolved crystal structures ofelectron transfer proteins makes it possible to estimate R and hence elec-tron tunneling rates for many systems by using Eq (7) together with freeenergies estimated from redox midpoint potentials of donor and acceptor,

and estimates of λ based on the likely polarity of the redox center ronments If λ is moderately well defined, Eq (7) predicts electron-tunneling rates with an uncertainty of about an order of magnitude or less.Once an appropriate crystal structure is known, an unknown λ may con-tribute the largest uncertainty in the tunneling rate calculation, since manybiological free energies are close to zero.

envi-3 PROTEIN STRUCTURAL HETEROGENEITY

The free energy optimized rate can be used to compare different tron tunneling reactions in different proteins and re-examine the electronicterm and the tunneling barrier of Eq (2) Because the heterogeneity of theprotein medium can change the height of the barrier, it is possible in prin-ciple for natural selection to favor a well bonded tightly packed medium toaccelerate productive electron transfers and to favor a poorly bonded,loosely packed medium between centers which can engage in unproductive,energy-wasting electron transfers Indeed, one might imagine that billions

elec-of years elec-of evolution would optimize protein structures for electrontunneling

A general method is needed to examine the structure between redoxcenters to determine if the barrier for any given productive or unproduc-tive reaction is larger or smaller than average A full quantum mechanicalcalculation being impossibly complex, various methods of different degrees

of complexity using different sets of approximations have been used.One popular general method searches for the shortest set of connectedbonds and short through-space gaps to define a path between redox centers,and then applies a rate penalty for each bond and a greater, distance depen-dent penalty for each through space gap (Beratan et al., 1991; Onuchic et al., 1992) Applying this method to a series of analogous reactions allows

the parameters to be adjusted to fit existing experimental rates This methodsuccessfully identifies protein regions that are more or less well bonded andare generally correlated with faster or slower tunneling

Users of this method often give the impression that the pathway soidentified, rather than the whole medium between the centers, is responsi-ble for guiding the tunneling electron rather like a wire The original authorshave tried to guard against this interpretation by introducing the concept

of ìtubesî rather than a single pathway (Curry et al., 1995) Nevertheless,

there is often a belief that the identified pathway has been naturally selected

to guide the electron and that changes to the pathway, for example throughmutagenesis, will spoil the electron tunneling rate In fact, a careful muta-genic crystallographic, electrochemical and kinetic series in the reaction

centers shows this is not the case (Dohse et al., 1995) Mutations often have

minor effects on tunneling rates that can be understood in terms of smallchanges in R, ∆G and λ (Page et al., 1999).

Other methods assay the protein structure without emphasizing abest path Kuki describes a conceptually attractive method using MonteCarlo sampling to simulate the scattering of the tunneling electron frommultiple centers in the protein on its way from donor to acceptor (Kuki andWolynes, 1987) Not surprisingly, this method shows that a cylindrical

to roughly ellipsoidal region of the protein containing the redox centers

as foci is most significant in determining the efficiency of electrontunneling

3.1 Monitoring Heterogeneity via Packing Density

The simplest method to assay protein heterogeneity uses a basic, easilyappreciated parameter, the density of the protein packing between redoxcenters The packing method distinguishes regions that are relativelydensely packed, well-bridged and have experimentally small β, from moreloosely packed regions that are experimentally associated with larger β(Page et al., 1999).

There are a number of ways to estimate the packing density if a proteinstructure is available We sample the region between donor and acceptor

by drawing lines from every donor atom to every acceptor atom and mine the fraction of the lines that falls within the united van der Waalsradius of a medium atom, ignoring any part of the lines that may passthrough cofactor atoms Because published structures usually do notinclude hydrogen atoms, we use the united-atom approximation which com-pensates for the missing hydrogens by multiplying the van der Waals radius

deter-of the heavier atoms by 1.4 Structures deter-often do not include atoms such aswater molecules that do not have a well defined position, but are likely to

be present in any real structure Thus we solvate structures using a ular graphics program, such as Sybyl, to make sure we are not working withunrealistically large voids

molec-Packing densities of proteins estimated by various means averageabout 75% (Levitt et al., 1997) When we examine the presumably arbitrary

protein interior packing between redox centers and aromatic residues Tyr,and Phe in 6 large proteins, including cytochrome oxidase and nitrogenase,

we find the packing follows a roughly Gaussian distribution with mean

ρ = 0.77 and standard deviation σ = 0.09 (gray background of Figure 4) Thepacking between synthetic donor and acceptor systems linked by a rigidcovalent bridges and associated with a β = 0.9 ≈ ñ1, is much higher, usuallybetween 0.9 and 1.0

FIGURE 4 Histograms of protein packing for productive (dark) electron transfers,

unpro-ductive (light) electron transfers and arbitrary (gray) chemical groups A Packing in synthetic reaction centers of Rb sphaeroides and Rp viridis B Packing in 63 redox reactions

photo-in multi-center protephoto-ins available photo-in the PDB, photo-includphoto-ing only one representative species per type of oxidoreductase.

We can turn this packing density into a β estimate by taking thepacking density weighted average of β = 0.9≈ ñ1

for the fraction of the vening medium within atoms and β = 2.8≈ ñ1 for the ìvacuumî regionoutside atoms

inter-(8)This permits an enhanced tunneling rate estimate based on Eq (7)

(9)where R is the edge-to-edge distance in ≈, and ∆G and λ are in eV asbefore

A comparison of the calculated vs experimental ∆G optimized neling rates for the productive charge separating electron transfers in twobacterial photosynthetic reaction centers shows that rate estimates have astandard deviation of 0.5 log units, or about a factor of 3 (Figure 5) Con-sidering the experimental errors of determining ∆G and especially λ, oreven the uncertainties in R of a dynamic protein, it is not clear that a cal-culation any more involved than the one we have just described is usuallyjustified

tun-A histogram of the ρ for these reaction centers shown in figure 4Ashows that ρ is distributed much as in the presumably arbitrary packingbetween cofactors and aromatic amino acids There is no tendency forproductive charge separation reactions to be accelerated by good packing