Spin-label electron paramagnetic resonance spectroscopy:
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| Beschreibung: | xvii, 495 Seiten Diagramme |
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| 100 | 1 | |a Marsh, Derek |e Verfasser |0 (DE-588)1031679154 |4 aut | |
| 245 | 1 | 0 | |a Spin-label electron paramagnetic resonance spectroscopy |c Derek Marsh, Max-Planck-Institut für biophysische Chemie, Göttingen, Germany |
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c [2020] | |
| 300 | |a xvii, 495 Seiten |b Diagramme | ||
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| 337 | |b n |2 rdamedia | ||
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| adam_text | Contents Preface Author xv xvii 1 Introduction 1.1 Introduction 1.2 Electron Spin, Magnetic Moment and Resonance Absorption 1.3 Angular Anisotropy of the Nitroxide Spectrum 1.4 Rotational Dynamics and Spin-Label Lineshapes 1.5 Transition Probabilities and Selection Rules 1.6 Spin-Lattice Relaxation and Saturation 1.7 Spin-Spin Relaxation and Linewidths Appendix A1 : SpinLabels Recommended Reading 2 The Nitroxide EPR Spectrum 2.1 Introduction 2.2 Nitroxide Spin Hamiltonian 2.3 Angular Variation of Nitroxide EPR Spectra 2.4 EPR Powder Patterns 2.5 Inhomogeneous Broadening 2.6 Voigt Lineshapes and Spectral Convolution 2.7 Concluding Summary Appendix A2: Spin-Hamiltonian Tensors References 3 Hyperfine Interactions and g-Values 3.1 Introduction 3.2 Hückel Molecular Orbitals for a Nitroxide 3.3 Isotropic Nitrogen Hyperfine Couplings 3.4 Anisotropic Nitrogen Hyperfine Couplings 3.5 Paramagnetic Shifts in Nitroxide NMR 3.6 13C-Hyperfine Couplings 3.7 13C-Hyperfine Couplings of ß-C Atoms 3.8 Proton Hyperfine Couplings 3.9 17O-Hyperfine Couplings 3.10 14N-Quadrupole Couplings 3.11 Electric Field Gradients and p-Orbital Occupancies 3.12 g-Tensor of Nitroxides 3.13 Concluding Summary Appendix A3.1 : Electron Spin Densities of Nitroxides Appendix A3.2:ProtonHyperfine Couplings of Nitroxides References 4 Polarity Dependence 4.1 4.2 Introduction Aprotic Environments 4.2.1 Reaction Fields 4.2.2 Onsager and Block-Walker Models for the Reaction Field 4.2.3 Influence of Local Electric Fields on Nitroxides 4.2.4 Isotropic Hyperfine Couplings in Aprotic Media 1 1 3 3 5 7 7 9 10 11 13 13 13 15
16 20 21 23 25 28 29 29 29 30 31 33 34 35 38 38 40 41 42 44 45 46 48 51 51 51 51 52 54 55 vii
viii Contents Local Fields from Fixed Electric Charges or Dipoles 4.3.1 Effect of Fixed Electric Charges on Hyperfine Couplings 4.3.2 Effect of Fixed Electric Dipoles on Hyperfine Couplings 4.3.3 Effect of Polarity and Fixed Charges on Isotropic g-Values 4.4 Protic Environments 4.4.1 Isotropic Hyperfine Couplings in Protic Media 4.4.2 Isotropic 17O-Hyperfine Couplings inProtic Media 4.4.3 Isotropic g-Va lues in Protic Media 4.4.4 g-Tensor Anisotropy in Protic Media 4.5 Quadrupole Interactions and Polarity: 14N-ESEEM of Nitroxides 4.6 Membrane Polarity Profiles 4.7 Concluding Summary References 4.3 5 Spin Relaxation Theory Introduction Time-Dependent Perturbation Theory for Random Fluctuations: Correlation Functions Spin Hamiltonian and Angular Averages Transition Probabilities for a Nitroxide 5.4.1 Electron Spin Relaxation 5.4.2 Nuclear Spin Relaxation 5.4.3 Cross Relaxation 5.5 Spectral Densities for a Nitroxide 5.5.1 Hyperfine Anisotropy (END) 5.5.2 g-Value Anisotropy (Zeeman Interaction) 5.5.3 END-Zeeman Cross Term 5.5.4 Spin-Rotation Interaction 5.6 Spin-Lattice Relaxation Rates 5.6.1 Electron Spin-Lattice Relaxation 5.6.2 Nuclear Spin-Lattice Relaxation 5.6.3 Cross Relaxation 5.7 Secular, Pseudosecular and Non-secular Transverse Relaxation 5.8 Nitroxide Transverse (Spin-Spin) Relaxation Rates 5.9 Concluding Summary Appendix A5: Transition Probabilities and Transverse Relaxation Rates for Fast Anisotropic Rotational Diffusion A5.1 Electron Spin-Lattice Relaxation A5.2 Nuclear Spin-Lattice Relaxation A5.3 Cross Relaxation A5.4 Electron Transverse Relaxation References
5.1 5.2 5.3 5.4 6 EPR Lineshape Theory 6.1 Introduction 6.2 Bloch Equations and Lorentzian Lineshape 6.3 Exchange-Coupled Bloch Equations 6.4 Bloch Equations with Slow Sudden Jumps 6.5 Bloch Equations Coupled by Slow RotationalDiffusion 6.6 Density-Matrix Methods 6.7 Slow-Motion Simulations: Stochastic Liouville Equation 6.8 A Simple Example: Axial g-Tensor 6.9 Example Including Axial 15N-Hyperfine Structure 6.10 Slow Motion for the Full 14N-Nitroxide 6.11 Composite Motions on Different Timescales 6.12 Concluding Summary Appendix A6.1 : Clebsch-Gordan Coefficients Needed for Slow-Motion Calculations Appendix A6.2: Solution of Stochastic Liouville Equation for Axially Anisotropic Rotation References 56 56 57 58 59 59 61 61 62 65 65 68 69 71 71 71 73 74 74 75 75 75 75 76 76 76 77 77 78 78 78 79 81 82 82 83 83 83 83 85 85 85 87 89 90 92 93 94 96 98 101 102 103 104 105
Contents ¡X 7 Dynamics and Rotational Diffusion 7.1 Introduction 7.2 Rotational Diffusion Equation 7.3 Rotational Friction Coefficients 7.4 Slip Boundary Conditions 7.5 Isotropie Rotational Diffusion 7.6 Anisotropic Rotational Diffusion 7.7 Linewidths and Fast Rotational Motion 7.8 Correlation Times for Fast Isotropic RotationalDiffusion 7.9 Correlation Times for Fast Anisotropic RotationalDiffusion 7.10 Measurements at High Field/Frequency 7.11 Fast Non-axial Rotation and HF-EPR 7.12 Free Rotation and Jump Diffusion 7.13 Slow Rotational Diffusion and Anisotropy 7.14 Slow-Motion Calibrations for Outer Splittingsand Linewidths 7.15 Concluding Summary Appendix A7.1 : Shape Factors for Rotational Dynamics of a General Ellipsoid Appendix A7.2: Spin-Hamiltonian Tensor Anisotropies References 107 W7 107 108 109 110 111 111 112 114 116 118 119 121 121 125 127 128 130 8 Dynamics and Orientational Ordering (Liquid Crystals and Membranes) 8.1 Introduction 8.2 Restricted Torsional Libration 8.3 Orientational Order Parameters 8.4 Motional Models for Uniaxial Order Parameters 8.5 Independent Ordering Components, Segmental Motion 8.6 Restricted Off-Axis Amplitudes and Lateral Ordering (HF-EPR) 8.7 Motional-Narrowing Theory: Linewidths and Order 8.8 Spin-Lattice Relaxation and Cross Relaxation with OrientationalOrdering 8.9 Linewidths and Lateral Ordering 8.10 Angular-Dependent Linewidths and Ordering: Strong Jump Model 8.11 Linewidths and Ordering: Brownian Diffusion 8.12 Ordering and Slow Motion 8.13 Order-Parameter Calculations from Powder Samples 8.14 Dynamics of Combined Slow and
Segmental Motions: Lipid Chains 8.15 Timescale Separation and Multifrequency EPR 8.16 Concluding Summary Appendix A8.1 : Clebsch-Gordon Coefficients Appendix A8.2: Allowance for Nitrogen Nuclear Quantization Axis Appendix A8.3: Slow-Motion Order Parameter Calibrations for Different dr References 133 133 133 134 136 138 139 141 142 144 146 150 153 154 157 160 162 163 163 165 167 9 Spin-Spin Interactions 9.1 Introduction 9.2 Magnetic Dipole-Dipole Interactions - Like Spins and Strong Coupling 9.3 Dipolar Powder Spectra: The Pake Doublet 9.4 Dipolar Coupling of Unlike Spins 9.5 Relaxation by Magnetic Dipole-DipoleInteraction 9.5.1 Dipolar Relaxation by Rotational Diffusion 9.5.2 Dipolar Relaxation by Translational Diffusion 9.5.3 Translational Diffusion Coefficients and Dipolar Relaxation 9.6 Exchange Interaction and Exchange Integral 9.7 Heisenberg Spin Exchange 9.8 Nitroxide Biradicals 9.9 Exchange Probability and Exchange Dynamics 9.10 Spin-Exchange Frequency and EPR Lineshapes 9.11 Exchange-Induced Dispersion 169 169 169 171 173 174 176 177 179 180 181 182 186 187 189
x Contents 9.12 Line Shifts and Re-encounters in Spin-Exchange Spectra 9.13 Translational Diffusion and Friction Coefficients 9.14 Bimolecular Collision Rates and Translational Diffusion 9.15 Spin Exchange Constant and Bimolecular Collisions 9.16 Translational Diffusion in Membranes 9.17 Dipolar-Induced Magnetization Transfer and Dispersion Lineshapes 9.18 Concluding Summary Appendix A9.1 : First-Derivative Absorption Lineshapes with Heisenberg Spin Exchange Appendix A9.2: Broadening, Line Shifts and Dispersion Admixture by Heisenberg Spin Exchange References 10 Spin-Lattice Relaxation 10.1 Introduction 10.2 Effective Spin-Lattice Relaxation Times 10.3 Reduction Factors for CW Electron-Electron Double Resonance (ELDOR) 10.4 Dependence of Spin-Lattice Relaxation on Rotational Dynamics 10.5 Paramagnetic Spin-Lattice Relaxation Enhancement 10.6 Paramagnetic 7¡-Relaxation Enhancements by Heisenberg Exchange 10.7 Paramagnetic Enhancement by Weak/lntermediate Heisenberg Exchange 10.8 Paramagnetic Enhancement by Heisenberg Exchange between Charged Species 10.9 Paramagnetic Enhancement by Static Magnetic Dipole-Dipole Interaction 10.10 Paramagnetic Enhancement by Dynamic Magnetic Dipolar Interaction 10.11 Spin-Lattice Relaxation Enhancement by Exchange Processes 10.12 Relaxation by Slow Two-Site Exchange 10.13 Concentration Dependence of Heisenberg Exchange Between Spin Labels 10.14 Concluding Summary Appendix A10.1 : Effective Spin-Lattice Relaxation Times and ELDOR Reduction Factors for 15N-Nitroxides Appendix A10.2: Further CW-ELDOR Reduction Factors for 14N-Nitroxides Appendix
A10.3: Cross Relaxation and ^-Dependent Intrinsic Spin-Lattice Relaxation Rates for 14N-Nitroxides Appendix A10.4: Heisenberg-Exchange Rate Constants for Paramagnetic Relaxants References 11 Nonlinear and Saturation-Transfer EPR 11.1 Introduction 11.2 Progressive Saturation: Bloch Equations 11.3 Progressive Saturation: Inhomogeneous Broadening 11.4 Field Modulation: Modulation-Coupled Bloch Equations 11.5 Progressive Saturation: Sudden-Jump Rotational Mobility 11.6 Progressive Saturation: Brownian Rotational Diffusion 11.7 Nonlinear Displays: Out-of-Phase Spectra (ST-EPR) 11.8 7,-Sensitive Nonlinear EPR Displays 11.9 First-Harmonic, Out-of-Phase Absorption K-EPR 11.10 Second-Harmonic, Out-of-Phase Absorption V2 -EPR Intensities 11.11 Example of Very Slow Two-Site Exchange in Lipid-Protein Interactions 11.12 Saturation Transfer EPR: Ultraslow Rotational Motion 11.13 Saturation-Transfer EPR: V2 -Lineshapes 11.14 Rotational Diffusion of Membrane Proteins 11.15 ST-EPR Simulations with the Bloch Equations 11.16 Stochastic-Liouville ST-EPR Simulations 11.17 Concluding Summary Appendices: Calibrations of Nonlinear EPR Spectra for Tb and for τκ Appendix A11.1 : Calibrations for 71-Measurements in Progressive-Saturation CW-EPR with Molecular Motion Appendix A11.2: Calibrations for 7¡-Measurements in First-Harmonic Out-of-Phase V/-EPR with Molecular Motion Appendix A11.3: Calibrations for тя in Second-Harmonic Absorption, Out-of-Phase V2 -EPR References 191 193 195 196 198 201 204 205 206 207 209 209 209 211 212 212 214 215 218 219 222 223 223 224 225 227 230 231 233 235 237 237 237
239 241 242 244 245 246 248 249 250 252 253 255 257 258 258 259 259 260 263 263
Contents 12 Saturation-Recovery EPR and ELDOR 12.1 Introduction 12.2 Saturation-Recovery Detection 12.3 Nuclear Relaxation in 15N-and 14N-Nitroxides 12.4 Rate Equations for SR-EPR and SR-ELDOR of 15N-Nitroxides 12.5 Rotational Dynamics and SR-EPR, SR-ELDOR of 15N-Nitroxides 12.6 Rate Equations for SR-EPR and SR-ELDOR of 14N-Nitroxides 12.7 Rotational Dynamics and SR-EPR, SR-ELDOR of 14N-Nitroxides 12.8 Solid-State (Vibrational) Contributions and Glassy Solvents 12.9 Spin-Lattice Relaxation Enhancements in SR-EPR 12.10 Slow Two-Site Exchange and SR-EPR 12.11 Heisenberg Spin Exchange in SR-EPR 12.12 14N-15N Nitroxide Pairs and Heisenberg Exchange 12.13 Slow Rotational Diffusion for SR-ELDOR and SR-EPR 12.14 Saturation-Recovery EPR and Molecular Ordering 12.15 Concluding Summary References 13 Spin-Echo EPR 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 13.12 13.13 13.14 Introduction Microwave Pulses in the Vector Model Finite Pulse Power and Width Vector Model for Primary Spin Echo Product Spin-Operator Method for Primary Spin Echo Density Matrix, Pulses and Transverse Relaxation Primary-Echo Decay and Rotational Dynamics (Phase-Memory Time) Rotational Diffusion and Primary-Echo Decay Stochastic-Liouville Simulations of Primary-Echo Decay Slow-Motion Simulations of Primary-Echo Decay Primary-Echo Decay in Sudden-Jump Model Experimental Phase-Memory Times Primary Echo-Detected Spectra and Librational Dynamics Spin-Spin Interactions and Spectral Diffusion 13.14.1 Jump Model for Short τ 13.14.2 Sudden Jump Model: General Case 13.14.3 Gauss-Markov Model: Long τ 13.15
Spin-Spin Interactions and Instantaneous Diffusion 13.16 Vector Model for Stimulated Echoes 13.17 Unwanted Echoes and Phase Cycling 13.18 Stimulated Echo and Rotational Dynamics 13.19 Stimulated-Echo Decay in Sudden-Jump Model 13.20 Stimulated Echo and Spin-Spin Interaction 13.21 Experimental Stimulated-Echo Decays 13.22 Concluding Summary Appendix A13: Lorentzian Spectral Diffusion A13.1 Conditional Probabilities and Spectral Diffusion A13.2 Echo Decays A13.3 Stationary Probabilities and Spectral Diffusion References xi 267 267 267 268 270 272 274 276 278 279 280 281 283 284 286 287 289 291 291 291 292 294 295 295 296 298 299 300 301 302 303 306 306 308 309 310 312 313 314 315 316 317 318 319 319 319 320 321 14 ESEEM and ENDOR: Hyperfine Spectroscopy 323 Introduction Echo Envelope Modulation Two-Pulse ESEEM for / = į Nuclei Two-Pulse ESEEM for/= 1 Nuclei Three-Pulse ESEEM 323 324 324 326 327 14.1 14.2 14.3 14.4 14.5
xii Contents_____________________________________ ________ ________________________________________________ 14.6 14.7 14.8 14.9 14.10 14.11 14.12 14.13 14.14 Standard Intensities for З-Pulse ESEEM Water-Penetration Profiles and Η-Bonding in 2H-ESEEM ESEEM in Disordered Samples: Powder Spectra ESEEM Powder Lineshapes Electron-Nuclear Double Resonance (ENDOR) Continuous-Wave Proton ENDOR Orientation Selection in Powder ENDOR Distances from ENDOR Frequencies Pulse ENDOR 14.14.1 Davies ENDOR 14.14.2 Example of Davies ENDOR 14.14.3 Mims ENDOR 14.14.4 Example of Mims ENDOR 14.15 ELDOR-Detected NMR 14.15.1 ELDOR-Detected NMR of 15N-Nitroxides 14.15.2 ELDOR-Detected NMR of ,4N-Nitroxides 14.16 Concluding Summary References 15 Distance Measurements Introduction Dipolar Pair Spectra Dipolar Convolution and Deconvolution Dipolar Deconvolution Random Distribution of Spins Absolute-Value First Moment and MeanDipolar Splitting Second Moment of Dipolar Lineshape Gaussian Distance Distributions Statistical Theory of Dipolar Broadeningfor Dilute Spins Echo-Detected ELDOR (DEER) 15.10.1 Three-Pulse DEER 15.10.2 Four-Pulse DEER 15.11 Processing and Analysing 4-Pulse DEER Signals 15.11.1 Background DEER Signal 15.11.2 Spin-Pair Distributions and Spin Counting 15.11.3 Tikhonov Regularization and Gaussian Fitting 15.12 Explicit Distance Distributions in Shells of Uniform Density 15.12.1 Spherical Surface and Volume Distance-Distributions 15.12.2 Sphere-within-Shell Distances 15.12.3 Distance Distribution within Spherical Shell 15.13 Excluded Volume in Background DEER Signals 15.14 Orientation
Selection in DEER Signals 15.15 Concluding Summary Appendix A15.1 : General Expressions for Distance Distribution in Spherical Shells Appendix A15.2: Decay Function a for Excluded Volume References 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 16 Site-Directed Spin Labelling (SDSL) 16.1 16.2 16.3 16.4 16.5 Introduction Side-Chain Accessibilities and Mobilities Nitroxide Scanning: Secondary Structure 16.3.1 Soluble Proteins 16.3.2 Membrane Proteins ß-Sheets and ß-Barrel Proteins Mobility Mapping 16.5.1 Angular Amplitudes 16.5.2 Rotational Rates 329 329 330 331 332 332 333 334 335 335 336 338 338 339 341 342 342 343 345 345 345 346 347 348 349 350 351 353 354 354 356 357 357 358 359 360 360 361 362 363 364 367 368 368 369 371 371 371 372 373 373 375 377 377 378
Contents 16.5.3 Order Parameters MTSSL (R1) Side-Chain Rotamers χ4/χ5 Lineshape Simulations for R1-Side Chains 16.7.1 Water-Exposed Non-interacting Sites on a-Helices 16.7.2 Lipid-Exposed Non-interacting Sites in Transmembrane Helices 16.7.3 Lipid-Exposed Sites on a Transmembrane ß-Barrel 16.7.4 Water-Exposed Residues in ß-Sheets 16.8 Lineshape Simulations from Molecular-Dynamics Trajectories 16.8.1 Order Parameters from MD 16.8.2 Orientation Potentials and SLE Simulations 16.8.3 Brownian Dynamics Trajectories 16.8.4 Spin Hamiltonian and Trajectory of Transverse Magnetization 16.8.5 Fourier Transformation 16.8.6 Trajectories 16.8.7 Discrete Markov States 16.9 SR-EPR: Spin-Lattice Relaxation and Conformational Exchange 16.10 TOAC Spin-Label Residue in Peptides: Helix Orientations 16.11 Distances Between Site-Directed Spin Labels: a-Helices, ß-Strands 16.11.1 α-helices 16.11.2 ß-sheets 16.11.3 Comparison withCrystalStructures 16.12 Rotamer Libraries 16.13 Helix Assembly and Interhelical Distances: Coiled Coils and a-Bundles 16.13.1 Coiled Coils 16.13.2 Example of 4-Stranded CoiledCoil: SNARE Complex 16.13.3 a-Helical Bundles 16.14 Beta-Sheet Topology: Interstrand Separations 16.14.1 a-Crystallin Chaperone Fold 16.14.2 Amyloid Fibril Cross-ß Structure 16.15 DEER and SDSL: Tertiary Fold, Subunits and Docking 16.15.1 Homo-oligomers 16.15.2 Triangulation and Distance Geometry 16.15.3 Distance Restraints in Modelling 16.15.4 Docking Subunits 16.15.5 Conformational Changes 16.16 Concluding Summary Appendix A16: Additional Conformational and Distance Data References 16.6 16.7
Fundamental Physical Constants Symbols Appendices A-M: Fundamentals Appendix A: Units and Conversions Appendix B: Vectors, Matrices and Tensors Appendix C: Quantum Mechanical Basics Appendix D: Schrödinger Equation and Heisenberg Equation of Motion Appendix E: Angular-Momentum/Spin Operators and their Matrix Elements Appendix F: Magnetic Field in Quantum Mechanics Appendix G: Quantum Mechanical Perturbation Theory Appendix H: Spin-Hamiltonian Diagonalization Appendix I: Rotation of Axes Appendix J: Second-Order Hyperfine Shifts Appendix K: Atomic Structure and Molecular Bonding Appendix L: g-Values for a p-Electron Appendix Μ: Time-Dependent Perturbation Theory and Selection Rules References xiii 379 380 383 384 385 386 386 387 387 387 388 388 389 389 390 391 392 394 394 395 395 397 397 397 399 400 401 401 403 403 403 404 405 405 406 406 407 413 417 418 429 429 431 434 436 437 439 440 442 444 446 447 452 453 454
xiv Contents Appendices N-V: Specialist Topics Appendix N: Spin Density-Matrix Appendix 0: Relaxation Theory with Density Matrices Appendix P: Product-Operator Formalism for Pulse EPR Appendix Q: Addition of Angular Momenta and Wigner 3/-symbols Appendix R: Rotation Operators, Euler Angles and Wigner Rotation Matrices Appendix S: Irreducible Spherical Tensors Appendix T: Fourier Transforms, Convolutions and Correlation Functions Appendix (J: Moments of EPR Lineshapes, and Traces of Spin Operators Appendix V: Spherical Harmonics and Legendre Polynomials References 455 455 458 466 472 475 478 481 483 488 490 Index 491
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Contents Preface Author xv xvii 1 Introduction 1.1 Introduction 1.2 Electron Spin, Magnetic Moment and Resonance Absorption 1.3 Angular Anisotropy of the Nitroxide Spectrum 1.4 Rotational Dynamics and Spin-Label Lineshapes 1.5 Transition Probabilities and Selection Rules 1.6 Spin-Lattice Relaxation and Saturation 1.7 Spin-Spin Relaxation and Linewidths Appendix A1 : SpinLabels Recommended Reading 2 The Nitroxide EPR Spectrum 2.1 Introduction 2.2 Nitroxide Spin Hamiltonian 2.3 Angular Variation of Nitroxide EPR Spectra 2.4 EPR Powder Patterns 2.5 Inhomogeneous Broadening 2.6 Voigt Lineshapes and Spectral Convolution 2.7 Concluding Summary Appendix A2: Spin-Hamiltonian Tensors References 3 Hyperfine Interactions and g-Values 3.1 Introduction 3.2 Hückel Molecular Orbitals for a Nitroxide 3.3 Isotropic Nitrogen Hyperfine Couplings 3.4 Anisotropic Nitrogen Hyperfine Couplings 3.5 Paramagnetic Shifts in Nitroxide NMR 3.6 13C-Hyperfine Couplings 3.7 13C-Hyperfine Couplings of ß-C Atoms 3.8 Proton Hyperfine Couplings 3.9 17O-Hyperfine Couplings 3.10 14N-Quadrupole Couplings 3.11 Electric Field Gradients and p-Orbital Occupancies 3.12 g-Tensor of Nitroxides 3.13 Concluding Summary Appendix A3.1 : Electron Spin Densities of Nitroxides Appendix A3.2:ProtonHyperfine Couplings of Nitroxides References 4 Polarity Dependence 4.1 4.2 Introduction Aprotic Environments 4.2.1 Reaction Fields 4.2.2 Onsager and Block-Walker Models for the Reaction Field 4.2.3 Influence of Local Electric Fields on Nitroxides 4.2.4 Isotropic Hyperfine Couplings in Aprotic Media 1 1 3 3 5 7 7 9 10 11 13 13 13 15
16 20 21 23 25 28 29 29 29 30 31 33 34 35 38 38 40 41 42 44 45 46 48 51 51 51 51 52 54 55 vii
viii Contents Local Fields from Fixed Electric Charges or Dipoles 4.3.1 Effect of Fixed Electric Charges on Hyperfine Couplings 4.3.2 Effect of Fixed Electric Dipoles on Hyperfine Couplings 4.3.3 Effect of Polarity and Fixed Charges on Isotropic g-Values 4.4 Protic Environments 4.4.1 Isotropic Hyperfine Couplings in Protic Media 4.4.2 Isotropic 17O-Hyperfine Couplings inProtic Media 4.4.3 Isotropic g-Va lues in Protic Media 4.4.4 g-Tensor Anisotropy in Protic Media 4.5 Quadrupole Interactions and Polarity: 14N-ESEEM of Nitroxides 4.6 Membrane Polarity Profiles 4.7 Concluding Summary References 4.3 5 Spin Relaxation Theory Introduction Time-Dependent Perturbation Theory for Random Fluctuations: Correlation Functions Spin Hamiltonian and Angular Averages Transition Probabilities for a Nitroxide 5.4.1 Electron Spin Relaxation 5.4.2 Nuclear Spin Relaxation 5.4.3 Cross Relaxation 5.5 Spectral Densities for a Nitroxide 5.5.1 Hyperfine Anisotropy (END) 5.5.2 g-Value Anisotropy (Zeeman Interaction) 5.5.3 END-Zeeman Cross Term 5.5.4 Spin-Rotation Interaction 5.6 Spin-Lattice Relaxation Rates 5.6.1 Electron Spin-Lattice Relaxation 5.6.2 Nuclear Spin-Lattice Relaxation 5.6.3 Cross Relaxation 5.7 Secular, Pseudosecular and Non-secular Transverse Relaxation 5.8 Nitroxide Transverse (Spin-Spin) Relaxation Rates 5.9 Concluding Summary Appendix A5: Transition Probabilities and Transverse Relaxation Rates for Fast Anisotropic Rotational Diffusion A5.1 Electron Spin-Lattice Relaxation A5.2 Nuclear Spin-Lattice Relaxation A5.3 Cross Relaxation A5.4 Electron Transverse Relaxation References
5.1 5.2 5.3 5.4 6 EPR Lineshape Theory 6.1 Introduction 6.2 Bloch Equations and Lorentzian Lineshape 6.3 Exchange-Coupled Bloch Equations 6.4 Bloch Equations with Slow Sudden Jumps 6.5 Bloch Equations Coupled by Slow RotationalDiffusion 6.6 Density-Matrix Methods 6.7 Slow-Motion Simulations: Stochastic Liouville Equation 6.8 A Simple Example: Axial g-Tensor 6.9 Example Including Axial 15N-Hyperfine Structure 6.10 Slow Motion for the Full 14N-Nitroxide 6.11 Composite Motions on Different Timescales 6.12 Concluding Summary Appendix A6.1 : Clebsch-Gordan Coefficients Needed for Slow-Motion Calculations Appendix A6.2: Solution of Stochastic Liouville Equation for Axially Anisotropic Rotation References 56 56 57 58 59 59 61 61 62 65 65 68 69 71 71 71 73 74 74 75 75 75 75 76 76 76 77 77 78 78 78 79 81 82 82 83 83 83 83 85 85 85 87 89 90 92 93 94 96 98 101 102 103 104 105
Contents ¡X 7 Dynamics and Rotational Diffusion 7.1 Introduction 7.2 Rotational Diffusion Equation 7.3 Rotational Friction Coefficients 7.4 Slip Boundary Conditions 7.5 Isotropie Rotational Diffusion 7.6 Anisotropic Rotational Diffusion 7.7 Linewidths and Fast Rotational Motion 7.8 Correlation Times for Fast Isotropic RotationalDiffusion 7.9 Correlation Times for Fast Anisotropic RotationalDiffusion 7.10 Measurements at High Field/Frequency 7.11 Fast Non-axial Rotation and HF-EPR 7.12 Free Rotation and Jump Diffusion 7.13 Slow Rotational Diffusion and Anisotropy 7.14 Slow-Motion Calibrations for Outer Splittingsand Linewidths 7.15 Concluding Summary Appendix A7.1 : Shape Factors for Rotational Dynamics of a General Ellipsoid Appendix A7.2: Spin-Hamiltonian Tensor Anisotropies References 107 W7 107 108 109 110 111 111 112 114 116 118 119 121 121 125 127 128 130 8 Dynamics and Orientational Ordering (Liquid Crystals and Membranes) 8.1 Introduction 8.2 Restricted Torsional Libration 8.3 Orientational Order Parameters 8.4 Motional Models for Uniaxial Order Parameters 8.5 Independent Ordering Components, Segmental Motion 8.6 Restricted Off-Axis Amplitudes and Lateral Ordering (HF-EPR) 8.7 Motional-Narrowing Theory: Linewidths and Order 8.8 Spin-Lattice Relaxation and Cross Relaxation with OrientationalOrdering 8.9 Linewidths and Lateral Ordering 8.10 Angular-Dependent Linewidths and Ordering: Strong Jump Model 8.11 Linewidths and Ordering: Brownian Diffusion 8.12 Ordering and Slow Motion 8.13 Order-Parameter Calculations from Powder Samples 8.14 Dynamics of Combined Slow and
Segmental Motions: Lipid Chains 8.15 Timescale Separation and Multifrequency EPR 8.16 Concluding Summary Appendix A8.1 : Clebsch-Gordon Coefficients Appendix A8.2: Allowance for Nitrogen Nuclear Quantization Axis Appendix A8.3: Slow-Motion Order Parameter Calibrations for Different dr References 133 133 133 134 136 138 139 141 142 144 146 150 153 154 157 160 162 163 163 165 167 9 Spin-Spin Interactions 9.1 Introduction 9.2 Magnetic Dipole-Dipole Interactions - Like Spins and Strong Coupling 9.3 Dipolar Powder Spectra: The Pake Doublet 9.4 Dipolar Coupling of Unlike Spins 9.5 Relaxation by Magnetic Dipole-DipoleInteraction 9.5.1 Dipolar Relaxation by Rotational Diffusion 9.5.2 Dipolar Relaxation by Translational Diffusion 9.5.3 Translational Diffusion Coefficients and Dipolar Relaxation 9.6 Exchange Interaction and Exchange Integral 9.7 Heisenberg Spin Exchange 9.8 Nitroxide Biradicals 9.9 Exchange Probability and Exchange Dynamics 9.10 Spin-Exchange Frequency and EPR Lineshapes 9.11 Exchange-Induced Dispersion 169 169 169 171 173 174 176 177 179 180 181 182 186 187 189
x Contents 9.12 Line Shifts and Re-encounters in Spin-Exchange Spectra 9.13 Translational Diffusion and Friction Coefficients 9.14 Bimolecular Collision Rates and Translational Diffusion 9.15 Spin Exchange Constant and Bimolecular Collisions 9.16 Translational Diffusion in Membranes 9.17 Dipolar-Induced Magnetization Transfer and Dispersion Lineshapes 9.18 Concluding Summary Appendix A9.1 : First-Derivative Absorption Lineshapes with Heisenberg Spin Exchange Appendix A9.2: Broadening, Line Shifts and Dispersion Admixture by Heisenberg Spin Exchange References 10 Spin-Lattice Relaxation 10.1 Introduction 10.2 Effective Spin-Lattice Relaxation Times 10.3 Reduction Factors for CW Electron-Electron Double Resonance (ELDOR) 10.4 Dependence of Spin-Lattice Relaxation on Rotational Dynamics 10.5 Paramagnetic Spin-Lattice Relaxation Enhancement 10.6 Paramagnetic 7¡-Relaxation Enhancements by Heisenberg Exchange 10.7 Paramagnetic Enhancement by Weak/lntermediate Heisenberg Exchange 10.8 Paramagnetic Enhancement by Heisenberg Exchange between Charged Species 10.9 Paramagnetic Enhancement by Static Magnetic Dipole-Dipole Interaction 10.10 Paramagnetic Enhancement by Dynamic Magnetic Dipolar Interaction 10.11 Spin-Lattice Relaxation Enhancement by Exchange Processes 10.12 Relaxation by Slow Two-Site Exchange 10.13 Concentration Dependence of Heisenberg Exchange Between Spin Labels 10.14 Concluding Summary Appendix A10.1 : Effective Spin-Lattice Relaxation Times and ELDOR Reduction Factors for 15N-Nitroxides Appendix A10.2: Further CW-ELDOR Reduction Factors for 14N-Nitroxides Appendix
A10.3: Cross Relaxation and ^-Dependent Intrinsic Spin-Lattice Relaxation Rates for 14N-Nitroxides Appendix A10.4: Heisenberg-Exchange Rate Constants for Paramagnetic Relaxants References 11 Nonlinear and Saturation-Transfer EPR 11.1 Introduction 11.2 Progressive Saturation: Bloch Equations 11.3 Progressive Saturation: Inhomogeneous Broadening 11.4 Field Modulation: Modulation-Coupled Bloch Equations 11.5 Progressive Saturation: Sudden-Jump Rotational Mobility 11.6 Progressive Saturation: Brownian Rotational Diffusion 11.7 Nonlinear Displays: Out-of-Phase Spectra (ST-EPR) 11.8 7,-Sensitive Nonlinear EPR Displays 11.9 First-Harmonic, Out-of-Phase Absorption K-EPR 11.10 Second-Harmonic, Out-of-Phase Absorption V2'-EPR Intensities 11.11 Example of Very Slow Two-Site Exchange in Lipid-Protein Interactions 11.12 Saturation Transfer EPR: Ultraslow Rotational Motion 11.13 Saturation-Transfer EPR: V2'-Lineshapes 11.14 Rotational Diffusion of Membrane Proteins 11.15 ST-EPR Simulations with the Bloch Equations 11.16 Stochastic-Liouville ST-EPR Simulations 11.17 Concluding Summary Appendices: Calibrations of Nonlinear EPR Spectra for Tb and for τκ Appendix A11.1 : Calibrations for 71-Measurements in Progressive-Saturation CW-EPR with Molecular Motion Appendix A11.2: Calibrations for 7¡-Measurements in First-Harmonic Out-of-Phase V/-EPR with Molecular Motion Appendix A11.3: Calibrations for тя in Second-Harmonic Absorption, Out-of-Phase V2'-EPR References 191 193 195 196 198 201 204 205 206 207 209 209 209 211 212 212 214 215 218 219 222 223 223 224 225 227 230 231 233 235 237 237 237
239 241 242 244 245 246 248 249 250 252 253 255 257 258 258 259 259 260 263 263
Contents 12 Saturation-Recovery EPR and ELDOR 12.1 Introduction 12.2 Saturation-Recovery Detection 12.3 Nuclear Relaxation in 15N-and 14N-Nitroxides 12.4 Rate Equations for SR-EPR and SR-ELDOR of 15N-Nitroxides 12.5 Rotational Dynamics and SR-EPR, SR-ELDOR of 15N-Nitroxides 12.6 Rate Equations for SR-EPR and SR-ELDOR of 14N-Nitroxides 12.7 Rotational Dynamics and SR-EPR, SR-ELDOR of 14N-Nitroxides 12.8 Solid-State (Vibrational) Contributions and Glassy Solvents 12.9 Spin-Lattice Relaxation Enhancements in SR-EPR 12.10 Slow Two-Site Exchange and SR-EPR 12.11 Heisenberg Spin Exchange in SR-EPR 12.12 14N-15N Nitroxide Pairs and Heisenberg Exchange 12.13 Slow Rotational Diffusion for SR-ELDOR and SR-EPR 12.14 Saturation-Recovery EPR and Molecular Ordering 12.15 Concluding Summary References 13 Spin-Echo EPR 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 13.12 13.13 13.14 Introduction Microwave Pulses in the Vector Model Finite Pulse Power and Width Vector Model for Primary Spin Echo Product Spin-Operator Method for Primary Spin Echo Density Matrix, Pulses and Transverse Relaxation Primary-Echo Decay and Rotational Dynamics (Phase-Memory Time) Rotational Diffusion and Primary-Echo Decay Stochastic-Liouville Simulations of Primary-Echo Decay Slow-Motion Simulations of Primary-Echo Decay Primary-Echo Decay in Sudden-Jump Model Experimental Phase-Memory Times Primary Echo-Detected Spectra and Librational Dynamics Spin-Spin Interactions and Spectral Diffusion 13.14.1 Jump Model for Short τ 13.14.2 Sudden Jump Model: General Case 13.14.3 Gauss-Markov Model: Long τ 13.15
Spin-Spin Interactions and Instantaneous Diffusion 13.16 Vector Model for Stimulated Echoes 13.17 Unwanted Echoes and Phase Cycling 13.18 Stimulated Echo and Rotational Dynamics 13.19 Stimulated-Echo Decay in Sudden-Jump Model 13.20 Stimulated Echo and Spin-Spin Interaction 13.21 Experimental Stimulated-Echo Decays 13.22 Concluding Summary Appendix A13: Lorentzian Spectral Diffusion A13.1 Conditional Probabilities and Spectral Diffusion A13.2 Echo Decays A13.3 Stationary Probabilities and Spectral Diffusion References xi 267 267 267 268 270 272 274 276 278 279 280 281 283 284 286 287 289 291 291 291 292 294 295 295 296 298 299 300 301 302 303 306 306 308 309 310 312 313 314 315 316 317 318 319 319 319 320 321 14 ESEEM and ENDOR: Hyperfine Spectroscopy 323 Introduction Echo Envelope Modulation Two-Pulse ESEEM for / = į Nuclei Two-Pulse ESEEM for/= 1 Nuclei Three-Pulse ESEEM 323 324 324 326 327 14.1 14.2 14.3 14.4 14.5
xii Contents_ _ _ 14.6 14.7 14.8 14.9 14.10 14.11 14.12 14.13 14.14 Standard Intensities for З-Pulse ESEEM Water-Penetration Profiles and Η-Bonding in 2H-ESEEM ESEEM in Disordered Samples: Powder Spectra ESEEM Powder Lineshapes Electron-Nuclear Double Resonance (ENDOR) Continuous-Wave Proton ENDOR Orientation Selection in Powder ENDOR Distances from ENDOR Frequencies Pulse ENDOR 14.14.1 Davies ENDOR 14.14.2 Example of Davies ENDOR 14.14.3 Mims ENDOR 14.14.4 Example of Mims ENDOR 14.15 ELDOR-Detected NMR 14.15.1 ELDOR-Detected NMR of 15N-Nitroxides 14.15.2 ELDOR-Detected NMR of ,4N-Nitroxides 14.16 Concluding Summary References 15 Distance Measurements Introduction Dipolar Pair Spectra Dipolar Convolution and Deconvolution Dipolar Deconvolution Random Distribution of Spins Absolute-Value First Moment and MeanDipolar Splitting Second Moment of Dipolar Lineshape Gaussian Distance Distributions Statistical Theory of Dipolar Broadeningfor Dilute Spins Echo-Detected ELDOR (DEER) 15.10.1 Three-Pulse DEER 15.10.2 Four-Pulse DEER 15.11 Processing and Analysing 4-Pulse DEER Signals 15.11.1 Background DEER Signal 15.11.2 Spin-Pair Distributions and Spin Counting 15.11.3 Tikhonov Regularization and Gaussian Fitting 15.12 Explicit Distance Distributions in Shells of Uniform Density 15.12.1 Spherical Surface and Volume Distance-Distributions 15.12.2 Sphere-within-Shell Distances 15.12.3 Distance Distribution within Spherical Shell 15.13 Excluded Volume in Background DEER Signals 15.14 Orientation
Selection in DEER Signals 15.15 Concluding Summary Appendix A15.1 : General Expressions for Distance Distribution in Spherical Shells Appendix A15.2: Decay Function a for Excluded Volume References 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 16 Site-Directed Spin Labelling (SDSL) 16.1 16.2 16.3 16.4 16.5 Introduction Side-Chain Accessibilities and Mobilities Nitroxide Scanning: Secondary Structure 16.3.1 Soluble Proteins 16.3.2 Membrane Proteins ß-Sheets and ß-Barrel Proteins Mobility Mapping 16.5.1 Angular Amplitudes 16.5.2 Rotational Rates 329 329 330 331 332 332 333 334 335 335 336 338 338 339 341 342 342 343 345 345 345 346 347 348 349 350 351 353 354 354 356 357 357 358 359 360 360 361 362 363 364 367 368 368 369 371 371 371 372 373 373 375 377 377 378
Contents 16.5.3 Order Parameters MTSSL (R1) Side-Chain Rotamers χ4/χ5 Lineshape Simulations for R1-Side Chains 16.7.1 Water-Exposed Non-interacting Sites on a-Helices 16.7.2 Lipid-Exposed Non-interacting Sites in Transmembrane Helices 16.7.3 Lipid-Exposed Sites on a Transmembrane ß-Barrel 16.7.4 Water-Exposed Residues in ß-Sheets 16.8 Lineshape Simulations from Molecular-Dynamics Trajectories 16.8.1 Order Parameters from MD 16.8.2 Orientation Potentials and SLE Simulations 16.8.3 Brownian Dynamics Trajectories 16.8.4 Spin Hamiltonian and Trajectory of Transverse Magnetization 16.8.5 Fourier Transformation 16.8.6 Trajectories 16.8.7 Discrete Markov States 16.9 SR-EPR: Spin-Lattice Relaxation and Conformational Exchange 16.10 TOAC Spin-Label Residue in Peptides: Helix Orientations 16.11 Distances Between Site-Directed Spin Labels: a-Helices, ß-Strands 16.11.1 α-helices 16.11.2 ß-sheets 16.11.3 Comparison withCrystalStructures 16.12 Rotamer Libraries 16.13 Helix Assembly and Interhelical Distances: Coiled Coils and a-Bundles 16.13.1 Coiled Coils 16.13.2 Example of 4-Stranded CoiledCoil: SNARE Complex 16.13.3 a-Helical Bundles 16.14 Beta-Sheet Topology: Interstrand Separations 16.14.1 a-Crystallin Chaperone Fold 16.14.2 Amyloid Fibril Cross-ß Structure 16.15 DEER and SDSL: Tertiary Fold, Subunits and Docking 16.15.1 Homo-oligomers 16.15.2 Triangulation and Distance Geometry 16.15.3 Distance Restraints in Modelling 16.15.4 Docking Subunits 16.15.5 Conformational Changes 16.16 Concluding Summary Appendix A16: Additional Conformational and Distance Data References 16.6 16.7
Fundamental Physical Constants Symbols Appendices A-M: Fundamentals Appendix A: Units and Conversions Appendix B: Vectors, Matrices and Tensors Appendix C: Quantum Mechanical Basics Appendix D: Schrödinger Equation and Heisenberg Equation of Motion Appendix E: Angular-Momentum/Spin Operators and their Matrix Elements Appendix F: Magnetic Field in Quantum Mechanics Appendix G: Quantum Mechanical Perturbation Theory Appendix H: Spin-Hamiltonian Diagonalization Appendix I: Rotation of Axes Appendix J: Second-Order Hyperfine Shifts Appendix K: Atomic Structure and Molecular Bonding Appendix L: g-Values for a p-Electron Appendix Μ: Time-Dependent Perturbation Theory and Selection Rules References xiii 379 380 383 384 385 386 386 387 387 387 388 388 389 389 390 391 392 394 394 395 395 397 397 397 399 400 401 401 403 403 403 404 405 405 406 406 407 413 417 418 429 429 431 434 436 437 439 440 442 444 446 447 452 453 454
xiv Contents Appendices N-V: Specialist Topics Appendix N: Spin Density-Matrix Appendix 0: Relaxation Theory with Density Matrices Appendix P: Product-Operator Formalism for Pulse EPR Appendix Q: Addition of Angular Momenta and Wigner 3/-symbols Appendix R: Rotation Operators, Euler Angles and Wigner Rotation Matrices Appendix S: Irreducible Spherical Tensors Appendix T: Fourier Transforms, Convolutions and Correlation Functions Appendix (J: Moments of EPR Lineshapes, and Traces of Spin Operators Appendix V: Spherical Harmonics and Legendre Polynomials References 455 455 458 466 472 475 478 481 483 488 490 Index 491 |
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| spelling | Marsh, Derek Verfasser (DE-588)1031679154 aut Spin-label electron paramagnetic resonance spectroscopy Derek Marsh, Max-Planck-Institut für biophysische Chemie, Göttingen, Germany Boca Raton ; London ; New York CRC Press [2020] xvii, 495 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Elektronenspinresonanz (DE-588)4132116-9 gnd rswk-swf Elektronenspinresonanz (DE-588)4132116-9 s DE-604 Äquivalent Druck-Ausgabe, Hardcover 978-1-4822-2089-6 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034080293&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marsh, Derek Spin-label electron paramagnetic resonance spectroscopy Elektronenspinresonanz (DE-588)4132116-9 gnd |
| subject_GND | (DE-588)4132116-9 |
| title | Spin-label electron paramagnetic resonance spectroscopy |
| title_auth | Spin-label electron paramagnetic resonance spectroscopy |
| title_exact_search | Spin-label electron paramagnetic resonance spectroscopy |
| title_exact_search_txtP | Spin-label electron paramagnetic resonance spectroscopy |
| title_full | Spin-label electron paramagnetic resonance spectroscopy Derek Marsh, Max-Planck-Institut für biophysische Chemie, Göttingen, Germany |
| title_fullStr | Spin-label electron paramagnetic resonance spectroscopy Derek Marsh, Max-Planck-Institut für biophysische Chemie, Göttingen, Germany |
| title_full_unstemmed | Spin-label electron paramagnetic resonance spectroscopy Derek Marsh, Max-Planck-Institut für biophysische Chemie, Göttingen, Germany |
| title_short | Spin-label electron paramagnetic resonance spectroscopy |
| title_sort | spin label electron paramagnetic resonance spectroscopy |
| topic | Elektronenspinresonanz (DE-588)4132116-9 gnd |
| topic_facet | Elektronenspinresonanz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034080293&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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