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The Nuclear Overhauser Effect in NMR Structure and Dynamics Analysis The Nuclear Overhauser Effect in NMR Structure and Dynamics Analysis Frühjahrssemester 2015 Eidgenössische Technische Hochschule Zürich PD Dr. Beat Vögeli Laboratory of Physical Chemistry, HCI F217, Wolfgang-Pauli-Str. 10, Swiss Federal Institute of Technology, ETH-Hönggerberg, CH-8093 Zürich, Switzerland, Tel: (+41)-44-633-4405, [email protected] Content The Nuclear Overhauser Enhancement or Effect (NOE) is the most important measure in liquid-state NMR for the characterization of the structure and dynamics of biomacromolecules. In this lecture, theoretical and practical aspects of the NOE are presented: A derivation of the NOE from relaxation theory, spin diffusion, traditional experiments to measure the NOE, exact measurements of the NOE (eNOE), transferred NOE (trNOE), the use of distance restraints from NOEs in structure calculation, and protocols for structural ensemble calculation in CYANA. Literature: Books D. Neuhaus, M.P. Williamson, The Nuclear Overhauser Effect in Structural and Conformational Analysis. Wiley: New York, 2000. K. Wüthrich, NMR of Proteins and Nucleic Acids. Wiley: New York, 1986. J.H. Noggle, R.E. Schirmer, The Nuclear Overhauser Effect: Chemical Applications. Academic Press: New York, 1971. Book Chapters M. Cavanagh, W.J. Fairbrother, A.G. Palmer, M. Rance, N.J. Skleton, Protein NMR Spectroscopy. Principles and Practice. Academic Press: San Diego, 2007. Chapter 5 M. Goldman, Quantum Description of High-Resolution NMR in Liquids, Oxford University Press: New York, 1988. Chapter 8.4 R.R. Ernst, G. Bodenhausen, A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon Press, Oxford, 1987. Chapter 9.7 2 Reviews B. Vögeli, The Nuclear Overhauser Effect from a Quantitative Perspective. Prog. Nucl. Magn. Reson. Spectrosc. 78, 1-46, 2014. N. Rama Krishna, V. Jayalakshmi, Complete Relaxation and Conformational Exchange Matrix Analysis of STD-NMR Spectra of Ligand-Receptor Complexes. Prog. Nucl. Magn. Reson. Spectrosc. 49, 1-25, 2006. T. Brand, E.J. Cabrita, S. Berger, Intermolecular Interaction as Investigated by NOE and Diffusion Studies. Prog. Nucl. Magn. Reson. Spectrosc. 46, 159-196, 2005. M. Nilges, S.I. O'Donoghue, Ambiguous NOEs and Automated NOE Assignment. Prog. Nucl. Magn. Reson. Spectrosc. 32, 107-139, 1998. R. Brüschweiler, Dipolar Averaging in NMR Spectroscopy: From Polarization Transfer to Cross Relaxation, Prog. Nucl. Magn. Reson. Spectrosc. 32, 1-19, 1998. H. Mo, T.C. Pochapsky, Intermolecular Interactions Characterized by Nuclear Overhauser Effects. Prog. Nucl. Magn. Reson. Spectrosc. 30, 1-38, 1997. F. Ni, Recent Developments in Transferred NOE Methods, Prog. Nucl. Magn. Reson. Spectrosc. 26, 517-606, 1994. R. Brüschweiler, D.A. Case, Characterization of Biomolecular Structure and Dynamics by NMR Cross Relaxation, Prog. Nucl. Magn. Reson. Spectrosc. 26, 27-58, 1994. B.A. Borgias, M. Gochin, D.J. Kerwood, T.L. James, Relaxation Matrix Analysis of 2D NMR Data, Prog. Nucl. Magn. Reson. Spectrosc. 22, 83-100, 1990. 3 Table of Contents 1.Introduction: A brief history of the NOE..................................................................................... 2. Theoretical background............................................................................................................... 2.1. Classical derivation of the NOE: The Solomon equations I........................................ 2.1.1. Steady state Overhauser effect...................................................................... 2.1.2. Transient Overhauser effect.......................................................................... 2.1.3. The cross-relaxation rate…........................................................................... 2.2. Semi-classical derivation of the NOE......................................................................... 2.2.1. The Master equation..................................................................................... 2.2.2. The relaxation matrix for NOESY analysis.................................................. 2.2.2.1. Non-degenerate transitions............................................................ 2.2.2.2. Like spins....................................................................................... 2.2.2.3. Near-degenerate transitions........................................................... 2.2.3. The Solomon equations II............................................................................ 2.2.4. Conformational/chemical exchange............................................................. 2.2.5. The spectral density function....................................................................... 2.2.5.1. Simplifications for methyl groups................................................. 2.2.6. Lipari-Szabo approximations....................................................................... 2.2.7. Practical expressions.................................................................................... 2.2.7.1. NOEs and distances between single spins.................................... 2.2.7.2. NOEs and distances between groups of equivalent spins............. 2.2.7.3. Expressions for molecular dynamics simulations........................ 4 3. Pulse sequences......................................................................................................................... 3.1. The basic 2D NOESY pulse sequence....................................................................... 3.2. Heteronucleus-resolved NOESY.............................................................................. 3.2.1. Practical recommendations for eNOE measurements................................ 3.3. Normalization to diagonal peak intensities............................................................... 3.4. Correction for deuteration…………………............................................................... 4. Extraction of exact NOE rates and distances…........................................................................ 4.1. Spin diffusion.............................................................................................................. 4.2. Full relaxation-matrix approach.................................................................................. 4.2.1. Iterative hybrid relaxation matrix approach with MD/DG.......................... 4.3. Non-linear ISPA with correction for spin diffusion.................................................... 4.3.1. Correction for spin diffusion........................................................................ 4.3.1.1. Full matrix approach…………………........................................ 4.3.1.2. Three-spin system approach......................................................... 4.3.1.3. Spin diffusion in (partially) deuterated molecules........................ 4.3.2. Validation and selection of experimental buildups...................................... 4.3.3. Distance calculation..................................................................................... 4.3.4. Impact of motion.......................................................................................... 4.3.5. Validation of experimental distances........................................................... 5. Structure calculation................................................................................................................. 5.1. Structure calculation using the full matrix approach................................................. 5.1.1. Nucleic acids............................................................................................... 5.1.2. From peptides to proteins........................................................................... 5 5.2. Ensemble calculation using conventional NOE-distance restraints.......................... 5.2.1. Restrained molecular dynamics simulation............................................... 5.2.2. Direct structural ensemble calculation....................................................... 5.3. Multiple-state structural ensemble calculation using eNOEs................................... 5.3.1. Conventional structure calculation............................................................ 5.3.2. Multiple-state structure calculation protocol.............................................. 5.3.2.1 Improvements to the protocol....................................................... 5.3.3. Cross-validation of the ensemble................................................................ 6. Transferred NOE...................................................................................................................... 7. Outlook..................................................................................................................................... 7.1. Future challenges....................................................................................................... 7.1.1. Experimental............................................................................................... 7.1.2. Ensemble calculation.................................................................................. 7.1.3. Transferred NOE........................................................................................ 8. Appendix.................................................................................................................................. 9. References................................................................................................................................ 10. Glossary...................................................................................................................................
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