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N◦ d’ordre : 287 Annee´ 2004 N◦ attribue´ par la bibliotheque` : 04ENSL0 287 THESE` ECOLE´ NORMALE SUPERIEURE´ DE LYON Laboratoire de Chimie ECOLE NORMALE SUPERIEURE DE LYON These` de doctorat En vue d’obtenir le titre de : Docteur de l’Ecole´ Normale Superieure´ de Lyon Specialit´ e´ : Physique Present´ ee´ et soutenue publiquement le 17 septembre 2004 par : Luminita DUMA Amelioration´ de la Resolution´ dans la Resonance´ Magnetique´ Nucleaire´ Multidimensionnelle des Proteines´ Directeur de these` : Lyndon EMSLEY Apres` avis de : Monsieur Geoffrey BODENHAUSEN, Membre/Rapporteur Monsieur Hartmut OSCHKINAT, Membre/Rapporteur Devant la Commission d’examen formee´ de : Monsieur Geoffrey BODENHAUSEN, Membre/ Rapporteur Monsieur Yannick CREMILLIEUX, Membre Monsieur Lyndon EMSLEY, Membre Monsieur Alain MILON, Membre Monsieur Hartmut OSCHKINAT, Membre/Rapporteur Lyon, 2004 Order N◦: 287 Year 2004 N◦ allocated by the library: 04ENSL0 287 ECOLE´ NORMALE SUPERIEURE´ DE LYON Chemistry Laboratory ECOLE NORMALE SUPERIEURE DE LYON Doctoral Thesis For the degree of: Doctor in Physics of the Ecole´ Normale Superieure´ de Lyon Presented and defended the 17th of September 2004 by: Luminita DUMA Resolution Improvement in Multidimensional Nuclear Magnetic Resonance Spectroscopy of Proteins Supervisor: Lyndon EMSLEY After recommendation of: Mr Geoffrey BODENHAUSEN, Member/Referee Mr Hartmut OSCHKINAT, Member/Referee In front of the jury made up of: Mr Geoffrey BODENHAUSEN, Member/Referee Mr Yannick CREMILLIEUX, Member Mr Lyndon EMSLEY, Member Mr Alain MILON, Member Mr Hartmut OSCHKINAT, Member/Referee Lyon, 2004 Pa˘rint¸ilor mei. A` mes parents. To my parents. ”The principle of science, the definition, almost, is the following: The test of all knowledge is experiment. Experiment is the sole judge of sci- entific ”truth”. But what is the source of knowledge? Where do the laws that are to be tested come from? Exper- iment, itself, helps to produce these laws, in the sense that it gives us hints. But also needed is imagination to create from these hints the great generalizations - to guess at the wonderful, simple, but very strange patterns beneath them all, and then to experiment to check again whether we have made the right guess... Everything is made of atoms. That is the key hypothesis. The most important hy- pothesis in all of biology, for example, is that everything that animals do, atoms do. In other words, there is nothing that living things do that cannot be understood from the point of view that they are made of atoms acting according to the laws of physics. This was not known from the beginning: it took some experimenting and theorizing to suggest this hypothesis, but now it is accepted, and it is the most useful theory for producing new ideas in the field of biology.” from ”Six easy pieces. Es- sentials of physics explained by its most brilliant teacher” by Richard P. Feynman Contents Contents 1 Introduction 3 1 Carbon-13 lineshapes in solid-state NMR of labelled compounds 7 1.1 Introduction ............................................ 7 1.2 Experimental results for carboxyl and methyl resonances .................... 9 1.3 Theoretical aspects and simulations ............................... 10 1.4 Discussion ............................................. 21 1.5 Conclusion ............................................ 22 2 Spin-state-selection techniques in solid-state NMR 25 2.1 Introduction ............................................ 25 2.2 Spin-state selection in solid-state NMR ............................. 26 2.2.1 Spectral selection using IPAP .............................. 26 2.2.2 ”Double IPAP” filter ................................... 30 2.2.3 Selectivity and efficiency of the IPAP filter ....................... 32 2.3 Other spin-state-selection filters ................................. 33 2.3.1 Spin-state-selective excitation (S3E) filter ........................ 33 2.3.2 Double-in-phase single-anti-phase (DIPSAP) filter ................... 35 2.3.3 INADEQUATE-CR .................................... 38 2.4 Conclusion ............................................ 41 3 State-selection for resolution improvement in solid-state NMR of proteins 43 3.1 Introduction ............................................ 43 3.2 Single-transition transfer ..................................... 44 3.3 2D COCA-IPAP .......................................... 48 3.3.1 Product operator description ............................... 48 3.3.2 Application to uniformly [13C, 15N]-enriched Crh protein ............... 52 3.3.3 Efficiency of 2D-COCA-IPAP experiment ........................ 52 3.4 2D CACB-IPAP .......................................... 55 3.5 Conclusion ............................................ 57 2 Contents 4 Carbon directly detected techniques for liquid-state NMR 59 4.1 Introduction ............................................ 59 4.2 Triple-resonance CBCACO experiment ............................. 60 4.2.1 Pulse sequence description ................................ 60 4.2.2 Results and discussion .................................. 62 4.2.3 Homodecoupling efficiency ............................... 64 4.3 Triple-resonance CANCO experiment .............................. 68 4.3.1 Alternatives for coherence transfer ............................ 68 4.3.2 Pulse sequence description ................................ 69 4.3.3 Results and discussion .................................. 72 4.4 Conclusion ............................................ 74 5 Spin-echo J-modulation in magic-angle-spinning solid-state NMR 75 5.1 Introduction ............................................ 75 5.2 Theoretical description ...................................... 77 5.2.1 Nuclear spin Hamiltonian ................................ 78 5.2.2 Evolution operators .................................... 80 5.2.3 Spin-echo modulation .................................. 81 5.2.4 Echo-modulation regimes ................................ 85 5.3 Numerical simulations ...................................... 90 5.4 Experiments ............................................ 95 5.5 Conclusion ............................................ 98 Conclusion and perspectives 99 Appendices 101 5.1 Appendix A: Geometric rotations and Eulerian representation .................. 101 5.2 Appendix B: Rotation transformation and spin-echo amplitude ................. 102 References 109 Abbreviations and symbols 125 Curriculum Vitae 127 Publication list 129 Acknowledgments 131 List of figures 133 List of tables 135 Introduction The development of the magnetic resonance phenomenon originates in the concept of spin1 as quantum mechanical property.[3, 4] If the discovery of nuclear magnetic resonance (NMR) spectroscopy was identified with the independent works of the Purcell and Bloch groups in 1945,[5, 6] its origin is undoubtedly based on the experiments which verified the original ideas of nuclear and electron spin. Indeed, developments like the inter- pretation of hyperfine spectral structures given by Pauli in 1924[7] and the application of atomic and molecular beams to nuclear magnetic moments and hyperfine structures measurements performed by Rabi[8] and Stern[9] largely contributed to the discovery of the NMR spectroscopy. Soon after its discovery, NMR spectroscopy imposed itself as a powerful technique with applications in numerous fields. The impact of magnetic resonance on physics and chemistry was its ability to give detailed in- formation about processes at atomic level. In fact, the technique originally developed into an important tool for chemistry research and became nowadays also a powerful method in biochemistry and biophysics for obtaining structure elucidation and molecular dynamics of complex systems like for example biomolecules[10] and poly- mers.[11] NMR is also widely used in medical imaging to diagnose different types of pathologies. Additionally, NMR has a variety of other applications: searching for oil or water, studying the composition and structure of various foods, testing wine adulteration, quantum computing, etc. The exploitation of structural and dynamical properties by NMR requires high resolution and sensitivity in order to accurately interpret the NMR spectra. Due to the orientation dependence of the anisotropic magnetic interactions, the anisotropy is the major contribution to the broadening of the lineshapes. In liquid-state NMR, the spectra show sharp lines because of the averaging of the anisotropic interactions by the molecular tumbling of the molecules.[2,12,13] On the other hand, in the solid state, the anisotropic interactions are all retained in addition to the isotropic chemical shifts and indirect spin-spin couplings. For powder samples, the anisotropic interactions usually dominate the spectrum and depend on the orientation of the crystallites with respect to the external magnetic field.[11,12, 14] Therefore, the spectra of powdered samples show broad lines which overlap each other whereas sharp lines in a liquid-like fashion can only be obtained for single crystals and oriented samples.[15, 16] Narrow lines can however be obtained for solids by spinning the solid sample about an axis which forms an angle of 54.74◦ with the direction of the external magnetic field and which is referred to as the ”magic angle”.[17, 18,19] The idea behind the magic-angle spinning is to average out the second-rank tensor interactions (i.e., chemical shift anisotropy (CSA), dipole-dipole (DD) interactions and a part of the quadrupole anisotropy). As the sample starts to rotate, the spin Hamiltonian

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