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Institut für Anorganische und Angewandte Chemie

Institut für Anorganische und Angewandte Chemie . Dieter Rehder NMR 1 – Fundamentals and Biological Applications PICB Winter School Chinese Academy of Sciences Shanghai 5th-10th March 2007. Why do some nuclei have a nuclear spin I and thus a magnetic moment µ ?.

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Institut für Anorganische und Angewandte Chemie

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  1. Institut für Anorganische und Angewandte Chemie Dieter Rehder NMR 1 – Fundamentals and Biological Applications PICB Winter School Chinese Academy of Sciences Shanghai 5th-10th March 2007

  2. Why do some nuclei have a nuclear spin I and thus a magnetic moment µ? Because the nuclei are charged, and they can possess a nuclear spin (“they rotate“). A rotating charge induces a magnetic moment

  3. When do nuclei have a nuclear spin I and thus a magnetic moment µ? Case 1: Even number of protons and even number of neutrons: I= 0(non-magnetic) Case 2: Oddnumber of protons or neutrons: I= 1/2,3/2,5/2 …(magnetic) Case 3: Oddnumber of protons and neutrons: I= 0(non-magnetic); I = 1, 2, …(magnetic)

  4. I = ½ (magnetic; spherical charge distribution): 1H, 13C, 31P, 183W, … I ½ (magnetic; ellipsoidal charge distribution: quadrupole): 2H, 7Li, 23Na, 39K, 43Ca, 51V, 95Mo, … - + + - Examples: I = 0 (non-magnetic): 12C, 16O, 32S, …

  5. Magnetic field (B) Absorption of energy: hn = 2µB0*) Relaxation Excited state Ground state What happens in an NMR experiment? µ “heat” *) n = radio-frequency, µ = magnetic moment , h = Planck constant, B0 = local magnetic field

  6. Parameters in solution NMR: - The differing environments of a magnetic nucleus in a molecule give rise to differing local magnetic fields B0 and thus to different resonance frequencies → Shielding (chemical shift) - From the excited state, the nucleus returns to its ground state (within nanoseconds to minutes, depending on the nucleus) → Relaxation time (→ line width) - If there are other spins present in the neighbourhood, the two (or more) spins communicate → Coupling constants J

  7. Shielding (chemical shifts)

  8. Chemical shift d and shielding s are related through: d = sref - s sref = Reference • Shielding s is a sum of three terms: • s = s(dia) + s(para) + s(non-local) • s(dia) is the local diamagnetic contribution • s(para) is the local paramagnetic contribution • s(non-local) arises from neighbouring atoms

  9. Shielding s is a sum of three terms: s = s(dia) + s(para) + s(non-local) s(non-local) is  small and disconsidered here Variations in s(dia) are only of relevance for 1H, 6Li and 7Li NMR; for havier nuclei it contributes with a constant value (because it arises from the core electrons) Variations in s(para) are those of interest for all heavier nuclei (they have their origin in the valence electrons)

  10. s(para) = -const∙<r3>-1∙DE-1∙c2 • ris the mean distance of the valence electrons from the nucleus • DE is the HOMO-LUMO splitting • c is a measure of the covalency of the bond(s) to adjacent atoms (the LCAO coefficient)

  11. s(para) = -const∙<r-3>-1∙DE-1∙c2 eg DE t2g Excited state Ground state 1A1g 1T2g Example: octahedral (Oh) low spin complex with a d6 configuration, e.g. Co3+, V-1

  12. PBr3 PCl3 P(OCH3)3 PF3 +229 +220 +141 +97 Increasing shielding Increasing electronegativity Examples: [Co(H2O)6]3+ [Co(NH3)6]3+ [Co(OCN)6]3- [Co(CN)6]3- [Co(PF3)6]3+ +15100 +8200 +1300 0 -4200 ppm Increasing shielding Increasing ligand strength

  13. Examples for species differentiation by chemical shifts 1. 51V NMR of an aqueous solution of 5 mM vanadate, pH 5.7

  14. Examples for species differentiation by chemical shifts 2. 31P NMR of rat heart Creatine-phosphate Inorganic phosphate Sugar- phosphate

  15. Relaxation (line widths)

  16. Relaxation: The shorter the relaxation times, the broader the signals • Relaxation mechanisms: • Spin-lattice (also: longitudinal) relaxation T1 • Spin-spin (also: transversal) relaxation T2 W1/2 = width at half-height In isotropic media: T1 T2 (T2)-1 = p∙W1/2

  17. Spin-spin relaxation (T2): entropy transfer by flip-flop motion: B0 • Spin-lattice relaxation (T1): energy transfer from the excited nucleus to the environment by • dipole-dipole interaction • chemical shift anisotropy • quadrupole interaction • paramagnetic relaxation enhancement

  18. Relaxation for quadrupolar nuclei: T-1 (1 + 2/3)tc  = e2qQ/h nuclear quadrupole coupling constant h = asymmetry parameter tc = molecular correlation time

  19. Broad lines (effective relaxation = short relaxation times) are expected if • the medium is viscous • the molecular mass of the molecule is large (proteins) • the temperature is low (increase of viscosity) • the nucleus has a quadrupole moment (and is in lower than cubic symmetry) • the nuclei interact with paramagnetic centres (paramagnetic shift reagents)

  20. In case of dynamic systems (exchange between 2 or more species in the millisecond regime), exchange broadening of the resonance lines is observed A  B

  21. Nuclei of interest in the context of cation transport

  22. Paramagnetic shift reagents influence • The line width: → lines become broader • The shielding (chemical shift): → shielding increases or decreases (signals are shifted) Dy3+, 4f9: 5 unpaired electrons, magnetic moment: 10.65 BM

  23. Selected applications to biological systems

  24. Sodium inside and outside erythrocytes (red blood cells) Na+ outside (Dy-sensitive) 23Na NMR in the presence of Na+ inside (Dy-insensitive) [Na(H2O)6]+

  25. Concentrations of selected cations (mM) intracellular extracellular Na+ 10 142 K+ 155 4 Ca2+ 0.001 2.5 Mg2+ 15 0.9

  26. Sodium inside and outside cancer cells (HeLa-cells) Na+ outside 23Na NMR in the presence of Na+ inside

  27. Cation transport across ion-channels Cell membrane with ion channel

  28. (Gramicidin-based ion channel for Na+) Gramicidin L = leucine Q = glutamine V = valine P = proline F = phenylalanine Blue: peptide-N Red: peptide-O Green: carbon

  29. Gramicidin-based ion channel for Na+ Lipid molecules Na+ Na+ Na+ Na+ in out Na+ Path of Na+: diffusion to channel entrance (1); attachment to entrance (2); transport through channel (3); detachment from exit (4); diffusion away from channel (5).

  30. Intra- and extracellular sodium in liposomes, Dy3+ added Na+ outside (Dy-sensitive) Na+ inside (Dy-insensitive) Na+(in) Na+(out)/Dy3+ Increasing amounts of gramicidin

  31. The exchange of Na+ inside and outside the cell membrane across the ion channels is a dynamic process: Na+(in)  Na+(out) Dynamic processes on the millisecond scale can be followed by 2-dimensional exchange spectroscopy, 2D-EXSY Species taking part in exchange appear as off-diagonal peaks

  32. Collect information The principle of EXSY

  33. The principle of EXSY Information-Transfer

  34. No exchange in the absence of gramicidin 23Na EXSY spectra Na+(out) Na+(in) Exchange in the presence of gramicidin Exchange peaks

  35. Same spectra, but “viewed from top“ No exchange in the absence of gramicidin Exchange in the presence of gramicidin Na+(out) Na+(in)

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