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NMR (PG503)

NMR (PG503). Solid-state NMR: Anisotropic interactions and how we use them. Dr Philip Williamson February 2009. Solid-state NMR spectra. Solid-state NMR. Anisotropic Interactions What are they, what do they do (to our spectra) How can we manipulate them Oriented samples

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NMR (PG503)

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  1. NMR (PG503) Solid-state NMR: Anisotropic interactions and how we use them Dr Philip Williamson February 2009

  2. Solid-state NMR spectra

  3. Solid-state NMR • Anisotropic Interactions • What are they, what do they do (to our spectra) • How can we manipulate them • Oriented samples • Magic angle spinning • How can we exploit them • Cross polarization • Dipolar recoupling • How can we use them to probe structure/dynamics (2nd series of lectures)

  4. Outline (1) • What is anisotropy • How does it effect NMR spectra • What interactions give rise to anisotropic properties? • Describing interactions: tensors • Chemical Shielding Anisotropy • Orientational dependence of resonance frequency • Powder spectra • Dipolar interactions • Quadrupolar interactions

  5. What is anisotropy • Something whose properties depend on its orientation e.g. stress

  6. How does it effect the NMR spectrum • Each molecular orientation gives rise to a difference resonance frequency • In powder we have the sum of all distributions • In the liquid state these anisotropic properties are averaged on the NMR timescale

  7. Which interactions in NMR Isotropic Anisotropic

  8. Describing interactions: tensors (1) We are concerned with 3 flavours • Zero rank tensors • Physical property independent of coordinate system in which it is described (scalar, distance) • First rank tensors • Coordinate, depends on frame of reference (vector, has size and direction) • Second rank tensors • Multiple first rank tensors e.g. stress (matrix) • Higher rank exist – but we will not be considering

  9. Describing interactions: tensors (2) Rank zero tensor Rank one tensor B0 r Isotropic chemical shift, J-coupling (0,0,Bz)

  10. Describing interactions: tensors (3) • Second rank tensors k i j k i j z szz syy sxx y x

  11. Parameterizing 2nd rank tensors • In cartesian notation tensors defined by principle components, Axx, Ayy andAzz • Frequently parameterized with • This assumes • Thus the asymmetry 0.0<<1.0 and anisotropy can be both positive and negative

  12. Chemical Shielding Anisotropy (1) • Perturbation of the magnetic field due to interaction with surrounding electrons • Inherently asymmetric (e.g. electron distribution surrounding carbonyl group)

  13. Chemical Shielding Anisotropy (2) • We can describe the perturbation of the main field (B0), by the second rank tensor, s. • The Hamiltonian which describes the interaction with the modified field is: Which can be written in a simplified form as:

  14. Chemical Shielding Anisotropy (3) Thus the chemical shielding Hamiltonian simplifies to: and the resonance frequency of the line is: Thus the resonance frequency is proportional to szz in the laboratory frame. However, s is usually defined in the principle axis system (PAS) not in the lab frame (LF). Therefore, we need to transform s from the PAS to LF.

  15. Transformations Principle Axis System z z Lab Frame szz syy • Rotation characterized by the three Euler angles (a, b and g) • Multiple s by rotation matrix R sxx y y x x

  16. Transformation matrix Can derive a rotation matrix which bring about the rotation described above: To determine s in the laboratory frame, need to apply to the chemical shielding tensor s in the principle axis system: This can be simplified to give general Hamiltonian for CSA in lab frame of:

  17. Effect on resonance position d/2 d z szz =3000Hz • siso = 1/3(sxx+syy+szz) = 0Hz • = szz-siso = 3000 Hz • h = (syy-sxx)/d = 0.0 syy=-1500Hz y sxx =-1500Hz x

  18. Powder Patterns • In powders we have a random distribution of molecular orientations. • Thus the lineshape is the weighted superposition of all the different orientations:

  19. Empirical relation between PAS and MF • Methyl carbons  axially symmetric, axis along threefold symmetry axis • Ring carbons  three distinct tensor elements, most shielded perpendicular to plane, least shielded bisecting C-C-C angle of ring • Most shielded direction: • Perpendicular to ring in aromatic carbons • Along C3 axis for methyl carbons • Perpendicular to the sp2 plane for carbonyl/carboxylic acids • Least shielded direction: • In the ring plane, bisecting C-C-C angle • Perpendicular to C3 axis for methyl groups • In the sp2 place for carbonyl/carboxylic acids • Intermediate shielding • Tangential to ring for aromatic systems • In the sp2 plane and perpendicular to the C-C bond for COOH

  20. Dipolar Interaction Classical interpretation Classical interaction energy between two magnetic (dipole) moments when both are aligned with the magnetic field: Quantum mechanical where: • Symmetric second rank axially symmetric tensor. • Again we need to rotate from the PAS to LF to obtain resonance frequency. B0 m2 q m1

  21. Orientation dependence of dipolar interaction Homo-nuclear Dipolar Hamiltonian: Hetero-nuclear Dipolar Hamiltonian: 1/2ddip 3/4ddip ddip=20 kHz

  22. Quadrupolar Interaction (1) If spin>1/2, nucleus contains an electronic quadrupole moment (Q). Electronic quadrupole moment interacts with surrounding electron cloud (electric field gradient(EFG), V). where: Again we can define the anisotropy and asymmetry:

  23. Quadrupolar Interaction (2) To calculate the resonance frequency, we must transform from the PAS of the EFG to the laboratory frame. Retaining only the “secular terms” gives the following Hamiltonian in the LF: Powder spectrum of Ala-d3 dQ Orientation dependence of a single crystal of Ala-d3

  24. Exploitation of anisotropic interaction • Oriented samples • Single Crystal studies • Oriented Biological Membranes • Dynamics • Averaging of anisotropic interaction • Local electronic environment • Perturbation in chemical shielding anisotropy

  25. Dynamics: averaging of anisotropy Axis of rotational averaging Gel Phase q Liquid Crystalline Phase Rotational diffusion: Scaling of interaction by where q is the angle between axis of motional averaging and the PAS of the interaction

  26. Orientation 0° 90° Oriented samples Necessary to introduce macroscopic alignment: • Crystallization • Oriented membranes • Fibres (Silk/DNA) Field (B0) C3’ Cys192/193 C3

  27. Orientation±5° Orientation±5° Mosaic Spread±5° Mosaic Spread±5° Oriented samples – ligand orientations B0 B0

  28. Protein Backbone Orientation 15N chemical shielding anisotropy Bo Opella et al. 1998 15N-1H hetero-nuclear dipolar coupling

  29. Local electronic environment HCl As we shall see next week, typically these parameters are obtained under conditions of magic-angle spinning to enhance signal to noise.

  30. An aside: spherical tensors • Make the calculations a lot easier to handle • Frequently used in papers

  31. Change of time • Unable to make next weeks seminar • Propose to move to 10 February – have one 2 hour solid-state 1st hour, liquid state 2nd hour. • Workshop scheduled for this Friday, move to the 6th February.

  32. Sensitivity and resolution enhancement in solid-state NMR

  33. Resume Isotropic Anisotropic

  34. Oriented samples • Increase resolution by orienting interactions, therefore all spins resonate at the same frequency • As all spins resonate with the same frequency the sensitivity of the measurements is higher

  35. Magic-angle spinning

  36. Magic Angle Spinning Seeks to reintroduce averaging process through mechanical rotation Sample rotors (Varian) Magic Angle Spinning Probehead (Doty)

  37. Averaging of anisotropic interactions

  38. Averaging of anisotropic interactions The Hamiltonian becomes time dependent: We can deconvolute this into the iso- and an-isotropic contributions: where and Where C1, C2, S1 and S2 relate the anisotropic interaction to magnetic field (Appendix 1).

  39. Analysis of MAS spectra • All anisotropic interactions become time dependent • To analyze spectra need to treat these time dependencies • Several mathematical descriptions that allow us to do this • Average Hamiltonian Treatment • Floquet Theory • Piece wise integration

  40. Slow speed spinning • Rotational echoes apparent in fid which characterise the anisotropy of the interaction • At lower spinning speed the intensity of the sidebands characterises the anisotropic interaction (d and h) 2ns

  41. Herzfeld-Berger Analysis Expression exist to calculate the intensity of sidebands for a given anisotropic interaction: where and 1) Herzfeld and Berger, J.Chem.Phys 73 (1980) 6021

  42. CSA analysis in reality Several programs now available that now facilitate this task: • Tables – Paper by Herzfeld and Berger • matNMR (routines for analysis of both CSA and quadrupolar interactions in bothe static and MAS spectra) http://matnmr.sourceforge.net/ (requires matlab) • MAS sideband analysis (Levitt group homepage) http://www.mhl.soton.ac.uk/public/Main/index.html (requires mathematica)

  43. Effect of off-angle MAS • Anisotropic interaction scaled by ½(3cos2q-1) • Useful for characterizing anisotropy whilst gaining some sensitivity • Indicates why magic angle should be carefully set!

  44. When does MAS not work? • Homogeneous interactions • e.g. Homonuclear dipolar interactions • Heterogeneous line-broadening • e.g. Samples with conformational heterogeneity (lyophilized solids) • Nuclei with large quadrupolar interactions • When samples are not ‘solid’

  45. Applications of MAS • Resolution/Sensitivity Enhancement • Low speed spinning – characterisation of anisotropy Isotropic chemical shifts in the protein backbone are sensitive to secondary structure Analysis of the principle components of the chemical shielding tensor reveals that larger changes are seen in s22 making it a sensitive probe of protein secondary structure. Wei et al. 2001 JACS 123: 6118-26

  46. Applications of MAS • Low speed spinning • anisotropymobility Amyloid precursor protein in differing lipid environments has different propensity to oligomerise. Sideband analysis reveals changes in peptide mobility Marenchino et al. Biophysical Journal 2008

  47. Cross Polarization

  48. Why don’t we normally detect protons in the solid-state • Strong couplings between protons (dII>20kHz) • Homogeneous interaction • Not readily averaged at moderate spinning speeds • Methods for removing the couplings between protons during acquisition challenging • Result • Typically we exploit low-g nuclei BPTI Rhodopsin

  49. Disadvantages of detecting low-g nuclei • Natural abundance levels not always high • enrichment • Low gyromagnetic ratio means the signal is attenuated • Solution transfer of polarization from protons to low g-nuclei (INEPT?)

  50. 1D 1H/15N INEPT NMR Spectrum I1x(p/2) I1x(p) I1y(p/2) t/2 t/2 1H H=2pJI1ZI2Z+W1I1z+W2I2z I2x(p) I2x(p/2) HCS=W1I1z+W2I2z QUESTION: What form does the 15N signal take?

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