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Metody szybkiej rejestracji wielowymiarowych widm NMR

Metody szybkiej rejestracji wielowymiarowych widm NMR. Wiktor Koźmiński Wydział Chemii Uniwersytetu Warszawskiego. M ultidimensional NMR Quadrature in indirectly sampled domains The new schemes of data acquisition Perspectives. Multidimensional NMR. Separation of signals

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Metody szybkiej rejestracji wielowymiarowych widm NMR

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  1. Metody szybkiej rejestracji wielowymiarowych widm NMR Wiktor Koźmiński Wydział Chemii Uniwersytetu Warszawskiego

  2. Multidimensional NMR Quadrature in indirectly sampled domains The new schemes of data acquisition Perspectives

  3. Multidimensional NMR • Separation of signals • Identification of mutually interacting nuclei • Sensitivity enhancement by polarization transfer and detection of high g nuclei • Indirect observation of multiple quantum transitions • MRI using the pulsed field gradients

  4. Applications • In chemistry: 2D NMR routine applications of : COSY, NOESY, ROESY, HSQC, HMBC, etc. • For biomolecules 2D to 5D resonance assignment, structural constrains • nD NMR also became popular in solid state studies

  5. t N t i exc mix i N–1 Measurement time and Sensitivity • Sample limited - concentration of active nuclei, g, B0, T, relaxation properties • Sampling limited • number of data points to acquire increases exponentially with the number of dimensions N - dimensional sequence : For ki data points in ti : k1k2 .... kN-12N-1measurements

  6. Reduced Dimensionality ND  2D with multiple quadrature (radial sampling): Koźmiński & Zhukov, J. Biomol. NMR, 26, 157 (2003) Kim & Szyperski, JACS, 125, 1385 (2003) Projection reconstruction (also radial sampling) : Kupče & Freeman, J. Biomol. NMR, 27, 383 (2003 Single scan acquisition of 2D (EPI) Frydman, Scherf & Lupulescu, PNAS, 99, 15858 (2002) Pelupessy, JACS, 125, 12345 (2003) New sampling and new processing strategies New approaches

  7. Single scan acquisitionFrydman, Scherf & Lupulescu, PNAS, 99, 15858 (2002) Spatially selective excitation Spatially selective acquisition (EPI) EPI – Echo Planar Imaging P. Mansfield, Magn. Reson. Med., 1, 370 (1984)

  8. Spatially selective excitation

  9. EPI acquisition S(k,t2)

  10. Example

  11. With a adiabatic frequency sweep pulsesPelupessy, JACS, 125, 12345 (2003) 1H-15N HSQC on protein sample

  12. Single scan approach • Very fast data collection • Limited resolution

  13. Time domain sampling conventional radial „Accordion Spectroscopy”

  14. Accordion SpectroscopyG. Bodenhausen and R.R. Ernst, J. Magn. Reson., 45, 367 (1981). • Synchronous incrementation of two (or more) periods • Original idea – application for exchange experiments, similar implementations for NOE and relaxation measurements are possible • tmix = kt1 • The exchange rates are reflected in lineshapes

  15. Arbitrarily scaled shifts and couplings Koźmiński , Sperandio & Nanz, Magn. Reson. Chem., 34, 311 (1996) Koźmiński & Nanz, J. Magn. Res., 124, 383 (1997) Accordion spectroscopysimultaneous sampling of chemical shifts and J-couplings

  16. Accordion sampling of two (or more shifts) – Reduced Dimensionality Radial sampling along one radius Linear combination of frequencies evolving in t1 and t2

  17. Reduced Dimensionality n chemical shifts encoded in (n - 1) dimensionsT. Szyperski, et al, J. Am. Chem. Soc., 115, 9307 (1993) Simultaneously sampled evolution of A and B nuclei 2nB nA nA +|nB| nA -|nB| F1d(A) • Main drawback of original implementation: • Quadrature for one chemical shift only • doubled number of peaks – reduced resolution • carrier offset for B-nuclei should be chosen outside of the region of interest – increased spectral width and number of increments.

  18. j x tx Quadrature in indirectly sampled domainscase 1) amplitude modulation Two experiments for each evolution time increment: Modulation: 1 j = x cos(Wtx) real part 2 j = y sin(Wtx) imaginary part States method: D.J. States et al., J. Magn. Reson., 48, 286 (1982) States – TPPI Modification by reversing j and receiver phase for even tx increments – axial peaks displacement D.J. Marion et al., J. Magn. Reson., 85, 393 (1989)

  19. tx G2 G1 PFG Quadrature in indirectly sampled domainscase 2) phase modulation PFG echo-antiecho, sensitivity enhanced and TROSY experiments Two experiments for each evolution time increment: 1G1 = (g2/g1)G2 cos(Wtx) – i sin(Wtx) echo 2 G1 = - (g2/g1)G2 cos(Wtx) + i sin(Wtx) antiecho Data recombination necessary

  20. Reduced Dimensionality with multiple quadratureKoźmiński & Zhukov, J. Biomol. NMR, 26, 157 (2003) • Sampling of each chemical shift requires acquisition of both sine and cosine modulated interferograms • Total number of 2n data sets should be collected for n synchronously sampled chemical shift evolutions (for each evolution time increment) • Phase modulation should be converted to amplitude modulation n = 1 number of data sets = 2 cos(WAt1) sin(WAt1) n = 2 number of data sets = 4 cos(WAt1) cos(WAt1) sin(WAt1) cos(WAt1) cos(WAt1) sin(WAt1) sin(WAt1) sin(WAt1) • In ND spectrum reduced to 2D with N-1 frequences sampled simultaneoulsy 2N-1 data sets • 2N-2 independent linear equations : ±W1 ± W2 ± .... ± WN-1 • Excess of information for N>3 (8 linear equations for 3 frequencies)

  21. antiecho antiecho echo echo - WA 2WB w1 0 2WB WA w2 WI WI cos(WAt1) sin(WAt1) cos(WAt1) sin(WAt1) cos(WBt1) sin(WBt1) 0 WA- WB WA+ WB WI - WA 2WB 0 2WB WA WI WI Example: simultaneously sampled two frequencies A and B with phase and amplitude modulation, respectively

  22. Basic applications 2D  3D HNCA 3D : HNi (t3)  Ni (t1)  Cai, Cai-1 (t2) 2D : HNi (t2)  Ni (t1)  Cai, Cai-1 (t1) HN(CO)CA 3D : HNi (t3)  Ni (t1)  CO  Cai-1 (t2) 2D : HNi (t2)  Ni (t1)  CO  Cai-1 (t1)

  23. HN(CO)CA – single quadrature HSQC HN(CO)CA – double quadrature

  24. HN(CO)CA HNCA

  25. N C N C ++ ++ HN(CO)CA + - + - ++ ++ HNCA + - + -

  26. 4D → 2D HACANH j1= x/y, j2= x/y,(G1,y)/(-G1,-y)

  27. HACANH +++ +–– +–+ ++–

  28. Ca – coupled DQ/ZQ HNCOW. Koźmiński, I. Zhukov, M. Pecul, J. Sadlej J. Biomol NMR, 31, 87 (2005) • simplicity • in double quantum spectrum 1J(C’,Ca) + 2J(N,Ca) • in zero quantum spectrum 1J(C’,Ca) - 2J(N,Ca) • 1J(C’,Ca) ca. 50 Hz, 2J(N,Ca) 5-10 Hz • systematic errors due to relaxation effects significantly reduced

  29. Spectra for 13C,15N-ubiquitine 1J(C’,Ca) - 2J(N,Ca) 1J(C’,Ca) + 2J(N,Ca)

  30. Comparison with calculations

  31. When it does not work?

  32. Projection reconstruction • Frequencies in 2D spectrum sampled along r at angle j are : • w2 cos(j) + w1 sin(j) • It is a projection of 3D spectrum into plane tilted by angle j. • The multiple quadrature is necessary • Back projection technique: • Lauterbur, Nature, 242, 190 (1973)

  33. F3 (1H) F2 (15N) F1 (13C) Projection reconstructionKupče & Freeman, J. Biomol. NMR, 27, 383 (2003) • If F3 chemical shifts are not degenerated only two planes : F1F3 and F2F3 are necessary. • In practice one need to acquire several differently tilted planes • No pick picking with calculator • F1F3 t2 =0 • F2F3t1 =0

  34. F3 (1H) a F2 (15N) F1 (13C) More planes should resolve ambiguities

  35. Kupče & Freeman, J. Biomol. NMR, 27, 383 (2003)13C,15N-ubiquitine reconstruction conventional two planes F3 (1H) =7.28 ppm F3 (1H) =8.31 ppm three planes F3 (1H) =8.77 ppm

  36. Perspectives • New schemes for sparse data sampling in multidimensional NMR • New processing methods – generalized Fourier transform

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