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  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. Measurement time and Sensitivity Sample limited - concentration of active nuclei, , B 0, T, relaxation properties Sampling limited -number of data points to acquire increases exponentially with the number of dimensions N - dimensional sequence : t N excmix i t i N–1 For k i data points in t i : k 1  k 2 ....  k N-1  2 N-1 measurements

6. New approaches 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

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

8. Spatially selective excitation

9. EPI acquisition S(k,t 2 )

10. Example

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

12. Single scan approach Very fast data collection Limited resolution

13. Time domain sampling conventional radial „Accordion Spectroscopy”

14. Accordion Spectroscopy G. 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  mix =  t 1 The exchange rates are reflected in lineshapes

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

16. Accordion sampling of two (or more shifts) – Reduced Dimensionality Radial sampling along one radius Linear combination of frequencies evolving in t 1 and t 2

17. Reduced Dimensionality n chemical shifts encoded in (n - 1) dimensions T. Szyperski, et al, J. Am. Chem. Soc., 115, 9307 (1993) 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. F 1  (A) A A - | B | A + | B | BB Simultaneously sampled evolution of A and B nuclei

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

19. Quadrature in indirectly sampled domains case 2) phase modulation PFG echo-antiecho, sensitivity enhanced and TROSY experiments Two experiments for each evolution time increment:  G 1 = (  2 /  1 )G 2 cos(  t x ) – i sin(  t x ) echo 2 G 1 = - (  )G 2 cos(  tx) + i sin(  t x ) antiecho Data recombination necessary txtx PFG G1G1 G2G2

20. Reduced Dimensionality with multiple quadrature Koźmiński & Zhukov, J. Biomol. NMR, 26, 157 (2003) Sampling of each chemical shift requires acquisition of both sine and cosine modulated interferograms Total number of 2 n 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 = 1number of data sets = 2 cos(  A t 1 ) sin(  A t 1 ) n = 2number of data sets = 4 cos(  A t 1 ) sin(  A t 1 ) cos(  A t 1 ) cos(  A t 1 ) sin(  A t 1 ) sin(  A t 1 ) In ND spectrum reduced to 2D with N-1 frequences sampled simultaneoulsy 2 N-1 data sets 2 N-2 independent linear equations : ±  1 ±  2 ±.... ±  N-1 Excess of information for N>3 (8 linear equations for 3 frequencies)

21. Example: simultaneously sampled two frequencies A and B with phase and amplitude modulation, respectively                             cos(  A t 1 ) sin(  A t 1 ) cos(  A t 1 ) sin(  A t 1 ) cos(  B t 1 ) sin(  B t 1 ) echo antiecho echo antiecho

22. Basic applications 2D  3D HNCA 3D : H N i (t 3 )  N i (t 1 )  C  i, C  i-1 (t 2 ) 2D : H N i (t 2 )  N i (t 1 )  C  i, C  i-1 (t 1 ) HN(CO)CA 3D : H N i (t 3 )  N i (t 1 )  CO  C  i-1 (t 2 ) 2D : H N i (t 2 )  N i (t 1 )  CO  C  i-1 (t 1 )

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

24. HN(CO)CA HNCA

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

26. 4D → 2D HACANH    x/y,    x/y,  (G 1,  )/(-G 1,-  )

27. HACANH +++ +–++–+ +– –+– – ++ –

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

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

30. Comparison with calculations

31. When it does not work?

33. Projection reconstruction Frequencies in 2D spectrum sampled along r at angle  are :  2 cos(  ) +  1 sin(  )  It is a projection of 3D spectrum into plane tilted by angle .  The multiple quadrature is necessary  Back projection technique:  Lauterbur, Nature, 242, 190 (1973)

34. Projection reconstruction Kupče & Freeman, J. Biomol. NMR, 27, 383 (2003) F 3 ( 1 H) F 1 ( 13 C) F 2 ( 15 N) F 1 F 3  t 2 =0 F 2 F 3  t 1 =0 If F 3 chemical shifts are not degenerated only two planes : F 1 F 3 and F 2 F 3 are necessary. In practice one need to acquire several differently tilted planes No pick picking with calculator

35. More planes should resolve ambiguities F 3 ( 1 H) F 1 ( 13 C) F 2 ( 15 N) 

36. Kupče & Freeman, J. Biomol. NMR, 27, 383 (2003) 13 C, 15 N-ubiquitine F 3 ( 1 H) =8.77 ppm F 3 ( 1 H) =7.28 ppm F 3 ( 1 H) =8.31 ppm two planes three planes reconstruction conventional

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