Metody szybkiej rejestracji wielowymiarowych widm NMR

Wiktor KoźmińskiWydział Chemii Uniwersytetu Warszawskiego

• Multidimensional NMR

• Quadrature in indirectly sampled domains

• The new schemes of data acquisition

• Perspectives

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

Applications

• In chemistry: 2D NMRroutine applications of : COSY, NOESY, ROESY, HSQC, HMBC, etc.

• For biomolecules 2D to 5Dresonance assignment, structural constrains

• nD NMR also became popular in solid state studies

Measurement time and Sensitivity

• Sample limited - concentration of active nuclei, , B0, T, relaxation properties

• Sampling limited

- number of data points to acquire increases exponentially with the number of dimensions

N - dimensional sequence :

t Nexc mix i

t i

N–1

For ki data points in ti : k1 k2 .... kN-1 2N-1 measurements

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

Single scan acquisitionFrydman, Scherf & Lupulescu, PNAS, 99, 15858 (2002)

EPI – Echo Planar ImagingP. Mansfield, Magn. Reson. Med., 1, 370 (1984)

Spatially selective excitation

Spatially selective acquisition (EPI)

Spatially selective excitation

Oi

t1

N1

+Ge

-Ge

RF

G

G = z

t1

t1

t1

t1

Offset O1

Offset O2

Excitation Offset

z

EPI acquisition

S(k,t2)

Example

With a adiabatic frequency sweep pulses

Pelupessy, JACS, 125, 12345 (2003)

1H-15N HSQC on protein sample

Single scan approach

• Very fast data collection

• Limited resolution

Time domain sampling

t1

t2

………………………………………………………………………………..

t1

t2

conventional radial„Accordion Spectroscopy”

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

mix = t1

The exchange rates are reflected in lineshapes

Accordion spectroscopysimultaneous 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)

Accordion sampling of two (or more shifts)

– Reduced Dimensionality

t1

t2

Radial sampling along one radius Linear combination of frequencies evolving in t1 and t2

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 resolutioncarrier offset for B-nuclei should be chosen outside of the region of interest – increased spectral width and number of increments.

F1 (A) A A - |B|

A + |B|

B

Simultaneously sampled evolution of A and B nuclei

Quadrature in indirectly sampled domainscase 1) amplitude modulation

Two experiments for each evolution time increment:Modulation:= x cos(tx) real part = y sin(tx) imaginary part

States method: D.J. States et al., J. Magn. Reson., 48, 286 (1982)

States – TPPIModification by reversing and receiver phase for even tx increments – axial peaks displacement

D.J. Marion et al., J. Magn. Reson., 85, 393 (1989)

tx

x

Quadrature in indirectly sampled domainscase 2) phase modulation

PFG echo-antiecho, sensitivity enhanced and TROSY experimentsTwo experiments for each evolution time increment:

G1 = (2/1)G2 cos(tx) – i sin(tx) echo

2 G1 = - ()G2 cos(tx) + i sin(tx) antiecho

Data recombination necessary

tx

PFGG1

G2

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 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 = 2cos(At1)sin(At1)

n = 2 number of data sets = 4cos(At1) cos(At1)sin(At1) cos(At1)cos(At1) sin(At1)sin(At1) sin(At1)

• In ND spectrum reduced to 2D with N-1 frequences sampled simultaneoulsy 2N-1

data sets • 2N-2 independent linear equations : ±1 ± 2 ± .... ± N-1

• Excess of information for N>3 (8 linear equations for 3 frequencies)

Example: simultaneously sampled two frequencies A and B with phase and amplitude modulation,

respectively

cos(At1) sin(At1) cos(At1) sin(At1) cos(Bt1) sin(Bt1)

echo antiecho echo antiecho

Basic applications 2D 3D

i i-1

HNCA3D : HN

i (t3) Ni (t1) Ci, Ci-1 (t2) 2D : HN

i (t2) Ni (t1) Ci, Ci-1 (t1)

HN(CO)CA 3D : HN

i (t3) Ni (t1) CO Ci-1 (t2) 2D : HN

i (t2) Ni (t1) CO Ci-1 (t1)

HSQCHN(CO)CA – single quadrature

HN(CO)CA – double quadrature

HN(CO)CA HNCA

++

+ -++

++

++HN(CO)CA

HNCA

N C N C

+ -

+ -

+ -

4D → 2D HACANH

x/y,x/y,(G1,)/(-G1,-)

HACANH

+++

+–+

+– –

++–

[H i) , H (i-1) C (i), C (i-1) N(i)] ( ) H (i) ( )t tN 21

C – coupled DQ/ZQ HNCOW. Koźmiński, I. Zhukov, M. Pecul, J. Sadlej J. Biomol NMR, 31, 87 (2005)

- simplicity - in double quantum spectrum 1J(C’,C) + 2J(N,C)- in zero quantum spectrum 1J(C’,C) - 2J(N,C)- 1J(C’,C) ca. 50 Hz, 2J(N,C) 5-10 Hz- systematic errors due to relaxation effects significantly reduced

1J(C’,C) + 2J(N,C)

1J(C’,C) - 2J(N,C)

Spectra for 13C,15N-ubiquitine

Comparison with calculations

When it does not work?

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)

t1

t2

r

Projection reconstructionKupče & Freeman, J. Biomol. NMR, 27, 383 (2003)

F3 (1H)

F1 (13C)

F2 (15N)

F1F3 t2 =0 F2F3 t1 =0

• 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

More planes should resolve ambiguities

F3 (1H)

F1 (13C)

F2 (15N)

Kupče & Freeman, J. Biomol. NMR, 27, 383 (2003)

13C,15N-ubiquitine

F3 (1H) =8.77 ppm

F3 (1H) =7.28 ppm

F3 (1H) =8.31 ppm

two planes

three planes

reconstruction conventional

Perspectives

• New schemes for sparse data sampling in multidimensional NMR

• New processing methods – generalized Fourier transform