Coherence Selection: Phase Cycling and Gradient Pulses

1. Coherence Selection: Phase Cycling andGradient Pulses

2. Purpose Systematically vary the phases of RF pulses and receiver in a pulsesequence to compensate for imperfections cancel artefacts select for the ‘desired signals’ only

3. A simple example CYCLOPS Cancels imbalances between x and y channel of the receiver system and eliminates the ‘Quad spike’ x, y, -x, -y are usually referred to as 0 1 2 3 or 0 90 180 270

4. Refocussing pulses F rec x y y –y -x y -y -y EXORCYCLE Removes the effects of an imperfect refocussing pulse The receiver only follows the signal that has been properly inverted

5. Difference Spectroscopy

6. Multiple Quantum Spectroscopy Coherences, of which transverse magnetization is one example, can be classified according to a coherence order, p, which is an integer taking values 0, ± 1, ± 2 ... Single quantum coherence has p = ± 1, double has p = ± 2 and so on; z-magnetization, "zz" terms and zero-quantum coherence have p = 0 ‘Number of transverse terms in a product operator’ if we consider a pulse which causes a change in coherence order of Dp then altering the phase of that pulse by an angle f will result in the coherence acquiring a phase label Dp f.

7. Coherence Transfer Pathways f1 f2 f3 f1 f2 f3 DQF-COSY NOESY The same pulsesequence is used for different experiments Different coherence orders are selected by a phasecycle f1 f2 f3 receiver x: Iy+Sy x: -Iz-Sz x: -Iy-Sy x Iy+Sy -2IxSz-2SxIz 2IxSy-2SxIy 2IxSz+2SxIz x y: -Ix-Sx y: -Iz-Sz x: -Iy-Sy x -Ix-Sx -2IySz-2SyIz2IySx+2SyIx-2IzSx-2SzIx -x -x: -Iy-Sy -x: -Iz-Sz x: -Iy-Sy x -Iy-Sy +2IxSz+2SxIz 2IxSy-2SxIy 2IxSz+2SxIz x -y: Ix+Sx -y: -Iz-Sz x: -Iy-Sy x Ix+Sx +2IySz+2SyIz 2IySx+2SyIx -2IzSx-2SzIx -x

8. Axial peak suppression Peaks at co-ordinates F1 = 0 and normal F2 frequency i.e. magnetization which has not evolved during t1 and has no frequency label. Common sources: z Magnetisation during evolution period Iz is made observable by subsequent pulses longitudinal relaxation during t1 or pulse imperfection / miscalibration to suppress axial peaks: select the pathway Dp = ±1 onthe first pulse with two-stepcycle 0°, 180° on the first pulse and the receiver Make sure there is transverse magnetisation Gives a total 8 step phasecycle when added to the 4 step coherence selection for NOESY f1: x ,-x, y, -y, -x, x, -y, y f2: 2x, 2y, 2(-x), 2(-y) f3 :x Rec: 4x, 4(-x)

9. Heteronuclear Experimentse.g 13C HMQC separate coherence orders are assigned to the I and S spins. DpS = ±1 for the first S pulse is desired +/- together with the receiver, can be combined with a phasecycle for the second S pulse and EXORCYCLE for the 180.. 16 steps

10. Problems with phasecycling two major practical problems. The firstis that the need to complete the cycle imposes a minimum time on the experiment. In two- and higher-dimensional experiments this minimum time can become excessively long, far longer than would be needed to achieve the desired signal-to-noise ratio. The second problem is that phase cycling always relies on recording all possible contributions and then cancelling out the unwanted ones by combining subsequent signals. It is a difference method. If the spectrum has high dynamic range, or if spectrometerstability is a problem, this cancellation is less than perfect. Especially when dealing with proton detected heteronuclear experiments on natural abundance samples(1% 13C), or spectra with intense solventresonances.

11. Selection with pulsed field Gradients PFG xy Magnetsation dephases under the influence of a field gradient The Rate of dephasing is proportional to the coherence order P (DQC twice as fast as SQC, ZQC or z-Magnetisations does not dephase) this is reversible and can be undone by an appropriate PFG of opposite polarity by applying gradient pulses of different strengths or durations it is possible to refocus coherences which have, for example, been changed from single- to double-quantum by a pulse. Advantage: Not a difference method, selection in a single scan, no need to complete a long and complex phasecycle Disadvantage: extra hardware required. PFG probes etc…

12. Selection by refocusing The gradients must be balanced Selection by suppression, z-Filter The desired signal is put along z and everything else is purged with a gradient The coherence selection is achieved with a spoiler gradient during tm. Axial peak suppression by phasecycling is still recommended, though

14. ge DQF COSY Possible solution Incorporate gradients into echos Problem Evolotion during gradients will give phase distortions

15. ge-HMQC I shift evolution during G1 is refocussed by the 180 Only the S contribution needs to be refocussed e.g for 13C HMQC G1=+/-2G2 Both pathways are required for ‘pure phase’ spectra

16. ge-HSQC gradient selection G1= +/- gI/gS G2 zz filter Suppresses uncoupled magnetization

17. Sensitivity enhancementse – HSQC

18. H2O suppressionWATERGATE For H2O 0 deg rotation No refocussing Other spins normal echo Can be easily incorporated into echo or INEPT elements

19. The ‘Full Monty’ct-ge HNCA