Lecture Coherence order and coherence selection

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Lecture Coherence order and coherence selection. After studying this section will help you understand: why we need coherence selection, concept of coherence order, coherence transfer pathways (CTPs), selecting a CTP with phase cycling,...

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Nội dung Text: Lecture Coherence order and coherence selection

EUROMAR 2011 Outline Further information • Why we need coherence selection • PDF of these slides available at Coherence order and http://www-keeler.ch.cam.ac.uk/ • Concept of coherence order coherence selection • See also: • Coherence transfer pathways (CTPs) Understanding NMR Spectroscopy, • Selecting a CTP with phase cycling James Keeler (Wiley) [Chapt. 11] James Keeler • Selecting a CTP with gradients • Suppression of zero-quantum Spin Dynamics. Basics of Nuclear coherence Magnetic Resonance, Malcolm Levitt (Wiley) Department of Chemistry Why we need coherence selection Coherence order, p Properties of coherence order Defined by phase acquired during • takes values 0, ±1, ±2 … DQF COSY rotation by about z 0 is z-magnetization, ±1 is single quantum, ρˆ ( p ) ⎯rotate ⎯⎯ by φ about z ⎯⎯ ⎯→ ρˆ ( p ) × exp(−ipφ) DQ spectrum ±2 is double quantum etc. phase acquired is −pφ • only p = −1 is observable NOESY • maximum/minimum value is ±N, where The spins don’t know what we want ! different p separated by using this property N is number of spins We want one out of many possibilities 1
Effect of pulses Coherence transfer pathway (CTP) Heteronuclear experiments Indicates the desired coherence order RF pulse all possible p at each point HMQC values of p - which is why we need selection special case: DQ spect. NOESY DQF COSY 180° pulse separate p for each nucleus (pI, pS) p −p note: always starts at p = 0 ends with p = −1 on observed nucleus always ends at p = −1 pulse to S only affects pS Frequency discrimination - or, alternatively and lineshapes in 2D for absorption mode spectra must retain p = ± 1 during t1: symmetrical pathways N-type Phase cycling P-type 1. record two separate spectra: echo or N-type: p = + 1 during t1 combine this with frequency discrimination anti-echo or P-type: p = − 1 during t1 using ‘TPPI’ or ‘States’ 2. combine to give absorption spectrum 2
Pulse phase Receiver (rx.) phase Receiver phase rx. phase fixed rx. phase If the signal generated by the pulse sequence shifts in phase, then this can always be compensated for by shifting rx. phase the receiver by the same amount. follows pulse phase the phase of the spectrum depends on the phase of the pulse Phase cycling Effect of phase shift of pulse Selection of a single pathway Selection of a pathway by repeating the sequence with a systematic variation of the pulse and rx. phases Pulse causes transfer from p1 to p2 +2 to −1, so Δp = –1 – (+2) = – 3 Change in coherence order Δp = p2 – p1 How to design the sequence of phases, phase acquired by signal when pulse - the phase cycle? If pulse phase shifted by Δφ phase shifted by Δφ is acquired by signal is − Δp × Δφ = 3 Δφ −Δp × Δφ 3
Four-step cycle Four-step cycle Four-step cycle step pulse Δφ 3 Δφ equiv(3 Δφ) step pulse Δφ 3 Δφ equiv(3 Δφ) step pulse Δφ 3 Δφ equiv(3 Δφ) 1 0° 1 0° 0° 1 0° 0° 0° 2 90° 2 90° 270° 2 90° 270° 270° 3 180° 3 180° 540° 3 180° 540° 180° 4 270° 4 270° 810° 4 270° 810° 90° Four-step cycle - other pathways Selected pathways Pulse goes e.g. Δp = – 2 so − Δp × Δφ = 2 Δφ rx. phase [0°, 270°, 180°, 90°] [0°, 90°, 180°, 270°] step pulse Δφ 2 Δφ equiv(2 Δφ) Pathway with Δp = −3 acquires phase 1 0° 0° 0° Δp= –3 [0°, 270°, 180°, 90°] 2 90° 180° 180° rx. phase coherence 3 180° 360° 0° phase If receiver phase follows these phases, 4 270° 540° 180° contribution from the pathway will add up For Δp= –3, rx. phase follows coherence Selected with rx. phases phase: - but what about other pathways? [0°, 270°, 180°, 90°] ? all four steps add up 4
Selected pathways Selectivity Combining phase cycles rx. phase [0°, 270°, 180°, 90°] A four-step cycle designed to select a particular value of Δp will also select Δp + 4, Δp + 8 … and Δp − 4, Δp − 8… Δp= –2 four-step cycle to select Δp = +1 rx. phase coherence - all other pathways are suppressed step pulse Δφ1 − Δφ1 equiv(− Δφ1) phase (−4) −3 (−2) (−1) (0) 1 (2) (3) (4) 5 1 0° 0° 0° 2 90° −90° 270° For Δp= –2, signal cancels on four steps 3 180° −180° 180° selected in bold, suppressed in () 4 270° −270° 90° Combining phase cycles Complete both cycles independently Tricks: 1 step Δφ1 − Δφ1 equiv(−Δφ1) Δφ2 2 Δφ2 equiv(2Δφ2) total 1 0° 0° 0° 0° 0° 0° 0° 2 90° −90° 270° 0° 0° 0° 270° 1. The first pulse can only generate 3 4 180° 270° −180° −270° 180° 90° 0° 0° 0° 0° 0° 0° 180° 90° p = ±1 from equilibrium magnetization 5 0° 0° 0° 90° 180° 180° 180° 6 90° −90° 270° 90° 180° 180° 90° four-step cycle to select Δp = −2 7 180° −180° 180° 90° 180° 180° 0° 8 270° −270° 90° 90° 180° 180° 270° - no need to phase cycle this pulse step pulse Δφ2 2 Δφ2 equiv(− Δφ2) 9 10 0° 90° 0° −90° 0° 270° 180° 180° 360° 360° 0° 0° 0° 270° 1 0° 0° 0° 11 180° −180° 180° 180° 360° 0° 180° 12 270° −270° 90° 180° 360° 0° 90° 2 90° 180° 180° 13 0° 0° 0° 270° 540° 180° 180° 14 90° −90° 270° 270° 540° 180° 90° 3 180° 360° 0° 15 180° −180° 180° 270° 540° 180° 0° 16 270° −270° 90° 270° 540° 180° 270° 4 270° 540° 180° 5
Tricks: 2 Tricks: 3 Tricks: 4 2. Group pulses together and cycle as a unit 3. Only p = −1 is observable, 4. Don’t worry about high orders of so it does not matter if other values of multiple quantum coherence p are generated by the last pulse e.g ≥ 4. - no need to phase cycle the last pulse, - they are hard to generate and likely if a coherence order has been selected to give weak signals, especially if All pulses: [0°, 90°, 180°, 270°] unambiguously before this pulse the lines are broad Rx. for Δp = ±2: [0°, 180°, 0°, 180°] Refocusing pulses: EXORCYCLE Axial peak suppression Examples: DQF COSY Refocusing pulses cause p → −p z-magnetization which recovers by symmetrical relaxation during a pulse sequence is pathways in t1 made observable by last pulse e.g. Δp = ±2 (single quantum) - leads to peaks at ω1=0: axial peaks final pulse has Δp = −3 and +1 - easily suppressed using a two-step cycle - select using four-step cycle: φ3 = [0°, 90°, 180°, 270°] Pulse: [0°, 90°, 180°, 270°] 1st pulse: [0°, 180°] φrx = [0°, 270°, 180°, 90°] Rx. for Δp = ±2: [0°, 180°, 0°, 180°] Rx. for Δp = ±1: [0°, 180°] this is sufficient, as p can only be ±1 in t1 6
DQF COSY (alternative) Examples: NOESY Examples: NOESY symmetrical symmetrical pathways in t1 pathways in t1 group first two pulses and select Δp = ±2 final pulse has Δp = −1 axial peak suppression also required - select using four-step cycle: - select using four-step cycle: φ1 = [0°, 180°] φrx = [0°, 180°] φ1 and φ2 = [0°, 90°, 180°, 270°] φ3 = [0°, 90°, 180°, 270°] Step 1 2 3 4 5 6 7 8 φrx = [0°, 180°, 0°, 180°] φrx = [0 °, 90°, 180°, 270°] Φ1 0° 0° 0° 0° 180° 180° 180° 180° Φ3 0° 90° 180° 270° 0° 90° 180° 270° this is sufficient, as p can only be −1 in t2 this is sufficient, as p can only be ±1 in t1 Φrx 0° 90° 180° 270° 180° 270° 0° 90° Problems with phase cycling Field gradient pulses • phase cycle must be completed: • the B0 field is made inhomogeneous - unacceptably long experiment, for a short period (few ms) especially for 2D/3D Gradient pulses • coherences dephase, all signal lost • cancellation of unwanted signals may • a subsequent gradient may rephase be imperfect (especially for proton some of the coherences detected experiments) 7
Effect of a gradient Dephasing and rephasing Spatially dependent phase gradient phase acquired by coherence p at dephase position z in sample, after time t φ(z) = −p × γ G z t gyromagnetic ratio gradient strength, G cm−1 active volume rephase off: sharp line on: v. broad line phase depends on position and p Selection with a gradient pair Selection with a gradient pair Selection with a gradient pair G1τ1 p =− 2 G2 τ 2 p1 phase due to G1: φ1(z) = −p1 × γ G1 z τ1 φ1(z) + φ2(z) = −p1 γ G1 z τ1 − p2 γ G2 z τ2 G1τ1 −1 1 e.g. p1 = +2, p2 = −1 =− = =0 G2 τ 2 +2 2 phase due to G2: φ2(z) = −p2 × γ G2 z τ2 G1τ 1 p if G1 = G2, τ2 = 2 τ1 refocusing condition: φ1(z)+ φ2(z) = 0 =− 2 alternatives G2τ 2 p1 if τ1 = τ2, G2 = 2 G1 8
Selection with a gradient pair Heteronuclear case Only one pathway selected G1τ1 p only pS =− 2 G1τ1 1 G2 τ 2 p1 changes = G2 τ 2 2 G1τ1 −1 1 G1τ1 1 e.g. p1 = −2, p2 = −1 =− =− φ1(z) = −(pI γI+ pS γS)G1zτ1 = −(−γI+γS)G1zτ1 =− G2 τ 2 −2 2 G2 τ 2 2 φ2(z) = −(pI gI+ pS γS)G2zτ2 = −(−γI−0)G2zτ2 can only select one of these pathways refocusing: τ1 = τ2, G2 = −2 G1 G1τ1 1 - potential loss of sensitivity ‘−G’ means opposite sense of gradient = G2 τ 2 (γS γI ) − 1 - problems in two-dimensional NMR Refocusing pulses 180° in heteronuclear case Phase errors DQF COSY no coherence on I spin Ideal 180° causes p → −p 180° to I is acting as inversion pulse Offsets continue to evolve during gradients Selected for all p by equal gradients Gradient pair ‘cleans up’ imperfect 180° - results in severe frequency-dependent - ‘cleans up’ imperfect 180° - leaves S spin coherences unaffected phase errors 9
Avoiding phase errors Selection of z-magnetization Examples: DQF COSY add refocusing pulse / use an existing one A gradient dephases all* coherences: offset evolution - leaves behind only z-magnetization refocused - simple and convenient by 180° pulse called a purge gradient or homospoil more time • symmetrical pathways in t1 (no gradient) efficient alternative *except homonuclear zero-quantum • extra 180° pulses to avoid phase errors • loss of sensitivity Examples: HMQC HMQC: refocusing condition HMQC: suppression of I spin magnetization not coupled to S I I I S S S P-type (solid line) (− γI G1 zτ1 − γS G1 zτ1 ) + (γI G1 zτ1 − γS G1 zτ1 ) + (γI G2 zτ 2 ) = 0 • separate expts. for P- and N-type • I magnetization dephased by 1st G1, − 2γS G1 zτ1 + γI G2 zτ 2 = 0 • additional 180° associated with both G1 but rephased by second G1, and then G1τ1 γ • G2 in existing delay, so no phase error = I dephased by G2 G2 τ 2 2γS 10
HSQC Advantages and disadvantages + minimizes experiment time + excellent suppression, especially in heteronuclear experiments with 1H obs. Zero-quantum dephasing - cannot select more than one pathway → possible loss of SNR • G1 is purge gradient → obtaining pure phase more complex • extra 180° associated with G2 - phase errors • G3 in existing spin echo → requires elaboration of sequence • can omit G2 and G3 (labelled samples) - loss due to diffusion An old, old problem in NMR Why is it a problem? Result: distorted multiplets in 2D z-magnetisation and zero-quantum a 90° pulse converts z-magnetization coherence cannot be separated using into in-phase magnetization along y phase cycling or gradients but converts ZQ into anti-phase because along x neither respond to z-rotations the result is phase distortion and i.e. both have coherence order, p, unwanted peaks of zero z-magn. + ZQ z-magn. only 11
Example: NOESY The z-filter but … Sørensen, Rance, Ernst 1984 90°(y) 90°(−y) t1 m t2 RF 90°(y) 90°(−y) RF G G RF wanted: z-magn. during m 2I1yI2z 2I1yI2x mixture of G DQ and ZQ → in-phase, absorption multiplets I1x −I1z I1x ½(2I1yI2x−2I1xI2y) ½(2I1yI2z−2I1zI2y) unwanted: ZQ during m everything else dephased ZQ → anti-phase, dispersion multiplets ‘J-peaks’ only in-phase magnetization survives Anti-phase component passes through Make evolution dependent on Zero-quantum evolution Zero-quantum dephasing position 90° 90° 180 z z As frequency is a function of position, RF the zero-quantum coherence will G dephase position The zero quantum evolves during Identical to dephasing in a conventional τz at (Ω1− Ω2), the difference of gradient the shifts Macura et al 1981 this is the key … how to make 180° position dependent? frequency time 12
Swept-frequency 180º z-filter with zero-quantum Typical parameters suppression normal spectrum • swept pulse of duration 15 to 30 ms apply gradient RF G • gradient 1 to 2 G cm−1 frequency position swept 180º with gradient • dephasing rate depends on ZQ frequency swept-frequency 180º pulse additional dephasing gradient • suppression of ZQ by factor of 100 (to make sure everything is dephased) different parts experience pulse at different times NOESY with zero-quantum NOESY results (strychnine) TOCSY suppression τm conventional + ZQ suppression t1 t1 DIPSI-2 t2 RF RF G G swept 180º with gradient isotropic mixing within z-filter additional dephasing gradient ZQ dephasing needed before and after mixing; unequal durations NOE continues to build up throughout 13
TOCSY results (strychnine) TOCSY results (strychnine) Advantages of the z-filter conventional + ZQ suppression conventional + ZQ suppress. • excellent suppression • no increase in experiment time • simple to implement • widely applicable • negligible reduction in signal Examples: HMQC Difference spectroscopy: HMQC The End select ΔpS = ±1 at first S pulse and ΔpI = ±2 at 180° I pulse The cycle [0°, 180°] on first S pulse and Phew! step φS 1 0° 2 3 4 5 6 7 180° 0° 180° 0° 180° 0° 180° 8 rx. is just difference spectroscopy: selects that part of the signal which φI 0° 0° 90° 90° 180° 180° 270° 270° goes via the S spin φrx 0° 180° 180° 0° 0° 180° 180° 0° 14
Difference spectroscopy In heteronuclear experiments, a simple two-step phase cycle (+x/−x) on the pulse causing the transfer often suffices - this is simply difference spectroscopy 15