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Design, principles and building blocks of Design, principles and building blocks of
heteronuclearheteronuclear NMR pulse sequencesNMR pulse sequences
Michael SattlerMichael Sattler
EMBL HeidelbergEMBL Heidelberg
GSFGSF--National Research Center for Environment and HealthNational Research Center for Environment and Health
Technical University Technical University MMüünchennchen
Prog. NMR Spectrosc. (1999) 34, 93-158.http://www.embl.de/nmr/sattler
EMBO Practical Course:EMBO Practical Course:
Structure determination of biological macromolecules by solutionStructure determination of biological macromolecules by solution NMRNMR
BiozentrumBiozentrum Basel, July 6Basel, July 6--13 200713 2007
ContentsContents
•• HeteronuclearHeteronuclear NMR: motivationNMR: motivation
•• Basic pulse sequence elements and 2D correlationsBasic pulse sequence elements and 2D correlations
•• RF pulses: calibration, selective pulsesRF pulses: calibration, selective pulses
•• Sensitivity enhancement, gradients, coherence selectionSensitivity enhancement, gradients, coherence selection
•• WaterWater--flip backflip back
•• SpinSpin--state selection, TROSYstate selection, TROSY
•• Triple resonance experimentsTriple resonance experiments
•• Isotope editing and filteringIsotope editing and filtering
Structure determination by NMRStructure determination by NMR
NOENOE--based assignment strategiesbased assignment strategies
11JJ-- and and 22JJ--couplings in proteinscouplings in proteins
H H| |
C C
Speed/efficiency of magnetization transferSpeed/efficiency of magnetization transfer
H H| |
C C
Homonuclearmagnetization transfer
via 3J coupling
Heteronuclearmagnetization transfer
via 1J couplings
10Hz
35Hz
140H
z
140H
z
100 ms100 ms 35 ms35 ms
S/NS/N ~ ~ NN γγexcexc γγdetdet3/23/2 BB00
3/23/2 NSNS1/21/2 TT22
Assignment based on JAssignment based on J--correlationscorrelations
MultiMulti--dimensional NMR experimentsdimensional NMR experiments
• To resolve signal overlap with increasing molecular weight
• 1/√2 loss of S/N per indirect dimension
• potential problems: time needed for sampling
ω2
ω3
ω1ΩΤ
ΩΤ’
ΩI
ΩS
ΩS’
t1 t2 t3preparation
I S T I
mixing mixing mixing detection
3D FT NMRφS φT
1
3
2
15N
1H
13C
15N
1H
Iz Iz
Ix,y Ix,y cosπΩ t ± Iy,x sinπΩ t
πΩ tChemical shiftChemical shift
PulsesPulses
9090°° pulsepulse
Scalar couplingScalar coupling
Iz Iz
IxSy IxSy
Ix,y Ix,y cosπJISt ± 2Iy,xSz sinπJISt
2Ix,ySz 2Ix,ySz cosπJISt ± Iy,x sinπJISt
πJIS2IzSz t
Iz Iz cosβ ± Ix,y sinβ
Ix,y Ix,ycosβ Iz sinβ
Ix,y Ix,y
+
Iz ± Ix,y
Ix,y Iz
90°y,x
β x,y
Pulse Pulse EductEduct ProductProductx y z & cyclic x y z & cyclic x z x z −−y y permutpermut..
Product operator formalismProduct operator formalism
+
Chemical Chemical shiftshift and and JJ--couplingcoupling evolutionevolution
HowHow to to analyzeanalyze pulse pulse sequencessequences
180o pulses can be combined if coherence order
magnitude is preserved inbetween
( i.e. no 90o pulse applied)
HeteronuclearHeteronuclear polarizationpolarization transfertransfer
S/NS/N ~ ~ NN γγexcexc γγdetdet3/23/2 BB00
3/23/2 NSNS1/21/2 TT22
Basic Basic heteronuclearheteronuclear correlationscorrelations: HMQC: HMQC
δδ((11H): refocusedH): refocused
δδ((1313C): evolution during tC): evolution during t11
J(J(11H,H,1313C): active during C): active during ΔΔ
J(H,H): active !J(H,H): active !
J(C,C): active !J(C,C): active !
Relaxation during tRelaxation during t11: multiple quantum line: multiple quantum line--narrowingnarrowing
Basic Basic heteronuclearheteronuclear correlationscorrelations: HSQC: HSQC
δδ((11H): refocusedH): refocused
δδ((1313C): evolution during tC): evolution during t11
J(J(11H,H,1313C): active during C): active during ΔΔ
J(H,H): not activeJ(H,H): not active
J(C,C): active !J(C,C): active !
Relaxation during tRelaxation during t11: T1(: T1(11H), T2(H), T2(1313C)C)
Basic building blocks: Basic building blocks: heteronuclearheteronuclear correlationcorrelation
Relaxation during tRelaxation during t11
T2MQ (IxSy) > T2(S)
Methyl TROSY
T1 I-spin (1H)
T2 S-spin (13C)
T2 S-spin (13C)
Bax et al JMR (1990) 86, 304-318
synchronous decoupling!
Transfer Transfer amplitudesamplitudes forfor antiphaseantiphase//inin--phasephaseconversionconversion in CH, CHin CH, CH22 and CHand CH33 spinspin systemssystems
-1
-0.5
0
0.5
1
0 1 2
1/(4J) 1/(2J)
3 4 5
CH
CH2
CH3
6 7 8 9
CH: 2HCH: 2HzzCCyy CCxx sin(sin(ππ11JJH,CH,C ΔΔ’’) )
CHCH22: 2H: 2HzzCCxx CCxx sin(sin(ππ11JJH,CH,C ΔΔ’’) cos() cos(ππ11JJH,CH,C ΔΔ’’) )
CHCH33: 2H: 2HzzCCxx CCxx sin(sin(ππ11JJH,CH,C ΔΔ’’) cos) cos22((ππ11JJH,CH,C ΔΔ’’) )
JJ--coupling evolution during thecoupling evolution during the
second half of a refocused INEPT:second half of a refocused INEPT:
ΔΔ’’ [ms][ms]
ConstantConstant--timetime HSQCHSQC
Set 2T = n/JSet 2T = n/JCCCC to refocus evolution of to refocus evolution of homonuclearhomonuclear C,C couplings during 2TC,C couplings during 2T
JJ--coupling evolution: cos(coupling evolution: cos(ππJJCCCC2T)2T)nn = = −−11nn
BIRD BIRD filterfilter to to suppresssuppress 1212C C magnetizationmagnetization
Excellent 12C suppression and fast acquisition (small, unlabeled molecules!)
Bax Subramanian JMR (1986) 67, 565-9Sattler et al JACS (1992) 114, 1126-7.
BIRD HSQC BIRD HSQC withwith multiplicitymultiplicity editingediting
J(H,C): refocusedJ(H,C): refocused
J(H,C): J(H,C): cos(cos(ππ))nn
Pulse calibration: considerationsPulse calibration: considerations
•• What sample to use for pulse calibration What sample to use for pulse calibration –– HH22O, protein, urea?O, protein, urea?
•• HH22O:O: ☺ large signal, very sensitive, optimize on FIDlarge signal, very sensitive, optimize on FID
radiation damping, different NMR properties than radiation damping, different NMR properties than biomoleculebiomolecule
•• protein:protein: ☺ NMR signals of interestNMR signals of interest
poor S/Npoor S/N
• urea: urea: ☺ high sensitivity, isolated signalshigh sensitivity, isolated signals
different NMR properties than actual sampledifferent NMR properties than actual sample
•• Calibration as 90Calibration as 90ºº, 180, 180ºº, 360, 360ºº pulse?pulse?
•• Problems: radiation damping, B1 Problems: radiation damping, B1 inhomogeneityinhomogeneity, amplifier power drop, amplifier power drop
•• Problems with Problems with cryoprobescryoprobes
•• salt concentration, B1 salt concentration, B1 inhomogeneityinhomogeneity, water suppression, water suppression
Pulse calibration: B1 Pulse calibration: B1 inhomogeneityinhomogeneity
•• Calibration of 180Calibration of 180°° or 360or 360°° pulsepulse
•• offoff--resonance effectsresonance effects
•• B1 B1 inhomogeneityinhomogeneity
Pulse calibration:
Center: [Z-shim detuned] Bulk [Z tuned] ERROR
90deg: 61us (expected) (app. 90)
180deg: 123us (2*90=122us) 132us (66.0us) 8%
360deg: 248us (4*90=244us) 257us (64.3us) 5%
Jerschow & Bodenhausen JMR (1999) 137, 108-115.
180180°°
360360°°
18001800°°
sample
NMR tube
11H H nutationnutation experimentexperiment
ZZ--shim detunedshim detuned0.1% Ethylbenzene
500 MHz Cryoprobe
180180°°
360360°°
Pulse calibrated on bulkPulse calibrated on bulk
sample
Pulse calibration: recommendationsPulse calibration: recommendations
•• calibrate 360calibrate 360°° pulse for pulse for 11HH
bulk pulse closer to bulk pulse closer to ““correctcorrect”” pulse at the center of pulse at the center of rfrf coilcoil
•• use use ShigemiShigemi (solvent susceptibility matched) tubes(solvent susceptibility matched) tubes
reduced effects of B1 reduced effects of B1 inhomogeneityinhomogeneity
reduced problems of higher salt concentrationsreduced problems of higher salt concentrations
•• optimize individual pulses in optimize individual pulses in multipulsemultipulse sequencessequences
i.e. p2 i.e. p2 ≠≠ p1*2, p1*2, ……
Pulse calibrationPulse calibration
ProblemProblem: no phase cycle : no phase cycle 11HH--1212C signals not suppressed!C signals not suppressed!
Phase cycling Phase cycling 11HH--1212C signals are suppressed!C signals are suppressed!
Experimental determination of relative RF phasesExperimental determination of relative RF phases
Why is this important?Why is this important?
RF at different RF power levels may have RF at different RF power levels may have
different relative phase. Such phase different relative phase. Such phase
shifts have to be compensated for in a shifts have to be compensated for in a
pulse sequence.pulse sequence.
How to determine the relative RF How to determine the relative RF
phase?phase?
For calibration, set For calibration, set ψψ = y; this should = y; this should
yield zero signal in the absence of phase yield zero signal in the absence of phase
shifts.shifts.
Adjusting the phase increment Adjusting the phase increment δδ to to
optimize for zero signal. This is then the optimize for zero signal. This is then the
required phase compensation.required phase compensation.
1D 1D 1313C spectrum of a proteinC spectrum of a protein
160.0 120.0 80.0 40.0 [ppm]δ13C
C' Carom. Caliph.
Selective RF pulses: rectangular pulsesSelective RF pulses: rectangular pulses
β = ω1∗ τp = −γB1∗ τp
Flip angle of RF pulse:ΔΩ
13Cα13C’
90° pulse:
βeff = 4∗β = 360° ⇒ (ω1eff)2 = (4ω1)
2 = ω12 + (ΔΩ)2 ⇒ ω1 = ΔΩ/√15
180° pulse:
βeff = 2∗β = 360° ⇒ (ω1eff)2 = (2ω1)
2 = ω12 + (ΔΩ)2 ⇒ ω1 = ΔΩ/√3
τp(90°) = β/ω1 = π/2 ∗ √15 / (2π∗ΔΩ)
τp(180°) = β/ω1 = π ∗ √3 / (2π∗ΔΩ)
BandBand--selective RF pulses: shaped pulsesselective RF pulses: shaped pulses
γB1rect/2π
τp τp
γB1max /2π
β = γB1rect ∗ τp
= γB1rect/2π ∗ τp ∗ 360°
β = γB1max ∗ ΣAi ∗ τp
= γB1rect / ΣAi ∗ τp
Rectangular pulse Shaped pulse
Σ (Ai ∗ τp/NP)
τp = pulse widthNP = number of points in shapeAi = relative intensity, 0…1
BandBand--selective RF pulses: rectangular vs. shaped selective RF pulses: rectangular vs. shaped pulsespulses
Mz
ΔΩ π/2 [kHz]
1.0
1.0
0
0.2
0.2
0.4
0.4
0.6
0.6
0.8
0.8
25 -2520 -2015 -1510 -105 -50
180rectangular
pulse
o
G3-pulse
C'
Caliph.
1.0
Mxy
ΔΩ π/2 [kHz]
0
0.2
0.4
0.6
0.8
25 -2520 -2015 -1510 -105 -50
90rectangular
pulse
o
G4-pulse
C'
Caliph.
Selective excitation Selective inversion
OffOff--resonance pulses: phaseresonance pulses: phase-- and amplitude modulationand amplitude modulation
Phase modulation:Phase modulation:
φφiimodmod = = φφii −− (2(2ππ ∗∗ ΔΩΔΩ ∗∗ττpp∗ ∗ i/NP)i/NP)
Amplitude modulation:Amplitude modulation:
AAiimodmod = A= Aii ∗∗ 2cos(22cos(2ππ ∗∗ ΔΩΔΩ ∗∗ττpp∗ ∗ i/NP)i/NP)
G3, 500G3, 500μμssno modulationno modulation
Mz
Mz
Mz
ΔΩ [Hz]
BandBand--selective RF pulsesselective RF pulses
GaussianGaussian(90(90°° / 270/ 270°°))
EE--BURPBURP
G4G4
Q5Q5
Selective inversion,Selective inversion,refocusing (180refocusing (180°°))
Selective excitationSelective excitation(90(90°°))
II--BURPBURP
RERE--BURPBURP
G3G3
Q3Q3
Adiabatic inversionAdiabatic inversion
HyperbolicHyperbolicsecantsecant
WURSTWURST
CHIRPCHIRP
References (shaped pulses and bandReferences (shaped pulses and band--selective decoupling):selective decoupling):
JMR (1991) 93, 93; Chem. Phys. Lett. (1990) 165, 469; JMR (1992) 97, 135;
JMR (1992) 100, 604; JMR (1993) A102, 364; JMR (1995) A115, 273; JMR (1996) A118, 299 .
shaped pulse: universal rotation
100
50
0
-50
[kHz]
[%]
2 1 0 -1 -2 -3
simulation
4.66 ms 2174.2 Hz 6.18 ms 742.1 Hz
[kHz] 2 1 0 -1 -2 -3
e-Burp2
Mz -> My
100
50
0
-50
[%]
G4
Q5u-Burp
7.82 ms 598.5 Hz4.94 ms 829.2 Hz
My -> Mz
time rev.My -> Mz
W. Bermel, Bruker
BandBand--selective RF pulses selective RF pulses -- adiabatic pulsesadiabatic pulses
G3, 250μs, γB1max/2π ≈ 14kHz
WURST, 2.7ms, γB1max/2π ≈ 3kHz
Mz
ΔΩ [Hz]
WURST
Amplitude Phase
•• AdiabaticAdiabatic””fastfast”” passage: keep magnetization and passage: keep magnetization and rfrf field field colinearcolinear: |: |ddζζ/dt/dt| | «« ωωeffeff
•• NonNon--linear pulse phase modulation linear pulse phase modulation frequency sweep: frequency sweep: ddΔωΔω/dt/dt
•• broadbroad--band inversion with low powerband inversion with low power
•• problem: problem: adiabaticityadiabaticity requires long requires long ττPP
ζ
BlochBloch--SiegertSiegert phase shifts (BSP)phase shifts (BSP)
Chem. Phys. Lett. (1990) 165, 469
Off-resonance: ΔΩ » ω1
Precession around ω1eff :
φoff-reson = ω1eff∗ τp
Instead of precessionaround z-axis with:φfree = ΔΩ∗ τp
ω = 2ω1 1effθ
ω1
ΔΩ = √3ω1
ΔΩ = 3√ ω1
Mx180°-pulse:τπ =π/ω1
0 −ΔΩ
φBSP(0) = −ΔΩ * τπ = −√3 ω1 * π/ω1 = −√3π ≈ 48.2°
1313CC’’ 1313CCαα
rotating coordinate system at :−ΔΩ
x
y
ΔΩ τπx
y
x
y
ΔΩ τπx
y
ΔΩ τπ
180°-pulse at −ΔΩ
360° on-resonance=̂
free evolution
((1313CCαα))
Bloch Siegert shift: inversion simulationMz -> Mz
[%]
100
50
0
-50
[kHz] 4 0 -4 -8
Q3 (2 msec, 1650.4Hz, freq: 2kHz, -3kHz)
W. Bermel, Bruker
Bloch Siegert shift: inversion simulationMz -> Mz
[%]
100
50
0
-50
[kHz] 4 0 -4 -8
Q3 (2 msec, 3300.8Hz, freq: 2kHz, -3kHz)
W. Bermel, Bruker
Bloch Siegert shift: inversion simulationphase
[°]
200
100
0
-100
[time] T/2 T
Q3 (2 msec, 1650.4Hz, freq: -3kHz)
without pulse, with Q3 pulse, difference
My (freq: 2kHz)
W. Bermel, Bruker
BSP compensationBSP compensation
ΔΩ/2π [kHz]
BSP [°]
120
-80
-60
-40
-20
0
20
40
60
80
100
10 12 14 16 18 20 22 24 26 28 30
Bloch-Siegert phasefor a band-selective(± 5kHz) G3 pulse
Determine phase empirically(0th and 1st order)
Use amplitude-modulatedinversion pulse (0th order)
Use additional pulse(all orders are corrected)
φ+BSP(0)
δCα
C'
G3, 250 s, 18 kHzphase modulation
μ
TT t12
t12
Intrinsic correction(all orders are corrected)
φδ'
G3, 700 s, 18 kHzamplitude modulation
μ
TT t12
t12
BSP
φTT t1
2t12 δCα
C'
TT t12
t12
G3 shape withadded BSP correction
φBSP = ω12/(2ΔΩ)*τP
Calculate φBSP for each subpulse
of a shaped pulse and add it to
the phase to compensate for the
BSP.
JMR (1992) 100, 604; JMR (2000) 146, 369.
Experimental determination of Bloch Experimental determination of Bloch SiegertSiegert PhasePhase
•• Zero order phase correction Zero order phase correction δδ00 applied to the phase of a flanking 90applied to the phase of a flanking 90oo pulsepulse
•• First order phase correction by addition of a delay First order phase correction by addition of a delay δδ11
Bloch Siegert shift: inversion simulationMz -> Mz
[%]
100
50
-50
[kHz] 4 0 -4 -8
Q3 (2 msec, 3300.8Hz, freq: 2kHz, -3kHz)
with BS compens.
without
W. Bermel, Bruker
BSP
φTT t1
2t12
ΔΩ/2π [kHz]
BSP [°]
120
-80
-60
-40
-20
0
20
40
60
80
100
10 12 14 16 18 20 22 24 26 28 30
Bloch-Siegert phasefor a band-selective(± 5kHz) G3 pulse
BSP compensation (intrinsic or add. pulse)BSP compensation (intrinsic or add. pulse)
GradientsGradients in in heteronuclearheteronuclear NMR NMR experimentsexperiments
x x
Gz
I
y
x
y
xa
b
y
xa
b
a
b
y
x
Spin echo with gradients
Δ2
Δ2
x x y
Gz
S
I
I: Iz
Iz
-Iy
-Iy 2I Sx z -2I Sz y2I Sz z2I Sz z
Iy Iy
I-S:
y
x
Spoil/purge gradients
Coherencerejection
Coherenceselection
Water Water suppressionsuppression methodsmethods
Concentration [Concentration [11H] in HH] in H22O O ≈≈ 110 M, concentration 110 M, concentration biomoleculebiomolecule ≈≈ 1010--33 MM
PROBLEMS: PROBLEMS: dynamic range (receiver); radiation dampingdynamic range (receiver); radiation damping
•• PresaturationPresaturation
depends on Bdepends on B00 homogeneity (shimming)homogeneity (shimming)
signals with near solvent frequency are suppressed as well (e.g.signals with near solvent frequency are suppressed as well (e.g. HHαα in proteins)in proteins)
reduces S/N of exchangeable protons due to saturation transferreduces S/N of exchangeable protons due to saturation transfer
•• JumpJump--andand--return / binominal sequencesreturn / binominal sequences☺ waterwater--flipflip--back intrinsic/possibleback intrinsic/possible
nonnon--optimum excitation profile optimum excitation profile
difficult to combine with triple resonance/multidifficult to combine with triple resonance/multi--pulse sequencespulse sequences
•• SpinSpin--lock, gradient spoil pulses, WATERGATElock, gradient spoil pulses, WATERGATE☺ can be combined with watercan be combined with water--flipflip--backback
suppression of signals near watersuppression of signals near water
•• HeteronuclearHeteronuclear gradient echoesgradient echoes☺ excellent waterexcellent water--suppression with sensitivity enhancement, combine with watersuppression with sensitivity enhancement, combine with water--flipflip--backback
•• PostPost--acquisitionacquisition
☺ apply lowapply low--pass filters to eliminate signals at 0 pass filters to eliminate signals at 0 ±± ωω, i.e. water on, i.e. water on--resonanceresonance
suppresses signal near water as wellsuppresses signal near water as well
RadiationRadiation dampingdamping
τp=20.5μs (<180°)
τp=20.8μs (>180°)
1H
FID
FID
detect
Δ [s]
Δ
0.050 0.100 0.150 0.200 0.250 0.300
Δ
1H
1H
Grad
Mxy
Warren, Hammes, Bates J.Chem. Phys (1989) 91, 5895Chen, Mao, Ye JMR (1997) 124, 490-494
WaterWater--flipflip--backback
1, 1, --1 Jump1 Jump--returnreturn
excitation null onexcitation null on--resonanceresonance
WATERGATE with waterWATERGATE with water--flipflip--backback
HSQC HSQC withwith WATERGATE & WATERGATE & waterwater--flipflip--backback
HH22O:O: zz --yy yy zz --zz zz zz
Suppress radiation damping Suppress radiation damping
of Hof H22O signal during tO signal during t11
waterwater--flipflip--backback
SensitivitySensitivity enhancementenhancement
•• Optimized coherence transfer, coherence order selective Optimized coherence transfer, coherence order selective
transferstransfers
•• sensitivity enhancement (coherence order selective coherence trasensitivity enhancement (coherence order selective coherence transfer)nsfer)
•• double sensitivity enhancementdouble sensitivity enhancement
•• TROSYTROSY
•• MQ lineMQ line--narrowing (methyl TROSY)narrowing (methyl TROSY)
•• Simultaneous acquisition, i.e. Simultaneous acquisition, i.e. 11HH--1313C, C, 11HH--1515N correlationN correlation
•• WaterWater--flipflip--back (for amides affected by solvent exchange)back (for amides affected by solvent exchange)
•• Longitudinal relaxation optimization (LHSQC, LTROSY)Longitudinal relaxation optimization (LHSQC, LTROSY)
•• Fast data acquisitionFast data acquisition
SensitivitySensitivity enhancementenhancement
RSH
amplitude modulation
Echo/anti-echo
Phase modulation
SensitivitySensitivity enhancementenhancement / / gradientgradient coherencecoherence selectionselection
Standard HSQCno gradient coherence selection
S/N = 1
Standard HSQCgradient coherence selection
S/N = 1/√2
Sensitivity enhanced HSQCgradient coherence selection
S/N = √2
S/N=: I/√n (I: Σ(intensities), n: # signals)
SensitivitySensitivity--enhancedenhanced HSQC HSQC withwith waterwater--flipflip--backback
HH22O:O: zz --yy yy zz --zz --yy yyyy --yy --zz zz
Suppress radiation damping Suppress radiation damping
of Hof H22O signal during tO signal during t11
waterwater--flipflip--backback
WaterWater--flipflip--backback
SE HSQCSE HSQC
2D: S/N*2D: S/N*√√22
WATERGATE HSQC WATERGATE HSQC
H2O: +zH2O: dephasedH2O: -z
H2O: +zH2O: dephasedH2O: -z
Longitudinal Longitudinal relaxationrelaxation optimizationoptimization
•• faster longitudinal relaxationfaster longitudinal relaxation
•• bandband--selective inversion of spins, i.e. amide protonsselective inversion of spins, i.e. amide protons
•• partially already achieved by waterpartially already achieved by water--flipflip--backback
•• faster repetition ratesfaster repetition rates
Pervushin et al JACS (2002)124, 12898Schanda & Brutscher JACS (2005), 127, 8014Attreya & Szyperski PNAS (2004) 101, 9624.Deschamps & Campbell JMR (2006) 178, 206
Double Double sensitivitysensitivity enhancementenhancement
Double sensitivity enhanced HCCHDouble sensitivity enhanced HCCH--TOCSYTOCSY
J. Biomol. NMR (1995) 6, 11-22.
•• can be recorded in Hcan be recorded in H22O due to excellent water suppression by O due to excellent water suppression by heteronuclearheteronuclear gradient echogradient echo
SimultaneousSimultaneous 1313C/C/1515N,N,11H HSQCH HSQC
JBN (1994) 4, 201-213; JMR (1994) B103, 197-201.
•• 11H H ↔↔ X transfer can be optimized simultaneously for X transfer can be optimized simultaneously for 1313C and C and 1515NNbut: some relaxation loss for but: some relaxation loss for 1313C due to longer delay.C due to longer delay.
•• poor waterpoor water--suppression, since E/AE cannot be implemented without sensitivitsuppression, since E/AE cannot be implemented without sensitivity loss.y loss.
•• building block for simultaneous 3D/4D NOESY experiments.building block for simultaneous 3D/4D NOESY experiments.
SimultaneousSimultaneous sensitivitysensitivity enhancementenhancement
SimultaneousSimultaneous sensitivitysensitivity enhancementenhancement
JBN (1995) 5, 97-102.
SimultaneousSimultaneous sensitivitysensitivity enhancedenhanced HSQC in HHSQC in H22OO
JBN (1995) 5, 97-102.
Basic building blocks: spinBasic building blocks: spin--statestate--selective filtersselective filters
JMR (1998) 131 373.
IP AP
ΔΣ
Basic building blocks: spinBasic building blocks: spin--statestate--selective filtersselective filters
J. Biomol. NMR (1997) 10, 181; JMR (1997) 128, 92; J. Biomol. NMR (1998) 12, 435.
Short filter, but sensitive to JShort filter, but sensitive to J--mismatch!mismatch!
Basic building blocks: spinBasic building blocks: spin--statestate--selective filtersselective filters
JBN (1997) 10, 181; JBN (1998) 12, 435.
Basic building blocks: spinBasic building blocks: spin--statestate--selective filtersselective filters
JMR (1999) 139, 439.
Basic building blocks: TROSYBasic building blocks: TROSY
Experiments to Experiments to measuremeasure RDCsRDCs
Criteria to consider for measuring Criteria to consider for measuring RDCsRDCs
•• spinspin--statestate--selection, sensitivity to J+D variationsselection, sensitivity to J+D variations
•• ωω1 lines usually narrower 1 lines usually narrower measure splitting in measure splitting in ωω11
•• Large molecules: splitting from TROSY and Large molecules: splitting from TROSY and decdec. HSQC. HSQC Bax JMR (2000) 143, 184
•• Sensitivity and resolution (2D vs. 3D) Sensitivity and resolution (2D vs. 3D)
Pulse sequencesPulse sequences1H-15N splittings
•• IPAP combined with E.COSY for passive spinsIPAP combined with E.COSY for passive spins Bax JMR (1998) 131, 373
•• interleaved interleaved α/βα/β ((ωω1 or 1 or ωω2) TROSY2) TROSY Sorensen JBN (1999) 13, 175; JMR (1999) 140, 259;
Otting JBN (1998) 12, 435.
•• DSSE HSQC DSSE HSQC Grzesiek JBN (1999) 13, 175.
•• QuantitativeQuantitative--J J Prestegard JMR (1996) B112, 245; Bodenhausen JBN (2002) 23, 195.
HN-N, HN-C’, N-C’, C’-Cα, HN-Cα splittings:
•• IPAP combined with E.COSY for passive spinsIPAP combined with E.COSY for passive spins Bax JACS (1998) 120, 7385
•• 3D HNCO based E.COSY experiments3D HNCO based E.COSY experiments Kay JBN (1999) 14, 333; JBN (1998) 12, 325.
•• Methyl Methyl 11HH--11H, H, 11HH--1313CC Otting JACS (2001) 123, 1770; Brutscher JACS (2002) 124, 14616
•• Aromatic Aromatic 1313CC--1313C, C, 11HH--1313CC Sattler JMB (2003) 327, 507
MultiMulti--dimensionaldimensional NMR experimentsNMR experiments• To resolve signal overlap with increasing molecular weight• 1/√2 loss of S/N per indirect dimension, but increased resolution
ω2
ω3
ω1ΩΤ
ΩΤ’
ΩI
ΩS
ΩS’t1 t2 t3preparation
I S T I
mixing mixing mixing detection
3D FT NMRφS φT
1
3
2
15N
1H
13C
15N
1H
sin2(π 1JHα,Cα Δ') exp(−Δ'/T2Hα)
* sin(π 1JCα,N 2τ1) cos(π 2JCα,N 2τ1) cos(π 1JCα,Cβ 2τ1) exp(−2τ1/T2Cα)
* sin(π 1JCα,N 2τ2) cos(π 2JCα,N 2τ2) exp(−2τ2/T2N)
* sin2(π 1JN,HNΔ) exp(-Δ/T2HN)
Transfer amplitude Transfer amplitude including Tincluding T22 relaxationrelaxation
sin4(π 1JN,HN Δ) exp(-2Δ/T2HN)
* sin2(π 1JCα,N 2τ) cos2(π 2JCα,N 2τ) exp(−4τ/T2N)
* cos(π 1JCα,Cβ t2) exp(−t2/T2Cα)
OutOut--andand--back vs. transfer experimentsback vs. transfer experiments
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 2τ12 /3τ1
2τ1-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0
t1 evolution:
∫(cos(πJ2τ1) exp(−2τ1/T2))dt1
∫(cos(πJt1) exp(-t1/T2))dt1
Constant Time (CT) vs. Real Time (RT) evolutionConstant Time (CT) vs. Real Time (RT) evolution
0 2 +tτ2 2max2τ2
0
0.2
0.4
0.6
0.8
1
2 +tτ2 2max2τ20
0
0.2
0.4
0.6
0.8
1
t2 evolution:
HNCO HNCO –– purging of dispersive purging of dispersive lineshapelineshape
JBN (1999) 14, 273-276.
• 2J(HN,C’) are ~ 4Hz
• If 2τ is not matched to 1/(21JN,C’) dispersive lineshape in F2 or F3 are observed
• Dispersive signals due to 2J(HN,C’) couplings can be removed
i) by a 90 deg C’ pulse or ii) by 13C’ decoupling during acquisition
H2O: z -y y z -x -y yy -y -z zz
2NyC’z2HzNy sin(π1JN,C’2τ) cosΩNt2 cos(π2JHN,C’t2) cosΩHNt2
4HzNyC’z cos(π1JN,C’2τ) sinΩNt2 sin(π2JHN,C’t2) cosΩHNt2
HN(CO)CAHN(CO)CA
HN N C’ Cα (t1) C’(t2) N(t2) H(t3)
H(N)COCA H(N)COCA -- CO chemical shift evolutionCO chemical shift evolution
HN(CA)COHN(CA)CO
HN N Cα C’(t2) Cα N(t2) H(t3)
HN(CA)COHN(CA)CO
Basic triple resonance experiments: CBCA(CO)NHBasic triple resonance experiments: CBCA(CO)NH
Transfer amplitude in a 13C spin system Cα−(Cβ)m−(Cγ)p
f(T,ζ) = cosm(2π 1JCα,Cβ T) cosm(2π 1JCα,Cβ ζ)
f(T,ζ) = sin(2π 1JCα,Cβ T) cosp(2π 1JCβ,Cγ T) sin(2π 1JCα,Cβ ζ)
Cα(i-1):
Cβ(i-1):
2 4 6 8
2T [ms]10 12 140
C (i-1)α
C (i-1)β
2 [ms]ζ2 4 60 8 1210 14 16 18
C (i-1)β
C (i-1)α
Basic triple resonance experiments: HBHA(CO)NHBasic triple resonance experiments: HBHA(CO)NH
CBCANH transfer amplitudesCBCANH transfer amplitudes
cosm(2π 1JCα,Cβ T)
cosm(2π 1JCα,Cβ τ1) sin(2π 1JCα,N τ1) cos(2π 2JCα,N τ1)
sin(2π 1JCα,N τ) cos(2π 2JCα,N τ)
cosm(2π 1JCα,Cβ T)
cosm(2π 1JCα,Cβ τ1) sin(2π 2JCα,N τ1) cos(2π 1JCα,N τ1)
sin(2π 2JCα,N τ) cos(2π 1JCα,N τ)
sin(2π 1JCα,Cβ T) cosp(2π 1JCβ,Cγ T)
sin(2π 1JCα,Cβ τ1) sin(2π 1JCα,N τ1) cos(2π 2JCα,N τ1)
sin(2π 1JCα,N τ) cos(2π 2JCα,N τ)
sin(2π 1JCα,Cβ T) cosp(2π 1JCβ,Cγ T)
sin(2π 1JCα,Cβ τ1) sin(2π 2JCα,N τ1) cos(2π 1JCα,N τ1)
sin(2π 2JCα,N τ) cos(2π 1JCα,N τ)
f(T, τ1, τ) in spin systemCα−(Cβ)m−(Cγ)p
Cα(i):
Cα(i-1):
Cβ(i):
Cβ(i-1):
2T 2τ1 2τ
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
2 [ms]τ1
5 10 150 20 25 30 35 40
C (i-1)β
C (i)β
C (i-1)α
C (i)α
Basic triple resonance experiments: CBCANHBasic triple resonance experiments: CBCANH
H2O: z -y y y x -y yy -y -z zz
x y”
Water flipback without water-selective shaped pulse
X
Basic triple resonance experiments: HNCACBBasic triple resonance experiments: HNCACB
Basic triple resonance experiments: (H)CCCONH Basic triple resonance experiments: (H)CCCONH TOCSYTOCSY
Basic triple resonance experiments: (H)CCCONH Basic triple resonance experiments: (H)CCCONH TOCSYTOCSY
Basic triple resonance experiments: H(CC)CONH Basic triple resonance experiments: H(CC)CONH TOCSYTOCSY
• using homo- and heteronuclear TOCSY transfer
• time-saving by simultaneous 1H-13C and 13C-13C transfer
HCCHHCCH--TOCSYTOCSY
H(t1) C(t2) C C H(t3)
• usually recorded in D2O for Hα detection
SemiSemi--constantconstant--time chemical shift evolutiontime chemical shift evolution
t12
t12 t1a t1b t1c2
Δ2Δ
I
S
I
Sreal time semi-constant- time
δ: t1a + t1b − t1c = t1
J: t1a − t1b + t1c= Δ (1)
With the requirement that t1(0) = 0, Eq. (1) yields:
t1a(0) = t1c(0) = Δ/2 and t1b(0) = 0. (2)
For a FID along t1 that is to be digitized by TD data points, two relations can be written for the
increments Δt1a, Δt1b and Δt1c (Δt1=1/SWH, where SWH is the spectral width in Hz):
δ: Δt1a + Δt1b − Δt1c = Δt1
J: Δt1a − Δt1b + Δt1c= 0 (3)
Since it is required that t1c(TD) ≥ 0;. this yields (for t1c(TD) = 0):
Δt1a = Δt1/2; Δt1b = Δt1/2 + Δt1c and Δt1c = −t1c(0)/TD (4)
Fulfilling Eqs. (2) and (4) assures chemical shift evolution with t1(0) = 0 < t1 < t1max and
evolution of the coupling during Δ for all increments. Note, that Δt1c is negative, reflecting the fact t1c is decremented.
JJ--coupling coupling =: =: ΔΔ
Chemical shift Chemical shift δδ =: t=: t11
Double sensitivity enhanced HCCHDouble sensitivity enhanced HCCH--TOCSYTOCSY
J. Biomol. NMR (1995) 6, 11-22.
Can be recorded in HCan be recorded in H22O due to excellent water suppression by O due to excellent water suppression by heteronuclearheteronuclear gradient echogradient echo
HBHDHE (aromatic side chain assignments)HBHDHE (aromatic side chain assignments)
JACS (1995) 115, 11054
Cβ
H
γδ ε
δ ε
H H
H H
H
H
Cα
•• Delay Delay ξξ for for 1,1,--1 1801 180o o 1313C pulse to decouple C pulse to decouple 11J(CJ(Cαα,C,Cββ) )
•• 1313C pulses are selective with excitation nulls at C pulses are selective with excitation nulls at 1313CCββ and and 1313CCarar, respectively, respectively
Relative sensitivity of triple resonance experimentsRelative sensitivity of triple resonance experiments
Experiment Assignment Comment RelativeS/N [%]
HNCO H(i), N(i), C’(i-1) <20 kD, above use 2H labeling 100
HNCA H(i), N(i), Cα(i),Cα(i-1) <20 kD, above use 2H labeling 50/15
HN(CO)CA H(i), N(i), Cα(i-1) <20 kD, above use 2H labeling 71
HN(CA)CO H(i), N(i), C’(i) <20 kD, above use 2H labeling 13/4
CBCA(CO)NH H(i), N(i), Cα(i-1), Cβ(i-1) <20 kD, above use 2H labeling 13/9 α/β
HBHA(CO)NH H(i), N(i), Hα(i-1), Hβ(i-1) <20 kD, above use 2H labeling 13/9 α/β
CBCANH,HNCACB
H(i), N(i), Cα(i), Cβ(i),
Cα(i-1),Cβ(i-1)<15 kD, above use 2H labeling 4/1.7 α/β(i)
1.3/0.5α/β(i-1)
(H)CC(CO)NH-TOCSY
H(i), N(i), Caliph.(i-1) <15-20 kD, above use 2H labeling
H(CC)(CO)NH-TOCSY
H(i), N(i), Haliph.(i-1) <15-20 kD, above use 2H labeling
HCCH-TOCSY Haliph., Caliph. <25 kD, - sensitive, but tedious to analyze,combine with HCCONH type experiments
Assignment based on JAssignment based on J--correlationscorrelations
In a uniformly 13C/15N-labeled protein numerous chemical shifts can be measured and correlated via 1J and 2J-couplings
Backbone assignment
Side chain assignment
Sattler et al. Prog. NMR Spectrosc. (1999) 34, 93-158.
Assignment strategy for Assignment strategy for 1313C/C/1515NN--labeled proteinslabeled proteins
Cβ
Cα
CBCANHintra-/interresidue correlation
(strong/weak)
CBCA(CO)NHinterresidue correlation
HN/N of residue
Cβ (i)
Cβ (i-1)
Cα (i)
Cα (i-1)
i (Gly)i-1i-2 i+1 i+2
HN
HN
NN
O
CαCα
Cβ
O Cβ
HN
N
O
Cα
Cβ HN
HN
NN
O
CαCα
Cβ
O
HeteronuclearHeteronuclear NOESY experimentsNOESY experiments
• water-flip-back during NOE mixing time due to radiation damping
• φ1 = 45o to enhance water flipback independent of TPPI on φ1
HeteronuclearHeteronuclear NOESY experimentsNOESY experiments
•• HMQC rather than HSQC for HMQC rather than HSQC for 1313C C edited NOESY to minimize offedited NOESY to minimize off--resonance effects for resonance effects for 1313C C rfrf pulsespulses
•• Alternatively use adiabatic Alternatively use adiabatic inversion pulses, i.e. at higher fieldsinversion pulses, i.e. at higher fields
Isotope edited/filtered experiments: single filterIsotope edited/filtered experiments: single filter
1H-12C and 1H-13C can be separated into subspectra
add ψ = +/- x → 1H-12C filteredsubtract ψ = +/- x → 1H-13C edited
Single J-filter: Δ = 1/(2J)
filter efficiency:residual magnetization = cos(πJΔ)
add a + b → 1H-12C filteredsubtract a − b → 1H-13C edited
13C,15N
12C,14N
13C,15N
12C,14N
13C,15N
12C,14Nediting filtering
editing/filtering
Double isotope filterDouble isotope filter
Double JDouble J--filter:filter:ΔΔ’’ = 1/(2J= 1/(2J’’))ΔΔ’’’’ = 1/(2J= 1/(2J””))
To use as a filtered/edited pulse sequence:To use as a filtered/edited pulse sequence:ΔΔ’’ ++ ΔΔ”” = 1/(J) = 1/(J) (single J(single J--filter)filter)ΔΔ’’’’−− ΔΔ’’ = 0= 0
((11HH--1212C and C and 11HH--1313C can be separated into C can be separated into subspectrasubspectra))
Double JDouble J--filter:filter:ΔΔ’’ = 1/(2J= 1/(2J’’))ΔΔ’’’’ = 1/(2J= 1/(2J””))
Double filter:Double filter:cos(cos(ππJJΔΔ’’) ) cos(cos(ππJJΔΔ””))
Single filter:Single filter:cos(cos(ππJ(J(ΔΔ’’++ΔΔ””)/2))/2)
J [Hz]J [Hz]
Res
idu
al m
agn
etiz
atio
nR
esid
ual
mag
net
izat
ion
Isotope filters employing adiabatic frequency Isotope filters employing adiabatic frequency sweepssweeps
• dJCH/dν = 40 Hz/120 ppm (1J(Car-Har) = 160 Hz, 1JCα-Hα = 140 Hz, 1JCH3 = 120 Hz)
• use frequency sweep for adiabatic 180 deg 13C inversion pulse in filter-element
Frequency sweep:dν/dt
Δ Δ
130ppm(J=160Hz)
55ppm(J=140Hz)
10ppm(J=120Hz)
Inversion of 13C spins at:
JACS (1997) 119, 6711
Isotope filtered 2D NOESYIsotope filtered 2D NOESY
1H-[12C]and
1H-[13C]
1H-[12C]
Intermolecular
NOEs
1D (protein + RNA)
1D filter experiment(RNA only)
Isotope filtered NOESYIsotope filtered NOESY
1D(protein + RNA)
1D filter experiment(RNA only)
Isotope edited/filtered Isotope edited/filtered 1313C HMQCC HMQC--NOESYNOESY
Isotope edited/filtered NOESYIsotope edited/filtered NOESY
Isotope filtered NOESYIsotope filtered NOESY
Problems with higher molecular weightsProblems with higher molecular weights
• slower tumbling in solution fast decay of NMR signal poor signal-to-noise
• larger number of signals signal overlap in NMR spectra
τc 4 nsMW 8 kDa
8 ns16 kDa
12 ns24 kDa
25 ns50 kDa
linewidth Δν1/2 = 1/πT2
78910 ppm78910 ppm78910 ppm78910 ppm
Transverse relaxation
optimized spectroscopy
TROSY and TROSY and 22HH--labeling for molecular weights > 50 labeling for molecular weights > 50 kDakDa
2H-labeling
• reduced relaxation (γD / γH ~ 1 / 6.5)
• improved signal-to-noise
• better resolution
• reduced number of cross peaks
• suppression of spin diffusion
•
13C
1H
dipole/dipolerelaxation
N
H
D D
DD
N
H
H H
HH
Pervushin et al. PNAS (1997) 94, 12366-71.
ConstantConstant--time HNCA with time HNCA with 22HH--decouplingdecoupling
H HN
HN
NN
HO
D HN
HN
NN
DO
75 % randomfractional 2H-
labeling
no 2H-labeling
Effect of Effect of deuterationdeuteration in 3D HNCA experimentsin 3D HNCA experiments
Larger proteins: Larger proteins: 22HH--labeling + TROSYlabeling + TROSY
JACS (1999) 121, 844; JACS (1999) 121, 2571.
TROSY HNCA with TROSY HNCA with 22H decoupling and H decoupling and 11H purgeH purge
1H purgeno purge
• CT-HNCA not sensitive enough
• real time HNCA needs 1H purge
Identification of Identification of interresidualinterresidual cross peaks in HNCA TROSYcross peaks in HNCA TROSY
JBN (2001) 20, 127-133
• C’ CSA relaxation increases with B0 field strength (JMR (1999) 141, 180-184), HN(CO)CA is insensitive
Add: Subtract:
Cα(i)
1J(Cα,C’)
Cα(i-1)
• shifted peak position in-phase and antiphase spectra of the Cα(i-1) peak by 1J(Cα,C’)
allows unique identification of the sequential peak in this HNCA experiment:
1J(Cα,C’)However, two signals per residue in HNCA introduces
additional undesirable signal overlap intra HNCA:
JMR (2002) 156, 155-159; JACS (2002) 124, 11199-11207;
JBN (2002), 201-209.