GRC 6/22/04© Thomas Szyperski
Rapid acquisition Rapid acquisition of multidimensional of multidimensional
NMR dataNMR data
‘‘The NMR sampling problemThe NMR sampling problem’’
GRC 6/22/04© Thomas Szyperski
LetLet’’s take stocks take stock……
Conventional, Conventional, multidimensional FT NMR multidimensional FT NMR spectroscopyspectroscopy…………
GRC 6/22/04© Thomas Szyperski
Measurement times scale with Measurement times scale with ΠΠnnjj
1 scan / second (16 complex / dimension) =>1 scan / second (16 complex / dimension) =>1D 1D --> 1 second> 1 second2D 2D --> ~0.5 minutes> ~0.5 minutes3D 3D --> ~0.25 hours> ~0.25 hours4D 4D --> ~8 hours> ~8 hours5D 5D --> ~12 days> ~12 days6D 6D --> ~1.1 years> ~1.1 years
Drawbacks of Multidimensional FT NMRDrawbacks of Multidimensional FT NMR
GRC 6/22/04© Thomas Szyperski
The ‘NMR sampling problem’:The ‘NMR sampling problem’:
minimal measurement minimal measurement ‘explodes’ with dimensionality‘explodes’ with dimensionality
GRC 6/22/04© Thomas Szyperski
SamplingSampling versus versus SensitivitySensitivity LimitationLimitation
ω1
ω2
ω3
t1t2
t3 FTFT
Time DomainTime Domain Frequency DomainFrequency Domain
3D and 4D:3D and 4D:
5D +:5D +:Sampling LimitationSampling Limitation
GRC 6/22/04© Thomas Szyperski
600 MHz Cryogenic Probe at UB
GRC 6/22/04© Thomas Szyperski
First FID of 3D HCCH-COSYConventional Cryogenic probe
GRC 6/22/04© Thomas Szyperski
Drawbacks of Multidimensional FT NMRDrawbacks of Multidimensional FT NMR
Measurement times scale with Measurement times scale with ΠΠnnjj
Low precision of chemical shift Low precision of chemical shift measurement in indirect dimensionsmeasurement in indirect dimensions
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
The The ‘‘Gordian knotGordian knot’’::Speeding up Speeding up multidimensional multidimensional
NMR data acquisition, NMR data acquisition,
while while increasingincreasing the the accuracy accuracy ofof
the measurement of NMR parametersthe measurement of NMR parameters
GRC 6/22/04© Thomas Szyperski
RD/GFT NMR SpectroscopyRD/GFT NMR Spectroscopy
GRC 6/22/04© Thomas Szyperski
Reduced dimensionality (RD)Reduced dimensionality (RD)
NMR SpectroscopyNMR Spectroscopy
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
33--dimensionaldimensional 22--dimensionaldimensional
ω1
ω2
ω3
ω1
ω2
2∆Ω3
Challenge: keep information upon projection
GRC 6/22/04© Thomas Szyperski
‘‘projectedprojected’’chemical shiftchemical shift
ω1
ω2
ω3
ω1
ω2
2∆Ω3
GRC 6/22/04© Thomas Szyperski
t2
t1
GRC 6/22/04© Thomas Szyperski
t2
t1
GRC 6/22/04© Thomas Szyperski
Challenge: keep information upon projection
‘‘projectedprojected’’chemical shiftchemical shift
ΩΩKK
ΩΩSS
ΩΩcarriercarrier∆Ω∆ΩSS
ΩΩKK
GRC 6/22/04© Thomas Szyperski
Structural genomics Structural genomics lead to increased interest lead to increased interest
in RD NMRin RD NMR
GRC 6/22/04© Thomas Szyperski
RDpackRDpack
GRC 6/22/04© Thomas Szyperski
Total Measurement time Total Measurement time for RD NMR spectra: for RD NMR spectra:
44.5 hours44.5 hours3D 3D HCHCCHCH--COSY: 8.9 hoursCOSY: 8.9 hours
GRC 6/22/04© Thomas Szyperski
RD NMR Data for NESGCRD NMR Data for NESGCProteins from TorontoProteins from Toronto
MT1362 (8 kDa)MT1362 (8 kDa)SH3SH3--peptide complex peptide complex (12.5 kDa)(12.5 kDa)SRm160 domain (13 kDa)SRm160 domain (13 kDa)MT1598 (15 kDa)MT1598 (15 kDa)VT1 (17 kDa)VT1 (17 kDa)TT212 (14 kDa)TT212 (14 kDa)
Proteins from RutgersProteins from RutgersWR4 (14 kDa)WR4 (14 kDa)WR33 (21 kDa)WR33 (21 kDa)MT467 (13 kDa)MT467 (13 kDa)SR17 (18 kDa)SR17 (18 kDa)ER14 (12 kDa)ER14 (12 kDa)ER75 (17 kDa)ER75 (17 kDa)QR6 (14 kDa)QR6 (14 kDa)GR2 (7 kDa)GR2 (7 kDa)MR19 (15 kDa)MR19 (15 kDa)SR64 (17 kDa)SR64 (17 kDa)HR41 (22 kDa)HR41 (22 kDa)PfR13 (12 kDa)PfR13 (12 kDa)CCR19 (16 kDa)CCR19 (16 kDa)HR532 (13 kDa)HR532 (13 kDa)HR2106 (11 kDa)HR2106 (11 kDa)
[Structures determinedin Szyperski Lab]
GRC 6/22/04© Thomas Szyperski
Why not leaning back?Why not leaning back?
GRC 6/22/04© Thomas Szyperski
From conventional 600 MHz to From conventional 600 MHz to 800 MHz spectrometer w/cryoprobe800 MHz spectrometer w/cryoprobe
•• Conventional 600: Conventional 600: S/N 1,200:1S/N 1,200:1
•• 800 w/cryoprobe: 800 w/cryoprobe: S/N 7,700:1S/N 7,700:1
•• Reduction in measurement time: ~20+Reduction in measurement time: ~20+•• (RD) DR/TR data for 17 KDa ER75 in ~12 h(RD) DR/TR data for 17 KDa ER75 in ~12 h•• Simultaneously: All spectral widths increase Simultaneously: All spectral widths increase
by 1.33 (~ 2.3by 1.33 (~ 2.3--fold increased sampling fold increased sampling demand for 3D)demand for 3D)
GRC 6/22/04© Thomas Szyperski
RD NMR spectroscopy not RD NMR spectroscopy not fast enoughfast enough
GRC 6/22/04© Thomas Szyperski
33--dim.dim.
ω1
ω2
ω3
33-->2>2--dim.dim.
ω1
ω2
ω3
44-->2>2--dim.dim.
ω1
ω2
ω3
ω4
K=1K=1 K=2K=2
‘chemical shift multiplets’
GRC 6/22/04© Thomas Szyperski
33--dim.dim.
ω1
ω2
ω3
33-->2>2--dim.dim.
ω1
ω2
ω3
44-->2>2--dim.dim.
ω1
ω2
ω3
ω4
K=1K=1 K=2K=2
Challenges: -keep information of conventional experiment
-avoid spectral crowding
GRC 6/22/04© Thomas Szyperski
GFT NMRGFT NMR-- SpeedSpeed: Phase: Phase--sensitive joint sampling sensitive joint sampling of of K+1K+1 dimensions and dimensions and ‘‘recursive recursive central peak detectioncentral peak detection’’
-- Alternative data processingAlternative data processing: Editing of : Editing of resulting resulting ‘‘chemical shift multipletschemical shift multiplets’’((‘‘GG--matrixmatrix’’) and ) and FourierFourierTransformation Transformation
-- PrecisionPrecision: Least squares fit to obtain : Least squares fit to obtain shifts from edited multipletsshifts from edited multiplets
GRC 6/22/04© Thomas Szyperski
A pictorial approach toA pictorial approach toGFT NMR….GFT NMR….
GRC 6/22/04© Thomas Szyperski
((NN,,NN--2)D2)DGFT NMR GFT NMR
GFT GFT ==Combined Combined
GG--matrix andmatrix andFFourierourier
TTransformationransformation
K=2K=2
GRC 6/22/04© Thomas Szyperski
Joint Sampling Joint Sampling of of 3D3D Subspace Subspace of an of an NDND FT FT
NMR NMR Experiment Experiment
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
cos(Ω0t)
GRC 6/22/04© Thomas Szyperski
ωGFT
ω1
ω2
ωdirect
ωGFT
ω1
ωdirect
ωGFT
ω0
ωdirect
GRC 6/22/04© Thomas Szyperski
‘‘ExhaustiveExhaustive’’ samplingsamplingof linear combinations of linear combinations of chemical shifts:of chemical shifts:
Basic spectraBasic spectra
11stst order central peaksorder central peaks
22ndnd order central peaksorder central peaks
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
Reduction of minimal measurement timeReduction of minimal measurement time
NDND (N,N(N,N--1)D1)D (N,N(N,N--2)D2)D (N,N(N,N--3)D3)D
11
100100
200200
300300
400400
50050012
2*1
1
1
−+
∑
∏K
K
K
i
K
i
n
n
GRC 6/22/04© Thomas Szyperski
An example…..An example…..
GRC 6/22/04© Thomas Szyperski
(5,2)D (5,2)D HACACONHACACONHNHN
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
8 8 BasicBasic SpectraSpectra
4 4 First Order First Order Central Peak SpectraCentral Peak Spectra
2 2 Second Order Second Order Central Peak SpectraCentral Peak Spectra
1 1 Third Order Third Order Central Peak SpectraCentral Peak Spectra
K = 3K = 3
GRC 6/22/04© Thomas Szyperski
complexcomplex GG--matrixmatrix
realreal GG--matrix for matrix for KK = 3= 3
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
2D 2D InformationInformation13.8 min13.8 min
GRC 6/22/04© Thomas Szyperski
3D 3D Information Information +25.2 min+25.2 min
GRC 6/22/04© Thomas Szyperski
4D 4D Information Information +52.8 min+52.8 min
GRC 6/22/04© Thomas Szyperski
5D 5D Information Information +108 min+108 min
GRC 6/22/04© Thomas Szyperski
How about the increased How about the increased precision of the shift precision of the shift
measurements?measurements?
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
GFT NMR: Increased precision GFT NMR: Increased precision
-- OverdeterminationOverdeterminationσσGFTGFT((ΩΩjj) = [1/) = [1/√√nn ] ] σσeditededited (..(..ΩΩjj ±± ΩΩk k ±± .... ) )
-- ConstantConstant--time chemical shift evolutiontime chemical shift evolutionσσeditededited = = σσFTFT((ΩΩjj) )
-->> σσGFTGFT((ΩΩjj) = [1/) = [1/√√nn ] ] σσFTFT ((ΩΩjj))
GRC 6/22/04© Thomas Szyperski
(5,2)D (5,2)D HACACONHACACONHNHN
-- 15*53(15*53(tt11)*512()*512(tt22))
-- 15*512(15*512(ωω11)*512()*512(ωω22) ) [16 [16 MbyteMbyte]]
-- Minimal measurement Minimal measurement time: 33 mintime: 33 min
-- Precision of chemical Precision of chemical shift measurement: shift measurement: ~2~2--3 fold increased3 fold increased
5D 5D HACACONHNHACACONHN
-- 10(10(tt11)*11()*11(tt22)*13()*13(tt33)*13()*13(tt44)*512()*512(tt55))
-- 32(32(ωω11)*32()*32(ωω22)*32()*32(ωω33)*32()*32(ωω44)*512()*512(ωω55))2.1 2.1 GbyteGbyte
-- 96(96(ωω11)*96()*96(ωω22)*256()*256(ωω33)*128()*128(ωω44)*512()*512(ωω55))[618 [618 GbyteGbyte]]
-- Minimal measurement time: 5.8 daysMinimal measurement time: 5.8 days
GFTGFT FTFT
GRC 6/22/04© Thomas Szyperski
Features of GFT NMRFeatures of GFT NMR•• Generally applicable acquisition schemeGenerally applicable acquisition scheme•• Adaptation of measurement times to Adaptation of measurement times to
sensitivity requirement sensitivity requirement withoutwithoutsacrificing digital resolution or high sacrificing digital resolution or high dimensional correlationdimensional correlation
•• Realize Realize 5+D5+D•• High Precision of Shift MeasurementsHigh Precision of Shift Measurements
--> Systems with high shift degeneracy (RNA, > Systems with high shift degeneracy (RNA, Lipids)Lipids)
GRC 6/22/04© Thomas Szyperski
Features of GFT NMR cont..Features of GFT NMR cont..•• No additional hardware requiredNo additional hardware required•• Data size reductionData size reduction•• Greatly accelerated processing speedGreatly accelerated processing speed•• Robustness of data analysisRobustness of data analysis•• Combine with other approaches to reduce Combine with other approaches to reduce
the ‘sampling demand’:the ‘sampling demand’:-- NonNon--linear sampling (Threelinear sampling (Three--way decomposition) and MEM, way decomposition) and MEM,
Filter Filter diagonalizationdiagonalization, , -- HadamardHadamard NMR, SingleNMR, Single--scan scan NDND acquisition, acquisition,
•• ‘Orthogonal’ to TROSY:‘Orthogonal’ to TROSY: GFTGFT--TROSYTROSY
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
Major developments 1997-20031. TROSY and large systems 2. Residual dipolar couplings3. Rapid data collection4. Functional protein dynamics
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
SizeSize
Measurement timeMeasurement time
Sensitivity limitedSensitivity limitedSampling limitedSampling limited
GRC 6/22/04© Thomas Szyperski
GRC 6/22/04© Thomas Szyperski
Side chain assignmentSide chain assignment
GRC 6/22/04© Thomas Szyperski
C C
H H
t1,GFT (1H(1),13C(1);13C(2))
t2(13C(2))
t3(1H(2))
3D HCC-CH COSY
GRC 6/22/04© Thomas Szyperski
Higher PrecisionHigher Precisionfor Shift Measurementsfor Shift Measurements
GRC 6/22/04© Thomas Szyperski
Gain is precision of shift measurementsGain is precision of shift measurementsin (5,3)D in (5,3)D HCCHCC--CH CH versusversus3D (H)CCH and 3D H(C)CH3D (H)CCH and 3D H(C)CH