gft nmr spectroscopy: theory and applications april 4 2… · gft nmr spectroscopy: theory and...
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ENC 2003 Savannah 4/4/03© Thomas Szyperski
GFTGFT NMR NMR Spectroscopy: Theory Spectroscopy: Theory
and Applicationsand Applications
Acquiring multidimensional Acquiring multidimensional NMR spectral informationNMR spectral information
with high with high speedspeed and and precisionprecision
ENC 2003 Savannah 4/4/03© Thomas Szyperski
Objectives: Objectives: HTP NMR Structure DeterminationHTP NMR Structure Determination•• Minimize NMR Measurement TimeMinimize NMR Measurement Time
(cryogenic probes)(cryogenic probes)-- Reduce costs per structureReduce costs per structure-- Reduce demand for longReduce demand for long--term sample stabilityterm sample stability
•• Automated Assignment: Automated Assignment: High Dimensionality and Spectral ResolutionHigh Dimensionality and Spectral Resolution
-- Redundancy of spectral dataRedundancy of spectral data-- Small number of spectraSmall number of spectra-- High precision for chemical shift measurementHigh precision for chemical shift measurement
ENC 2003 Savannah 4/4/03© Thomas Szyperski
TT212
GR2
QR6
ER75
ENC 2003 Savannah 4/4/03© Thomas Szyperski
SamplingSampling versus versus SensitivitySensitivity LimitationLimitation
ω1
ω2
ω3
t1
t2
t3 FTFT
Time DomainTime Domain Frequency DomainFrequency Domain
3D and 4D:3D and 4D:
5D +:5D +:Sampling LimitationSampling Limitation
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
Drawbacks of Drawbacks of Multidimensional FT NMRMultidimensional FT NMR
•• Sampling limited data acquisitionSampling limited data acquisition•• 5+ dimensional spectra impractical5+ dimensional spectra impractical•• Low precision of chemical shift Low precision of chemical shift
measurement in indirect dimensionsmeasurement in indirect dimensions
ENC 2003 Savannah 4/4/03© Thomas Szyperski
33--dim.dim.
Rethinking the concept of high Rethinking the concept of high dimensional NMR: dimensional NMR: GFT NMRGFT NMR
ω1
ω2
ω3
33-->2>2--dim.dim.
ω1
ω2
ω3
Challenges: -keep information of conventional experiment
-avoid spectral crowding
44-->2>2--dim.dim.
ω1
ω2
ω3
ω4
K=1K=1 K=2K=2
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
GFT NMRGFT NMR-- SpeedSpeed: : PhasePhase--sensitive joint sampling of sensitive joint sampling of
KK+1 dimensions and ‘recursive central +1 dimensions and ‘recursive central peak detection’peak detection’
-- Alternative data processingAlternative data processing: Editing of : Editing of resulting ‘chemical shift multiplets’ resulting ‘chemical shift multiplets’ (G(G--matrix) and Fourier Transformation matrix) and Fourier Transformation
-- PrecisionPrecision: Least squares fit to obtain : Least squares fit to obtain shifts from edited multipletsshifts from edited multiplets
ENC 2003 Savannah 4/4/03© Thomas Szyperski
((NN,,NN--2)D 2)D GFT NMR GFT NMR
GFT GFT ==Combined Combined
GG--matrix andmatrix andFFourierourier
TTransformationransformation
K=2K=2
ENC 2003 Savannah 4/4/03© Thomas Szyperski
Joint Sampling Joint Sampling of 3D Subspace of 3D Subspace
of an of an NND FT NMR D FT NMR Experiment Experiment
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
cos(Ω0t)
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ωGFT
ω1
ω2
ωdirect
ωGFT
ω1
ωdirect
ωGFT
ω0
ωdirect
ENC 2003 Savannah 4/4/03© Thomas Szyperski
‘‘Recursive’ CentralRecursive’ CentralPeak DetectionPeak Detection
‘Bottom‘Bottom--up’ Assignmentup’ Assignment
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
pp = 2= 2KK+1+1 –– 11((N N --K K )) D FT NMR spectraD FT NMR spectra
((NN,,N N --K K )D GFT experiment)D GFT experiment
ENC 2003 Savannah 4/4/03© Thomas Szyperski
GFT NMR: a closer lookGFT NMR: a closer look•• ‘‘Phase Sensitive’ Joint SamplingPhase Sensitive’ Joint Sampling
-- SW = SW = ΣΣ SWSWjj
•• Editing of Chemical Shift MultipletsEditing of Chemical Shift Multiplets•• ‘Recursive’ Central Peak Detection‘Recursive’ Central Peak Detection
-- Resolve chemical shift degeneracyResolve chemical shift degeneracy•• Precision of shift measurementsPrecision of shift measurements
ENC 2003 Savannah 4/4/03© Thomas Szyperski
‘‘Cosine RD’Cosine RD’::QuadratureQuadrature for cosine modulated RD offor cosine modulated RD of ΩΩ11cos[(cos[(ΩΩ00++ΩΩ11)) tt11] + cos[(] + cos[(ΩΩ00--ΩΩ11)) tt11]] (1): S1r(1): S1rsin[(sin[(ΩΩ00++ΩΩ11)) tt11] + sin[(] + sin[(ΩΩ00--ΩΩ11)) tt11]] (2): S1i(2): S1i
‘‘Sine RD’Sine RD’::QuadratureQuadrature for sine modulated RD offor sine modulated RD of ΩΩ11cos[(cos[(ΩΩ00++ΩΩ11)) tt11] ] -- cos[(cos[(ΩΩ00--ΩΩ11)) tt11]] –– (4): (4): −− S2iS2isin[(sin[(ΩΩ00++ΩΩ11)) tt11] ] -- sin[(sin[(ΩΩ00--ΩΩ11)) tt11]] (3): S2r(3): S2r
EditingEditing::QuadratureQuadrature forfor ΩΩ00++ΩΩ11cos[(cos[(ΩΩ00++ΩΩ11)) tt11] ] (1)(1) –– (4):(4): T1rT1rsin[(sin[(ΩΩ00++ΩΩ11)) tt11] ] (2)(2) + + (3 ):(3 ): T1iT1iQuadratureQuadrature forfor ΩΩ00--ΩΩ11cos[(cos[(ΩΩ00--ΩΩ11)) tt11]] (1)(1) + + (4 ):(4 ): T2rT2rsin[(sin[(ΩΩ00--ΩΩ11)) tt11] ] (2)(2) –– (3 ):(3 ): T2iT2i
Ω0
Ω0
Ω0+Ω1 Ω0 – Ω1
Ω0+Ω1 Ω0 – Ω1
Ω0
Ω0
Ω0+Ω1
Ω0 – Ω1
Phase Sensitive RD (K=1): Phase Sensitive RD (K=1): QuadratureQuadrature Detection of joint tDetection of joint t11 evolution of evolution of ΩΩ00 and and ΩΩ11
cos(cos(ΩΩ00tt11) cos() cos(ΩΩ11tt11) ) = cos[(= cos[(ΩΩ00++ΩΩ11)) tt11] + cos[(] + cos[(ΩΩ00--ΩΩ11)) tt11]] (1)(1)sin(sin(ΩΩ00tt11) cos() cos(ΩΩ11tt11) ) = sin[(= sin[(ΩΩ00++ΩΩ11)) tt11] + sin[(] + sin[(ΩΩ00--ΩΩ11)) tt11]] (2)(2)
cos(cos(ΩΩ00tt11) sin() sin(ΩΩ11tt11) ) = sin[(= sin[(ΩΩ00++ΩΩ11)) tt11] ] -- sin[(sin[(ΩΩ00--ΩΩ11)) tt11]] (3)(3)sin(sin(ΩΩ00tt11) sin() sin(ΩΩ11tt11) ) = = --cos[(cos[(ΩΩ00++ΩΩ11)) tt11] + cos[(] + cos[(ΩΩ00--ΩΩ11)) tt11]] (4)(4)
ENC 2003 Savannah 4/4/03© Thomas Szyperski
)()()(
2211
0110100101101001
2211
KKK
iSrSiSrS
iTrTiTrT
SGT =⇔
•
−
−
=
For For K K = 1= 1: two dimensions being jointly sampled: two dimensions being jointly sampled
For For arbitraryarbitrary KK: K : K ++ 1 dimensions being jointly sampled1 dimensions being jointly sampled
withwith
ENC 2003 Savannah 4/4/03© Thomas Szyperski
complexcomplex GG--matrixmatrix
realreal GG--matrix for matrix for KK=3=3
ENC 2003 Savannah 4/4/03© Thomas Szyperski
G/F-matrix interconversion
Frequency domain editingFrequency domain editingB (K) = F (K) A (K)
Time domain editingTime domain editingT (K) = G (K) S (K)
B (K)A(K)
ENC 2003 Savannah 4/4/03© Thomas Szyperski
FF (K+1) = (K+1) = FF (K) (K) ⊗⊗ FF (1)(1)KK = 3= 3
KK = 2= 2 KK = 1= 1
ENC 2003 Savannah 4/4/03© Thomas Szyperski
GG (K) = [(K) = [FF (K)(K)⊗⊗11 ] ] PP (K)(K)
H H (K) = (K) = FF (K)⊗(K)⊗11
PP’ (K+1) = ’ (K+1) = PP’ (K) ’ (K) ⊗⊗ PP ’’(1)(1)
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
complexcomplex GG--matrixmatrix
realreal GG--matrix for matrix for KK=3=3
ENC 2003 Savannah 4/4/03© Thomas Szyperski
GFT NMR: a closer lookGFT NMR: a closer look•• ‘‘Phase Sensitive’ Joint SamplingPhase Sensitive’ Joint Sampling
-- SW = SW = ΣΣ SWSWjj
•• Editing of Chemical Shift MultipletsEditing of Chemical Shift Multiplets•• ‘Recursive’ Central Peak Detection‘Recursive’ Central Peak Detection
-- Resolve chemical shift degeneracyResolve chemical shift degeneracy•• Precision of shift measurementsPrecision of shift measurements
ENC 2003 Savannah 4/4/03© Thomas Szyperski
GFT NMR: a closer lookGFT NMR: a closer look•• ‘‘Phase Sensitive’ Joint SamplingPhase Sensitive’ Joint Sampling
-- SW = SW = ΣΣ SWSWjj
•• Editing of Chemical Shift MultipletsEditing of Chemical Shift Multiplets•• ‘Recursive’ Central Peak Detection‘Recursive’ Central Peak Detection
-- Resolve chemical shift degeneracyResolve chemical shift degeneracy•• Precision of shift measurementsPrecision of shift measurements
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
Implementation of central peak Implementation of central peak acquisitionacquisition
•• Option 1: Option 1: pp data sets defining GFT NMR experiment are data sets defining GFT NMR experiment are separately recordedseparately recorded
•• Option 2: Simultaneous acquisition from incomplete INEPTOption 2: Simultaneous acquisition from incomplete INEPT
•• Option 3: Acquisition using heteronuclear magnetizationOption 3: Acquisition using heteronuclear magnetization
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
GFT NMR: a closer lookGFT NMR: a closer look•• ‘‘Phase Sensitive’ Joint SamplingPhase Sensitive’ Joint Sampling
-- SW = SW = ΣΣ SWSWjj
•• Editing of Chemical Shift MultipletsEditing of Chemical Shift Multiplets•• ‘Recursive’ Central Peak Detection‘Recursive’ Central Peak Detection
-- Resolve chemical shift degeneracyResolve chemical shift degeneracy•• Precision of shift measurementsPrecision of shift measurements
ENC 2003 Savannah 4/4/03© Thomas Szyperski
GFT NMR: Increased precisionGFT NMR: Increased precision-- OverdeterminationOverdetermination::σσGFTGFT((ΩΩjj) = [1/) = [1/√√nn ] ] σσeditededited (..(..ΩΩjj ±± ΩΩk k ±± .... ) )
ENC 2003 Savannah 4/4/03© Thomas Szyperski
GFT NMR: Increased precisionGFT NMR: Increased precision-- OverdeterminationOverdetermination::σσGFTGFT((ΩΩjj) = [1/) = [1/√√nn ] ] σσeditededited (..(..ΩΩjj ±± ΩΩk k ±± .... ))
-- ConstantConstant--time chemical shift evolution:time chemical shift evolution:σσeditededited == σσFTFT((ΩΩjj) )
ENC 2003 Savannah 4/4/03© Thomas Szyperski
GFT NMR: Increased precisionGFT NMR: Increased precision-- OverdeterminationOverdetermination::σσGFTGFT((ΩΩjj) = [1/) = [1/√√nn ] ] σσeditededited (..(..ΩΩjj ±± ΩΩk k ±± .... ) )
-- ConstantConstant--time chemical shift evolution:time chemical shift evolution:σσeditededited = = σσFTFT((ΩΩjj) )
σσGFTGFT((ΩΩjj) = [1/) = [1/√√nn ] ] σσFTFT ((ΩΩjj))
ENC 2003 Savannah 4/4/03© Thomas Szyperski
GFT NMR: a closer lookGFT NMR: a closer look•• ‘‘Phase Sensitive’ Joint SamplingPhase Sensitive’ Joint Sampling
–– SW = SW = ΣΣ SWSWjj
•• Editing of Chemical Shift Editing of Chemical Shift MultipletsMultiplets
•• ‘Recursive’ Central Peak ‘Recursive’ Central Peak DetectionDetection–– Resolve chemical shift degeneracyResolve chemical shift degeneracy
•• Precision of shift measurementsPrecision of shift measurements
ENC 2003 Savannah 4/4/03© Thomas Szyperski
Application: Application: (5,2)D (5,2)D HACACONHACACONHNHN
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© 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 OrderThird OrderCentral Peak SpectraCentral Peak Spectra
KK = 3= 3
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
ENC 2003 Savannah 4/4/03© Thomas Szyperski
2D 2D Information: Information:
13.8 min13.8 min
ENC 2003 Savannah 4/4/03© Thomas Szyperski
3D 3D Information: Information:
+25.2 min+25.2 min
ENC 2003 Savannah 4/4/03© Thomas Szyperski
4D 4D Information: Information:
+52.8 min+52.8 min
ENC 2003 Savannah 4/4/03© Thomas Szyperski
5D 5D Information: Information:
+108 min+108 min
ENC 2003 Savannah 4/4/03© 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: 3shift measurement: 3--4 4 fold increasedfold increased
•• 5D HACACONHN5D HACACONHN–– 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
ENC 2003 Savannah 4/4/03© Thomas Szyperski
PerspectivesPerspectives•• Rapid data collectionRapid data collection::
–– Fast (cheap) Assignment & NMR structure determinationFast (cheap) Assignment & NMR structure determination–– High time resolution: Dynamic phenomena (protein High time resolution: Dynamic phenomena (protein
folding)folding)
•• 5+ dimensional spectral information5+ dimensional spectral information
•• High precision of chemical shift measurement in High precision of chemical shift measurement in indirect dimensions:indirect dimensions:–– Systems with high shift degeneracy (RNA, Lipids)Systems with high shift degeneracy (RNA, Lipids)–– RDC determinationRDC determination
•• Transverse relaxation optimized Transverse relaxation optimized (GFT(GFT--TROSY)TROSY)
ENC 2003 Savannah 4/4/03© Thomas Szyperski
PerspectivesPerspectives•• Rapid data collection:Rapid data collection:
–– Fast (cheap) Assignment & NMR structure determinationFast (cheap) Assignment & NMR structure determination–– High time resolution: Dynamic phenomena (protein High time resolution: Dynamic phenomena (protein
folding)folding)
•• 5+ dimensional spectral information5+ dimensional spectral information
•• High precision of chemical shift measurement in High precision of chemical shift measurement in indirect dimensions:indirect dimensions:–– Systems with high shift degeneracySystems with high shift degeneracy–– RDC determinationRDC determination
•• Transverse relaxation optimized Transverse relaxation optimized (GFT(GFT--TROSY)TROSY)
ENC 2003 Savannah 4/4/03© Thomas Szyperski
PerspectivesPerspectives•• Rapid data collection:Rapid data collection:
–– Fast (cheap) Assignment & NMR structure determinationFast (cheap) Assignment & NMR structure determination–– High time resolution: Dynamic phenomena (protein High time resolution: Dynamic phenomena (protein
folding)folding)
•• 5+ dimensional spectral information5+ dimensional spectral information
•• High precisionHigh precision of chemical shift measurement in of chemical shift measurement in indirect dimensions:indirect dimensions:–– Systems with high shift degeneracySystems with high shift degeneracy–– RDC determinationRDC determination
•• Transverse relaxation optimized Transverse relaxation optimized (GFT(GFT--TROSY)TROSY)
ENC 2003 Savannah 4/4/03© Thomas Szyperski
PerspectivesPerspectives•• Rapid data collection:Rapid data collection:
–– Fast (cheap) Assignment & NMR structure determinationFast (cheap) Assignment & NMR structure determination–– High time resolution: Dynamic phenomena (protein High time resolution: Dynamic phenomena (protein
folding)folding)
•• 5+ dimensional spectral information5+ dimensional spectral information
•• High precision of chemical shift measurement in High precision of chemical shift measurement in indirect dimensions:indirect dimensions:–– Systems with high shift degeneracySystems with high shift degeneracy–– RDC determinationRDC determination
•• Transverse relaxation optimized Transverse relaxation optimized (GFT(GFT--TROSY)TROSY)