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)