Method of using G-matrix Fourier transformation nuclear magnetic resonance (GFT NMR) spectroscopy for rapid chemical shift assignment and secondary structure determination of proteins

[0002] The present invention claims the benefit of U.S. Provisional Patent Application Serial Nos. 60/395,591, filed Jul. 11, 2002, and 60/441,385, filed Jan. 16, 2003, which are hereby incorporated by reference in their entirety.

[0004] The present invention relates to methods of using G-matrix Fourier transformation nuclear magnetic resonance (GFT NMR) spectroscopy for rapidly obtaining and connecting precise chemical shift values and determining the structure of proteins and other molecules.

[0005] Nuclear magnetic resonance (NMR) (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987); Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986); Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996))-based structural studies rely on two broad classes of experimental radio-frequency pulse schemes for recording two-dimensional (2D) (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987)), three-dimensional (3D) (Oschkinat et al., Nature, 332:374-376 (1988)), or four-dimensional (4D) (Kay et al., Science, 249:411-414 (1990)) Fourier transformation (FT) NMR spectra. Correlation spectroscopy (COSY) delineates exclusively scalar coupling connectivities to measure chemical shifts, and (heteronuclear resolved) ¹H, ¹H-nuclear Overhauser enhancement spectroscopy (NOESY) reveals the strength of through-space dipolar couplings of ¹H spins to estimate distances (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987); Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986)). NMR spectra need to exhibit (i) signal-to-noise (S/N) ratios warranting reliable data interpretation, (ii) digital resolutions ensuring adequate precision for the measurement of NMR parameters such as chemical shifts, and (iii) a dimensionality at which a sufficient number of NMR parameters is correlated (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987); Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996)). While increased intensity of NOESY peaks ensures their more accurate integration (which, in turn, may translate into increased accuracy of the NMR structure), the mere identification of COSY peaks suffices to obtain the desired chemical shifts. Hence, COSY peak signal-to noise ratios larger that ˜3:1 reflect, in essence, inappropriately long measurement times. Moreover, the total number of peaks in COSY grows only linearly with the number of spins involved and is, for a defined magnetization transfer pathway, “independent” of the dimensionality N. Thus, a minimal “target dimensionality” N_tat which most of the COSY peaks detected for a given molecule are resolved can be defined. Further increased dimensionality does not aim at resolving peak overlap but at increasing the number of correlations obtained in a single data set. This eliminates ambiguities when several multidimensional NMR spectra are combined for resonance assignment, for example, when using ¹H, ¹³C, ¹⁵N triple-resonance NMR to assign protein resonances (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996)).

[0006] An increase in dimensionality is, however, limited by the need to independently sample the indirect dimensions, because this leads to longer measurement times. Although the measurement time can be somewhat reduced by aliasing signals (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996)) or accepting a lower digital resolution in the indirect dimensions, high dimensionality often prevents one from tuning the measurement time to a value that ensures to obtain sufficient, but not unnecessarily large S/N ratios.

[0007] In view of these considerations, “sampling” and “sensitivity limited” data collection regimes are defined (Szyperski et al., Proc. Natl. Acad. Sci. USA, 99:8009-8014 (2002)), depending on whether the sampling of the indirect dimensions or the sensitivity of the FT NMR experiment determines the minimal measurement time. In the sensitivity limited regime, long measurement times are required to achieve sufficient S/N ratios, so that the sampling of indirect dimensions is not necessarily constraining the adjustment of the measurement time. In the sampling limited regime, some or even most of the instrument time is invested for sampling, which yields excessively large S/N ratios. In view of the ever increasing sensitivity of NMR instrumentation, new methodology to avoid the sampling limited regime is needed. (Szyperski et al., Proc. Natl. Acad. Sci. USA, 99:8009-8014 (2002)).

[0008] In general, phase-sensitive acquisition of an N-dimensional (ND) FT NMR experiment (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987); Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996)) requires sampling of N−1 indirect dimensions with n₁×n₂. . . n_N−1complex points representing $n_{\mathrm{FID}}=2^{N-1}·\prod _{j=1}^{N-1}{n}_j$

[0009] free induction decays (FIDs). The resulting steep increase of the minimal measurement time, T_m, with dimensionality prevents one from recording five- or higher-dimensional FT NMR spectra: acquiring 16 complex points in each indirect dimension (with one scan per FID each second) yields T_m(3D)=0.5 hour, T_m(4D)=9.1 hours, T_m(5D)=12 days, and T_m(6D)=1.1 years.

[0010] Thus, higher-dimensional FT NMR spectroscopy suffers from two major drawbacks: (i) The minimal measurement time of an ND FT NMR experiment, which is constrained by the need to sample N−1 indirect dimensions, may exceed by far the measurement time required to achieve sufficient signal-to-noise ratios. (ii) The low resolution in the indirect dimensions severely limits the precision of the indirect chemical shift measurements.

[0011] The present invention is directed to overcoming the deficiencies in the art.

[0012] The present invention relates to a method of conducting a (N,N−K) dimensional (D) G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiment, where N is the dimensionality of an N-dimensional (ND) Fourier transformation (FT) NMR experiment and K is the desired reduction in dimensionality relative to N. The method involves providing a sample and applying radiofrequency pulses for the ND FT NMR experiment to the sample. Then, m indirect chemical shift evolution periods of the ND FT NMR experiment are selected, where m equals K+1, and the m indirect chemical shift evolution periods are jointly sampled. Next, NMR signals detected in a direct dimension are independently cosine and sine modulated to generate (N−K)D basic NMR spectra containing frequency domain signals with 2^Kchemical shift multiplet components, thereby enabling phase-sensitive sampling of all jointly sampled m indirect chemical shift evolution periods. Finally, the (N−K) D basic NMR spectra are transformed into (N−K) D phase-sensitively edited basic NMR spectra, where the 2^Kchemical shift multiplet components of the (N−K) D basic NMR spectra are edited to yield (N−K) D phase-sensitively edited basic NMR spectra having individual chemical shift multiplet components.

[0013] Another aspect of the present invention relates to a method for sequentially assigning chemical shift values of an α-proton, ¹H^α, an α-carbon, ¹³C^α, a polypeptide backbone carbonyl carbon, ¹³C′, a polypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backbone amide proton, ¹H^N, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,2)D [HACACONHN] GFT NMR experiment to measure and connect the chemical shift values of the α-proton of amino acid residue i−1, ¹H^α_i−1, the α-carbon of amino acid residue i−1, ¹³C^α_i−1, the polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i, and the polypeptide backbone amide proton of amino acid residue i, ¹H^N_iand (2) a (5,2)D [HACA,CONHN] GFT NMR experiment to measure and connect the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, ¹³C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i−1, ¹⁵N_i−1, and the polypeptide backbone amide proton of amino acid residue i−1, ¹H^N_i−1. Then, sequential assignments of the chemical shift values of ¹H^α,13C^α, ¹³C′, ¹⁵N, and ¹H^Nare obtained by (i) matching the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1measured by the (5,2)D [HACACONHN] GFT NMR experiment with the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1measured by the (5,2)D [HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1to identify the type of amino acid residue i−1, and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements within the polypeptide chain.

[0014] Yet another aspect of the present invention relates to a method for sequentially assigning chemical shift values of an α-proton, ¹H^α, an α-carbon, ¹³C^α, a polypeptide backbone carbonyl carbon, ¹³C′, a polypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backbone amide proton, ¹H^N, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HACACONHN] GFT NMR experiment to measure and connect the chemical shift values of the α-proton of amino acid residue i−1, ¹H^α_i−1, the α-carbon of amino acid residue i−1, ¹³C^α_i−1, the polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i, and the polypeptide backbone amide proton of amino acid residue i, ¹H^N_iand (2) a (5,3)D [HACA,CONHN] GFT NMR experiment to measure and connect the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, ¹³C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i−1, ¹⁵N_i−1, and the polypeptide backbone amide proton of amino acid residue i−1, ¹H^N_i−1. Then, sequential assignments of the chemical shift values of ¹H^α, ¹³C^α, ¹³C′, ¹⁵N, and ¹H^Nare obtained by (i) matching the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1measured by the (5,3)D [HACACONHN] GFT NMR experiment with the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1measured by the (5,3)D [HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1to identify the type of amino acid residue i−1, and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements within the polypeptide chain.

[0015] A further aspect of the present invention relates to a method for sequentially assigning chemical shift values of α- and β-carbons, ¹³C^α/β, a polypeptide backbone carbonyl carbon, ¹³C′, a polypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backbone amide proton, ¹H^N, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,3)D [CBCACONHN] GFT NMR experiment to measure and connect the chemical shift values of the α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1, the polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i, and the polypeptide backbone amide proton of amino acid residue i, ¹H^N_iand (2) a (4,3)D [CBCA,CONHN] GFT NMR experiment to measure and connect the chemical shift values of ¹³C^α/β_i−1^{, 13}C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i−1, ¹⁵N_i−1, and the polypeptide backbone amide proton of amino acid residue i−1, ¹H^N_i−1. Then, sequential assignments of the chemical shift values of ¹³C^α/β, ¹³C′, ¹⁵N, and ¹H^Nare obtained by (i) matching the chemical shift values of ¹³C^α/β_i−1and ¹³C′_i−1measured by the (4,3)D [CBCACONHN] GFT NMR experiment with the chemical shift values of ¹³C^α/β_i−1and ¹³C′_i−1measured by the (4,3)D [CBCA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of ¹³C^α/β_i−1, and ¹³C′_i−1to identify the type of amino acid residue i−1, and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements within the polypeptide chain.

[0016] The present invention also relates to a method for sequentially assigning chemical shift values of α- and β-carbons, ¹³C^α/β, a polypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backbone amide proton, ¹H^N, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,3)D [HNNCACBCA] GFT NMR experiment to measure and connect the chemical shift values of the α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1, the α-carbon of amino acid residue i−1, ¹³C^α_i−1, the polypeptide backbone amide nitrogen of amino acid residue i−1, ¹⁵N_i−1, and the polypeptide backbone amide proton of amino acid residue i−1, ¹H^N_i−1and (2) a GFT NMR experiment selected from the group consisting of a (4,3)D [HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of ¹³C^α/β_i−1, ¹³C^α_i−1, the polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i, and the polypeptide backbone amide proton of amino acid residue i, ¹H^N_i. Then, sequential assignments of the chemical shift values of ¹³C^α/β, ¹⁵N, and ¹H^Nare obtained by (i) matching the chemical shift values of ¹³C^α/β_i−1measured by the GFT NMR experiment selected from the group consisting of a (4,3)D [HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment with the chemical shift values of ¹³C^α/β_i−1measured by the (4,3)D [HNNCACBCA] GFT NMR experiment, (ii) using the chemical shift values of ¹³C^α/β_i−1to identify the type of amino acid residue i−1, and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements within the polypeptide chain.

[0017] Another aspect of the present invention relates to a method for assigning chemical shift values of γ-, δ-, and ε-aliphatic sidechain protons, ¹H^γ/δ/ε, and chemical shift values of γ-, δ-, and ε-aliphatic sidechain carbons located peripheral to β-carbons, ¹³C^γ/δ/ε, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HCC,CH-COSY] GFT NMR experiment to measure and connect the chemical shift values of a proton of amino acid residue i−1, ¹H_i−1, a carbon of amino acid residue i−1 coupled to ¹H_i−1, ¹³C_i−1, a carbon coupled to ¹³C_i−1, ¹³C_i−1^coupled, and a proton coupled to ¹³C_i−1^coupled, ¹H_i−1^coupled, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of α- and β-protons of amino acid residue i−1, ¹H^α/β_i−1, and α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1. Then, assignments of the chemical shift values of ¹H^γ/δ/ε and ¹³C^γ/δ/ε are obtained by (i) identifying ¹H_i−1, ¹³C_i−1, ¹³C_i−1^coupled, and ¹H_i−1^coupledmeasured by the (5,3)D [HCC,CH-COSY] GFT NMR experiment as ¹H^α_i−1, ¹³C^α_i−1, ¹³C^β_i−1, and ¹H^β_i−1, respectively, and thereby matching the chemical shift values of ¹H^α/β_i−1, and ¹³C^α/β_i−1with the chemical shift values of ¹H^α/β_i−1and ¹³C^α/β_i−1measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and (ii) using the chemical shift values of ¹H^α/β_i−1and ¹³C^α/β_i−1in conjunction with other chemical shift connections from the (5,3)D [HCC,CH-COSY] GFT NMR experiment to measure the chemical shift values of ¹H^γ/δ/ε_i−1and ¹³C^γ/δ/ε_i−1.

[0018] Yet another aspect of the present invention relates to a method for assigning chemical shift values of γ-, δ-, and ε-aliphatic sidechain protons, ¹H^γ/δ/ε, and chemical shift values of γ-, δ-, and ε-aliphatic sidechain carbons located peripheral to β-carbons, ¹³C^γ/δ/ε, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,2)D [HCCH-COSY] GFT NMR experiment to measure and connect the chemical shift values of a proton of amino acid residue i−1, ¹H_i−1, a carbon of amino acid residue i−1 coupled to ¹H_i−1, ¹³C_i−1, a carbon coupled to ¹³C_i−1, ¹³C_i−1^coupled, and a proton coupled to ¹³C_i−1^coupled, ¹H_i−1^coupled, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of α- and β-protons of amino acid residue i−1, ¹H^α/β_i−1, and α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1. Then, assignments of the chemical shift values of ¹H^γ/δ/ε and ¹³C^γ/δ/ε are obtained by (i) identifying ¹H_i−1, ¹³C_i−1, ¹³C_i−1^coupled, and ¹H^N_i−1^coupledmeasured by the (4,2)D [HCCH-COSY] GFT NMR experiment as ¹H^α_i−1, C^α_i−1, ¹³C^β_i−1, and ¹H^β_i−1respectively, and thereby matching the chemical shift values of ¹H^α/β_i−1and ¹³C^α/β_i−1with the chemical shift values of ¹H^α/β_i−1and ¹³C^α/β_i−1measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and (ii) using the chemical shift values of ¹H^α/β_i−1and ¹³C^α/β_i−1in conjunction with other chemical shift connections from the (4,2)D [HCCH-COSY] GFT NMR experiment to measure the chemical shift values of ¹H^γ/δ/ε_i−1and 3C^γ/δ/ε_i−1.

[0019] A further aspect of the present invention relates to a method for assigning chemical shift values of a γ-carbon, ¹³C^γ, a δ-carbon, ¹³C^δ, and a δ-proton, ¹H^δ, of an amino acid residue containing an aromatic spin system in a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HBCBCGCDHD] GFT NMR experiment to measure and connect the chemical shift values of a β-proton of amino acid residue i−1, ¹H^β_i−1, a β-carbon of amino acid residue i−1, ¹³C^β_i−1, a γ-carbon of amino acid residue i−1, ¹³C^γ_i−1, a δ-carbon of amino acid residue i−1, ¹³C^δ_i−1, and a δ-proton of amino acid residue i−1, ¹H^δ_i−1, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of ¹H^β_i−1and ¹³C^β_i−1. Then, assignments of the chemical shift values of ¹³C^γ, ¹³C^δ, and ¹H^δ are obtained by (i) matching the chemical shift values of ¹H^β_i−1and ¹³C^β_i−1measured by the (5,3)D HBCBCACA(CO)NHN GFT NMR experiment with the chemical shift values of ¹H^β_i−1and ¹³C^β_i−1, measured by the (5,3)D [HBCBCGCDHD] GFT NMR experiment, and (ii) using the chemical shift values of ¹³C^γ, ¹³C^δ, and ¹H^δ to identify the type of amino acid residue containing the aromatic spin system.

[0020] The present invention also relates to a method for assigning chemical shift values of aliphatic and aromatic protons and aliphatic and aromatic carbons of an amino acid residue containing aliphatic and aromatic spin systems in a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a first GFT NMR experiment, which is selected from the group consisting of a (5,3)D [HCC,CH-COSY] GFT NMR experiment, a (4,2)D [HCCH-COSY] GFT NMR experiment, a (5,2)D [HCCCH-COSY] GFT NMR experiment, and a (5,3)D [HCCCH-COSY] GFT NMR experiment and is acquired for the aliphatic spin system, to measure and connect the chemical shift values of α- and β-protons of amino acid residue i, ¹H^α/β_i, α- and β-carbons of amino acid residue i, ¹³C^α/β_i, a δ-carbon of amino acid residue i, ¹³C^γ_i, and (2) a second GFT NMR experiment, which is selected from the group consisting of a (5,3)D [HCC,CH-COSY] GFT NMR experiment, a (4,2)D [HCCH-COSY] GFT NMR experiment, a (5,2)D [HCCCH-COSY] GFT NMR experiment, and a (5,3)D [HCCCH-COSY] GFT NMR experiment and is acquired for the aromatic spin system, to measure and connect the chemical shift values of ¹³C^γ_iand other aromatic protons and carbons of amino acid residue i. Then, assignments of the chemical shift values of the aliphatic and aromatic protons and aliphatic and aromatic carbons are obtained by matching the chemical shift value of ¹³C^γ_imeasured by the first GFT NMR experiment with the chemical shift value of ¹³C^γ_imeasured by the second GFT NMR experiment.

[0021] Another aspect of the present invention relates to a method for obtaining assignments of chemical shift values of ¹H, ¹³C, and ¹⁵N of a protein molecule. The method involves providing a protein sample and conducting five G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample, where (1) a first experiment is a (4,3)D [HNNCACBCA] GFT NMR experiment for obtaining intraresidue correlations of chemical shift values; (2) a second experiment is a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment for obtaining interresidue correlations of chemical shift values; (3) a third experiment is a (5,3)D [HCC,CH-COSY] GFT NMR experiment for obtaining assignments of aliphatic sidechain chemical shift values; (4) a fourth experiment is a (5,3)D [HBCBCGCDHD] GFT NMR experiment for linking chemical shift values of aliphatic protons, ¹H^β and ¹³C^β, and aromatic protons, ¹³C^δ and ¹H^δ; and (5) a fifth experiment is a (4,2)D [HCCH-COSY] GFT NMR experiment for obtaining assignments of aromatic sidechain chemical shift values.

[0022] The present invention discloses a number of specific GFT NMR experiments and different combinations of those experiments which allows one to obtain sequential backbone chemical shift assignments for determining the secondary structure of a protein molecule and complete assignments of chemical shift values for a protein molecule including aliphatic and aromatic sidechain spin systems.

[0023] The present invention provides a generally applicable approach for NMR data acquisition and processing named “GFT NMR spectroscopy”. This approach is based on the phase-sensitive joint sampling of several indirect dimensions while ensuring that all chemical shift correlations are retained. The employment of GFT NMR focuses on the sampling limited data collection regime and, considering that NMR measurements longer than about a week are impracticable, on the acquisition of five- or higher-dimensional spectral information.

[0024] GFT NMR relaxes on constraints arising from two major drawbacks of FT NMR, that is, the problem of having excessive or prohibitively long measurement times due to sampling of indirect dimensions and the limited precision of chemical shift measurements in the indirect dimensions arising from comparably low digital resolution. Within a few hours or less, GFT NMR spectroscopy affords the correlations of even five- or higher-dimensional FT NMR spectra acquired with high digital resolution. Thus, GFT NMR spectroscopy allows one to tune measurement times to sensitivity requirements without compromising on the dimensionality or the digital resolution. High-throughput efforts such as NMR-based structural genomics (Montelione et al., Nat. Struct. Biol., 7:982-984 (2000), which is hereby incorporated by reference in its entirety) will profit from this feature, because automated resonance assignment (Szyperski et al., J. Biomol. NMR, 11:387-405 (1998); Moseley et al, Curr. Opin. Struct. Biol., 9:635-642 (1999); Moseley et al., Methods Enzymol., 339:91-108 (2001), which are hereby incorporated by reference in their entirety) benefits from maximizing the number of correlations obtained from in a single NMR experiment. Moreover, the rapid sampling realized with GFT NMR spectroscopy will allow researchers to obtain highest dimensional NMR information with exceptional time resolution when, for example, studying slow protein folding in real time (Dyson et al., Annu. Rev. Phys. Chem., 47:369-395 (1996), which is hereby incorporated by reference in its entirety). The high precision of the chemical shift measurements is of potential importance for a broad range of NMR applications in natural sciences and engineering, for example, for automated assignment, or when studying systems with high chemical shift degeneracy such as RNA ribose spin systems (Cromsigt et al., Methods Enzymol., 338:371-399 (2001), which is hereby incorporated by reference in its entirety), (partially) unfolded proteins (Neri et al., FEBS Lett., 303:129-135 (1992), which is hereby incorporated by reference in it its entirety), or lipids (Wang et al., Biochemistry, 41:5453-5461 (2002), which is hereby incorporated by reference in its entirety). Finally, the high precision of the shift measurements may be recruited to accurately measure other NMR parameters such as residual dipolar couplings for structural refinement (Tjandra et al., Science, 278:1111-1114 (1997); Prestegard, Nat. Struct. Biol., 5:517-522 (1998), which are hereby incorporated by reference in their entirety), and transverse relaxation optimized (Pervushin et al., Proc. Natl. Acad. Sci. USA, 94:12366-12371 (1997), which is hereby incorporated by reference in its entirety) GFT NMR may develop into a powerful approach to investigate larger systems.

[0025] In the sensitivity limited regime, GFT NMR may be advantageous in cases where an extended radiofrequency (rf) phase cycle is desirable for spectral editing and/or improved artifact suppression (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996), which is hereby incorporated by reference in its entirety).

[0026] FIG. 1 compares the conventional sampling of a 3D time domain subspace of an ND FT NMR experiment (on the left) with the phase-sensitive joint sampling of the three dimensions in an (N,N-2)D GFT NMR (on the right), that is, with K=2. Processing of the FT NMR experiment requires a 3D FT of the subspace, while the GFT NMR experiment requires time domain editing of chemical shift multiplet components by application of the so-called G-matrix (see equation 1 in the “Detailed Description of the Invention”) and ID FT of the resulting p=2^K+1data sets. For the GFT NMR experiment, the phase settings of ø₁and ø₂of the rf pulses creating transverse magnetization for frequency labeling with Ω₁and Ω₂are indicated for basic spectra (top four rows), first-order central peak spectra (two rows in the middle), and the second-order central peak spectrum (bottom row). Instead of a single peak in FT NMR which encodes three chemical shifts, one obtains a p-fold overdetermined system of equations. A least-squares fit calculation yields the three shifts from the position of seven peaks. In a GFT NMR experiment with constant-time chemical shift evolution periods, the lines forming the chemical shift multiplets have the same width as the resonances in FT NMR (if recorded with corresponding maximal evolution times; see also FIGS. 18A-B). (The width at half height of the frequency domain sinc centre lobe resulting from truncation in the time domain at t_maxis given (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety) by 0.604/t_max. In the current implementation of (5,2)D HACACONHN (FIG. 6) all indirect evolution periods except for Ω(¹H^α) are constant-time periods. The evolution of Ω(¹H^α) is implemented in a semiconstant-time manner (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996), which is hereby incorporated by reference in its entirety), so that signal losses due to transverse relaxation of ¹H^α are negligible for 8.6 kDa ubiquitin at short t_maxvalues around 6.5 ms. For larger systems with short T₂(¹H^α), however, the semiconstant-time frequency labeling may lead to a detectable increase of ω₁-line widths in the basic when compared to central peak spectra.) This yields the same standard deviation ΔΩ for the identification of peak positions in the two experiments. Hence, the standard deviation of the chemical shift measurements obtained “after” the least-squares fit is reduced (Eadie et al., Statistical Methods in Experimental Physics, North-Holland, N.Y. (1982), which is hereby incorporated by reference in its entirety) by a factor 1/√{square root over (n)} in GFT NMR. For simplicity, it is assumed that the n peaks which contribute to the calculation of a given shift exhibit the same line widths (see descriptions of FIGS. 19-20).

[0027] FIGS. 2A-D show a stick diagram exemplifying the formation of chemical shift multiplets (on the left) for K=3 and phase-sensitively edited multiplet components (on the right) in the frequency domain. FIG. 2A shows the basic spectra yielding the following linear combinations: B1 [Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8; B2 [Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8; B3 [Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8; B4 [Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8; B5 [Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8; B6 [Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8; B7 [Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8; B8 [Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8. FIG. 2B shows the first order central peak spectra: B9 [Ω₀+Ω₁+Ω₂]=A9+A10+A11+A12; B10 [Ω₀−Ω₁+Ω₂]=A9−A10+A11−A12; B11 [Ω₀+Ω₁−Ω₂]=A9+A10−A11−A12; B12 [Ω₀−Ω₁−Ω₂]=A9−A10−A11+A12. FIG. 2C shows the second order centralpeak spectra: B13 [Ω₀+Ω₁]=A13+A14; B14 [Ω₀−Ω₁]=A13−A14. FIG. 2D shows the third order central peak spectra: B15=A15. For the calculation of the matrices F(K), see Example 1. To facilitate the comparison of the left and the right section the positions of multiplet components are indicated with thin lines.

[0028] FIGS. 3A-B illustrate the “bottom-up” identification of the peaks forming a chemical shift multiplet in GFT NMR, provided that three indirect dimensions of a FT NMR experiment are jointly sampled (FIG. 1; K=2). FIG. 3A shows that two spin systems exhibiting degenerate chemical shifts in all other conventionally sampled N_t−1 dimensions give rise to basic, first order central and second order central peaks shown in bold (spin system 1) and lighter shade (spin system 2), respectively. Knowledge of the position of the second order central peak of spin system 1 allows identification of the corresponding first order central peaks of spin system 1. In turn, their knowledge allows unambiguous identification of the corresponding peaks of spin system 1 in the basic spectra. As indicated by the dashed line on the left in FIG. 3A, the peaks in B1 and B3 (shown in bold) are centered around the peak in B5 (shown in bold), while, as indicated by the dashed line on the right in FIG. 3A, the peaks in B2 and B4 (shown in bold) are centered around the peak in B5 (shown in bold). This strategy can readily be extended for K>2. In practice, the identification of components belonging to a given shift multiplets is greatly facilitated by inspection of peak intensities: the components forming a given multiplet are expected to exhibit (nearly) the same intensity. To illustrate this point, the resonance lines of spin system 2 were assumed to be more intense than those of spin system 1. FIG. 3B shows that, in addition to chemical shift degeneracy in the conventionally sampled N_t−1 dimensions, the central peaks of spin system 1 (as described in FIG. 3A) and those of spin system 3 (peaks shown in lighter shade) overlap. In this case, the two spin systems exhibit degenerate chemical shifts in all but one dimension of an ND FT NMR spectrum. In (N,N_t)D GFT NMR, the bottom-up identification of multiplet components resolves and groups the signals of the two spin systems in the basic spectra, thus yielding the equivalent of the ND chemical shift correlation.

[0029] FIGS. 4A-C illustrate magnetization transfer pathways of the following GFT NMR experiments: (5,2)D HACACONHN and (5,2)D HACA,CONHN (FIG. 4A); (5,3)D HACACONHN and (5,3)D HACA,CO NHN (FIG. 4B); and (4,3)D CBCACONHN and (4,3)D CBCA,CO NHN (FIG. 4C). INEPT-type polarization transfers (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) are indicated by arrows, and Löhr's “en passant” frequency labeling module is indicated by a double arrow. The nuclei for which the chemical shift is detected in quadrature are shown in bold and are underlined. The nuclei with a grey background are simultaneously sampled in the GFT NMR dimension, and the chemical shifts of the boxed nuclei are used to establish sequential connectivities. In FIG. 4B, the chemical shifts of nitrogen spins shown in circles are measured is a separate dimension.

[0030] FIGS. 5A-G illustrate magnetization transfer pathways generating the basic spectra of GFT NMR experiments: (i) (4,3)D HNNCACBCA (FIG. 5A), (ii) (4,3)D HNN(CO)CACBCA and (4,3)D CBCACA(CO)NHN (FIG. 5B), (iii) (5,3)D HBHACBCACA(CO)NHN (FIG. 5C), (iv) (5,3)D HCC,CH-COSY (FIG. 5D), (v) (5,3)D HBCBCGCDHD (FIG. 5E), (vi) (4,2) HCC,CH-COSY (FIG. 5F), and (vii) (5,2)D HCCCH-COSY (FIG. 5G). In experiments (iv) and (vi), only magnetization transfer pathways corresponding to cross peaks in a 4D HCCH-COSY are shown. In experiment (vii), only the magnetization transfer pathway corresponding to cross peaks in a relayed 5D HCCCH-COSY is shown. INEPT-type polarization transfer are indicated by double arrows for “out-and-back” type experiments and single arrows for “out-and-stay” type experiments. The nucleus for which the chemical shift is detected in quadrature in all spectra constituting the GFT NMR experiment is underlined. The nuclei with grey background are simultaneously sampled in a single GFT NMR dimension, and the chemical shifts of the boxed nuclei are measured in the direct dimension. The chemical shifts of nitrogen spins (shown in circles) are measured in a separate dimension in experiments (i), (ii), and (iii), and the chemical shifts of ¹³C^δ and ¹³C_i^coupled(shown in circles) are measured in a separate dimension in experiments (iv) and (v), respectively. The double headed arrows between ¹³C^α and ¹³C^β in experiments (i), (ii), and (iii) indicate that the chemical shifts of ¹³C^α/β [and ¹H^α/β in (iii)] first evolve independently, prior to transferring to ¹³C^α for frequency labeling.

[0031] FIG. 6 illustrates the rf pulse sequence used to record the (5,2)D HACACONHN GFT NMR experiment. Rectangular 90° and 180° pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no rf phase is marked, the pulse is applied along x. The high power 90° pulse lengths were: 5.6 μs for ¹H and 15.3 μs for ¹³C, and 39 μs for ¹⁵N. Pulses on ¹³C prior to t₁(¹³C) are applied at high power, and ¹³C decoupling during t₁(¹H) is achieved using a (90_x-180_y-90_x) composite pulse (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford 1987), which is hereby incorporated by reference in its entirety). Subsequently, the 90° and 180° pulse lengths of ¹³C^α are adjusted to 51.6 μs and 46 μs, respectively, to minimize perturbation of the ¹³CO spins (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996), which is hereby incorporated by reference in its entirety). The width of the 90° pulses applied to ¹³CO pulse is 51.6 μs and the corresponding 180° pulses are applied with same power. A SEDUCE (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996), which is hereby incorporated by reference in its entirety) 180° pulse with a length 252 μs is used to decouple ¹³CO during t₁. WALTZ16 (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety) is employed to decouple ¹H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple ¹⁵N (rf=1.78 kHz) during acquisition. The SEDUCE sequence (rf=1.0 kHz) is used for decoupling of ¹³C^α during the ¹⁵N chemical shift evolution period. The ¹H rf carrier is placed at 4.78 ppm. The ¹³C^α, ¹³C′ and ¹⁵N rf carriers are set to 56.3 ppm, 174.3 and 119.3 ppm, respectively. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 μs, 16 G/cm); G3 (1 ms, 24 G/cm); G4 (250 μs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, 30 G/cm); G7 (500 μs, 8 G/cm); G8 (125 μs, 29.5 G/cm). All PFG pulses are of rectangular shape. The delays are: τ₁=1.6 ms, τ₂=3.6 ms, τ₃=4.4 ms, τ₄=τ₅=24.8 ms, τ₆=5.5 ms, τ₇=4.6 ms, τ₈=1 ms. ¹H-frequency labeling is achieved in a semi constant-time fashion with t₁^a(0)=1.79 ms, t₁^b(0)=1 μs, t₁^c(0)=1.791 ms, Δt₁^a=62.5 μs, Δt₁^b=32.9 μs, Δt₁^c=29.6 μs. Hence, the fractional increase of the semi constant-time period with t₁equals to λ=1+Δt₁^c/Δt₁^a=0.53. Phase cycling: φ₀=x; φ₁=x, −x; φ₂=x, x, −x, −x; φ₃=x; φ₄=4x,4(−x); φ₆(receiver)=2(x,−x,−x,x). The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G6 is inverted in concert with a 180° shift of φ₅. In case this enhancement scheme is not employed, quadrature detection is accomplished by altering the phase 4o according to States-TPPI (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996), which is hereby incorporated by reference in its entirety). For the setting of the phases φ₀, φ₁, φ₂and φ₃see Example 4.

[0032] FIGS. 7A-B depict the experimental scheme for the (5,2)D HACA,CONHN (FIG. 7A) and (4,3)D CBCA,CO NHN GFT NMR (FIG. 7B) experiments. Rectangular 90° and 180° pulses are indicated by filled and open vertical bars or shaped pulses, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high power 90° pulse lengths were: 5.8 μs for ¹H and 15.4 μs for ¹³C, and 38 μs for ¹⁵N. In FIG. 7A, pulses on ¹³C prior to t₁(¹³C) are applied at high power, and ¹³C decoupling during t₁(¹H) is achieved using a (90_x-180_y-90_x) composite pulse (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety). Subsequently, the 90° and 180° pulse lengths of ¹³C^α are adjusted to 51.5 μs and 46 μs, respectively, to minimize perturbation of the ¹³CO spins. The width of the 90° pulses applied to ¹³CO pulse is 52 μs and the corresponding 180° pulses are applied with same power. A SEDUCE (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) 180° pulse with a length 252 μs is used to decouple ¹³CO during t₁(¹³C^α). WALTZ16 (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) is employed to decouple ¹H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple ¹⁵N (rf=1.78 kHz) during acquisition. The SEDUCE sequence (rf=1.0 kHz) is used for decoupling of ¹³C^α during the ¹⁵N chemical shift evolution period. The ¹H rf carrier is placed at 4.78 ppm. The ¹³C^α and ¹⁵N rf carriers are set to 56.3 ppm and 119.3 ppm, respectively. All ¹³C′ pulses are laminar shifted (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) by 118 ppm relative to the ¹³C^α carrier position. By setting the spectral width of the jointly sampled dimension to one half of 118 ppm, the apparent carrier position for sampling of ¹³C′ chemical shift (174.3 ppm) is folded on the position of the ¹³C^α carrier position at 56.3 ppm. The duration and strengths of the pulsed z-field gradients (PFGs) are: G₁(1 ms, 24 G/cm); G₂(100 μs, 16 G/cm); G₃(1 ms, 24 G/cm); G₅(1.5 ms, 20 G/cm); G₆(1.25 ms, 30 G/cm); G₇(500 μs, 8 G/cm); G₈(125 μs, 29.5 G/cm). All PFG pulses are of rectangular shape. The delays are: τ₁=1.6 ms, τ₂=9.0 ms, τ₄=11.0 ms, τ₅=22.0 ms, τ₆=5.5 ms, τ₇=4.6 ms, τ₈=1 ms. ¹H-frequency labeling is achieved in a semi constant-time fashion with t₁^a(0)=1.7 ms, t₁^b(0)=1 μs, t₁^c(0)=1.701 ms, Δt₁^a=60 μs, Δt₁^b=35.4 μs, Δt₁^c=−24.6 μs. Hence, the fractional increase of the semi constant-time period with t₁equals to λ=1+Δt₁^c/Δt₁^a=0.58. Phase cycling for artefact suppression: φ₀=x; φ₁=x, −x; φ₂=x, x, −x, −x; φ₃=x; φ₄=4x, 4(−x); φ₅=x; φ₆=φ₇=x; φ₈(receiver)=2(x,−x,−x,x). Phases φ₆and φ₇are shifted by 500 to compensate for non-resonance effects. GFT NMR super phase-cycling for recording the 8 basic spectra: φ₁=x,y; φ₂=2x,2y; φ₃=4x,4y (the G-matrix required for time domain editing is shown in equation 15 in Example 5). For acquisition of central peaks derived from ¹³C steady state magnetization, a second set of data sets with a 180° shift for φ₃is collected and data are “pre-processed” as described (see equations 13 and 14 in Example 5). For second order central peak detection, the ¹H^α and ¹³C^α chemical shift evolution periods are omitted and φ₁=x,y; φ₂=x; φ₃=x. Third order central peaks were detected in 2D [¹⁵N, ¹H]-HSQC (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety). (The G-matrices required for the central peak spectra are shown in equations 16-18 in Example 5). The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G6 is inverted in concert with a 180° shift of φ₅. For implementation of (5,3)D HACA,CONHN, t₁(¹⁵N) is replaced by t₂(¹⁵N), and quadrature detection in t₁is accomplished by altering the phase φ_Iaccording to States-TPPI. GFT NMR super phase cycle for the 4 basic spectra: φ₂=x,y; φ₃=2x,2y (the G-matrix required for time domain editing is shown in equation 16 of Example 5). First order central peaks are derived from ¹³C magnetization and are obtained by acquiring a second set of data sets with a 180° shift for φ₃. For second order central peak detection, t₁(¹H^α) and t₁(¹³C^α) are omitted. (The G-matrices required for time domain editing of the central peak spectra are shown in equations 17 and 18 of Example 5). In FIG. 7B, pulses on ¹³C prior to t₁(¹³C) are applied at high power. Subsequently, the 90° and 180° pulse lengths applied for ¹³C^α/β are adjusted to 47.5 μs and 42.5 μs, respectively, to minimize perturbation of ¹³CO spins. The width of the 90° pulses applied to ¹³CO pulse is 52 μs and the corresponding 180° pulses are applied with same power. SEDUCE 180° pulses of 200 μs pulse length are used to decouple ¹³CO during t₁and τ₄. WALTZ16 is employed to decouple ¹H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers, as well as to decouple ¹⁵N (rf=1.78 kHz) during acquisition. The SEDUCE sequence is used for decoupling of ¹³C′ during the ¹⁵N chemical shift evolution period (rf=1.0 kHz). The ¹H rf carrier is placed at 4.78 ppm. Initially, the ¹³C and ¹⁵N rf carriers are set to 41.3 ppm and 119.3 ppm, respectively. The ¹³C′ carrier position is folded from 174.3 to 41.3 ppm by setting the spectral width in ω₁to one half of 133 ppm (=174.3 ppm−41.3 ppm). The ¹³C carrier is set to 56.3 ppm during the τ₇delay. The duration and strengths of the pulsed z-field gradients (PFGs) are: G₁(1 ms, 24 G/cm); G₂(100 μs, 16 G/cm); G₃(250 μs, 29.5 G/cm); G₄(250 μs, 30 G/cm); G₅(1.5 ms, 20 G/cm); G₆(1.25 ms, 30 G/cm); G₇(500 μs, 8 G/cm); G₈(125 μs, 29.5 G/cm). All PFG pulses are of rectangular shape. The delays are: τ₀=1.7 ms, τ₁=800 μs, τ₂=2.8 ms, τ₃32 3.3 ms, τ₄=6.6 ms, τ₆=8.8 ms, τ₇=24 ms, τ₈=5.5 ms, τ₀=4.6 ms, τ₁₀=1.0 ms. Phase cycling for artefact suppression: φ₁=x; φ₂=2(x), 2(−x); φ₃=x; φ₄=x, −x; φ₅=φ₆=φ₇=φ₈=x; φ₉(receiver)=x,−x,−x,x. Phases φ₆and φ₇are shifted by 120° to compensate for non-resonance effects. GFT NMR super phase-cycling for recording the two basic spectra: φ₂=x,y (the G-matrix required for time domain editing is shown in equation 17 of Example 5). The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G6 is inverted in concert with a 180° shift of φ₈. Quadrature detection in t₁(¹³C′) is accomplished by altering the phase φ₆according to States-TPPI (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety).

[0033] FIG. 8 depicts the experimental scheme for recording the (4,3)D CBCACONHN GFT NMR experiment. Rectangular 90° and 180° pulses are indicated by filled and open vertical bars or shaped pulses, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high power 90° pulse lengths were: 5.8 μs for ¹H and 15.4 μs for ¹³C, and 38 μs for ¹⁵N. Pulses on ¹³C prior to t₁(¹³C) are applied at high power. Subsequently, the 90° and 180° pulse lengths applied for ¹³C^α/β are adjusted to 47.5 μs is and 42.5 μs, respectively, to minimize perturbation of ¹³CO spins. The width of the 90° pulse applied on ¹³CO pulse is 52 μs and the corresponding 180° pulses are applied with same power. A SEDUCE (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) 180° pulse with a length of 200 μs is used to decouple ¹³CO during t₁and τ₄. The length of the spin-lock purge pulses SL_xand SL_yare 1.2 ms and 0.6 ms, respectively. WALTZ16 (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) is employed to decouple ¹H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple ¹⁵N during acquisition (rf=1.78 kHz) during acquisition. The SEDUCE sequence is used for decoupling of ¹³C^α during ¹⁵N evolution period (rf=1.0 kHz). The ¹H rf carrier is placed at the water line at 4.78 ppm. Initially, the ¹³C and ¹⁵N rf carriers are set to 41.3 ppm and 119.3 ppm, respectively. The ¹³C carrier is set to 56 ppm during the second τ₄/2 delay. The ¹³C′ carrier position is set to 174.3 ppm. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 μs, 16 G/cm); G3 (250 μs, 29.5 G/cm); G4 (250 μs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, 30 G/cm); G7 (500 μs, 8 G/cm); G8 (125 μs, 29.5 G/cm). All PFG pulses are of rectangular shape. The delays are: τ₁=800 μs, τ₂=3.1 ms, τ₃=3.6 ms, τ₄32 7.2 ms, τ₅=4.4 ms, τ₆=24.8 ms, τ₇=24.8 ms, τ₈=5.5 ms, τ₉=4.6 ms, τ₁₀=1.0 ms. Phase cycling for artefact suppression: φ₁=x; φ₂=x,x,−x,−x; φ₃=x, −x; φ₄=x, −x; φ₅=−x; φ6=x, x, −x, −x; φ₇=x; φ8(receiver)=x, −x, −x, x. The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G₆is inverted in concert with a 180° shift of φ₇Quadrature detection in t₁(¹³C′) is accomplished by altering the phase φ₄according to States-TPPI. GFT NMR super phase-cycle for acquisition of the two basic spectra: φ₂=x,y (the G-matrix required for time domain editing is shown in equation 17 of Example 5). For first order central peak detection an HNNCO pulse scheme (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) is employed.

[0034] FIG. 9 depicts the experimental scheme for the (4,3)D HNNCACBCA experiment. Rectangular 90° and 180° pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high-power 90° pulse lengths were: 6.0 μs for ¹H, 15.0 μs for ¹³C and 42 μs for ¹⁵N. The 90° and 180° pulse lengths applied on ¹³C^α/β are adjusted to 40 μs and 36 μs, respectively, to minimize perturbation of ¹³CO spins. One lobe sinc pulses of duration 65 μs were applied on ¹³CO with null at ¹³C^α to decouple ¹³CO from ¹³C^α spins during t₁and from ¹⁵N spins during t₂. The selective 90° ¹H pulse used to flip back the water magnetization is applied for 1.8 ms duration before the first 90° pulse on ¹³C^α. WALTZ16 is employed to decouple ¹H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple of ¹⁵N (rf=1.78 kHz) during acquisition. The ¹H rf carrier is placed at the position of the solvent line at 4.78 ppm. The ¹³C^α and ¹⁵N carriers are set to 43.0 ppm and 120.9 ppm, respectively. The ¹³C carrier is switched to 56 ppm during the second t₁delay. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1.0 μs, 24 G/cm); G2 (100 μs, 16 G/cm); G3 (500 μs, 29.5 G/cm); G5 (100 μs, 16 G/cm); G4 (1.5 ms, 20 G/cm); G6(1.5 ms, 20 G/cm); G7 (1.25 ms, 30 G/cm); G8 (500 μs, 8 G/cm); G9 (125 μs, 29.5 G/cm). All PFG pulses are of rectangular shape. A recovery delay of at least 100 μs duration is inserted between a PFG pulse and an rf pulse. The delays have the following values: τ₁=4.6 ms, τ₂=5.4 ms, τ₃=24 ms, τ₄=24 ms, τ₅=4.8 ms, τ_c=7.0 ms. Phase cycling: φ₁=x, −x; φ₂=y; φ₃=x,x, −x, −x; φ₄=x, φ₅=4(x), 4(−x); φ₆=x; φ₇(receiver)=x, −x, −x, x. The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G7 is inverted in concert with a 180° shift of φ₆. Quadrature detection in t₁(¹³C^α) and t₂(¹⁵N) is accomplished by altering the phases φ₃and φ₄, respectively, according to States-TPPI. GFT-NMR super phase-cycling for recording the 2 basic spectra are: φ₁=x,y; φ₂=y,x.

[0035] FIG. 10 depicts the experimental scheme for the (4,3)D HNN(CO)CACBCA experiment. Rectangular 90° and 180° pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high-power 90° pulse lengths were: 6.0 μs for ¹H, 15.0 μs for ¹³C and 42 μs for ¹⁵N. The 90° and 180° pulse lengths applied on ¹³C^α/β are adjusted to 40 μs and 36 μs, respectively, to minimize perturbation of ¹³CO spins. One lobe sinc pulses of duration 65 μs and with null at ¹³C^α were applied on ¹³CO to decouple from ¹³C^α spins during t₁and from ¹⁵N spins during t₂. The 90° pulse lengths for the one lobe sinc pulse on ¹³CO was 71 μs. The selective 90° ¹H pulse used to flip back the water magnetization is applied for 1.8 ms duration before the first 90° pulse on ¹³C^α. WALTZ16 is employed to decouple ¹H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple of ¹⁵N (rf=1.78 kHz) during acquisition. The ¹H rf carrier is placed at the position of the solvent line at 4.78 ppm. The ¹³C^α and ¹⁵N carriers are set to 43 ppm and 120.9 ppm, respectively. The ¹³C carrier is switched to 56 ppm during the second t₁delay. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1.0 ms, 24 G/cm); G2 (100 μs, 16 G/cm); G3 (1.0 ms, 29.5 G/cm); G4 (1.5 ms, 20 G/cm); G5 (100 μs, 16 G/cm); G6(1.5 ms, 20 G/cm); G7 (1.25 ms, 30 G/cm); G8 (500 μs, 8 G/cm); G9 (125 μs, 29.5 G/cm). All PFG pulses are of rectangular shape. A recovery delay of at least 100 μs duration is inserted between a PFG pulse and an rf pulse. The delays have the following values: τ₁=4.4 ms, τ₂=5.4 ms, τ₃=24 ms, τ₄=24 ms, τ₅=4.8 ms, τ_a=4.6 ms, τ_b=6.8 ms, τ_c=6.9 ms. Phase cycling: φ₁=x, −x; φ₂=y; φ₃=x,x, −x, −x; φ₄=x, φ₅=4(x), 4(−x); φ₆=x; φ₇(receiver)=x, −x, −x, x. The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G7 is inverted in concert with a 180° shift of φ₆Quadrature detection in t₁(¹³C) and t₂(¹⁵N) is accomplished by altering the phases φ₃and φ₄, respectively, according to States-TPPI. GFT-NMR super phase-cycle for recording the 2 basic spectra are: φ₁=x,y; φ₂=y,x.

[0036] FIG. 11 depicts the experimental scheme for the (4,3)D CBCACA(CO)NHN experiment. Rectangular 90° and 180° pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high-power 90° pulse lengths were: 5.9 μs for ¹H, 15.4 μs for ¹³C, and 38 μs for ¹⁵N. Pulses on ¹³C prior to t₁(¹³C) are applied at high power, and ¹³C decoupling during t₁(¹H) is achieved using a (90_x-180_y-90_x) composite pulse. Subsequently, the 90° and 180° pulse lengths applied for ¹³C^α/β are adjusted to 47.5 μs and 42.5 μs, respectively, to minimize perturbation of ¹³CO spins. The width of the 90° pulse applied on ¹³CO pulse is 52 μs and the corresponding 180° pulses are applied with same power. A SEDUCE 180° pulse with a length of 200 μs is used to decouple ¹³CO during t₁and τ₄. The length of the spin-lock purge pulses SL_xand SL_yare 1.2 ms and 0.6 ms, respectively. WALTZ16 is employed to decouple ¹H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple ¹⁵N during acquisition (rf=1.78 kHz) during acquisition. The SEDUCE sequence is used for decoupling of ¹³C^α during ¹⁵N evolution period (rf=1.0 kHz). The ¹H rf carrier is placed at 4.78 ppm. Initially, the ¹³C and ¹⁵N r. f. carriers are set to 43 ppm and 120.9 ppm, respectively. The ¹³C carrier is set to 56 ppm before the first τ₄/2 delay period. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 μs, 16 G/cm); G3 (250 μs, 29.5 G/cm); G4 (250 μs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, 30 G/cm); G7 (500 μs, 8 G/cm); G8 (125 μs, 29.5 G/cm). All PFG pulses are of rectangular shape. A recovery delay of at least 100 μs duration is inserted between a PFG pulse and an rf pulse. The delays are: τ₁=600 μs, τ₂=3.1 ms, τ₃=3.35 ms, τ₄=6.8 ms, τ₅=4.4 ms, τ₆=24.6 ms, τ₇=24.6 ms, τ₈=5.5 ms, τ₉=4.6 ms, τ₁₀=1.0 ms. Phase cycling: φ₁=x; φ₂=x,x,−x,−x; φ₃=x, −x; φ₄=x, −x; φ₅=x; φ₆=x, x, −x, −x; φ₇=x; φ₈=x; φ9(receiver)=x, −x, −x, x. The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G6 is inverted in concert with a 180° shift of φ₇. GFT-NMR super phase-cycling for recording the 2 basic spectra are: φ₂=x,y. Quadrature detection in t₁(¹³C) and t₂(¹⁵N) is accomplished by altering the phases 48 and 45, respectively, according to States-TPPI.

[0037] FIG. 12 depicts the experimental scheme for the (5,3)D HBHACBCACA(CO)NHN experiment. Rectangular 90° and 180° pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The scaling factor K, for ¹H chemical shift evolution during t₁is set to 1.0. The high-power 90° pulse lengths were: 5.9 μs for ¹H, 15.4 μs for ¹³C, and 38 μs for ¹⁵N. Pulses on ¹³C prior to t₁(¹³C) are applied at high power, and ¹³C decoupling during t₁(¹H) is achieved using a (90_x-180_y-90_x) composite pulse. Subsequently, the 90° and 180° pulse lengths applied for ¹³C^α/β are adjusted to 47.5 μs and 42.5 μs, respectively, to minimize perturbation of ¹³CO spins. The width of the 90° pulse applied on ¹³CO pulse is 52 μs and the corresponding 180° pulses are applied with same power. A SEDUCE 180° pulse with a length of 200 μs is used to decouple ¹³CO during t₁and τ₄. The length of the spin-lock purge pulses SL_xand SL_yare 1.2 ms and 0.6 ms, respectively. WALTZ16 is employed to decouple ¹H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple ¹⁵N during acquisition (rf=1.78 kHz) during acquisition. The SEDUCE sequence is used for decoupling of ¹³C^α during ¹⁵N evolution period (rf=1.0 kHz). The ¹H rf carrier is placed at −1 ppm before the start of the semi constant time ¹H chemical shift evolution period, and then switched to the water line at 4.78 ppm after the second 90° ¹H pulse. Initially, the ¹³C and ¹⁵N r. f. carriers are set to 43 ppm and 120.9 ppm, respectively. The ¹³C carrier is set to 56 ppm during the second τ₄/2 delay. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 μs, 16 G/cm); G3 (250 μs, 29.5 G/cm); G4 (250 μs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, G/cm); G7 (500 μms, 8 G/cm); G8 (125 μs, 29.5 G/cm). All PFG pulses are of rectangular shape. A recovery delay of at least 100 μs duration is inserted between a PFG pulse and an rf pulse. The delays are: τ₁=600 μs, τ₂=3.1 ms, τ₃=3.35 ms, τ₄=6.8 ms, τ₅=4.4 ms, τ₆=24.6 ms, τ₇=24.6 ms, τ₈=5.5 ms, τ₉=4.6 ms, τ₁₀=1.0 ms. ¹H-frequency labeling, at a ¹H resonance frequency of 600 MHz is achieved in a semi constant-time fashion with t₁^a(0)=1.7 ms, t₁^b(0)=1 μs, t₁^c(0)=1.701 ms, Δt₁^a=33.3 μs, Δt₁^b=19.3 μs, Δt₁^c=−14 μs. Hence, the fractional increase of the semi constant-time period with t₁equals to k=1+Δt₁^c/Δt₁^a=0.58. Phase cycling: φ₁=x; φ₂=x,x,−x,−x; φ₃=x, −x; φ₄=x, −x; φ₅=x; φ₆=x, x, −x, −x; φ₇=x; φ₈=x; φ₉(receiver)=x, −x, −x, x. The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G6 is inverted in concert with a 180° shift of φ₇. Quadrature detection in t₁(¹³C) and t₂(¹⁵N) is accomplished by altering the phases φ₈and φ₅, respectively, according to States-TPPI. GFT-NMR super phase-cycling for recording the 4 basic spectra are: φ₁=x,y; φ₂=x,y. For acquisition of central peaks derived from ¹³C steady state magnetization, a second data set with he shifted by 180°, is collected.

[0038] FIG. 13 depicts the experimental scheme for the (5,3)D HCC,CH-COSY experiment. Rectangular 90° and 180° pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The scaling factor κ for ¹H chemical shift evolution during t₁is set to 1.0. The high power 90° pulse lengths were: 5.8 μs for ¹H and 15.4 μs for ¹³C, and 38 μs for ¹⁵N. The lengths of the ¹H spin-lock purge pulses are: first SL_x, 2.8 ms; second SL_x, 1.7 ms; SL_y: 4.9 ms. SEDUCE is used for decoupling of ¹³CO during t₁and t₂(rf field strength=1 kHz). WURST is used for decoupling of ¹³C during acquisition. The ¹H carrier is placed at the position of the solvent line at 0 ppm before the start of the first semi constant time ¹H evolution period, and then switched to the water line at 4.78 ppm after the second 90° ¹H pulse. The ¹³C and ¹⁵N rf carriers are set to 43 ppm and 120.9 ppm, respectively. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (500 μs, 6 G/cm); G2 (500 μs, 11 G/cm); G3 (100 μs, 12 G/cm); G4 (100 μs, 12.5 G/cm); G5 (4.0 ms, 22 G/cm); G6 (500 μs, 5 G/cm); G7 (3.0 ms, 22 G/cm); G8 (400 μs, 6 G/cm). All gradients are applied along z-axis and are of rectangular shape. All PFG pulses are of rectangular shape. A recovery delay of at least 100 μs duration is inserted between a PFG pulse and an rf pulse. The delays are: τ₁=1.6 ms, τ₂=750 μs, τ₃=2.65 ms, τ₄=3.4 ms, τ₅=6.8 ms, τ₆=1.6 ms, τ₇=2.4 ms, τ_a=350 μs, τ_b=1.65 ms and τ_c=2.4 ms. Phase cycling: φ₁=x; φ₂=x, −x; φ₃=x, −x; φ₄=x; φ₅=y; φ₆(receiver)=x, −x. Quadrature detection in t₁(¹³C/¹H) and t₂(¹³C) is accomplished by altering the phases φ₄and φ₅, respectively, according to States-TPPI. Water suppression is accomplished by coherence pathway rejection using spin-lock purge pulses and pulsed field z-gradients. GFT-NMR super phase-cycle for recording the 4 basic spectra are: φ₁=x,y; φ₂=x,y. For acquisition of central peaks derived from ¹³C steady state magnetization, a second data set with 4) shifted by 180° is collected.

[0039] FIG. 14 depicts the experimental scheme for the (5,3)D HBCBCGCDHD experiment. Rectangular 90° and 180° pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The scaling factor K for ¹H chemical shift evolution during t₁is set to 1.0. The high power 90° pulse lengths were: 5.8 μs for ¹H and 15.4 μs for ¹³C. The first 180° pulse on ¹³C prior to t₁(¹³C) is applied at high power. Subsequently, the 90° pulse lengths of ¹³C^β is adjusted to 66 μs. The 180° ¹³C^β and ¹³C^aropulses are of gaussian-3 shape and 375 μs duration. WALTZ16 is used for decoupling of ¹H (rf field strength=4.5 kHz) during the magnetization transfer from ¹³C^α to ¹³C^aro, and GARP is employed to decouple ¹³C^aro(rf=2.5 kHz) during acquisition. The ¹H rf carrier is placed at 4.78 ppm. The ¹³C rf carrier is set to 38 ppm during ω₀(¹³C) and then switched to 135 ppm before the first 90° pulse on ¹³C^aro(pulse labeled with φ₄). The ¹³C rf carrier is switched back to 125 ppm before the second 90° pulse on ¹³C^aro. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (500 μs, 2 G/cm); G2 (1 ms, 22 G/cm); G3 (2 ms, 10 G/cm); G4 (500 μs, 4 G/cm); G5 (1 ms, −14 G/cm); G6 (500 μs, −2 G/cm). All PFG pulses are of rectangular shape. A recovery delay of at least 100 μs duration is inserted between a PFG pulse and an rf pulse. The delays are: τ₁=1.8 ms, τ₂=8.8 ms, τ₃=71 μs, τ₄=4.3 ms, τ₅=2.1 ms, τ₆=710 μs, τ₈=1.4 ms, τ₇=2.5 ms. ¹H-frequency labeling, at a ¹H resonance frequency of 600 MHz is achieved in a semi constant-time fashion with t₁(0)=1.7 ms, t₁^b(0)=1 82 s, t₁^c(0)=1.701 Δt₁^a=33.3 μs, Δt₁^b=19.3 μs, Δt₁^c=−14 μs. Hence, the fractional increase of the semi constant-time period with t₁equals to λ=1+Δt₁^c/Δt₁^a=0.58. Phase cycling: φ₁=x; φ₂=x; φ₃=x, y, −x, −y; φ₄=4(x), 4(−x); φ₅=x; φ₆(receiver)=x, −x, x, −x, −x, Quadrature detection in t₁(¹³C^δ) and t₂(¹³C^γ) is accomplished by altering the phases φ₄and φ₅, respectively, according to States-TPPI. Water suppression is accomplished by presaturation of the water line during the relaxation delay and coherence pathway rejection using spin-lock purge pulses and pulsed field z-gradients. GFT-NMR super phase-cycling for recording the 4 basic spectra are: φ₁=x,y; φ₂=x,y. For acquisition of central peaks derived from ¹³C steady state magnetization, a second data set with φ₁shifted by 180° is collected.

[0040] FIG. 15 depicts the experimental scheme for the (4,2)D HCCH-COSY experiment. Rectangular 90° and 180° pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high power 90° pulse lengths were: 5.8 μs for ¹H and 15.4 μs for ¹³C, and 38 μs for ¹⁵N. The lengths of the ¹H spin-lock purge pulses are: first SL_x, 2.8 ms; second SL_x, 1.7 ms; SL_y: 4.9 ms. SEDUCE is used for decoupling of ¹³CO during t₁and t₂(rf field strength=1 kHz). WURST is used for decoupling of ¹³C during acquisition. The ¹H carrier is placed at 4.78 ppm. The ¹³C and ¹⁵N rf carriers are set to 43 ppm and 120.9 ppm, respectively. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (500 is, 6 G/cm); G2 (500 is, 11 G/cm); G3 (100 μs, 12 G/cm); G4 (100 μs, 12.5 G/cm); G5 (4 ms, 22 G/cm); G6 (500 μs, 5 G/cm); G7 (3 ms, 30 G/cm); G8 (400 μs, 6 G/cm). All gradients are applied along z-axis and are of rectangular shape. All PFG pulses are of rectangular shape. A recovery delay of at least 100 μs duration is inserted between a PFG pulse and an rf pulse. The delays are: τ₁=1.6 ms, τ₂=750 μs, τ₃=2.65 ms, τ₄=3.4 ms, τ₅=6.8 ms, τ₆=0.7 ms, τ₇=3.2 ms. Phase cycling: φ₁=x; φ₂=x, −x; φ₃=x, −x; φ₄=x; φ₅=y; φ₆(receiver)=x, −x. Quadrature detection in t₁(¹³C) is accomplished by altering the phases φ₄according to States-TPPI. Water suppression is accomplished by coherence pathway rejection using spin-lock purge pulses and pulsed field z-gradients. GFT-NMR super phase-cycle for recording the 4 basic spectra are: φ₁=x,y; φ₂=x,y. For acquisition of central peaks derived from ¹³C steady state magnetization, a second data set with φ₁shifted by 180° is collected.

[0041] FIGS. 16A-B show the ω₁[(¹⁵N;¹³C′, ¹³C^α, ¹H^α), ω₂(¹H^N)]-, [ω₁(¹⁵N;¹³C′, ¹³C^α), ω₂(¹H^N)]-, [ω₁(¹⁵N;¹³C′), ω₂(¹H^N)]-, and [ω₁(¹⁵N), ω₂(¹H^N)]-strips taken from the (5,2)D HACACONHN GFT NMR experiment (see FIG. 17). The signals were detected on the amide proton chemical shift of Ser 20. FIG. 16A shows spectra A1-A 15 containing the chemical shift multiplets. FIG. 16B shows spectra B1-B15 containing the individual edited chemical shift multiplet components. Note that when compared with FIG. 2 the order of the chemical shift multiplets appears to have changed. However, this is because ω₁(¹H^α)<0 ppm (i.e., upfield relative to the carrier position) for Ser 20, and ω₁(¹³C′), ω₁(¹³C^α) and ω₁(¹⁵N) >0 ppm (i.e, downfield relative to the respective carrier position). For simplicity, FIG. 2 was designed with the assumption that all resonances are located downfield to the respective carrier positions. The signals located at higher field in A15 and B15 arise from a side chain moiety and have thus no corresponding peaks in the other spectra (see also FIG. 17D). To facilitate the comparison of FIGS. 16A and 16B, the positions of multiplet components are indicated with thin lines.

[0042] FIGS. 17A-E show the 15 2D planes constituting the (5,2)D HACACONHN GFT NMR experiment (K=3) recorded for the 8.6 kDa protein ubiquitin. The linear combination of chemical shifts detected in a given plane is indicated. FIG. 17A shows the basic spectra B1 to B8. FIG. 17B shows the first order central peak spectra B9 to B12. FIG. 17C shows the second order central peak spectra B13 and B14. FIG. 17D shows the third order central peak spectrum B15. Signals arising from side chain moieties are in dashed boxes. FIG. 17E shows cross sections taken along ω₁(¹⁵N;¹³C′, ¹³C^α, ¹H^α) at the peak of Ser 20 in B1 (at the top), along ω₁(¹⁵N;¹³C′, ¹³C^α) in B9 (second from top), along ω₁(¹⁵N;¹³C′) in B13 (third from top), and along ω₁(¹⁵N) in B15 (at the bottom). The sections are indicated in green in the corresponding panel. Comparison of sections from B1 and B9 shows that signals do not broaden with increasing K (FIG. 18), while the smaller line widths observed in spectra B13 to B15 result from longer t_maxvalues (see Example 4). The 15 signals detected on the backbone amide proton of Ile 36 are circled. Doublets are observed in B1-B8 since Gly 35 exhibits non-degenerate ¹H^α chemical shifts, yielding the correlation of six shifts: δ(¹H^α2)=4.135±0.006 ppm, δ(¹H^α1)=3.929±0.006 ppm, δ(¹³C^α)=46.10±0.019 ppm, δ(¹³C′)=173.911±0.017 ppm for Gly 35, and δ(¹⁵N)=120.295±0.043 ppm and δ(¹H^N)=6.174±0.005 ppm for Ile 36 (Table 2). The standard deviations of the indirectly detected chemical shifts were estimated from a Monte Carlo simulation (see description of FIG. 19). In accordance, the ω₂(¹H^N) line width of the directly detected amid proton (20 Hz) was identified with±3σ (99.5% confidence interval) for locating the peak positions. Notably, phase sensitive editing of the chemical shift multiplets yields increasing peak dispersion (and thus resolution) in each of the constituent spectra compared to 2D [¹⁵N, ¹H]-HSQC (panel B15). Nearly the same number of peaks is detected in each of 15 spectra, while the spectral width increases from SW₁(¹⁵N)=1,440 Hz in B15 to SW₁(¹⁵N/¹³C′/¹³C^α/¹H^α)=8,000 Hz in B1 . . . B8.

[0043] FIGS. 18A-C compare line widths and digital resolution of peaks detected in GFT and FT NMR. FIG. 18A shows (5,2)D HACACONHN GFT NMR: cross sections taken along ω₁(¹⁵N;¹³C′, ¹³C^α, ¹H^α) at the peak of Ser 20 in spectrum B1 (at the top), along ω₁(¹⁵N;¹³C′, ¹³C^α) in spectrum B9 (second from top), along ω₁(¹⁵N;¹³C′) in spectrum B13 (third from top), and along ω₁(¹⁵N) in spectrum B15 (at the bottom). The same t_maxvalue was chosen for all spectra in order to demonstrate that resonances do not broaden when increasing K from 0 to 3. FIG. 18B shows HACACONHN FT NMR: ω₁(¹H^α), ω₁(¹³C^α), ω₁(¹³C^α), and ω₁(¹⁵N) cross sections taken from 2D [ω₁, ω₂(¹H^N)]- planes obtained with the HACACONHN rf pulse scheme which were (i) recorded with the same t_maxvalues and spectral widths, and (ii) were processed as (5,2)D HACACONHN. Comparison of FIG. 18A and FIG. 18B shows that the linewidth registered in the GFT NMR experiment equals the linewidth in the FT NMR experiment. FIG. 18C shows the same cross sections as in FIG. 18B are shown except that the planes were recorded and processed as a conventional 5D NMR spectrum would be [same maximal evolution times as in the basic spectra, 10(t₁)*11(t₂)*22(t₃)*13(t₄)*512(t₅) complex points with spectral widths of SW₁(¹⁵N)=1,440 Hz, SW₂(¹³C′)=1,500 Hz, SW₃(¹³C^α)=3,260 Hz, and SW₄(¹H^α)=1,800 Hz and linear prediction to 20(t₁)*22(t₂)*32(t₃)*26(t₄)*512(t₅) complex points]. This would yield a frequency domain data set of 32(ω₁)*32(ω₂)*32(ω3)*32(ω₄)*512((ω₅) real points of 2.1 GByte size as compared to 16.8 MByte for (5,2)D HACACONHN. Comparison with FIG. 18B and FIG. 18C makes the relatively poor resolution obtainable in 5D FT NMR apparent. Note that linear prediction and zero filling to ⁹⁶(ω₁)*96(ω₂)*256(ω₃)*128(ω₄)*512(ω₅) real points, which would be the closest match to the digital resolution obtained in (5,2)D HACACONHN, would result in an unrealistically large data size of 618 GByte.

[0044] FIG. 19 illustrates Monte-Carlo simulations performed to assess the increased precision of chemical shift measurements in (5,2)D HACACONHN GFT NMR. Standard deviations for the chemical shift measurements are plotted versus the number of spectra selected from the 15 2D spectra constituting this experiment (FIG. 17) in order to calculate the chemical shifts. σ(¹H^α), σ(¹³C^α), σ(¹³C′) and σ¹⁵N) represent the deviations for Ω₃(¹H^α), Ω₂(¹³C), Ω₁(¹³C′) and Ω₀(¹⁵N) measurements, respectively. The following conservative statistical model is adopted. Line widths at half height, Δν_1/2, were measured along Ω₁in (i) B1-B12 (basic spectra and first order central peaks) providing Δν_1/2(basic)=Δν_1/2(first)=60.1 Hz, (ii) B13 and B14 (second order central peaks) providing Δν_1/2(second)=38.2 Hz and (iii) B15 (third order central peaks) providing Δν_1/2(3rd)=28.1 Hz [FIG. 17E; these values are close to those expected from the t_maxvalues obtained after linear prediction]. It is then assumed that the error for the identification of peak positions is associated with a Gaussian distribution, and that the Lorenzian line width, Δν_1/2, represents ±3σ (99.5% confidence interval), i.e., Δν_1/2=6σ. Δν_1/2(basic) is equal to the line widths in the indirect dimensions of conventional FT NMR spectra recorded with the same maximal evolution time (FIGS. 17E and 18). Hence, σ(basic) likewise represents the standard deviation obtained in FT NMR. Correspondingly are σ(second)=Δν_1/2(second)/6 and σ(third)=Δν_1/2(third)/6 the standard deviations for peak position identification in B13 and B14, and B15. The deviations σ(¹H^α), σ(¹³C^α), σ(¹³C′) and σ(¹⁵N) were obtained from Monte Carlo simulations of error propagation for which the following systems of equations were considered: (i) a minimal number of four out of the eight basic spectra (B1, B4, B6, B7; FIG. 20) (ii) B1-B8, (iii) B1-B12, (iv) B1-B14, or (v) B1-B15. Peak positions were randomly varied 10,000 times according to Gaussian distributions characterized by σ(basic), σ(second) and σ(third). Subsequently, the systems of equations were solved using a least-squares fitting routine, and the deviations among the 10,000 solutions yielded σ(¹H^α), σ(¹³C^α), σ(¹³C′) and σ(¹⁵N). Note that σ(¹H^α) is not further reduced when central peaks are involved since those do not encode Ω(¹H^α). Similarly, σ(¹³C^α) and σ(¹³C′) are not further reduced when second and third order central peaks are considered for calculation of chemical shifts. Notably, the standard deviations (labeled with an asterisk) obtained with four spectra critically depend on the particular selection (FIG. 20). The highest precision is obtained when choosing either B1, B4, B6 and B7, or B2, B3, B5 and B8 (FIGS. 20 and 17). The simulations are in neat agreement with calculations using the Gaussian law of error propagation (see FIG. 20).

[0045] FIGS. 20A-E show the results of Monte-Carlo simulations for the case that only four out of eight basic spectra of (5,2)D HACACONHN (FIG. 17A) are selected to calculate the chemical shifts. The standard deviations for the chemical shift measurements are plotted versus the number assigned to a particular combination. FIGS. 20A-D show σ(¹⁵N), σ(¹³C′), σ(¹³C^α) and σ(¹H^α), respectively, which represent the standard deviations for the measurement of the chemical shifts Ω₀(¹⁵N), Ω₁(¹³C′), Ω₂(¹³C^α) and Ω₃(¹H^α), respectively. FIG. 20E illustrates the assignment of numbers to the selections of four out of the 64 possible combinations $\left\{\left(\begin{array}{c}8\\ 4\end{array}\right)-6=\left(8·7·6·5\right)/\left(4·3·2·1\right)-6=64\right\}.$

[0046] The six combinations which are subtracted from the binomial coefficient $\left(\begin{array}{c}8\\ 4\end{array}\right)$

[0047] correspond to the cases where one of the three chemical shifts Ω₁, Ω₂or Ω₃is added to or subtracted from Ω₀in all of the four selected spectra (i.e., no splitting is present among the four selected spectra which encodes the respective chemical shift). The spectra selected for a particular combination number are indicated as dots. The statistical model used for the Monte Carlo simulations is the same as described in the legend of FIG. 19.

[0048] FIGS. 21A-B show the composite plot of [ω₁,ω₂]-strips taken from (5,2)D HACA,CONHN (FIG. 21A) and HACACONHN data (FIG. 21B) collected for the 8.6 kDa protein ubiquitin with a total measurement time of 10.5 hours. The 2D data were acquired with 58(t₁):512(t₂) complex points and t_1max(¹⁵N; ¹³C′, ¹³C^α, ¹H^α)=6.5 ms and t_2max(¹H^N)=73.2 ms. In FIG. 21A, the strips were taken from basic spectra (B1 to B8), first order central peak spectra (B9 to B12), second order central peak spectra (B13 and B14) and third order central peak spectra (B15) and are centered about the amide proton chemical shift of Glu 64. The position of the backbone ¹⁵N chemical shift of Glu 64 is indicated by a dashed horizontal line, and the type of linear combination of chemical shifts detected for a given strip along ω₁is indicated at the top of the strip: B1 [Ω₀+Ω₁+Ω₂+Ω₃]; B2 [Ω₀−Ω₁+Ω₂+Ω₃]; B3 [Ω₀+Ω₁−Ω₂+Ω₃]; B4 [Ω₀−Ω₁−Ω₂+Ω₃]; B5 [Ω₀+Ω₁+Ω₂−Ω₃]; B6 [Ω₀−Ω₁+Ω₂−Ω₃]; B7 [Ω₀+Ω₁−Ω₂−Ω₃]; B8 [Ω₀−Ω₁−Ω₂−Ω₃]; B9 [Ω₀+Ω₁+Ω₂]; B10 [Ω₀−Ω₁+Ω₂]; B11 [Ω₀+Ω₁−Ω₂]; B12 [Ω₀−Ω₁−Ω₂]; B13 [Ω₀+Ω₁]; B14 [Ω₀−Ω₁]; B15 [Ω₀]. In FIG. 21 B, the corresponding strips are centered about the amide proton chemical shift of Ser 65. The variation of the 15 peaks relative to the ¹⁵N chemical shift of Ser 65 (indicated by a dashed horizontal line) matches the variation about the ¹⁵N chemical shift of Glu 64 in FIG. 21A. This allows one to establish the sequential connectivity between Glu 64 and Ser 65 based on the measurement of three chemical shifts, i.e., Ω(¹³C′),Ω(¹³C^α) and Ω(¹H^α). The shifts are obtained with high precision (Table 3) since the errors are reduced by the following factors when compared with FT NMR. For Ω(¹⁵N): √{square root over (15)}=3.9; Ω(¹³C′): √{square root over (14)}=3.7; Ω(¹³C^α): √{square root over (12)}=3.5; Ω(¹H^α): √{square root over (8)}=2.8. ¹H and ¹³C chemical shifts are in ppm relative to 2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).

[0049] FIG. 22 shows the composite plot of [ω₁,ω₃]-strips taken from (5,3)D HACACONHN (strips labeled with ‘a’) and (5,3)D HACA,CONHN data (strips labeled with ‘b’) collected for the 14 kDa NESG consortium target protein TT212 with a total measurement time of 60 hours. The 3D data were acquired with 56(t₁):24(t₂):512(t₃) complex points and t_1max(¹³C′; ¹³C^α, ¹H^α)=6.2 ms, t_2max(¹⁵N)=16.4 ms and t_3max(¹H^N)=73.2 ms. The first, second and third pair of strips in each block has been taken, respectively, at the ¹⁵N chemical shift of Ala 24, Ile 25 and Glu 26 along ω₂(¹⁵N). The strips are centered about the corresponding amide proton shifts detected along ω₃(¹H^N). The ¹⁵N shifts are given at the bottom of each pair of strips, which were taken from basic spectra (B1 to B4), the first order central peak spectra (B5 and B6) and the second order central peak spectra (B7). The type of linear combination of chemical shifts detected along ω₁is indicated at the top of the strips: B1 [Ω₀+Ω₁+Ω₂]; B2 [Ω₀−Ω₁+Ω₂]; B3 [Ω₀+Ω₁−Ω₂]; B4 [Ω₀−Ω₁−Ω₂]; B5 [Ω₀+Ω₁]; B6 [Ω₀−Ω₁]; B7 [Ω₀]. Sequential connectivities are indicated by horizontal lines and are established based on the measurement of three chemical shifts, i.e., Ω(¹³C′), Ω(¹³C^α), and Ω(¹H^α). The chemical shifts were obtained with high precision (Table 4), since the errors are reduced by the following factors when compared with FT NMR. For Ω(¹³C′): √{square root over (7)}=2.6; Ω(¹³C^α): √{square root over (4)}=2.4; Ω(¹H^α): √{square root over (4)}=2. ¹H and ¹³C chemical shifts are in ppm relative to 2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).

[0050] FIG. 23 shows the composite plot of [ω₁,ω₃]-strips taken from (4,3)D CBCACONHN (strips labeled with ‘a’) and (4,3)D CBCA,CONHN data (strips labeled with ‘b’) collected for the 8.6 kDa protein ubiquitin with a total measurement time of 11.2 hours. The 3D data were acquired with 60(t₁):24(t₂):512(t₃) complex points and t_1max(¹³C′; ¹³C^α/β)=5.9 ms, t_2max(¹⁵N)=17.2 ms and t_3max(¹H^N)=73.2 ms. The first, second, and third pair of strips in each block has been taken, respectively, at the ¹⁵N chemical shift of Glu 64, Ser 65, and Thr 66 along ω₂(¹⁵N). The strips are centered about the corresponding amide proton shifts detected along ω₃(¹H^N). The ¹⁵N shifts are given at the bottom of each pair of strips, which were taken from basic spectra (B1 and B2) and the first order central peak spectra (B3). The type of linear combination of chemical shifts detected along ω₁is indicated at the top of the strips: B1 [Ω₀+Ω₁]; B2 [Ω₀−Ω]; B3 [Ω₀]. Sequential connectivities are indicated by horizontal lines and are established based on the measurement of three chemical shifts, i.e., Ω(¹³C′),Ω(¹³C^α) and Ω(¹³C^β). [Since the ¹³C^α/β carrier was set in between the ¹³C^α, and ¹³C^βchemical shift ranges (FIG. 7), one has that peaks at ω₂(¹³C′+¹³C^α) and ω₁(¹³C′+¹³C^β) in B1 appear in a “reversed order” when compared with B2, which exhibits peaks at ω₂(¹³C′−¹³C^α) and ω₃(¹³C′−¹³C^β).] The chemical shifts were obtained with high precision (Table 5) since the errors are reduced by the following factors when compared with FT NMR. For Ω(¹³C′): √{square root over (3)}=1.7; Ω(¹³C^α): √{square root over (2)}=1.4; Ω(¹³C^β): √{square root over (2)}=1.4. ¹H and ¹³C chemical shifts are in ppm relative to 2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).

[0051] FIG. 24 shows a composite plot of [ω₁,ω₃]-strips taken from (5,3)D HACACONHN (strips labeled with ‘a’) and (5,3)D HACA,CONHN data (strips labeled with ‘b’) collected for ubiquitin with a total measurement time of 20.8 hours. The 3D data were acquired with 56(t₁):24(t₂):512(t₃) complex points and t_1max(¹³C′; ¹³C^α, ¹H^α)=6.2 ms, t_2max(¹⁵N)=17.2 ms and t_3max(¹H^N)=73.2 ms. The first, second, and third pair of strips in each block has been taken, respectively, at the ¹⁵N chemical shift of Lys 63, Glu 64, and Ser 65 along ω₂(¹⁵N). The strips are centered about the corresponding amide proton shifts detected along ω₃(¹H^N). The ¹⁵N shifts are given at the bottom of each pair of strips, which were taken from basic spectra (B1 to B4), the first order central peak spectra (B5 and B6) and the second order central peak spectra (B7). The type of linear combination of chemical shifts detected along ω₁is indicated at the top of the strips: B1 [Ω₀+Ω₁+Ω₂]; B2 [Ω₀−Ω₁+Ω₂]; B3 [Ω₀+Ω₁−Ω₂]; B4 [Ω₀−Ω₁−Ω₂]; B5 [Ω₀+Ω₁]; B6 [Ω₀−Ω₁]; B7 [Ω₀]. Sequential connectivities are indicated by horizontal lines and are established based on the measurement of three chemical shifts, i.e., Ω(¹³C′),(¹³C^α) and Ω(¹H^α). The chemical shifts were obtained with high precision (Table 6), since the errors are reduced by the following factors when compared with FT NMR. For Ω(¹³C′):; Ω(¹³C^α):; Ω(¹H^α):. ¹H and ¹³C chemical shifts are in ppm relative to 2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).

[0052] FIG. 25 shows the composite plot of [ω₁(¹³C^α; ¹³C^α/β), ω₃(¹H^N)] strips taken from the basic spectra of (a) (4,3)D HNNCACBCA (B1a, B2a) and (b) (4,3)D HNN(CO)CACBCA (B1b, B2b). The [ω₁(¹³C^α), ω₃(¹H^N)] strips taken from 3D HNNCA (B3a) and 4D HNN(CO)CA (B3b) spectra represent the first order central peaks for (4,3)D HNNCACBCA and (4,3)D HNN(CO)CACBCA, respectively. As an example, strips corresponding to Ω₂(¹⁵N) and Ω₃(¹H^N) chemical shifts for the residue Glu 73 of the 16 kDa protein ER75 are shown. Dashed lines connecting peaks establish sequential connectivities. Peaks labeled 1 to 9 in the figure correspond to the following linear combination of chemical shifts (i≡Glu 73; i−1≡Ala 71):

[0053] 1: Ω₀(¹³C_i−1^α)+Ω₁(¹³C_i−1^α);

[0054] 2: Ω₀(¹³C_i^α)+Ω₁(¹³C_i^α)

[0055] 3: Ω₀(¹³C_i^α)+Ω₁(¹³C_i^α), Ω₀(¹³C_i−1^α)+Ω₁(¹³C_i−1^α)

[0056] 4: Ω₀(¹³C_i^α)−Ω₁(¹³C_i^α)

[0057] 5: Ω₀(¹³C_i−1^α)−Ω₁(¹³C_i−1^α)

[0058] 6: Ω₀(¹³C_i^α)−Ω₁(¹³C_i^β)

[0059] 7: Ω₀(¹³C_i−1^α)−Ω₁(¹³C_i−1^β)

[0060] 8: Ω₀(¹³C_i^α)

[0061] 9: Ω₀(¹³C_i−1^α)

[0062] FIG. 26 shows the composite plot of [ω₁(¹³C^α; ¹³C^α/β), ω₃(¹H^N)] strips taken from the basic spectra of (a) (4,3)D CBCACA(CO)NHN (B1a and B2a) and (b) (4,3)D HNNCACBCA (B1b and B2b) illustrating how sequential resonance assignments along the polypeptide chain are obtained. As an example, the sequential walk for residues Val 27 to Ile 30 of the 7 kDa protein GR2 is shown. For simplicity, only the sequential connectivities inferred from the basic spectra are shown. The observed peak patterns are as described in FIG. 25.

[0063] FIG. 27 shows the composite plot of [ω₁(¹³C^α; ¹³C^α/β, ¹H^α/β), ω₃(¹H^N)] strips taken from the basic and first order central peak spectra of (5,3)D HBHACBCACA(CO)NHN (B1a, B2a, B3a and B4a). Note that [ω₁(¹³C^α; ¹³C^α/β), ω₃(¹H^N)] strips taken from the basic spectra of (4,3)D CBCACA(CO)NHN (B5b and B6b) show the same peak patterns as those observed in the first order central peak spectra of (5,3)D HBHACBCACA(CO)NHN (B5a and B6a). As an example, strips corresponding to ω₂(¹⁵N) and ω₃(¹H^N) chemical shifts for Ile 30 of GR2 are shown. Peaks labeled 1 to 12 in the figure correspond to the following linear combination of chemical shifts for residue Ile 29:

[0064] 1: Ω₀(¹³C^α)+Ω₁(¹³C^α)+Ω₂(¹H^α)

[0065] 2: Ω₀(¹³C^α)+Ω₁(¹³C^β)+Ω₂(¹H^β)

[0066] 3: Ω₀(¹³C^α)+Ω₁(¹³C^α)−Ω₂(¹H^α)

[0067] 4: Ω₀(¹³C^α)+Ω₁(¹³C^β)−Ω₂(¹H^β)

[0068] 5: Ω₀(¹³C^α)−Ω₁(¹³C^β)−Ω₂(¹H^β)

[0069] 6: Ω₀(¹³C^α)−Ω₁(¹³C^α)−Ω₂(¹H^α)

[0070] 7: Ω₀(¹³C^α)−Ω₁(¹³C^β)+Ω₂(¹H^β)

[0071] 8: Ω₀(¹³C^α)−Ω₁(¹³C^α)+Ω₂(¹H^α)

[0072] 9: Ω₀(¹³C^α)−Ω₁(¹³C^β)

[0073] 10: Ω₀(¹³C^α)−Ω₁(¹³C^α)

[0074] 11: Ω₀(¹³C^α)+Ω₁(¹³C^α)

[0075] 12: Ω₀(¹³C^α)+Ω₁(¹³C^β)

[0076] FIG. 28 shows the composite plot of [ω₁(¹³C; ¹³C, ¹H), ω₃(¹H)] strips taken from the basic (B1-B4) and first order central peak (B5 and B6) spectra of (5,3)D HCC,CH-COSY. The [ω₁(¹³C), ω₃(¹H)] strips taken from 3D (H)C,CH—COSY (B7) represents the second order central peak spectra of (5,3)D HCC,CH-COSY. As an example, strips corresponding to ω₂(¹³C^α) and ω₃(¹H^α) chemical shifts for residue Ile 30 of GR2 are shown. Peaks shown in rectangular boxes correspond to cross peaks in a conventional 4D HCCH-COSY. Peaks labeled 1 to 13 correspond to the following linear combination of chemical shifts:

[0077] FIG. 29 shows the composite plot of [ω₁(¹³C^δ; ¹³C^β, ¹H^β), ω₃(¹H^β)] strips taken from the basic (B1-B4) and first order central peak (B5 and B6) spectra of (5,3)D HBCBCGCDHD illustrating how resonance assignments for aromatic side-chain spins are obtained. The [ω₁(¹³C^δ;¹³C^β), ω₃(¹H^δ)] strips taken from 3D [¹³C^{δ, 13}C^γ, H^δ]-COSY represent the second order central peak spectra of (5,3)D HBCBCGCDHD. As an example, strips corresponding to ω₂(¹³C^γ) and ω₃(¹H^δ) chemical shifts for His 68 of Ubiquitin are shown. Peaks labeled 1 to 7 correspond to the following linear combination of chemical shifts:

[0078] 1: Ω₀(¹³C^δ2)−Ω₁(¹³C^β)−Ω₂(¹H^β)

[0079] 2: Ω₀(¹³C^δ2)−Ω₁(¹³C^β)+Ω₂(¹H^β)

[0080] 3: Ω₀(¹³C^δ2)+Ω₁(¹³C^β)+Ω₂(¹H^β)

[0081] 4: Ω₀(¹³C^δ2)+Ω₁(¹³C^β)−Ω₂(¹H^β)

[0082] 5: Ω₀(¹³C^δ2)−Ω₁(¹³C^β)

[0083] 6: Ω₀(¹³C^δ2)+Ω₁(¹³C^β)

[0084] 7: Ω₀(¹³C^δ2)

[0085] FIG. 30 shows the composite plot of [ω₁(¹³C; ¹³C, ¹H), Ω₂(¹H)] strips taken from the basic (B1-B4) and first order central peak (B5 and B6) spectra of (4,2)D HCCH-COSY spectra illustrating how resonance assignments for aromatic side-chain spins are obtained. The [ω₁(¹³C), ω₂(¹H)] strip taken from 2D [¹³C-¹H] HSQC (B7) represents the second order central peak spectra for (4,2)D HCCH-COSY. As an example, strips corresponding to ω₂(H^δ) chemical shift for residue Tyr 59 of the 8.6 kDa protein Ubiquitin are shown. Peaks shown in rectangular boxes correspond to cross peaks in the conventional 4D HCCH-COSY. Peaks labeled 1 to 15 correspond to the following linear combination of chemical shifts:

[0086] The present invention provides an NMR data acquisition scheme which is based on the phase sensitive joint sampling of the indirect dimensions spanning a subspace of a conventional NMR experiment. This allows one to very rapidly obtain high dimensional NMR spectral information. Since the phase-sensitive joint sampling yields subspectra containing “chemical shift multiplets”, alternative data processing is required for editing the components of the multiplets. The subspectra are linearly combined using a so-called “G-matrix” and subsequently Fourier transformed. The chemical shifts are multiply encoded in the resonance lines constituting the shift multiplets. This corresponds to performing statistically independent multiple measurements, and the chemical shifts can thus be obtained with high precision. To indicate that a combined G-matrix and FT is employed, the new approach is named “GFT NMR spectroscopy”.

[0087] In GFT NMR spectroscopy, the chemical shift evolution periods spanning a given multidimensional subspace of an FT NMR experiment are “jointly” sampled (FIG. 1). Thereby, the dimensionality N of an FT NMR spectrum can be adjusted to a given target dimensionality, N_t, by combined sampling of K+1 chemical shifts Ω₀, Ω₁, . . . Ω_Kencoded in K+1 indirect dimensions of the ND FT NMR experiment (K=N−N,). Assuming that Ω₀is detected in quadrature (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety) and that the setting of the phases ø_jof the radiofrequency pulses exciting the spins of dimensions (j=1 . . . K) ensures cosine modulation, the transfer amplitude (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety) of the N_tD experiment is proportional to $e^{i{\Omega }_{0}t}·\prod _{j=1}^K\cos \left({\Omega }_{j}t\right).$

[0088] The resulting peak centered around Ω₀contains 2^Kcomponents and is designated a “chemical shift multiplet” (FIG. 2).

[0089] A shift of ø_jby 90° yields a sin(Ω_jt) instead of a cos(Ω_jt) modulation, (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety), and 2^KN_tD spectra are recorded if all phases Ok are systematically varied between 0° and 90° (FIG. 1). In turn, a linear combination of these 2^Kspectra allows for the editing of the chemical shift multiplet components (FIG. 2). For brevity, c_j=cos(Ω_j·t), s_j=sin(Ω_j·t), and e^iΩt=eⁱare defined, so that $e^{i_j}=c_j+i·s_j=\left[1i\right]·\left[\begin{array}{c}{c}_j\\ s_j\end{array}\right].$

[0090] With K=1, one obtains for the time evolution of the two shift multiplet components encoding sum and difference of Ω₀and Ω₁. $\begin{array}{c}\left[\begin{array}{c}{e}^{j_1}\\ e^{-i_1}\end{array}\right]\otimes e^{j_0}=e^{i_0}=\left[\begin{array}{c}{e}^{i_1}·e^{i_1}\\ e^{-i_1}·e^{i_0}\end{array}\right]\\ =\left[\begin{array}{c}\left[1i\right]\otimes \left[1i\right]\\ \left[1-i\right]\otimes \left[1i\right]\end{array}\right]·\left[\left[\begin{array}{c}{c}_1\\ s_1\end{array}\right]\otimes \left[\begin{array}{c}{c}_0\\ s_0\end{array}\right]\right]\\ =\left[\left[\begin{array}{c}1i\\ 1-i\end{array}\right]\otimes \left[1i\right]\right]·\left[\left[\begin{array}{c}{c}_1\\ s_1\end{array}\right]\otimes \left[\begin{array}{c}{c}_0\\ s_0\end{array}\right]\right]\end{array}$

[0091] Accordingly, one obtains with K=2 for three chemical shifts Ω₀, Ω₁, and Ω₂: $\left[\begin{array}{c}{e}^{i_2}\\ e^{-i_2}\end{array}\right]\otimes \left[\begin{array}{c}{e}^{i_1}\\ e^{-i_1}\end{array}\right]\otimes e^{i_o}=\left[\left[\begin{array}{c}1i\\ 1-i\end{array}\right]\otimes \left[\begin{array}{c}1i\\ 1-i\end{array}\right]\otimes \left[1i\right]\right]·\left[\left[\begin{array}{c}{c}_2\\ s_2\end{array}\right]\otimes \left[\begin{array}{c}{c}_1\\ s_1\end{array}\right]\otimes \left[\begin{array}{c}{c}_0\\ s_0\end{array}\right]\right],$

[0092] and, in general, for K+1 chemical shifts Ω₀, Ω₁, . . . Ω_K: $\left[\begin{array}{c}{e}^{i_K}\\ e^{-i_K}\end{array}\right]\otimes \dots \otimes \left[\begin{array}{c}{e}^{i_1}\\ e^{-i_1}\end{array}\right]\otimes e^{i_o}=\left[\left[\begin{array}{c}1i\\ 1-i\end{array}\right]\otimes \dots \otimes \left[\begin{array}{c}1i\\ 1-i\end{array}\right]\otimes \left[1i\right]\right]·\left[\left[\begin{array}{c}{c}_K\\ s_K\end{array}\right]\otimes \dots \otimes \left[\begin{array}{c}{c}_1\\ s_1\end{array}\right]\otimes \left[\begin{array}{c}{c}_0\\ s_0\end{array}\right]\right]$

[0093] The 2^Kdimensional complex vector on the left side of the equation is proportional to the vector {circumflex over (T)}_c(K) comprising the desired edited spectra with the individual components of the chemical shift multiplets, that is, ${\hat{T}}_c\left(K\right)\sim \left[\begin{array}{c}{e}^{i_K}\\ e^{-i_K}\end{array}\right]\otimes \dots \otimes \left[\begin{array}{c}{e}^{i_1}\\ e^{-i_1}\end{array}\right]\otimes e^{i_o}$

[0094] The 2^K+1dimensional real vector of the 2^K+1trigonometric modulations on the right side of the equation is proportional to the vector containing the spectra with the chemical shift multiplets in the real, Sjr, and imaginary parts, Sji, of the 2^KN_tD spectra (J=1 . . . 2^K). Hence, with Ŝ(K)=[S_1rS_1iS_2rS_2i. . . S₂^K_rS₂^K_i]^T, $\hat{S}\left(K\right)\sim \left[\begin{array}{c}{c}_K\\ s_K\end{array}\right]\otimes \dots \otimes \left[\begin{array}{c}{c}_1\\ s_1\end{array}\right]\otimes \left[\begin{array}{c}{c}_0\\ s_0\end{array}\right]$

[0095] For the 2^K×2^K+1complex G-matrix, which transforms Ŝ(K) into {circumflex over (T)}(K) according to the following equation (1):

[0096] {circumflex over (T)}_c(K)32 Ĝ_c(K)19 Ŝ(K)  (1)

[0097] one then obtains $G_c\left(K\right)=\left[\left[\begin{array}{cc}1& i\\ 1& -i\end{array}\right]\otimes \dots \otimes \left[\begin{array}{cc}1& i\\ 1& -i\end{array}\right]\otimes \left[1i\right]\right]$

[0098] Alternatively, the multiplet components may be edited in the frequency domain (FIG. 2). The spectra of Ŝ(K) are Fourier transformed and a zero-order phase correction of n·90° is applied, depending on the number n of chemical shift sine modulations (see Example 1). The resulting real parts contain purely absorptive chemical shift multiplets and form the 2^Kdimensional real vector Â(K). Their linear combination yields the edited spectra contained in the 2^Kdimensional real vector according to the following equation (2):

[0099] {circumflex over (B)}(K)={circumflex over (F)}(K)·Â(K)  (2)

[0100] Hence, {circumflex over (B)}(K) represents spectra which contain the edited 2^Kindividual multiplet components at Ω₀±Ω₁± . . . Ω_Kencoding the desired K+1 chemical shifts. {circumflex over (F)}(K) can be readily obtained from {circumflex over (F)}(K−1) by tensor product formation using the relation {circumflex over (F)}(K)={circumflex over (F)}=(K−1){circle around (X)}{circumflex over (F)}(1), with $F\left(1\right)=\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]$

[0101] for details and the relation between F and the G-matrix see Example 1).

[0102] The 2^Kspectra of {circumflex over (T)}_c(K) and {circumflex over (B)}(K) are designated “basic spectra”. Additional information is required to unambiguously derive all shift correlations of the parent ND experiment (which resolves degeneracy in up to N−1 dimensions) if two multiplets exhibit degenerate chemical shifts in all of the “conventionally” sampled N_t−1 dimensions. The acquisition of peaks defining the centers of the chemical shift splittings (“central peaks”) at the frequencies Ω₀+Ω₁± . . . ±Ω_K−1, Ω₀±Ω₁± . . . Ω_K−2, . . . , Ω₀±Ω₁, and Ω₀is then needed for identifying the components forming a given multiplet (FIG. 3A). Such “central peak acquisition” has been introduced in the framework of the reduced-dimensionality NMR approach (Szyperski et al., Proc. Natl. Acad. Sci. USA, 99:8009-8014 (2002); Szyperski et al. J. Biomol. NMR. 3:127-132 (1993); Szyperski et al., J. Am. Chem. Soc. 115:9307-9308 (1993); Szyperski et al., J. Magn. Reson. B 105:188-191 (1994); Brutscher et al., J. Magn. Reson. B 105:77-82 (1994); Szyperski et al., J. Magn. Reson. B 108:197-203 (1995); Brutscher et al., J. Magn. Reson. B 109:238-242 (1995); Szyperski et al., J. Am. Chem. Soc. 118:8146-8147 (1996); Bracken et al., J. Biomol. NMR9:94-100 (1997); Szyperski et al., J. Biomol NMR, 11:387-405 (1998); Astrof et al., J. Magn. Reson. 152:303-307 (2001); Xia et al., J. Biomol. NMR24:41-40 (2002), which are hereby incorporated by reference in their entirety). The shift correlations of the ND spectrum can be obtained by “bottom-up” identification of the shift multiplets. This procedure essentially groups the peaks of the basic spectra into sets each belonging to one multiplet (FIG. 3). Because the basic peaks of two spin systems can be grouped even if central peaks overlap (FIG. 3B), this approach ensures that all correlations of the ND experiment are retained. GFT NMR (FIG. 1) thus requires one to record a total of $p=\sum _{k=0}^K{2}^k=2^{K+1}-1$

[0103] N_tD spectra, including 2^Kbasic spectra and 2^K−1 central peak spectra. The p data sets constitute an “(N,N_t)D GFT NMR experiment”, and central peaks arising from omission of m chemical shifts are denoted to be of m-th order. For practical purposes, it is important to note that all components of a given multiplet have quite similar intensities since they are generated by multiple sine or cosine modulation of the transfer amplitude. Usually this does not hold for two peaks belonging to two different spin systems (FIG. 3A), because the nuclear spin relaxation times determining the peak intensities vary from spin system to spin system. Hence, inspection of peak intensities greatly facilitates the grouping of the peaks.

[0104] The joint sampling of several indirect dimensions reduces the minimal measurement time, T_m, of an (N,N_t)D GFT NMR experiment when compared with the parent ND FT experiment. The K+1 dimensions of an FT NMR spectrum exhibiting the spectral widths SW₀, SW₁, . . . , SW_Kare sampled with n₀, n₁, . . . n_Kcomplex points and yield maximal evolution times of t_0,max, t_1,max, . . . t_K,max. In the (N,N_t)D GFT NMR experiment, the same maximal evolution times of the parent ND experiment can be realized by appropriate scaling of increments. (Szyperski et al. J. Biomol. NMR. 3:127-132 (1993); Szyperski et al., J. Magn. Reson. B 105:188-191 (1994), which are hereby incorporated by reference in their entirety). The acquisition of both cosine and sine modulated spectra for all jointly sampled chemical shifts (equation 1) corresponds to their phase-sensitive acquisition (Brutscher et al., J. Magn. Reson. B 109:238-242 (1995), which is hereby incorporated by reference in its entirety) and allows one to place the rf carrier positions in the center of the spectral ranges. Hence, the spectral width required for combined sampling is given by $\mathrm{SW}=\sum _{j=0}^K{\kappa }_j·{\mathrm{SW}}_j,$

[0105] where κ_jrepresents the factor to scale (Szyperski et al. J. Am. Chem. Soc. 115:9307-9308 (1993); Szyperski et al., J. Magn. Reson. B 105:188-191 (1994), which are hereby incorporated by reference in their entirety) the sampling increments of the jth dimension to adjust maximal evolution times. If the same maximal evolution time is chosen for all dimensions and assuming, for simplicity, that delayed acquisition starts $\mathrm{at}1/{\mathrm{SW}}_j,n=\sum _{j=0}^K{n}_j$

[0106] complex points are required to sample the resulting single dimension [if acquisition starts at t=0, one obtains that $n=\left(\sum _{j=0}^K{n}_j\right)-K].$

[0107] The ratio ε of the minimal measurement time of an FT NMR experiment, T_m(FT), and the corresponding GFT NMR experiment, T_m(GFT), is then given by the number of FIDs that are required to sample the K+1 FT NMR dimensions divided by p times the number of FIDs required to sample the resulting single dimension: $\begin{array}{cc}ϵ=\frac{T_m\left(\mathrm{FT}\right)}{T_m\left(\mathrm{GFT}\right)}=\left(2^K/\left(2^{K+1}-1\right)\right)·\left(\prod _{j=0}^K{n}_j\right)/\left(\sum _{j=0}^K{n}_j\right)& \left(3\right)\end{array}$

[0108] This ratio scales with the product of the number of points over the corresponding sum and, thus, predicts large reductions in T_m(see Table 1 in Example 3; different ways to implement central peak acquisition as well as the impact of a particular implementation on ε are described in Examples 2 and 3). (The GFT NMR scheme can be generalized by its M-fold application. Since this would involve M different G-matrices, such an experiment could be designated a G^MFT NMR experiment. For example, two groups of dimensions can be identified with each group being combined to a single dimension. First an (N,N′)D experiment is devised in which dimensions 1,2 . . . i are jointly sampled. Subsequently, the dimensionality of this experiment is to reduced to an (N,N_t) experiment by jointly sampling dimensions i+1, i+2, . . . K+2. For M projection steps, each invoking different sets of dimensions combined to a single one, the total reduction in minimal measurement time is then given by ${ϵ}^{\mathrm{tot}}=\prod _{j=1}^M{ϵ}_j,$

[0109] where ε_jis the reduction due to the j-th projection (equation 3)). The S/N of each of the 2^Kcomponents in the basic spectra is reduced by (1/√{square root over (2)})^Kcompared to the single peak in FT NMR. This is because each chemical shift splitting reduces the S/N by a factor of 2 relative to the FT NMR spectrum, while a factor of √{square root over (2)} is gained, because frequency discrimination is not associated with a FT (see FIG. 2: both cosine and sine modulated parts contribute equally to the signal intensity in the edited spectra) (The S/N ratio of FT NMR can be recovered by symmetrization about central peaks as described for reduced-dimensionality NMR (Szyperski et al., J. Magn. Reson. B 108:197-203 (1995), which is hereby incorporated by reference in its entirety) using the “bottom up” strategy employed for identification of shift multiplets (FIG. 3). Note that a reduced sensitivity is not relevant in the sampling limited regime.)

[0110] GFT NMR spectroscopy combines (i) multiple phase sensitive RD NMR, (ii) multiple ‘bottom-up’ central peak detection, and (iii) (time domain) editing of the components of the chemical shift multiplets. The resulting formalism embodies a flexible, generally applicable NMR data acquisition scheme. Provided that m=K+1 chemical shift evolution periods of an ND experiments are jointly sampled in a single indirect “GFT dimension”, p=2^m−1 different (N−K)D spectra represent the GFT NMR experiment containing the information of the parent ND experiment. Hence, such a set of p spectra is named an (N,N−K)D GFT NMR experiment.

[0111] Thus, the present invention relates to a method of conducting a (N,N−K) dimensional (D) G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiment, where N is the dimensionality of an N-dimensional (ND) Fourier transformation (FT) NMR experiment and K is the desired reduction in dimensionality relative to N. The method involves providing a sample and applying radiofrequency pulses for the ND FT NMR experiment to the sample. Then, m indirect chemical shift evolution periods of the ND FT NMR experiment are selected, where m equals K+1, and the m indirect chemical shift evolution periods are jointly sampled. Next, NMR signals detected in a direct dimension are independently cosine and sine modulated to generate (N−K)D basic NMR spectra containing frequency domain signals with 2^Kchemical shift multiplet components, thereby enabling phase-sensitive sampling of all jointly sampled m indirect chemical shift evolution periods. Finally, the (N−K) D basic NMR spectra are transformed into (N−K) D phase-sensitively edited basic NMR spectra, where the 2^Kchemical shift multiplet components of the (N−K) D basic NMR spectra are edited to yield (N−K) D phase-sensitively edited basic NMR spectra having individual chemical shift multiplet components.

[0112] As described earlier, the (N−K) D basic NMR spectra can be transformed into (N−K) D phase-sensitively edited basic NMR spectra by applying a G-matrix defined as $\hat{G}\left(K\right)=\left[\left[\begin{array}{cc}1& i\\ 1& -i\end{array}\right]\otimes \dots \otimes \left[\begin{array}{cc}1& i\\ 1& -i\end{array}\right]\otimes \left[1i\right]\right],$

[0113] where i=√{square root over (−1)}, under conditions effective to edit the chemical shift multiplet components in the time domain. Alternatively, the transforming can be carried out by applying a F-matrix defined as {circumflex over (F)}(K)={circumflex over (F)}(K−1){circle around (X)}{circumflex over (F)}(1), where $\hat{F}\left(1\right)=\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right],$

[0114] under conditions effective to edit the chemical shift multiplet components in the frequency domain.

[0115] In an alternate embodiment, the method of conducting a (N,N−K)D GFT NMR experiment can further involve selecting m′ indirect chemical shift evolution periods of the (N−K)D FT NMR experiment, where m′ equals K′+1. Then, the m′ indirect chemical shift evolution periods are jointly sampled. Next, NMR signals detected in a direct dimension are independently cosine and sine modulated to generate (N−K−K′)D basic NMR spectra containing frequency domain signals with 2^K′ chemical shift multiplet components, thereby enabling phase-sensitive sampling of all jointly sampled m′ indirect chemical shift evolution periods. Finally, the (N−K−K′) D basic NMR spectra are transformed into (N−K−K′) D phase-sensitively edited basic NMR spectra, wherein the 2^K′ chemical shift multiplet components of the (N−K−K′) D basic NMR spectra are edited to yield (N−K−K′) D phase-sensitively edited basic NMR spectra having individual chemical shift multiplet components. The above-mentioned steps of selecting, jointly sampling, independently cosine and sine modulating, and transforming can be repeated one or more times, where m′ is modified for each repetition.

[0116] In an alternate embodiment, the method of conducting a (N,N−K)D GFT NMR experiment can further involve repeating one or more times the steps of selecting, jointly sampling, independently cosine and sine modulating, and transforming, where, for each repetition, the selecting involves selecting m-j indirect chemical shift evolution periods out of the m indirect chemical shift evolution periods, wherein j ranges from 1 to K, under conditions effective to generate 2^K-jjth order central peak NMR spectra.

[0117] The method of conducting a (N,N−K)D GFT NMR experiment can also involve applying radiofrequency pulses of N-dimensional nuclear Overhauser enhancement spectroscopy (NOESY) (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety). Alternatively, the method can involve applying radiofrequency pulses of N-dimensional transverse relaxation optimized spectroscopy (TROSY) (Pervushin et al., Proc. Natl. Acad. Sci. USA, 94:12366-12371 (1997), which is hereby incorporated by reference in its entirety). In addition, the method can involve applying radiofrequency pulses so that spin-spin couplings are measured (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety). The spin-spin couplings can be residual dipolar spin-spin coupling constants (Bax, Protein Sci., 12:1-16 (2003), which is hereby incorporated by reference in its entirety). The method can also involve applying radiofrequency pulses so that nuclear spin relaxation times are measured by sampling nuclear spin relaxation delays (Palmer, Annu. Rev. Biophys. Biomol. Struct., 30:129-155 (2001), which is hereby incorporated by reference in its entirety). The spin relaxation delays can be further jointly sampled with chemical shift evolution periods (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety). In another embodiment, the jointly sampling the m indirect chemical shift evolution periods is achieved with a single continuous acquisition (Frydman et al., Proc. Natl. Acad. Sci., U.S.A., 99:15858-15862 (2002), which is hereby incorporated by reference in its entirety).

[0118] The present invention also discloses specific GFT NMR experiments and different combinations of those experiments which allows one to obtain sequential backbone chemical shift assignments for determining the secondary structure of a protein molecule and complete assignments of chemical shift values for a protein molecule including aliphatic and aromatic sidechain spin systems.

[0119] Specific GFT NMR Experiments

[0120] The present invention discloses the following six (N,N−K)D GFT NMR experiments for the assignment of polypeptide backbone and ¹³C^β resonance: (i) with K=3, (5,2)D [HACACONHN] GFT NMR experiment and (5,2)D [HACA,CONHN] GFT NMR experiment for sequential assignment, (ii) with K=2, (5,3)D [HACA,CONHN GFT NMR experiment and (5,3)D [HACACONHN] GFT NMR experiment, where, in contrast to the (5,2)D experiments in (i), the ¹⁵N chemical shifts evolve separately, and (iii) with K=1, (4,3)D [CBCACONHN] GFT NMR experiment and (4,3)D [CBCA,CONHN] GFT NMR. The underlined letters indicate which chemical shifts that are jointly sampled. After G-matrix transformation, one obtains 2³⁺¹−1=15 2D planes for the (5,2)D experiments (K=3), seven 3D spectra for the (5,3)D experiments (K=2) and three 3D spectra for the (4,3)D experiments (K=1). FIG. 4 illustrates the magnetization transfer pathways of the specific embodiments of these six GFT NMR experiments. (5,2)D [HACA,CONHN]/(5,2)D [HACACONHN] GFT NMR experiments and (5,3)D [HACA,CONH]/(5,3)D [HACACONHN] GFT NMR experiments correlate the backbone amide ¹⁵N and ¹HN chemical shifts of residue i with the ¹³C′, ¹³C^α and ¹H^α chemical shifts of residue i−1 and i, respectively, via one-bond scalar couplings (FIGS. 4A-B). In addition, the often smaller two-bond scalar couplings between the ¹⁵N_iand ¹³C^α_i−1may yield sequential connectivities in the HACA,CONHN experiments. The comma separating “CA” from “CO” indicates that the intraresidue ¹³C′ chemical shift is obtained by creating two-spin coherence involving ¹³C′ and ¹³C′ during the intraresidue polarization transfer from ¹³C^α to ¹⁵N (Löhr et al., J. Biomol. NMR6:189-197 (1995), which is hereby incorporated by reference in its reference). (4,3)D [CBCACONHN] and (4,3)D [CBCA,CONHN] GFT NMR experiments correlate the backbone amide ¹⁵N and ¹HN chemical shifts of residue i with the ¹³C′, ¹³C^α and ¹³C^β chemical shifts of residue i−1 and i, respectively, via one-bond scalar couplings (FIG. 4C), and the often smaller two-bond scalar couplings between the ¹⁵N_iand ¹³C^α_i−1may yield additional sequential connectivities in (4,3)D [CBCA,CONHN].

[0121] Thus, the present invention relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 and K equals 3 to conduct a (5,2)D [HACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) an α-proton of amino acid residue i−1, ¹H^α_i−1; (2) an α-carbon of amino acid residue i−1, ¹³C^α_i−1; (3) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1; (4) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (5) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_I, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, ¹H^α_i−1, ¹³C^α_i−1, ¹³C′_i−1, and ¹⁵N_i, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H^α_i−1, ¹³C^α_i−1, ¹³C′_i−1, ¹⁵N_i). One specific embodiment of this method ((5,2)D HACACONHN) involves applying radiofrequency pulses for a 5D FT NMR experiment according to the scheme shown in FIG. 6.

[0122] The present invention also relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 and K equals 3 to conduct a (5,2)D [HACA,CONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having an amino acid residue, i, and the chemical shift values for the following nuclei are measured: (1) an α-proton of amino acid residue i−1, ¹H^α_i−1; (2) an α-carbon of amino acid residue i−1, ¹³C^α_i−1; (3) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1; (4) a polypeptide backbone amide nitrogen of amino acid residue i−1, ¹⁵N_i−1; and (5) a polypeptide backbone amide proton of amino acid residue i−1, ¹H^N_i−1, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, ¹H^α_i−1, ¹³C^α_i−1, ¹³C′_i−1, and ¹⁵N_i−1, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H^α_i−1, ¹³C^α_i−1, ¹³C′_i−1, ¹⁵N_i−1). One specific embodiment of this method ((5,2)D HACA,CONHN) involves applying radiofrequency pulses for a 5D FT NMR experiment according to the scheme shown in FIG. 7A.

[0123] Another aspect of the present invention relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 and K equals 2 to conduct a (5,3)D [HACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) an α-proton of amino acid residue i−1, ¹H^α_i−1; (2) an α-carbon of amino acid residue i−1, ¹³C^α_i−1; (3) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1; (4) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (5) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H^α_i−1, ¹³C^α_i−1, ¹³C′_i−1).

[0124] Yet another aspect of the present invention relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 and K equals 2 to conduct a (5,3)D [HACA,CONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having an amino acid residue, i−1, and the chemical shift values for the following nuclei are measured: (1) an α-proton of amino acid residue i−1, ¹H^α_i−1; (2) an α-carbon of amino acid residue i−1, ¹³C^α_i−1; (3) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1; (4) a polypeptide backbone amide nitrogen of amino acid residue i−1, ¹⁵N_i−1; and (5) a polypeptide backbone amide proton of amino acid residue i−1, ¹H^N_i, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H^α_i−1,¹³C^α_i−1, ¹³C′_i−1).

[0125] A further aspect of the present invention relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 4 and K equals 1 to conduct a (4,3)D [CBCACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (2) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1; (3) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (4) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 2 chemical shift evolution periods of the 4D FT NMR experiment, ¹³C^α/β_i−1and ¹³C′_i−11and (c) the jointly sampling involves jointly sampling the 2 chemical shift evolution periods in an indirect time domain dimension, t₁(¹³C^α/β_i−1, ¹³C′_i−1). One specific embodiment of this method ((4,3)D CBCACONHN) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 8.

[0126] The present invention also relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 4 and K equals 1 to conduct a (4,3)D [CBCA,CONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having an amino acid residue, i−1, and the chemical shift values for the following nuclei are measured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (2) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1; (3) a polypeptide backbone amide nitrogen of amino acid residue i−1, ¹⁵N_i−1; and (4) a polypeptide backbone amide proton of amino acid residue i−1, ¹H^N_i−1, (b) the selecting involves selecting 2 chemical shift evolution periods of the 4D FT NMR experiment, ¹³C^α/β_i−1and ¹³C′_i−1, and (c) the jointly sampling involves jointly sampling the 2 chemical shift evolution periods in an indirect time domain dimension, t₁(¹³C^α/β_i−1, ¹³C′_i−1). One specific embodiment of this method ((4,3)D CBCA,CONHN) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 7B.

[0127] In addition, the present invention discloses the following GFT NMR experiments for the assignment of polypeptide backbone and sidechain resonances: (i) (4,3)D [HNNCACBCA] GFT NMR experiment, (ii) (4,3)D [CBCACA(CO)NHN]/(4,3)D [HNN(CO)CACBCA] GFT NMR experiments, (iii) (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment, (iv) (5,3)D [HCC,CH-COSY] GFT NMR experiment, (v) (5,3)D [HBCBCGCDHD] GFT NMR experiment, (vi) (4,2)D [HCCH-COSY] GFT NMR experiment, and (vii) (5,2)D [HCCCH-COSY] GFT NMR experiment. Experiment (i) and (ii)/(iii) form pairs to sequentially assign backbone ¹³C^α and ¹³C^β resonances. Experiment (iii) also provides ¹H^α/β chemical shifts. The ¹³C^α/β and ¹H^α/β chemical shifts, in turn, allow one to assign more peripheral spins of the aliphatic side-chain of a given amino acid residue using experiment (iv). Experiments (v) and (vi) can be used for resonance assignments of aromatic side-chain spins. The assignment of the side-chain chemical shifts can be further supported with experiment (vii). The magnetization transfer pathways of specific embodiments of these GFT NMR experiments (i)-(vii) are depicted in FIGS. 5A-G, respectively.

[0128] Thus, the present invention also relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 4 and K equals 1 to conduct a (4,3)D [HNNCACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) α- and β-carbons of amino acid residues i and i−1, ¹³C^α/β_i/i−1; (2) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (3) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 2 chemical shift evolution periods of the 4D FT NMR experiment, ¹³C^α/β_i/i−1and ¹³C^α_i/i−1, and (c) the jointly sampling involves jointly sampling the 2 chemical shift evolution periods in an indirect time domain dimension, t₁(¹³C^α/β_i/i−1, ¹³C^α_i/i−1). One specific embodiment of this method ((4,3)D HNNCACBCA) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 9.

[0129] In an alternate embodiment, the above method can be modified, where N equals 4 and K equals 2, to conduct a (4,2)D [HNNCACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) α- and β-carbons of amino acid residues i and i−1, ¹³C^α/β_i/i−1; (2) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (3) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 3 chemical shift evolution periods of the 4D FT NMR experiment, ¹³C^α/β_i/i−1, ¹³C^α_i/i−1, and ¹⁵N_i, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹³C^α/β_i/i−1, ¹³C^α_i/i−1, ¹⁵N_i).

[0130] In another alternate embodiment, the above method can be modified, where N equals 4 and K equals 1 to conduct a (4,3)D [HNN(CO)CACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (2) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (3) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 2 chemical shift evolution periods of the 4D FT NMR experiment, ¹³C^α/β_i−1and ¹³C^α_i−1, and (c) the jointly sampling involves jointly sampling the 2 chemical shift evolution periods in an indirect time domain dimension, t₁(¹³C^α/β_i−1, ¹³C^α_i−1). One specific embodiment of this method ((4,3)D HNN(CO)CACBCA) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 10.

[0131] In yet another alternate embodiment, the above method can be modified, where N equals 4 and K equals 2 to conduct a (4,2)D [HNN(CO)CACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (2) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (3) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 3 chemical shift evolution periods of the 4D FT NMR experiment, ¹³C^α/β_i−1, ¹³C^α_i−1, and ¹⁵N_i; and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹³C^α/β_i−1, ¹³C^α_i−1, ¹⁵N_i).

[0132] In another alternate embodiment, the above method can be modified, where N equals 5 and K equals 2 to conduct a (5,3)D [HNNCOCACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) (α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (2) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1, (3) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (4) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, ¹³C^α/β_i−1, ¹³C^α_i−1, and ¹³C′_i−1, (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹³C^α/β_i−1, ¹³C^α_i−1, ¹³C′_i−1).

[0133] In yet another alternate embodiment, the above method can be modified, where N equals 5 and K equals 3 to conduct a (5,2)D [HNNCOCACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (2) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1, (3) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (4) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, ¹³C^α/β_i−1, ¹³C^α_i−1, ¹³C′_i−1, and ¹⁵N_i; and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension,

[0134] Another aspect of the present invention relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 4 and K equals 1 to conduct a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (2) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (3) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 2 chemical shift evolution periods of the 4D FT NMR experiment, ¹³C^α/β_i−1and ¹³C^α_i−1, and (c) the jointly sampling involves jointly sampling the 2 chemical shift evolution periods in an indirect time domain dimension, t₁(¹³C^α/β_i−1, ¹³C^α_i−1). One specific embodiment of this method ((4,3)D CBCACA(CO)NHN) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 11.

[0135] In an alternate embodiment, the above method can be modified, where N equals 4 and K equals 2 to conduct a (4,2)D [CBCACA(CO)NHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) (α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (2) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (3) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 3 chemical shift evolution periods of the 4D FT NMR experiment, ¹³C^α/β_i−1, ¹³C^α_i−1, and ¹⁵N_i, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹³C^α/β_i−1, ¹³C^α_i−1, ¹⁵N_i).

[0136] In another alternate embodiment, the above method can be modified, where N equals 5 and K equals 2 to conduct a (5,3)D [CBCACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) (α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (2) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1, (3) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (4) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, ¹³C^α/β_i−1, ¹³C^α_i−1, and ¹³C′_i−1, (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹³C^α/β_i−1, ¹³C^α_i−1, ¹³C′_i−1).

[0137] In yet another alternate embodiment, the above method can be modified, where N equals 5 and K equals 3 to conduct a (5,2)D [CBCACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, i−1 and i, and the chemical shift values for the following nuclei are measured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (2) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1, (3) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (4) a polypeptide backbone amide proton of amino acid residue i, 1 H^N_i, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, ¹³C^α/β_i−1, ¹³C^α_i−1, ¹³C′_i−1and ¹⁵N_i; (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t₁(¹³C^α/β_i−1, ¹³C^α_i−1, ¹³C′_i−1, ¹⁵N_i).

[0138] Another aspect of the present invention relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 and K equals 2 to conduct a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two amino acid residues, i and i−1, and the chemical shift values for the following nuclei are measured: (1) α- and β-protons of amino acid residue i−1, ¹H^α/β_i−1; (2) α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (3) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (4) a polypeptide backbone amide proton of amino acid residue i, H^N_i, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, ¹H^α/β_i−1, ¹³C^α/β_i−1, and ¹³C^α_i−1, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H^α/β_i−1, ¹³C^α/β_i−1, ¹³C^α_i−1). One specific embodiment of this method ((5,3)D HBHACBCACA(CO)NHN) involves applying radiofrequency pulses for a 5D FT NMR experiment according to the scheme shown in FIG. 12.

[0139] In an alternate embodiment, the above method can be modified, where N equals 6 and K equals 3 to conduct a (6,3)D [HBHACBCACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two amino acid residues, i and i−1, and the chemical shift values for the following nuclei are measured: (1) α- and β protons of amino acid residue i−1, ¹H^α/β_i−1; (2) α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (3) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1; (4) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (5) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 4 chemical shift evolution periods of the 6D FT NMR experiment, ¹H^α/β_i−1, ¹³C^α/β_i−1, ¹³C^α_{i−l, and}¹³C′_i−1, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H^α/β_i−1, ¹³C^α/β_i−1, ¹³C^α_i−1, ¹³C′_i−1).

[0140] In another alternate embodiment, the above method can be modified, where N equals 5 and K equals 3 to conduct a (5,2)D [HBHACBCACA(CO)NHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two amino acid residues, i and i−1, and the chemical shift values for the following nuclei are measured: (1) α- and β protons of amino acid residue i−1, ¹H^α/β_i−1; (2) α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (3) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (4) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, ¹H^α/β_i−1, ¹³C^α/β_i−1, ¹³C^α_i−1, and ¹⁵N_i, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H^α/β_i−1, ¹³C^α/β_i−1, ¹³C^α_i−1, ¹⁵N_i).

[0141] In yet another alternate embodiment, the above method can be modified, where N equals 6 and K equals 4 to conduct a (6,2)D [HBHACBCACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two amino acid residues, i and i−1, and the chemical shift values for the following nuclei are measured: (1) α- and β protons of amino acid residue i−1, ¹H^α/β_i−1; (2) α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1; (3) a polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1; (4) a polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i; and (5) a polypeptide backbone amide proton of amino acid residue i, ¹H^N_i, (b) the selecting involves selecting 5 chemical shift evolution periods of the 6D FT NMR experiment, ¹H^α/β_i−1, ¹³C^α/β_i−1, ¹³C^α_i−1, ¹³C′_i−1, and ¹⁵N_i, and (c) the jointly sampling involves jointly sampling the 5 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H^α/β_i−1, ¹³C^α/β_i−1, ¹³C^α_i−1, ¹³C′_i−1, ¹⁵N_i).

[0142] Yet another aspect of the present invention relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 and K equals 2 to conduct a (5,3)D [HCC,CH-COSY] GFT NMR experiment. In this method, (a) the chemical shift values for the following nuclei are measured: (1) a proton, ¹H; (2) a carbon coupled to ¹H, ¹³C; and (3) a carbon coupled to ¹³C, ¹³C^coupled; and (4) a proton coupled to ¹³C^coupled, ¹H^coupled, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, ¹H, ¹³C, and ¹³C^coupled, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H, ¹³C, ¹³C^coupled). The sample in this method can be any molecule such as (metallo)-organic molecules and complexes, nucleic acid molecules such as DNA and RNA, lipids, or polymers. In one embodiment, the chemical shift evolution periods for ¹³C and ¹³C^coupledcan be correlated using total correlation spectroscopy (TOCSY) (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety). In another embodiment, (a) the sample is a protein molecule having an amino acid residue, i, and the chemical shift values for the following nuclei are measured: (1) a proton of amino acid residue i, ¹H_i; (2) a carbon of amino acid residue i coupled to ¹H_i, ¹³C_i; and (3) a carbon coupled to ¹³C_i, ¹³C_i^coupled; and (4) a proton coupled with ¹³C_i^coupled, ¹H_i^coupled, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, ¹H_i, ¹³C_i, and ¹³C_i^coupled, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H_i, ¹³C_i, ¹³C_i^coupled). One specific embodiment of this method ((5,3)D HCC,CH-COSY) involves applying radiofrequency pulses for a 5D FT NMR experiment according to the scheme shown in FIG. 13.

[0143] The present invention also relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 and K equals 2 to conduct a (5,3)D [HBCBCGCDHD] GFT NMR experiment. In this method, (a) the sample is a protein molecule having an amino acid residue, i, with an aromatic side chain, and the chemical shift values for the following nuclei are measured: (1) a β-proton of amino acid residue i, ¹H^β_i; (2) a β-carbon of amino acid residue i, ¹³C^β_i; (3) a γ-carbon of amino acid residue i, ¹³C^γ_i; (4) a δ-carbon of amino acid residue i, ¹³C^δ_i; and (5) a δ-proton of amino acid residue i, ¹H^δ_i, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, ¹H^β_i, ¹³C^β_i, and ¹³C^δ_i, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H^β_i, ¹³C^β_i, ¹³C^δ_i). One specific embodiment of this method ((5,3)D HBCBCGCDHD) involves applying radiofrequency pulses for a 5D FT NMR experiment according to the scheme shown in FIG. 14.

[0144] In an alternate embodiment, the above method can be modified, where N equals 5 and K equals 3 to conduct a (5,2)D [HBCBCGCDHD] GFT NMR experiment. In this method, (a) the sample is a protein molecule having an amino acid residue, i, with an aromatic side chain, and the chemical shift values for the following nuclei are measured: (1) a β-proton of amino acid residue i, ¹H^β_i; (2) a β-carbon of amino acid residue i, ¹³C^β_i; (3) a γ-carbon of amino acid residue i; (4) a δ-carbon of amino acid residue i, ¹³C^δ_i; and (5) a δ-proton of amino acid residue i, ¹H^δ_i, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, ¹H^β_i, ¹³C^β_i, ¹³C^γ_i, and ¹³C^δ_i, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H^β_i, ¹³C^β_i, ¹³C^γ_i, ¹³C^δ_i).

[0145] Another aspect of the present invention relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 4 and K equals 2 to conduct a (4,2)D [HCCH-COSY] GFT NMR experiment. In this method, (a) the chemical shift values for the following nuclei are measured: (1) a proton, ¹H; (2) a carbon coupled to ¹H, ¹³C; (3) a carbon coupled to ¹³C, ¹³C^coupled; and (4) a proton coupled to ¹³C^coupled, ¹H^coupled, (b) the selecting involves selecting 3 chemical shift evolution periods of the 4D FT NMR experiment, ¹H, ¹³C, and ¹³C^coupled, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H, ¹³C, ¹³C^coupled). The sample in this method can be any molecule such as (metallo)-organic molecules and complexes, nucleic acid molecules such as DNA and RNA, lipids, or polymers. In one embodiment, the chemical shift evolution periods for ¹³C and ¹³C^coupledare correlated using total correlation spectroscopy (TOCSY). In another embodiment, (a) the sample is a protein molecule having an amino acid residue, i, and the chemical shift values for the following nuclei are measured: (1) a proton of amino acid residue i, ¹H_i; (2) a carbon of amino acid residue i coupled to ¹H_i, ¹³C_i; (3) a carbon coupled to ¹³C_i, ¹³C_i^coupled; and (4) a proton coupled to ¹³C_i^coupled, ¹H_i^coupled, (b) the selecting involves selecting 3 chemical shift evolution periods of the 4D FT NMR experiment, ¹H_i, ¹³C_i, and ¹³C_i^coupled, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H_i, ¹³C_i, ¹³C_i^coupled). One specific embodiment of this method ((4,2)D HCCH-COSY) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 15.

[0146] Yet another aspect of the present invention relates to the above method of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 and K equals 3 to conduct a (5,2)D [HCCCH-COSY] GFT NMR experiment. In this method, (a) the chemical shift values for the following nuclei are measured: (1) a proton ¹H; (2) a carbon coupled to ¹H, ¹³C; (3) a carbon coupled to ¹³C, ¹³C^coupled; (4) a carbon coupled to ¹³C^coupled, ¹³C^coupled-2; and (5) a proton coupled with ¹³C^coupled-2, ¹H^coupled-2, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, H, ¹³C, ¹³C^coupled, and ¹³C^coupled-2and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H, ¹³C, ¹³C^coupled, ¹³C^coupled-2). The sample in this method can be any molecule such as (metallo)-organic molecules and complexes, nucleic acid molecules such as DNA and RNA, lipids, or polymers. In one embodiment, (a) the sample is a protein molecule having an amino acid residue, i, and the chemical shift values for the following nuclei are measured: (1) a proton of amino acid residue i, ¹H_i; (2) a carbon of amino acid residue i coupled to ¹H_i, ¹³C_i; (3) a carbon coupled to ¹³C_i, ¹³C_i^coupled; (4) a carbon coupled to ¹³C_i^coupled, ¹³C_i^coupled2; and (5) a proton coupled with ¹³C_i^coupled-2, ¹H_i^coupled-2, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, ¹H_i, ¹³C_i, ¹³C_i^coupledand ¹³C_i^coupled-2, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H_i, ^—C_i, ¹³C_i^coupled, ¹³C_i^coupled-2).

[0147] In an alternate embodiment, the above method can be modified, where N equals 5 and K equals 3 to conduct a (5,3)D [HCCCH-COSY] GFT NMR experiment. In this method, (a) the chemical shift values for the following nuclei are measured: (1) a proton, ¹H; (2) a carbon coupled to ¹H, ¹³C; (3) a carbon coupled to ¹³C, ¹³C^coupled; (4) a carbon coupled to ¹³C^coupled, ¹³C^coupled-2; and (5)a proton coupled with ¹³C^coupled-2, ¹H^coupled-2, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, ¹H, ¹³C, and ¹³C^coupled, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H, ¹³C, ¹³C^coupled). The sample in this method can be any molecule such as (metallo)-organic molecules and complexes, nucleic acid molecules such as DNA and RNA, lipids, or polymers. In another embodiment, (a) the sample is a protein molecule having an amino acid residue, i, and the chemical shift values for the following nuclei are measured: (1) a proton of amino acid residue i, ¹H_i; (2) a carbon of amino acid residue i coupled to ¹H_i, ¹³C_i; (3) a carbon coupled to ¹³C_i, ¹³C_i^coupled; (4) a carbon coupled to ¹³C_i^coupled, ¹³C_i^coupled-2; and (5) a proton coupled with ¹³C_i^coupled-2, ¹H_i^coupled-2, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, ¹H_i, ¹³C_i, and ¹³C_i^coupled(c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t₁(¹H_i, ¹³C_i^coupled).

[0148] Combinations of GFT NMR Experiments

[0149] A set of multidimensional GFT NMR experiments enables one to devise strategies for GFT NMR-based (high throughput) resonance assignment of proteins or other molecules.

[0150] Thus, another aspect of the present invention relates to a method for sequentially assigning chemical shift values of an α-proton, ¹H^α an α-carbon, ¹³C^α, a polypeptide backbone carbonyl carbon, ¹³C′, a polypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backbone amide proton, ¹H, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,2)D [HACACONHN] GFT NMR experiment to measure and connect the chemical shift values of the α-proton of amino acid residue i−1, ¹H^α_i−1, the α-carbon of amino acid residue i−1, ¹³C^α_i−1, the polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i, and the polypeptide backbone amide proton of amino acid residue i, ¹H^N_iand (2) a (5,2)D [HACA,CONHN] GFT NMR experiment to measure and connect the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, ¹³C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i−1, ¹⁵N_i−1, and the polypeptide backbone amide proton of amino acid residue i−1, ¹H^N_i−1. Then, sequential assignments of the chemical shift values of ¹H^α, ¹³C^α, ¹³C′, ¹⁵N, and ¹H^Nare obtained by (i) matching the chemical shift values of ¹H^α_i−1,¹³C^α_i−1, and ¹³C′_i−1measured by the (5,2)D [HACACONHN] GFT NMR experiment with the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1measured by the (5,2)D [HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1to identify the type of amino acid residue i−1 (Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986); Grzesiek et al., J. Biomol. NMR, 3: 185-204 (1993), which are hereby incorporated by reference in their entirety), and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements (such as α-helices and β-sheets) within the polypeptide chain (Spera et al., J. Am. Chem. Soc., 113:5490-5492 (1991); Wishart et al., Biochemistry, 31:1647-1651 (1992), which are hereby incorporated by reference in their entirety).

[0151] Yet another aspect of the present invention relates to a method for sequentially assigning chemical shift values of an α-proton, ¹H^α, an α-carbon, ¹³C^α, a polypeptide backbone carbonyl carbon, ¹³C′, a polypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backbone amide proton, ¹H^N, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HACACONHN] GFT NMR experiment to measure and connect the chemical shift values of the α-proton of amino acid residue i−1, ¹H^α_i−1, the α-carbon of amino acid residue i−1, ¹³C^α_i−1, the polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i, and the polypeptide backbone amide proton of amino acid residue i, ¹H^N_iand (2) a (5,3)D [HACA,CONHN]0 GFT NMR experiment to measure and connect the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, ¹³C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i−1, ¹⁵N_i−1, and the polypeptide backbone amide proton of amino acid residue i−1, ¹H^N_i−1. Then, sequential assignments of the chemical shift values of ¹H^α, ¹³C^α,13C′, ¹⁵N, and ¹H^Nare obtained by (i) matching the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1measured by the (5,3)D [HACACONHN] GFT NMR experiment with the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1measured by the (5,3)D [HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of ¹H^α_i−1, ¹³C^α_i−1, and ¹³C′_i−1to identify the type of amino acid residue i−1 (Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986); Grzesiek et al., J. Biomol. NMR, 3: 185-204 (1993), which are hereby incorporated by reference in their entirety), and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements (such as α-helices and β-sheets) within the polypeptide chain (Spera et al., J. Am. Chem. Soc., 113:5490-5492 (1991); Wishart et al., Biochemistry, 31:1647-1651 (1992), which are hereby incorporated by reference in their entirety).

[0152] A further aspect of the present invention relates to a method for sequentially assigning chemical shift values of α- and β-carbons, ¹³C^α/β, a polypeptide backbone carbonyl carbon, ¹³C′, a polypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backbone amide proton, ¹H^N, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,3)D [CBCACONHN] GFT NMR experiment to measure and connect the chemical shift values of the α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1, the polypeptide backbone carbonyl carbon of amino acid residue i−1, ¹³C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i, and the polypeptide backbone amide proton of amino acid residue i, ¹H^N_iand (2) a (4,3)D [CBCA,CONHN] GFT NMR experiment to measure and connect the chemical shift values of ¹³C^α/β_i−1, ¹³C′_i−1, the polypeptide backbone amide nitrogen of amino acid residue i−1, ¹⁵N_i−1, and the polypeptide backbone amide proton of amino acid residue i−1, H^N_i−1. Then, sequential assignments of the chemical shift values of ¹³C^α/β, ¹³C′, ¹⁵N, and ¹H^Nare obtained by (i) matching the chemical shift values of ¹³C^α/β_i−1and ¹³C′_i−1measured by the (4,3)D [CBCACONHN] GFT NMR experiment with the chemical shift values of ¹³C^α/β_i−1and ¹³C′_i−1measured by the (4,3)D [CBCA, CONHN] GFT NMR experiment, (ii) using the chemical shift values of ¹³C^α/β_i−1and ¹³C′_i−1to identify the type of amino acid residue i−1 (Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986); Grzesiek et al., J. Biomol. NMR. 3: 185-204 (1993), which are hereby incorporated by reference in their entirety), and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements (such as α-helices and β-sheets) within the polypeptide chain (Spera et al., J. Am. Chem. Soc., 113:5490-5492 (1991); Wishart et al., Biochemistry, 31:1647-1651 (1992), which are hereby incorporated by reference in their entirety).

[0153] The present invention also relates to a method for sequentially assigning chemical shift values of α- and β-carbons, ¹³C^α/β, a polypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backbone amide proton, ¹H^N, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,3)D [HNNCACBCA] GFT NMR experiment to measure and connect the chemical shift values of the α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1, the α-carbon of amino acid residue i−1, ¹³C^α_i−1, the polypeptide backbone amide nitrogen of amino acid residue i−1, ¹⁵N_i−1, and the polypeptide backbone amide proton of amino acid residue i−1, ¹H^N_i−1and (2) a GFT NMR experiment selected from the group consisting of a (4,3)D [HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of ¹³C^α/β_i−1, ¹³C^α_i−1, the polypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_i, and the polypeptide backbone amide proton of amino acid residue i, ¹H^N_i. Then, sequential assignments of the chemical shift values of ¹³C^α/β, ¹⁵N, and ¹H^Nare obtained by (i) matching the chemical shift values of ¹³C^α/β_i−1measured by the GFT NMR experiment selected from the group consisting of a (4,3)D [HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment with the chemical shift values of ¹³C^α/β_i−1measured by the (4,3)D [HNNCACBCA] GFT NMR experiment, (ii) using the chemical shift values of ¹³C^α/β_i−1to identify the type of amino acid residue i−1 (Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986); Grzesiek et al., J. Biomol. NMR, 3: 185-204 (1993), which are hereby incorporated by reference in their entirety), and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements (such as α-helices and β-sheets) within the polypeptide chain (Spera et al., J. Am. Chem. Soc., 113:5490-5492 (1991); Wishart et al., Biochemistry, 31:1647-1651 (1992), which are hereby incorporated by reference in their entirety).

[0154] Another aspect of the present invention relates to a method for assigning chemical shift values of γ-, δ-, and ε-aliphatic sidechain protons, ¹H^γ/δ/ε, and chemical shift values of γ-, δ-, and ε-aliphatic sidechain carbons located peripheral to β-carbons, ¹³C^γ/δ/ε, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HCC,CH-COSY] GFT NMR experiment to measure and connect the chemical shift values of a proton of amino acid residue i−1, ¹H_i−1, a carbon of amino acid residue i−1 coupled to ¹H_i−1, ¹³C_i−1, a carbon coupled to ¹³C_i−1, ¹³C^α_i−1^coupled, and a proton coupled to ¹³C−^coupled, ¹H^N_i−1^coupled, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of α- and β-protons of amino acid residue i−1, ¹H^α/β_i−1, and α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1. Then, assignments of the chemical shift values of ¹H^γ/δ/ε and ¹³C^γ/δ/ε are obtained by (i) identifying ¹H_i−1, ¹³C_i−1, ¹³C_i−1^coupled, and ¹H_i−1^coupledmeasured by the (5,3)D [HCC,CH-COSY] GFT NMR experiment as ¹H^α_i−1, ¹³C^α_i−1, ¹³C^β_i−1, and ¹H^β_i−1, respectively, and thereby matching the chemical shift values of ¹H^α/β_i−1and ¹³C^α/β_i−1with the chemical shift values of ¹H^α/β_i−1and ¹³C^α/β_i−1measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and (ii) using the chemical shift values of ¹H^α/β_i−1and ¹³C^α/β_i−1in conjunction with other chemical shift connections from the (5,3)D [HCC,CH-COSY] GFT NMR experiment to measure the chemical shift values of ¹H^γ/δ/ε_i−1and ¹³C^γ/δ/ε_i−1.

[0155] Yet another aspect of the present invention relates to a method for assigning chemical shift values of γ-, δ-, and ε-aliphatic sidechain protons, ¹H^γ/δ/ε, and chemical shift values of γ-, δ-, and ε-aliphatic sidechain carbons located peripheral to β-carbons, ¹³C^γ/δ/ε, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,2)D [HCCH-COSY] GFT NMR experiment to measure and connect the chemical shift values of a proton of amino acid residue i−1, ¹H_i−1, a carbon of amino acid residue i−1 coupled to ¹H_i−1, ¹³C_i−1, a carbon coupled to ¹³C_i−1, ¹³C _i−1^coupled, and a proton coupled to ¹³C_i−1^coupled, ¹H_i−1^coupled, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of α- and β-protons of amino acid residue i−1, ¹H^α/β_i−1, and α- and β-carbons of amino acid residue i−1, ¹³C^α/β_i−1. Then, assignments of the chemical shift values of ¹H^γ/δ/ε and ¹³C^γ/δ/ε are obtained by (i) identifying ¹H_i−1, ¹³C_i−1, ^13C_i−1^coupled, and ¹H^N_i−1^coupledmeasured by the (4,2)D [HCCH-COSY] GFT NMR experiment as ¹H^α_i−1, ¹³C^α_i−1, ¹³Cβ_i−1, and ¹H^β_i−1, respectively, and thereby matching the chemical shift values of ¹H^α/β_i−1and ¹³C^α/β_i−1with the chemical shift values of ¹H^α/β_i−1and ¹³C^α/β_i−1measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and (ii) using the chemical shift values of ¹H^α/β_i−1, and ¹³C^α/β_i−1in conjunction with other chemical shift connections from the (4,2)D [HCCH-COSY] GFT NMR experiment to measure the chemical shift values of ¹H^γ/δ/ε_i−1and ¹³C^γ/δ/ε_i−1.

[0156] A further aspect of the present invention relates to a method for assigning chemical shift values of a γ-carbon, ¹³C^γ, a δ-carbon, ¹³C^δ, and a δ-proton, ¹H5, of an amino acid residue containing an aromatic spin system in a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HBCBCGCDHD] GFT NMR experiment to measure and connect the chemical shift values of a β-proton of amino acid residue i−1, ¹H^β_i−1, a β-carbon of amino acid residue i−1, ¹³C^β_i−1, a δ-carbon of amino acid residue i−1, ¹³C^γ_i−1, a δ-carbon of amino acid residue i−1, ¹³C^δ_i−1, and a δ-proton of amino acid residue i−1, ¹H^δ_i−1, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of ¹H^β_i−1and ¹³C^β_i−1. Then, assignments of the chemical shift values of ¹³C^γ, ¹³C^δ, and ¹H^δ are obtained by (i) matching the chemical shift values of ¹H^β_i−1and ¹³C^β_i−1measured by the (5,3)D HBCBCACA(CO)NHN GFT NMR experiment with the chemical shift values of ¹H^β_i−1and ¹³C^β_i−1measured by the (5,3)D [HBCBCGCDHD] GFT NMR experiment, and (ii) using the chemical shift values of ¹³C^γ, ¹³C^δ, and ¹H^δ to identify the type of amino acid residue containing the aromatic spin system.

[0157] The present invention also relates to a method for assigning chemical shift values of aliphatic and aromatic protons and aliphatic and aromatic carbons of an amino acid residue containing aliphatic and aromatic spin systems in a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a first GFT NMR experiment, which is selected from the group consisting of a (5,3)D [HCC,CH-COSY] GFT NMR experiment, a (4,2)D [HCCH-COSY] GFT NMR experiment, a (5,2)D [HCCCH-COSY] GFT NMR experiment, and a (5,3)D [HCCCH-COSY] GFT NMR experiment and is acquired for the aliphatic spin system, to measure and connect the chemical shift values of α- and β-protons of amino acid residue i, ¹H^α/β_i, α- and β-carbons of amino acid residue i, ¹³C^α/β_i, a γ-carbon of amino acid residue i, ¹³C^γ_i, and (2) a second GFT NMR experiment, which is selected from the group consisting of a (5,3)D [HCC,CH-COSY] GFT NMR experiment, a (4,2)D [HCCH-COSY] GFT NMR experiment, a (5,2)D [HCCCH-COSY] GFT NMR experiment, and a (5,3)D [HCCCH-COSY] GFT NMR experiment and is acquired for the aromatic spin system, to measure and connect the chemical shift values of ¹³C^γ_iand other aromatic protons and carbons of amino acid residue i. Then, assignments of the chemical shift values of the aliphatic and aromatic protons and aliphatic and aromatic carbons are obtained by matching the chemical shift value of ¹³C^γ_imeasured by the first GFT NMR experiment with the chemical shift value of ¹³C^γ_imeasured by the second GFT NMR experiment. In another embodiment, the set of GFT NMR experiments can be conducted by using ¹³C^γsteady state magnetization to generate first order central peaks.

[0158] The above-described methods for assigning chemical shift values in a protein molecule can involve further subjecting the protein sample to nuclear Overhauser enhancement spectroscopy (NOESY) (Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986), which is hereby incorporated by reference in its entirety), to NMR experiments that measure scalar coupling constants (Eberstadt et al., Angew. Chem. Int. Ed. Engl., 34:1671-1695 (1995); Cordier et al., J. Am. Chem. Soc., 121:1601-1602 (1999), which are hereby incorporated by reference in their entirety), or to NMR experiments that measure residual dipolar coupling constants (Prestegard, Nature Struct. Biol., 5:517-522 (1998); Tjandra et al., Science, 278:1111-1114 (1997), which are hereby incorporated by reference in their entirety), to deduce the tertiary fold or tertiary structure of the protein molecule.

[0159] Another aspect of the present invention relates to a method for obtaining assignments of chemical shift values of ¹H, ¹³C, and ¹⁵N of a protein molecule. The method involves providing a protein sample and conducting five G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample, where (1) a first experiment is a (4,3)D [HNNCACBCA] GFT NMR experiment for obtaining intraresidue correlations of chemical shift values; (2) a second experiment is a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment for obtaining interresidue correlations of chemical shift values; (3) a third experiment is a (5,3)D [HCC,CH-COSY] GFT NMR experiment for obtaining assignments of aliphatic sidechain chemical shift values; (4) a fourth experiment is a (5,3)D [HBCBCGCDHD] GFT NMR experiment for linking chemical shift values of aliphatic protons, ¹H^β and ¹³C^β, and aromatic protons, ¹³C^δ and ¹H^δ; and (5) a fifth experiment is a (4,2)D [HCCH-COSY] GFT NMR experiment for obtaining assignments of aromatic sidechain chemical shift values. These five GFT NMR experiments can be employed for obtaining nearly complete resonance assignments of proteins including aliphatic and aromatic side chain spin systems.

[0160] The following examples are provided to illustrate embodiments of the present invention but are by no means intended to limit its scope.

[0161] When designing a GFT NMR experiment (FIG. 1), one first identifies a “target” dimensionality, N_t, at which the majority of the peaks are resolved. The dimensionality N of a given FT NMR spectrum is then adapted to N_tby jointly sampling K+1 chemical shifts (K=N−N_t) in a hypercomplex manner, while N_t−1 dimensions are sampled in a conventional fashion. As outlined, this yields 2^KN_tD spectra. As an example, the case of K=3 in the frequency domain (FIGS. 2, 16, and 17) is described in this example. The indirect evolution time shall be t, and Ω₀shall be the chemical shift detected in quadrature in each of the N_tD spectra. Ω₁, Ω₂and Ω₃are the three jointly sampled shifts. The phases of the 90° pulses generating transverse magnetization for frequency labeling are chosen so that the transfer amplitudes of the real parts of the 2^K=8 spectra, Sjr (=1 . . . 8) are proportional to:

[0162] S1r∝ cos(Ω₀t) cos(Ω₁t) cos(Ω₂t) cos(Ω₃t)

[0163] S2r∝ cos(Ω₀t) sin(Ω₁t) cos(Ω₂t) cos(Ω₃t)

[0164] S3r∝ cos(Ω₀t) cos(Ω₁t) sin(Ω₂t) cos(Ω₃t)

[0165] S4r∝ cos(Ω₀t) sin(Ω₁t) sin(Ω₂t) cos(Ω₃t)

[0166] S5r∝ cos(Ω₀t) cos(Ω₁t) cos(Ω₂t) sin(Ω₃t)

[0167] S6r∝ cos(Ω₀t) sin(Ω₁t) cos(Ω₂t) sin(Ω₃t)

[0168] S7r∝ cos(Ω₀t) cos(Ω₁t) sin(Ω₂t) sin(Ω₃t)

[0169] S8r∝ cos(Ω₀t) sin(Ω₁t) sin(Ω₂t) sin(Ω₃t).

[0170] FT and, depending on the number n of chemical shift sine modulations the application of a zero-order phase correction of n·90° yields the frequency domain spectra A1 . . . A8. These spectra encode Ω₁, Ω₂, and Ω₃in signal splittings of “chemical shift multiplets” each comprising 2^K=8 components. Cosine and sine modulations give rise (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety) to in-phase and anti-phase splittings, respectively, and linear combinations of spectra A1 . . . A8 provide spectra B1 . . . B8 with peaks only at the frequencies of the individual multiplet components. Spectrum B1: Ω₀+Ω₁+Ω₂+Ω₃, B2: Ω₀−Ω₁+Ω₂+Ω₃, B3: Ω₀+Ω₁−Ω₂+Ω₃, B4: Ω₀−Ω₁−Ω₂+Ω₃, B5: Ω₀+Ω₁+Ω₂−Ω₃, B6: Ω₀−Ω₁+Ω₂−Ω₃, B7: Ω₀+Ω₁−Ω₂−Ω₃, and B8: Ω₀−Ω₁−Ω₂−Ω₃(FIG. 2). Spectra B1 to B8 are the “basic spectra”, and the selection of chemical shift multiplet components represents the phase-sensitive “editing of chemical shift multiplets”.

[0171] Acquisition of peaks defining the centers of the chemical shift splittings (“central peaks”) is required for unambiguous assignment, if two chemical shift quartets, (Ω₀, Ω₁, Ω₂, Ω₃) and (Ω′₀, Ω′₁, Ω′₂, Ω′₃), are correlated with degenerate chemical shifts in the other N_t−1 dimensions. Furthermore, degeneracy may occur between two or more shifts of the quartet itself, e.g., one may have that Ω₁=Ω_′1. The information of the ND experiment resolving degeneracy in up to N−1 dimensions, is made available if central peaks are detected. First, spectra with transfer amplitudes of the real parts of 2^K−1=4 spectra, Sjr (j=9 . . . 12), encode Ω₁and Ω₂, but no Ω₃signal splittings,

[0172] S9r∝ cos(Ω₀t) cos(Ω₁t) cos(Ω₂t)

[0173] S10r∝ cos(Ω₀t) sin(Ω₁t) cos(Ω₂t)

[0174] S11r∝ cos(Ω₀t) cos(Ω₁t) sin(Ω₂t)

[0175] S12r∝ cos(Ω₀t) sin(Ω₁t) sin(Ω₂t)

[0176] and provide the centers of the Ω₃-splittings. S9 . . . S12 yield, as described, spectra B9 . . . B12 with peaks at: B9: Ω₀+Ω₁+Ω₂, B10: Ω₀−Ω₂+Ω₂, B11: Ω₀+Ω₁−Ω₂, B12: Ω₀−Ω₂. Second, spectra with transfer amplitudes for the real parts 2^K−2=2 spectra, Sjr (1=13, 14), encode only Ω₁-signal splittings

[0177] S13r∝ cos(Ω₀t) cos(Ω₁t)

[0178] S14r∝ cos(Ω₀t) sin(Ω₂t)

[0179] and provide the centers of the Ω₂-splittings. S13 and S14 yield B13 and B14 comprising peaks at: B13: Ω₀+Ω₁, B14: Ω₀−Ω₁. Third, 2^K−3=1 spectrum, S15 with a transfer amplitude for the real part encoding no signal splittings,

[0180] S15r∝ cos(Ω₀t)

[0181] provides the centers of the Ω₁-splittings.

[0182] GFT NMR data acquisition (FIG. 1) requires recording of a total of $p=\sum _{k=0}^K{2}^k=2^{K+1}-1$

[0183] N_tD spectra (e.g., S1 . . . S15 for K=3) with 2^Kbasic spectra and a total of 2^K−1central peak spectra. This set of p data sets is designated an “(N,N_t)D GFT NMR experiment”, and central peaks due to omission of m chemical shifts are denoted to be of m-th order (e.g., B9 . . . B12, B13, B14, and B15 represent first, second and third order central peaks, respectively).

[0184] For frequency domain editing, the data sets S1 . . . S15 are Fourier transformed to yield spectra A1 . . . A15 (FIG. 2), and, depending on the number n of chemical shift sine modulations, a zero-order phase correction of n·90° is applied. Subsequent linear combination yields the edited spectra B1 . . . B15 (FIGS. 16 and 17) according to

[0185] {circumflex over (B)}(K)={circumflex over (F)}(K)·Â(K)  (4),

[0186] where {circumflex over (F)}(K) can be readily obtained from {circumflex over (F)}(K−1) by tensor product formation:

[0187] {circumflex over (F)}(K)={circumflex over (F)}(K−1)⊕{circumflex over (F)}(1)  with

[0188] $\begin{array}{cc}\stackrel{⋒}{F}\left(1\right)=\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right].& \left(5\right)\end{array}$

[0189] One thus obtains for K=2 $\begin{array}{cc}\left[\begin{array}{c}\mathrm{B9}\\ \mathrm{B10}\\ \mathrm{B11}\\ \mathrm{B12}\end{array}\right]=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& -1& 1& -1\\ 1& 1& -1& -1\\ 1& -1& -1& 1\end{array}\right]·\left[\begin{array}{c}\mathrm{A9}\\ \mathrm{A10}\\ \mathrm{A11}\\ \mathrm{A12}\end{array}\right],\mathrm{and}\mathrm{for}K=3& \left(6\right)\\ \left[\begin{array}{c}\mathrm{B1}\\ \mathrm{B2}\\ \mathrm{B3}\\ \mathrm{B4}\\ \mathrm{B5}\\ \mathrm{B6}\\ \mathrm{B7}\\ \mathrm{B8}\end{array}\right]=\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& 1& 1\\ 1& -1& 1& -1& 1& -1& 1& -1\\ 1& 1& -1& -1& 1& 1& -1& -1\\ 1& -1& -1& 1& 1& -1& -1& 1\\ 1& 1& 1& 1& -1& -1& -1& -1\\ 1& -1& 1& -1& -1& 1& -1& 1\\ 1& 1& -1& -1& -1& -1& 1& 1\\ 1& -1& -1& 1& -1& 1& 1& -1\end{array}\right]·\left[\begin{array}{c}\mathrm{A1}\\ \mathrm{A2}\\ \mathrm{A3}\\ \mathrm{A4}\\ \mathrm{A5}\\ \mathrm{A6}\\ \mathrm{A7}\\ \mathrm{A8}\end{array}\right].& \left(7\right)\end{array}$

[0190] The equations for K=1 $\begin{array}{cc}\left[\begin{array}{c}\mathrm{B13}\\ \mathrm{B14}\end{array}\right]=\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]·\left[\begin{array}{c}\mathrm{A13}\\ \mathrm{A14}\end{array}\right],& \left(8\right)\end{array}$  and for K=0

[0191] B15=A15  (9),

[0192] are likewise given here.

[0193] The matrices Ĝ(K) and {circumflex over (F)}(K) for time and frequency domain editing of chemical shift multiplets (FIGS. 1 and 2) are related to each other according to Ĝ(K)=Ĥ(K) ·{circumflex over (P)}(K) with $\stackrel{⋒}{H}\left(K\right)=\stackrel{⋒}{F}\left(K\right)\otimes \left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]·\stackrel{⋒}{H}\left(K\right)$

[0194] applies the addition scheme of {circumflex over (F)}(K) (equation 5) to both real and imaginary parts. To derive {circumflex over (P)}(K), ${\stackrel{⋒}{P}}^{\prime }\left(1\right)=\left[\begin{array}{cc}\stackrel{⋒}{E}& 0\\ 0& \hat{P}\end{array}\right]$

[0195] is first defined with $\stackrel{⋒}{E}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\mathrm{and}\hat{P}=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right].$

[0196] The matrix {circumflex over (P)} maps the real onto the imaginary, and the imaginary onto the negative real part. This corresponds to a zero-order 90° phase correction in the frequency domain. Accordingly, application of {circumflex over (P)}ⁿcorresponds to applying the n·90° zero-order phase correction alluded to above. {circumflex over (P)}′(K+1) can be constructed from the {circumflex over (P)}′(K) according to ${\stackrel{⋒}{P}}^{\prime }\left(K+1\right)={\stackrel{⋒}{P}}^{\prime }\left(K\right)\otimes \left[\begin{array}{cc}\stackrel{⋒}{E}& 0\\ 0& \stackrel{⋒}{P}\end{array}\right].$

[0197] Expansion of the products of Ê and {circumflex over (P)} resulting “after” (multiple) tensor product formation yields {circumflex over (P)}(K), a matrix with a 2×2 block diagonal form.

[0198] For K=3, 2, and 1, thus, the following is obtained for Ĥ(K) and {circumflex over (P)}(K). $\stackrel{⋒}{H}\left(3\right)=\left[\begin{array}{cccccccccccccccc}1& 0& 1& 0& 1& 0& 1& 0& 1& 0& 1& 0& 1& 0& 1& 0\\ 0& 1& 0& 1& 0& 1& 0& 1& 0& 1& 0& 1& 0& 1& 0& 1\\ 1& 0& -1& 0& 1& 0& -1& 0& 1& 0& -1& 0& 1& 0& -1& 0\\ 0& 1& 0& -1& 0& 1& 0& -1& 0& 1& 0& -1& 0& 1& 0& -1\\ 1& 0& 1& 0& -1& 0& -1& 0& 1& 0& 1& 0& -1& 0& -1& 0\\ 0& 1& 0& 1& 0& -1& 0& -1& 0& 1& 0& 1& 0& -1& 0& -1\\ 1& 0& -1& 0& -1& 0& 1& 0& 1& 0& -1& 0& -1& 0& 1& 0\\ 0& 1& 0& -1& 0& -1& 0& 1& 0& 1& 0& -1& 0& -1& 0& 1\\ 1& 0& 1& 0& 1& 0& 1& 0& -1& 0& -1& 0& -1& 0& -1& 0\\ 0& 1& 0& 1& 0& 1& 0& 1& 0& -1& 0& -1& 0& -1& 0& -1\\ 1& 0& -1& 0& 1& 0& -1& 0& -1& 0& 1& 0& -1& 0& 1& 0\\ 0& 1& 0& -1& 0& 1& 0& -1& 0& -1& 0& 1& 0& -1& 0& 1\\ 1& 0& 1& 0& -1& 0& -1& 0& -1& 0& -1& 0& 1& 0& 1& 0\\ 0& 1& 0& 1& 0& -1& 0& -1& 0& -1& 0& -1& 0& 1& 0& 1\\ 1& 0& -1& 0& -1& 0& 1& 0& -1& 0& 1& 0& 1& 0& -1& 0\\ 0& 1& 0& -1& 0& -1& 0& 1& 0& -1& 0& 1& 0& 1& 0& -1\end{array}\right],\stackrel{⋒}{H}\left(2\right)=\left[\begin{array}{cccccccc}1& 0& 1& 0& 1& 0& 1& 0\\ 0& 1& 0& 1& 0& 1& 0& 1\\ 1& 0& -1& 0& 1& 0& -1& 0\\ 0& 1& 0& -1& 0& 1& 0& -1\\ 1& 0& 1& 0& -1& 0& -1& 0\\ 0& 1& 0& 1& 0& -1& 0& -1\\ 1& 0& -1& 0& -1& 0& 1& 0\\ 0& 1& 0& -1& 0& -1& 0& 1\end{array}\right],\stackrel{⋒}{H}\left(1\right)=\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 1\\ 1& 0& -1& 0\\ 0& 1& 0& -1\end{array}\right]\mathrm{and}$ $\stackrel{⋒}{P}\left(3\right)=\left[\begin{array}{cccccccccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& -1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& -1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& -1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& -1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& -1& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& -1& 0\end{array}\right],\stackrel{⋒}{P}\left(2\right)=\left[\begin{array}{cccccccc}1& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& -1& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& -1& 0\\ 0& 0& 0& 0& 0& 0& 0& -1\end{array}\right],\stackrel{⋒}{P}\left(1\right)=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 0& -1\\ 0& 0& 1& 0\end{array}\right].$