Accelerating NMR-Based Structural Studies of Proteins by Combining Amino Acid Selective Unlabeling and Fast NMR Methods

In recent years, there has been a growing interest in fast acquisition and analysis of nuclear magnetic resonance (NMR) spectroscopy data for high throughput protein structure determination. Towards this end, rapid data collection techniques and methods to simplify the NMR spectrum such as amino acid selective unlabeling have been proposed recently. Combining these two approaches can speed up further the structure determination process. Based on this idea, we present three new two-dimensional (2D) NMR experiments, which together provide 15N, 1HN, 13Cα, 13Cβ, 13C′ chemical shifts for amino acid residues which are immediate C-terminal neighbors (i + 1) of residues that are selectively unlabeled. These experiments have high sensitivity and can be acquired rapidly using the methodology of G-matrix Fourier transform (GFT) NMR spectroscopy combined with non-uniform sampling (NUS). This is a first study involving the application of fast NMR methods to proteins samples prepared using a specific labeling scheme. Taken together, this opens up new avenues to using the method of selective unlabeling for rapid resonance assignment of proteins.


Introduction
During the last decade, there has been a growing emphasis on speeding up the structure determination process of proteins by NMR spectroscopy, especially in the context of structural genomics projects, which require high throughput structure determination [1][2][3][4].This is due to the fact that the conventional approaches for NMR data acquisition and analysis are time consuming.Typically, protein samples enriched uniformly with 13 C and/or 15 N isotopes are prepared and a suite of 2D and 3D heteronuclear spectra are acquired for sequence specific resonance assignments [5].With the conventional approach of data collection (e.g., linear sampling) this requires a few days to weeks of measurement time.Acquiring data in two different ways can accelerate this.One involves the rapid collection of multidimensional data using the recently proposed methods for fast data acquisition [1][2][3][4][6][7][8][9].These methods reduce the time taken for data collection by an order of magnitude or more.The second approach involves augmenting the data acquired using uniformly 13 C, 15 N labeled protein sample with those acquired with selectively labeled/unlabeled samples [10][11][12].
Selective unlabeling or "reverse" labeling involves the 13 C/ 15 N enrichment of all but specific chosen amino acids in a protein, which are rendered unlabeled ( 12 C/ 14 N) [11,[13][14][15][16][17].This helps in simplifying the NMR spectrum by reducing the number of peaks in the spectrum, and thereby, aiding unambiguous resonance assignments.

Implementation of NMR Experiments
All the experiments proposed are "HNCA" [5] based and involve the transfer of 15 N magnetization of residue i + 1 ( 15 N i+1 ) to 13 C α i+1 or 13 CO i+1 .They, however, detect selectively the resonances ( 1 H/ 13 C/ 15 N) of residue i + 1 corresponding to the selectively unlabeled residue, i.This selection is achieved by tuning the delay periods in the radio frequency (r.f.) pulse sequence appropriately such that the magnetization on 15 N i+1 is attenuated by coupling to both 13 CO i and 13 C α i by one-bond and two-bond scalar couplings, 1 J NCO (~15 Hz) and 2 J NCα (~7 Hz), respectively.For this purpose, a delay period of 1/2J (J is the scalar coupling) is used which converts an in-phase magnetization of a nuclei to anti-phase magnetization with respect to its J-coupled partner.This is depicted schematically in Figure 1a.In the case where both residues i and i + 1 are 13 C, 15 N labeled, 15 N i+1 magnetization is attenuated by the scalar coupling evolution to 13 CO i and 13 C α i (passive coupling via 2 J NCα ).Thus, if residue i is a labeled ( 13 C/ 15 N) residue the chemical shift correlations from its neighbor: i + 1 are not detected.However, if the residue i among a given pair (i, i + 1) is unlabeled (i.e., 12 C/ 14 N), 15 N i+1 is coupled only to 13 C α i+1 and hence the delay period of 1/2J corresponding to 1 J NCO and 2 J NCα has no effect and 15 N i+1 magnetization gets selected (product operator treatment is discussed below).

Resonance Assignment Strategy
Using the above set of experiments, resonance assignment is carried out as follows.For each [ 15 N i+1 , 1 H i+1 ] chemical shifts identified in 2D HN(CA)(i + 1), the amino acid type corresponding to residue i + 1 (self) is identified using (3,2)D HNCACB(i + 1) based on 13 C α i+1 , 13 C β i+1 values.Similarly using the (3,2)D HN(CA)CO(i + 1) the CO i+1 shifts are identified.Once the identity of the amino acid type corresponding to i + 1 is identified, and given that the amino acid type of i is known which is selectively unlabeled, the dipeptide pair i-i + 1 can be mapped onto the primary sequence for sequence-specific resonance assignment.Note that this is approach, that is different from the conventional strategy where the di-peptide pairs i-i − 1 are identified using 3D HNCACB and 3D CBCA(CO)NH for given residue i.Thus, the GFT experiments using selectively unlabeling can augment the conventional assignment approach resulting in a tri-peptide stretch (i − 1, i, i + 1) around a selectively unlabeled residue i.This is depicted in Figure 3.The experiments presented here thus increase the assignment speed compared to the approach presented earlier which did not yield directly the 13 C α i+1 , 13 C β i+1 shifts.
Using the above set of experiments, resonance assignment is carried out as follows.For each [ 15 Ni+1, 1 Hi+1] chemical shifts identified in 2D HN(CA)(i + 1), the amino acid type corresponding to residue i + 1 (self) is identified using (3,2)D HNCACB(i + 1) based on 13 C α i+1, 13 C β i+1 values.Similarly using the (3,2)D HN(CA)CO(i + 1) the COi+1 shifts are identified.Once the identity of the amino acid type corresponding to i + 1 is identified, and given that the amino acid type of i is known which is selectively unlabeled, the dipeptide pair i-i + 1 can be mapped onto the primary sequence for sequence-specific resonance assignment.Note that this is approach, that is different from the conventional strategy where the di-peptide pairs i-i − 1 are identified using 3D HNCACB and 3D CBCA(CO)NH for given residue i.Thus, the GFT experiments using selectively unlabeling can augment the conventional assignment approach resulting in a tri-peptide stretch (i − 1, i, i + 1) around a selectively unlabeled residue i.This is depicted in Figure 3.The experiments presented here thus increase the assignment speed compared to the approach presented earlier which did not yield directly the 13 C α i+1, 13 C β i+1 shifts.
In a given sample, more than one amino acid type can be chosen for simultaneous selective unlabeling so that the number of samples to be prepared is minimized.Two or more amino acid types are chosen for selectively unlabeling such that their 13 C β i+1 shifts lie in distinct spectral regions enabling their type identification.For instance, in the current study, Arg and Asn were used for selective unlabeling in the same sample due to their distinct 13 C β i+1 shifts.However, in such cases the [ 15 Ni+1, 1 Hi+1] pair of shifts obtained from 2D HN(CA)(i + 1) do not provide any information directly on the type of amino acid residue i.Hence, a 3D CBCA(CO)NH spectrum acquired on the uniformly 13 C, 15 N labeled sample is needed.In the 3D CBCA(CO)NH spectrum, at a given [ 15 Ni+1, 1 Hi+1] pair of shifts, the amino acid type corresponding to residue i can be identified based on 13 C α i, 13 C β i values (Figure 3).In a given sample, more than one amino acid type can be chosen for simultaneous selective unlabeling so that the number of samples to be prepared is minimized.Two or more amino acid types are chosen for selectively unlabeling such that their 13 C β i+1 shifts lie in distinct spectral regions enabling their type identification.For instance, in the current study, Arg and Asn were used for selective unlabeling in the same sample due to their distinct 13 C β i+1 shifts.However, in such cases the [ 15 N i+1 , 1 H i+1 ] pair of shifts obtained from 2D HN(CA)(i + 1) do not provide any information directly on the type of amino acid residue i.Hence, a 3D CBCA(CO)NH spectrum acquired on the uniformly 13 C, 15 N labeled sample is needed.In the 3D CBCA(CO)NH spectrum, at a given [ 15 N i+1 , 1 H i+1 ] pair of shifts, the amino acid type corresponding to residue i can be identified based on 13 C α i , 13 C β i values (Figure 3).

Data Acquisition Using Non-Uniform Sampling (NUS)
The measurement time required for acquiring the GFT spectra can be reduced further by using the non-uniform sampling (NUS) approach [24][25][26].The NUS approach is based on the premise that the conventional method involving linear sampling of interferogram in the inderct dimension requires a lot more number of points although the number of frequencies encoded in the interferogram is much less.Thus, by reducing the number of sampling points in the indirect dimensions the total measurement time can be proportionately reduced.The dataset obtained using NUS is then reconstructed either in the time domain using the multiway decomposition method (MDD) or directly in the frequency domain using the maximum entropy reconstruction (MER) approach.The sampling points are chosen based on the decay of the Free Induction Decay (FID).In case of a constant time experiment, the NUS points can be chosen randomly.In the present study, the MDD approach was used for spectral reconstruction in the time domain.The data were acquired a random sampling of 25% of the points (i.e., the omission of 75% of the time domain points) in the GFT dimension.
Figure 4a shows an overlay of the 2D [ 15 N, 1 H] HSQC spectrum of the uniformly 13 C, 15 N labeled (shown in red) and Arg, Asn selectively unlabeled (in blue) ubiquitin.The resonances, which are absent in the selectively unlabeled sample, corresponding to Arg and Asn residues as indicated.No other residues were observed to be absent indicating minimal mis-incorporation of 14 N isotope of Arg and Asn (also referred to as 'isotope scrambling').Figure 4b shows 2D HN(CA)(i + 1) spectrum acquired on the Arg, Asn selectively unlabeled sample.All expected [ 15 N i+1 , 1 H i+1 ] correlations are observed in the spectrum as indicated.

Data Acquisition Using Non-Uniform Sampling (NUS)
The measurement time required for acquiring the GFT spectra can be reduced further by using the non-uniform sampling (NUS) approach [24][25][26].The NUS approach is based on the premise that the conventional method involving linear sampling of interferogram in the inderct dimension requires a lot more number of points although the number of frequencies encoded in the interferogram is much less.Thus, by reducing the number of sampling points in the indirect dimensions the total measurement time can be proportionately reduced.The dataset obtained using NUS is then reconstructed either in the time domain using the multiway decomposition method (MDD) or directly in the frequency domain using the maximum entropy reconstruction (MER) approach.The sampling points are chosen based on the decay of the Free Induction Decay (FID).In case of a constant time experiment, the NUS points can be chosen randomly.In the present study, the MDD approach was used for spectral reconstruction in the time domain.The data were acquired a random sampling of 25% of the points (i.e., the omission of 75% of the time domain points) in the GFT dimension.
Figure 4a shows an overlay of the 2D [ 15 N, 1 H] HSQC spectrum of the uniformly 13 C, 15 N labeled (shown in red) and Arg, Asn selectively unlabeled (in blue) ubiquitin.The resonances, which are absent in the selectively unlabeled sample, corresponding to Arg and Asn residues as indicated.No other residues were observed to be absent indicating minimal mis-incorporation of 14 N isotope of Arg and Asn (also referred to as 'isotope scrambling').Figure 4b shows 2D HN(CA)(i + 1) spectrum acquired on the Arg, Asn selectively unlabeled sample.All expected [ 15 Ni+1, 1 Hi+1] correlations are observed in the spectrum as indicated.The correlation of 55T is presumably absent due to its weak intensity in the HSQC spectrum and shorter transverse relaxation time of its 13 C nuclei.The 13 C α i+1 , 13 C β i+1 and 13 CO i+1 chemical shifts values are obtained by linearly combining the sums and differences of the chemical shifts observed in the two GFT sub-spectra of each experiment and taking into account the appropriate scaling factor.Note that a 3D spectrum with an equivalent resolution would have taken more than 3 days of measurement time (2 days 7 h 9 min for 3D HNCACB(i + 1) and 19 h 23 min for 3D HN(CA)CO(i + 1)).Thus, the GFT experiments potentially reduce the measurement time by about an order of magnitude.
Magnetochemistry 2018, 4, 2 7 of 13 chemical shifts values are obtained by linearly combining the sums and differences of the chemical shifts observed in the two GFT sub-spectra of each experiment and taking into account the appropriate scaling factor.Note that a 3D spectrum with an equivalent resolution would have taken more than 3 days of measurement time (2 days 7 h 9 min for 3D HNCACB(i + 1) and 19 h 23 min for 3D HN(CA)CO(i + 1)).Thus, the GFT experiments potentially reduce the measurement time by about an order of magnitude.chemical shifts values are obtained by linearly combining the sums and differences of the chemical shifts observed in the two GFT sub-spectra of each experiment and taking into account the appropriate scaling factor.Note that a 3D spectrum with an equivalent resolution would have taken more than 3 days of measurement time (2 days 7 h 9 min for 3D HNCACB(i + 1) and 19 h 23 min for 3D HN(CA)CO(i + 1)).Thus, the GFT experiments potentially reduce the measurement time by about an order of magnitude.The acquisition of GFT spectra is further accelerated using the NUS approach.Figures 7 and 8 show the 25% NUS spectrum of (3,2)D HNCACB(i + 1) and (3,2)D HN(CA)CO(i + 1) experiments acquired in less than 14 and 9 min respectively.All expected correlations as observed in the non-NUS counterparts are observed without any spectral distortions or artifacts.The signal-to-noise ratio (S/N) by NUS is not compromised as shown in Figure 7c,d  The acquisition of GFT spectra is further accelerated using the NUS approach.Figures 7 and 8 show the 25% NUS spectrum of (3,2)D HNCACB(i + 1) and (3,2)D HN(CA)CO(i + 1) experiments acquired in less than 14 and 9 min respectively.All expected correlations as observed in the non-NUS counterparts are observed without any spectral distortions or artifacts.The signal-to-noise ratio (S/N) by NUS is not compromised as shown in Figures 7c,d and 8c,d which compares the 1D traces from the non-NUS and NUS GFT data.(c,d), represents the overlay of 1D projection of linearly acquired data (red) and non-uniformly acquired data (blue) along 1 for Ω( 15 Ni+1 + κ * 13 C α i+1/ 13 C β i+1) and Ω( 15 Ni+1 -κ * 13 C α i+1/ 13 C β i+1) respectively.There is 28% reduction in signal to noise (SNR) ratio ongoing from linearly acquired data to NUS data as measured by the SNR of the projections.We also have calculated SNR of G75 (highlighted in red) individually and there also we have seen ~30% decrease in SNR on going from linearly acquired data to NUS data. ) respectively.There is 28% reduction in signal to noise (SNR) ratio ongoing from linearly acquired data to NUS data as measured by the SNR of the projections.We also have calculated SNR of G75 (highlighted in red) individually and there also we have seen ~30% decrease in SNR on going from linearly acquired data to NUS data.

Discussion
Amino acid selective unlabeling has been shown to be a robust, easy and cost-effective method for simplifying NMR spectrum and obtaining useful structural information in proteins [11,15,[27][28][29][30]. On the other hand, GFT NMR is a powerful technique for speeding up NMR data acquisition and has been shown to be useful in various applications [2,18,19,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46].In the present study, the application of two fast NMR methods, namely GFT NMR and non-uniform sampling to selectively unlabeled protein samples expands the repertoire of applications possible with selective unlabeling.In our previous study, we reported an experiment for identification of [ 15 N i+1 , 1 H i+1 ] shifts based on a 2D 12 CO-filtered [ 15 N, 1 H] HSQC.The new experiment proposed herein, namely, 2D HN(CA)(i + 1) improves upon the selection of unlabeled (i)-labeled (i + 1) pair by incorporating two filters simultaneously.That is, attenuating the 15 N i+1 magnetization by allowing its scalar coupling to both 13 CO i and 13 C α i .The delay periods used in the r.f.pulse sequences are appropriately tuned to achieve the desired selection.The only limitation of the approach is the additional sample requirement.Additionally, not all the amino acids can be used for unlabeling as cross metabolism is an issue.However, we have extensively studied on the cross metabolism issue and came up with excellent solutions of many different combinations of amino acids which can be used as starting point.These combinations greatly cover a large percentage of residues in the sequences and the resonance assignment strategies can be simplified to a large extent.Considering the cost-effective solution this approach is much better than selective labeling as the cross metabolism is also an issue there.
Having thus achieved a selection of [ 15 N i+1 , 1 H i+1 ] resonances, the application of GFT NMR and NUS methodology helps to provide high dimensional spectral information, namely 13 C α i+1 , 13 C β i+1 and 13 CO i+1 correlations, rapidly.The two (3,2)D GFT experiments proposed thus augment the conventional assignment strategy involving 3D HNCACB and 3D CBCA(CO)NH without severely increasing the overall measurement time.Further, the information obtained can be used for automated resonance assignment strategies to speed up data analysis.Since the experiments are based on the "HNCA" based approach, the methodology can be extended in a straightforward manner to detect 1 H α or measure scalar/dipolar couplings, which involve HNCA type editing.

Sample Preparation
The plasmid (P GLUB ) coding for ubiquitin was transformed into E. coli BL21 cells (New England Biolabs, Ipswich, MA, USA).Cells were grown at 37 • C in M9 medium containing 1 g/L of 15 NH 4 Cl (Cambridge Isotope Laboratories, Tewksbury, MA, USA) and 4 g/L of 13 C-Glucose (Cambridge Isotope Laboratories, Tewksbury, MA, USA).For selective unlabeling, 1.0 g/L each of desired unlabeled amino acid(s): Arg and Asn (stock solution of 1.0 g in 50 mL of H 2 O was prepared and filter sterilized) was added to the growth medium.To induce protein expression, 1.0 mM isopropyl β-D-thiogalactoside (IPTG) (Sigma-Aldrich, St. Louis, MO, USA) was added at midlog phase (O.D 600 ~0.6).Cells were harvested by centrifugation and suspended in acetate buffer (5 mM EDTA (Sigma-Aldrich, St. Louis, MO, USA), 50 mM Na acetate (Sigma-Aldrich, St. Louis, MO, USA), pH 5) and taken up for sonication.Following sonication, the supernatant containing the protein was loaded on to a pre-equilibrated ion exchange column (SP Sepharose fast flow from GE) and the protein eluted with a salt gradient of 0-0.6 M NaCl.The protein sample was further purified using size-exclusion chromatography with Superdex 75 (Sigma-Aldrich, St. Louis, MO, USA).For NMR data acquisition, a sample containing ~1.0 mM of protein in 50 mM phosphate buffer (10% 2 H 2 O, pH 6.0) was prepared.

NMR Data Collection
All NMR data were acquired at 298 K on a Bruker Avance 800 MHz NMR spectrometer (Billerica, MA, USA) equipped with a room temperature triple resonance probe with a z-axis shielded gradient.Data were processed with NMRPipe [47] and analyzed using XEASY [48].

Conclusions
Three new NMR experiments are presented which are applicable to protein samples prepared with amino acid selective unlabeling.The experiments provide 15 N, 1 HN, 13 C α , 13 C β , 13 C chemical shifts for amino acid residues which are immediate C-terminal neighbors (i + 1) of selectively unlabeled residues.Two of the experiments provide 3D shift correlations rapidly using the methodology of GFT NMR and non-uniform sampling.The data acquisition time can be further reduced using the method of longitudinal 1 H relaxation optimization [19].The spectral simplification obtained combined with rapid data collection will help in reducing the time required for data analysis.In addition to resonance assignments, the proposed methodology can also be used for studies such as protein-ligand and protein-protein interactions, which involve monitoring the changes in shifts of certain residues against a background of unshifted resonances.Taken together, the proposed methodology expands the repertoire of applications possible with amino acid selective unlabeling for rapid protein structural studies.

Figure 1 .
Figure 1.(a) Schematic illustration of the selection of magnetization in all the filter experiments employing one-bond and two-bond scalar couplings, 1 J NCO (~15 Hz) and 2 J NCα (~7 Hz), respectively; (b) Figure 1b shows a plot of the transfer function as a function of τ NCα delays.Panels (I), (II) and (III) shows variation of Г(selected), Г(suppressed) the ratio of Г(selected)/Г(suppressed) as a function of τ NCα delays respectively.

Figure 1 .
Figure 1.(a) Schematic illustration of the selection of magnetization in all the filter experiments employing one-bond and two-bond scalar couplings, 1 JNCO (~15 Hz) and 2 JNCα (~7 Hz), respectively; (b) Figure 1b shows a plot of the transfer function as a function of τNCα delays.Panels (I), (II) and (III) shows variation of Г(selected), Г(suppressed) the ratio of Г(selected)/Г(suppressed) as a function of τNCα delays respectively.

Figure 3 .
Figure 3. Schematic illustration of the sequential assignment strategy used with selective unlabeling.

Figure 3 .
Figure 3. Schematic illustration of the sequential assignment strategy used with selective unlabeling.

Figure 4 .
Figure 4. (a) overlay of the 2D [ 15 N, 1 H] HSQC spectrum of the uniformly 13 C, 15 N labeled ubiquitin as shown in red and Arg, Asn selectively unlabeled sample as shown in blue; (b) 2D HN(CA)(i + 1) spectrum acquired on the Arg, Asn selectively unlabeled sample.Assignments are indicated on the spectra.The sequence is shown above and the unlabeled residues are highlighted in red.

Figure 4 .
Figure 4. (a) overlay of the 2D [ 15 N, 1 H] HSQC spectrum of the uniformly 13 C, 15 N labeled ubiquitin as shown in red and Arg, Asn selectively unlabeled sample as shown in blue; (b) 2D HN(CA)(i + 1) spectrum acquired on the Arg, Asn selectively unlabeled sample.Assignments are indicated on the spectra.The sequence is shown above and the unlabeled residues are highlighted in red.
and Figure 8c,d which compares the 1D traces from the non-NUS and NUS GFT data.Magnetochemistry 2018, 4, 2 8 of 13

Figure 7 .
Figure 7. (a,b) shows the different linear combinations of non-uniformly sampled (3,2)D HNCACB(i + 1) of Arg, Asn selectively unlabeled sample of ubiquitin.Total measurement time for two spectra was 14 min with 8 scans each.Peaks shown in blue and green correspond to Ω( 15 Ni+1 ± κ * 13 C α i+1) and Ω( 15 Ni+1 ± κ * 13 C β i+1), respectively.The scaling factor κ was set to 0.5.The NUS time increments in the shared dimension which was actually acquired in the experiment are shown in blue bars;(c,d), represents the overlay of 1D projection of linearly acquired data (red) and non-uniformly acquired data (blue) along 1 for Ω( 15 Ni+1 + κ * 13 C α i+1/ 13 C β i+1) and Ω( 15 Ni+1 -κ * 13 C α i+1/ 13 C β i+1) respectively.There is 28% reduction in signal to noise (SNR) ratio ongoing from linearly acquired data to NUS data as measured by the SNR of the projections.We also have calculated SNR of G75 (highlighted in red) individually and there also we have seen ~30% decrease in SNR on going from linearly acquired data to NUS data.

Figure 7 .
Figure 7. (a,b) shows the different linear combinations of non-uniformly sampled (3,2)D HNCACB(i + 1) of Arg, Asn selectively unlabeled sample of ubiquitin.Total measurement time for two spectra was 14 min with 8 scans each.Peaks shown in blue and green correspond to Ω( 15 N i+1 ± κ * 13 C α i+1 ) and Ω( 15 N i+1 ± κ * 13 C β i+1 ), respectively.The scaling factor κ was set to 0.5.The NUS time increments in the shared dimension which was actually acquired in the experiment are shown in blue bars; (c,d), represents the overlay of 1D projection of linearly acquired data (red) and non-uniformly acquired data (blue) along ω 1 for Ω( 15 N i+1 + κ * 13 C α i+1 / 13 C β i+1) and Ω( 15 N i+1 -κ * 13 C α i+1 / 13 C β i+1 ) respectively.There is 28% reduction in signal to noise (SNR) ratio ongoing from linearly acquired data to NUS data as measured by the SNR of the projections.We also have calculated SNR of G75 (highlighted in red) individually and there also we have seen ~30% decrease in SNR on going from linearly acquired data to NUS data.

Figure 8 .
Figure 8. (a,b) shows the different linear combinations of non-uniformly sampled (3,2)D HN(CA)CO(i + 1) of Arg, Asn selectively unlabeled sample of ubiquitin.Total measurement time for two spectra was ~9 min with 8 scans each.Peaks shown in blue in figure (a,b) correspond to Ω( 15 Ni+1 + κ * 13 C ′ i+1) and Ω( 15 Ni+1 − κ * 13 C ′ i+1), respectively.The scaling factor κ was set to 0.5.The NUS time increments in the shared dimension which was actually acquired in the experiment are shown in blue bars; (c,d), represents the overlay of 1D projection of linearly acquired data (cyan) and non-uniformly acquired data (blue) along 1 for Ω( 15 Ni+1 + κ * 13 C ′ i+1) and Ω( 15 Ni+1 − κ * 13 C ′ i+1) respectively.There is 27% reduction in signal to noise ratio ongoing from linearly acquired data to NUS data as measured by the SNR of the projections.

Figure 8 .
Figure 8. (a,b) shows the different linear combinations of non-uniformly sampled (3,2)D HN(CA)CO(i + 1) of Arg, Asn selectively unlabeled sample of ubiquitin.Total measurement time for two spectra was ~9 min with 8 scans each.Peaks shown in blue in figure (a,b) correspond to Ω( 15 N i+1 + κ * 13 C i+1 ) and Ω( 15 N i+1 − κ * 13 C i+1 ), respectively.The scaling factor κ was set to 0.5.The NUS time increments in the shared dimension which was actually acquired in the experiment are shown in blue bars;(c,d), represents the overlay of 1D projection of linearly acquired data (cyan) and non-uniformly acquired data (blue) along ω 1 for Ω( 15 N i+1 + κ * 13 C i+1 ) and Ω( 15 N i+1 − κ * 13 C i+1 ) respectively.There is 27% reduction in signal to noise ratio ongoing from linearly acquired data to NUS data as measured by the SNR of the projections.