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Chemistry LibreTexts

6.2: Heteronuclear 3D NMR- Resonance Assignment in Proteins

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  • Page ID 398288

  • Serge L. Smirnov and James McCarty
  • Western Washington University

In the previous Chapter we described 2D NMR spectroscopy, which offers significantly greater spectral resolution than basic 1D spectra. In this Chapter we will show how the well-resolved 2D 15 N-HSQC resonances can be assigned to specific residues and chemical groups within protein samples. As an example, we will consider a couple of complementary types of 3D NMR data: HNCACB and CBCA(CO)NH and their joint application for making heteronuclear NMR resonance assignment in proteins. Such an assignment opens a number of ways to probe structure and function (e.g. ligand binding) for the target protein samples.

Learning Objectives

  • Grasp why the resonance assignment of 2D 15 N-HSQC can be beneficial : the case of ligand (drug) binding by a protein (therapeutic target)
  • Familiarize with 3D heteronuclear through-bond (J-coupling) NMR : introduction and case of HNCACB and CBCA(CO)NH pair of 3D experiments
  • Follow an example of assignment of heteronuclear NMR resonances ( 1 H N , 15 N H , 13 Cα, 13 Cβ) from a combination of 2D 15 N-HSQC and 3D HNCACB/CBCA(CO)NH

15 N-HSQC as an assay for probing protein – ligand interactions: the need for the NMR resonance assignment

During the process of rational drug design, it is often necessary to characterize the interactions between the therapeutic target (protein) and candidate drug (ligand) beyond determination of the binding affinity ( K d ). Heteronuclear solution NMR experiments 15 N-HSQC can provide significant insight for such interactions. Let’s recall that most of the signals in this 2D NMR spectra originate from backbone H-N amide groups and some (minority) from the side chain NH and NH 2 groups. The position of 15 N-HSQC resonances are defined by the 1 H N and 15 N H chemical shift values, which in tern depend on the local electronic environment. Ligand binding changes such an environment for the residues forming the binding site even if the tertiary structure of the rest of the protein does not get perturbed. In such a case, the 15N-HSQC resonance pattern undergoes local changes: only the resonances representing NH groups involved in the binding site change their position significantly (>0.05 ppm in 1 H and/or >0.2 ppm in 15 N dimension) or signal intensity (including peak disappearance). Figure VI.2.A illustrates such a change.

Figure_VI.2.Ab_.png

Importantly, every 15 N-HSQC resonance in Figure VI.2.A is labeled with a single letter to help identify specific peaks which undergo spectral changes upon ligand binding. This data could have much greater impact if the peaks which underwent the most pronounced changes in position and/or intensity were assigned to specific amino acid residues within the polypeptide and chemical groups within those residues (backbone vs. side chain). The rest of this Chapter demonstrates some of the fundamentals of the heteronuclear NMR resonance assignment methodology.

Heteronuclear 3D NMR introduction: CBCA(CO)NH spectrum as an example

Just like every 2D 15N-HSQC resonance reports a J-coupling via a covalent bond between an 15N and 1H spin-½ nuclei, there are 3D NMR experiments which report resonances originating from J-coupling (through-bond) of three types of spin-½ nuclei ( 1 H, 13 C, 15 N). In this section we will introduce two such types of 3D NMR data: HNCAB and CBCA(CO)NH. In order to produce a protein sample with nearly complete uniform labeling with 13 C and 15 N isotopes, bacterial recombinant protein expression can be performed in a minimal media supplemented with 13 C-labeled glucose and 15 N-labeled ammonium chloride as the sole sources of carbon and nitrogen respectively. Figure VI.2.B introduces a general concept of a 3D NMR data and shows an element of 3D CBCA(CO)NH spectrum.

Figure_VI.2.Bd_.png

Each resonance (“cross-peak”) of a 3D CBCA(CO)NH spectrum indicates a through-bond (J-coupling scalar) interaction between two atoms of the backbone amide group ( 1 H N and 15 N H ) or residue j and Cα and Cβ nuclei ( 13 C) of preceding residue j -1. The name of the experiment, CBCA(CO)NH refers to the specific spin-½ nuclei involved (and not involved) in relevant J-coupling interactions: Cβ and Cα are J-coupled to NH while the connecting carbonyl carbon is not reporting any NMR signal (although its magnetization state is affected during the experiment). Two types of residues generate special CBCA(CO)NH peak pattern: prolines have no amide proton, so they do not have CBCA(CO)NH peaks linked with their amide groups. Glycine residues have no Cβ, therefore for any residue following a glycine only a single CBCA(CO)NH resonance will be observed (from glycine NH to previous Cα).

The NMR resonance assignment: combined use of two complementary datasets HNCACB and CBCA(CO)NH

By itself, CBCA(CO)NH does not convey much of sequential information. Another heteronuclear 3D NMR dataset, HNCACB, affords a powerful complement here. Just like CBCA(CO)NH, HNCACB reports resonances originating from J-coupling between backbone amide group and Cα / Cβ nuclei. The difference is that HNCACN reports two additional peaks, all intra-residual: between HN and Cα a Cβ spins ( Figure VI.2.C ).

Figure_VI.2.Clast_.png

Typically, HNCACB and CBCA(CO)NH are acquired with identical parameters including spectral width in all three dimensions and the same number of data points in the 15 N dimension (or 15 N planes as on panel B of Figure VI.2.B ) Now, let’s imagine that we go through every 15 N plane and build the pairs of “residue j / residue j -1″ HNCAB/CBCA(CO)NH peaks. This does not give us the sequence-specific NMR resonance assignments yet but already creates such pairs of 3D cross-peaks linked to di-peptides within the sequence. Now, let’s take into account that for some types of residues their 13Cα and 13Cβ chemical shift values differs remarkably from those from other residue types. For details, take a look at BMRB chemical shift statistics for amino acid residues with emphasis on Gly, Ala, Ser, Thr. Knowing where such residues are positioned within the polypeptide sequence, we can start “connecting the dots” by mapping HNCACB/CBCA(CO)NH planes and di-peptides on actual amino acid sequence.

Figure_VI.2.D.png

Figure VI.2.D provides a general idea of how the two 3D NMR experiments HNCACB and CBCA(CO)NH can be utilized together to map the signals on the amino acid sequence of a protein sample. The C of Ala residues typically has chemical shift values below 20.0 ppm, which is unique. This allows identification of Ala patterns HNCACB/CBCA(CO)NH spectral patters. Starting from this starting points (as well from other distinct values, e.g. Cα for Gly and Cβ for Ser/Thr), one can continue “connecting the dots” process outlined in Figure VI.2.D to cover the entire sequence. If these two 3D NMR datasets encounter resonance overlaps, which are impossible to resolve, more 3D NMR dataset pairs are utilized in a similar way, e.g. HNCO/HN(CA)CO and others. This process allows assignment to specific residues and chemical groups of nearly all backbone and some side-chain resonances ( 1 H N , 15 N H , 13 Cα, 13 Cβ). Methods for assigning side-chain chemical shift values are not discussed in this chapter but conceptually they are similar to the ones described here.

With the general process of the protein NMR resonance assignment described, let’s assume that this method was successfully applied to the protein target (T) sample presented in Figure VI.2.A. The resonance assignment completion allows one to replace letter labels with residue-number labels (similar to the ones used in Figure VI.2.D). This in turn allows one to determine the specific residues affected directly or allosterically by binding of the ligand (L) to the target. In many cases, such information together with other data leads to the determination of the ligand binding residues within the target. If the ligand is a candidate therapeutic agent, identification of the ligand binding residues greatly advances ensuing efforts to optimize the drug.

Example \(\PageIndex{1}\)

Analyze Figure VI.2.A and list at least two resonances which undergo major spectral changes upon binding of the unlabeled ligand (L) to the 15 N-labeled target protein (T). Major spectral changes for this model spectrum include resonances moving by >0.05 ppm in 1 H or >0.2 ppm in 15 N dimensions as well as peak disappearance (peak intensity going down to zero).

Upon ligand L binding target protein (T), resonance f disappears and resonance s moves by >0.05 ppm in 1 H dimension.

Example \(\PageIndex{2}\)

Inspect BMRB entry 50205 and list all the heteronuclear NMR datasets utilized for the NMR resonance assignment.

BMRB entry 50205 contains the chemical shift assignment data for the target sample and offers several ways to look at its underlying NMR data including the list of experiments used to perform the NMR resonance assignment and the chemical shift values. E.g., the NMR-STAR v3 text file has a section titled _Experiment_list, which sums up the heteronuclear NMR data types used for making the assignments: 2D 1 H- 15 N HSQC and 3D HNCACB, CBCA(CO)NH, HNCO and HN(CA)CO.

Example \(\PageIndex{3}\)

How many 3D HNCACB resonances would you expect to originate from a Lys residue which is preceded by a Met?

four as both Lys and Met have backbone amide (HN) groups and both have Cα and Cβ atoms.

Practice Problems

Problem 1 . Analyze Figure VI.2.A and list all the resonances which undergo major spectral changes upon binding of the unlabeled ligand (L) to the 15 N-labeled target protein (T). Example 1 above will help you start the analysis.

Problem 2 . From BMRB entry linked to PDB 5VNT, list all the heteronuclear NMR datasets utilized for the NMR resonance assignment for the target sample.

Problem 3 . Let’s consider panel B of Figure VI.2.B . Imagine that the 13 C dimension is taken out of the spectrum (all 13 C planes are collapsed together). What type of 2D spectrum will remain after such a dimension reduction?

Problem 4 . How many 3D HNCACB resonances would you expect to originate from a Gly residue which is preceded by a Pro?

Problem 5 . How many 3D HNCACB resonances would you expect to originate from a Pro residue which is preceded by a Gly?

Problem 6* . Look up the amino acid NMR chemical shift values statistics table presented with BMRB repository and list the average values for the following resonances: 15 N, 13 Cα and 13 Cβ for Gly, Ala, Tyr, Glu, Arg, Ser, Thr, Pro. From this analysis, suggest what types of residues tend to report unusually low or high chemical shift values in comparison with the rest of the amino acids?

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A Practical Implementation of Cross-spectrum in Protein Backbone Resonance Assignment

† Laboratory of Molecular Biophysics, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, MD 20892

Frank Delaglio

‡ Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892

Nico Tjandra

The concept of cross-spectrum is applied in protein NMR spectroscopy to assist in the backbone sequential resonance assignment. Cross-spectrum analysis is used routinely to reveal correlations in frequency domains as a means to reveal common features contained in multiple time series. Here the cross-spectrum between related NMR spectra, for example HNCO and HN(CA)CO, can be calculated with point-by-point multiplications along their common C′ carbon axis. In the resulting higher order cross-spectrum, an enhanced correlation signal occurs at every common i −1 carbon frequency allowing the amide proton H N (and nitrogen N) resonances from residues i and i −1 to be identified. The cross-spectrum approach is demonstrated using 2D spectra H(N)CO, H(NCA)CO, H(NCO)CACB, and H(N)CACB measured on a 15 N/ 13 C double-labeled Ubiquitin sample. These 2D spectra are used to calculate two pseudo-3D cross-spectra, H i -H i −1 -C′ i −1 and H i -H i −1 -CA i −1 CB i −1 . We show using this approach, backbone resonances of H, C′, CA, and CB can be fully assigned without ambiguity. The cross-spectrum principle is expected to offer an easy, practical, and more quantitative approach for heteronuclear backbone resonance assignment.

Introduction

In protein NMR spectroscopy the backbone resonance assignment is a key step in the characterization of protein structure and dynamics. Numerous efforts have been made to expedite this critical, time-consuming, and labor-intensive task by improvements to the NMR data collection schemes as well as the analysis methods. Novel data acquisition methods were developed to reduce the sampling space, thus experimental time, for multidimensional experiments. Approaches to reduce measurement time include non-uniform sampling,[ 1 ] G-matrix Fourier-transform (GFT) NMR,[ 2 ] Projection-Reconstruction (PR) NMR,[ 3 ; 4 ], Covariance NMR,[ 5 ] and Automated Projection Spectroscopy (APSY).[ 6 ] For the purpose of resonance assignments, additional correlations among lower dimensional (mostly 2–4D) data sets have to be established. In protein NMR spectroscopy one relies on approaches, either visual discrimination or computer algothrim or both, to identify paired i −1 carbon resonances from a pair of spectra, acquired using either conventional or reduced-sampling methods.[ 7 ; 8 ; 9 ; 10 ] We should note experimentally Kupce and Freeman[ 11 ; 12 ] have demonstrated the applicability of Hyperdimensional NMR spectroscopy, which correlates up to ten spin nuclei, by further exploiting PR-NMR. In theory Hyperdimensional NMR excludes the need for peak-matching assignments, but up to now this effort is still under development. Nevertheless, all of the above developments illustrate the demand for better and faster resonance assignment approaches.

At the outset, it is noted that, computational methods to automatically correlate pairs of lower dimensional NMR data sets through their common axis have been demonstrated by calculating the linear correlation coefficient between two time domain series, such as COBRA (COrrelation Based Reconstruction Algorithm)[ 13 ], or the covariance between two frequency or time domains, e.g. Generalized Indirect Covariance (GIC) NMR.[ 14 ] Both involve sophisticated formulas and algorithms. Our objective here is to provide an alternative that is easier to implement using existing common NMR processing and analysis tools.

Here we present a rather simple and practical idea for protein sequential spin assignments based on the principle of a cross-spectrum calculation to replace the resonance-matching step. Instead of calculating the cross-correlation from two time series,[ 13 ] we employ a fast-Fourier-transform algothrim which allows the equivalent cross-correlation calculation using frequency domain spectra.[ 15 ] The cross-spectrum is very useful in revealing correlations in spectra of related time series.[ 16 ] If a common frequency component exists in all of the related time series, a peak will result at that given frequency in the Fourier transform of the cross-correlated time series. This simplifies identification of the common frequencies. Sequential backbone assignment generally requires identification of common frequencies such as CA and CB for a given residue in multiple time function experiments, for example, as in inter-residue correlations expressed in HNCACB and HN(CO)CACB spectra. Therefore it seems fitting to employ the cross-spectrum approach for sequential assignment purposes.

The cross-spectrum can be calculated most easily in the frequency domain, as the simple product of the frequency functions. Specifically, the cross-spectrum is formed via point-by-point multiplication between the common axes where the frequencies are to be compared. For example, the cross spectrum of two 2D spectra H(N)CO and H(NCA)CO will be a pseudo 3D spectrum whose axes are H N of residue i , H N of residue i −1, and the common C′ chemical shift of residue i −1 (nuclei such as nitrogen contained within the parenthesis in the description of the NMR experiment are involved in magnetization transfer but do not evolve under chemical shift). The strong cross peaks in the cross-spectrum will have their coordinates corresponding to H N chemical shifts of both residues i and i −1, which unambiguously provides the backbone assignment. Furthermore, the cross-spectrum of two 3D spectra, e.g. HNCO and HN(CA)CO, will be a pseudo 5D spectrum whose axes are H N and N of residue i , H N and N of residue i −1, and the common C′ chemical shift of residue i −1. Similarly, the sequential connection can also be established by calculating the cross-spectrum where the carbon axes containing CA and CB chemical shifts are convolved, leading to the complete backbone resonance assignments.

Methods and Results

We demonstrated the applicability of the cross-spectrum approach in protein backbone sequential assignments using 2D H(N)CO, H(NCA)CO, H(NCO)CACB, and H(N)CACB spectra collected on a 15 N/ 13 C double-labeled Ubiquitin sample. NMRPipe[ 17 ] was used for all data processing and spectral multiplication. Figures of NMR spectra were prepared using NMRWish scripts within the NMRPipe package.

Cross-spectrum through Carbonyl Carbon

Shown in Figure 1A and 1B are small regions of the H(N)CO and H(NCA)CO 2D spectra, respectively. The through-bond J -correlations are between H i (H now denotes HN) and C′ i −1 within the H(N)CO spectrum, and primarily between H i −1 and C′ i −1 within the H(NCA)CO spectra. For example both resonances in red in Figure 1A and 1B have the same C′ chemical shift of 176.0 ppm from residue Q2. They indicate connection between amide protons of I3 ( Figure 1A ) and Q2 ( Figure 1B ) at chemical shifts of 8.30 ppm and 8.95 ppm, respectively. The cyan resonance in Figure 1B yields the same i / i −1 correlation as H(N)CO in Figure 1A does, but it usually bears weaker intensity than the intra-residue connection. This is due to the smaller two-bond J NC〈 coupling. The objective is to calculate the cross-spectrum through the carbonyl carbon C′ i −1 so that we can correlate sequential proton resonances. The pseudo 3D cross-spectra, H i -H i −1 -C′ i −1 , were calculated using Equation (1) and the real part of the two Fourier-transformed 2D spectral matrices, S H(N)CO and S H(NCA)CO . In Equation (1) i and k index the H i and C′ i −1 axes of the 2D H(N)CO matrix ( S H(N)CO ), respectively, while j and k index H i −1 and C′ i −1 axes of the 2D H(NCA)CO matrix ( S H(NCA)CO ), respectively. Since the same carbon indexing k is used in both 2D spectra, it is essential to keep the measurement conditions, chemical shift range and digital resolution identical for each related axis by suitable acquisition and processing. The calculated 3D matrix S cross kept both proton dimensions ( i and j ) and obtained a new crossed carbon dimension ( k ) through point-by-point multiplication. As a result, axes H i and H i −1 were preserved from both spectra of H(N)CO and H(NCA)CO, respectively, and the new C′ i −1 dimension encodes the cross-correlated or convoluted axis.

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Illustrations of cross-spectrum based sequential resonance assignment using 2D spectra of H(N)CO ( A ) and H(NCA)CO ( B ). The resonances in red correlate H-I3 and C′-Q2, and H-Q2 and C′-Q2 in A and B , respectively. The cyan resonance in B is the inter-residue cross peak and provides the same correlation as the red peak in A . Both 2D spectra were multiplied according to Equation (1) to produce the pseudo 3D cross-spectrum H i -H i −1 -C′ i −1 . Part of the 2D projection of the cross-spectrum onto H i and H i −1 dimensions is shown ( C ). The red resonance peak in C represents the cross peak yielding correlation between H-I3 and H-Q2. The cyan resonance peak in C is the diagonal peak at chemical shifts of H-I3. The 1D slice at C′-Q2 chemical shift of 176.0 ppm and H-I3 chemical shift of 8.30 ppm from the 3D cross-spectrum illustrates the correct diagonal peak (cyan) and the cross peak (red) for Q2-I3 sequential proton assignment ( D ). The 2D experiments were collected on a 0.5-mM 15 N/ 13 C labeled Ubiquitin sample at 22.5 °C using a Bruker DMX600 spectrometer equipped with a room-temperature TXI probe equipped with a xyz-gradient. Pulse sequences for HNCO[ 20 ] and HN(CA)CO[ 21 ] experiments were used without chemical shift evolution on nitrogen dimension. Proton and carbonyl carbon carrier were at 4.76 ppm and 175.46 ppm, respectively. Spectral widths of 6602 Hz and 1786 Hz were used for proton and carbon, respectively. Data matrices used were 640*256* (* denotes complex points) for both experiments. Total experimental time were 2 hours and 10 hours for H(N)CO and H(NCA)CO, respectively. Proton and carbon dimensions were apodized with cosine-squared and cosine functions respectively, the data matrices were zero-filled to 2048*512* points prior to Fourier transformation, and only the data corresponding to the proton chemical shift range of 9.7 ppm to 5.7 ppm was retained. The multiplications between the two spectra were carried out using NMRPipe. The final size of the 3D cross-spectrum was 793793512 for H i , H i −1 , and C ′ i −1 , respectively.

Shown in Figure 1C is a region of the 2D projection of the pseudo 3D cross-spectrum H i -H i −1 -C′ i −1 onto the H i and H i −1 dimensions, displaying the same proton chemical shift range as the spectra in Figure 1A and 1B . The two red peaks in Figure 1A and 1B are now correlated in a single resonance also indicated in red in Figure 1C , which correlates proton chemical shifts of Q2 and I3 along H i −1 and H i axes, respectively. The cyan diagonal peak of Figure 1C originates from the red peak in Figure 1A and the cyan peak in Figure 1B , and it is much less enhanced after multiplication. The cyan diagonal peak provides the chemical shifts of H-I3 and C′-Q2 only and does not carry any assignment connectivity. The correct cross peak providing connectivity can be identified by its strong intensity in the cross-spectrum. In this example, since we only use the 2D versions of these heteronuclear NMR experiments, diagonal peak coordinates are needed to identify a 1D vector along the H i −1 dimension for resonance intensity evaluation. For instance, the position of the diagonal peak, C′ i −1 at 176.0 ppm and H i at 8.30 ppm (the red peak in Figure 1A ) was used to identify the proper 1D vector/slice ( Figure 1D ) from the 3D cross-spectrum, that readily shows the resonance at 8.95 ppm for H i −1 (identified in red) to be the strongest cross peak ( Figure 1D ). In this C′-only example with Ubiquitin, this simple “strongest cross peak” criterion produces the correct sequential assignment for about 75% of the residues. Exceptions occur due to resonance overlap in C′ i −1 dimension, as well as relaxation effects which change peak intensities and linewidths. One exception example is shown in Figure 2A , where the correct cross peak for T7/L8 (colored red) is not the strongest one.

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Examples of T7–L8 amide proton sequential assignment using three cross peaks from two pseudo 3D cross-spectra, H i -H i −1 -C ′ i −1 and H i -H i −1 -CA i −1 CB i −1 . The 1D slices were extracted at chemical shifts of H of L8 and that of C′ ( A ), CA ( B ), and CB ( C ) of T7. Cross peaks in red correlate T7-L8 amide proton chemical shifts. Cyan peaks are diagonal peaks of H of L8. Noting the consensus agreement among them for the proton chemical shift of T7 at H i −1 axes. Pulse sequences for HNCACB[ 22 ] and HN(CO)CACB[ 23 ] experiments were used without chemical shift evolution on the nitrogen dimension. Proton and carbon carrier were at 4.75 ppm and 43.98 ppm, respectively. Spectral widths of 7212 Hz and 10000 Hz were used for proton and carbon, respectively. The size of the data matrices were 640*180* for both experiments. Total experimental time were 8 hours and 9 hours for H(N)CACB and H(NCO)CACB, respectively. Data processing details were similar to those for H(N)CO and H(NCA)CO given in Figure 1 . The final size of the 3D cross-spectra were 811811512 for H i , H i −1 , and CA i −1 CB i −1 , respectively.

Verification using Cross-spectrum through CA and CB

The resonance overlap problem can be reduced substantially if a suitable complementary cross-spectrum exists. To illustrate this, 2D spectra of H(NCO)CACB and H(N)CACB were collected and multiplied similarly to produce pseudo 3D cross-spectrum, H i -H i −1 -CA i −1 CB i −1 . Shown in Figure 2B and 2C are the 1D-slices corresponding to CA and CB cross-spectrum for T7/L8 connectivity, respectively. The correct cross peaks, shown in red ( Figure 2 ), from all three slices of the cross-correlation spectra yield the same H i −1 chemical shift. Ambiguities such as the one illustrated in Figure 2A can be resolved immediately. In fact when both H i -H i −1 -C′ i −1 and H i -H i −1 -CA i −1 CB i −1 cross-spectra were employed together, all observed peaks from Ubiquitin could be assigned correctly.

Discussions

We have demonstrated a simple, general-purpose cross-spectrum method for protein heteronuclear backbone sequential resonance assignment on 13 C and 15 N labeled Ubiquitin. This approach replaces peak-matching steps commonly used during manual- and auto-assignment. Four Fourier-transformed 2D spectra were used to calculate two pseudo 3D cross-correlated spectra (cross-spectra). Here a single Tcl-tk script within NMRPipe converts two real-FT spectra into one cross-spectrum in the same format as any regular NMR spectrum. We then directly read out the chemical shift of H i −1 spins from strong cross peaks at the proper 1D-slice given by the H i -C i −1 position within the pseudo 3D spectra. The use of two cross-spectra through C′ and CA/CB allows valid cross-peaks to be differentiated from accidental correlations, so that assignments can be generated unambiguously. The signal to noise ( S/N ) of the cross-peak of interest ( S/N cross = S/N A × S/N B ) is significantly improved compared to its parent spectra. This feature always distinguishes the strongest peaks from the parent spectra that are capable of yielding the right cross-peak. For instance a weak resonance peak in one experiment can be significant if multiplied by a relatively intense resonance peak in the other.

We do need to point out that other methods, COBRA[ 13 ] and covariance [ 14 ], reveal correlations between two spectra as well, and all share the same principle of cross-correlation. In fact, the summation over k in Equation (1) would yield covariance NMR. Here we chose not to collapse the correlation dimension k , the carbon axis, because it is essential in our cross-spectrum method to use the C i −1 chemical shift values for choosing the proper diagonal and cross-peaks. In addition, the cross-spectrum implementation described here is free of any adjustable parameters that need to be taken care of in sophisticated manners. For example, in COBRA, the optimal phase value in calculating phase-weighted correlation coefficient has to be empirically determined; in the GIC method, the matrix exponential factor λ needs optimization.

The cross-spectrum approach holds further potential in automatic peak assignment. Accuracy of peak position will depend on the signal to noise of a given spectrum. Therefore when one compares two spectra with different signal to noise profiles, it is rather difficult to use a single value for deviation of peak positions to decide whether two resonances are related. Ideally an evaluation that takes into account relative peak intensities is preferred. Our cross-spectrum implementation inherently affords the quantification of correlations in the cross-spectra from intensity and line width information of the parent spectra. Figure 3 shows the simulated cross-peak intensities as a function of frequency offsets between two peaks. The cross-spectrum intensity provides a possible function for assignment evaluation (e.g.: the use of a intensity cutoff as a criteria). The further cross (multiplication) of cross-spectra (for instance spectra in Figure 2 along the proton axis) can differentiate between valid cross-peaks and accidental correlations because only the real (red resonance peak in Figure 2 ) cross-peak will be further enhanced. This is in contrast to the conventional assignment procedure, where the resonance intensity and line width are often not used to assist in evaluation.

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Simulated cross-peak intensity as a function of frequency difference between two resonances. Simulation parameters were set to follow spectral width typically used for the carbonyl carbon in real experiments at a 600 MHz spectrometer. Time series (e -i⌉t ) were simulated with 64 pairs of complex points at a sampling interval of 667 micro-seconds. The reference peak was at zero frequency. FID was then zero-filled to a total of 512 points and Fourier-transformed. The reference peak line-width at half-height was 26 Hz. The other peak carried an offset ranging from -26 Hz to 26 Hz and was identically processed as the reference spectrum. The cross-spectrum was calculated with point-by-point multiplication between two 1D spectra. All intensities were normalized to the reference peak. Each point in the figure corresponds to relative intensity of the cross-spectrum peak versus the offset expressed in fractions of peak line-width. MATLAB 2007b (Mathworks, MA) was employed for the simulation.

Previously, Szalma and Pelczer [ 18 ] proposed a reconstruction of a 3D solid from a pair of 2D spectra using Boolean algebra. This was done to recover the full J -coupled spin network from 2D H,H-COSY and H,C-COSY. The 2D spectra were converted to Boolean matrices that identify peak positions. The method then searches for correlations of peak positions in these matrices that allow the reconstruction of the full 3D solid correlation matrix. By contrast, our cross-spectrum method generates correlations directly without the need for systematically searching through spectra and matching peak positions.

The cross-spectrum method can easily be extended to accommodate larger and more complicated molecular systems. For example, it is clear in the illustration used here that the diagonal peak identification would be much easier to perform if an additional nitrogen dimension is used. In this analysis, the cross-spectrum will be five dimensions, H i -N i -H i −1 -N i −1 -C i −1 , with cross peaks readily identifying assignments. The cross-spectrum approach can also be extended to other assignment tasks. For instance inclusion of side chain experiments such as CC(CO)NH[ 19 ] and its cross-spectrum with CA and CB resonances in the typical backbone experiments could assist with side chain assignments. Potentially, this can also be applied to the combination of NOESY and TOCSY types of experiments to extract distance information, unambiguously. In all these experiments, we can envision general-purpose spectral viewing and analysis schemes which generate and display suitable regions of the cross-spectra “on the fly” rather than pre-computing entire spectral products with five or more dimensions.

Acknowledgments

We thank Xiongwu Wu, Melvin J. Hinich, Robert Gahl and Yang Shen for helpful discussions. This work was supported by the Intramural Research Program of the NIH, National Heart, Lung, and Blood Institute.

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Integrated Structural Biology

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1.1 Deciphering Resonance Assignment: The What, Why and How?

1.2 routine backbone assignment, 1.2.1 backbone sequential walk for small proteins (<25 kda), 1.2.2 backbone sequential walk for larger proteins (>25 kda), 1.2.3 amino acid type identification and resonance assignment, 1.2.4 selective isotopic labeling and unlabeling of individual amino acid types, 1.2.5 secondary structure assessment, 1.3 routine side-chain assignment, 1.3.1 assignment of aliphatic spin systems, 1.3.2 choice of the tocsy sequence, 1.3.3 assignment of aromatic spin systems, 1.4 new frontiers in backbone resonance assignment of proteins, 1.4.1 metabolic labeling using pyruvate to mitigate 13 c homonuclear coupling, 1.4.2 incorporating additional information on the ca resonance by band-selective ca/cb decoupling, 1.5 new developments for side-chain assignment, 1.5.1 new ideas for side-chain assignment, 1.5.2 structure-guided assignment of methyl groups, 1.6 covariance nmr for resonance assignment, 1.7 strategies for assignment of intrinsically disordered proteins, 1.7.1 higher dimensionality experiments, 1.7.2 13 c-direct detected strategies for resonance assignment, 1.7.3 direct 15 n detection: exploiting slow relaxation properties and absence of homonuclear coupling for enhanced resolution at high magnetic fields, 1.8 conclusion, note added after first publication, chapter 1: decoding atomic addresses: solution nmr resonance assignment of proteins.

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T. Viennet, A. Dubey, R. Törner, M. A. Droemer, P. Coote, D. P. Frueh, ... H. Arthanari, in Integrated Structural Biology, ed. T. Polenova, C. M. Quinn, and A. M. Gronenborn, Royal Society of Chemistry, 2023, vol. 30, ch. 1, pp. 1-42.

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NMR is a powerful analytical technique that permits the exploration of biomolecules under physiological conditions with atomic resolution. It is especially applicable for examining protein structures and their interactions and dynamics in environments closely resembling their native state, extending its utility to uniquely study disordered proteins. Nevertheless, to extract atomic resolution details, one must successfully correlate observed resonances with their originating nuclei, a process known as ‘resonance assignment’. Even with over fifty years of technical advancements, resonance assignment frequently becomes a bottleneck in the utilization of NMR for the comprehensive study of structure, dynamics, and interactions. In this context, we delve into both the traditional methods and the emerging frontiers in protein resonance assignment strategies for solution NMR. Our goal is to provide a comprehensive view of the existing experimental methodologies, with a focused discussion on their strengths and potential limitations. In this chapter, we will strictly focus on resonance assignment strategies for proteins.

Resonance assignment signifies the process through which an NMR signal at a certain resonance frequency, or chemical shift, is correlated to a specific atom in a protein. The resonance frequency depends, quite naturally, on the type of nucleus involved – such as 1 H, 13 C, or 15 N – but also hinges on the precise chemical environment of the nuclei, which in turn is dictated by the three-dimensional structure of the molecule. This aspect renders the chemical shift particularly sensitive to modifications in the molecular structure, dynamics, and interactions. The true power of NMR lies in its potential to chart these changes to the chemical shift, providing an atomic resolution picture of proteins. However, actualizing this potential necessitates a thorough understanding of the point of origin of the resonance, commonly referred to as its assignment.

For small to medium-sized proteins, ranging from 500 to 2000 Da, which are gaining prominence as a new pharmacological modality, resonance calculations can be performed using a blend of quantum mechanics, such as density functional theory, and empirical data. These calculations take into account various factors like the structure and solvent. However, predicting chemical shifts with the necessary precision and creating an assignment solely based on computational methods remains a challenge, particularly for molecules containing chemically similar moieties. Therefore, a combination of homonuclear 1 H– 1 H 2D experiments, including DQF-COSY, TOCSY, and NOESY/ROESY, is usually employed for resonance assignments of such small to medium-sized molecules.

When we consider a polypeptide and focus specifically on the i th amino acid residue, the majority of protons within that amino acid are part of a single 1 H– 1 H 3 J scalar coupling network. Given the unique side-chain structure of each amino acid residue, the 3 J spin coupling patterns and chemical shifts can be utilized to determine the amino acid type. However, these 3 J scalar coupling networks are separated by amide bonds, and as such the connection between amino acid residues cannot be determined using 1 H– 1 H scalar couplings alone. This connectivity is instead defined by the spatial proximity of protons from the i th to the i  − 1th residue, as identified through dipolar coupling-mediated NOESY/ROESY experiments. Regardless of the secondary structure, proton pairs within a 4 Å distance can be found between the i th and i  − 1th residues. Therefore, a NOESY spectrum can effectively establish sequential connectivity between neighboring residues in polypeptides. It is worth noting that NOESY/ROESY-based sequential assignment strategies have also been established for nucleic acids. However, strategies that rely exclusively on proton resonances face limitations due to the pronounced chemical shift degeneracy of proton resonances and the challenge of distinguishing sequential NOEs from long-range NOEs from non-sequential amino acids as a result of the tertiary structure. As a result, this strategy is generally applicable up to peptides consisting of around 50 amino acid residues and becomes difficult to apply for larger proteins and nucleic acids. It should be noted that for proteins in this size range isotopic labeling is not required.

Pioneering advancements in stable isotopic labeling, NMR instrumentation, and novel NMR methods have significantly expanded the molecular weight range for resonance assignments. Protein NMR spectroscopists utilize an array of experiments specifically designed for assigning protein residue resonances, factoring in the system’s molecular weight and relaxation rates. These experiments necessitate isotopic enrichment of proteins with 13 C, and 15 N, enabling a sequential walk along the protein backbone by correlating the amide 1 H N – 15 N resonances of a given residue to that of its predecessor. This is achieved by transferring magnetization through 13 CA nuclei and encoding 13 CA, 13 CO, or 13 CB resonances, as demonstrated in the triple-resonance experiments (refer to Figure 1.1 ). This approach to resonance assignment capitalizes on the fact that there is substantial scalar coupling between the amide nitrogen nuclei and its corresponding CA nuclei, as well as the CA nuclei of the preceding amino acid. The goal of this chapter is to provide a comprehensive review of both the currently available experiments and novel methodologies employed for protein resonance assignments in solution NMR. This resource is intended for the biomolecular NMR community, and it assumes that the reader possesses a fundamental understanding of protein NMR.

Schematic workflow for protein backbone resonance assignment. Each cross-peak in a 15N–1H HSQC spectrum (allocated random numbers #1–4) is inspected in a third 13C dimension visualized as a strip at given 1H and 15N chemical shifts. The combination of different spectra allows the attribution of cross-peaks to the given 13CA, 13CB and 13CO chemical shifts of the own and previous spin systems. This information is used to classify spin systems in groups of amino acid types and to sort spin systems in their order in the primary sequence. Finally, this information is mapped onto an unambiguous suite of residues in the primary sequence and cross-peaks are assigned to their corresponding residues. Assignments are then used to understand the protein secondary structure and topology or to map interactions and dynamics onto the primary sequence (or 3D structure if known).

Schematic workflow for protein backbone resonance assignment. Each cross-peak in a 15 N– 1 H HSQC spectrum (allocated random numbers #1–4) is inspected in a third 13 C dimension visualized as a strip at given 1 H and 15 N chemical shifts. The combination of different spectra allows the attribution of cross-peaks to the given 13 CA, 13 CB and 13 CO chemical shifts of the own and previous spin systems. This information is used to classify spin systems in groups of amino acid types and to sort spin systems in their order in the primary sequence. Finally, this information is mapped onto an unambiguous suite of residues in the primary sequence and cross-peaks are assigned to their corresponding residues. Assignments are then used to understand the protein secondary structure and topology or to map interactions and dynamics onto the primary sequence (or 3D structure if known).

The early 1990s marked a significant period in protein NMR assignment as key technologies became readily available for these experiments. One major advancement was the recombinant expression of proteins, which facilitated isotope labeling and thereby expanded NMR-visible nuclei from solely 1 H to include 1 H, 13 C, and 15 N. This expansion introduced an additional dispersion of resonances along these heteronuclear dimensions and enabled the use of 15 N– 13 C heteronuclear couplings for scalar coupling-based sequential assignments, as opposed to the older NOE-based method. This method made sequential assignments of macromolecules more streamlined and reliable.

Simultaneously, NMR spectrometer hardware evolved, increasing its power both in terms of magnetic field – with magnets capable of reaching up to a 600 MHz 1 H Larmor frequency – and probe design, which now included 4-channel probes for 1 H, 13 C, and 15 N triple-resonance experiments and 2 H lock/decoupling. Lastly, all the essential components of triple-resonance pulse sequences were developed. These include efficient magnetization transfer schemes such as INEPT 1   and TOCSY; 2   heteronuclear decoupling using continuous wave 3   or composite pulses; 4   homonuclear decoupling using constant-time evolution; 5   water suppression schemes such as WATERGATE 6 , 7   and excitation sculpting; 8 , 9   sensitivity enhancement blocks (preservation of equivalent pathways or PEP); 10 , 11   and quadrature detection and phase cycling schemes. 12 , 13  

In conjunction, these advancements resulted in the development of an initial set of triple-resonance experiments in the early 1990s. This suite of experiments is still in routine use today, with new methods continually being explored (as reviewed in Sections 1.4 and 1.5 ). In this chapter, we will delve into the optimal experiment suite for achieving a backbone sequential walk for both small and larger proteins, and explain how to garner amino acid type information to achieve assignment.

For small folded proteins up to approximately 25 kDa, their favorable relaxation properties and low spectral crowding allow them to be readily assigned without deuteration using the simplest set of triple-resonance experiments. Essentially, three sets of correlations are generated to match the spin system of a given residue i (H i , N i , CA i , CO i , and CB i ) to the carbon chemical shifts of the preceding residue in the primary sequence (CA i −1 , CO i −1 , and CB i −1 ). These chemical shifts are then used to find the corresponding spin system of residue i  − 1, including the amide chemical shifts (H i −1 , N i −1 ). This procedure is reiterated until an unambiguous stretch of residues can be mapped onto the primary sequence, and the spin system can be assigned to specific residues (refer to Figure 1.1 ). The following set of experiments are employed:

2D 15 N– 1 H HSQC: this experiment correlates the chemical shifts of amide 1 H and amide 15 N for each residue. This acts as the protein fingerprint as one residue yields one cross-peak (Pro is not present, and Trp, Gln, Lys, Asn, and Arg provide additional side-chain cross-peaks). 14  

3D HNCA: an INEPT is used to transfer magnetization from 15 N to 13 CA. Given the proximity of the J -coupling values for the intra-residue N i –CA i (around 11 Hz) and sequential N i –CA i −1 (around 8 Hz), it correlates an HSQC cross-peak to the preceding CA i −1 and its own CA i resonances. 15  

3D HNCO: in contrast to HNCA, the J -coupling value of the intra-residue N i –CO i pair is too low for efficient magnetization transfer, so HNCO only correlates a 15 N– 1 H HSQC cross-peak to the preceding CO i −1 resonance. 9 , 15  

3D HN(co)CA: magnetization is first transferred to CO i −1 but is not encoded. Instead, it is transferred again to CA, establishing correlation of a 15 N– 1 H HSQC cross-peak to the preceding CA i −1 resonance. 16   Due to the utilization of two strong 1 J NCO and 1 J COCA couplings, HN(co)CA is often more efficient than HNCA, particularly for small proteins in low magnetic fields (<800 MHz) (see Figure 1.2A ).

3D HN(ca)CO: magnetization is initially transferred to both CA i and CA i −1 but is not frequency-encoded. It is instead transferred again to CO, correlating a 15 N– 1 H HSQC cross-peak to both CO i and CO i −1 resonances. 17  

3D HNCACB: extending from HNCA, magnetization is further transferred from CA to CB using an INEPT and the approximately 35 Hz CA–CB J -coupling. This experiment can be tuned to achieve either both CA and CB encoding (half transfer) or CB-only encoding (full transfer). The latter often exhibits better sensitivity in detecting CB resonances for small proteins, despite requiring twice longer coherence transfer steps. It correlates a 15 N– 1 H HSQC cross-peak to the preceding CB i −1 and its own CB i resonances. 18  

3D HN(coca)CB: magnetization is transferred to CO, then CA, and finally to CB, which enables the correlation of a 15 N– 1 H HSQC cross-peak to solely the preceding CB i −1 resonance. 19  

Considerations in the sensitivity of triple-resonance experiments. (A) Relative first scan sensitivity of regular out-and-back experiments for small proteins (here GB1) at 600 MHz. (B) Relative first scan sensitivity of 1HN TROSY-based experiments for large deuterated proteins (here MBP) at 800 MHz. (C) 13C strips for selected GB1 residues exemplifying the relative intensities of 3D cross-peaks from different experiments (top) and statistical analysis of all non-overlapped 3D cross-peak intensities for GB1. (D) Magnetic field dependence of the relative signal height of TROSY and non-TROSY 1HN detected experiments. (E) NaCl concentration dependence of the relative signal height of 1HN and 15NH TROSY detected experiments.

Considerations in the sensitivity of triple-resonance experiments. (A) Relative first scan sensitivity of regular out-and-back experiments for small proteins (here GB1) at 600 MHz. (B) Relative first scan sensitivity of 1 H N TROSY-based experiments for large deuterated proteins (here MBP) at 800 MHz. (C) 13 C strips for selected GB1 residues exemplifying the relative intensities of 3D cross-peaks from different experiments (top) and statistical analysis of all non-overlapped 3D cross-peak intensities for GB1. (D) Magnetic field dependence of the relative signal height of TROSY and non-TROSY 1 H N detected experiments. (E) NaCl concentration dependence of the relative signal height of 1 H N and 15 N H TROSY detected experiments.

A significant limitation of the assignment routine that involves collecting four to six 3D triple-resonance experiments is the associated measurement time. Therefore, speeding up data collection can be particularly beneficial. Established non-uniform sampling schedules 20   and reconstruction algorithms 21–24   can be deployed to achieve a substantial time reduction, approximately tenfold, for 3D experiments.

Furthermore, the principle of SOFAST, 25   or band-selective excitation short-transient (BEST), can be applied to backbone assignment experiments. In essence, the magnetization of aliphatic and solvent 1 H nuclei is left undisturbed, achieved through the use of narrow bandwidth amide-selective shaped pulses. This strategy serves as a reservoir to accelerate the T 1 relaxation of amide protons, thereby minimizing inter-scan delays. A full suite of BEST triple-resonance experiments is available for use. 26  

The following out-and-stay experiments are available:

3D (hbha)CBCANH: this experiment correlates a 15 N– 1 H HSQC cross-peak to the previous CB i −1 /CA i −1 and the own CB i /CA i resonances. 27  

3D (hbha)CBCA(co)NH: this correlates a 15 N– 1 H HSQC cross-peak to the previous CB i −1 /CA i −1 resonances. 27  

For proteins larger than approximately 25 kDa, slower tumbling in solution leads to unfavorable relaxation properties and losses in both sensitivity and achievable resolution. These factors collectively render sequential assignment challenging. However, this issue can be circumvented through perdeuteration of proteins expressed in bacteria, followed by their exchange into a protonated buffer solution (back exchange). This process results in samples where labile amide hydrogens are NMR active ( 1 H), but background aliphatic/aromatic deuterons remain invisible to conventional triple-resonance experiments ( 2 H). Effectively, this removes the contribution of side-chain 1 H nuclei to relaxation, and the impact of the 2 H– 13 C J -coupling in aliphatic spin systems can readily be eliminated using 2 H decoupling during 13 C evolution. Deuteration renders “out-and-stay” type experiments unfeasible, thereby necessitating sole reliance on “out-and-back” experiments.

A crucial aspect of protein perdeuteration is the back-exchange process, through which amide protons are re-protonated by interacting with the solvent. This process often fails for amide groups concealed within the core of well-structured proteins, rendering these residues undetectable to triple-resonance experiments. It is critical to ensure sufficient back-exchange by comparing the number of cross-peaks on the 15 N– 1 H HSQC spectrum of the deuterated sample with that of its protonated counterpart. To optimize back-exchange, the sample may be exposed to high temperature and basic pH to increase the rate of exchange. Alternatively, or additionally, mild denaturing conditions (1–2 M GdnHCl or urea) can be applied to ‘open’ the protein core and increase the accessibility of the buried amide groups. However, it is crucial to test and optimize these procedures for each sample, as some proteins may lack stability under these conditions.

Furthermore, TROSY selection instead of 15 N decoupling during 1 H-direct detection becomes advantageous for larger proteins, where the slowest relaxing component has increased resolution and signal-to-noise ratio. A suite of experiments employing both TROSY and BEST approaches is available but generally does not support 2 H decoupling and is thus advantageous mostly for larger disordered proteins (see Section 1.7 ). 28   BEST experiments depend on aliphatic hydrogens to serve as a sink, assisting in the rapid longitudinal relaxation of the amide hydrogens. This effect is absent when deuterated, necessitating reliance on bulk water as a sink, which is effective for disordered proteins. The routine experiments with TROSY selection and 2 H decoupling are as follows:

2D 15 N– 1 H TROSY-HSQC: this correlates the chemical shifts of amide 1 H and amide 15 N. 29  

3D TROSY HNCA 2H : this correlates a 15 N– 1 H HSQC cross-peak to the previous CA i −1 and the own CA i resonances. 30 , 31  

3D TROSY HNCO 2H : this correlates a 15 N– 1 H HSQC cross-peak to the previous CO i −1 resonance. 31 , 32  

3D TROSY HN(co)CA 2H : this correlates a 15 N– 1 H HSQC cross-peak to the previous CA i −1 resonance. 31 , 32  

3D TROSY HN(ca)CO 2H : this correlates a 15 N– 1 H HSQC cross-peak to both CO i and CO i −1 resonances. 31 , 32  

3D TROSY HNCACB 2H : this correlates a 15 N– 1 H HSQC cross-peak to the previous CB i −1 and the own CB i resonances. 31–33  

3D TROSY HN(coca)CB 2H : this correlates a 15 N– 1 H HSQC cross-peak to only the previous CB i −1 resonance. 31 , 33  

The optimal field strengths for TROSY have been estimated to be on spectrometers operating around 900 MHz (21.14 T) for the 1 H N TROSY. 29   This initial rationale was based on the consideration of where the quadratic B 0 field dependences of the TROSY relaxation rates reach a minimum. The optimal DD-CSA interference gives rise to the longest transverse relaxation times ( T 2 ) of TROSY components at this magnetic field strength. However, in terms of sensitivity, the peak height is not only directly proportional to T 2 but also dependent on the strength of the magnetic field by B 0 3/2 . Therefore, the sensitivity is proportional to the product of T 2 ( B 0 ) and B 0 3/2 and shifts the maximum of the peak height significantly to a higher field. Considering this effect, the maximum sensitivity of the 1 H N TROSY shifts to around 1.5 GHz. 34   Theoretical estimates clearly show the advantage of higher-field magnets, above 1 GHz ( Figure 1.2D ); however, in practice, this gain in sensitivity for 1 H-detected TROSY can be partly offset by adverse ionic strength effects in high Q -factor probes at higher field strengths ( Figure 1.2E ). One should also consider the contribution of additional relaxation due to exchange broadening ( R ex ). This is especially true when the exchange is fast on the NMR time scale, where R ex is proportional to the field strength. In such a case, the advantages of higher-field magnets are lower in magnitude, while the field dependencies are largely unchanged. Furthermore, while the 1 H N TROSY prefers high field, 13 CO resonances suffer from the large contribution of CSA to their transverse relaxation rates which scales up quadratically with the magnetic field. More generally, one should consider the effect of the magnetic field strength on the relaxation of each coherence participating in transfer periods when assessing the sensitivity of multidimensional experiments.

Chemical shift statistics for nuclear spins in the protein backbone. Data are grouped by amino acid type and secondary structure and their mean value ± one standard deviation is plotted. Note that 13CA and 13CB are plotted on the same panel but are easily distinguishable (13CA 45–65 ppm; 13CB 15–45 ppm), except for Ser/Thr which have 13CB around 62–72 ppm.

Chemical shift statistics for nuclear spins in the protein backbone. Data are grouped by amino acid type and secondary structure and their mean value ± one standard deviation is plotted. Note that 13 CA and 13 CB are plotted on the same panel but are easily distinguishable ( 13 CA 45–65 ppm; 13 CB 15–45 ppm), except for Ser/Thr which have 13 CB around 62–72 ppm.

Once the backbone sequential walk has been performed, multiple smaller or longer series of 15 N– 1 H HSQC cross-peaks that have been linked together in their primary sequence order are available. In practice, it is often impossible to create a single series spanning the whole primary sequence due to missing cross-peaks in the spectra and to the presence of Pro residues which by essence do not have 15 N– 1 H HSQC cross-peaks. To assign these series of cross-peaks onto the primary sequence, one needs amino acid type information that can fortunately be extracted from the chemical shifts measured for each spin system ( Figure 1.1 ).

The Biological Magnetic Resonance Data Bank (BMRB) 35   is a public archive of chemical shifts of proteins, nucleic acids and metabolites. It is used for depositing, querying, and extracting chemical shift data and currently has over 6000 protein data sets. We used the data deposited in BMRB as of April 2023 to calculate the mean and standard deviation of chemical shifts for backbone nuclear spins. Chemical shift values that differ more than 5 standard deviations from the mean were omitted ( ca. 0.04% of the dataset). Ultimately 561 776 1 H, 431 739 1 HA, 529 242 15 N, 375 712 13 CO, 520 054 13 CA and 460 486 13 CB were used for statistics. Values were grouped by amino acid type and are plotted in Figure 1.3 . All amino acid type and nuclei-specific entries have at least 10 000 chemical shifts. The only exception was Pro where only 2563 chemical shifts of 15 N are available. Notably, the 13 CB chemical shift of Cys shows high standard deviation because Cys exists in oxidized and reduced states. Indeed, it has been shown that the 13 CB chemical shift for oxidized cysteine is 40.7 ± 3.8 ppm and that for reduced cysteine is 28.4 ± 2.4 ppm. 36  

Figure 1.3 reveals the distinctive power of certain nuclear spin chemical shifts. 1 H does not provide information on the amino acid type. However, Gly and Pro can easily be distinguished based on 15 N chemical shifts alone. Next, 13 CO and 1 HA contain little distinguishing power. 13 CA is more useful and a group of amino acid residues (Val/Thr/Pro/Ile) can be identified from their higher chemical shifts. On the other hand, 13 CB has the highest amino acid type dependence. Six categories can be made using 13 CB chemical shifts: Ala; Glu/Gln/His/Lys/Met/Pro/Arg/Val/Trp; Asp/Phe/Ile/Leu/Asn/Tyr; Gly; Ser; and Thr. Cys can occur in an oxidized or reduced state which makes it difficult to identify a priori . This classification of amino acid types based on backbone resonances is in practice enough to remove most ambiguities in the assignment of a series of cross-peaks to the primary sequence.

As proteins under study increase in size, spectral crowding and relaxation cause significant challenges that demand attention. The base fingerprint spectrum 1 H– 15 N HSQC may lack sufficient resolution to discern all residues, and more complex spectra such as HNCA and, more crucially, HNCACB – which provides the indispensable amino acid type information necessary for backbone assignment – may become unmanageable due to rapid relaxation. To mitigate these issues, selective labeling of amino acid residues can be deployed to simplify spectra, resolve overlapping resonances, and identify amino acid types. Here we are able to reduce the complexity by isotopically labeling only one type of amino acid. For instance, consider a protein composed of 500 residues, of which 480 are non-proline residues and 25 are valine. With standard labeling, one would observe 480 resonances in the 1 H– 15 N HSQC spectrum. However, if we specifically label valine, we would observe only 25 resonances, significantly reducing the spectral overlap.

Selective amino acid labeling involves introducing stable isotopes ( 13 C and/or 15 N) into only selected types of amino acids in proteins, a departure from the uniform labeling typically carried out for resonance assignment. This approach can easily be implemented in bacterial culture, by adding selected isotope-labeled amino acids into an amino acid-depleted medium like M9, devoid of nitrogen or carbon sources. The remaining amino acids are supplemented in their NMR-inactive form. Generally, a 15 N– 1 H HSQC is utilized as readout and examined for the presence or absence of cross-peaks in differentially labeled samples. This offers a straightforward method for assigning amino types to specific cross-peaks.

The approach can be made more sophisticated by employing different 15 N- and 13 C-labeled amino acids, enabling the identification of specific dipeptides, which provides sequential information in addition to amino acid type information. This technique is referred to as double labeling, 37   for example, to assign three Met residues appearing as different dipeptides in the protein sequence (Met-Cys, Met-Val and Met-Asn), one only needs to produce two samples with 13 C-Met/ 15 N-Val and 13 C-Met/ 15 N-Cys. Modified versions of the double labeling techniques are also available such as combinatorial labeling. 38   This combinatorial labeling can be extended to selectively labeled tripeptides to further eliminate ambiguities in sequence-specific assignment. 39  

The major limitation of selective labeling approaches is the price of isotope-labeled amino acids. To circumvent this problem, selective ‘unlabeling’ of amino acids can be achieved by supplementing 12 C/ 14 N amino acids in otherwise uniformly labeled minimal medium. 40   The resonance of selectively unlabeled residues will disappear from the NMR spectra of the control sample, leading to direct identification of amino acid types. Additionally, experiments were designed to exploit the absence of 12 C– 15 N J -coupling to filter the neighboring residues of unlabeled amino acid residues. If the tripeptide is unique in the protein sequence, resonance assignment is directly achieved. 41   An important concern in labeling/unlabeling strategies is scrambling of isotopes in amino acids through metabolic pathways in the organism expressing the protein of interest. In practice, in Escherichia coli , selective 15 N unlabeling of the following groups of amino acids can be achieved: Arg, Lys, Asn, Gln, His, Met, Ala/Trp, Phe/Tyr, Ile/Leu/Val, Gly/Cys/Ser/Thr. 42   The main source of 15 N scrambling in bacteria is the transaminase and it is typically less active in insect cells and in vitro expression systems, and thus more amino acids can be selectively labeled in these expression systems. It is worth mentioning that the amino acid selective labeling strategy is also established in these systems and contributes the sensitive detection of NMR resonance in large molecular weight proteins that are difficult to express in E. coli . 43   An expression strain that is auxotrophic for a particular amino acid can also be exploited to efficiently incorporate a specifically isotopically labeled amino acid. Today, numerous auxotrophic strains are available that are compatible with the widely-used T7 RNA polymerase overexpression systems, which minimizes metabolic scrambling and facilitates efficient incorporation of labeled amino acids. 44 , 45  

It should be also noted that 13 C is typically less prone to scrambling than 15 N, and thus the number of amino acid residues that can be selectively 13 C-labeled/unlabeled is increased. This can be achieved by adding amino acids that are 13 C-labeled at the carbonyl position to a deuterated minimal medium supplemented with 15 N ammonium chloride (for uniform 2 H– 15 N labeling). Selective TROSY-HNCO cross-peaks can be observed with high sensitivity for amino acid pairs connected by the labeling schemes (combinatorial labeling), and the amide proton resonance of the residue following the 13 C labeled amino acid is very sharp since its HA position is deuterated. This approach is cost effective and has been successfully applied to proteins larger than 40 kDa. 46  

The correlation between the chemical shift and protein secondary structure was experimentally recognized almost fifty years ago. 47   We used our BMRB dataset (April 2023) and, where applicable, assigned SwissProt identifiers to the BMRB entries. These were used to extract experimentally determined residue-specific secondary structure information using the PDB entries referenced in UniProt. Where available, this secondary structure information was used to annotate the original chemical shift entries from the BMRB. This yielded a total of 2 879 009 entries with secondary structure information confirmed by experimental methods, after filtering of outliers (832 703 α-helix, 700 370 β-strand, 103 996 turn; and 1 241 940 unstructured). Figure 1.3 illustrates the power of 1 HA, 13 CA, 13 CB and 13 CO chemical shifts in determining the secondary structure, whereas 1 H N and 15 N do not have strong dependence on the secondary structure.

Several automated methods have been developed to predict the secondary structure of proteins using chemical shifts. We can broadly classify these prediction methods into two categories. The first type of method, akin to circular dichroism, interprets NMR spectra in terms of secondary structure content without requiring sequence assignments. One such approach is the ‘CD-by-NMR’ method, which uses various unassigned 2D NMR spectra to extract information about the secondary structure. Here, an ‘average chemical shift (ACS)’ is computed for each nucleus type, and empirical equations are subsequently used to resolve the proportions of α-helix and β-strand structures. 48  

In contrast, the second category of methods, represented by the ‘chemical shift index (CSI)’ approach, relies on backbone assignments to provide residue-specific secondary structure information. 49   The authors generated a database of chemical shifts from residues known to assume ‘random coil’ conformations. They calculate the secondary shifts of 1 HA, 13 CA, 13 CB and 13 CO for a given residue by subtracting these random coil chemical shifts from the observed shifts. They define threshold values for secondary shifts, beyond which a specific secondary structure is assigned to the residue. This is carried out for each nucleus type, and a consensus is reached for each residue, which is demonstrated to improve accuracy. 50   The strength of the CSI method lies in its ability to specify the location (start and end residues) and type of secondary structure (α-helix, β-sheet, random coil; later expanded to 11 types of secondary and super-secondary structures 51   ). However, the CSI approach does face limitations, including its sensitivity to the chosen thresholds and random coil chemical shift values, as well as the difficulties it encounters with missing or incomplete assignments. Improved methods like PSSI (probabilistic secondary structure identification) 52   partially address these challenges. PECAN (protein energetic conformation analysis using NMR) 53   also mitigates some of these issues by incorporating sequence information and energetics models to refine the boundary determination of secondary structure elements, achieving approximately 90% accuracy in determining residue-specific secondary structure information.

Besides assigning secondary structure types, it can be desirable to calculate actual torsion angles, e.g. for 3D structure determination. Three-bond scalar couplings 3 J HA-HN , 3 J CO-HA and 3 J N-HA directly correlate with torsion angles 54   but are not easily measured in large proteins. Alternatively, chemical shifts of 1 HA, 13 CA, 13 CB and 13 CO can be used to predict torsion angles as done by the software TALOS 55   and its upgraded version TALOS-N (based on neural networks). 56  

Similar to the case of backbone resonance assignment, most experiments still used for assigning side-chain resonances were developed in the early 1990s from newly developed pulse sequence building blocks at the time. The basic idea is to achieve magnetization transfer from the side-chain aliphatic 1 H nuclei to a previously assigned nucleus (from backbone assignment), e.g. , 13 CB or 13 CA. Since the base spectrum here is a 13 C– 1 H HSQC, it is advisable to assign 1 HB/ 1 HA to establish unambiguous HSQC cross-peaks as starting points for the assignment process. As the frequencies of side-chain resonances help to determine the amino acid type, incorporating the side-chain resonance information already during backbone assignment is often useful. Technically, rather than using multiple INEPT steps, isotropic mixing of all 13 C nuclei along the side chain is used to transfer magnetization (TOCSY). 2   We detail the use of TOCSY sequences and their advantages in terms of bandwidth and sensitivity in Section 1.3.2 . This results in correlation of all 1 H or 13 C nuclei along the side chain. Such an approach can result in overly crowded spectra, in which case replacing the TOCSY by a COSY step simplifies the spectra by correlating only pairs of neighboring 13 C nuclei. Notably, for small proteins (less than 10 kDa), the 1 H– 15 N HSQC-TOCSY experiment, which relies on weak coupling between the side-chain hydrogens, is used to achieve resonance assignment of these side-chain hydrogens. 57   This method, however, is not effective for larger proteins due to the challenges posed by relaxation and the requirement for extended TOCSY mixing times, necessitated by the weak scalar coupling between side-chain hydrogens.

The experiments routinely used for side-chain assignment are as follows:

13 C– 1 H HSQC: this correlates the chemical shifts of each 1 H and 13 C pair in aliphatic side chains.

HBHA(cbca)NH: this correlates a 15 N– 1 H HSQC cross-peak to the previous HA/HB i −1 and the own HA/HB i resonances. 58   It is identical to the (hbha)CBCANH experiment, but aliphatic 1 H nuclei are encoded instead of 13 C.

HBHA(cbcaco)NH: this correlates a 15 N– 1 H HSQC cross-peak to the previous HA/HB i −1 resonances. 58  

H(cc)H COSY: this correlates pairs of neighboring 1 H resonances within a side-chain spin system. Magnetization is first transferred from 1 H to their attached 13 C nuclei using INEPT, followed by 90° COSY transfer to the neighboring 13 C nuclei, and then INEPT back to 1 H nuclei for detection. 59  

HC(-c)H TOCSY: this correlates all 1 H resonances within a side-chain spin system. The experiment is identical to H(cc)H-COSY, except that an isotropic mixing between all 13 C nuclei is employed (see Section 1.3.2 ). 60–62  

(h)C-CH TOCSY: this correlates all 13 C resonances within a side-chain spin system. The experiment is identical to H(c-c)H-TOCSY, except that chemical shift evolution happens after the initial INEPT transfer, on 13 C. 60–62  

The approach described above is based on a combination of the most sensitive spectra that can be used to achieve exhaustive assignment of aliphatic side chains; however, it requires prior rigorous assignment of 1 HA/ 13 CA (and 1 HB/ 13 CB) which is not always easy to obtain. For that reason, more complex experiments have been developed that can directly correlate side-chain nuclei to a cross-peak on a 15 N– 1 H HSQC spectrum. The following two experiments are available:

H(c-cco)NH: this correlates all 1 H resonances within a side chain to the successive 1 H i +1 / 15 N i +1 cross-peak of a HSQC. Magnetization is first transferred from 1 H to their attached 13 C via INEPT, then it is mixed between all 13 C nuclei using TOCSY. Finally, magnetization on 13 CA is transferred by successive INEPT steps to 13 CO i −1 , 15 N i −1 and ultimately 1 HN i −1 for detection. 63 , 64  

(h)C-C(co)NH: this correlates all 13 C resonances within a side chain to the successive 1 H i +1 / 15 N i +1 cross-peak of a HSQC. Chemical shift evolution happens after the initial INEPT transfer on 13 C. 63 , 64  

These experiments can readily be combined with TROSY selection for larger proteins; however, they require a protonated sample since they are 1 H-start out-and-stay type. Whenever relaxation is particularly problematic, the equivalent 13 C-start experiment CC(co)NH is available but otherwise suffers from reduced sensitivity due to the lower magnetization of 13 C as compared to 1 H.

To achieve isotropic mixing along the side chain, total correlation spectroscopy (TOCSY) sequences utilize the relatively large and homogenous 1 J CC couplings in aliphatic systems ( ca. 35 Hz). In this system, magnetization transfer is allowed under the Hartmann–Hahn condition, i.e. when the difference in resonance frequencies between neighboring 13 C nuclei is much smaller than 2π 1 J CC ( ca. 220 Hz). 65   However, this is unrealistic in protein samples at high magnetic fields. For example, the aliphatic carbons span about 70 ppm, which corresponds to a bandwidth of about 14 kHz at 18.8 T (800 MHz). The purpose of a TOCSY pulse is thus to remove effective chemical shift differences from the sample, while maintaining at least some of the coupling magnitude. This offers a way to indirectly fulfill the Hartmann–Hahn mixing condition and achieve TOCSY mixing over a larger range of chemical shifts.

The simplest example of a TOCSY pulse is a high-power transverse plane pulse, known as a spin-lock pulse. If this pulse power is much stronger than the chemical shift offsets, then it continually and rapidly reverses the sense of the chemical shifts’ precession. This repeatedly refocuses the dispersion caused by chemical shift offsets. Importantly, this conserves the homonuclear J -coupling evolution so that the effective Hartmann–Hahn condition is satisfied, and TOCSY transfer takes place. This scheme requires an extremely high RF power in the spin-lock pulse to cover experimentally relevant bandwidths. In practice, such RF power levels cannot safely be utilized in NMR spectrometers, 66   and the problem continuously grows with increasing magnetic fields available. This is the reason for the need of improved TOCSY sequences with better effective bandwidths, robustness to RF inhomogeneity, and minimized signal losses from relaxation during the mixing period.

The first composite pulse to achieve broadband mixing by effectively satisfying the Hartmann–Hahn condition worked by repeated application of the 90 x –180 y –90 x compensated inversion element, which has a slightly broader inversion profile than a simple 180° pulse. 67   The compensated inversion elements were arranged into an MLEV-16 supercycle so that the phase of the inversion element was varied systematically, which averages out some of the error, especially around the edges of the bandwidth. The mixing bandwidth of this approach is about 80% of the RF amplitude. 68  

The most widely used mixing pulses in liquid state NMR are DIPSI-2 69   (decoupling in the presence of scalar interactions) and FLOPSY-16 70   (flip–flop spectroscopy). The design principle underlying the DIPSI scheme is to apply an arbitrary sequence of hard pulses with arbitrary duration along a single axis, i.e. , alternating in the plus or minus x -direction. The pulse durations were numerically optimized to maximize the pulse fidelity. The FLOPSY sequence works in a similar way, but the arbitrary sequence of hard pulses is applied with an arbitrary phase. The flip angles and phases were numerically optimized, and improved performance over DIPSI was achieved. The mixing bandwidths of DIPSI-2 and FLOPSY-16 are limited to approximately twice the RF amplitude. 68  

TOCSY sequences behave differently from one another in a variety of ways, such as the offset dependence of transfer efficiency, robustness to RF inhomogeneity, and relaxation effects. Therefore, attempts to quantitatively compare and rank the performance of different sequences must employ a precise definition of performance that considers these various properties. Active bandwidth and the global quality factor are the two main metrics used to quantitatively compare the performance of TOCSY mixing sequences. Active bandwidth refers to the spectral region over which at least 50% of the magnetization is transferred via a coupling. Global quality factors score mixing sequences according to the worst-case transfer over a range of possible mixing times and chemical shifts. It is possible to use both active bandwidth and the global quality factor as cost functions in optimal control theory to directly optimize a TOCSY sequence. This approach yielded a shaped TOCSY pulse termed RRF-AB that scores 23% higher than FLOPSY in active bandwidth. 71 , 72  

Figure 1.4 shows a side-by-side comparison of active bandwidths for MLEV-16, DIPSI-2, FLOPSY-16 and RRF-AB, plotted as contours lines for transfer efficiencies of 90%, 70%, 50% (red line) and 30%. Of note, the point marked with a red ‘ x ’ corresponds to the farthest off-diagonal cross-peak that experiences 50% transfer efficiency using RRF-AB. This cross-peak has under 30% transfer efficiency using any of the other sequences. The active bandwidths for the four sequences are 0.61 A , 0.85 A , 1.05 A , and 1.31 A , respectively (where A is the RF amplitude).

Simulation of the efficiency of various TOCSY sequences: (A) MLEV-16, (B) DIPSI-2, (C) FLOPSY-16 and (D) RRF-AB. Simulation parameters were root-mean-square RF amplitude A = 4 kHz, J = 35 Hz, and t_mix = 1/(2J). Contour lines are plotted at 90%, 70%, 50% (red), and 30% transfer efficiencies.

Simulation of the efficiency of various TOCSY sequences: (A) MLEV-16, (B) DIPSI-2, (C) FLOPSY-16 and (D) RRF-AB. Simulation parameters were root-mean-square RF amplitude A  = 4 kHz, J  = 35 Hz, and t _mix = 1/(2 J ). Contour lines are plotted at 90%, 70%, 50% (red), and 30% transfer efficiencies.

The strategy for assigning aromatic side chains mirrors that of aliphatic side chains, where all side-chain resonances are interconnected and ultimately linked to resonances identified from backbone assignment routines (typically 13 CB). Aromatic side chains exhibit unique NMR properties, most notably a significant chemical shift anisotropy arising from the planarity of aromatic rings, which subsequently enhances transverse relaxation rates. However, the beneficial interplay between chemical shift anisotropy and dipolar interactions can be harnessed to boost resolution in aromatic side chains using TROSY selection. 73   Still, the robust homonuclear 1 J CC couplings (approximately 57 Hz) curtail the resolution potential of the aromatic TROSY experiment. The implementation of constant-time evolution may help, yet it often results in signal reduction in rapidly relaxing, high molecular weight complexes. To mitigate this issue, alternative labeling of aromatic side chains can be achieved by utilizing 2- 13 C-glycerol or 2- or 3- 13 C-pyruvate as a carbon source during protein expression. 74   The combination of TROSY and alternative labeling generates highly resolved 2D spectra, laying the groundwork for aromatic side-chain assignment.

The assignment of aromatic side chains via isotropic TOCSY mixing presents significant challenges, primarily due to two factors: (i) the substantial chemical shift distance exceeding 80 ppm between aromatic and aliphatic carbons, which is not conducive to TOCSY transfer; and (ii) the aromatic carbons resonating around 120 ppm are strongly coupled amongst themselves (∼57 Hz), while exhibiting weak coupling with the CB carbon (∼35 Hz). This discrepancy severely restricts the TOCSY-based transfer of magnetization from aromatic carbons to the protein backbone. Hence most experiments employed for assignment rely on COSY-type magnetization transfer steps. These steps correlate 1 HB/ 13 CB to various aromatic carbons or protons in a series of 2D experiments. The use of TOCSY is generally limited to isotropic mixing of aromatic 13 C nuclei alone. The following experiments can be employed:

Aromatic TROSY: this correlates the resonances of each 1 H and 13 C pair in aromatic side chains. 73  

(hc)C-(c)CH-TOCSY: this correlates the resonances of all 1 H to all 13 C nuclei. 75  

(hb)CB(cgcd)HD: this correlates the resonances of 13 CB and 1 HD. 76  

(hb)CB(cgcdce)HE: this correlates the resonances of 13 CB and 1 HE. 76  

HB(cb)CG: this correlates the resonances of 1 HB and 13 CG. 75 , 77  

HD(cd)CG: this correlates the resonances of 1 HD and 13 CG. 75 , 77  

HE(cecd)CG: this correlates the resonances of 1 HE and 13 CG. 75 , 77  

HZ(czcecd)CG: this correlates the resonances of 1 HZ and 13 CG. 77  

Histidine is a special case of aromatic residue that contains amide side-chain groups, where the protonation state can be important for protein function ( e.g. enzyme catalysis). NE and ND resonances can be assigned using H(c)N and H C N experiments. H(c)N transfers magnetization from HD/HE to CE/CD first, and then to NE/ND in a second step, both via INEPT transfer using the 1 J coupling. The H C N experiment however uses the 2 J HN coupling directly. 78   Notably, the protonation state of NE and ND changes the relative 1 J and 2 J coupling strengths. Additionally, measurement of the chemical shifts of CE and CD allows for determination of the tautomeric state of singly protonated histidine. 79  

Figure 1.2 demonstrates the striking disparity in sensitivity among the triple-resonance experiments typically used for routine sequential backbone assignment, especially for large molecular weight systems. Despite implementing deuteration and TROSY selection, those experiments with prolonged coherence steps are significantly hindered by rapid transverse relaxation. This challenge is particularly critical in the HNCACB experiment due to its lengthy 13 CA– 13 CB INEPT transfer steps, a predicament illustrated by the 40 kDa protein VSP/PTEN. 80   The HNCA experiment, being roughly four times more sensitive than HNCACB for larger proteins at high magnetic fields, 81   offers an optimal trade-off between sensitivity and information content for assignment.

In theory, the HNCA experiment encapsulates all necessary data for sequential assignments (both CA i and CA i −1 resonances). However, the limited dispersion of CA chemical shifts in practical scenarios generates ambiguities, obstructing sequential assignment. This challenge can be partially mitigated by conducting an HNCA with high resolution in the CA dimension, a feat made feasible due to the availability of high magnetic fields and the use of non-uniform sampling, 20   complemented by reconstruction algorithms. 21–24   Deuteration significantly mitigates the relaxation rates of CA, thus facilitating the acquisition of high-resolution signals even for exceptionally large proteins. However, the presence of 13 CA– 13 CB coupling places a practical limit on the achievable resolution.

Moreover, 13 CA chemical shifts are generally insufficient for identifying amino acid types, adding another layer of complexity in assigning the protein backbone exclusively from HNCA. Therefore, it becomes extremely advantageous to amplify the benefits of the sensitive HNCA experiment by integrating additional layers of information. The strategies detailed below supplement the conventional HNCA experiment to surmount chemical shift degeneracy and enhance the identification of amino acid types, thus enabling backbone assignment using exclusively HNCA spectra.

The most direct method to achieve a high-resolution HNCA spectrum without 13 C splitting is to ‘unlabel’ the 13 CB nucleus during sample preparation, a process referred to as metabolic decoupling. Several approaches to metabolic labeling are available, including the use of 2- 13 C-glycerol instead of uniform 13 C-glucose in growth media 82   and stereo-array isotope labeling (SAIL) which employs specialized 13 C-labeled and deuterated precursors. 83   However, these strategies have limitations in terms of incorporation rates and costs. More recently, pyruvate has been utilized as the sole carbon source during bacterial growth. 84   E. coli can synthesize all metabolites from pyruvate as a precursor and does not require an additional carbon source. Various pyruvate isotopomers (1-, 2-, 3- 13 C or combinations) are commercially available, and pyruvate labeling can be readily combined with deuteration. This is easily accomplished by dissolving protonated pyruvate in D 2 O at pD = 13. The CH acidity of the methyl protons allows them to exchange with deuterons before the pD is restored by adding a phosphate buffer. Consequently, the contributions of both 1 H– 13 C and 13 C– 13 C couplings to 13 CA transverse relaxation rates are eliminated, and HNCA spectra with exceptional resolution can be obtained, significantly reducing sequential matching ambiguities.

In terms of pyruvate metabolism, amino acids can be categorized into three groups: (i) amino acids synthesized directly from pyruvate or through conjugation with directly pyruvate-derived metabolites that conserve the carbon structure of pyruvate (Ala, Ser, Cys, Gly, Trp, Phe, Tyr, Lys, Asp); (ii) the branched-chain amino acids Val and Leu that are synthesized by conjugating pyruvate with acetyl-CoA, and Ile that is formed by conjugating pyruvate with a threonine derivative; and (iii) TCA-cycle-derived amino acids (glutamate-type Glu, Gln, Pro, Arg and aspartate-type Asp, Asn, Thr, Met). Based on this knowledge, incorporation of 13 C at the CA and CB positions can be calculated for all amino acid types.

Notably, it was shown that by using a mix of 2- 13 C pyruvate and 3- 13 C pyruvate (mixed pyruvate labeling), the 13 CA– 13 CB coupling is reintroduced for specific amino acid types. 84   The respective 13 CA signals in a high-resolution HNCA spectrum exhibit superpositions of singlet (from 13 CA that is attached to a 12 CB) and doublet signals (from 13 CA that is attached to a 13 CB) which allows to quantify the relative amount of adjacently incorporated 13 CB. Thus, as a result of the biochemical pathway, we obtain unique peak shapes for different amino acid types. This introduces amino acid type information in the HNCA experiment because, as a general trend, amino acids in group (i) show singlets, those in group (ii) show mostly doublets, and those in group (iii) show a singlet/doublet mix. The singlet-to-doublet ratio is always identical in the internal peak and its sequential match and thus provides another means to distinguish between ambiguous sequential matches. 84   This pyruvate labeling technique provides a high-resolution CA resonance, free of coupling, and an additional split doublet that furnishes further information about the amino acid type. The well-defined, uncoupled central resonance facilitates resonance matching for establishing sequential connectivity, and any existing degeneracy can be resolved using the additional data derived from peak shape. Importantly, this is achieved while maintaining the relaxation demands of an HNCA experiment.

Elimination of the effect of 13 CA– 13 CB coupling can be achieved by adding decoupling schemes to the HNCA pulse sequence. Constant time evolution for 13 CA chemical shift encoding can be used but greatly limits sensitivity, especially for large proteins. Alternatively, band-selective pulses such as adiabatic WURST pulses can be used. 85   However, three bands are required to decouple all CB nuclei (including those of Ala and Ser/Thr) and need proper calibration not to touch 13 CA (which is almost inevitable for Gly). Moreover, such homonuclear decoupling schemes give rise to Bloch–Siegert shifts 86   of the 13 CA resonances that have to be properly calibrated and compensated for.

More recently, a suite of homonuclear shaped decoupling pulses was designed using optimal control theory and optimized to invert only selected 13 CB frequency bands without perturbing other frequencies. This suite of pulses was termed beta/alpha decoupling pulse (BADCOP). 87   Importantly, the pulses have been designed to avoid introducing any Bloch–Siegert shifts. Overall, they allow refocusing of the 13 CA– 13 CB coupling using a single pulse placed in the center of the 13 CA evolution period. This technique allows selective decoupling of 13 CB nuclei resonating in a defined chemical shift range, resulting in a singlet in the HNCA (while other cross-peaks appear as doublets). The individual line shape of a 13 CA cross-peak is therefore only determined by the chemical shift of its adjacent 13 CB. Because 13 CB is particularly sensitive to the amino acid type, this effectively encodes information on the amino acid type in an HNCA spectrum.

Three variations of BADCOP pulses were designed which vary in the chemical shift bandwidth and range of 13 CB inversion. 87   They all additionally invert all 13 CO resonances. BADCOP1 inverts 13 CB spins with chemical shifts <35 ppm, thereby decoupling all amino acids but Lys, Tyr, Asp, Asn, Phe, Ile, Ser, and Thr (that appear as doublets). BADCOP2 decouples 13 CB with chemical shifts between 28 and 35 ppm (Cys, Arg, Met, His, Lys, Glu, Val, Trp, Pro, and Gln). BADCOP3 decouples 13 CB spins with chemical shifts <43 ppm so that only Ser and Thr cross-peaks appear as doublets. Acquiring multiple high resolution HNCA spectra using different BADCOP pulses enables assignment of signals to defined groups of amino acid types (depending on their respective 13 CB chemical shifts). 87   Moreover, the line shapes are always identical in the internal peak and its sequential match. Differential line shape distortions of signals with chemical shifts close to the different BADCOP cut-off frequencies are of extraordinary value to identify the correct sequential match out of a set of candidates. Similarly, the variety of 13 CA– 13 CB coupling constants usually causing issues when implementing homonuclear decoupling strategies become beneficial as a characteristic signal feature. Thus, BADCOP decoupling provides an excellent means to increase the resolution of the HNCA experiment, remove ambiguities in sequential matching and extract amino acid type information for backbone assignment.

Note that pyruvate labeling and band-selective CB decoupling are orthogonal methods that do not rely on the same principles and therefore do not overlap in the information they provide. In particularly tricky cases where many residues’ 13 C frequencies are nearly degenerate (whose likelihood increases in larger proteins), combining the two methods proves to be very efficient in obtaining faithful sequential links and ultimately resonance assignments. A simulated case is presented in Figure 1.5 , where the proper sequential match (the Arg) can only be identified by combining pyruvate labeling and band-selective CB decoupling.

Complementarity of pyruvate labeling and band-selective decoupling. Three sequential match candidates (CAi candidates in blue matching to CAi−1 in orange) have completely degenerate 13CA chemical shifts of 55.56 ppm in a constant time HNCA spectrum. Mixed pyruvate labeling allows the last candidate to be excluded via line shape matching, but the first two candidates remain. BADCOP1 generates distinct splitting patterns (singlet and doublet) for these two cross-peaks, allowing the first candidate to be excluded. Additionally, combining these methods provides finer amino acid type distinction than either method alone.

Complementarity of pyruvate labeling and band-selective decoupling. Three sequential match candidates (CA i candidates in blue matching to CA i −1 in orange) have completely degenerate 13 CA chemical shifts of 55.56 ppm in a constant time HNCA spectrum. Mixed pyruvate labeling allows the last candidate to be excluded via line shape matching, but the first two candidates remain. BADCOP1 generates distinct splitting patterns (singlet and doublet) for these two cross-peaks, allowing the first candidate to be excluded. Additionally, combining these methods provides finer amino acid type distinction than either method alone.

The applicability of assignment strategies discussed in Sections 1.2 and 1.3 is limited to proteins of about 50 kDa as the sensitivity is severely decreased for fast-relaxing high molecular weight assemblies. The power of methyl NMR was recognized as a way to tackle much larger proteins and molecular assemblies up to the MDa range. Detecting the multiple quantum coherence between 13 C and 1 H in methyl groups has favorable relaxation properties with a small dependence on the overall tumbling rate, referred to as the ‘methyl TROSY’ effect. 88   To make use of the full power of methyl TROSY, isolated isotope labeled methyl groups need to be introduced in otherwise deuterated proteins of interest. Several approaches have been developed to introduce Met, Ala, Thr, Ile, Val and Leu residues with specific methyl isotope labeling during protein recombinant expression. These approaches rely either on addition of synthetic selectively labeled amino acids in the growth medium (for Met, 89   Ala 90   and Thr 91   ) or on using metabolic precursors (α-ketobutyrate for Ile and α-ketoisovalerate for Leu and Val). 92   Notably, utilization of stereo-isotopomers of acetolactate allows stereo-selective labeling of pro-S and pro-R methyl groups in Val and Leu. 93 , 94   Furthermore, a synthetic route to stereo-selective methyl labeled Leu has been reported which expands the use of this approach to non-bacterial protein expression systems (cell-free, insect cells). 43  

Application of methyl TROSY also necessitated adaptations in side-chain assignment strategies. Isotropic mixing (TOCSY) performs poorly in such spin systems due to the presence of undesirable 1 J CC couplings at branching points. 95   Protein labeling with a linearized chain of 13 C nuclei along the side chain allows efficient magnetization transfer in perdeuterated proteins. 96 , 97   Moreover, unidirectional transfer from methyl groups to backbone 13 CA or 13 CO or even amides can be achieved with COSY-type relay experiments. Magnetization is transferred stepwise from carbon to carbon by using suitably designed concatenated blocks and selective pulses to avoid magnetization leakage in two separate directions at each step. Different COSY-based experiments are used for different amino acids: (hm)CM(cgcbca)NH 95 , 96   for Ile and Leu, and (hm)CM(cbca)NH for Val. 96   Out-and-back type HMCM(cgcbca)CO and HMCM(cg)CBCA experiments are also available and can outperform the aforementioned experiments in some cases.

A different approach uses precursors which generate linearized 13 C-labeled versions of Leu and Val side chains in a deuterated background. 98   A TOCSY out-and-back (hmcm)CCMHM pulse sequence is used to connect methyl resonances with other aliphatic 13 C resonances. 98   The J -splitting between neighboring 13 C nuclei greatly limits achievable resolution but can be deconvoluted during processing using machine learning tools. 99   The advantages are that TOCSY mixing is shorter than relayed COSY transfer and that it can be easily tuned just by changing the mixing time, which increases the versatility of experiments.

As pointed out in Section 1.5.1 , assigning methyl resonances by transferring magnetization and correlating methyl resonances with backbone resonances ( e.g. , using HCCH-TOCSY type experiments; see Section 1.3.1 ) is challenging for large proteins. However, in the era of AlphaFold, a structure or structural model of nearly all proteins is available and can be used to predict methyl–methyl NOESY patterns. Then, these can be compared to experimentally measured NOESY spectra ( e.g. , using 3D (h)CCH HMQC NOESY) to extract methyl-specific assignments. However, the problem of mapping methyl resonances to a protein structure requires searching in a high-dimensional space and the number of maps to test grows exponentially with the number of methyl bearing residues in the protein. Algorithms have been designed to incorporate heuristic and probabilistic approaches to navigate the problem of combinatorial explosion. Several such algorithms are available that employ different methods to combine NOE data and protein structures and optimize the accuracy of methyl assignments.

FLAMEnGO 100   uses Monte Carlo simulations along with a scoring function to assign methyl resonances. It starts from random assignments and then iteratively swaps assignments using Monte Carlo simulations, and the swap is accepted or rejected based on a scoring function whose main contributing term is the difference in simulated and experimental methyl–methyl NOE spectra. Methyl Assignment by Graph Matching (MAGMA) 101   uses exact graph matching to compare the data graph generated using NOE restraints and the structure graph generated using a high-resolution protein structure. Heuristics are used to prioritize the matching of vertices and to maximize the number of edges in the data graph explained by the structure graph. Methyl Assignment by Graphing Interference Construct (MAGIC) 102   works in a similar manner but prioritizes assigning high density vertices and the high confidence local search results are propagated for the next iteration. This avoids combinatorial explosion and is faster than MAGMA as it is traversing the search space hierarchically from a local dense network to global assignment. Methyl Fully Automated Assignment (MethylFLYA) 103   uses an evolutionary algorithm to optimize methyl assignment. At each iteration, a subset of parents is selected based on scoring, mutated, and recombined to produce the next generation. The entire process is run multiple times with different random seeds each time and solutions that consistently appear in several runs are finally selected. Methyl Assignment Using Satisfiability (MAUS) 104   generates a structure graph and all possible data graphs from NOE data. The fitting of a sparse data graph to a structure graph is a nondeterministic polynomial complete subgraph isomorphism problem. MAUS converts it to a satisfiability problem and uses the general solver method CryptoMiniSat to solve the satisfiability problem.

Practical considerations for the applicability of these structure-based assignment methods are the goodness of the available high-resolution structure and the quality of NOE data. Maximizing the number of methyl probes is a straightforward way to improve the density of the NOE network. Conversely, deuteration increases the maximum distance of the measured NOE cross-peaks up to 12 Å 105   and therefore the number of NOEs in the network. Assigning amino acid types to methyl resonances also largely reduces ambiguities in assigning the NOE network. Whilst Ile and Met are easily identified by their distinct 1 HM and 13 CM chemical shifts, identifying the signals of Leu, Val, Ala and Thr is not as straightforward and should be addressed by selective labeling (Thr, Ala) 90 , 91   and use of optimal-control pulses that effectively invert the sign of Leu vs. Val methyl resonances. 106   Stereospecific labeling of proR and proS methyl groups in Leu and Val further improves the assignment outcome by increasing the NOE distance threshold, reducing spectral crowding, and reducing ambiguities in the NOE network. Additionally, knowledge of the internal dynamics of the protein (from crystal structure B -factors or NMR relaxation experiments) is useful in assessing the outcome of structure-guided assignment and refining the network of NOEs that should be observed. Finally, in homo-oligomeric complexes, distinction between inter- and intramolecular NOEs is useful both as prior information (omission of interchain NOEs) or as a validation tool. 107  

One take-home message from the discussions above is that the information provided separately by different spectra is increased when all are considered simultaneously. For example, side-chain proton resonances can be tentatively assigned with an H(c-cco)NH spectrum, whereas HC(-c)H or (h)C-CH TOCSY spectra help identify (H,C) correlations belonging to the same side chain but do not pair them with assigned resonances unless HA and HB have been assigned in addition to CA and CB. However, when both are used together, unassigned 1 H and 13 C resonances can be linked to the assigned amide resonances reliably, albeit somewhat tediously. Covariance NMR aims at exploiting this property by combining the information provided by separate spectra into new, artificial correlation maps. Here, spectra are treated as multi-dimensional arrays 108   that can be subjected to matrix operations. 109–111   Most importantly, matrix multiplication along dimensions common to two different spectra will lead to correlations between signals in the remaining dimensions if they carry the same signals in the subsumed dimension. For example, multiplying the H N /H ali planes of H(c-cco)NH ( Figure 1.6A ) with the H C /H ali planes of HC-(c)H TOCSY ( Figure 1.6B ) will provide correlations (H N , H C ) only if the 1D traces along H ali at the H N and H C coordinates feature overlapping signals ( Figure 1.6C ). By repeating this procedure for all points in the nitrogen and carbon dimensions of H(c-cco)NH and HC(c)H-TOCSY, respectively, we could build an [H,N,H,C] four-dimensional array, in which the 13 C– 1 H HSQC of an unassigned side chain can be visualized for every assigned amide (H,N) correlation ( Figure 1.6D ). The assignment then becomes trivial. Unfortunately, while such matrix operations have been routinely employed for small molecules, 112 , 113   too many residues feature similar frequencies in proteins and, in combination with line-broadening and artefactual correlations, the resulting correlation maps are impractical. To overcome this challenge, a spectral derivative must first be taken along the subsumed dimension. 114   The dispersive spectra then feature inflexion points instead of maxima, and partially overlapped but mismatched signals will cancel each other during matrix multiplication. For spectra where several common signals are compared during multiplication, applying matrix square-rooting further reduces artefacts. 115   Figure 1.6C and D demonstrates the quality of correlation maps combining spectral derivatives and square-rooting. 116   In practice, the entire 3D input arrays are subject to spectral derivatives along H ali and multiplied and rooted via singular-value decomposition. 117  

Covariance NMR for resonance assignments. Multiplications between the HN/Hali planes (A) of H(c-cco)NH and the HC/Hali planes of HC(-c)H TOCSY lead to HN/HC planes (C). HN and HC resonances that are correlated via common signals along Hali (dashed lines in A and B) lead to correlations in the output correlation map (grey arrow in C). (D) A four-dimensional array is built by repeating the process for all nitrogen and carbon datapoints in H(c-cco)NH and HC(-c)H TOCSY, respectively. With this 4D array, each assigned amide is paired with a 13C–1H HSQC of its unassigned side chain, and side-chain resonance assignments are done through visual inspection. To remove the artefacts in (D), spectral derivatives were applied along the Hali dimension and matrix square-rooting was applied to the 4D array. In practice, the entire 3D input arrays are subject to spectral derivatives along Hali and multiplied and rooted via singular-value decomposition.

Covariance NMR for resonance assignments. Multiplications between the H N /H ali planes (A) of H(c-cco)NH and the H C /H ali planes of HC(-c)H TOCSY lead to H N /H C planes (C). H N and H C resonances that are correlated via common signals along H ali (dashed lines in A and B) lead to correlations in the output correlation map (grey arrow in C). (D) A four-dimensional array is built by repeating the process for all nitrogen and carbon datapoints in H(c-cco)NH and HC(-c)H TOCSY, respectively. With this 4D array, each assigned amide is paired with a 13 C– 1 H HSQC of its unassigned side chain, and side-chain resonance assignments are done through visual inspection. To remove the artefacts in (D), spectral derivatives were applied along the H ali dimension and matrix square-rooting was applied to the 4D array. In practice, the entire 3D input arrays are subject to spectral derivatives along H ali and multiplied and rooted via singular-value decomposition.

The procedure has also been successfully employed to assign amide resonances using maps calculated from HNCO, HN(ca)CO, HNCA, HN(co)CA, HN(ca)CB, and HN(coca)CB. 118   Here, correlations between sequential residues can be seen in [H,N,Hs,Ns] correlation maps, where Hs and Ns refer to either residue i  + 1 or i  − 1 depending on how the 4D is transposed. Further improvements are obtained when applying element-wise multiplication between the maps obtained from different carbon dimensions as CA, CB, and CO chemical shifts are all unlikely to be accidentally the same for non-sequential residues. Asparagine side chains can be assigned with a different combination of the same spectra. 116   Similarly, methyl resonances can be assigned by combining HMCMCGCB or HMCM(cg)CBCA spectra with HNCA and HN(ca)CB. 119  

Although covariance correlation maps have been greatly improved by recent advances, they are not meant to replace peak picking and visual inspections but to help overcome challenges. 120   Notably, artefacts may remain when large dynamic ranges in sensitivity are present, e.g. for a disordered region attached to a folded core, as artefacts stemming from intense signals may compare with true correlations between weak signals. Thus, correlation maps are best used in conjunction with the original data. Since the maps do not require specific data acquisition, we envision that they may be routinely employed for quality control and rescue of stalled resonance assignments.

NMR spectroscopy is particularly useful to study intrinsically disordered proteins and protein regions, where other structural biology techniques fail due to their high flexibility and degrees of freedom. However, these proteins come with their own challenges in terms of resonance assignment. The traditional resonance assignment experiments involving 1 H N direct detection suffer from poor chemical shift dispersion and from exchange broadening of 1 H N with the solvent protons. Further, IDPs are rich in Pro residues which lack amide protons and are thus absent from traditional experiments.

The counterpart to this is that disordered protein regions have favorable relaxation properties, which allows multiple magnetization transfer steps and encoding of more than two indirect dimensions. However, obtaining uniform sampling in four or more dimensions would require unrealistic measurement times. Consequently, various approaches have been proposed to decrease the number of recorded data points during the experiment. The availability of efficient non-uniform sampling (NUS) schedules 20   and reconstruction algorithms 21–24   makes NUS a valid approach to increase the dimensionality of NMR spectra. The most attractive feature of NUS is that the requirement in the number of collected points in the Nyquist grid in fact goes down with the number of dimensions to reconstruct (10% for 2 reconstructed dimensions, 4% for 3 reconstructed dimensions, etc. ).

Another way of measuring high-dimensionality NMR spectra in a time-efficient way is automated projection spectroscopy (APSY), which allows reconstruction of up to 7-dimensional spectra from a set of 2D projection spectra at different angles. An automated algorithm retrieves the peak positions and yields a final N- dimensional peak list. 121   The strategy relies on incrementing two or more evolution periods simultaneously, first described as accordion spectroscopy. 122  

Both APSY and NUS have successfully been applied to increase the number of dimensions by correlating different combinations of internal and sequential N, H, CO, CA and HA nuclei, which increases spectral dispersion for crowded IDPs with repetitive amino acid sequences. The following experiments have successfully been utilized:

4D HNCOCA: this correlates a set of H i , N i , CO i −1 and CA i −1 resonances. 121  

4D HNCACO: this correlates H i , N i , CO i , CO i −1 , CA i and CA i −1 resonances. 123  

4D HACANH: this correlates H i , N i , HA i , HA i −1 , CA i and CA i −1 resonances. 123  

5D HACACONH: this correlates a set of H i , N i , CO i −1 , HA i −1 and CA i −1 resonances. 121  

4D CBCANH: this correlates H i , N i , CA i , CA i −1 , CB i and CB i −1 resonances. 123  

5D CBCACONH: this correlates a set of H i , N i , CO i −1 , CA i −1 and CB i −1 resonances. 123  

5D HNCOCACB: this is an out-and-back experiment correlating a set of H i , N i , CO i −1 , CA i −1 and CB i −1 resonances. 124  

Similarly, the high number of transfer steps and encoded nuclei allows creation of new connectivities for unambiguous sequential matching. In essence, these experiments shift the base spectrum for backbone assignment from a 2D 15 N– 1 H HSQC to a 3D HNCO:

5D HACA(n)CONH: this connects HA i , CA i and HA i −1 , CA i −1 to a given set of N i , H i , CO i −1 (HNCO) coordinates. 124  

5D (haca)CON(ca)CONH: this is an out-and-stay experiment connecting CO i −1 , N i and CO i −2 , N i −1 to a given set of N i , H i , CO i −1 (HNCO) coordinates. 124  

5D (h)NCO(nca)CONH: this is an out-and-back experiment connecting CO i −1 , N i and CO i −2 , N i −1 to a given set of N i , H i , CO i −1 (HNCO) coordinates. 124  

6D HNCO(nca)CONH: this is a variant of the previous experiment additionally encoding the first amide proton resonance, essentially connecting two sequential HNCO cross-peaks. 125  

7D HNCO(n)CACONH: this is a variant of the previous experiment additionally encoding the CA resonance. 125  

In a similar but more easy-to-implement approach, correlation of sequential nitrogen resonances was proposed early on to benefit from the higher resolution of 15 N in order to alleviate spectral crowding. 126   These experiments are referred to as HNN experiments and are particularly useful for IDPs:

4D HN(ca)NH: this correlates a set of H i , N i resonances (HSQC cross-peak) to H i −1 and N i −1 (previous HSQC cross-peak) and H i +1 , N i +1 (following HSQC cross-peak). 127  

4D HN(coca)NH: this correlates a set of H i , N i resonances (HSQC cross-peak) to H i −1 and N i −1 (previous HSQC cross-peak). 128  

4D HN(cocanca)NH: this correlates a set of H i , N i resonances (HSQC cross-peak) to H i −2 and N i −2 resonances, which allows us to ‘walk’ through Pro residues that are abundant in IDPs but invisible to 1 H detected NMR. 129  

Heteronuclear or low gyromagnetic nuclei ( 13 C and 15 N) direct detection can overcome the problems described above by circumventing the use of 1 H N nuclei altogether. It is beneficial to detect 13 C/ 15 N in the direct dimension to fully utilize the available high resolution and high chemical shift dispersion by sampling more points ‘for free’. Sampling a higher number of points in the direct dimension does not add to the experimental time. Owing to the low gyromagnetic ratio of 13 C or 15 N, these experiments are relatively less sensitive than 1 H N direct detection, but with the improvement in hardware and availability of high-field magnets it has become feasible without impractical sample concentrations. Note that these experiments can be engineered with starting magnetization of 1 HA to retain higher sensitivity and short interscan delays. 1 HA direct detected experiments were also developed 130   which retain sensitive detection and observe Pro residues, but the issue of poor chemical shift dispersion of 1 HA remains.

Historically 13 C direct detection experiments were designed for studying proteins with a paramagnetic center without involving 1 H in any step, thus named ‘protonless NMR’. 131   Due to its low gyromagnetic ratio, 13 C does not suffer from transverse paramagnetic relaxation rate enhancement as much as 1 H. The benefits of 13 C direct detection for disordered proteins were later recognized and a suite of experiments were designed with polarization starting on 1 H. 132  

Ideally one would like to detect 13 CA owing to its large chemical shift dispersion and rich information content in terms of the amino acid type and secondary structure. However, 13 CA has large one-bond homonuclear scalar couplings with neighboring 13 CO and 13 CB nuclei. Several schemes have been developed to remove the couplings including band selective decoupling pulses applied by interrupting the FID collection 133   and machine learning algorithms for virtual decoupling during processing. 99   However, the most commonly used technique relies on the spin state selection method, i.e. , the in-phase/anti-phase (IPAP) scheme. The in-phase and anti-phase spin states are evolved and selected in an interleaved fashion and the respective FIDs are stored and processed separately. Since the one-bond scalar coupling 1 J CACO is constant, the two peaks in the doublet are shifted by half of 1 J CACO to the center frequency and added to obtain a decoupled peak. For 13 CA detection, this must be done twice to remove the effect of 1 J CACO and 1 J CACB separately, which requires the measurement of four FIDs per increment (double IPAP). 131  

A way of alleviating the need for double IPAP is with an alternate 13 C– 12 C isotope labeling scheme. This can be achieved using mixtures of 2- 13 C pyruvate and 3- 13 C pyruvate or of 2- 13 C glycerol and 1,3- 13 C glycerol as carbon sources for bacterial expression. This strategy enables alternate 13 C– 12 C labeling at most positions and allows detection of 13 CA without the substantial loss in sensitivity for high molecular weight systems due to the use of IPAP schemes. Complete deuteration at HA sites is critical for taking advantage of reduced dipole relaxation and can readily be achieved in 100% D 2 O medium with protonated amino acid precursors. 134   A 2D NCA experiment optimized for deuterated and alternately- 13 C labeled proteins correlates the chemical shifts of 13 CA with the two neighboring nitrogen nuclei (CA i –N i and CA i –N i +1 ). Thus, it allows sequential linking of the backbone resonances. The strategy can be extended to 3D experiments for higher spectral dispersion, like the 3D CANCA experiment for perdeuterated proteins that correlates 13 CA with the i and i  + 1 15 N and 13 CA resonances. 135  

However, strategies relying on direct detection of 13 CO are more popular, where only a single IPAP to remove the 1 J COCA coupling is necessary. Protein resonance assignment can be achieved using the following experiments that use the basic building blocks discussed in Sections 1.2.1 and 1.3.1 : 132 , 136  

(ha)CANCO: this connects both CA i and CA i −1 resonances to a specific N i –CO i −1 cross-peak.

(ha)CA(co)NCO: this connects only the CA i −1 resonance to a specific N i –CO i −1 cross-peak.

(hbha)CBCA(co)NCO: this connects the CA i −1 and CB i −1 resonances to a specific N i –CO i −1 cross-peak.

(hc)C(co)NCO: this connects all i  − 1 aliphatic side-chain resonances (TOCSY mixing) to a specific N i –CO i −1 cross-peak.

As intrinsically disordered proteins of interest become larger and their spectra become crowded and complex, optimal chemical shift dispersion and spectral resolution are desired, which are theoretically achieved by 15 N-direct detection. The main limitation of 15 N detection resides in its poor sensitivity due to the very low gyromagnetic ratio of 15 N. Nevertheless, 15 N has the advantage of a low CSA (compared to 13 CO), and thus 15 N detection becomes advantageous as the magnetic field increases. Moreover, 15 N detection does not require homonuclear decoupling which avoids the need for IPAP schemes. Broadband 13 C decoupling is readily achieved using adiabatic WURST pulses. Finally, TROSY selection can be employed in 15 N direct detection. It is also shown that, under physiological pH and ionic strength, 15 N TROSY direct detection is comparably sensitive to 1 H N TROSY detection. 137   This is especially important in high-field magnets with high Q -factor probes. Indeed, in a triple-resonance cryogenically cooled TXO probe (inner coil for 15 N and 13 C), the signal height of 1 H-detected resonances was reduced by more than 75% from 10 mM to 1 M NaCl concentration ( Figure 1.2E ). In contrast, the signal height of the 15 N-detected resonances was substantially less affected, reduced by 20% from 10 mM to 1 M NaCl concentration.

Unlike for 1 H-detected TROSY, deuteration is not mandatory to benefit from 15 N-detected TROSY due to its lower sensitivity to 1 H dipolar broadening. 137   This facilitates studies of proteins that require eukaryotic expression and cannot be fully deuterated. It is shown that the combination of 15 N TROSY detection with CRINEPT coherence transfer allows the observation of the main chain amide resonances of nondeuterated proteins as large as 150 kDa. 138  

Two approaches have successively been developed for 15 N detection. The first relies on buffer deuteration and direct detection of the slowly relaxing 15 N 2H resonances. 139   The second employs TROSY selection of the slowly relaxing spin state of 15 N in protonated buffers. 140   It can be used in physiological conditions, but it requires the IPAP scheme for TROSY selection. At ultra-high magnetic fields (1 GHz and above), TROSY 15 N direct detection is expected to provide the best sensitivity and resolution for intrinsically disordered proteins. 34   In both cases, protein resonance assignment is done with the following experiments:

(haca)COCAN: this connects both CA i and CA i −1 resonances to a specific N i –CO i −1 cross-peak.

(ha)CACON: this connects only the CA i −1 resonance to a specific N i –CO i −1 cross-peak.

(hbha)CBCACON: this connects the CA i −1 and CB i −1 resonances to a specific N i –CO i −1 cross-peak.

(hc)C(ca)CON: this connects all i −1 aliphatic side-chain resonances (TOCSY mixing) to a specific N i –CO i −1 cross-peak.

Groundbreaking advances in solution NMR have unfurled hitherto hidden vistas of structural and mechanistic biology. Techniques such as relaxation dispersion and CEST experiments have illuminated the existence of minor conformations, thus unveiling their biological significance. Key phenomena such as protein allostery, conformational exchanges and selections, drug binding to allosteric pockets, and the mechanistic effects of disease-causing mutations have been brought to the fore by astute NMR studies. However, these intricate investigations invariably hinge on resonance assignments. Presently, we are equipped with an arsenal of methods for obtaining resonance assignments of proteins, meticulously detailed in the preceding sections. For larger proteins—those exceeding 50 kDa—utilizing backbone amine and side-chain methyl (AILVMT) resonances forms the cornerstone of effective analysis. Furthermore, strategic inclusion of key aromatic residues in a deuterated background can prove invaluable when necessary. For disordered proteins, the utilization of 13 C and 15 N detection experiments presents a host of benefits, not least of which includes the enhanced resolution and the ability to detect proline residues, often found abundantly in disordered proteins. The application of non-uniform sampling further heightens resolution in the indirect dimension, with the added benefit of augmenting sensitivity through the collection of more scans. The path forward in NMR resonance assignment is paved with a fusion of inventive biochemistry (such as pyruvate labeling and ILV labeling), cutting-edge hardware improvements (like high-field magnets, cryogenically cooled probes, and specially designed probes for low gamma nuclei), and the development of novel NMR experimental methods and data processing and analysis techniques. The judicious utilization of chemical shift resources can significantly bolster these endeavors. Looking ahead, there is a burgeoning array of innovative techniques on the horizon, including those leveraging artificial intelligence and machine learning, poised to automate resonance assignment. These avant-garde methods have the potential to harness the existing technologies and techniques, significantly transforming the landscape of resonance assignment, providing access to larger molecular weight systems in the coming years.

This chapter replaces the version published December 2023, which contained errors in Section 1.2.4 and in the References section.

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  • Published: 09 March 2017

Backbone assignment of perdeuterated proteins by solid-state NMR using proton detection and ultrafast magic-angle spinning

  • Pascal Fricke 1 ,
  • Veniamin Chevelkov 1 ,
  • Maximilian Zinke 1 ,
  • Karin Giller 2 ,
  • Stefan Becker 2 &
  • Adam Lange 1 , 3 , 2  

Nature Protocols volume  12 ,  pages 764–782 ( 2017 ) Cite this article

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  • Solid-state NMR
  • Supramolecular assembly

This article has been updated

Solid-state NMR (ssNMR) is a technique that allows the study of protein structure and dynamics at atomic detail. In contrast to X-ray crystallography and cryo-electron microscopy, proteins can be studied under physiological conditions—for example, in a lipid bilayer and at room temperature (0–35 °C). However, ssNMR requires considerable amounts (milligram quantities) of isotopically labeled samples. In recent years, 1 H-detection of perdeuterated protein samples has been proposed as a method of alleviating the sensitivity issue. Such methods are, however, substantially more demanding to the spectroscopist, as compared with traditional 13 C-detected approaches. As a guide, this protocol describes a procedure for the chemical shift assignment of the backbone atoms of proteins in the solid state by 1 H-detected ssNMR. It requires a perdeuterated, uniformly 13 C- and 15 N-labeled protein sample with subsequent proton back-exchange to the labile sites. The sample needs to be spun at a minimum of 40 kHz in the NMR spectrometer. With a minimal set of five 3D NMR spectra, the protein backbone and some of the side-chain atoms can be completely assigned. These spectra correlate resonances within one amino acid residue and between neighboring residues; taken together, these correlations allow for complete chemical shift assignment via a 'backbone walk'. This results in a backbone chemical shift table, which is the basis for further analysis of the protein structure and/or dynamics by ssNMR. Depending on the spectral quality and complexity of the protein, data acquisition and analysis are possible within 2 months.

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protein nmr backbone assignment

Change history

27 march 2017.

In the supplementary information originally posted online, the file: Supplementary Data 1–10 was not attached. The error has been corrected in the HTML and PDF versions as of 27 March 2017.

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Acknowledgements

We thank S. Lange and E. Ousby for valuable discussions. This work was supported by the Leibniz-Institut für Molekulare Pharmakologie, the Max Planck Society, the European Research Council (ERC Starting Grant to A.L.), the German Research Foundation (Deutsche Forschungsgemeinschaft; Emmy Noether Fellowship to A.L.) and the Fonds der Chemischen Industrie (Kekulé Scholarship to P.F.).

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Department of Molecular Biophysics, Leibniz-Institut für Molekulare Pharmakologie, Berlin, Germany

Pascal Fricke, Veniamin Chevelkov, Maximilian Zinke & Adam Lange

Department of NMR-based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany

Karin Giller, Stefan Becker & Adam Lange

Institut für Biologie, Humboldt-Universität zu Berlin, Berlin, Germany

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P.F., V.C. and M.Z. implemented the protocol; K.G. and S.B. produced the protein sample; V.C. and A.L. designed the research; P.F. and A.L. wrote the manuscript; and all authors commented on the manuscript.

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Correspondence to Veniamin Chevelkov .

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Fricke, P., Chevelkov, V., Zinke, M. et al. Backbone assignment of perdeuterated proteins by solid-state NMR using proton detection and ultrafast magic-angle spinning. Nat Protoc 12 , 764–782 (2017). https://doi.org/10.1038/nprot.2016.190

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protein nmr backbone assignment

Backbone 1 H, 13 C and 15 N resonance assignment of the ubiquitin specific protease 7 catalytic domain (residues 208-554) in complex with a small molecule ligand

Affiliations.

  • 1 Manchester Institute of Biotechnology, University of Manchester, Manchester, United Kingdom.
  • 2 C4X Discovery Ltd, Manchester One, 53 Portland Street, Manchester, M1 3LD, United Kingdom.
  • 3 C4X Discovery Ltd, Manchester One, 53 Portland Street, Manchester, M1 3LD, United Kingdom. [email protected].
  • 4 Biophysics Department, NMR and Protein Production, Evotec SE, Hamburg, Germany.
  • PMID: 38472728
  • DOI: 10.1007/s12104-024-10165-7

The backbone 1 H, 13 C and 15 N resonance assignment of Ubiquitin Specific Protease 7 catalytic domain (residues 208-554) was performed in its complex with a small molecule ligand and in its apo form as a reference. The amide 1 H- 15 N signal intensities were boosted by an amide hydrogen exchange protocol, where expressed 2 H, 13 C, 15 N-labeled protein was unfolded and re-folded to ensure exchange of amide deuterons to protons. The resonance assignments were used to determine chemical shift perturbations on ligand binding, which are consistent with the binding site observed by crystallography.

Keywords: Amide hydrogen exchange; Chemical shift perturbation; Ligand binding; NMR resonance assignment; USP7.

© 2024. The Author(s), under exclusive licence to Springer Nature B.V.

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Protein NMR

A practical guide, double resonance backbone assignment.

For smaller proteins, it is possible to do the backbone assignment using just 15 N-labelled protein. The spectra used for this are the 15N-NOESY-HSQC and the 15N-TOCSY-HSQC . The 15N-NOESY-HSQC will show for each NH group all 1 H resonances which are within about 5-7Å of the NH hydrogen. Assignment is done on the assumption that the two neighbouring NH groups are always visible. Thus two NH groups can be linked because they each have an NOE to the other NH group.

Note that you always end up with a square motif between strips which are linked by an NOE: each strip has an NOE to the diagonal peak of the other strip.

Helical sections are generally easier to assign, as NOEs from NH(i) are visible not only to NH(i±1), but also to NH(i±2) and sometimes NH(i±3).

β-sheet structures include short NH-NH distances between the strands. This means that in addition to the NH(i±1) NOEs, a strong cross-strand NOE is also observed.

Having a rough idea of the secondary structure and topology of the protein can thus significantly aid backbone assignment using double resonance spectra only. Further help with assignment is provided by the 15N-TOCSY-HSQC. This should show links from the backbone NH group to all side-chain hydrogens of that residue. Using this spectrum the amino acid type can be identified or narrowed down significantly. The side-chain NOEs from the 15N-NOESY-HSQC can also be useful during the assignment process, as NH(i)-Hα(i-1) are generally very strong, in particular in β-sheet sections.

Backbone 1 H, 13 C and 15 N resonance assignment of the ubiquitin specific protease 7 catalytic domain (residues 208–554) in complex with a small molecule ligand

  • Published: 12 March 2024

Cite this article

  • Maya J. Pandya 1 , 2 ,
  • Wojciech Augustyniak 2 ,
  • Matthew J. Cliff 1 ,
  • Ilka Lindner 3 ,
  • Anne Stinn 3 ,
  • Jan Kahmann 3 ,
  • Koen Temmerman 3 ,
  • Hugh R. W. Dannatt 2 ,
  • Jonathan P. Waltho 1 &
  • Martin J. Watson 2  

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The backbone 1 H, 13 C and 15 N resonance assignment of Ubiquitin Specific Protease 7 catalytic domain (residues 208–554) was performed in its complex with a small molecule ligand and in its apo form as a reference. The amide 1 H- 15 N signal intensities were boosted by an amide hydrogen exchange protocol, where expressed 2 H, 13 C, 15 N-labeled protein was unfolded and re-folded to ensure exchange of amide deuterons to protons. The resonance assignments were used to determine chemical shift perturbations on ligand binding, which are consistent with the binding site observed by crystallography.

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protein nmr backbone assignment

Data availability

The backbone 1 H, 13 C and 15 N resonance assignment of apo Ubiquitin Specific Protease 7 catalytic domain (residues 208–554) was deposited in Biological Magnetic Resonance Bank under accession code 51912. The assignment for the complex with compound 21 (O’Dowd et al. 2018a ) was deposited under code 51913.

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This work was supported by Innovate UK (Knowledge Transfer Partnership 11447).

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Contributions

M.J.P., M.J.C., J.P.W. and M.J.W. initiated the project and designed the experimental protocol. I.L, A.S., J.K. and K.T. expressed and purified protein. M.J.P. performed hydrogen exchange/protein re-folding. M.J.P. M.J.C and H.R.W.D. recorded spectra. W.A. performed resonance assignments, analysed the results, wrote the manuscript and prepared the figures. All authors reviewed the manuscript.

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Correspondence to Wojciech Augustyniak .

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Pandya, M.J., Augustyniak, W., Cliff, M.J. et al. Backbone 1 H, 13 C and 15 N resonance assignment of the ubiquitin specific protease 7 catalytic domain (residues 208–554) in complex with a small molecule ligand. Biomol NMR Assign (2024). https://doi.org/10.1007/s12104-024-10165-7

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Published : 12 March 2024

DOI : https://doi.org/10.1007/s12104-024-10165-7

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IMAGES

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COMMENTS

  1. Triple Resonance Backbone Assignment

    Standard triple resonance backbone assignment of proteins is based on the CBCANNH and CBCA (CO)NNH spectra. The idea is that the CBCANNH correlates each NH group with the Cα and Cβ chemical shifts of its own residue (strongly) and of the residue preceding (weakly). The CBCA (CO)NNH only correlates the NH group to the preceding Cα and Cβ ...

  2. Time-optimized protein NMR assignment with an integrative ...

    Using the small sets of spectra identified in this study, the NMR measurements, and thus the effort and cost for the NMR assignment of a protein can be reduced several-fold, proteins may be labeled only with 15 N for backbone HN assignment, and larger proteins can likely be assigned, which enlarges the protein family easily accessible by NMR to ...

  3. Protein NMR

    Much space and discussion is devoted to practical aspects. The implementation of protein NMR assignment is described using the program CCPNmr Analysis. This program has been developed by CCPN and actively seeks input from the NMR community. CCPNmr Analysis is based on the detailed and well thought-out CCPN Data Model which has the advantage (a ...

  4. 6.2: Heteronuclear 3D NMR- Resonance Assignment in Proteins

    In order to produce a protein sample with nearly complete uniform labeling with 13 C and 15 N isotopes, ... (CO)NH experiments for the backbone NMR resonance assignment in proteins. Cα and Cα labels are color coded: blue for intra-residual signals and green for preceding carbons (Cα-1, Cβ-1). HNCACB contours are color-coded: black for ...

  5. Robust automated backbone triple resonance NMR assignments of ...

    Triple resonance assignments of the protein backbone permit access, either directly or by tethering to side chain resonance assignments, to a wide range of dynamic phenomena 17,18 and structural ...

  6. Assignment Practice

    There are several ways in which triple resonance backbone assignment, in particular, can be approached in CCPNmr Analysis using more or less automated methods. Initially a more manual method will be described, as this makes it easier to understand the process of assignment for those who are new to protein NMR assignment.

  7. Protein NMR Resonance Assignment

    Therefore, the establishment of the sequential assignment procedure was a mile stone for the protein NMR. Backbone amide proton (H N ) and α proton (H α ) signals were sequentially assigned based on the distance information between H N i and \({\rm H}^{\alpha}_{{\rm i}-1}\) , and were aligned on the amino acid sequence of the particular protein.

  8. Fast Protein Backbone NMR Resonance Assignment Using the ...

    Protein backbone resonance assignment using the BATCH strategy requires a 15 N/ 13 C labeled protein sample, typically in the concentration range of 100 μM to a few mM. Since high-level deuteration of aliphatic protons is incompatible with the BATCH strategy, this approach is best suited for proteins below ∼20 kDa.

  9. Rapid protein assignments and structures from raw NMR spectra with the

    The histogram shows the number of spectra for backbone assignment, side-chain assignment, and NOE measurement. ... allowing rapid protein NMR assignment and structure determination by non-experts.

  10. Assignment of Protein NMR Spectra Using Heteronuclear NMR ...

    1 Introduction. The assignment of resonances in the complex nuclear magnetic resonance (NMR) spectrum of a protein is the first step in any NMR study of protein structure, function or dynamics. Before 1980, the assignment was achieved using one-dimensional (1D) NMR and was based, to a large extent, on the assumption that the structure of the ...

  11. PDF CcpNmr Analysis Version 3 Backbone Assignment Tutorial

    Learn how to use CCPN software to perform semi-automatic backbone assignment of biological NMR data in this tutorial. The tutorial covers the basic steps of importing spectra, creating a project, running the assignment routine and checking the results. You will also find tips and tricks to improve the accuracy and efficiency of your assignments.

  12. Practical aspects of NMR signal assignment in larger and challenging

    The principles of the conventional approach for assigning protein backbone resonances were developed in the early 1990s following cost-effective production of 15 N ... Many NMR assignment software packages feature automated routines for performing this so-called sequence alignment and provide a ranking of polypeptide fragments that match the ...

  13. A Practical Implementation of Cross-spectrum in Protein Backbone

    In protein NMR spectroscopy the backbone resonance assignment is a key step in the characterization of protein structure and dynamics. Numerous efforts have been made to expedite this critical, time-consuming, and labor-intensive task by improvements to the NMR data collection schemes as well as the analysis methods.

  14. Triple Resonance Backbone Assignment

    Triple Resonance Backbone Assignment. The description here assumes that the backbone assignment will be carried out using CBCA (CO)NH and CBCANH spectra. Many of the steps are the same if using HNCA, HN (CO)CA, HNCO and HN (CA)CO spectra, and differences are highlighted in a separate section. Now comes the actual assignment part which follows ...

  15. NMR Structure Determination for Larger Proteins Using Backbone-Only

    The first step in protein structure determination by nuclear magnetic resonance (NMR) is chemical-shift assignment for the backbone atoms. In contrast to the subsequent assignment of the side chains, this process is now rapid, reliable, and largely automated (1-5).Global backbone structural information complementing the local structure information provided by backbone chemical-shift ...

  16. A method for validating the accuracy of NMR protein structures

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  17. Protein NMR Resonance Assignment

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  18. Assignment Theory

    The most simple and straight forward method of backbone resonance assignment involves the use of 15 N, 13 C labelled protein and the measurement of CBCANNH and CBCA(CO)NNH spectra. Large Proteins. Large proteins give worse NMR spectra, because they tumble more slowly. For this reason the CBCANNH and CBCA(CO)NNH spectra of larger proteins (> 150 ...

  19. Decoding Atomic Addresses: Solution NMR Resonance Assignment of

    The early 1990s marked a significant period in protein NMR assignment as key technologies became readily available for these experiments. One major advancement was the recombinant expression of proteins, which facilitated isotope labeling and thereby expanded NMR-visible nuclei from solely 1 H to include 1 H, 13 C, and 15 N.

  20. Backbone assignment of perdeuterated proteins by solid-state NMR using

    The sample needs to be spun at a minimum of 40 kHz in the NMR spectrometer. With a minimal set of five 3D NMR spectra, the protein backbone and some of the side-chain atoms can be completely assigned.

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    Here, using multidimensional solution NMR, we report the 1 H, 15 N, and 13 C chemical shift assignments (~ 86% of backbone resonance assignments) for human SERF2. TALOS-N predicted secondary structure of SERF2 showed three very short helices (3-4 residues long) in the N-terminal region of the protein and a long helix in the C-terminal region ...

  22. APSY-NMR for protein backbone assignment in high-throughput structural

    A standard set of three APSY-NMR experiments has been used in daily practice to obtain polypeptide backbone NMR assignments in globular proteins with sizes up to about 150 residues, which had been identified as targets for structure determination by the Joint Center for Structural Genomics (JCSG) under the auspices of the Protein Structure Initiative (PSI). In a representative sample of 30 ...

  23. Manual Assignment

    The assignment is done using the assignment panel (press a when the mouse is over the peak to be assigned). Select New for the carbon dimension. This will create a new carbon resonance and assign it to this peak. Since it belongs to the same spin system as the N and H resonances, click on Set Same Spin System, so as to add the new carbon ...

  24. Backbone 1H, 13C and 15N resonance assignment of the ubiquitin ...

    The backbone 1 H, 13 C and 15 N resonance assignment of Ubiquitin Specific Protease 7 catalytic domain (residues 208-554) was performed in its complex with a small molecule ligand and in its apo form as a reference. The amide 1 H-15 N signal intensities were boosted by an amide hydrogen exchange protocol, where expressed 2 H, 13 C, 15 N-labeled protein was unfolded and re-folded to ensure ...

  25. Double Resonance Backbone Assignment

    Double Resonance Backbone Assignment. For smaller proteins, it is possible to do the backbone assignment using just 15 N-labelled protein. The spectra used for this are the 15N-NOESY-HSQC and the 15N-TOCSY-HSQC. The 15N-NOESY-HSQC will show for each NH group all 1 H resonances which are within about 5-7Å of the NH hydrogen.

  26. Backbone 1H, 13C and 15N resonance assignment of the ...

    The backbone 1H, 13C and 15N resonance assignment of Ubiquitin Specific Protease 7 catalytic domain (residues 208-554) was performed in its complex with a small molecule ligand and in its apo form as a reference. The amide 1H-15N signal intensities were boosted by an amide hydrogen exchange protocol, where expressed 2H, 13C, 15N-labeled protein was unfolded and re-folded to ensure exchange ...