Side Chain Conformational Distributions of a Small Protein Derived from Model-Free Analysis of a Large Set of Residual Dipolar Couplings

The transient expression of recombinant proteins in plant cell packs facilitates stable isotope labelling for NMR spectroscopy

Nuclear magnetic resonance (NMR) spectroscopy can be used to determine the structure, dynamics and interactions of proteins. However, protein NMR requires stable isotope labelling for signal detection. The cells used for the production of recombinant proteins must therefore be grown in medium containing isotopically labelled substrates. Stable isotope labelling is well established in Escherichia coli, but bacteria are only suitable for the production of simple proteins without post-translational modifications. More complex proteins require eukaryotic production hosts, but their growth can be impaired by labelled media, thus reducing product yields and increasing costs. To address this limitation, we used media supplemented with isotope-labelled substrates to cultivate the tobacco-derived cell line BY-2, which was then cast into plant cell packs (PCPs) for the transient expression of a labelled version of the model protein GB1. Mass spectrometry confirmed the feasibility of isotope labelling with ¹⁵ N and ² H using this approach. The resulting NMR spectrum featured a signal dispersion comparable to recombinant GB1 produced in E. coli. PCPs therefore offer a rapid and cost-efficient alternative for the production of isotope-labelled proteins for NMR analysis, especially suitable for complex proteins that cannot be produced in microbial systems.

Proton TOCSY NMR relaxation rates quantitate protein side chain mobility in the Pin1 WW domain

Protein side chain dynamics play a vital role in many biological processes, but differentiating mobile from rigid side chains remains a technical challenge in structural biology. Solution NMR spectroscopy is ideally suited for this but suffers from limited signal-to-noise, signal overlap, and a need for fractional ¹³C or ²H labeling. Here we introduce a simple strategy measuring initial ¹H relaxation rates during a ¹H TOCSY sequence like DIPSI-2, which can be appended to the beginning of any multi-dimensional NMR sequence that begins on ¹H. The TOCSY RF field compels all ¹H atoms to behave similarly under the influence of strong coupling and rotating frame cross-relaxation, so that differences in relaxation rates are due primarily to side chain mobility. We apply the scheme to a thermostable mutant Pin1 WW domain and demonstrate that the observed ¹H relaxation rates correlate well with two independent NMR measures of side-chain dynamics, cross-correlated ¹³C relaxation rates in ¹³C^βH₂ methylene groups and maximum observable ³J couplings sensitive to the χ₁ side chain dihedral angle (³J_Hα,Hβ, ³J_N,Hβ, and ³J_CO,Hβ). The most restricted side chains belong to Trp26 and Asn40, which are closely packed to constitute the folding center of the WW domain. None of the other conserved aromatic residues is as immobile as the first tryptophan side chain of the WW domain. The proposed ¹H relaxation methodology should make it relatively easy to measure side chain dynamics on uniformly ¹⁵N- or ¹³C-labeled proteins, so long as chemical shift assignments are obtainable.

Programmable alignment media from self-assembled oligopeptide amphiphiles for the measurement of independent sets of residual dipolar couplings in organic solvents

NMR spectroscopy in anisotropic media has emerged as a powerful technique for the structural elucidation of organic molecules. Its application requires weak alignment of analytes by means of suitable alignment media. Although a number of alignment media, that are compatible with organic solvents, have been introduced in the last 20 years, acquiring a number of independent, non-linearly related sets of anisotropic NMR data from the same organic solvent system remains a formidable challenge, which is however crucial for the alignment simulations and deriving dynamic and structural information of organic molecules unambiguously. Herein, we introduce a programmable strategy to construct several distinct peptide-based alignment media by adjusting the amino acid sequence, which allows us to measure independent sets of residual dipolar couplings (RDCs) in a highly efficient and accurate manner. This study opens a new avenue for de novo structure determination of organic compounds without requiring prior structural information.

We report a programmable strategy to construct multi-alignment media via peptide self-assembly for the measurement of independent sets of residual dipolar couplings (RDCs).

Advances in NMR Spectroscopy of Weakly Aligned Biomolecular Systems

The measurement and application of residual dipolar couplings (RDCs) in solution NMR studies of biological macromolecules has become well established over the past quarter of a century. Numerous methods for generating the requisite anisotropic orientational molecular distribution have been demonstrated, each with its specific strengths and weaknesses. In parallel, an enormous number of pulse schemes have been introduced to measure the many different types of RDCs, ranging from the most widely measured backbone amide ¹⁵N-¹H RDCs, to ¹H-¹H RDCs and couplings between low-γ nuclei. Applications of RDCs range from structure validation and refinement to the determination of relative domain orientations, the measurement of backbone and domain motions, and de novo structure determination. Nevertheless, it appears that the power of the RDC methodology remains underutilized. This review aims to highlight the practical aspects of sample preparation and RDC measurement while describing some of the most straightforward applications that take advantage of the exceptionally precise information contained in such data. Some emphasis will be placed on more recent developments that enable the accurate measurement of RDCs in larger systems, which is key to the ongoing shift in focus of biological NMR spectroscopy from structure determination toward gaining improved understanding of how molecular flexibility drives protein function.

NMR hawk-eyed view of AlphaFold2 structures

The prediction of the three‐dimensional (3D) structure of proteins from the amino acid sequence made a stunning breakthrough reaching atomic accuracy. Using the neural network‐based method AlphaFold2, 3D structures of almost the entire human proteome have been predicted and made available (https://www.alphafold.ebi.ac.uk). To gain insight into how well AlphaFold2 structures represent the conformation of proteins in solution, I here compare the AlphaFold2 structures of selected small proteins with their 3D structures that were determined by nuclear magnetic resonance (NMR) spectroscopy. Proteins were selected for which the 3D solution structures were determined on the basis of a very large number of distance restraints and residual dipolar couplings and are thus some of the best‐resolved solution structures of proteins to date. The quality of the backbone conformation of the AlphaFold2 structures is assessed by fitting a large set of experimental residual dipolar couplings (RDCs). The analysis shows that experimental RDCs fit extremely well to the AlphaFold2 structures predicted for GB3, DinI, and ubiquitin. In the case of GB3, the accuracy of the AlphaFold2 structure even surpasses that of a 1.1 Å crystal structure. Fitting of experimental RDCs furthermore allows identification of AlphaFold2 structures that are best representative of the protein's conformation in solution as seen for the EF hands of the N‐terminal domain of Ca²⁺‐ligated calmodulin. Taken together, the analysis shows that structures predicted by AlphaFold2 can be highly representative of the solution conformation of proteins. The combination of AlphaFold2 structures with RDCs promises to be a powerful approach to study structural changes in proteins.

13C NMR Relaxation Analysis of Protein GB3 for the Assessment of Side Chain Dynamics Predictions by Current AMBER and CHARMM Force Fields

Molecular simulations with seven current AMBER- and CHARMM-based force fields yield markedly differing internal bond vector autocorrelation function predictions for many of the 223 methine and methylene H-C bonds of the 56-residue protein GB3. To enable quantification of accuracy, ¹³C R₁, R₂, and heteronuclear NOE relaxation rates have been determined for the methine and stereochemically assigned methylene C^α and C^β positions. With only three experimental relaxation values for each bond vector, central to this analysis is the accuracy with which MD-derived autocorrelation curves can be represented by a 3-parameter equation which, in turn, maps onto the NMR relaxation values. In contrast to the more widely used extended Lipari-Szabo order parameter representation, 95% of these MD-derived internal autocorrelation curves for GB3 can be fitted to within 1.0% rmsd over the time frame from 30 ps to 4 ns by a biexponential Larmor frequency-selective representation (LF-S²). Applying the LF-S² representation to the experimental relaxation rates and uncertainties serves to determine the boundary range for the autocorrelation function of each bond vector consistent with the experimental data. Not surprisingly, all seven force fields predict the autocorrelation functions for the more motionally restricted ¹H^α-¹³C^α and ¹H^β-¹³C^β bond vectors with reasonable accuracy. However, for the ¹H^β-¹³C^β bond vectors exhibiting aggregate order parameter S² values less than 0.85, only 1% of the MD-derived predictions lie with 1 σ of the experimentally determined autocorrelation functions and only 7% within 2 σ. On the other hand, substantial residue type-specific improvements in predictive performance were observed among the recent AMBER force fields. This analysis indicates considerable potential for the use of ¹³C relaxation measurements in guiding the optimization of the side chain dynamics characteristics of protein molecular simulations.

Residual Dipolar Couplings for Resolving Cysteine Bridges in Disulfide-Rich Peptides

Disulfide bridges in proteins are formed by the oxidation of pairs of cysteine residues. These cross-links play a critical role in stabilizing the 3D-structure of small disulfide rich polypeptides such as hormones and venom toxins. The arrangement of the multiple disulfide bonds directs the peptide fold into distinct structural motifs that have evolved for resistance against biochemical and physical insults. These structural scaffolds have, therefore, proven to be very attractive in bioengineering efforts to develop novel biologics with applications in health and agriculture. Structural characterization of small disulfide rich peptides (DRPs) presents unique challenges when using commonly applied biophysical methods. NMR is the most commonly used method for studying such molecules, where the relatively small size of these molecules results in highly precise structural ensembles defined by a large number of distance and dihedral angle restraints per amino acid. However, in NMR the sulfur atoms that are involved in three of the five dihedral angles in a disulfide bond cannot be readily measured. Given the central role of disulfide bonds in the structure of these molecules, it is unclear what the inherent resolution of such NMR structures is when using traditional NMR methods. Here, we use an extensive set of long-range residual dipolar couplings (RDCs) to assess the resolution of the NMR structure of a disulfide-rich peptide. We find that structures based primarily on NOEs, yield ensembles that are equivalent to a crystallographic resolution of 2-3 Å in resolution, and that incorporation of RDCs reduces this to ~1-1.5 Å resolution. At this resolution the sidechain of ordered amino acids can be defined accurately, allowing the geometry of the cysteine bridges to be better defined, and allowing for disulfide-bond connectivities to be determined with high confidence. The observed improvements in resolution when using RDCs is remarkable considering the small size of these peptides.

Inferring protein 3D structure from deep mutation scans

We describe an experimental method of three-dimensional (3D) structure determination that exploits the increasing ease of high-throughput mutational scans. Inspired by the success of using natural, evolutionary sequence covariation to compute protein and RNA folds, we explored whether 'laboratory', synthetic sequence variation might also yield 3D structures. We analyzed five large-scale mutational scans and discovered that the pairs of residues with the largest positive epistasis in the experiments are sufficient to determine the 3D fold. We show that the strongest epistatic pairings from genetic screens of three proteins, a ribozyme and a protein interaction reveal 3D contacts within and between macromolecules. Using these experimental epistatic pairs, we compute ab initio folds for a GB1 domain (within 1.8 Å of the crystal structure) and a WW domain (2.1 Å). We propose strategies that reduce the number of mutants needed for contact prediction, suggesting that genomics-based techniques can efficiently predict 3D structure.

Utilizing dipole-dipole cross-correlated relaxation for the measurement of angles between pairs of opposing CαHα-CαHα bonds in anti-parallel β-sheets

Dipole-dipole cross-correlated relaxation (CCR) between two spin pairs is rich with macromolecular structural and dynamic information on inter-nuclear bond vectors. Measurement of short range dipolar CCR rates has been demonstrated for a variety of inter-nuclear vector spin pairs in proteins and nucleic acids, where the multiple quantum coherence necessary for observing the CCR rate is created by through-bond scalar coupling. In principle, CCR rates can be measured for any pair of inter-nuclear vectors where coherence can be generated between one spin of each spin pair, regardless of both the distance between the two spin pairs and the distance of the two spins forming the multiple quantum coherence. In practice, however, long range CCR (lrCCR) rates are challenging to measure due to difficulties in linking spatially distant spin pairs. By utilizing through-space relaxation allowed coherence transfer (RACT), we have developed a new method for the measurement of lrCCR rates involving CαHα bonds on opposing anti-parallel β-strands. The resulting lrCCR rates are straightforward to interpret since only the angle between the two vectors modulates the strength of the interference effect. We applied our lrCCR measurement to the third immunoglobulin-binding domain of the streptococcal protein G (GB3) and utilize published NMR ensembles and static NMR/X-ray structures to highlight the relationship between the lrCCR rates and the CαHα-CαHα inter-bond angle and bond mobility. Furthermore, we employ the lrCCR rates to guide the selection of sub-ensembles from the published NMR ensembles for enhancing the structural and dynamic interpretation of the data. We foresee this methodology for measuring lrCCR rates as improving the generation of structural ensembles by providing highly accurate details concerning the orientation of CαHα bonds on opposing anti-parallel β-strands.

Direct Observation of CH/CH van der Waals Interactions in Proteins by NMR

van der Waals interactions are important to protein stability and function. These interactions are usually identified empirically based on protein 3D structures. In this work, we performed a solution nuclear magnetic resonance (NMR) spectroscopy study of van der Waals interactions by detecting the through-space vdw JCC-coupling between protein aliphatic side chain groups. Specifically, vdw JCC-coupling values up to ∼0.5 Hz were obtained between the methyl and nearby aliphatic groups in protein GB3, providing direct experimental evidence for the van der Waals interactions. Quantum mechanical calculations suggest that the J-coupling is correlated with the exchange-repulsion term of van der Waals interaction. NMR detection of vdw JCC-coupling offers a new tool to characterize such interactions in proteins.

Detection of Correlated Protein Backbone and Side-Chain Angle Fluctuations

NMR methods for the characterization of local protein motions have attained a high level of sophistication. Measurement of the synchronization between those motions, however, poses a serious challenge. Such correlated motions are one of the underlying mechanisms for the propagation of local changes to remote sites and as such for information transfer. Here, we demonstrate the experimental detection of the synchronization of motion over an intermediate range. To that purpose, we designed pulse sequences for the measurement of cross-correlated relaxation between the backbone H^N -N and side-chain H^β -C^β dipoles in Ile, Thr, and Val in the protein GB3. These bonds are related through two and three intervening dihedral angles. We show that the correlated motions inherent in a structural ensemble obtained from a large and diverse array of NMR probes are in excellent agreement with our measurements.

Integrating NOE and RDC using sum-of-squares relaxation for protein structure determination

We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms-RDC-SOS and RDC-NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramér-Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.

Conformational Populations of β-(1→4) O-Glycosidic Linkages Using Redundant NMR J-Couplings and Circular Statistics

Twelve disaccharides containing β-(1→4) linkages and displaying systematic structural variations in the vicinity of these linkages were selectively labeled with ¹³C to facilitate measurements of multiple NMR spin-spin (scalar; J) coupling constants (J_CH and J_CC values) across their O-glycosidic linkages. Ensembles of spin-couplings (²J_COC, ³J_COCH, ³J_COCC) sensitive to the two linkage torsion angles, phi (ϕ) and psi (ψ), were analyzed by using parametrized equations obtained from density functional theory (DFT) calculations, Fredholm theory, and circular statistics to calculate experiment-based rotamer populations for ϕ and ψ in each disaccharide. With the statistical program MA'AT, torsion angles ϕ and ψ were modeled as a single von Mises distribution, which yielded two parameters, the mean position and the circular standard deviation (CSD) for each angle. The NMR-derived rotamer populations were compared to those obtained from 1 μs aqueous molecular dynamics (MD) simulations and crystallographic database statistical analyses. Conformer populations obtained exclusively from the MA'AT treatment of redundant J-couplings were in very good agreement with those obtained from the MD simulations, providing evidence that conformational populations can be determined by NMR for mobile molecular elements such as O-glycosidic linkages with minimal input from theory. The approach also provides an experimental means to validate the conformational preferences predicted from MD simulations. The conformational behaviors of ϕ in the 12 disaccharides were very similar, but those of ψ varied significantly, allowing a classification of the 12 disaccharides based on preferred linkage conformation in solution.

ARTSY-J: Convenient and precise measurement of (3)JHNHα couplings in medium-size proteins from TROSY-HSQC spectra

A new and convenient method, named ARTSY-J, is introduced that permits extraction of the (3)JHNHα couplings in proteins from the relative intensities in a pair of (15)N-(1)H TROSY-HSQC spectra. The pulse scheme includes (3)JHNHα dephasing of the narrower TROSY (1)H(N)-{(15)N} doublet component during a delay, integrated into the regular two-dimensional TROSY-HSQC pulse scheme, and compares the obtained intensity with a reference spectrum where (3)JHNHα dephasing is suppressed. The effect of passive (1)H(α) spin flips downscales the apparent (3)JHNHα coupling by a uniform factor that depends approximately linearly on both the duration of the (3)JHNHα dephasing delay and the (1)H-(1)H cross relaxation rate. Using such a correction factor, which accounts for the effects of both inhomogeneity of the radiofrequency field and (1)H(α) spin flips, agreement between prior and newly measured values for the small model protein GB3 is better than 0.3Hz. Measurement for the HIV-1 protease homodimer (22kDa) yields (3)JHNHα values that agree to better than 0.7Hz with predictions made on the basis of a previously parameterized Karplus equation. Although for Gly residues the two individual (3)JHNHα couplings cannot be extracted from a single set of ARTSY-J spectra, the measurement provides valuable ϕ angle information.

Site-Specific Internal Motions in GB1 Protein Microcrystals Revealed by 3D ²H-¹³C-¹³C Solid-State NMR Spectroscopy

(2)H quadrupolar line shapes deliver rich information about protein dynamics. A newly designed 3D (2)H-(13)C-(13)C solid-state NMR magic angle spinning (MAS) experiment is presented and demonstrated on the microcrystalline β1 immunoglobulin binding domain of protein G (GB1). The implementation of (2)H-(13)C adiabatic rotor-echo-short-pulse-irradiation cross-polarization (RESPIRATION CP) ensures the accuracy of the extracted line shapes and provides enhanced sensitivity relative to conventional CP methods. The 3D (2)H-(13)C-(13)C spectrum reveals (2)H line shapes for 140 resolved aliphatic deuterium sites. Motional-averaged (2)H quadrupolar parameters obtained from the line-shape fitting identify side-chain motions. Restricted side-chain dynamics are observed for a number of polar residues including K13, D22, E27, K31, D36, N37, D46, D47, K50, and E56, which we attribute to the effects of salt bridges and hydrogen bonds. In contrast, we observe significantly enhanced side-chain flexibility for Q2, K4, K10, E15, E19, N35, N40, and E42, due to solvent exposure and low packing density. T11, T16, and T17 side chains exhibit motions with larger amplitudes than other Thr residues due to solvent interactions. The side chains of L5, V54, and V29 are highly rigid because they are packed in the core of the protein. High correlations were demonstrated between GB1 side-chain dynamics and its biological function. Large-amplitude side-chain motions are observed for regions contacting and interacting with immunoglobulin G (IgG). In contrast, rigid side chains are primarily found for residues in the structural core of the protein that are absent from protein binding and interactions.

Observation of α-Helical Hydrogen-Bond Cooperativity in an Intact Protein

The presence and extent of hydrogen-bonding (H-bonding) cooperativity in proteins remains a fundamental question, which in the past has been studied extensively, mostly by infrared and fluorescence measurements on model peptides. We demonstrate that such cooperativity can be studied in an intact protein by hydrogen/deuterium exchange NMR spectroscopy. The method is based on the fact that substitution of NH by ND in a backbone amide group slightly weakens the N-H···O═C hydrogen bond. Our results show that such substitution at position i in an α-helix impacts the (1)H and (15)N chemical shifts of the amide sites of residues i - 3 to i + 3. Quantum mechanical calculations indicate that the upfield shifts of (1)H and (15)N resonances at site i, observed upon H/D exchanges at sites i - 3, i + 1, i + 2, and i + 3, correspond to a decrease of the ith backbone amide electric dipole moment, which weakens its H-bonding and long-range electrostatic interactions with other backbone amides in the α-helix. These results provide new quantitative insights into the cooperativity of H-bonding in protein α-helices.