Nuclear magnetic dipole interactions in field-oriented proteins: information for structure determination in solution

Molecular Structure Refinement Based on Residual Dipolar Couplings: A Comparison of the Molecular Rotational-Sampling Method with the Alignment-Tensor Approach

In NMR experiments, residual dipolar couplings (RDCs) in a molecule can be measured by averaging the dipolar couplings (DCs) over the rotational motion of a molecule in an environment that induces a slight anisotropic orientation distribution of the molecule. Since the shape of the anisotropic distribution cannot be measured, it is standard practice to use a particular orientation distribution of the molecule with respect to the magnetic field, in the form of a so-called alignment tensor (AT), to calculate RDC-values for the molecule. Since the same alignment tensor is commonly used to calculate the different RDCs of a molecule, this approach rests on the assumption that the rotational motion of the molecule is decoupled from its internal motions and that the molecule is rigid. The validity of these two assumptions is investigated for a small, simple molecule, using a relatively rigid atomic interaction function or force field and a more flexible one. By simulating the molecule using an orientation-biasing force an anisotropic rotational distribution can be generated, for which RDCs can be obtained. Using these RDCs as target RDCs when applying one of the two approaches of structure refinement based on RDCs, it can be investigated how well the target RDCs are approximated in the RDC restraining and whether the corresponding nonuniform orientation distribution is reproduced. For the relatively rigid version of the molecule, the AT approach reproduces the target RDC-values, although the nonuniform orientation distribution of the angle θab,H between the vector r⃗ab connecting two atoms a and b in the molecule and the vector representing the direction of the magnetic field H⃗ as generated in the orientation-biasing simulation cannot be reproduced in the AT RDC-restraining simulation. For the relatively flexible version of the molecule, the AT approach fails to reproduce both the target RDC values and the nonuniform orientation distribution. For biomolecules with flexible parts, the application of the AT approach is thus not recommended. Instead, a method based on sampling of the rotational and internal degrees of freedom of the molecule should be applied in molecular structure determination or refinement based on measured RDCs.

An RNA excited conformational state at atomic resolution

Sparse and short-lived excited RNA conformational states are essential players in cell physiology, disease, and therapeutic development, yet determining their 3D structures remains challenging. Combining mutagenesis, NMR spectroscopy, and computational modeling, we determined the 3D structural ensemble formed by a short-lived (lifetime ~2.1 ms) lowly-populated (~0.4%) conformational state in HIV-1 TAR RNA. Through a strand register shift, the excited conformational state completely remodels the 3D structure of the ground state (RMSD from the ground state = 7.2 ± 0.9 Å), forming a surprisingly more ordered conformational ensemble rich in non-canonical mismatches. The structure impedes the formation of the motifs recognized by Tat and the super elongation complex, explaining why this alternative TAR conformation cannot activate HIV-1 transcription. The ability to determine the 3D structures of fleeting RNA states using the presented methodology holds great promise for our understanding of RNA biology, disease mechanisms, and the development of RNA-targeting therapeutics.

Kinetic Resolution of the Atomic 3D Structures Formed by Ground and Excited Conformational States in an RNA Dynamic Ensemble

Knowing the 3D structures formed by the various conformations populating the RNA free-energy landscape, their relative abundance, and kinetic interconversion rates is required to obtain a quantitative and predictive understanding of how RNAs fold and function at the atomic level. While methods integrating ensemble-averaged experimental data with computational modeling are helping define the most abundant conformations in RNA ensembles, elucidating their kinetic rates of interconversion and determining the 3D structures of sparsely populated short-lived RNA excited conformational states (ESs) remains challenging. Here, we developed an approach integrating Rosetta-FARFAR RNA structure prediction with NMR residual dipolar couplings and relaxation dispersion that simultaneously determines the 3D structures formed by the ground-state (GS) and ES subensembles, their relative abundance, and kinetic rates of interconversion. The approach is demonstrated on HIV-1 TAR, whose six-nucleotide apical loop was previously shown to form a sparsely populated (∼13%) short-lived (lifetime ∼ 45 μs) ES. In the GS, the apical loop forms a broad distribution of open conformations interconverting on the pico-to-nanosecond time scale. Most residues are unpaired and preorganized to bind the Tat-superelongation protein complex. The apical loop zips up in the ES, forming a narrow distribution of closed conformations, which sequester critical residues required for protein recognition. Our work introduces an approach for determining the 3D ensemble models formed by sparsely populated RNA conformational states, provides a rare atomic view of an RNA ES, and kinetically resolves the atomic 3D structures of RNA conformational substates, interchanging on time scales spanning 6 orders of magnitude, from picoseconds to microseconds.

Base Dynamics in the HhaI Protein Binding Site

Protein-DNA interactions play an important role in numerous biological functions within the living cell. In many of these interactions, the DNA helix is significantly distorted upon protein-DNA complex formation. The HhaI restriction-modification system is one such system, where the methylation target is flipped out of the helix when bound to the methyltransferase. However, the base flipping mechanism is not well understood. The dynamics of the binding site of the HhaI methyltransferase and endonuclease (underlined) within the DNA oligomer [d(G1A2T3A4G5C6G7C8T9A10T11C12)]2 are studied using deuterium solid-state NMR (SSNMR). SSNMR spectra obtained from DNAs deuterated on the base of nucleotides within and flanking the [5'-GCGC-3']2 sequence indicate that all of these positions are structurally flexible. Previously, conformational flexibility within the phosphodiester backbone and furanose ring within the target sequence has been observed and hypothesized to play a role in the distortion mechanism. However, whether that distortion was occurring through an active or passive mechanism remained unclear. These NMR data demonstrate that although the [5'-GCGC-3']2 sequence is dynamic, the target cytosine is not passively flipping out of the double-helix on the millisecond-picosecond time scale. Additionally, although previous studies have shown that both the furanose ring and phosphodiester backbone experience a change in dynamics upon methylation, which may play a role in recognition and cleavage by the endonuclease, our observations here indicate that methylation has no effect on the dynamics of the base itself.

Synergism between x-ray crystallography and NMR residual dipolar couplings in characterizing protein dynamics

The important role of structural dynamics in protein function is widely recognized. Thermal or B-factors and their anisotropy, seen in x-ray analysis of protein structures, report on the presence of atomic coordinate heterogeneity that can be attributed to motion. However, their quantitative evaluation in terms of protein dynamics by x-ray ensemble refinement remains challenging. NMR spectroscopy provides quantitative information on the amplitudes and time scales of motional processes. Unfortunately, with a few exceptions, the NMR data do not provide direct insights into the atomic details of dynamic trajectories. Residual dipolar couplings, measured by solution NMR, are very precise parameters reporting on the time-averaged bond-vector orientations and may offer the opportunity to derive correctly weighted dynamic ensembles of structures for cases where multiple high-resolution x-ray structures are available. Applications to the SARS-CoV-2 main protease, M^pro, and ubiquitin highlight this complementarity of NMR and crystallography for quantitative assessment of internal motions.

Structural Evolution of Paramagnetic Lanthanide Compounds in Solution Compared to Time- and Ensemble-Average Structures

Anisotropy in the magnetic susceptibility strongly influences the paramagnetic shifts seen in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) experiments. A previous study on a series of C3-symmetric prototype MRI contrast agents showed that their magnetic anisotropy was highly sensitive to changes in molecular geometry and concluded that changes in the average angle between the lanthanide-oxygen (Ln-O) bonds and the molecular C3 axis due to solvent interactions had a significant impact on the magnetic anisotropy and, consequently, the paramagnetic shift. However, this study, like many others, was predicated on an idealized C3-symmetric structural model, which may not be representative of the dynamic structure in solution at the single-molecule level. Here, we address this by using ab initio molecular dynamics simulations to simulate how the molecular geometry, in particular the angles between the Ln-O bonds and the pseudo-C3 axis, evolves over time in the solution, mimicking typical experimental conditions. We observe large-amplitude oscillations in the O-Ln-C̃3 angles, and complete active space self-consistent field spin-orbit calculations show that this leads to similarly large oscillations in the pseudocontact (dipolar) paramagnetic NMR shifts. The time-averaged shifts show good agreement with experimental measurements, while the large fluctuations suggest that an idealized structure provides an incomplete description of the solution dynamics. Our observations have significant implications for modeling the electronic and nuclear relaxation times in this and other systems where the magnetic susceptibility is exquisitely sensitive to the molecular structure.

Paramagnetic NMR restraints for the characterization of protein structural rearrangements

Mobility is a common feature of biomacromolecules, often fundamental for their function. Thus, in many cases, biomacromolecules cannot be described by a single conformation, but rather by a conformational ensemble. NMR paramagnetic data demonstrated quite informative to monitor this conformational variability, especially when used in conjunction with data from different sources. Due to their long-range nature, paramagnetic data can, for instance, i) clearly demonstrate the occurrence of conformational rearrangements, ii) reveal the presence of minor conformational states, sampled only for a short time, iii) indicate the most representative conformations within the conformational ensemble sampled by the molecule, iv) provide an upper limit to the weight of each conformation.

Elucidating the concentration-dependent effects of thiocyanate binding to carbonic anhydrase

Many proteins naturally carry metal centers, with a large share of them being in the active sites of several enzymes. Paramagnetic effects are a powerful source of structural information and, therefore, if the native metal is paramagnetic, or it can be functionally substituted with a paramagnetic one, paramagnetic effects can be used to study the metal sites, as well as the overall structure of the protein. One notable example is cobalt(II) substitution for zinc(II) in carbonic anhydrase. In this manuscript we investigate the effects of sodium thiocyanate on the chemical environment of the metal ion of the human carbonic anhydrase II. The electron paramagnetic resonance (EPR) titration of the cobalt(II) protein with thiocyanate shows that the EPR spectrum changes from A-type to C-type on passing from 1:1 to 1:1000-fold ligand excess. This indicates the occurrence of a change in the electronic structure, which may reflect a sizable change in the metal coordination environment in turn caused by a modification of the frozen solvent glass. However, paramagnetic nuclear magnetic resonance (NMR) data indicate that the metal coordination cage remains unperturbed even in 1:1000-fold ligand excess. This result proves that the C-type EPR spectrum observed at large ligand concentration should be ascribed to the low temperature at which EPR measurements are performed, which impacts on the structure of the protein when it is destabilized by a high concentration of a chaotropic agent.

Magnetically aligned nanodiscs enable direct measurement of 17O residual quadrupolar coupling for small molecules

The use of 17O in NMR spectroscopy for structural studies has been limited due to its low natural abundance, low gyromagnetic ratio, and quadrupolar relaxation. Previous solution 17O work has primarily focused on studies of liquids where the 17O quadrupolar coupling is averaged to zero by isotropic molecular tumbling, and therefore has ignored the structural information contained in this parameter. Here, we use magnetically aligned polymer nanodiscs as an alignment medium to measure residual quadrupolar couplings (RQCs) for 17O-labelled benzoic acid in the aqueous phase. We show that increasing the magnetic field strength improves spectral sensitivity and resolution and that each satellite peak of the expected pentet pattern resolves clearly at 18.8 T. We observed no significant dependence of the RQC magnitudes on the magnetic field strength. However, changing the orientation of the alignment medium alters the RQC by a consistent factor, suggesting that 17O RQCs measured in this way can provide reliable orientational information for elucidations of molecular structures.

Interdomain Dynamics via Paramagnetic NMR on the Highly Flexible Complex Calmodulin/Munc13-1

Paramagnetic NMR constraints are very useful to study protein interdomain motion, but their interpretation is not always straightforward. On the example of the particularly flexible complex Calmodulin/Munc13-1, we present a new approach to characterize this motion with pseudocontact shifts and residual dipolar couplings. Using molecular mechanics, we sampled the conformational space of the complex and used a genetic algorithm to find ensembles that are in agreement with the data. We used the Bayesian information criterion to determine the ideal ensemble size. This way, we were able to make an accurate, unambiguous, reproducible model of the interdomain motion of Calmodulin/Munc13-1 without prior knowledge about the domain orientation from crystallography.

The evolution of paramagnetic NMR as a tool in structural biology

Paramagnetic NMR data contain extremely accurate long-range information on metalloprotein structures and, when used in the frame of integrative structural biology approaches, they allow for the retrieval of structural details to a resolution that is not achievable using other techniques. Paramagnetic data thus represent an extremely powerful tool to refine protein models in solution, especially when coupled to X-ray or cryoelectron microscopy data, to monitor the formation of complexes and determine the relative arrangements of their components, and to highlight the presence of conformational heterogeneity. More recently, theoretical and computational advancements in quantum chemical calculations of paramagnetic NMR observables are progressively opening new routes in structural biology, because they allow for the determination of the structure within the coordination sphere of the metal center, thus acting as a loupe on sites that are difficult to observe but very important for protein function.

Synthesis of lanthanide tag and experimental studies on paramagnetically induced residual dipolar couplings

Nuclear Magnetic Resonance (NMR) spectroscopy is an indispensable technique for the structure elucidation of molecules and determination of their characteristic interactions. Residual Dipolar Coupling (RDC) is an NMR parameter that provides global orientation information of molecules but necessitates the use of an anisotropic orientation medium for the partial alignment of the target molecule with respect to the magnetic field. Importantly, anisotropic paramagnetic tags have been successful as orienting media in biomolecular NMR applications but their use in small organic molecules remains imperfect due to challenges in designing functional lanthanide complexes with varying degrees of bonding in the Ln(III) inner coordination sphere. In this study, we propose a strategy for the synthesis of the lanthanide tag 4-mercaptomethylpyridine-2,6-dicarboxylic acid, 4-MMDPA and the measurement of RDCs in a target molecule using several paramagnetic lanthanide complexes.

Paramagnetic Chemical Probes for Studying Biological Macromolecules

Paramagnetic chemical probes have been used in electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) spectroscopy for more than four decades. Recent years witnessed a great increase in the variety of probes for the study of biological macromolecules (proteins, nucleic acids, and oligosaccharides). This Review aims to provide a comprehensive overview of the existing paramagnetic chemical probes, including chemical synthetic approaches, functional properties, and selected applications. Recent developments have seen, in particular, a rapid expansion of the range of lanthanoid probes with anisotropic magnetic susceptibilities for the generation of structural restraints based on residual dipolar couplings and pseudocontact shifts in solution and solid state NMR spectroscopy, mostly for protein studies. Also many new isotropic paramagnetic probes, suitable for NMR measurements of paramagnetic relaxation enhancements, as well as EPR spectroscopic studies (in particular double resonance techniques) have been developed and employed to investigate biological macromolecules. Notwithstanding the large number of reported probes, only few have found broad application and further development of probes for dedicated applications is foreseen.

Concurrent Identification and Characterization of Protein Structure and Continuous Internal Dynamics with REDCRAFT

Internal dynamics of proteins can play a critical role in the biological function of some proteins. Several well documented instances have been reported such as MBP, DHFR, hTS, DGCR8, and NSP1 of the SARS-CoV family of viruses. Despite the importance of internal dynamics of proteins, there currently are very few approaches that allow for meaningful separation of internal dynamics from structural aspects using experimental data. Here we present a computational approach named REDCRAFT that allows for concurrent characterization of protein structure and dynamics. Here, we have subjected DHFR (PDB-ID 1RX2), a 159-residue protein, to a fictitious, mixed mode model of internal dynamics. In this simulation, DHFR was segmented into 7 regions where 4 of the fragments were fixed with respect to each other, two regions underwent rigid-body dynamics, and one region experienced uncorrelated and melting event. The two dynamical and rigid-body segments experienced an average orientational modification of 7° and 12° respectively. Observable RDC data for backbone C′-N, N-HN, and C′-HN were generated from 102 uniformly sampled frames that described the molecular trajectory. The structure calculation of DHFR with REDCRAFT by using traditional Ramachandran restraint produced a structure with 29 Å of structural difference measured over the backbone atoms (bb-rmsd) over the entire length of the protein and an average bb-rmsd of more than 4.7 Å over each of the dynamical fragments. The same exercise repeated with context-specific dihedral restraints generated by PDBMine produced a structure with bb-rmsd of 21 Å over the entire length of the protein but with bb-rmsd of less than 3 Å over each of the fragments. Finally, utilization of the Dynamic Profile generated by REDCRAFT allowed for the identification of different dynamical regions of the protein and the recovery of individual fragments with bb-rmsd of less than 1 Å. Following the recovery of the fragments, our assembly procedure of domains (larger segments consisting of multiple fragments with a common dynamical profile) correctly assembled the four fragments that are rigid with respect to each other, categorized the two domains that underwent rigid-body dynamics, and identified one dynamical region for which no conserved structure could be defined. In conclusion, our approach was successful in identifying the dynamical domains, recovery of structure where it is meaningful, and relative assembly of the domains when possible.

Pseudocontact Shifts in Biomolecular NMR Spectroscopy

Paramagnetic centers in biomolecules, such as specific metal ions that are bound to a protein, affect the nuclei in their surrounding in various ways. One of these effects is the pseudocontact shift (PCS), which leads to strong chemical shift perturbations of nuclear spins, with a remarkably long range of 50 Å and beyond. The PCS in solution NMR is an effect originating from the anisotropic part of the dipole-dipole interaction between the magnetic momentum of unpaired electrons and nuclear spins. The PCS contains spatial information that can be exploited in multiple ways to characterize structure, function, and dynamics of biomacromolecules. It can be used to refine structures, magnify effects of dynamics, help resonance assignments, allows for an intermolecular positioning system, and gives structural information in sensitivity-limited situations where all other methods fail. Here, we review applications of the PCS in biomolecular solution NMR spectroscopy, starting from early works on natural metalloproteins, following the development of non-natural tags to chelate and attach lanthanoid ions to any biomolecular target to advanced applications on large biomolecular complexes and inside living cells. We thus hope to not only highlight past applications but also shed light on the tremendous potential the PCS has in structural biology.

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.

REDCRAFT: A computational platform using residual dipolar coupling NMR data for determining structures of perdeuterated proteins in solution

Nuclear Magnetic Resonance (NMR) spectroscopy is one of the three primary experimental means of characterizing macromolecular structures, including protein structures. Structure determination by solution NMR spectroscopy has traditionally relied heavily on distance restraints derived from nuclear Overhauser effect (NOE) measurements. While structure determination of proteins from NOE-based restraints is well understood and broadly used, structure determination from Residual Dipolar Couplings (RDCs) is relatively less well developed. Here, we describe the new features of the protein structure modeling program REDCRAFT and focus on the new Adaptive Decimation (AD) feature. The AD plays a critical role in improving the robustness of REDCRAFT to missing or noisy data, while allowing structure determination of larger proteins from less data. In this report we demonstrate the successful application of REDCRAFT in structure determination of proteins ranging in size from 50 to 145 residues using experimentally collected data, and of larger proteins (145 to 573 residues) using simulated RDC data. In both cases, REDCRAFT uses only RDC data that can be collected from perdeuterated proteins. Finally, we compare the accuracy of structure determination from RDCs alone with traditional NOE-based methods for the structurally novel PF.2048.1 protein. The RDC-based structure of PF.2048.1 exhibited 1.0 Å BB-RMSD with respect to a high-quality NOE-based structure. Although optimal strategies would include using RDC data together with chemical shift, NOE, and other NMR data, these studies provide proof-of-principle for robust structure determination of largely-perdeuterated proteins from RDC data alone using REDCRAFT.

Residual Dipolar Couplings have the potential to improve the accuracy and reduce the time needed to characterize protein structures. In addition, RDC data have been demonstrated to concurrently elucidate structure of proteins, provide assignment of resonances, and characterize the internal dynamics of proteins. Given all the advantages associated with the study of proteins from RDC data, based on the statistics provided by the Protein Databank (PDB), surprisingly only 124 proteins (out of nearly 150,000 proteins) have utilized RDCs as part of their structure determination. Even a smaller subset of these proteins (approximately 7) have utilized RDCs as the primary source of data for structure determination. One key factor in the use of RDCs is the challenging computational and analytical aspects of this source of data. In this report, we demonstrate the success of the REDCRAFT software package in structure determination of proteins using RDC data that can be collected from small and large proteins in a routine fashion. REDCRAFT accomplishes the challenging task of structure determination from RDCs by introducing a unique search and optimization technique that is both robust and computationally tractable. Structure determination from routinely collectable RDC data using REDCRAFT can complement existing methods to provide faster and more accurate studies of larger and more complex protein structures by NMR spectroscopy in solution state.

Chemical shifts-based similarity restraints improve accuracy of RNA structures determined via NMR

Determination of structure of RNA via NMR is complicated in large part by the lack of a precise parameterization linking the observed chemical shifts to the underlying geometric parameters. In contrast to proteins, where numerous high-resolution crystal structures serve as coordinate templates for this mapping, such models are rarely available for smaller oligonucleotides accessible via NMR, or they exhibit crystal packing and counter-ion binding artifacts that prevent their use for the chemical shifts analysis. On the other hand, NMR-determined structures of RNA often are not solved at the density of restraints required to precisely define the variable degrees of freedom. In this study we sidestep the problems of direct parameterization of the RNA chemical shifts/structure relationship and examine the effects of imposing local fragmental coordinate similarity restraints based on similarities of the experimental secondary ribose ¹³C/¹H chemical shifts instead. The effect of such chemical shift similarity (CSS) restraints on the structural accuracy is assessed via residual dipolar coupling (RDC)-based cross-validation. Improvements in the coordinate accuracy are observed for all of the six RNA constructs considered here as test cases, which argues for routine inclusion of these terms during NMR-based oligonucleotide structure determination. Such accuracy improvements are expected to facilitate derivation of the chemical shift/structure relationships for RNA.

Rapid and accurate determination of atomistic RNA dynamic ensemble models using NMR and structure prediction

Biomolecules form dynamic ensembles of many inter-converting conformations which are key for understanding how they fold and function. However, determining ensembles is challenging because the information required to specify atomic structures for thousands of conformations far exceeds that of experimental measurements. We addressed this data gap and dramatically simplified and accelerated RNA ensemble determination by using structure prediction tools that leverage the growing database of RNA structures to generate a conformation library. Refinement of this library with NMR residual dipolar couplings provided an atomistic ensemble model for HIV-1 TAR, and the model accuracy was independently supported by comparisons to quantum-mechanical calculations of NMR chemical shifts, comparison to a crystal structure of a substate, and through designed ensemble redistribution via atomic mutagenesis. Applications to TAR bulge variants and more complex tertiary RNAs support the generality of this approach and the potential to make the determination of atomic-resolution RNA ensembles routine.

Determining dynamic ensembles of biomolecules is still challenging. Here the authors present an approach for rapid RNA ensemble determination that combines RNA structure prediction tools and NMR residual dipolar coupling data and use it to determine atomistic ensemble models for a variety of RNAs.

PRE-driven protein NMR structures: an alternative approach in highly paramagnetic systems

Metalloproteins play key roles across biology, and knowledge of their structure is essential to understand their physiological role. For those metalloproteins containing paramagnetic states, the enhanced relaxation caused by the unpaired electrons often makes signal detection unfeasible near the metal center, precluding adequate structural characterization right where it is more biochemically relevant. Here, we report a protein structure determination by NMR where two different sets of restraints, one containing Nuclear Overhauser Enhancements (NOEs) and another containing Paramagnetic Relaxation Enhancements (PREs), are used separately and eventually together. The protein PioC from Rhodopseudomonas palustris TIE-1 is a High Potential Iron-Sulfur Protein (HiPIP) where the [4Fe-4S] cluster is paramagnetic in both oxidation states at room temperature providing the source of PREs used as alternative distance restraints. Comparison of the family of structures obtained using NOEs only, PREs only, and the combination of both reveals that the pairwise root-mean-square deviation (RMSD) between them is similar and comparable with the precision within each family. This demonstrates that, under favorable conditions in terms of protein size and paramagnetic effects, PREs can efficiently complement and eventually replace NOEs for the structural characterization of small paramagnetic metalloproteins and de novo-designed metalloproteins by NMR. DATABASES: The 20 conformers with the lowest target function constituting the final family obtained using the full set of NMR restraints were deposited to the Protein Data Bank (PDB ID: 6XYV). The 20 conformers with the lowest target function obtained using NOEs only (PDB ID: 7A58) and PREs only (PDB ID: 7A4L) were also deposited to the Protein Data Bank. The chemical shift assignments were deposited to the BMRB (code 34487).

HERMES - A Software Tool for the Prediction and Analysis of Magnetic-Field-Induced Residual Dipolar Couplings in Nucleic Acids

Field-Induced Residual Dipolar Couplings (fiRDC) are a valuable source of long-range information on structure of nucleic acids (NA) in solution. A web application (HERMES) was developed for structure-based prediction and analysis of the (fiRDCs) in NA. fiRDC prediction is based on input 3D model structure(s) of NA and a built-in library of nucleobase-specific magnetic susceptibility tensors and reference geometries. HERMES allows three basic applications: (i) the prediction of fiRDCs for a given structural model of NAs, (ii) the validation of experimental or modeled NA structures using experimentally derived fiRDCs, and (iii) assessment of the oligomeric state of the NA fragment and/or the identification of a molecular NA model that is consistent with experimentally derived fiRDC data. Additionally, the program's built-in routine for rigid body modeling allows the evaluation of relative orientation of domains within NA that is in agreement with experimental fiRDCs.

Paramagnetic NMR Spectroscopy Is a Tool to Address Reactivity, Structure, and Protein–Protein Interactions of Metalloproteins: The Case of Iron–Sulfur Proteins

The study of cellular machineries responsible for the iron–sulfur (Fe–S) cluster biogenesis has led to the identification of a large number of proteins, whose importance for life is documented by an increasing number of diseases linked to them. The labile nature of Fe–S clusters and the transient protein–protein interactions, occurring during the various steps of the maturation process, make their structural characterization in solution particularly difficult. Paramagnetic nuclear magnetic resonance (NMR) has been used for decades to characterize chemical composition, magnetic coupling, and the electronic structure of Fe–S clusters in proteins; it represents, therefore, a powerful tool to study the protein–protein interaction networks of proteins involving into iron–sulfur cluster biogenesis. The optimization of the various NMR experiments with respect to the hyperfine interaction will be summarized here in the form of a protocol; recently developed experiments for measuring longitudinal and transverse nuclear relaxation rates in highly paramagnetic systems will be also reviewed. Finally, we will address the use of extrinsic paramagnetic centers covalently bound to diamagnetic proteins, which contributed over the last twenty years to promote the applications of paramagnetic NMR well beyond the structural biology of metalloproteins.

Magnetically Induced Alignment of Natural Products for Stereochemical Structure Determination via NMR

Anisotropic NMR has gained increasing popularity to determine the structure and specifically the configuration of small, flexible, non‐crystallizable molecules. However, it suffers from the necessity to dissolve the analyte in special media such as liquid crystals or polymer gels. Generally, small degrees of alignment are also caused by an anisotropic magnetic susceptibility of the molecule, for example, induced by aromatic moieties. For this mechanism, the alignment can be predicted via density functional theory. Here we show that both residual dipolar couplings and residual chemical shift anisotropies can be acquired from natural products without special sample preparation using magnetically induced alignment. On the two examples of the novel natural product gymnochrome G and the alkaloid strychnine, these data, together with the predicted alignment, yield the correct configuration with high certainty.

Lanthanide Tagging of Oligonucleotides to Nucleobase for Paramagnetic NMR

Although lanthanide tags, which have large anisotropic magnetic susceptibilities, have already been introduced to enrich NMR parameters by long‐range pseudoconact shifts (PCSs) and residual dipolar couplings (RDCs) of proteins, their application to nucleotides has so far been limited to one previous report, due to the high affinities of lanthanides for the phosphodiester backbone of nucleotides and difficult organic synthesis. Herein, we report successful attachment of a lanthanide tag to a chemically synthesized oligonucleotide via a disulfide bond. NMR experiments reveal PCSs of up to 1 ppm and H−H RDCs of up to 8 Hz at 950 MHz. Although weaker magnetic alignment was achieved than with proteins, the paramagnetic data could be fitted to the known structure of the DNA, taking the mobility of the tag into account. While further rigidification of the tag is desirable, this tag could also be used to measure heteronuclear RDCs of ¹³C,¹⁵N‐labeled chemically synthesized DNA and RNA.

The Advanced Floating Chirality Distance Geometry Approach-How Anisotropic NMR Parameters Can Support the Determination of the Relative Configuration of Natural Products

The configurational analysis of complex natural products by NMR spectroscopy is still a challenging task. The assignment of the relative configuration is usually carried out by analysis of interproton distances from NOESY or ROESY spectra (qualitative or quantitative) and scalar (J) couplings. About 15 years ago, residual dipolar couplings (RDCs) were introduced as a tool for the configurational determination of small organic molecules. In contrast to NOEs/ROEs which are local parameters (distances up to 400 pm can be detected for small organic molecules), RDCs are global parameters which allow to obtain structural information also from long-range relationships. RDCs have the disadvantage that the sample needs a setup in an alignment medium in order to obtain the required anisotropic environment. Here, we will discuss the configurational analysis of five complex natural products: axinellamine A (1), tetrabromostyloguanidine (2), 3,7-epi-massadine chloride (3), tubocurarine (4), and vincristine (5). Compounds 1-3 are marine natural products whereas 4 and 5 are from terrestrial sources. The chosen examples will carefully work out the limitations of NOEs/ROEs in the configurational analysis of natural products and will also provide an outlook on the information obtained from RDCs.

NMR "Crystallography" for Uniformly (13 C, 15 N)-Labeled Oriented Membrane Proteins

In oriented-sample (OS) solid-state NMR of membrane proteins, the angular-dependent dipolar couplings and chemical shifts provide a direct input for structure calculations. However, so far only ¹ H-¹⁵ N dipolar couplings and ¹⁵ N chemical shifts have been routinely assessed in oriented ¹⁵ N-labeled samples. The main obstacle for extending this technique to membrane proteins of arbitrary topology has remained in the lack of additional experimental restraints. We have developed a new experimental triple-resonance NMR technique, which was applied to uniformly doubly (¹⁵ N, ¹³ C)-labeled Pf1 coat protein in magnetically aligned DMPC/DHPC bicelles. The previously inaccessible ¹ H_α -¹³ C_α dipolar couplings have been measured, which make it possible to determine the torsion angles between the peptide planes without assuming α-helical structure a priori. The fitting of three angular restraints per peptide plane and filtering by Rosetta scoring functions has yielded a consensus α-helical transmembrane structure for Pf1 protein.

Opportunities and Challenges of Backbone, Sidechain, and RDC Experiments to Study Membrane Protein Dynamics in a Detergent-Free Lipid Environment Using Solution State NMR

Whereas solution state NMR provided a wealth of information on the dynamics landscape of soluble proteins, only few studies have investigated membrane protein dynamics in a detergent-free lipid environment. Recent developments of smaller nanodiscs and other lipid-scaffolding polymers, such as styrene maleic acid (SMA), however, open new and promising avenues to explore the function-dynamics relationship of membrane proteins as well as between membrane proteins and their surrounding lipid environment. Favorably sized lipid-bilayer nanodiscs, established membrane protein reconstitution protocols and sophisticated solution NMR relaxation methods probing dynamics over a wide range of timescales will eventually reveal unprecedented lipid-membrane protein interdependencies that allow us to explain things we have not been able to explain so far. In particular, methyl group dynamics resulting from CEST, CPMG, ZZ exchange, and RDC experiments are expected to provide new and surprising insights due to their proximity to lipids, their applicability in large 100+ kDa assemblies and their simple labeling due to the availability of commercial precursors. This review summarizes the recent developments of membrane protein dynamics with a special focus on membrane protein dynamics in lipid-bilayer nanodiscs. Opportunities and challenges of backbone, side chain and RDC dynamics applied to membrane proteins are discussed. Solution-state NMR and lipid nanodiscs bear great potential to change our molecular understanding of lipid-membrane protein interactions.

Magnetic susceptibility and paramagnetism-based NMR

The magnetic interactions between the nuclear magnetic moment and the magnetic moment of unpaired electron(s) depend on the structure and dynamics of the molecules where the paramagnetic center is located and of their partners. The long-range nature of the magnetic interactions is thus a reporter of invaluable information for structural biology studies, when other techniques often do not provide enough data for the atomic-level characterization of the system. This precious information explains the flourishing of paramagnetism-assisted NMR studies in recent years. Many paramagnetic effects are related to the magnetic susceptibility of the paramagnetic metal. Although these effects have been known for more than half a century, different theoretical models and new approaches have been proposed in the last decade. In this review, we have summarized the consequences for NMR spectroscopy of magnetic interactions between nuclear and electron magnetic moments, and thus of the presence of a magnetic susceptibility due to metals, and we do so using a unified notation.

Probing the dynamic stalk region of the ribosome using solution NMR

We describe an NMR approach based on the measurement of residual dipolar couplings (RDCs) to probe the structural and motional properties of the dynamic regions of the ribosome. Alignment of intact 70S ribosomes in filamentous bacteriophage enabled measurement of RDCs in the mobile C-terminal domain (CTD) of the stalk protein bL12. A structural refinement of this domain using the observed RDCs did not show large changes relative to the isolated protein in the absence of the ribosome, and we also found that alignment of the CTD was almost independent of the presence of the core ribosome particle, indicating that the inter-domain linker has significant flexibility. The nature of this linker was subsequently probed in more detail using a paramagnetic alignment strategy, which revealed partial propagation of alignment between neighbouring domains, providing direct experimental validation of a structural ensemble previously derived from SAXS and NMR relaxation measurements. Our results demonstrate the prospect of better characterising dynamical and functional regions of more challenging macromolecular machines and systems, for example ribosome–nascent chain complexes.

What are the methodological and theoretical prospects for paramagnetic NMR in structural biology? A glimpse into the crystal ball

NMR spectroscopy is very sensitive to the presence of unpaired electrons, which perturb the NMR chemical shifts, J splittings and nuclear relaxation rates. These paramagnetic effects have attracted increasing attention over the last decades, and their use is expected to increase further in the future because they can provide structural information not easily achievable with other techniques. In fact, paramagnetic data provide long range structural restraints that can be used to assess the accuracy of crystal structures in solution and to improve them by simultaneous refinements with the X-ray data. They are also precious for obtaining information on the conformational variability of biomolecular systems, possibly in conjunction with SAXS and/or DEER data. We foresee that new tools will be developed in the next years for the simultaneous analysis of the paramagnetic data with data obtained from different techniques, in order to take advantage synergistically of the information content of all of them. Of course, the use of the paramagnetic data for structural purposes requires the knowledge of the relationship between these data and the molecular coordinates. Recently, the equations commonly used, dating back to half a century ago, have been questioned by first principle quantum chemistry calculations. Our prediction is that further theoretical/computational improvements will essentially confirm the validity of the old semi-empirical equations for the analysis of the experimental paramagnetic data.

Partial alignment, residual dipolar couplings and molecular symmetry in solution NMR

Residual dipolar couplings (RDCs) and residual anisotropic chemical shifts (RACSs) are produced by the partial alignment of solution NMR samples. RDCs and RACSs yield high-resolution structural and dynamic information on the orientation of bonds and chemical groups in molecules. Many molecules form oligomers or have intrinsic symmetries, which may simplify the analysis of their partial alignment datasets. In this report, we explore the theory of partial alignment using an irreducible spherical representation, and we investigate the impact of molecular symmetry on the alignment of molecules. Though previous studies have reported simplified relationships on the partial alignment of molecules bearing different symmetry groups, we show that these simplified relationships may not be universal and only apply to a limited set of systems.

Life During Wartime: A Personal Recollection of the Circa 1990 Prestegard Lab and Its Contributions to Membrane Biophysics

A subjective account is presented of challenges and excitement of being a postdoctoral trainee in the lab of James H. Prestegard at Yale University in New Haven, Connecticut from 1989 to 1991. This includes accounts of the early development of bicelles and of oriented sample NMR results that contributed to our modern understanding of the properties of the water-lipid interface of disordered phase biological membranes.

Joint X-ray/NMR structure refinement of multidomain/multisubunit systems

Data integration in structural biology has become a paradigm for the characterization of biomolecular systems, and it is now accepted that combining different techniques can fill the gaps in each other's blind spots. In this frame, one of the combinations, which we have implemented in REFMAC-NMR, is residual dipolar couplings from NMR together with experimental data from X-ray diffraction. The first are exquisitely sensitive to the local details but does not give any information about overall shape, whereas the latter encodes more the information about the overall shape but at the same time tends to miss the local details even at the highest resolutions. Once crystals are obtained, it is often rather easy to obtain a complete X-ray dataset, however it is time-consuming to obtain an exhaustive NMR dataset. Here, we discuss the effect of including a-priori knowledge on the properties of the system to reduce the number of experimental data needed to obtain a more complete picture. We thus introduce a set of new features of REFMAC-NMR that allow for improved handling of RDC data for multidomain proteins and multisubunit biomolecular complexes, and encompasses the use of pseudo-contact shifts as an additional source of NMR-based information. The new feature may either help in improving the refinement, or assist in spotting differences between the crystal and the solution data. We show three different examples where NMR and X-ray data can be reconciled to a unique structural model without invoking mobility.

Characterizing micro-to-millisecond chemical exchange in nucleic acids using off-resonance R1ρ relaxation dispersion

This review describes off-resonance R1ρ relaxation dispersion NMR methods for characterizing microsecond-to-millisecond chemical exchange in uniformly 13C/15N labeled nucleic acids in solution. The review opens with a historical account of key developments that formed the basis for modern R1ρ techniques used to study chemical exchange in biomolecules. A vector model is then used to describe the R1ρ relaxation dispersion experiment, and how the exchange contribution to relaxation varies with the amplitude and frequency offset of an applied spin-locking field, as well as the population, exchange rate, and differences in chemical shifts of two exchanging species. Mathematical treatment of chemical exchange based on the Bloch-McConnell equations is then presented and used to examine relaxation dispersion profiles for more complex exchange scenarios including three-state exchange. Pulse sequences that employ selective Hartmann-Hahn cross-polarization transfers to excite individual 13C or 15N spins are then described for measuring off-resonance R1ρ(13C) and R1ρ(15N) in uniformly 13C/15N labeled DNA and RNA samples prepared using commercially available 13C/15N labeled nucleotide triphosphates. Approaches for analyzing R1ρ data measured at a single static magnetic field to extract a full set of exchange parameters are then presented that rely on numerical integration of the Bloch-McConnell equations or the use of algebraic expressions. Methods for determining structures of nucleic acid excited states are then reviewed that rely on mutations and chemical modifications to bias conformational equilibria, as well as structure-based approaches to calculate chemical shifts. Applications of the methodology to the study of DNA and RNA conformational dynamics are reviewed and the biological significance of the exchange processes is briefly discussed.

Maximizing accuracy of RNA structure in refinement against residual dipolar couplings

Structural information about ribonucleic acid (RNA) is lagging behind that of proteins, in part due to its high charge and conformational variability. Molecular dynamics (MD) has played an important role in describing RNA structure, complementing information from both nuclear magnetic resonance (NMR), or X-ray crystallography. We examine the impact of the choice of the empirical force field for RNA structure refinement using cross-validation against residual dipolar couplings (RDCs) as structural accuracy reporter. Four force fields, representing both the state-of-the art in RNA simulation and the most popular selections in NMR structure determination, are compared for a prototypical A-RNA helix. RNA structural accuracy is also evaluated as a function of both density and nature of input NMR data including RDCs, anisotropic chemical shifts, and distance restraints. Our results show a complex interplay between the experimental restraints and the force fields indicating two best-performing choices: high-fidelity refinement in explicit solvent, and the conformational database-derived potentials. Accuracy of RNA models closely tracks the density of 1-bond C-H RDCs, with other data types having beneficial, but smaller effects. At lower RDC density, or when refining against NOEs only, the two selected force fields are capable of accurately describing RNA helices with little or no experimental RDC data, making them available for the higher order structure assembly or better quantification of the intramolecular dynamics. Unrestrained simulations of simple RNA motifs with state-of-the art MD force fields appear to capture the flexibility inherent in nucleic acids while also maintaining a good agreement with the experimental observables.

Paramagnetic NMR in solution and the solid state

The field of paramagnetic NMR has expanded considerably in recent years. This review addresses both the theoretical description of paramagnetic NMR, and the way in which it is currently practised. We provide a review of the theory of the NMR parameters of systems in both solution and the solid state. Here we unify the different languages used by the NMR, EPR, quantum chemistry/DFT, and magnetism communities to provide a comprehensive and coherent theoretical description. We cover the theory of the paramagnetic shift and shift anisotropy in solution both in the traditional formalism in terms of the magnetic susceptibility tensor, and using a more modern formalism employing the relevant EPR parameters, such as are used in first-principles calculations. In addition we examine the theory first in the simple non-relativistic picture, and then in the presence of spin-orbit coupling. These ideas are then extended to a description of the paramagnetic shift in periodic solids, where it is necessary to include the bulk magnetic properties, such as magnetic ordering at low temperatures. The description of the paramagnetic shift is completed by describing the current understanding of such shifts due to lanthanide and actinide ions. We then examine the paramagnetic relaxation enhancement, using a simple model employing a phenomenological picture of the electronic relaxation, and again using a more complex state-of-the-art theory which incorporates electronic relaxation explicitly. An additional important consideration in the solid state is the impact of bulk magnetic susceptibility effects on the form of the spectrum, where we include some ideas from the field of classical electrodynamics. We then continue by describing in detail the solution and solid-state NMR methods that have been deployed in the study of paramagnetic systems in chemistry, biology, and the materials sciences. Finally we describe a number of case studies in paramagnetic NMR that have been specifically chosen to highlight how the theory in part one, and the methods in part two, can be used in practice. The systems chosen include small organometallic complexes in solution, solid battery electrode materials, metalloproteins in both solution and the solid state, systems containing lanthanide ions, and multi-component materials used in pharmaceutical controlled-release formulations that have been doped with paramagnetic species to measure the component domain sizes.

Characterizing Protein-Protein Interactions Using Solution NMR Spectroscopy

In this chapter, we describe how NMR chemical shift titrations can be used to study the interaction between two proteins with emphasis on mapping the interface of the complex and determining the binding affinity from a quantitative analysis of the experimental data. In particular, we discuss the appearance of NMR spectra in different chemical exchange regimes (fast, intermediate, and slow) and how these regimes affect NMR data analysis.

Combining NMR Spectroscopy and Molecular Dynamic Simulations to Solve and Analyze the Structure of Protein-RNA Complexes

Understanding the RNA binding specificity of protein is of primary interest to decipher their function in the cell. Here, we review the methodology used to solve the structures of protein-RNA complexes using solution-state NMR spectroscopy: from sample preparation to structure calculation procedures. We also describe how molecular dynamics simulations can help providing additional information on the role of key amino acid side chains and of water molecules in protein-RNA recognition.

Characterization of intrinsically disordered proteins and their dynamic complexes: From in vitro to cell-like environments

Over the last two decades, it has become increasingly clear that a large fraction of the human proteome is intrinsically disordered or contains disordered segments of significant length. These intrinsically disordered proteins (IDPs) play important regulatory roles throughout biology, underlining the importance of understanding their conformational behavior and interaction mechanisms at the molecular level. Here we review recent progress in the NMR characterization of the structure and dynamics of IDPs in various functional states and environments. We describe the complementarity of different NMR parameters for quantifying the conformational propensities of IDPs in their isolated and phosphorylated states, and we discuss the challenges associated with obtaining structural models of dynamic protein-protein complexes involving IDPs. In addition, we review recent progress in understanding the conformational behavior of IDPs in cell-like environments such as in the presence of crowding agents, in membrane-less organelles and in the complex environment of the human cell.

Conformational Properties of a Peptidic Catalyst: Insights from NMR Spectroscopic Studies

Peptides have become valuable as catalysts for a variety of different reactions, but little is known about the conformational properties of peptidic catalysts. We investigated the conformation of the peptide H-dPro-Pro-Glu-NH₂, a highly reactive and stereoselective catalyst for conjugate addition reactions, and the corresponding enamine intermediate in solution by NMR spectroscopy and computational methods. The combination of nuclear Overhauser effects (NOEs), residual dipolar couplings (RDCs), J-couplings, and temperature coefficients revealed that the tripeptide adopts a single predominant conformation in its ground state. The structure is a type I β-turn, which gains stabilization from three hydrogen bonds that are cooperatively formed between all functional groups (secondary amine, carboxylic acid, amides) within the tripeptide. In contrast, the conformation of the enamine intermediate is significantly more flexible. The conformational ensemble of the enamine is still dominated by the β-turn, but the backbone and the side chain of the glutamic acid residue are more dynamic. The key to the switch between rigidity and flexibility of the peptidic catalyst is the CO₂H group in the side chain of the glutamic acid residue, which acts as a lid that can open and close. As a result, the peptidic catalyst is able to adapt to the structural requirements of the intermediates and transition states of the catalytic cycle. These insights might explain the robustness and high reactivity of the peptidic catalyst, which exceeds that of other secondary amine-based organocatalysts. The data suggest that a balance between rigidity and flexibility, which is reminiscent of the dynamic nature of enzymes, is beneficial for peptidic catalysts and other synthetic catalysts.

Predicting the Structures of Glycans, Glycoproteins, and Their Complexes

Complex carbohydrates are ubiquitous in nature, and together with proteins and nucleic acids they comprise the building blocks of life. But unlike proteins and nucleic acids, carbohydrates form nonlinear polymers, and they are not characterized by robust secondary or tertiary structures but rather by distributions of well-defined conformational states. Their molecular flexibility means that oligosaccharides are often refractory to crystallization, and nuclear magnetic resonance (NMR) spectroscopy augmented by molecular dynamics (MD) simulation is the leading method for their characterization in solution. The biological importance of carbohydrate-protein interactions, in organismal development as well as in disease, places urgency on the creation of innovative experimental and theoretical methods that can predict the specificity of such interactions and quantify their strengths. Additionally, the emerging realization that protein glycosylation impacts protein function and immunogenicity places the ability to define the mechanisms by which glycosylation impacts these features at the forefront of carbohydrate modeling. This review will discuss the relevant theoretical approaches to studying the three-dimensional structures of this fascinating class of molecules and interactions, with reference to the relevant experimental data and techniques that are key for validation of the theoretical predictions.

Accurate Electron-Nucleus Distances from Paramagnetic Relaxation Enhancements

Measurements of paramagnetic relaxation enhancements (PREs) in ¹H NMR spectra are an important tool to obtain long-range distance information in proteins, but quantitative interpretation is easily compromised by nonspecific intermolecular PREs. Here we show that PREs generated by lanthanides with anisotropic magnetic susceptibilities offer a route to accurate calibration-free distance measurements. As these lanthanides change ¹H chemical shifts due to pseudocontact shifts, the relaxation rates in the paramagnetic and diamagnetic state can be measured with a single sample that simultaneously contains the protein labeled with a paramagnetic and a diamagnetic lanthanide ion. Nonspecific intermolecular PREs are thus automatically subtracted when calculating the PREs as the difference in nuclear relaxation rates between paramagnetic and diamagnetic protein. Although PREs from lanthanides with anisotropic magnetic susceptibilities are complicated by additional cross-correlation effects and residual dipolar couplings (RDCs) in the paramagnetic state, these effects can be controlled by the choice of lanthanide ion and experimental conditions. Using calbindin D_9k with erbium, we succeeded in measuring intramolecular PREs with unprecedented accuracy, resulting in distance predictions with a root-mean-square-deviation of <0.9 Å in the range 11-24 Å.