Solid-state NMR crystallography through paramagnetic restraints

Machine Learning-Enhanced Quantum Chemistry-Assisted Refinement of the Active Site Structure of Metalloproteins

Understanding the fine structural details of inhibitor binding at the active site of metalloenzymes can have a profound impact on the rational drug design targeted to this broad class of biomolecules. Structural techniques such as NMR, cryo-EM, and X-ray crystallography can provide bond lengths and angles, but the uncertainties in these measurements can be as large as the range of values that have been observed for these quantities in all the published structures. This uncertainty is far too large to allow for reliable calculations at the quantum chemical (QC) levels for developing precise structure-activity relationships or for improving the energetic considerations in protein-inhibitor studies. Therefore, the need arises to rely upon computational methods to refine the active site structures well beyond the resolution obtained with routine application of structural methods. In a recent paper, we have shown that it is possible to refine the active site of cobalt(II)-substituted MMP12, a metalloprotein that is a relevant drug target, by matching to the experimental pseudocontact shifts (PCS) those calculated using multireference ab initio QC methods. The computational cost of this methodology becomes a significant bottleneck when the starting structure is not sufficiently close to the final one, which is often the case with biomolecular structures. To tackle this problem, we have developed an approach based on a neural network (NN) and a support vector regression (SVR) and applied it to the refinement of the active site structure of oxalate-inhibited human carbonic anhydrase 2 (hCAII), another prototypical metalloprotein target. The refined structure gives a remarkably good agreement between the QC-calculated and the experimental PCS. This study not only contributes to the knowledge of CAII but also demonstrates the utility of combining machine learning (ML) algorithms with QC calculations, offering a promising avenue for investigating other drug targets and complex biological systems in general.

Structure Determination and Refinement of Paramagnetic Materials by Solid-State NMR

Paramagnetism in solid-state materials has long been considered an additional challenge for structural investigations by using solid-state nuclear magnetic resonance spectroscopy (ssNMR). The strong interactions between unpaired electrons and the surrounding atomic nuclei, on the one hand, are complex to describe, and on the other hand can cause fast decaying signals and extremely broad resonances. However, significant progress has been made over the recent years in developing both theoretical models to understand and calculate the frequency shifts due to paramagnetism and also more sophisticated experimental protocols for obtaining high-resolution ssNMR spectra. While the field is continuously moving forward, to date, the combination of state-of-the-art numerical and experimental techniques enables us to obtain high-quality data for a variety of systems. This involves the determination of several ssNMR parameters that represent different contributions to the frequency shift in paramagnetic solids. These contributions encode structural information on the studied material on various length scales, ranging from crystal morphologies, to the mid- and long-range order, down to the local atomic bonding environment. In this perspective, the different ssNMR parameters characteristic for paramagnetic materials are discussed with a focus on their interpretation in terms of structure. This includes a summary of studies that have explored the information content of these ssNMR parameters, mostly to complement experimental data from other methods, e.g., X-ray diffraction. The presented overview aims to demonstrate how far ssNMR has hitherto been able to determine and refine the structures of materials and to discuss where it currently falls short of its full potential. We attempt to highlight how much further ssNMR can be pushed to determine and refine structure to deliver a comprehensive structural characterization of paramagnetic materials comparable to what is to date achieved by the combined effort of electron microscopy, diffraction, and spectroscopy.

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.

Machine Learning Full NMR Chemical Shift Tensors of Silicon Oxides with Equivariant Graph Neural Networks

The nuclear magnetic resonance (NMR) chemical shift tensor is a highly sensitive probe of the electronic structure of an atom and furthermore its local structure. Recently, machine learning has been applied to NMR in the prediction of isotropic chemical shifts from a structure. Current machine learning models, however, often ignore the full chemical shift tensor for the easier-to-predict isotropic chemical shift, effectively ignoring a multitude of structural information available in the NMR chemical shift tensor. Here we use an equivariant graph neural network (GNN) to predict full ²⁹Si chemical shift tensors in silicate materials. The equivariant GNN model predicts full tensors to a mean absolute error of 1.05 ppm and is able to accurately determine the magnitude, anisotropy, and tensor orientation in a diverse set of silicon oxide local structures. When compared with other models, the equivariant GNN model outperforms the state-of-the-art machine learning models by 53%. The equivariant GNN model also outperforms historic analytical models by 57% for isotropic chemical shift and 91% for anisotropy. The software is available as a simple-to-use open-source repository, allowing similar models to be created and trained with ease.

Determining Local Magnetic Susceptibility Tensors in Paramagnetic Lanthanide Crystalline Powders from Solid-State NMR Chemical Shift Anisotropies

Exploring magnetic properties at the molecular level is a challenge that has been met by developing many experimental and theoretical solutions, such as polarized neutron diffraction (PND), muon-spin rotation (μ-SR), electron paramagnetic resonance (EPR), SQUID-based magnetometry measurements, and advanced modeling on open-shell systems and relativistic calculations. These methods are powerful tools that shed light on the local magnetic response in specifically designed magnetic materials such as contrast agents, for MRI, molecular magnets, magnetic tags for biological NMR, etc. All of these methods have their advantages and disadvantages. In order to complement the possibilities offered by these methods, we propose a new tool that implements a new approach combining simulation and fitting for high-resolution solid-state NMR spectra of lanthanide-based paramagnetic species. This method relies on a rigorous acquisition thanks to short high-power adiabatic pulses (SHAP) of high-resolution solid-state NMR isotropic and anisotropic data on a powdered magnetic material. It is also based on an efficient modeling of this data thanks to a semiempirical model based on a parametrization of the local magnetism and the crystal structure provided by diffraction methods. The efficiency of the calculation relies on a thorough simplification of the electron-nucleus interactions (point-dipole interaction, no Fermi contact) which is validated by experimental analysis. By taking advantage of the efficient calculation possibilities offered by our method, we can compare a great number of simulated spectra to experimental data and find the best-matching local magnetic susceptibility tensor. This method was applied to a series of isostructural lanthanide oxalates which are used as a benchmark system for many analytical methods. We present the results of thorough solid-state NMR and extensive modeling of the hyperfine interaction (including up to 400 paramagnetic centers) that yield local magnetic susceptibility tensor measurements that are self-consistent as well as consistent with bulk susceptibility measurements.

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.

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.

1H-Detected Biomolecular NMR under Fast Magic-Angle Spinning

Since the first pioneering studies on small deuterated peptides dating more than 20 years ago, 1H detection has evolved into the most efficient approach for investigation of biomolecular structure, dynamics, and interactions by solid-state NMR. The development of faster and faster magic-angle spinning (MAS) rates (up to 150 kHz today) at ultrahigh magnetic fields has triggered a real revolution in the field. This new spinning regime reduces the 1H-1H dipolar couplings, so that a direct detection of 1H signals, for long impossible without proton dilution, has become possible at high resolution. The switch from the traditional MAS NMR approaches with 13C and 15N detection to 1H boosts the signal by more than an order of magnitude, accelerating the site-specific analysis and opening the way to more complex immobilized biological systems of higher molecular weight and available in limited amounts. This paper reviews the concepts underlying this recent leap forward in sensitivity and resolution, presents a detailed description of the experimental aspects of acquisition of multidimensional correlation spectra with fast MAS, and summarizes the most successful strategies for the assignment of the resonances and for the elucidation of protein structure and conformational dynamics. It finally outlines the many examples where 1H-detected MAS NMR has contributed to the detailed characterization of a variety of crystalline and noncrystalline biomolecular targets involved in biological processes ranging from catalysis through drug binding, viral infectivity, amyloid fibril formation, to transport across lipid membranes.

Imaging active site chemistry and protonation states: NMR crystallography of the tryptophan synthase α-aminoacrylate intermediate

NMR-assisted crystallography-the integrated application of solid-state NMR, X-ray crystallography, and first-principles computational chemistry-holds significant promise for mechanistic enzymology: by providing atomic-resolution characterization of stable intermediates in enzyme active sites, including hydrogen atom locations and tautomeric equilibria, NMR crystallography offers insight into both structure and chemical dynamics. Here, this integrated approach is used to characterize the tryptophan synthase α-aminoacrylate intermediate, a defining species for pyridoxal-5'-phosphate-dependent enzymes that catalyze β-elimination and replacement reactions. For this intermediate, NMR-assisted crystallography is able to identify the protonation states of the ionizable sites on the cofactor, substrate, and catalytic side chains as well as the location and orientation of crystallographic waters within the active site. Most notable is the water molecule immediately adjacent to the substrate β-carbon, which serves as a hydrogen bond donor to the ε-amino group of the acid-base catalytic residue βLys87. From this analysis, a detailed three-dimensional picture of structure and reactivity emerges, highlighting the fate of the L-serine hydroxyl leaving group and the reaction pathway back to the preceding transition state. Reaction of the α-aminoacrylate intermediate with benzimidazole, an isostere of the natural substrate indole, shows benzimidazole bound in the active site and poised for, but unable to initiate, the subsequent bond formation step. When modeled into the benzimidazole position, indole is positioned with C3 in contact with the α-aminoacrylate Cβ and aligned for nucleophilic attack. Here, the chemically detailed, three-dimensional structure from NMR-assisted crystallography is key to understanding why benzimidazole does not react, while indole does.

Structure of membrane diacylglycerol kinase in lipid bilayers

Diacylglycerol kinase (DgkA) is a small integral membrane protein, responsible for the ATP-dependent phosphorylation of diacylglycerol to phosphatidic acid. Its structures reported in previous studies, determined in detergent micelles by solution NMR and in monoolein cubic phase by X-ray crystallography, differ significantly. These differences point to the need to validate these detergent-based structures in phospholipid bilayers. Here, we present a well-defined homo-trimeric structure of DgkA in phospholipid bilayers determined by magic angle spinning solid-state NMR (ssNMR) spectroscopy, using an approach combining intra-, inter-molecular paramagnetic relaxation enhancement (PRE)-derived distance restraints and CS-Rosetta calculations. The DgkA structure determined in lipid bilayers is different from the solution NMR structure. In addition, although ssNMR structure of DgkA shows a global folding similar to that determined by X-ray, these two structures differ in monomeric symmetry and dynamics. A comparative analysis of DgkA structures determined in three different detergent/lipid environments provides a meaningful demonstration of the influence of membrane mimetic environments on the structure and dynamics of membrane proteins.

Jianping Li et al. present the homo-trimeric structure of the small integral membrane protein diacylglycerol kinase (DgkA) in phospholipid bilayers determined by magic angle spinning solid-state NMR spectroscopy. They compare the structure with structures solved by solution NMR and X-ray crystallography and provide insights into the influence of membrane mimetic environments on membrane proteins.

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).

Bridging photochemistry and photomechanics with NMR crystallography: the molecular basis for the macroscopic expansion of an anthracene ester nanorod

Crystals composed of photoreactive molecules represent a new class of photomechanical materials with the potential to generate large forces on fast timescales. An example is the photodimerization of 9-tert-butyl-anthracene ester (9TBAE) in molecular crystal nanorods that leads to an average elongation of 8%. Previous work showed that this expansion results from the formation of a metastable crystalline product. In this article, it is shown how a novel combination of ensemble oriented-crystal solid-state NMR, X-ray diffraction, and first principles computational modeling can be used to establish the absolute unit cell orientations relative to the shape change, revealing the atomic-resolution mechanism for the photomechanical response and enabling the construction of a model that predicts an elongation of 7.4%, in good agreement with the experimental value. According to this model, the nanorod expansion does not result from an overall change in the volume of the unit cell, but rather from an anisotropic rearrangement of the molecular contents. The ability to understand quantitatively how molecular-level photochemistry generates mechanical displacements allows us to predict that the expansion could be tuned from +9% to -9.5% by controlling the initial orientation of the unit cell with respect to the nanorod axis. This application of NMR-assisted crystallography provides a new tool capable of tying the atomic-level structural rearrangement of the reacting molecular species to the mechanical response of a nanostructured sample.

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.

Picometer Resolution Structure of the Coordination Sphere in the Metal-Binding Site in a Metalloprotein by NMR

Most of our understanding of chemistry derives from atomic-level structures obtained with single-crystal X-ray diffraction. Metal centers in X-ray structures of small organometallic or coordination complexes are often extremely well-defined, with errors in the positions on the order of 10^-4-10^-5 Å. Determining the metal coordination geometry to high accuracy is essential for understanding metal center reactivity, as even small structural changes can dramatically alter the metal activity. In contrast, the resolution of X-ray structures in proteins is limited typically to the order of 10^-1 Å. This resolution is often not sufficient to develop precise structure-activity relations for the metal sites in proteins, because the uncertainty in positions can cover all of the known ranges of bond lengths and bond angles for a given type of metal complex. Here we introduce a new approach that enables the determination of a high-definition structure of the active site of a metalloprotein from a powder sample, by combining magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy, tailored radio frequency (RF) irradiation schemes, and computational approaches. This allows us to overcome the "blind sphere" in paramagnetic proteins, and to observe and assign ¹H, ¹³C, and ¹⁵N resonances for the ligands directly coordinating the metal center. We illustrate the method by determining the bond lengths in the structure of the Co^II coordination sphere at the core of human superoxide dismutase 1 (SOD) with 0.7 pm precision. The coordination geometry of the resulting structure explains the nonreactive nature of the Co^II/Zn^II centers in these proteins, which allows them to play a purely structural role.

Molecular Mechanism of Crystalline-to-Amorphous Conversion of Pharmaceutical Solids from 19F Magic Angle Spinning NMR

Crystalline and amorphous materials usually possess distinct physicochemical properties due to major variations in long-range and local molecular packings. Enhanced fundamental knowledge of the molecular details of crystalline-to-amorphous interconversions is necessary to correlate the intermolecular structure to material properties and functions. While crystal structures can be readily obtained by X-ray crystallography, the microstructure of amorphous materials has rarely been explored due to a lack of high-resolution techniques capable of probing local molecular structures. Moreover, there is increasing interest in understanding the molecular nature of amorphous solids in pharmaceutical sciences due to the widespread utilization of amorphous active pharmaceutical ingredients (APIs) in pharmaceutical development for solubility and bioavailability enhancement. In this study, we explore multidimensional ¹³C and ¹⁹F magic angle spinning (MAS) NMR spectroscopy to study the molecular packing of amorphous posaconazole (POSA) in conjunction with the crystalline counterpart. Utilizing methods integrating homonuclear and heteronuclear ¹H, ¹³C, and ¹⁹F correlation spectroscopy and atomic ¹⁹F-to-¹³C distance measurements, we identified the major differences in molecular packing between crystalline and amorphous POSA. The intermolecular "head-to-head" interaction along the molecule's major axis, as well as the "head-to-tail" molecular packing perpendicular to the major axis in POSA crystals, was recapitulated by MAS NMR. Furthermore, critical intermolecular distances in the crystal lattice were determined. Most importantly, the head-to-tail contact of two neighboring molecules was found to be preserved in amorphous POSA, suggesting localized molecular order, whereas crucial interactions for head-to-head packing are absent in the amorphous form resulting in long-range disorder. Our study, likely one of the first documented examples, provides molecular-level structural details to understand the molecular mechanism of crystalline-to-amorphous conversion of fluorine-containing drug substances occurring in drug processing and development and establish a high-resolution experimental protocol for investigating amorphous materials.

Gadolinium Complexes as Contrast Agent for Cellular NMR Spectroscopy

Aqua Gd³⁺ and Gd-DOTA (gadolinium-1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacete) complexes were studied as a contrast agent in cellular NMR (nuclear magnetic resonance) spectroscopy for distinguishing between intracellular and extracellular spaces. The contrast agents for this purpose should provide strong paramagnetic relaxation enhancement and localize in the extracellular space without disturbing biological functions. Cell membrane permeability to Gd complexes was evaluated from the concentrations of gadolinium complexes in the inside and outside of E. coli cells measured by the ¹H-NMR relaxation. The site-specific binding of the complexes to E. coli cells was also analyzed by high-resolution solid-state ¹³C-NMR. The aqua Gd³⁺ complex did not enhance T₁ relaxation in proportion to the amount of added Gd³⁺. This Gd³⁺ concentration dependence and the ¹³C-NMR indicated that its strong cytotoxicity should be due to the binding of the paramagnetic ions to cellular components especially at the lipid membranes. In contrast, Gd-DOTA stayed in the solution states and enhanced relaxation in proportion to the added amount. This agent exhibited strong T₁ contrast between the intra- and extracellular spaces by a factor of ten at high concentrations under which the cells were viable over a long experimental time of days. These properties make Gd-DOTA suitable for selectively contrasting the living cellular space in NMR spectroscopy primarily owing to its weak interaction with cellular components.

NMR crystallography of molecular organics

Developments of NMR methodology to characterise the structures of molecular organic structures are reviewed, concentrating on the previous decade of research in which density functional theory-based calculations of NMR parameters in periodic solids have become widespread. With a focus on demonstrating the new structural insights provided, it is shown how "NMR crystallography" has been used in a spectrum of applications from resolving ambiguities in diffraction-derived structures (such as hydrogen atom positioning) to deriving complete structures in the absence of diffraction data. As well as comprehensively reviewing applications, the different aspects of the experimental and computational techniques used in NMR crystallography are surveyed. NMR crystallography is seen to be a rapidly maturing subject area that is increasingly appreciated by the wider crystallographic community.

Paramagnetic solid-state NMR of proteins

The paramagnetic properties of metal ions and stable radicals can affect NMR spectra, which can lead to changes in peak intensities, relaxation times and chemical shifts. The changes from paramagnetic effects provide intriguing opportunities for solid-state NMR studies of proteins. In this review, we summarized the trends and progress of paramagnetic solid-state NMR of proteins in the past decade, and showed that paramagnetic effects have great potential applications for sensitivity enhancement, structure determination and topological analysis for microcrystalline proteins, protein complexes, protein aggregates and membrane proteins.

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.

Metal centers in biomolecular solid-state NMR

Solid state NMR (SSNMR) has earned a substantial success in the characterization of paramagnetic systems over the last decades. Nowadays, the resolution and sensitivity of solid state NMR in biological molecules has improved significantly and these advancements can be translated into the study of paramagnetic biomolecules. However, the electronic properties of different metal centers affect the quality of their SSNMR spectra differently, and not all systems turn out to be equally easy to approach by this technique. In this review we will try to give an overview of the properties of different paramagnetic centers and how they can be used to increase the chances of experimental success.

Structural Studies of Amyloid Fibrils by Paramagnetic Solid-State Nuclear Magnetic Resonance Spectroscopy

Application of paramagnetic solid-state NMR to amyloids is demonstrated, using Y145Stop human prion protein modified with nitroxide spin-label or EDTA-Cu²⁺ tags as a model. By using sample preparation protocols based on seeding with preformed fibrils, we show that paramagnetic protein analogs can be induced into adopting the wild-type amyloid structure. Measurements of residue-specific intramolecular and intermolecular paramagnetic relaxation enhancements enable determination of protein fold within the fibril core and protofilament assembly. These methods are expected to be widely applicable to other amyloids and protein assemblies.

Hydrogen motional disorder in crystalline iron group chloride dihydrates

The principal components and the relative orientation of the ²H paramagnetic shift and quadrupolar coupling tensors have been measured for the MCl₂·2D₂O family of compounds, M = Mn, Fe, Co, Ni, and Cu, using the two-dimensional shifting-d echo nuclear magnetic resonance experiment in order to determine (1) the degree of unpaired electron delocalization and (2) the number and location of crystallographically distinct hydrogen sites around oxygen and their fractional occupancies. Expressions for the molecular susceptibility of 3d ion systems, where the spin-orbit coupling is a weak perturbation onto the crystal field, are derived using the generalized Van Vleck equation and used to predict molecular susceptibilities. These predicted molecular susceptibilities are combined with various point dipole source configurations modeling unpaired electron delocalization to predict ²H paramagnetic shift tensors at potential deuterium sites. The instantaneous deuterium quadrupolar coupling and shift tensors are then combined with parameterized motional models, developed for trigonally (M = Mn, Fe, Co, and Cu) and pyramidally (M = Ni) coordinated D₂O ligands, to obtain the best fit of the experimental 2D spectra. Dipole sources placed onto metal nuclei with a small degree of delocalization onto the chlorine ligands yield good agreement with the experiment for M = Mn, Fe, Co, and Ni, while good agreement for CuCl₂·2D₂O is obtained with additional delocalization onto the oxygen. Our analysis of the salts with trigonally coordinated water ligands (M = Mn, Fe, Co, and Cu) confirms the presence of bisector flipping and the conclusions from neutron scattering measurements that hydrogen bonding to chlorine on two adjacent chains leads to the water molecule in the [M(D₂O)₂Cl₄] cluster being nearly coplanar with O-M-Cl involving the shortest metal-chlorine bonds of the cluster. In the case of NiCl₂·2D₂O, the experimental parameters were found to be consistent with a motional model where the D₂O ligands are pyramidally coordinated to the metal and undergo bisector flipping while the water ligand additionally hops between two orientations related by a 120° rotation about the Ni-O bond axis. The position of the three crystallographically distinct hydrogen sites in the unit cell was determined along with fractional occupancies. This restricted water ligand motion is likely due to van der Waals interactions and is concerted with the motion of neighboring ligands.

Does Z' equal 1 or 2? Enhanced powder NMR crystallography verification of a disordered room temperature crystal structure of a p38 inhibitor for chronic obstructive pulmonary disease

The crystal structure of the Form A polymorph of N-cyclopropyl-3-fluoro-4-methyl-5-[3-[[1-[2-[2-(methylamino)ethoxy]phenyl]cyclopropyl]amino]-2-oxo-pyrazin-1-yl]benzamide (i.e., AZD7624), determined using single-crystal X-ray diffraction (scXRD) at 100 K, contains two molecules in the asymmetric unit (Z' = 2) and has regions of local static disorder. This substance has been in phase IIa drug development trials for the treatment of chronic obstructive pulmonary disease, a disease which affects over 300 million people and contributes to nearly 3 million deaths annually. While attempting to verify the crystal structure using nuclear magnetic resonance crystallography (NMRX), we measured ¹³C solid-state NMR (SSNMR) spectra at 295 K that appeared consistent with Z' = 1 rather than Z' = 2. To understand this surprising observation, we used multinuclear SSNMR (¹H, ¹³C, ¹⁵N), gauge-including projector augmented-wave density functional theory (GIPAW DFT) calculations, crystal structure prediction (CSP), and powder XRD (pXRD) to determine the room temperature crystal structure. Due to the large size of AZD7624 (ca. 500 amu, 54 distinct ¹³C environments for Z' = 2), static disorder at 100 K, and (as we show) dynamic disorder at ambient temperatures, NMR spectral assignment was a challenge. We introduce a method to enhance confidence in NMR assignments by comparing experimental ¹³C isotropic chemical shifts against site-specific DFT-calculated shift distributions established using CSP-generated crystal structures. The assignment and room temperature NMRX structure determination process also included measurements of ¹³C shift tensors and the observation of residual dipolar coupling between ¹³C and ¹⁴N. CSP generated ca. 90 reasonable candidate structures (Z' = 1 and Z' = 2), which when coupled with GIPAW DFT results, room temperature pXRD, and the assigned SSNMR data, establish Z' = 2 at room temperature. We find that the polymorphic Form A of AZD7624 is maintained at room temperature, although dynamic disorder is present on the NMR timescale. Of the CSP-generated structures, 2 are found to be fully consistent with the SSNMR and pXRD data; within this pair, they are found to be structurally very similar (RMSD₁₆ = 0.30 Å). We establish that the CSP structure in best agreement with the NMR data possesses the highest degree of structural similarity with the scXRD-determined structure (RMSD₁₆ = 0.17 Å), and has the lowest DFT-calculated energy amongst all CSP-generated structures with Z' = 2.

Paramagnetic NMR as a new tool in structural biology

NMR (nuclear magnetic resonance) investigation through the exploitation of paramagnetic effects is passing from an approach limited to few specialists in the field to a generally applicable method that must be considered, especially for the characterization of systems hardly affordable with other techniques. This is mostly due to the fact that paramagnetic data are long range in nature, thus providing information for the structural and dynamic characterization of complex biomolecular architectures in their native environment. On the other hand, this information usually needs to be complemented by data from other sources. Integration of paramagnetic NMR with other techniques, and the development of protocols for a joint analysis of all available data, is fundamental for achieving a comprehensive characterization of complex biological systems. We describe here a few examples of the new possibilities offered by paramagnetic data used in integrated structural approaches.

Perspectives on paramagnetic NMR from a life sciences infrastructure

The effects arising in NMR spectroscopy because of the presence of unpaired electrons, collectively referred to as "paramagnetic NMR" have attracted increasing attention over the last decades. From the standpoint of the structural and mechanistic biology, paramagnetic NMR provides long range restraints that can be used to assess the accuracy of crystal structures in solution and to improve them by simultaneous refinements through NMR and X-ray data. These restraints also provide information on structure rearrangements and conformational variability in biomolecular systems. Theoretical improvements in quantum chemistry calculations can nowadays allow for accurate calculations of the paramagnetic data from a molecular structural model, thus providing a tool to refine the metal coordination environment by matching the paramagnetic effects observed far away from the metal. Furthermore, the availability of an improved technology (higher fields and faster magic angle spinning) has promoted paramagnetic NMR applications in the fast-growing area of biomolecular solid-state NMR. Major improvements in dynamic nuclear polarization have been recently achieved, especially through the exploitation of the Overhauser effect occurring through the contact-driven relaxation mechanism: the very large enhancement of the ¹³C signal observed in a variety of liquid organic compounds at high fields is expected to open up new perspectives for applications of solution NMR.

NMR Crystallography of a Carbanionic Intermediate in Tryptophan Synthase: Chemical Structure, Tautomerization, and Reaction Specificity

Carbanionic intermediates play a central role in the catalytic transformations of amino acids performed by pyridoxal-5'-phosphate (PLP)-dependent enzymes. Here, we make use of NMR crystallography-the synergistic combination of solid-state nuclear magnetic resonance, X-ray crystallography, and computational chemistry-to interrogate a carbanionic/quinonoid intermediate analogue in the β-subunit active site of the PLP-requiring enzyme tryptophan synthase. The solid-state NMR chemical shifts of the PLP pyridine ring nitrogen and additional sites, coupled with first-principles computational models, allow a detailed model of protonation states for ionizable groups on the cofactor, substrates, and nearby catalytic residues to be established. Most significantly, we find that a deprotonated pyridine nitrogen on PLP precludes formation of a true quinonoid species and that there is an equilibrium between the phenolic and protonated Schiff base tautomeric forms of this intermediate. Natural bond orbital analysis indicates that the latter builds up negative charge at the substrate Cα and positive charge at C4' of the cofactor, consistent with its role as the catalytic tautomer. These findings support the hypothesis that the specificity for β-elimination/replacement versus transamination is dictated in part by the protonation states of ionizable groups on PLP and the reacting substrates and underscore the essential role that NMR crystallography can play in characterizing both chemical structure and dynamics within functioning enzyme active sites.

Pseudo-Contact NMR Shifts over the Paramagnetic Metalloprotein CoMMP-12 from First Principles

Long-range pseudo-contact NMR shifts (PCSs) provide important restraints for the structure refinement of proteins when a paramagnetic metal center is present, either naturally or introduced artificially. Here we show that ab initio quantum-chemical methods and a modern version of the Kurland-McGarvey approach for paramagnetic NMR (pNMR) shifts in the presence of zero-field splitting (ZFS) together provide accurate predictions of all PCSs in a metalloprotein (high-spin cobalt-substituted MMP-12 as a test case). Computations of 314 ¹³ C PCSs using g- and ZFS tensors based on multi-reference methods provide a reliable bridge between EPR-parameter- and susceptibility-based pNMR formalisms. Due to the high sensitivity of PCSs to even small structural differences, local structures based either on X-ray diffraction or on various DFT optimizations could be evaluated critically by comparing computed and experimental PCSs. Many DFT functionals provide insufficiently accurate structures. We also found the available 1RMZ PDB X-ray structure to exhibit deficiencies related to binding of a hydroxamate inhibitor. This has led to a newly refined PDB structure for MMP-12 (5LAB) that provides a more accurate coordination arrangement and PCSs.

(1)H-detected solid-state NMR of proteins entrapped in bioinspired silica: a new tool for biomaterials characterization

Proton-detection in solid-state NMR, enabled by high magnetic fields (>18 T) and fast magic angle spinning (>50 kHz), allows for the acquisition of traditional (1)H-(15)N experiments on systems that are too big to be observed in solution. Among those, proteins entrapped in a bioinspired silica matrix are an attractive target that is receiving a large share of attention. We demonstrate that (1)H-detected SSNMR provides a novel approach to the rapid assessment of structural integrity in proteins entrapped in bioinspired silica.

How to tackle protein structural data from solution and solid state: An integrated approach

Long-range NMR restraints, such as diamagnetic residual dipolar couplings and paramagnetic data, can be used to determine 3D structures of macromolecules. They are also used to monitor, and potentially to improve, the accuracy of a macromolecular structure in solution by validating or "correcting" a crystal model. Since crystal structures suffer from crystal packing forces they may not be accurate models for the macromolecular structures in solution. However, the presence of real differences should be tested for by simultaneous refinement of the structure using both crystal and solution NMR data. To achieve this, the program REFMAC5 from CCP4 was modified to allow the simultaneous use of X-ray crystallographic and paramagnetic NMR data and/or diamagnetic residual dipolar couplings. Inconsistencies between crystal structures and solution NMR data, if any, may be due either to structural rearrangements occurring on passing from the solution to solid state, or to a greater degree of conformational heterogeneity in solution with respect to the crystal. In the case of multidomain proteins, paramagnetic restraints can provide the correct mutual orientations and positions of domains in solution, as well as information on the conformational variability experienced by the macromolecule.

Solid-state NMR and DFT predictions of differences in COOH hydrogen bonding in odd and even numbered n-alkyl fatty acids

n-Alkyl fatty acids with an even or odd number of carbons are predicted to differ in COOH hydrogen bonding in the solid state.

Differences in Dynamics between Crosslinked and Non-Crosslinked Hyaluronates Measured by using Fast Field-Cycling Relaxometry

The dynamic properties of water molecules in gels containing linear and crosslinked hyaluronic acid polymers are investigated by using an integrated approach that includes relaxometry, solid-state NMR spectroscopy, and scanning electron microscopy. A model-free analysis of field-dependent nuclear relaxation is applied to obtain information on mobility and the population of different pools of water molecules in the gels. Differences between linear and crosslinked hyaluronic acid polymers are observed, indicating that crosslinking increases both the fraction and the correlation time of water molecules with slow dynamics.

Information content of long-range NMR data for the characterization of conformational heterogeneity

Long-range NMR data, namely residual dipolar couplings (RDCs) from external alignment and paramagnetic data, are becoming increasingly popular for the characterization of conformational heterogeneity of multidomain biomacromolecules and protein complexes. The question addressed here is how much information is contained in these averaged data. We have analyzed and compared the information content of conformationally averaged RDCs caused by steric alignment and of both RDCs and pseudocontact shifts caused by paramagnetic alignment, and found that, despite the substantial differences, they contain a similar amount of information. Furthermore, using several synthetic tests we find that both sets of data are equally good towards recovering the major state(s) in conformational distributions.

Converging nuclear magnetic shielding calculations with respect to basis and system size in protein systems

Ab initio chemical shielding calculations greatly facilitate the interpretation of nuclear magnetic resonance (NMR) chemical shifts in biological systems, but the large sizes of these systems requires approximations in the chemical models used to represent them. Achieving good convergence in the predicted chemical shieldings is necessary before one can unravel how other complex structural and dynamical factors affect the NMR measurements. Here, we investigate how to balance trade-offs between using a better basis set or a larger cluster model for predicting the chemical shieldings of the substrates in two representative examples of protein-substrate systems involving different domains in tryptophan synthase: the N-(4'-trifluoromethoxybenzoyl)-2-aminoethyl phosphate (F9) ligand which binds in the α active site, and the 2-aminophenol quinonoid intermediate formed in the β active site. We first demonstrate that a chemically intuitive three-layer, locally dense basis model that uses a large basis on the substrate, a medium triple-zeta basis to describe its hydrogen-bonding partners and/or surrounding van der Waals cavity, and a crude basis set for more distant atoms provides chemical shieldings in good agreement with much more expensive large basis calculations. Second, long-range quantum mechanical interactions are important, and one can accurately estimate them as a small-basis correction to larger-basis calculations on a smaller cluster. The combination of these approaches enables one to perform density functional theory NMR chemical shift calculations in protein systems that are well-converged with respect to both basis set and cluster size.

Structural studies of proteins by paramagnetic solid-state NMR spectroscopy

Paramagnetism-based nuclear pseudocontact shifts and spin relaxation enhancements contain a wealth of information in solid-state NMR spectra about electron-nucleus distances on the ∼20 Å length scale, far beyond that normally probed through measurements of nuclear dipolar couplings. Such data are especially vital in the context of structural studies of proteins and other biological molecules that suffer from a sparse number of experimentally-accessible atomic distances constraining their three-dimensional fold or intermolecular interactions. This perspective provides a brief overview of the recent developments and applications of paramagnetic magic-angle spinning NMR to biological systems, with primary focus on the investigations of metalloproteins and natively diamagnetic proteins modified with covalent paramagnetic tags.

NMR of sedimented, fibrillized, silica-entrapped and microcrystalline (metallo)proteins

Resolution and sensitivity in solid state NMR (SSNMR) can rival the results achieved by solution NMR, and even outperform them in the case of large systems. However, several factors affect the spectral quality in SSNMR samples, and not all systems turn out to be equally amenable for this methodology. In this review we attempt at analyzing the causes of this variable behavior and at providing hints to increase the chances of experimental success.

Broadband solid-state MAS NMR of paramagnetic systems

The combination of new magnet and probe technology with increasingly sophisticated pulse sequences has resulted in an increase in the number of applications of solid-state nuclear magnetic resonance (NMR) spectroscopy to paramagnetic materials and biomolecules. The interaction between the paramagnetic metal ions and the NMR-active nuclei often yields crucial structural or electronic information about the system. In particular the application of magic-angle spinning (MAS) has been shown to be crucial to obtaining resolution that is sufficiently high for studying complex systems. However such systems are generally extremely difficult to study as the shifts and shift anisotropies resulting from the same paramagnetic interaction broaden the spectrum beyond excitation and detection, and the paramagnetic relaxation enhancement (PRE) shortens the lifetimes of the excited signals considerably. One specific area that has therefore been receiving significant attention in recent years, and for which great improvements have been seen, is the development of broadband NMR sequences. The development of new excitation and inversion sequences for paramagnetic systems under MAS has often made the difference between the spectrum being unobtainable, and a complete NMR study being possible. However the development of the new sequences must explicitly take account of the modulation of the anisotropic shift interactions due to the sample rotation, with the resulting spin dynamics often being complicated considerably. The NMR sequences can either be helped or hindered by MAS, with the efficiency of some pulse schemes being destroyed, and others being greatly enhanced. This review describes the pulse sequences that have recently been proposed for broadband excitation, inversion, and refocussing of the signal components of paramagnetic systems. In doing so we define exactly what is meant by "broadband" under spinning conditions, and what the perfect pulse scheme should deliver. We also give a unified description of the spin dynamics under MAS which highlights the strengths and weaknesses of the various schemes, and which can be used as guidance for future research in this area. All the reviewed pulse schemes are evaluated both with simulations and experimental data obtained on the battery material LiFe(0.5)Mn(0.5)PO(4) which is typical of the complexity of the paramagnetic systems that are currently under study.

Recent advances in biological applications of cage metal complexes

This review highlights advances in biochemical and medical applications of cage metal complexes (clathrochelates) and related polyhedral compounds.

Protein structural studies by paramagnetic solid-state NMR spectroscopy aided by a compact cyclen-type Cu(II) binding tag

Paramagnetic relaxation enhancements (PREs) are a rich source of structural information in protein solid-state NMR spectroscopy. Here we demonstrate that PRE measurements in natively diamagnetic proteins are facilitated by a thiol-reactive compact, cyclen-based, high-affinity Cu(2+) binding tag, 1-[2-(pyridin-2-yldisulfanyl)ethyl]-1,4,7,10-tetraazacyclododecane (TETAC), that overcomes the key shortcomings associated with the use of larger, more flexible metal-binding tags. Using the TETAC-Cu(2+) K28C mutant of B1 immunoglobulin-binding domain of protein G as a model, we find that amino acid residues located within ~10 Å of the Cu(2+) center experience considerable transverse PREs leading to severely attenuated resonances in 2D (15)N-(13)C correlation spectra. For more distant residues, electron-nucleus distances are accessible via quantitative measurements of longitudinal PREs, and we demonstrate such measurements for (15)N-Cu(2+) distances up to ~20 Å.

Transition Ion Strikes Back: Large Magnetic Susceptibility Anisotropy in Cobalt(II) Clathrochelates

Transition-metal complexes are rarely considered as paramagnetic tags for NMR spectroscopy due to them generally having relatively low magnetic anisotropy. Here we report cobalt(II) cage complexes with the largest (among the transition-metal complexes) axial anisotropy of magnetic susceptibility, reaching as high as 12.6 × 10(-32) m(3) at room temperature. This remarkable anisotropy, which results from an unusual trigonal prismatic geometry of the complexes and translates into large negative value of the zero-field splitting energy, is high enough to promote reliable paramagnetic pseudocontact shifts at the distance beyond 2 nm. Our finding paves the way toward the applications of cobalt(II) clathrochelates as future paramagnetic tags. Given the incredible stability and functionalization versatility of clathrochelates, the fine-tuning of the caging ligand may lead to new chemically stable mononuclear single-molecule magnets, for which magnetic anisotropy is of importance.

Recent advances in magic angle spinning solid state NMR of membrane proteins

Membrane proteins mediate many critical functions in cells. Determining their three-dimensional structures in the native lipid environment has been one of the main objectives in structural biology. There are two major NMR methodologies that allow this objective to be accomplished. Oriented sample NMR, which can be applied to membrane proteins that are uniformly aligned in the magnetic field, has been successful in determining the backbone structures of a handful of membrane proteins. Owing to methodological and technological developments, Magic Angle Spinning (MAS) solid-state NMR (ssNMR) spectroscopy has emerged as another major technique for the complete characterization of the structure and dynamics of membrane proteins. First developed on peptides and small microcrystalline proteins, MAS ssNMR has recently been successfully applied to large membrane proteins. In this review we describe recent progress in MAS ssNMR methodologies, which are now available for studies of membrane protein structure determination, and outline a few examples, which highlight the broad capability of ssNMR spectroscopy.

Simultaneous use of solution NMR and X-ray data in REFMAC5 for joint refinement/detection of structural differences

The program REFMAC5 from CCP4 was modified to allow the simultaneous use of X-ray crystallographic data and paramagnetic NMR data (pseudocontact shifts and self-orientation residual dipolar couplings) and/or diamagnetic residual dipolar couplings. Incorporation of these long-range NMR restraints in REFMAC5 can reveal differences between solid-state and solution conformations of molecules or, in their absence, can be used together with X-ray crystallographic data for structural refinement. Since NMR and X-ray data are complementary, when a single structure is consistent with both sets of data and still maintains reasonably `ideal' geometries, the reliability of the derived atomic model is expected to increase. The program was tested on five different proteins: the catalytic domain of matrix metalloproteinase 1, GB3, ubiquitin, free calmodulin and calmodulin complexed with a peptide. In some cases the joint refinement produced a single model consistent with both sets of observations, while in other cases it indicated, outside the experimental uncertainty, the presence of different protein conformations in solution and in the solid state.

SedNMR: a web tool for optimizing sedimentation of macromolecular solutes for SSNMR

We have proposed solid state NMR (SSNMR) of sedimented solutes as a novel approach to sample preparation for biomolecular SSNMR without crystallization or other sample manipulations. The biomolecules are confined by high gravity--obtained by centrifugal forces either directly in a SSNMR rotor or in a ultracentrifugal device--into a hydrated non-crystalline solid suitable for SSNMR investigations. When gravity is removed, the sample reverts to solution and can be treated as any solution NMR sample. We here describe a simple web tool to calculate the relevant parameters for the success of the experiment.