Recovering Invisible Signals by Two-Field NMR Spectroscopy

Comprehensive analysis of relaxation decays from high-resolution relaxometry

Relaxometry consists in measuring relaxation rates over orders of magnitude of magnetic fields to probe motions of complex systems. High-resolution relaxometry (HRR) experiments can be performed on conventional high-field NMR magnets equipped with a sample shuttle. During the experiment, the sample shuttle transfers the sample between the high-field magnetic center and a chosen position in the stray field for relaxation during a variable delay, thus using the stray field as a variable field. As the relaxation delay occurs outside of the probe, HRR experiments cannot rely on the control of cross-relaxation pathways, which is standard in high-field relaxation pulse sequences. Thus, decay rates are not pure relaxation rates, which may impair a reliable description of the dynamics. Previously, we took into account cross-relaxation effects in the analysis of high-resolution relaxometry data by applying a correction factor to relaxometry decay rates in order to estimate relaxation rates. These correction factors were obtained from the iterative simulation of the relaxation decay while the sample lies outside of the probe and a preceding analysis of relaxation rates which relies on the approximation of a priori multi-exponential decays by mono-exponential functions. However, an analysis protocol matching directly experimental and simulated relaxometry decays should be more self consistent and more generally applicable as it can accommodate deviations from mono-exponential decays. Here, we introduce Matching INtensities for the Optimization of Timescales and Amplitudes of motions Under Relaxometry (MINOTAUR), a framework for the analysis of high-resolution relaxometry that takes as input the intensity decays at all fields. This approach uses the full relaxation matrix to calculate intensity decays, allowing complex relaxation pathways to be taken into account. Therefore, it eliminates the need for a correction of decay rates and for fitting multi-exponential decays with mono-exponential functions. The MINOTAUR software is designed as a flexible framework where relaxation matrices and spectral density functions corresponding to various models of motions can be defined on a case-by-case basis. The agreement with our previous analyses of protein side-chain dynamics from carbon-13 relaxation is excellent, while providing a more robust analysis tool. We expect MINOTAUR to become the tool of choice for the analysis of high-resolution relaxometry.

Convergent views on disordered protein dynamics from NMR and computational approaches

Intrinsically disordered proteins (IDPs) or intrinsically disordered regions (IDRs) is a class of biologically important proteins exhibiting specific biophysical characteristics. They lack a hydrophobic core, and their conformational behavior is strongly influenced by electrostatic interactions. IDPs and IDRs are highly dynamic, and a characterization of the motions of IDPs and IDRs is essential for their physically correct description. NMR together with molecular dynamics simulations are the methods best suited to such a task because they provide information about dynamics of proteins with atomistic resolution. Here, we present a study of motions of a disordered C-terminal domain of the delta subunit of RNA polymerase from Bacillus subtilis. Positively and negatively charged residues in the studied domain form transient electrostatic contacts critical for the biological function. Our study is focused on investigation of ps-ns dynamics of backbone of the delta subunit based on analysis of amide 15N NMR relaxation data and molecular dynamics simulations. In order to extend an informational content of NMR data to lower frequencies, which are more sensitive to slower motions, we combined standard (high-field) NMR relaxation experiments with high-resolution relaxometry. Altogether, we collected data reporting the relaxation at 12 different magnetic fields, resulting in an unprecedented data set. Our results document that the analysis of such data provides a consistent description of dynamics and confirms the validity of so far used protocols of the analysis of dynamics of IDPs also for a partially folded protein. In addition, the potential to access detailed description of motions at the timescale of tens of ns with the help of relaxometry data is discussed. Interestingly, in our case, it appears to be mostly relevant for a region involved in the formation of temporary contacts within the disordered region, which was previously proven to be biologically important.

Fast Magic‐Angle‐Spinning NMR Reveals the Evasive Hepatitis B Virus Capsid C‐Terminal Domain**

Experimentally determined protein structures often feature missing domains. One example is the C‐terminal domain (CTD) of the hepatitis B virus capsid protein, a functionally central part of this assembly, crucial in regulating nucleic‐acid interactions, cellular trafficking, nuclear import, particle assembly and maturation. However, its structure remained elusive to all current techniques, including NMR. Here we show that the recently developed proton‐detected fast magic‐angle‐spinning solid‐state NMR at >100 kHz MAS allows one to detect this domain and unveil its structural and dynamic behavior. We describe the experimental framework used and compare the domain's behavior in different capsid states. The developed approaches extend solid‐state NMR observations to residues characterized by large‐amplitude motion on the microsecond timescale, and shall allow one to shed light on other flexible protein domains still lacking their structural and dynamic characterization.

Lead-207 NMR spectroscopy at 1.4 T: Application of benchtop instrumentation to a challenging I = ½ nucleus

The practicality of obtaining liquid- and solid-state ²⁰⁷ Pb nuclear magnetic resonance (NMR) spectra with a low permanent-field magnet is investigated. Obtaining ²⁰⁷ Pb NMR spectra of salts in solution is shown to be viable for samples as dilute as 0.05 M. The concentration dependence of the ²⁰⁷ Pb chemical shifts for lead nitrate was investigated; the results are comparable with those obtained with high-field instruments. Likewise, the isotope effect of substituting D₂ O for H₂ O as the solvent was investigated and found to be comparable with those reported previously. Obtaining solid-state ²⁰⁷ Pb NMR spectra is challenging, but we demonstrate the ability to obtain such spectra for three unique solid samples. An axially symmetric ²⁰⁷ Pb powder pattern for lead nitrate and the powder pattern expected for lead chloride reveal linewidths dominated by shielding anisotropy, while ²⁰⁷ Pb-^35/37 Cl J-coupling dominates in the methylammonium lead chloride perovskite material. Finally, recent innovations and the future potential of the instruments are considered.

Surprising absence of strong homonuclear coupling at low magnetic field explored by two-field nuclear magnetic resonance spectroscopy

Strong coupling of nuclear spins, which is achieved when their scalar coupling 2 π J is greater than or comparable to the difference Δ ω in their Larmor precession frequencies in an external magnetic field, gives rise to efficient coherent longitudinal polarization transfer. The strong coupling regime can be achieved when the external magnetic field is sufficiently low, as Δ ω is reduced proportional to the field strength. In the present work, however, we demonstrate that in heteronuclear spin systems these simple arguments may not hold, since heteronuclear spin-spin interactions alter the Δ ω value. The experimental method that we use is two-field nuclear magnetic resonance (NMR), exploiting sample shuttling between the high field, at which NMR spectra are acquired, and the low field, where strong couplings are expected and at which NMR pulses can be applied to affect the spin dynamics. By using this technique, we generate zero-quantum spin coherences by means of a nonadiabatic passage through a level anticrossing and study their evolution at the low field. Such zero-quantum coherences mediate the polarization transfer under strong coupling conditions. Experiments performed with a 13 C -labeled amino acid clearly show that the coherent polarization transfer at the low field is pronounced in the 13 C spin subsystem under proton decoupling. However, in the absence of proton decoupling, polarization transfer by coherent processes is dramatically reduced, demonstrating that heteronuclear spin-spin interactions suppress the strong coupling regime, even when the external field is low. A theoretical model is presented, which can model the reported experimental results.

Recent advances in solid-state relaxation dispersion techniques

This review describes two rotating-frame (R_1ρ) relaxation dispersion methods, namely the Bloch-McConnell Relaxation Dispersion and the Near-rotary Resonance Relaxation Dispersion, which enable the study of microsecond time-scale conformational fluctuations in the solid state using magic-angle-spinning nuclear magnetic resonance spectroscopy. The goal is to provide the reader with key ideas, experimental descriptions, and practical considerations associated with R_1ρ measurements that are needed for analyzing relaxation dispersion and quantifying conformational exchange. While the focus is on protein motion, many presented concepts can be equally well adapted to study the microsecond time-scale dynamics of other bio- (e.g. lipids, polysaccharides, nucleic acids), organic (e.g. pharmaceutical compounds), or inorganic molecules (e.g., metal organic frameworks). This article summarizes the essential contributions made by recent theoretical and experimental solid-state NMR studies to our understanding of protein motion. Here we discuss recent advances in fast MAS applications that enable the observation and atomic level characterization of sparsely populated conformational states which are otherwise inaccessible for other experimental methods. Such high-energy states are often associated with protein functions such as molecular recognition, ligand binding, or enzymatic catalysis, as well as with disease-related properties such as misfolding and amyloid formation.

Theoretical and computational framework for the analysis of the relaxation properties of arbitrary spin systems. Application to high-resolution relaxometry

A wide variety of nuclear magnetic resonance experiments rely on the prediction and analysis of relaxation processes. Recently, innovative approaches have been introduced where the sample travels through a broad range of magnetic fields in the course of the experiment, such as dissolution dynamic nuclear polarization or high-resolution relaxometry. Understanding the relaxation properties of nuclear spin systems over orders of magnitude of magnetic fields is essential to rationalize the results of these experiments. For example, during a high-resolution relaxometry experiment, the absence of control of nuclear spin relaxation pathways during the sample transfers and relaxation delays leads to systematic deviations of polarization decays from an ideal mono-exponential decay with the pure longitudinal relaxation rate. These deviations have to be taken into account to describe quantitatively the dynamics of the system. Here, we present computational tools to (1) calculate analytical expressions of relaxation rates for a broad variety of spin systems and (2) use these analytical expressions to correct the deviations arising in high-resolution relaxometry experiments. These tools lead to a better understanding of nuclear spin relaxation, which is required to improve the sensitivity of many pulse sequences, and to better characterize motions in macromolecules.

Boosting the resolution of low-field [Formula: see text] relaxation experiments on intrinsically disordered proteins with triple-resonance NMR

Improving our understanding of nanosecond motions in disordered proteins requires the enhanced sampling of the spectral density function obtained from relaxation at low magnetic fields. High-resolution relaxometry and two-field NMR measurements of relaxation have, so far, only been based on the recording of one- or two-dimensional spectra, which provide insufficient resolution for challenging disordered proteins. Here, we introduce a 3D-HNCO-based two-field NMR experiment for measurements of protein backbone [Formula: see text] amide longitudinal relaxation rates. The experiment provides accurate longitudinal relaxation rates at low field (0.33 T in our case) preserving the resolution and sensitivity typical for high-field NMR spectroscopy. Radiofrequency pulses applied on six different radiofrequency channels are used to manipulate the spin system at both fields. The experiment was demonstrated on the C-terminal domain of [Formula: see text] subunit of RNA polymerase from Bacillus subtilis, a protein with highly repetitive amino-acid sequence and very low dispersion of backbone chemical shifts.

Two-dimensional NMR lineshape analysis of single, multiple, zero and double quantum correlation experiments

NMR spectroscopy provides a powerful approach for the characterisation of chemical exchange and molecular interactions by analysis of series of experiments acquired over the course of a titration measurement. The appearance of NMR resonances undergoing chemical exchange depends on the frequency difference relative to the rate of exchange, and in the case of one-dimensional experiments chemical exchange regimes are well established and well known. However, two-dimensional experiments present additional complexity, as at least one additional frequency difference must be considered. Here we provide a systematic classification of chemical exchange regimes in two-dimensional NMR spectra. We highlight important differences between exchange in HSQC and HMQC experiments, that on a practical level result in more severe exchange broadening in HMQC spectra, but show that complementary alternatives to the HMQC are available in the form of HZQC and HDQC experiments. We present the longitudinal relaxation optimised SOFAST-H(Z/D)QC experiment for the simultaneous acquisition of sensitivity-enhanced HZQC and HDQC spectra, and the longitudinal and transverse relaxation optimised BEST-ZQ-TROSY for analysis of large molecular weight systems. We describe the application of these experiments to the characterisation of the interaction between the Hsp90 N-terminal domain and a small molecule ligand, and show that the independent analysis of HSQC, HMQC, HZQC and HDQC experiments provides improved confidence in the fitted dissociation constant and dissociation rate. Joint analysis of such data may provide improved sensitivity to detect and analyse more complex multi-state interaction mechanisms such as induced fit or conformational selection.

Protein Dynamics from Accurate Low-Field Site-Specific Longitudinal and Transverse Nuclear Spin Relaxation

Nuclear magnetic relaxation provides invaluable quantitative site-specific information on the dynamics of complex systems. Determining dynamics on nanosecond time scales requires relaxation measurements at low magnetic fields incompatible with high-resolution NMR. Here, we use a two-field NMR spectrometer to measure carbon-13 transverse and longitudinal relaxation rates at a field as low as 0.33 T (proton Larmor frequency 14 MHz) in specifically labeled side chains of the protein ubiquitin. The use of radiofrequency pulses enhances the accuracy of measurements as compared to high-resolution relaxometry approaches, where the sample is moved in the stray field of the superconducting magnet. Importantly, we demonstrate that accurate measurements at a single low magnetic field provide enough information to characterize complex motions on low nanosecond time scales, which opens a new window for the determination of site-specific nanosecond motions in complex systems such as proteins.

Emerging solution NMR methods to illuminate the structural and dynamic properties of proteins

The first recognition of protein breathing was more than 50 years ago. Today, we are able to detect the multitude of interaction modes, structural polymorphisms, and binding-induced changes in protein structure that direct function. Solution-state NMR spectroscopy has proved to be a powerful technique, not only to obtain high-resolution structures of proteins, but also to provide unique insights into the functional dynamics of proteins. Here, we summarize recent technical landmarks in solution NMR that have enabled characterization of key biological macromolecular systems. These methods have been fundamental to atomic resolution structure determination and quantitative analysis of dynamics over a wide range of time scales by NMR. The ability of NMR to detect lowly populated protein conformations and transiently formed complexes plays a critical role in its ability to elucidate functionally important structural features of proteins and their dynamics.

Recommended strategies for spectral processing and post-processing of 1D 1H-NMR data of biofluids with a particular focus on urine

1H NMR spectra from urine can yield information-rich data sets that offer important insights into many biological and biochemical phenomena. However, the quality and utility of these insights can be profoundly affected by how the NMR spectra are processed and interpreted. For instance, if the NMR spectra are incorrectly referenced or inconsistently aligned, the identification of many compounds will be incorrect. If the NMR spectra are mis-phased or if the baseline correction is flawed, the estimated concentrations of many compounds will be systematically biased. Furthermore, because NMR permits the measurement of concentrations spanning up to five orders of magnitude, several problems can arise with data analysis. For instance, signals originating from the most abundant metabolites may prove to be the least biologically relevant while signals arising from the least abundant metabolites may prove to be the most important but hardest to accurately and precisely measure. As a result, a number of data processing techniques such as scaling, transformation and normalization are often required to address these issues. Therefore, proper processing of NMR data is a critical step to correctly extract useful information in any NMR-based metabolomic study. In this review we highlight the significance, advantages and disadvantages of different NMR spectral processing steps that are common to most NMR-based metabolomic studies of urine. These include: chemical shift referencing, phase and baseline correction, spectral alignment, spectral binning, scaling and normalization. We also provide a set of recommendations for best practices regarding spectral and data processing for NMR-based metabolomic studies of biofluids, with a particular focus on urine.

High-resolution two-field nuclear magnetic resonance spectroscopy

Two-field NMR provides correlations of nuclear spins at the most favourable magnetic fields in a single experiment.