Deuteron off-resonance rotating frame relaxation for the characterization of slow motions in rotating and static solid-state proteins

We demonstrate the feasibility of deuterium solid-state NMR off-resonance rotating frame relaxation measurements for studies of slow motions in biomolecular solids. The pulse sequence, which includes adiabatic pulses for magnetization alignment, is illustrated for static and magic-angle spinning conditions away from rotary resonances. We apply the measurements for three systems with selective deuterium labels at methyl groups: a) a model compound, Fluorenylmethyloxycarbonyl methionine-D3 amino acid, for which the principles of the measurements and corresponding motional modeling based on rotameric interconversions are demonstrated; b) amyloid-β1-40 fibrils labeled at a single alanine methyl group located in the disordered N-terminal domain. This system has been extensively studied in prior work and here serves as a test of the method for complex biological systems. The essential features of the dynamics consist of large-scale rearrangements of the disordered N-terminal domain and the conformational exchange between the free and bound forms of the domain, the latter one due to transient interactions with the structured core of the fibrils. and c) a 15-residue helical peptide which belongs to the predicted α-helical domain near the N-terminus of apolipoprotein B. The peptide is solvated with triolein and incorporates a selectively labeled leucine methyl groups. The method permits model refinement, indicating rotameric interconversions with a distribution of rate constants.

Ultrafast Magic Angle Spinning Solid-State NMR Spectroscopy: Advances in Methodology and Applications

Solid-state NMR spectroscopy is one of the most commonly used techniques to study the atomic-resolution structure and dynamics of various chemical, biological, material, and pharmaceutical systems spanning multiple forms, including crystalline, liquid crystalline, fibrous, and amorphous states. Despite the unique advantages of solid-state NMR spectroscopy, its poor spectral resolution and sensitivity have severely limited the scope of this technique. Fortunately, the recent developments in probe technology that mechanically rotate the sample fast (100 kHz and above) to obtain "solution-like" NMR spectra of solids with higher resolution and sensitivity have opened numerous avenues for the development of novel NMR techniques and their applications to study a plethora of solids including globular and membrane-associated proteins, self-assembled protein aggregates such as amyloid fibers, RNA, viral assemblies, polymorphic pharmaceuticals, metal-organic framework, bone materials, and inorganic materials. While the ultrafast-MAS continues to be developed, the minute sample quantity and radio frequency requirements, shorter recycle delays enabling fast data acquisition, the feasibility of employing proton detection, enhancement in proton spectral resolution and polarization transfer efficiency, and high sensitivity per unit sample are some of the remarkable benefits of the ultrafast-MAS technology as demonstrated by the reported studies in the literature. Although the very low sample volume and very high RF power could be limitations for some of the systems, the advantages have spurred solid-state NMR investigation into increasingly complex biological and material systems. As ultrafast-MAS NMR techniques are increasingly used in multidisciplinary research areas, further development of instrumentation, probes, and advanced methods are pursued in parallel to overcome the limitations and challenges for widespread applications. This review article is focused on providing timely comprehensive coverage of the major developments on instrumentation, theory, techniques, applications, limitations, and future scope of ultrafast-MAS technology.

Rotating Frame Relaxation in Magic Angle Spinning Solid State NMR, a Promising Tool for Characterizing Biopolymer Motion

Magic angle spinning NMR rotating frame relaxation measurements provide a unique experimental window into biomolecules dynamics, as is illustrated by numerous recent applications. We discuss experimental strategies for this class of experiments, with a particular focus on systems where motion-driven modulation of the chemical shift interaction is the main mechanism for relaxation. We also explore and describe common strategies for interpreting the data sets to extract motion time scale, activation energy, and angle or order parameters from rotating frame relaxation data. Using model free analysis and numerical simulations, including time domain treatment, we explore conditions under which it is possible to obtain accurate and precise information about the time scales of motions. Overall, with rapid technical advances in solid state NMR, there is a bright future for this class of studies.

Deuteron rotating frame relaxation for the detection of slow motions in rotating solids

We demonstrate experimental and computational approaches for measuring ²H rotating frame NMR relaxation for solid samples under magic angle spinning (MAS) conditions. The relaxation properties of the deuterium spin-1 system are dominated by the reorientation of the anisotropic quadrupolar tensors, with the effective quadrupolar coupling constant around 55 kHz for methyl groups. The technique is demonstrated using the model compound dimethyl-sulfone at MAS rates of 10 and 60 kHz as well as for an amyloid fibril sample comprising an amyloid-β (1-40) protein with a selective methyl group labeled in the disordered domain of the fibrils, at an MAS rate of 8 kHz. For both systems, the motional parameters fall well within the ranges determined by other techniques, thus validating its feasibility. Experimental and computational factors such as i) the probe's radio frequency inhomogeneity profiles, ii) rotary resonances at conditions for which the spin-lock field strength matches the half- or full-integer of the MAS rate, iii) the choice of MAS rates and spin-lock field strengths, and iv) simulations that account for the interconversion of multiple coherences for the spin-1 system under MAS and deviations from the analytical Redfield treatment are thoroughly considered.

Solid-State NMR: Methods for Biological Solids

In the last two decades, solid-state nuclear magnetic resonance (ssNMR) spectroscopy has transformed from a spectroscopic technique investigating small molecules and industrial polymers to a potent tool decrypting structure and underlying dynamics of complex biological systems, such as membrane proteins, fibrils, and assemblies, in near-physiological environments and temperatures. This transformation can be ascribed to improvements in hardware design, sample preparation, pulsed methods, isotope labeling strategies, resolution, and sensitivity. The fundamental engagement between nuclear spins and radio-frequency pulses in the presence of a strong static magnetic field is identical between solution and ssNMR, but the experimental procedures vastly differ because of the absence of molecular tumbling in solids. This review discusses routinely employed state-of-the-art static and MAS pulsed NMR methods relevant for biological samples with rotational correlation times exceeding 100's of nanoseconds. Recent developments in signal filtering approaches, proton methodologies, and multiple acquisition techniques to boost sensitivity and speed up data acquisition at fast MAS are also discussed. Several examples of protein structures (globular, membrane, fibrils, and assemblies) solved with ssNMR spectroscopy have been considered. We also discuss integrated approaches to structurally characterize challenging biological systems and some newly emanating subdisciplines in ssNMR spectroscopy.

Experimental Characterization of the Hepatitis B Virus Capsid Dynamics by Solid-State NMR

Protein plasticity and dynamics are important aspects of their function. Here we use solid-state NMR to experimentally characterize the dynamics of the 3.5 MDa hepatitis B virus (HBV) capsid, assembled from  240 copies of the Cp149 core protein. We measure both T₁ and T_1ρ relaxation times, which we use to establish detectors on the nanosecond and microsecond timescale. We compare our results to those from a 1 microsecond all-atom Molecular Dynamics (MD) simulation trajectory for the capsid. We show that, for the constituent residues, nanosecond dynamics are faithfully captured by the MD simulation. The calculated values can be used in good approximation for the NMR-non-detected residues, as well as to extrapolate into the range between the nanosecond and microsecond dynamics, where NMR has a blind spot at the current state of technology. Slower motions on the microsecond timescale are difficult to characterize by all-atom MD simulations owing to computational expense, but are readily accessed by NMR. The two methods are, thus, complementary, and a combination thereof can reliably characterize motions covering correlation times up to a few microseconds.

Deuteration for High-Resolution Detection of Protons in Protein Magic Angle Spinning (MAS) Solid-State NMR

Proton detection developed in the last 20 years as the method of choice to study biomolecules in the solid state. In perdeuterated proteins, proton dipolar interactions are strongly attenuated, which allows yielding of high-resolution proton spectra. Perdeuteration and backsubstitution of exchangeable protons is essential if samples are rotated with MAS rotation frequencies below 60 kHz. Protonated samples can be investigated directly without spin dilution using proton detection methods in case the MAS frequency exceeds 110 kHz. This review summarizes labeling strategies and the spectroscopic methods to perform experiments that yield assignments, quantitative information on structure, and dynamics using perdeuterated samples. Techniques for solvent suppression, H/D exchange, and deuterium spectroscopy are discussed. Finally, experimental and theoretical results that allow estimation of the sensitivity of proton detected experiments as a function of the MAS frequency and the external B₀ field in a perdeuterated environment are compiled.

Model-Free or Not?

Relaxation in nuclear magnetic resonance is a powerful method for obtaining spatially resolved, timescale-specific dynamics information about molecular systems. However, dynamics in biomolecular systems are generally too complex to be fully characterized based on NMR data alone. This is a familiar problem, addressed by the Lipari-Szabo model-free analysis, a method that captures the full information content of NMR relaxation data in case all internal motion of a molecule in solution is sufficiently fast. We investigate model-free analysis, as well as several other approaches, and find that model-free, spectral density mapping, LeMaster's approach, and our detector analysis form a class of analysis methods, for which behavior of the fitted parameters has a well-defined relationship to the distribution of correlation times of motion, independent of the specific form of that distribution. In a sense, they are all "model-free." Of these methods, only detectors are generally applicable to solid-state NMR relaxation data. We further discuss how detectors may be used for comparison of experimental data to data extracted from molecular dynamics simulation, and how simulation may be used to extract details of the dynamics that are not accessible via NMR, where detector analysis can be used to connect those details to experiments. We expect that combined methodology can eventually provide enough insight into complex dynamics to provide highly accurate models of motion, thus lending deeper insight into the nature of biomolecular dynamics.

Spectroscopic glimpses of the transition state of ATP hydrolysis trapped in a bacterial DnaB helicase

The ATP hydrolysis transition state of motor proteins is a weakly populated protein state that can be stabilized and investigated by replacing ATP with chemical mimics. We present atomic-level structural and dynamic insights on a state created by ADP aluminum fluoride binding to the bacterial DnaB helicase from Helicobacter pylori. We determined the positioning of the metal ion cofactor within the active site using electron paramagnetic resonance, and identified the protein protons coordinating to the phosphate groups of ADP and DNA using proton-detected 31P,1H solid-state nuclear magnetic resonance spectroscopy at fast magic-angle spinning > 100 kHz, as well as temperature-dependent proton chemical-shift values to prove their engagements in hydrogen bonds. 19F and 27Al MAS NMR spectra reveal a highly mobile, fast-rotating aluminum fluoride unit pointing to the capture of a late ATP hydrolysis transition state in which the phosphoryl unit is already detached from the arginine and lysine fingers.

Structures of Pathological and Functional Amyloids and Prions, a Solid-State NMR Perspective

Infectious proteins or prions are a remarkable class of pathogens, where pathogenicity and infectious state correspond to conformational transition of a protein fold. The conformational change translates into the formation by the protein of insoluble amyloid aggregates, associated in humans with various neurodegenerative disorders and systemic protein-deposition diseases. The prion principle, however, is not limited to pathogenicity. While pathological amyloids (and prions) emerge from protein misfolding, a class of functional amyloids has been defined, consisting of amyloid-forming domains under natural selection and with diverse biological roles. Although of great importance, prion amyloid structures remain challenging for conventional structural biology techniques. Solid-state nuclear magnetic resonance (SSNMR) has been preferentially used to investigate these insoluble, morphologically heterogeneous aggregates with poor crystallinity. SSNMR methods have yielded a wealth of knowledge regarding the fundamentals of prion biology and have helped to solve the structures of several prion and prion-like fibrils. Here, we will review pathological and functional amyloid structures and will discuss some of the obtained structural models. We will finish the review with a perspective on integrative approaches combining solid-state NMR, electron paramagnetic resonance and cryo-electron microscopy, which can complement and extend our toolkit to structurally explore various facets of prion biology.

Recent developments in deuterium solid-state NMR for the detection of slow motions in proteins

Slow timescale dynamics in proteins are essential for a variety of biological functions spanning ligand binding, enzymatic catalysis, protein folding and misfolding regulations, as well as protein-protein and protein-nucleic acid interactions. In this review, we focus on the experimental and theoretical developments of 2H static NMR methods applicable for studies of microsecond to millisecond motional modes in proteins, particularly rotating frame relaxation dispersion (R1ρ), quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) relaxation dispersion, and quadrupolar chemical exchange saturation transfer NMR experiments (Q-CEST). With applications chosen from amyloid-β fibrils, we show the complementarity of these approaches for elucidating the complexities of conformational ensembles in disordered domains in the non-crystalline solid state, with the employment of selective deuterium labels. Combined with recent advances in relaxation dispersion backbone measurements for 15N/13C/1H nuclei, these techniques provide powerful tools for studies of biologically relevant timescale dynamics in disordered domains in the solid state.

Broadband Dynamics of Ubiquitin by Anionic and Cationic Nanoparticle Assisted NMR Spin Relaxation

The quantitative and comprehensive description of the internal dynamics of proteins is critical for understanding their function. Nanoparticle-assisted ¹⁵ N NMR spin relaxation spectroscopy is a new method for the observation of picosecond to microsecond dynamics of proteins when transiently interacting with the surface of the nanoparticles (NPs). The method is applied here to the protein ubiquitin in the presence of anionic and cationic silica NPs (SNPs) of different sizes. The backbone dynamics profiles are reproducible and strikingly similar to each other, indicating that specific protein-SNP interactions are unimportant. The dynamics profiles closely match the sub-nanosecond dynamics S² values observed by model-free analysis of standard ¹⁵ N relaxation of ubiquitin in free solution, indicating that the bulk of the ubiquitin backbone dynamics in solution is confined to sub-nanosecond timescales and, hence, it is dynamically more restrained than previous NMR studies have suggested.

Asparagine and Glutamine Side-Chains and Ladders in HET-s(218-289) Amyloid Fibrils Studied by Fast Magic-Angle Spinning NMR

Asparagine and glutamine side-chains can form hydrogen-bonded ladders which contribute significantly to the stability of amyloid fibrils. We show, using the example of HET-s(218–289) fibrils, that the primary amide side-chain proton resonances can be detected in cross-polarization based solid-state NMR spectra at fast magic-angle spinning (MAS). J-coupling based experiments offer the possibility to distinguish them from backbone amide groups if the spin-echo lifetimes are long enough, which turned out to be the case for the glutamine side-chains, but not for the asparagine side-chains forming asparagine ladders. We explore the sensitivity of NMR observables to asparagine ladder formation. One of the two possible asparagine ladders in HET-s(218–289), the one comprising N226 and N262, is assigned by proton-detected 3D experiments at fast MAS and significant de-shielding of one of the NH₂ proton resonances indicative of hydrogen-bond formation is observed. Small rotating-frame ¹⁵N relaxation-rate constants point to rigidified asparagine side-chains in this ladder. The proton resonances are homogeneously broadened which could indicate chemical exchange, but is presently not fully understood. The second asparagine ladder (N243 and N279) in contrast remains more flexible.

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.

Molecular packing of pharmaceuticals analyzed with paramagnetic relaxation enhancement and ultrafast magic angle pinning NMR

Probing molecular details of fluorinated pharmaceutical compounds at a faster acquisition utilizing paramagnetic relaxation enhancement and better resolution from ultrafast magic angle spinning (ν_rot = 110 kHz) and high magnetic field (B₀ = 18.8 T).

Quantifying proton NMR coherent linewidth in proteins under fast MAS conditions: a second moment approach

Proton detected solid-state NMR under fast magic-angle-spinning (MAS) conditions is currently redefining the applications of solid-state NMR, in particular in structural biology. Understanding the contributions to the spectral linewidth is thereby of paramount importance. When disregarding the sample-dependent inhomogeneous contributions, the NMR proton linewidth is defined by homogeneous broadening, which has incoherent and coherent contributions. Understanding and disentangling these different contributions in multi-spin systems like proteins is still an open issue. The coherent contribution is mainly caused by the dipolar interaction under MAS and is determined by the molecular structure and the proton chemical shifts. Numerical simulation approaches based on numerically exact direct integration of the Liouville-von Neumann equation can give valuable information about the lineshape, but are limited to small spin systems (<12 spins). We present an alternative simulation method for the coherent contributions based on the rapid and partially analytic calculation of the second moments of large spin systems. We first validate the method on a simple system by predicting the ¹⁹F linewidth in CaF₂ under MAS. We compare simulation results to experimental data for microcrystalline ubiquitin (deuterated 100% back-exchanged at 110 kHz and fully-protonated at 125 kHz). Our results quantitatively explain the observed linewidth per-residue basis for the vast majority of residues.

100 kHz MAS Proton-Detected NMR Spectroscopy of Hepatitis B Virus Capsids

We sequentially assigned the fully-protonated capsids made from core proteins of the Hepatitis B virus using proton detection at 100 kHz magic-angle spinning (MAS) in 0.7 mm rotors and compare sensitivity and assignment completeness to previously obtained assignments using carbon-detection techniques in 3.2 mm rotors and 17.5 kHz MAS. We show that proton detection shows a global gain of a factor ~50 in mass sensitivity, but that signal-to-noise ratios and completeness of the assignment was somewhat higher for carbon-detected experiments for comparable experimental times. We also show that deuteration and HN back protonation improves the proton linewidth at 100 kHz MAS by a factor of 1.5, from an average of 170-110 Hz, and by a factor of 1.3 compared to deuterated capsids at 60 kHz MAS in a 1.3 mm rotor. Yet, several HN protons cannot be back-exchanged due to solvent inaccessibility, which results in a total of 15% of the amides missing in the spectra.

Localized and Collective Motions in HET-s(218-289) Fibrils from Combined NMR Relaxation and MD Simulation

Nuclear magnetic resonance (NMR) relaxation data and molecular dynamics (MD) simulations are combined to characterize the dynamics of the fungal prion HET-s(218-289) in its amyloid form. NMR data is analyzed with the dynamics detector method, which yields timescale-specific information. An analogous analysis is performed on MD trajectories. Because specific MD predictions can be verified as agreeing with the NMR data, MD was used for further interpretation of NMR results: for the different timescales, cross-correlation coefficients were derived to quantify the correlation of the motion between different residues. Short timescales are the result of very local motions, while longer timescales are found for longer-range correlated motion. Similar trends on ns- and μs-timescales suggest that μs motion in fibrils is the result of motion correlated over many fibril layers.

Deuteron Solid-State NMR Relaxation Measurements Reveal Two Distinct Conformational Exchange Processes in the Disordered N-Terminal Domain of Amyloid-β Fibrils

We employed deuterium solid-state NMR techniques under static conditions to discern the details of the μs-ms timescale motions in the flexible N-terminal subdomain of Aβ1-40 amyloid fibrils, which spans residues 1-16. In particular, we utilized a rotating frame (R1ρ ) and the newly developed time domain quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) relaxation measurements at the selectively deuterated side chains of A2, H6, and G9. The two experiments are complementary in terms of probing somewhat different timescales of motions, governed by the tensor parameters and the sampling window of the magnetization decay curves. The results indicated two mobile "free" states of the N-terminal domain undergoing global diffusive motions, with isotropic diffusion coefficients of 0.7-1 ⋅ 108 and 0.3-3 ⋅ 106 ad2  s-1 . The free states are also involved in the conformational exchange with a single bound state, in which the diffusive motions are quenched, likely due to transient interactions with the structured hydrophobic core. The conformational exchange rate constants are 2-3 ⋅ 105  s-1 and 2-3 ⋅ 104  s-1 for the fast and slow diffusion free states, respectively.

Solid-state NMR reveals a comprehensive view of the dynamics of the flexible, disordered N-terminal domain of amyloid-β fibrils

Amyloid fibril deposits observed in Alzheimer's disease comprise amyloid-β (Aβ) protein possessing a structured hydrophobic core and a disordered N-terminal domain (residues 1-16). The internal flexibility of the disordered domain is likely essential for Aβ aggregation. Here, we used ²H static solid-state NMR methods to probe the dynamics of selected side chains of the N-terminal domain of Aβ_1-40 fibrils. Line shape and relaxation data suggested a two-state model in which the domain's free state undergoes a diffusive motion that is quenched in the bound state, likely because of transient interactions with the structured C-terminal domain. At 37 °C, we observed freezing of the dynamics progressively along the Aβ sequence, with the fraction of the bound state increasing and the rate of diffusion decreasing. We also found that without solvation, the diffusive motion is quenched. The solvent acted as a plasticizer reminiscent of its role in the onset of global dynamics in globular proteins. As the temperature was lowered, the fraction of the bound state exhibited sigmoidal behavior. The midpoint of the freezing curve coincided with the bulk solvent freezing for the N-terminal residues and increased further along the sequence. Using ²H R _1ρ measurements, we determined the conformational exchange rate constant between the free and bound states under physiological conditions. Zinc-induced aggregation leads to the enhancement of the dynamics, manifested by the faster conformational exchange, faster diffusion, and lower freezing-curve midpoints.

Spinning faster: protein NMR at MAS frequencies up to 126 kHz

We report linewidth and proton T₁, T_1ρ and T₂' relaxation data of the model protein ubiquitin acquired at MAS frequencies up to 126 kHz. We find a predominantly linear improvement in linewidths and coherence decay times of protons with increasing spinning frequency in the range from 93 to 126 kHz. We further attempt to gain insight into the different contributions to the linewidth at fast MAS using site-specific analysis of proton relaxation parameters and present bulk relaxation times as a function of the MAS frequency. For microcrystalline fully-protonated ubiquitin, inhomogeneous contributions are only a minor part of the proton linewidth, and at 126 kHz MAS coherent effects are still dominating. We furthermore present site-specific proton relaxation rate constants during a spinlock at 126 kHz MAS, as well as MAS-dependent bulk T_1ρ (¹H^N).

Deuterium Rotating Frame NMR Relaxation Measurements in the Solid State under Static Conditions for Quantification of Dynamics

The feasibility of static deuterium rotating frame NMR relaxation measurements for characterization of slow timescale motions in powder systems is demonstrated. Using a model compound dimethyl sulfone-d6 , we show that these measurements yield conformational exchange rates and activation energy values in accordance with results obtained with other techniques. Furthermore, we demonstrate that the full Liouvillian approach as opposed to the Redfield approximation is necessary to analyze the experimental data.

Mechanistic Insights into Microsecond Time-Scale Motion of Solid Proteins Using Complementary 15N and 1H Relaxation Dispersion Techniques

NMR relaxation dispersion methods provide a holistic way to observe microsecond time-scale protein backbone motion both in solution and in the solid state. Different nuclei (¹H and ¹⁵N) and different relaxation dispersion techniques (Bloch-McConnell and near-rotary-resonance) give complementary information about the amplitudes and time scales of the conformational dynamics and provide comprehensive insights into the mechanistic details of the structural rearrangements. In this paper, we exemplify the benefits of the combination of various solution- and solid-state relaxation dispersion methods on a microcrystalline protein (α-spectrin SH3 domain), for which we are able to identify and model the functionally relevant conformational rearrangements around the ligand recognition loop occurring on multiple microsecond time scales. The observed loop motions suggest that the SH3 domain exists in a binding-competent conformation in dynamic equilibrium with a sterically impaired ground-state conformation both in solution and in crystalline form. This inherent plasticity between the interconverting macrostates is compatible with a conformational-preselection model and provides new insights into the recognition mechanisms of SH3 domains.

Conformational Dynamics in the Core of Human Y145Stop Prion Protein Amyloid Probed by Relaxation Dispersion NMR

Microsecond to millisecond timescale backbone dynamics of the amyloid core residues in Y145Stop human prion protein (PrP) fibrils were investigated by using ¹⁵ N rotating frame (R_1ρ ) relaxation dispersion solid-state nuclear magnetic resonance spectroscopy over a wide range of spin-lock fields. Numerical simulations enabled the experimental relaxation dispersion profiles for most of the fibril core residues to be modelled by using a two-state exchange process with a common exchange rate of 1000 s^-1 , corresponding to protein backbone motion on the timescale of 1 ms, and an excited-state population of 2 %. We also found that the relaxation dispersion profiles for several amino acids positioned near the edges of the most structured regions of the amyloid core were better modelled by assuming somewhat higher excited-state populations (∼5-15 %) and faster exchange rate constants, corresponding to protein backbone motions on the timescale of ∼100-300 μs. The slow backbone dynamics of the core residues were evaluated in the context of the structural model of human Y145Stop PrP amyloid.

Refocusing CSA during magic angle spinning rotating-frame relaxation experiments

We examine coherent evolution of spin-locked magnetization during magic-angle spinning (MAS), in the context of relaxation experiments designed to probe chemical exchange (rotating-frame relaxation (R_1ρ)). Coherent evolution is expected in MAS based rotating-frame relaxation decay experiments if matching conditions are met (such as, ω₁ = nω_r) and if the chemical shielding anisotropy (CSA) is substantial. We show here using numerical simulations and experiments that even when such matching requirements are avoided (e.g., ω₁ < 0.5ω_r, ∼1.5ω_r, >2.5ω_r), coherent evolution of spin-locked magnetization with large CSA is still considerable. The coherent evolution has important consequences on the analysis of relaxation decay and the ability to extract accurate information of interest about dynamics. We present a pulse sequence that employs rotary echoes and refocuses CSA contributions, allowing for more sensitive measurement of rotating-frame relaxation with less interference from coherent evolution. In practice, the proposed pulse sequence, REfocused CSA Rotating-frame Relaxation (RECRR) is robust to carrier frequency offset, B₁-field inhomogeneity, and slight miscalibrations of the refocusing pulses.

Setting the magic angle for fast magic-angle spinning probes

Fast magic-angle spinning, coupled with ¹H detection is a powerful method to improve spectral resolution and signal to noise in solid-state NMR spectra. Commercial probes now provide spinning frequencies in excess of 100 kHz. Then, one has sufficient resolution in the ¹H dimension to directly detect protons, which have a gyromagnetic ratio approximately four times larger than ¹³C spins. However, the gains in sensitivity can quickly be lost if the rotation angle is not set precisely. The most common method of magic-angle calibration is to optimize the number of rotary echoes, or sideband intensity, observed on a sample of KBr. However, this typically uses relatively low spinning frequencies, where the spinning of fast-MAS probes is often unstable, and detection on the ¹³C channel, for which fast-MAS probes are typically not optimized. Therefore, we compare the KBr-based optimization of the magic angle with two alternative approaches: optimization of the splitting observed in ¹³C-labeled glycine-ethylester on the carbonyl due to the Cα-C' J-coupling, or optimization of the H-N J-coupling spin echo in the protein sample itself. The latter method has the particular advantage that no separate sample is necessary for the magic-angle optimization.

Optimized "detectors" for dynamics analysis in solid-state NMR

Relaxation in nuclear magnetic resonance (NMR) results from stochastic motions that modulate anisotropic NMR interactions. Therefore, measurement of relaxation-rate constants can be used to characterize molecular-dynamic processes. The motion is often characterized by Markov processes using an auto-correlation function, which is assumed to be a sum of multiple decaying exponentials. We have recently shown that such a model can lead to severe misrepresentation of the real motion, when the real correlation function is more complex than the model. Furthermore, multiple distributions of motion may yield the same set of dynamics data. Therefore, we introduce optimized dynamics "detectors" to characterize motions which are linear combinations of relaxation-rate constants. A detector estimates the average or total amplitude of motion for a range of motional correlation times. The information obtained through the detectors is less specific than information obtained using an explicit model, but this is necessary because the information contained in the relaxation data is ambiguous, if one does not know the correct motional model. On the other hand, if one has a molecular dynamics trajectory, one may calculate the corresponding detector responses, allowing direct comparison to experimental NMR dynamics analysis. We describe how to construct a set of optimized detectors for a given set of relaxation measurements. We then investigate the properties of detectors for a number of different data sets, thus gaining an insight into the actual information content of the NMR data. Finally, we show an example analysis of ubiquitin dynamics data using detectors, using the DIFRATE software.

Microsecond motions probed by near-rotary-resonance R1ρ15N MAS NMR experiments: the model case of protein overall-rocking in crystals

Solid-state near-rotary-resonance measurements of the spin-lattice relaxation rate in the rotating frame (R_1ρ) is a powerful NMR technique for studying molecular dynamics in the microsecond time scale. The small difference between the spin-lock (SL) and magic-angle-spinning (MAS) frequencies allows sampling very slow motions, at the same time it brings up some methodological challenges. In this work, several issues affecting correct measurements and analysis of ¹⁵N R_1ρ data are considered in detail. Among them are signal amplitude as a function of the difference between SL and MAS frequencies, "dead time" in the initial part of the relaxation decay caused by transient spin-dynamic oscillations, measurements under HORROR condition and proper treatment of the multi-exponential relaxation decays. The multiple ¹⁵N R_1ρ measurements at different SL fields and temperatures have been conducted in 1D mode (i.e. without site-specific resolution) for a set of four different microcrystalline protein samples (GB1, SH3, MPD-ubiquitin and cubic-PEG-ubiquitin) to study the overall protein rocking in a crystal. While the amplitude of this motion varies very significantly, its correlation time for all four sample is practically the same, 30-50 μs. The amplitude of the rocking motion correlates with the packing density of a protein crystal. It has been suggested that the rocking motion is not diffusive but likely a jump-like dynamic process.

Because the Light is Better Here: Correlation-Time Analysis by NMR Spectroscopy

Relaxation data in NMR spectra are often used for dynamics analysis, by modeling motion in the sample with a correlation function consisting of one or more decaying exponential terms, each described by an order parameter, and a correlation time. This method has its origins in the Lipari-Szabo model-free approach, which originally considered overall tumbling plus one internal motion and was later expanded to several internal motions. Considering several of these cases in the solid state it is found that if the real motion is more complex than the assumed model, model fitting is biased towards correlation times where the relaxation data are most sensitive. This leads to unexpected distortions in the resulting dynamics description. Therefore dynamics detectors should be used, which characterize different ranges of correlation times and can help in the analysis of protein motion without assuming a specific model of the correlation function.

Slow conformational exchange and overall rocking motion in ubiquitin protein crystals

Proteins perform their functions in solution but their structures are most frequently studied inside crystals. Here we probe how the crystal packing alters microsecond dynamics, using solid-state NMR measurements and multi-microsecond MD simulations of different crystal forms of ubiquitin. In particular, near-rotary-resonance relaxation dispersion (NERRD) experiments probe angular backbone motion, while Bloch–McConnell relaxation dispersion data report on fluctuations of the local electronic environment. These experiments and simulations reveal that the packing of the protein can significantly alter the thermodynamics and kinetics of local conformational exchange. Moreover, we report small-amplitude reorientational motion of protein molecules in the crystal lattice with an ~3–5° amplitude on a tens-of-microseconds time scale in one of the crystals, but not in others. An intriguing possibility arises that overall motion is to some extent coupled to local dynamics. Our study highlights the importance of considering the packing when analyzing dynamics of crystalline proteins.

X-ray crystallography is the main method for protein structure determination. Here the authors combine solid-state NMR measurements and molecular dynamics simulations and show that crystal packing alters the thermodynamics and kinetics of local conformational exchange as well as overall rocking motion of protein molecules in the crystal lattice.

Microsecond Time Scale Proton Rotating-Frame Relaxation under Magic Angle Spinning

This paper deals with the theoretical foundation of proton magic angle spinning rotating-frame relaxation (R_1ρ) and establishes the range of validity and accuracy of the presented approach to describe low-amplitude microsecond time scale motion in the solid state. Beside heteronuclear dipolar and chemical shift anisotropy interactions, a major source of relaxation for protons is the homonuclear dipolar interaction. For this latter relaxation process, no general analytical equation has been published until now, which would describe the R_1ρ relaxation at any spinning speed, spin-lock field, or tilt angle. To validate the derived equations, we compared the analytical relaxation rates, obtained by solving the master equation within the framework of Redfield theory, with numerically simulated relaxation rates. We found that for small opening angles (∼10°), the relaxation rates obtained with stochastic Liouville simulations agree well with the analytical Redfield relaxation rates for a large range of motional correlation times. However, deviations around the rotary-resonance conditions highlight the fact that Redfield treatment of the solid-state relaxation rates can only provide qualitative insights into the microsecond time scale motion.