Slow motions in microcrystalline proteins as observed by MAS-dependent 15N rotating-frame NMR relaxation

Unravelling the structure of CO2 in silica adsorbents: an NMR and computational perspective

This comprehensive review describes recent advancements in the use of solid-state NMR-assisted methods and computational modeling strategies to unravel gas adsorption mechanisms and CO2 speciation in porous CO2-adsorbent silica materials at the atomic scale. This work provides new perspectives for the innovative modifications of these materials rendering them more amenable to the use of advanced NMR methods.

Kinetics of 1H →31P NMR cross-polarization and dynamics in a layered crystalline α-Sn(IV) phosphate

The proton-phosphorus (H-P) cross-polarization (CP) is effective in Sn(HPO4)2·H2O despite of the presence of paramagnetic ion impurities. Polarization constants TH-P and 1H T1ρ times are measured in static Sn(HPO4)2·H2O by the kinetic variable-temperature H-P CP experiments. The temperature dependence of the 1H T1ρ times is interpreted in terms of proton movements in the interlayer space occurring between the phosphate groups without participation of the water molecules. The process requires an activation energy of 8.7 ± 0.7 kcal/mol. The MAS effect on the 1H T1ρ times is shown and discussed.

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.

Aromatic ring flips in differently packed ubiquitin protein crystals from MAS NMR and MD

Probing the dynamics of aromatic side chains provides important insights into the behavior of a protein because flips of aromatic rings in a protein's hydrophobic core report on breathing motion involving a large part of the protein. Inherently invisible to crystallography, aromatic motions have been primarily studied by solution NMR. The question how packing of proteins in crystals affects ring flips has, thus, remained largely unexplored. Here we apply magic-angle spinning NMR, advanced phenylalanine ¹H-¹³C/²H isotope labeling and MD simulation to a protein in three different crystal packing environments to shed light onto possible impact of packing on ring flips. The flips of the two Phe residues in ubiquitin, both surface exposed, appear remarkably conserved in the different crystal forms, even though the intermolecular packing is quite different: Phe4 flips on a ca. 10-20 ns time scale, and Phe45 are broadened in all crystals, presumably due to µs motion. Our findings suggest that intramolecular influences are more important for ring flips than intermolecular (packing) effects.

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.

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.

Exploring Molecular Dynamics of Adsorbed CO2 Species in Amine-Modified Porous Silica by Solid-State NMR Relaxation

Previous studies on CO₂ adsorbents have mainly addressed the identification and quantification of adsorbed CO₂ species in amine-modified porous materials. Investigation of molecular motion of CO₂ species in confinement has not been explored in depth yet. This work entails a comprehensive study of molecular dynamics of the different CO₂ species chemi- and physisorbed at amine-modified silica materials through the determination of the rotating frame spin-lattice relaxation times (T _1ρ) by solid-state NMR. Rotational correlation times (τ_C) were also estimated using spin relaxation models based on the Bloch, Wangsness, and Redfield and the Bloembergen-Purcell-Pound theories. As expected, the τ_C values for the two physisorbed CO₂ species are considerably shorter (32 and 20 μs) than for the three identified chemisorbed CO₂ species (162, 62, and 123 μs). The differences in molecular dynamics between the different chemisorbed species correlate well with the structures previously proposed. In the case of the physisorbed CO₂ species, the τ_C values of the CO₂ species displaying faster molecular dynamics falls in the range of viscous liquids, whereas the species presenting slower dynamics exhibit T _1ρ and τ_C values compatible with a CO₂ layer of weakly interacting molecules with the silica surface. The values for chemical shift anisotropy (CSA) and ¹H-¹³C heteronuclear dipolar couplings have also been estimated from T _1ρ measurements, for each adsorbed CO₂ species. The CSA tensor parameters obtained from fitting the relaxation data agree with the experimentally measured CSA values, thus showing that the theories are well suited to study CO₂ dynamics in silica surfaces.

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.

Functional control of a 0.5 MDa TET aminopeptidase by a flexible loop revealed by MAS NMR

Large oligomeric enzymes control a myriad of cellular processes, from protein synthesis and degradation to metabolism. The 0.5 MDa large TET2 aminopeptidase, a prototypical protease important for cellular homeostasis, degrades peptides within a ca. 60 Å wide tetrahedral chamber with four lateral openings. The mechanisms of substrate trafficking and processing remain debated. Here, we integrate magic-angle spinning (MAS) NMR, mutagenesis, co-evolution analysis and molecular dynamics simulations and reveal that a loop in the catalytic chamber is a key element for enzymatic function. The loop is able to stabilize ligands in the active site and may additionally have a direct role in activating the catalytic water molecule whereby a conserved histidine plays a key role. Our data provide a strong case for the functional importance of highly dynamic - and often overlooked - parts of an enzyme, and the potential of MAS NMR to investigate their dynamics at atomic resolution.

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.

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.

Deuteron Chemical Exchange Saturation Transfer for the Detection of Slow Motions in Rotating Solids

We utilized the ²H Chemical Exchange Saturation Transfer (CEST) technique under magic angle spinning (MAS) conditions to demonstrate the feasibility of the method for studies of slow motions in the solid state. For the quadrupolar anisotropic interaction, the essence of CEST is to scan the saturation pattern over a range of offsets corresponding to the entire spectral region(s) for all conformational states involved, which translates into a range of −60–+ 60 kHz for methyl groups. Rotary resonances occur when the offsets are at half-and full-integer of the MAS rates. The choice of the optimal MAS rate is governed by the condition to reduce the number of rotary resonances in the CEST profile patterns and retain a sufficiently large quadrupolar interaction active under MAS to maintain sensitivity to motions. As examples, we applied this technique to a well-known model compound dimethyl-sulfone (DMS) as well as amyloid-β fibrils selectively deuterated at a single methyl group of A2 belonging to the disordered domain. It is demonstrated that the obtained exchange rate between the two rotameric states of DMS at elevated temperatures fell within known ranges and the fitted model parameters for the fibrils agree well with the previously obtained value using static ²H NMR techniques. Additionally, for the fibrils we have observed characteristic broadening of rotary resonances in the presence of conformational exchange, which provides implications for model selection and refinement. This work sets the stage for future potential extensions of the ²H CEST under MAS technique to multiple-labeled samples in small molecules and proteins.

Evaluation of the Rotating-Frame Relaxation (T1ρ) Filter and Its Application in Metabolomics as an Alternative to the Transverse Relaxation (T2) Filter

Nuclear magnetic resonance (NMR)-based metabolomic studies commonly involve the use of T2 filter pulse sequences to eliminate or attenuate the broad signals from large molecules and improve spectral resolution. In this paper, we demonstrate that the T1ρ filter-based pulse sequence represents an interesting alternative because it allows the stability and the reproducibility needed for statistical analysis. The integrity of the samples and the stability of the instruments were assessed for different filter durations and amplitudes. We showed that the T1ρ filter pulse sequence did not induce sample overheating for a filter duration of up to 500 ms. The reproducibility was evaluated and compared with the T2 filter in serum and liver samples. The implementation is relatively simple and provides the same statistical and analytical results as those obtained with the standard filters. Regarding tissues analysis, because the duration of the filter is the same as that of the spin-lock, the synchronization of the echo delays with the magic angle spinning (MAS) rate is no longer necessary as for T2 filter-based sequences. The results presented in this article aim at establishing a new protocol to improve metabolomic studies and pave the way for future developments on T1ρ alternative filters, in liquid and HR-MAS NMR experiments.

Dynamics of uniformly labelled solid proteins between 100 and 300 K: A 2D 2H-13C MAS NMR approach

We describe a ²H based MAS nuclear magnetic resonance (NMR) method to obtain site-specific molecular dynamics of biomolecules. The method utilizes the use of deuterium nucleus as a spin label that is proven to be very useful in dynamics studies of solid biological and functional materials. The aim is to understand overall characteristics of protein backbone and side-chain motions for CD₃, CD₂ and CD groups, in terms of timescale, type and activation energy of the underlying processes. Variable temperature two-dimensional (2D) ²H-¹³C correlation MAS NMR spectra were recorded for the uniformly ²H,¹³C,¹⁵N labelled Alanine and microcrystalline SH3 at a broad temperature range, from 320 K down to 100 K. First, the deuterium quadrupolar-coupling constant from specific D-C sites is obtained with the 2D experiment by utilizing carbon chemical shifts. Second, the static quadrupolar patterns are obtained at 100 K. Third, variable temperature approach enabled the observation of quadrupolar pattern over different motional regimes; slow, intermediate and fast. And finally, the apparent activation energies for C-D sites are determined and compared, by evaluating the temperature induced signal intensities. This information led to the determination of the dynamic processes for different D-C sites at a broad range of temperature and motional timescales. This is a first representation of 2D ²H-¹³C MAS NMR approach applied to fully isotope labelled deuterated protein covering 220 K temperature range.

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.

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.

Aromatic Ring Dynamics, Thermal Activation, and Transient Conformations of a 468 kDa Enzyme by Specific 1H-13C Labeling and Fast Magic-Angle Spinning NMR

Aromatic residues are located at structurally important sites of many proteins. Probing their interactions and dynamics can provide important functional insight but is challenging in large proteins. Here, we introduce approaches to characterize the dynamics of phenylalanine residues using ¹H-detected fast magic-angle spinning (MAS) NMR combined with a tailored isotope-labeling scheme. Our approach yields isolated two-spin systems that are ideally suited for artifact-free dynamics measurements, and allows probing motions effectively without molecular weight limitations. The application to the TET2 enzyme assembly of ∼0.5 MDa size, the currently largest protein assigned by MAS NMR, provides insights into motions occurring on a wide range of time scales (picoseconds to milliseconds). We quantitatively probe ring-flip motions and show the temperature dependence by MAS NMR measurements down to 100 K. Interestingly, favorable line widths are observed down to 100 K, with potential implications for DNP NMR. Furthermore, we report the first ¹³C R_1ρ MAS NMR relaxation-dispersion measurements and detect structural excursions occurring on a microsecond time scale in the entry pore to the catalytic chamber and at a trimer interface that was proposed as the exit pore. We show that the labeling scheme with deuteration at ca. 50 kHz MAS provides superior resolution compared to 100 kHz MAS experiments with protonated, uniformly ¹³C-labeled samples.

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).

Microsecond Protein Dynamics from Combined Bloch-McConnell and Near-Rotary-Resonance R1p Relaxation-Dispersion MAS NMR

Studying protein dynamics on microsecond-to-millisecond (μs-ms) time scales can provide important insight into protein function. In magic-angle-spinning (MAS) NMR, μs dynamics can be visualized by R 1 ρ rotating-frame relaxation dispersion experiments in different regimes of radio-frequency field strengths: at low RF field strength, isotropic-chemical-shift fluctuation leads to "Bloch-McConnell-type" relaxation dispersion, while when the RF field approaches rotary resonance conditions bond angle fluctuations manifest as increased R 1 ρ rate constants ("Near-Rotary-Resonance Relaxation Dispersion", NERRD). Here we explore the joint analysis of both regimes to gain comprehensive insight into motion in terms of geometric amplitudes, chemical-shift changes, populations and exchange kinetics. We use a numerical simulation procedure to illustrate these effects and the potential of extracting exchange parameters, and apply the methodology to the study of a previously described conformational exchange process in microcrystalline ubiquitin.

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.

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.

Protein Rotational Dynamics in Aligned Lipid Membranes Probed by Anisotropic T1ρ NMR Relaxation

A membrane-bound form of Pf1 coat protein reconstituted in magnetically aligned DMPC/DHPC bicelles was used as a molecular probe to quantify for the viscosity of the lipid membrane interior by measuring the uniaxial rotational diffusion coefficient of the protein. Orientationally dependent ¹⁵N NMR relaxation times in the rotating frame, or T_1ρ, were determined by fitting individually the decay of the resolved NMR peaks corresponding to the transmembrane helix of Pf1 coat protein as a function of the spin-lock time incorporated into the 2D SAMPI4 pulse sequence. The T_1ρ relaxation mechanism was modeled by uniaxial rotational diffusion on a cone, which yields a linear correlation with respect to the bond factor sin⁴θ_B, where θ_B is the angle that the NH bond forms with respect to the axis of rotation. Importantly, the bond factors can be independently measured from the dipolar couplings in the separated local-field SAMPI4 spectra. From this dependence, the value of the diffusion coefficient D_|| = 8.0 × 10⁵ s^-1 was inferred from linear regression of the experimental T_1ρ data even without any spectroscopic assignment. Alternatively, a close value of D_|| = 7.7 × 10⁵ s^-1 was obtained by fitting the T_1ρ relaxation data for the assigned NMR peaks of the transmembrane domain of Pf1 to a wavelike pattern as a function of residue number. The method illustrates the use of single-helix transmembrane peptides as molecular probes to assess the dynamic parameters of biological membranes by NMR relaxation in oriented lipid bilayers.

Microsecond Timescale Protein Dynamics: a Combined Solid-State NMR Approach

Conformational exchange in proteins is a major determinant in protein functionality. In particular, the μs-ms timescale is associated with enzymatic activity and interactions between biological molecules. We show here that a comprehensive data set of R1ρ relaxation dispersion profiles employing multiple effective fields and tilt angles can be easily obtained in perdeuterated, partly back-exchanged proteins at fast magic-angle spinning and further complemented with chemical-exchange saturation transfer NMR experiments. The approach exploits complementary sources of information and enables the extraction of multiple exchange parameters for μs-ms timescale conformational exchange, most notably including the sign of the chemical shift differences between the ground and excited states.

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.

Studying Dynamics by Magic-Angle Spinning Solid-State NMR Spectroscopy: Principles and Applications to Biomolecules

Magic-angle spinning solid-state NMR spectroscopy is an important technique to study molecular structure, dynamics and interactions, and is rapidly gaining importance in biomolecular sciences. Here we provide an overview of experimental approaches to study molecular dynamics by MAS solid-state NMR, with an emphasis on the underlying theoretical concepts and differences of MAS solid-state NMR compared to solution-state NMR. The theoretical foundations of nuclear spin relaxation are revisited, focusing on the particularities of spin relaxation in solid samples under magic-angle spinning. We discuss the range of validity of Redfield theory, as well as the inherent multi-exponential behavior of relaxation in solids. Experimental challenges for measuring relaxation parameters in MAS solid-state NMR and a few recently proposed relaxation approaches are discussed, which provide information about time scales and amplitudes of motions ranging from picoseconds to milliseconds. We also discuss the theoretical basis and experimental measurements of anisotropic interactions (chemical-shift anisotropies, dipolar and quadrupolar couplings), which give direct information about the amplitude of motions. The potential of combining relaxation data with such measurements of dynamically-averaged anisotropic interactions is discussed. Although the focus of this review is on the theoretical foundations of dynamics studies rather than their application, we close by discussing a small number of recent dynamics studies, where the dynamic properties of proteins in crystals are compared to those in solution.

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

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

The "long tail" of the protein tumbling correlation function: observation by (1)H NMR relaxometry in a wide frequency and concentration range

Inter-protein interactions in solution affect the auto-correlation function of Brownian tumbling not only in terms of a simple increase of the correlation time, they also lead to the appearance of a weak slow component ("long tail") of the correlation function due to a slowly changing local anisotropy of the microenvironment. The conventional protocol of correlation time estimation from the relaxation rate ratio R1/R2 assumes a single-component tumbling correlation function, and thus can provide incorrect results as soon as the "long tail" is of relevance. This effect, however, has been underestimated in many instances. In this work we present a detailed systematic study of the tumbling correlation function of two proteins, lysozyme and bovine serum albumin, at different concentrations and temperatures using proton field-cycling relaxometry combined with R1ρ and R2 measurements. Unlike high-field NMR relaxation methods, these techniques enable a detailed study of dynamics on a time scale longer than the normal protein tumbling correlation time and, thus, a reliable estimate of the parameters of the "long tail". In this work we analyze the concentration dependence of the intensity and correlation time of the slow component and perform simulations of high-field (15)N NMR relaxation data demonstrating the importance of taking the "long tail" in the analysis into account.