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

A set of cross-correlated relaxation experiments to probe the correlation time of two different and complementary spin pairs

Intrinsically disordered proteins (IDPs) defy the conventional structure-function paradigm by lacking a well-defined tertiary structure and exhibiting inherent flexibility. This flexibility leads to distinctive spin relaxation modes, reflecting isolated and specific motions within individual peptide planes. In this work, we propose a new pulse sequence to measure the longitudinal 13C' CSA-13C'-13Cα DD CCR rate [Formula: see text] and present a novel 3D version of the transverse [Formula: see text] CCR rate, adopting the symmetrical reconversion approach. We combined these rates with the analogous ΓxyN/NH and ΓzN/NH CCR rates to derive residue-specific correlation times for both spin-pairs within the same peptide plane. The presented approach offers a straightforward and intuitive way to compare the correlation times of two different and complementary spin vectors, anticipated to be a valuable aid to determine IDPs backbone dihedral angles distributions. We performed the proposed experiments on two systems: a folded protein ubiquitin and Coturnix japonica osteopontin, a prototypical IDP. Comparative analyses of the results show that the correlation times of different residues vary more for IDPs than globular proteins, indicating that the dynamics of IDPs is largely heterogeneous and dominated by local fluctuations.

Unraveling motion in proteins by combining NMR relaxometry and molecular dynamics simulations: A case study on ubiquitin

Nuclear magnetic resonance (NMR) relaxation experiments shine light onto the dynamics of molecular systems in the picosecond to millisecond timescales. As these methods cannot provide an atomically resolved view of the motion of atoms, functional groups, or domains giving rise to such signals, relaxation techniques have been combined with molecular dynamics (MD) simulations to obtain mechanistic descriptions and gain insights into the functional role of side chain or domain motion. In this work, we present a comparison of five computational methods that permit the joint analysis of MD simulations and NMR relaxation experiments. We discuss their relative strengths and areas of applicability and demonstrate how they may be utilized to interpret the dynamics in MD simulations with the small protein ubiquitin as a test system. We focus on the aliphatic side chains given the rigidity of the backbone of this protein. We find encouraging agreement between experiment, Markov state models built in the χ1/χ2 rotamer space of isoleucine residues, explicit rotamer jump models, and a decomposition of the motion using ROMANCE. These methods allow us to ascribe the dynamics to specific rotamer jumps. Simulations with eight different combinations of force field and water model highlight how the different metrics may be employed to pinpoint force field deficiencies. Furthermore, the presented comparison offers a perspective on the utility of NMR relaxation to serve as validation data for the prediction of kinetics by state-of-the-art biomolecular force fields.

The Potential of Cyclodextrins as Inhibitors for the BM2 Protein: An In Silico Investigation

The influenza BM2 transmembrane domain (BM2TM), an acid-activated proton channel, is an attractive antiviral target due to its essential roles during influenza virus replication, whereas no effective inhibitors have been reported for BM2. In this study, we draw inspiration from the properties of cyclodextrins (CDs) and hypothesize that CDs of appropriate sizes may possess the potential to act as inhibitors of the BM2TM proton channel. To explore this possibility, molecular dynamics simulations were employed to assess their inhibitory capabilities. Our findings reveal that CD4, CD5, and CD6 are capable of binding to the BM2TM proton channel, resulting in disrupted water networks and reduced hydrogen bond occupancy between H19 and the solvent within the BM2TM channel necessary for proton conduction. Notably, CD4 completely obstructs the BM2TM water channel. Based on these observations, we propose that CD4, CD5, and CD6 individually contribute to diminishing the proton transfer efficiency of the BM2 protein, and CD4 demonstrates promising potential as an inhibitor for the BM2 proton channel.

Analysis of the Dynamics of the Human Growth Hormone Secretagogue Receptor Reveals Insights into the Energy Landscape of the Molecule

G protein-coupled receptors initiate signal transduction in response to ligand binding. Growth hormone secretagogue receptor (GHSR), the focus of this study, binds the 28 residue peptide ghrelin. While structures of GHSR in different states of activation are available, dynamics within each state have not been investigated in depth. We analyze long molecular dynamics simulation trajectories using "detectors" to compare dynamics of the apo and ghrelin-bound states yielding timescale-specific amplitudes of motion. We identify differences in dynamics between apo and ghrelin-bound GHSR in the extracellular loop 2 and transmembrane helices 5-7. NMR of the GHSR histidine residues reveals chemical shift differences in these regions. We evaluate timescale specific correlation of motions between residues of ghrelin and GHSR, where binding yields a high degree of correlation for the first 8 ghrelin residues, but less correlation for the helical end. Finally, we investigate the traverse of GHSR over a rugged energy landscape via principal component analysis.

The Intriguing Molecular Dynamics of Cer[EOS] in Rigid Skin Barrier Lipid Layers Requires Improvement of the Model

Omega-O-acyl ceramides such as 32-linoleoyloxydotriacontanoyl sphingosine (Cer[EOS]) are essential components of the lipid skin barrier, which protects our body from excessive water loss and the penetration of unwanted substances. These ceramides drive the lipid assembly to epidermal-specific long periodicity phase (LPP), structurally much different than conventional lipid bilayers. Here, we synthesized Cer[EOS] with selectively deuterated segments of the ultralong N-acyl chain or deuterated or ¹³C-labeled linoleic acid and studied their molecular behavior in a skin lipid model. Solid-state ²H NMR data revealed surprising molecular dynamics for the ultralong N-acyl chain of Cer[EOS] with increased isotropic motion towards the isotropic ester-bound linoleate. The sphingosine moiety of Cer[EOS] is also highly mobile at skin temperature, in stark contrast to the other LPP components, N-lignoceroyl sphingosine acyl, lignoceric acid and cholesterol, which are predominantly rigid. The dynamics of the linoleic chain is quantitatively described by distributions of correlation times and using dynamic detector analysis. These NMR results along with neutron diffraction data suggest an LPP structure with alternating fluid (sphingosine chain-rich), rigid (acyl chain-rich), isotropic (linoleate-rich), rigid (acyl-chain rich), and fluid layers (sphingosine chain-rich). Such an arrangement of the skin barrier lipids with rigid layers separated with two different dynamic "fillings" i) agrees well with ultrastructural data, ii) satisfies the need for simultaneous rigidity (to ensure low permeability) and fluidity (to ensure elasticity, accommodate enzymes or antimicrobial peptides), and iii) offers a straightforward way to remodel the lamellar body lipids into the final lipid barrier.

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.

Slowly Relaxing Local Structure Analysis of 15N Relaxation from the Proteins p50 and Human Neutrophil Gelatinase-Associated Lipocalin: New Insights into the Dynamic Structure of β-Barrel Proteins

Nuclear magnetic resonance relaxation analysis is a powerful method for studying the internal mobility of proteins. We have developed for analysis the slowly relaxing local structure (SRLS) approach. SRLS is general in its nature in several respects, including the tensorial representation of the physical quantities comprising the dynamic model. By controlling tensor symmetry, a broad range of systems can be treated with physical relevance, typically with data-fitting techniques. In simple limits, SRLS yields the traditional model-free (MF) method. In the present context, MF simplicity means featuring the highest possible tensor symmetry. This renders MF-based data-fitting susceptible to the usage of fit parameters, yielding physically ill-defined results. A typical candidate is the R_ex term, devised to represent ms-μs motions but often invoked by the fitting scheme just to improve the statistics. Here, we consider two such cases using the N-H bond as probe and the proteins p50 and human neutrophil gelatinase-associated lipocalin as paradigm systems. We illustrate the harm caused by the physically unjustified involvement of R_ex in MF-based ¹⁵N relaxation analysis. Then, we show that forgoing the usage of R_ex, SRLS analysis of the very same experimental data provides interesting new information.

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.

A method to construct the dynamic landscape of a bio-membrane with experiment and simulation

Biomolecular function is based on a complex hierarchy of molecular motions. While biophysical methods can reveal details of specific motions, a concept for the comprehensive description of molecular dynamics over a wide range of correlation times has been unattainable. Here, we report an approach to construct the dynamic landscape of biomolecules, which describes the aggregate influence of multiple motions acting on various timescales and on multiple positions in the molecule. To this end, we use 13C NMR relaxation and molecular dynamics simulation data for the characterization of fully hydrated palmitoyl-oleoyl-phosphatidylcholine bilayers. We combine dynamics detector methodology with a new frame analysis of motion that yields site-specific amplitudes of motion, separated both by type and timescale of motion. In this study, we show that this separation allows the detailed description of the dynamic landscape, which yields vast differences in motional amplitudes and correlation times depending on molecular position.

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.

Detecting anisotropic segmental dynamics in disordered proteins by cross-correlated spin relaxation

Among the numerous contributions of Geoffrey Bodenhausen to NMR spectroscopy, his developments in the field of spin-relaxation methodology and theory will definitely have a long lasting impact. Starting with his seminal contributions to the excitation of multiple-quantum coherences, he and his group thoroughly investigated the intricate relaxation properties of these "forbidden fruits" and developed experimental techniques to reveal the relevance of previously largely ignored cross-correlated relaxation (CCR) effects, as "the essential is invisible to the eyes". Here we consider CCR within the challenging context of intrinsically disordered proteins (IDPs) and emphasize its potential and relevance for the studies of structural dynamics of IDPs in the future years to come. Conventionally, dynamics of globularly folded proteins are modeled and understood as deviations from otherwise rigid structures tumbling in solution. However, with increasing protein flexibility, as observed for IDPs, this apparent dichotomy between structure and dynamics becomes blurred. Although complex dynamics and ensemble averaging might impair the extraction of mechanistic details even further, spin relaxation uniquely encodes a protein's structural memory. Due to significant methodological developments, such as high-dimensional non-uniform sampling techniques, spin relaxation in IDPs can now be monitored in unprecedented resolution. Not embedded within a rigid globular fold, conventional 15 N spin probes might not suffice to capture the inherently local nature of IDP dynamics. To better describe and understand possible segmental motions of IDPs, we propose an experimental approach to detect the signature of anisotropic segmental dynamics by quantifying cross-correlated spin relaxation of individual 15 N 1 H N and 13 C ' 13 C α spin pairs. By adapting Geoffrey Bodenhausen's symmetrical reconversion principle to obtain zero frequency spectral density values, we can define and demonstrate more sensitive means to characterize anisotropic dynamics in IDPs.

Structural Dynamics from NMR Relaxation by SRLS Analysis: Local Geometry, Potential Energy Landscapes, and Spectral Densities

We have developed the two-body coupled-rotator slowly relaxing local structure (SRLS) approach for elucidating protein dynamics by nuclear magnetic resonance (NMR) relaxation. The rotators are represented by diffusion tensors D₁ for overall protein tumbling and D₂ for locally ordered probe motion. D₁ and D₂ are coupled dynamically by a potential, u, typically given by linear combinations of the Wigner functions D₀₀² and (D₀₂² + D_0-2²). Until now, our SRLS analyses provided the tensors, D₁ and D₂, the potential, u, and the geometric link between SRLS and NMR. Here we enhance this description by also examining the SRLS spectral densities obtained by solving the SRLS Smoluchowski equation. In addition, we show that the form of u specified above complies with two NMR-detected potential energy landscapes representing preferential ordering along N-H or C^α-C^α. Pictorial illustrations thereof are provided. The extended SRLS analysis is applied to ¹⁵N-H relaxation from the carbohydrate recognition domain of galectin-3 (Gal3C) in complex with two diastereomeric ligands, S and R. We find that D₂ is isotropic with a principal value, D₂, of 10¹⁰ s^-1 on average, and it is faster in the strands β₃, β₅, and β₈. The potential, u, is strong (∼20 kT); it is slightly rhombic when N-H is the main ordering axis and highly rhombic when C^α-C^α is the main ordering axis. Gal3C-S exhibits primarily preferential ordering along C^α-C^α; Gal3C-R exhibits both types of ordering. The binding-associated polypeptide chain segment of Gal3C-S is homogeneous, whereas that of Gal3C-R is diversified, with regard to D₂ and ordering preference. We associate these features with the previously determined diminished binding constant of Gal3C-R in comparison with Gal3C-S. Thus, the present study enhances the SRLS analysis, in general, and provides new insights into the dynamic structure and binding properties of Gal3C-S and Gal3C-R, in particular.

Water orientation and dynamics in the closed and open influenza B virus M2 proton channels

The influenza B M2 protein forms a water-filled tetrameric channel to conduct protons across the lipid membrane. To understand how channel water mediates proton transport, we have investigated the water orientation and dynamics using solid-state NMR spectroscopy and molecular dynamics (MD) simulations. 13C-detected water 1H NMR relaxation times indicate that water has faster rotational motion in the low-pH open channel than in the high-pH closed channel. Despite this faster dynamics, the open-channel water shows higher orientational order, as manifested by larger motionally-averaged 1H chemical shift anisotropies. MD simulations indicate that this order is induced by the cationic proton-selective histidine at low pH. Furthermore, the water network has fewer hydrogen-bonding bottlenecks in the open state than in the closed state. Thus, faster dynamics and higher orientational order of water molecules in the open channel establish the water network structure that is necessary for proton hopping.

How wide is the window opened by high-resolution relaxometry on the internal dynamics of proteins in solution?

The dynamics of molecules in solution is usually quantified by the determination of timescale-specific amplitudes of motions. High-resolution nuclear magnetic resonance (NMR) relaxometry experiments-where the sample is transferred to low fields for longitudinal (T₁) relaxation, and back to high field for detection with residue-specific resolution-seeks to increase the ability to distinguish the contributions from motion on timescales slower than a few nanoseconds. However, tumbling of a molecule in solution masks some of these motions. Therefore, we investigate to what extent relaxometry improves timescale resolution, using the "detector" analysis of dynamics. Here, we demonstrate improvements in the characterization of internal dynamics of methyl-bearing side chains by carbon-13 relaxometry in the small protein ubiquitin. We show that relaxometry data leads to better information about nanosecond motions as compared to high-field relaxation data only. Our calculations show that gains from relaxometry are greater with increasing correlation time of rotational diffusion.

Multimodal Response to Copper Binding in Superoxide Dismutase Dynamics

Copper/zinc superoxide dismutase (SOD) is a homodimeric metalloenzyme that has been extensively studied as a benchmark for structure-function relationships in proteins, in particular because of its implication in the familial form of the neurodegenerative disease amyotrophic lateral sclerosis. Here, we investigate microcrystalline preparations of two differently metalated forms of SOD, namely, the fully mature functional Cu,Zn state and the E,Zn-SOD state in which the Cu site is empty. By using solid-state NMR with fast magic-angle spinning (MAS) at high magnetic fields (¹H Larmor frequency of 800-1000 MHz), we quantify motions spanning a dynamic range from ns to ms. We determine that metal ion uptake does not act as a rigidification element but as a switch redistributing motional processes on different time scales, with coupling of the dynamics of histidine side chains and those of remote key backbone elements of the protein.

Conformational Entropy from Mobile Bond Vectors in Proteins: A Viewpoint that Unifies NMR Relaxation Theory and Molecular Dynamics Simulation Approaches

A new method for determining conformational entropy in proteins is reported. Proteins prevail as conformational ensembles, p ∝ exp(-u). By selecting a bond vector (e.g., N-H) as a conformation representative, molecular dynamics simulations can provide (relative to a reference structure) p as approximate Boltzmann probability density and u as N-H potential of mean force (POMF). The latter is as accurate as implied by the force field but statistical in character; this limits the insights it can provide and its utilization. Conformational entropy is given exclusively by u. Deriving it from POMFs renders it accurate but statistical in character. Previously, we devised explicit (i.e., analytical but not exact) potentials made of Wigner functions, D_0K^L, with L ≤ 4, which closely resemble the corresponding POMFs in form; hence, they also approach the latter in accuracy. Such potentials can be beneficially characterized/compared in terms of composition, symmetry, and associated order parameters. In this study, we develop a method for deriving conformational entropy from them, which also features the benefits specified above. The method developed is applied to the dimerization of the Rho GTPase-binding domain of plexin-B1. Insights into local ordering, entropy compensation, and features of allostery are gained. In previous work, we developed the slowly relaxing local structure (SRLS) approach for the analysis of NMR relaxation from restricted bond vector motion in proteins. SRLS comprises explicit (restricting) potentials of the kind developed here. It also comprises diffusion tensors describing the local motion and related features of local geometry. The complete model fits experimental data. In future work, the explicit potentials developed here will be inserted unchanged in SRLS-based data fitting, thereby improving the picture of structural dynamics. Given that SRLS is unique in featuring potentials that can closely approach the corresponding POMFs in accuracy, the present study is an important step toward generally improving protein dynamics by NMR relaxation.

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.

Simultaneous recording of intra- and inter-residue linking experiments for backbone assignments in proteins at MAS frequencies higher than 60 kHz

Obtaining site-specific assignments for the NMR spectra of proteins in the solid state is a significant bottleneck in deciphering their biophysics. This is primarily due to the time-intensive nature of the experiments. Additionally, the low resolution in the [Formula: see text]-dimension requires multiple complementary experiments to be recorded to lift degeneracies in assignments. We present here an approach, gleaned from the techniques used in multiple-acquisition experiments, which allows the recording of forward and backward residue-linking experiments in a single experimental block. Spectra from six additional pathways are also recovered from the same experimental block, without increasing the probe duty cycle. These experiments give intra- and inter residue connectivities for the backbone [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] resonances and should alone be sufficient to assign these nuclei in proteins at MAS frequencies > 60 kHz. The validity of this approach is tested with experiments on a standard tripeptide N-formyl methionyl-leucine-phenylalanine (f-MLF) at a MAS frequency of 62.5 kHz, which is also used as a test-case for determining the sensitivity of each of the experiments. We expect this approach to have an immediate impact on the way assignments are obtained at MAS frequencies [Formula: see text].

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.

Reducing bias in the analysis of solution-state NMR data with dynamics detectors

Nuclear magnetic resonance (NMR) is sensitive to dynamics on a wide range of correlation times. Recently, we have shown that analysis of relaxation rates via fitting to a correlation function with a small number of exponential terms could yield a biased characterization of molecular motion in solid-state NMR due to limited sensitivity of experimental data to certain ranges of correlation times. We introduced an alternative approach based on "detectors" in solid-state NMR, for which detector responses characterize motion for a range of correlation times and reduce potential bias resulting from the use of simple models for the motional correlation functions. Here, we show that similar bias can occur in the analysis of solution-state NMR relaxation data. We have thus adapted the detector approach to solution-state NMR, specifically separating overall tumbling motion from internal motions and accounting for contributions of chemical exchange to transverse relaxation. We demonstrate that internal protein motions can be described with detectors when the overall motion and the internal motions are statistically independent. We illustrate the detector analysis on ubiquitin with typical relaxation data sets recorded at a single high magnetic field or at multiple high magnetic fields and compare with results of model-free analysis. We also compare our methodology to LeMaster's method of dynamics analysis.

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.

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.

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.