Conformational Flexibility of a Microcrystalline Globular Protein: Order Parameters by Solid-State NMR Spectroscopy

Dynamics in the Intact fd Bacteriophage Revealed by Pseudo 3D REDOR-Based Magic Angle Spinning NMR

The development of robust NMR methodologies to probe dynamics on the atomic scale is vital to elucidate the close relations between structure, motion, and function in biological systems. Here, we present an automated protocol to measure, using magic-angle spinning NMR, the effective 13C-15N dipolar coupling constants between multiple spin pairs simultaneously with high accuracy. We use the experimental dipolar coupling constants to quantify the order parameters of multiple C-N bonds in the thousands of identical copies of the coat protein in intact fd-Y21M filamentous bacteriophage virus and describe its overall dynamics on the submillisecond time scale. The method is based on combining three pseudo three-dimensional NMR experiments, where a rotational echo double resonance (REDOR) dephasing block, designed to measure internuclear distances, is combined with three complementary 13C-13C mixing schemes: dipolar-assisted rotational resonance, through-bond transfer-based double quantum/single quantum correlation, and radio frequency driven recoupling. These mixing schemes result in highly resolved carbon spectra with correlations that are created by different transfer mechanisms. We show that the helical part of the coat protein undergoes a uniform small (∼30°) amplitude motion, while the N-terminus is highly flexible. In addition, our results suggest that the reduced mobility of lysine sidechains at the C-terminus are a signature of binding to the single stranded DNA.

Comparison of methods for the NMR measurement of motionally averaged dipolar couplings

Motionally averaged dipolar couplings are an important tool for understanding the complex dynamics of catalysts, polymers, and biomolecules. While there is a plethora of solid-state NMR pulse sequences available for their measurement, in can be difficult to gauge the methods' strengths and weaknesses. In particular, there has not been a comprehensive comparison of their performance in natural abundance samples, where 1H homonuclear dipolar couplings are important and the use of large MAS rotors may be required for sensitivity reasons. In this work, we directly compared some of the more common methods for measuring C-H dipolar couplings in natural abundance samples using L-alanine (L-Ala) and the N-formyl-L-methionyl-L-leucyl-L-phenylalanine (fMLF) tripeptide as model systems. We evaluated their performance in terms of accuracy, resolution, sensitivity, and ease of implementation. We found that, despite the presence of 1H homonuclear dipolar interactions, all methods, with the exception of REDOR, were able to yield the reasonable dipolar coupling strengths for both mobile and static moieties. Of these methods, PDLF provides the most convenient workflow and precision at the expense of low sensitivity. In low-sensitivity cases, MAS-PISEMA and DIPSHIFT appear to be the better options.

Double echo symmetry-based REDOR and RESPDOR pulse sequences for proton detected measurements of heteronuclear dipolar coupling constants

¹H{X} symmetry-based rotational echo double resonance pulse sequences (S-REDOR) and symmetry-based rotational echo saturation pulse double resonance (S-RESPDOR) solid-state NMR experiments have found widespread application for ¹H detected measurements of difference NMR spectra, dipolar coupling constants, and internuclear distances under conditions of fast magic angle spinning (MAS). In these experiments the supercycled R4₁² (SR4₁²) symmetry-based recoupling pulse sequence is typically applied to the ¹H spins to reintroduce heteronuclear dipolar couplings. However, the timing of SR4₁² and other symmetry-based pulse sequences must be precisely synchronized with the rotation of the sample, otherwise, the evolution of ¹H CSA and other interactions will not be properly refocused. For this reason, significant distortions are often observed in experimental dipolar dephasing difference curves obtained with S-REDOR or S-RESPDOR pulse sequences. Here we introduce a family of double echo (DE) S-REDOR/S-RESPDOR pulse sequences that function in an analogous manner to the recently introduced t₁-noise eliminated (TONE) family of dipolar heteronuclear multiple quantum coherence (D-HMQC) pulse sequences. Through numerical simulations and experiments the DE S-REDOR/S-RESPDOR sequences are shown to provide dephasing difference curves similar to those obtained with S-REDOR/S-RESPDOR. However, the DE sequences are more robust to the deviations of the MAS frequency from the ideal value that occurs during typical solid-state NMR experiments. The DE sequences are shown to provide more reliable ¹H detected dipolar dephasing difference curves for nuclei such as ¹⁵N (with isotopic labelling), ¹⁸³W and ³⁵Cl. The double echo sequences are therefore recommended to be used in place of conventional S-REDOR/S-RESPDOR sequences for measurement of weak dipolar coupling constants and long-range distances.

Solid-State NMR Dipolar and Chemical Shift Anisotropy Recoupling Techniques for Structural and Dynamical Studies in Biological Systems

With the development of NMR methodology and technology during the past decades, solid-state NMR (ssNMR) has become a particularly important tool for investigating structure and dynamics at atomic scale in biological systems, where the recoupling techniques play pivotal roles in modern high-resolution MAS NMR. In this review, following a brief introduction on the basic theory of recoupling in ssNMR, we highlight the recent advances in dipolar and chemical shift anisotropy recoupling methods, as well as their applications in structural determination and dynamical characterization at multiple time scales (i.e., fast-, intermediate-, and slow-motion). The performances of these prevalent recoupling techniques are compared and discussed in multiple aspects, together with the representative applications in biomolecules. Given the recent emerging advances in NMR technology, new challenges for recoupling methodology development and potential opportunities for biological systems are also discussed.

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.

Solid-State NMR and Impedance Spectroscopy Study of Spin Dynamics in Proton-Conducting Polymers: An Application of Anisotropic Relaxing Model

The 1H-13C cross-polarization (CP) kinetics in poly[2-(methacryloyloxy)ethyltrimethylammonium chloride] (PMETAC) was studied under moderate (10 kHz) magic-angle spinning (MAS). To elucidate the role of adsorbed water in spin diffusion and proton conductivity, PMETAC was degassed under vacuum. The CP MAS results were processed by applying the anisotropic Naito and McDowell spin dynamics model, which includes the complete scheme of the rotating frame spin-lattice relaxation pathways. Some earlier studied proton-conducting and nonconducting polymers were added to the analysis in order to prove the capability of the used approach and to get more general conclusions. The spin-diffusion rate constant, which describes the damping of the coherences, was found to be strongly depending on the dipolar I-S coupling constant (DIS). The spin diffusion, associated with the incoherent thermal equilibration with the bath, was found to be most probably independent of DIS. It was deduced that the drying scarcely influences the spin-diffusion rates; however, it significantly (1 order of magnitude) reduces the rotating frame spin-lattice relaxation times. The drying causes the polymer hardening that reflects the changes of the local order parameters. The impedance spectroscopy was applied to study proton conductivity. The activation energies for dielectric relaxation and proton conductivity were determined, and the vehicle-type conductivity mechanism was accepted. The spin-diffusion processes occur on the microsecond scale and are one order faster than the dielectric relaxation. The possibility to determine the proton location in the H-bonded structures in powders using CP MAS technique is discussed.

Structure and Dynamics Perturbations in Ubiquitin Adsorbed or Entrapped in Silica Materials Are Related to Disparate Surface Chemistries Resolved by Solid-State NMR Spectroscopy

Protein immobilization on material surfaces is emerging as a powerful tool in the design of devices and active materials for biomedical and pharmaceutical applications as well as for catalysis. Preservation of the protein's biological functionality is crucial to the design process and is dependent on the ability to maintain its structural and dynamical integrity while removed from the natural surroundings. The scientific techniques to validate the structure of immobilized proteins are scarce and usually provide limited information as a result of poor resolution. In this work, we benchmarked the ability of standard solid-state NMR techniques to resolve the effects of binding to dissimilar silica materials on a model protein. In particular, the interactions between ubiquitin and the surfaces of MCM41, SBA15, and silica formed in situ were tested for their influence on the structure and dynamics of the protein. It is shown that the protein's globular fold in the free state is only slightly perturbed in the three silica materials. Local motions on a residue level that are quenched by immobilization or, conversely, that arise from the process are also detailed. NMR measurements show that these perturbations are unique to each silica material and can serve as reporters of the characteristic surface chemistry.

Transferred-Rotational-Echo Double Resonance

Internuclear distance determination is the foundation for NMR-based structure calculation. However, high-precision distance measurement is a laborious process requiring lengthy data acquisitions due to the large set of multidimensional spectra needed at different mixing times. This prevents application to large or challenging molecular systems. Here, we present a new approach, transferred-rotational-echo double resonance (TREDOR), a heteronuclear transfer method in which we simultaneously detect both starting and transferred signals in a single spectrum. This co-acquisition is used to compensate for coherence decay, resulting in accurate and precise distance determination by a single parameter fit using a single spectrum recorded at an ideal mixing time. We showcase TREDOR with the microcrystalline SH3 protein using 3D spectra to resolve resonances. By combining the measured N-C and H-C distances, we calculate the structure of SH3, which converges to the correct fold, with a root-mean-square deviation of 2.1 Å compared to a reference X-ray structure. The TREDOR data used in the structure calculation were acquired in only 4 days on a 600 MHz instrument. This is achieved due to the more than 2-fold time saving afforded by co-acquisition of additional information and demonstrates TREDOR as a fast and straightforward method for determining structures via magic-angle spinning NMR.

A modification of γ-encoded RN symmetry pulses for increasing the scaling factor and more accurate measurements of the strong heteronuclear dipolar couplings

Symmetry based γ-encoded RN_n^ν elements are broadly used in magic-angle spinning solid-state NMR experiments to achieve selective recoupling of the heteronuclear dipolar interactions. The recoupled dipolar couplings in such experiments are scaled by a factor, K_sc, which theoretically depends on the chosen symmetry numbers N, n, and ν. However, the maximum theoretical value of K_sc for γ-encoded RN_n^ν pulses is limited to ~0.25, resulting in long RN_n^ν experiment times. Also, the dependence of K_sc on the experimental parameters can result in systematic errors in the experimental determination of the dipolar couplings, especially at low and moderate MAS rates. In this manuscript, we investigate the use of MODifiEd RN_n^ν symmetry (MODERN_n^ν(ϕ_M)) pulses that increase the dipolar scaling factor by at least 1.45 fold compared to γ-encoded RN_n^ν. The second advantage of MODERN_n^ν(ϕ_M) pulses with respect to traditional RN_n^ν pulses is the reduced influence of experimental parameters on K_sc, which allows for more accurate measurement of short-range distances. The robustness of MODERN_n^ν(ϕ_M) is compared with γ-encoded R14₂³ symmetry pulses. The enhanced performance is demonstrated on two uniformly-¹³C-enriched samples, N-acetyl valine and the microcrystalline protein GB1, at a 31.111 kHz MAS rate.

CP MAS kinetics in soft matter: Spin diffusion, local disorder and thermal equilibration in poly(2-hydroxyethyl methacrylate)

The ¹H-¹³C cross-polarization magic angle spinning kinetics was studied in poly(2-hydroxyethyl methacrylate) (pHEMA), i.e. a soft material with high degrees of internal freedom and molecular disorder, having the purpose to track the influence of increasing local incoherent contributions to the effects of coherent nature in the open quantum spin systems. The experimental CP MAS kinetic curves were analyzed in the frame of the models of isotropic and anisotropic spin diffusion with thermal equilibration. The rates of spin diffusion and spin-lattice relaxation as well as the profiles of distribution of dipolar coupling, the parameters accounting the effective size of spin clusters and the local order parameters were determined. The intensities of the peaks of periodic quasi-equilibrium origin gradually decrease with increasing disorder, i.e. going from most ordered to more disordered sites in the polymer. Assuming that the thermal motion induced by the temperature gradients is much faster than the equilibration driven by spin diffusion due the difference in spin temperatures, it was deduced that the thermal equilibration in pHEMA occurs in the time scale of 10^-4 s. This is one order of magnitude faster than the spectral spin diffusion, which occurs between spins having different resonance frequencies. The thermal equilibration in the case of remote spin clusters was described by the 'stretched exponent' decay. This led to the fractal dimension D_p ≈ 1.65 for both carbon sites (quaternary and carbonyl). The obtained D_p value corresponds to the aggregates, which images are very similar to those for pHEMA and some other related polymer structures are usually conceived.

Accounting for the temperature dependence of 13C spin-lattice relaxation of methyl groups in the glycyl-alanyl-leucine model system under MAS with spin diffusion

The difficulties in quantitatively modeling the temperature dependence of spin-lattice relaxation in a model isotope-enriched peptide are explored as a prelude to obtaining dynamics parameters for motions in proteins from such measurements. The degree to which this can be handled by adding spin diffusion to a bath in standard rate matrix relaxation theory is studied using a small tri-peptide model system, glycyl-alanyl-leucine (GAL). We observe in this molecule that the relaxation of backbone carbons CO and Cα is not dominated by local fluctuations of the ¹³C-¹H dipolar couplings, but rather by ¹³C-¹³C spin diffusion to nearby methyl relaxation sinks. A treatment of the methyl relaxation itself, which ignores ¹³C-¹³C spin diffusion effects back to the otherwise slowly relaxing bath, provides poor agreement between theory and experimental data obtained for the temperature dependence of the methyl relaxation rates. Closed form approximate spectral densities and relaxation rates for a methyl group during magic angle spinning are obtained to compute the needed transition rates. These average computed rates, in conjunction with an extended form of the Solomon equations, are found to adequately model the temperature dependence of the methyl relaxation rates when spin diffusion is included. The barrier to rotation for the alanine methyl in GAL is determined to be 3.5 kcal mol^-1.

Molecular Dynamics Simulations of Macromolecular Crystals

The structures of biological macromolecules would not be known to their present extent without X-ray crystallography. Most simulations of globular proteins in solution begin by surrounding the crystal structure of the monomer in a bath of water molecules, but the standard simulation employing periodic boundary conditions is already close to a crystal lattice environment. With simple protocols, the same software and molecular models can perform simulations of the crystal lattice, including all asymmetric units and solvent to fill the box. Throughout the history of molecular dynamics, studies of crystal lattices have served to investigate the quality of the underlying force fields, correlate the simulated ensembles to experimental structure factors, and extrapolate the behavior in lattices to behavior in solution. Powerful new computers are enabling molecular simulations with greater realism and statistical convergence. Meanwhile, the advent of exciting new methods in crystallography, including femtosecond free-electron lasers and image reconstruction for time-resolved crystallography on slurries of small crystals, is expanding the range of structures accessible to X-ray diffraction. We review past fusions of simulations and crystallography, then look ahead to the ways that simulations of crystal structures will enhance structural biology in the future.

Quasi-Equilibria and Polarization Transfer Between Adjacent and Remote Spins: 1H-13C CP MAS Kinetics in Glycine

The ¹H-¹³C CP MAS kinetic curves were measured in glycine powder sample at the MAS rates of 7, 10, and 12 kHz. Each experimental curve contained up to 1000 equidistant points over the whole contact time range of 10 μs - 10 ms. The CP kinetic data for CH₂ group, i.e., for the system containing adjacent ¹H-¹³C spin pairs with a definite dominant dipolar coupling can be described in the frame of the isotropic spin-diffusion approach. The local order parameter ⟨ S⟩ ≈ 1.0, determined as the ratio of the measured dipolar ¹H-¹³C coupling constant and the calculated static dipolar coupling constant, is very close to the values deduced in series of other amino acids. The strong narrow peaks observed in the spin coupling spectrum at multiples of the MAS frequency can be considered as the confirmation that the periodic quasi-equilibrium state can appear also in the powder samples. The anisotropic spin-diffusion approach improved by the introducing of the thermal equilibration in the proton bath is the most proper model to describe the CP kinetics in the system containing remote spins. Very realistic values of the spin-cluster size ( N) have been obtained without any constraint on the flow of the nonlinear curve fitting. The finite values of N ≤ 4 means that CP transfer is located within one glycine molecule.

Hidden motions and motion-induced invisibility: Dynamics-based spectral editing in solid-state NMR

Solid-state nuclear magnetic resonance (ssNMR) spectroscopy enables the structural characterization of a diverse array of biological assemblies that include amyloid fibrils, non-amyloid aggregates, membrane-associated proteins and viral capsids. Such biological samples feature functionally relevant molecular dynamics, which often affect different parts of the sample in different ways. Solid-state NMR experiments' sensitivity to dynamics represents a double-edged sword. On the one hand, it offers a chance to measure dynamics in great detail. On the other hand, certain types of motion lead to signal loss and experimental inefficiencies that at first glance interfere with the application of ssNMR to overly dynamic proteins. Dynamics-based spectral editing (DYSE) ssNMR methods leverage motion-dependent signal losses to simplify spectra and enable the study of sub-structures with particular motional properties.

Protein conformational dynamics studied by 15N and 1H R1ρ relaxation dispersion: Application to wild-type and G53A ubiquitin crystals

Solid-state NMR spectroscopy can provide site-resolved information about protein dynamics over many time scales. Here we combine protein deuteration, fast magic-angle spinning (~45-60kHz) and proton detection to study dynamics of ubiquitin in microcrystals, and in particular a mutant in a region that undergoes microsecond motions in a β-turn region in the wild-type protein. We use ¹⁵N R_1ρ relaxation measurements as a function of the radio-frequency (RF) field strength, i.e. relaxation dispersion, to probe how the G53A mutation alters these dynamics. We report a population-inversion of conformational states: the conformation that in the wild-type protein is populated only sparsely becomes the predominant state. We furthermore explore the potential to use amide-¹H R_1ρ relaxation to obtain insight into dynamics. We show that while quantitative interpretation of ¹H relaxation remains beyond reach under the experimental conditions, due to coherent contributions to decay, one may extract qualitative information about flexibility.

Sine-squared shifted pulses for recoupling interactions in solid-state NMR

Rotational-Echo DOuble-Resonance (REDOR) is a versatile experiment for measuring internuclear distance between two heteronuclear spins in solid-state NMR. At slow to intermediate magic-angle spinning (MAS) frequencies, the measurement of distances between strongly coupled spins is challenging due to rapid dephasing of magnetisation. This problem can be remedied by employing the pulse-shifted version of REDOR known as Shifted-REDOR (S-REDOR) that scales down the recoupled dipolar coupling. In this study, we propose a new variant of the REDOR sequence where the positions of the π pulses are determined by a sine-squared function. This new variant has scaling properties similar to S-REDOR. We use theory, numerical simulations, and experiments to compare the dipolar recoupling efficiencies and the experimental robustness of the three REDOR schemes. The proposed variant has advantages in terms of radiofrequency field requirements at fast MAS frequencies.

Expression, Functional Characterization, and Solid-State NMR Investigation of the G Protein-Coupled GHS Receptor in Bilayer Membranes

The expression, functional reconstitution and first NMR characterization of the human growth hormone secretagogue (GHS) receptor reconstituted into either DMPC or POPC membranes is described. The receptor was expressed in E. coli. refolded, and reconstituted into bilayer membranes. The molecule was characterized by ¹⁵N and ¹³C solid-state NMR spectroscopy in the absence and in the presence of its natural agonist ghrelin or an inverse agonist. Static ¹⁵N NMR spectra of the uniformly labeled receptor are indicative of axially symmetric rotational diffusion of the G protein-coupled receptor in the membrane. In addition, about 25% of the ¹⁵N sites undergo large amplitude motions giving rise to very narrow spectral components. For an initial quantitative assessment of the receptor mobility, ¹H-¹³C dipolar coupling values, which are scaled by molecular motions, were determined quantitatively. From these values, average order parameters, reporting the motional amplitudes of the individual receptor segments can be derived. Average backbone order parameters were determined with values between 0.56 and 0.69, corresponding to average motional amplitudes of 40–50° of these segments. Differences between the receptor dynamics in DMPC or POPC membranes were within experimental error. Furthermore, agonist or inverse agonist binding only insignificantly influenced the average molecular dynamics of the receptor.

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.

Structure of the Dimerization Interface in the Mature HIV-1 Capsid Protein Lattice from Solid State NMR of Tubular Assemblies

The HIV-1 capsid protein (CA) forms the capsid shell that encloses RNA within a mature HIV-1 virion. Previous studies by electron microscopy have shown that the capsid shell is primarily a triangular lattice of CA hexamers, with variable curvature that destroys the ideal symmetry of a planar lattice. The mature CA lattice depends on CA dimerization, which occurs through interactions between helix 9 segments of the C-terminal domain (CTD) of CA. Several high-resolution structures of the CTD-CTD dimerization interface have been reported, based on X-ray crystallography and multidimensional solution nuclear magnetic resonance (NMR), with significant differences in amino acid side chain conformations and helix 9-helix 9 orientations. In a structural model for tubular CA assemblies based on cryogenic electron microscopy (cryoEM) [Zhao et al. Nature, 2013, 497, 643-646], the dimerization interface is substantially disordered. The dimerization interface structure in noncrystalline CA assemblies and the extent to which this interface is structurally ordered within a curved lattice have therefore been unclear. Here we describe solid state NMR measurements on the dimerization interface in tubular CA assemblies, which contain the curved triangular lattice of a mature virion, including quantitative measurements of intermolecular and intramolecular distances using dipolar recoupling techniques, solid state NMR chemical shifts, and long-range side chain-side chain contacts. When combined with restraints on the distance and orientation between helix 9 segments from the cryoEM study, the solid state NMR data lead to a unique high-resolution structure for the dimerization interface in the noncrystalline lattice of CA tubes. These results demonstrate that CA lattice curvature is not dependent on disorder or variability in the dimerization interface. This work also demonstrates the feasibility of local structure determination within large noncrystalline assemblies formed by high-molecular-weight proteins, using modern solid state NMR methods.

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.

Dynamic Nuclear Polarization Enhanced MAS NMR Spectroscopy for Structural Analysis of HIV-1 Protein Assemblies

Mature infectious HIV-1 virions contain conical capsids composed of CA protein, generated by the proteolytic cleavage cascade of the Gag polyprotein, termed maturation. The mechanism of capsid core formation through the maturation process remains poorly understood. We present DNP-enhanced MAS NMR studies of tubular assemblies of CA and Gag CA-SP1 maturation intermediate and report 20-64-fold sensitivity enhancements due to DNP at 14.1 T. These sensitivity enhancements enabled direct observation of spacer peptide 1 (SP1) resonances in CA-SP1 by dipolar-based correlation experiments, unequivocally indicating that the SP1 peptide is unstructured in assembled CA-SP1 at cryogenic temperatures, corroborating our earlier results. Furthermore, the dependence of DNP enhancements and spectral resolution on magnetic field strength (9.4-18.8 T) and temperature (109-180 K) was investigated. Our results suggest that DNP-based measurements could potentially provide residue-specific dynamics information by allowing for the extraction of the temperature dependence of the anisotropic tensorial or relaxation parameters. With DNP, we were able to detect multiple well-resolved isoleucine side-chain conformers; unique intermolecular correlations across two CA molecules; and functionally relevant conformationally disordered states such as the 14-residue SP1 peptide, none of which are visible at ambient temperatures. The detection of isolated conformers and intermolecular correlations can provide crucial constraints for structure determination of these assemblies. Overall, our results establish DNP-based MAS NMR spectroscopy as an excellent tool for the characterization of HIV-1 assemblies.

Investigating protein conformational energy landscapes and atomic resolution dynamics from NMR dipolar couplings: a review

Nuclear magnetic resonance spectroscopy is exquisitely sensitive to protein dynamics. In particular inter-nuclear dipolar couplings, that become measurable in solution when the protein is dissolved in a dilute liquid crystalline solution, report on all conformations sampled up to millisecond timescales. As such they provide the opportunity to describe the Boltzmann distribution present in solution at atomic resolution, and thereby to map the conformational energy landscape in unprecedented detail. The development of analytical methods and approaches based on numerical simulation and their application to numerous biologically important systems is presented.

Accurate measurement of heteronuclear dipolar couplings by phase-alternating R-symmetry (PARS) sequences in magic angle spinning NMR spectroscopy

We report a Phase-Alternating R-Symmetry (PARS) dipolar recoupling scheme for accurate measurement of heteronuclear (1)H-X (X = (13)C, (15)N, (31)P, etc.) dipolar couplings in MAS NMR experiments. It is an improvement of conventional C- and R-symmetry type DIPSHIFT experiments where, in addition to the dipolar interaction, the (1)H CSA interaction persists and thereby introduces considerable errors in the dipolar measurements. In PARS, phase-shifted RN symmetry pulse blocks applied on the (1)H spins combined with π pulses applied on the X spins at the end of each RN block efficiently suppress the effect from (1)H chemical shift anisotropy, while keeping the (1)H-X dipolar couplings intact. Another advantage over conventional DIPSHIFT experiments, which require the signal to be detected in the form of a reduced-intensity Hahn echo, is that the series of π pulses refocuses the X chemical shift and avoids the necessity of echo formation. PARS permits determination of accurate dipolar couplings in a single experiment; it is suitable for a wide range of MAS conditions including both slow and fast MAS frequencies; and it assures dipolar truncation from the remote protons. The performance of PARS is tested on two model systems, [(15)N]-N-acetyl-valine and [U-(13)C,(15)N]-N-formyl-Met-Leu-Phe tripeptide. The application of PARS for site-resolved measurement of accurate (1)H-(15)N dipolar couplings in the context of 3D experiments is presented on U-(13)C,(15)N-enriched dynein light chain protein LC8.

Theoretical study of CP-VC: a simple, robust and accurate MAS NMR method for analysis of dipolar C-H interactions under rotation speeds faster than ca. 60 kHz

We show that Cross-Polarization with Variable Contact-time (CP-VC) allows an accurate determination of C-H dipolar interactions, which permits an easy detailed analysis of bond lengths and local dynamics, e.g. in biomolecules. The method presents a large dipolar scaling factor of 1/√2, leading to a better determination of dipolar interactions, especially for long C-H distances, and it allows the observation of very small local details such as those related either to CH(2) three spin systems, or even to hydrogen bonds. CP-VC is very simple to set up and very robust with respect to most experimental parameters, such as: rf-offsets, chemical-shift anisotropies, imperfect Hartmann-Hahn setting, and rf-inhomogeneity. The only required condition is the use of a sufficiently fast MAS spinning speed of at least ca. 60 kHz.

Ensemble MD simulations restrained via crystallographic data: accurate structure leads to accurate dynamics

Currently, the best existing molecular dynamics (MD) force fields cannot accurately reproduce the global free-energy minimum which realizes the experimental protein structure. As a result, long MD trajectories tend to drift away from the starting coordinates (e.g., crystallographic structures). To address this problem, we have devised a new simulation strategy aimed at protein crystals. An MD simulation of protein crystal is essentially an ensemble simulation involving multiple protein molecules in a crystal unit cell (or a block of unit cells). To ensure that average protein coordinates remain correct during the simulation, we introduced crystallography-based restraints into the MD protocol. Because these restraints are aimed at the ensemble-average structure, they have only minimal impact on conformational dynamics of the individual protein molecules. So long as the average structure remains reasonable, the proteins move in a native-like fashion as dictated by the original force field. To validate this approach, we have used the data from solid-state NMR spectroscopy, which is the orthogonal experimental technique uniquely sensitive to protein local dynamics. The new method has been tested on the well-established model protein, ubiquitin. The ensemble-restrained MD simulations produced lower crystallographic R factors than conventional simulations; they also led to more accurate predictions for crystallographic temperature factors, solid-state chemical shifts, and backbone order parameters. The predictions for (15) N R1 relaxation rates are at least as accurate as those obtained from conventional simulations. Taken together, these results suggest that the presented trajectories may be among the most realistic protein MD simulations ever reported. In this context, the ensemble restraints based on high-resolution crystallographic data can be viewed as protein-specific empirical corrections to the standard force fields.

NMR studies of dynamic biomolecular conformational ensembles

Multidimensional heteronuclear NMR approaches can provide nearly complete sequential signal assignments of isotopically enriched biomolecules. The availability of assignments together with measurements of spin relaxation rates, residual spin interactions, J-couplings and chemical shifts provides information at atomic resolution about internal dynamics on timescales ranging from ps to ms, both in solution and in the solid state. However, due to the complexity of biomolecules, it is not possible to extract a unique atomic-resolution description of biomolecular motions even from extensive NMR data when many conformations are sampled on multiple timescales. For this reason, powerful computational approaches are increasingly applied to large NMR data sets to elucidate conformational ensembles sampled by biomolecules. In the past decade, considerable attention has been directed at an important class of biomolecules that function by binding to a wide variety of target molecules. Questions of current interest are: "Does the free biomolecule sample a conformational ensemble that encompasses the conformations found when it binds to various targets; and if so, on what time scale is the ensemble sampled?" This article reviews recent efforts to answer these questions, with a focus on comparing ensembles obtained for the same biomolecules by different investigators. A detailed comparison of results obtained is provided for three biomolecules: ubiquitin, calmodulin and the HIV-1 trans-activation response RNA.

Site-specific analysis of heteronuclear Overhauser effects in microcrystalline proteins

Relaxation parameters such as longitudinal relaxation are susceptible to artifacts such as spin diffusion, and can be affected by paramagnetic impurities as e.g. oxygen, which make a quantitative interpretation difficult. We present here the site-specific measurement of [(1)H](13)C and [(1)H](15)N heteronuclear rates in an immobilized protein. For methyls, a strong effect is expected due to the three-fold rotation of the methyl group. Quantification of the [(1)H](13)C heteronuclear NOE in combination with (13)C-R 1 can yield a more accurate analysis of side chain motional parameters. The observation of significant [(1)H](15)N heteronuclear NOEs for certain backbone amides, as well as for specific asparagine/glutamine sidechain amides is consistent with MD simulations. The measurement of site-specific heteronuclear NOEs is enabled by the use of highly deuterated microcrystalline protein samples in which spin diffusion is reduced in comparison to protonated samples.

The G-protein-coupled neuropeptide Y receptor type 2 is highly dynamic in lipid membranes as revealed by solid-state NMR spectroscopy

In spite of the recent success in crystallizing several G-protein-coupled receptors (GPCRs), a comprehensive biophysical characterization of these molecules under physiological conditions also requires the study of the molecular dynamics of these proteins. The molecular mobility of the human neuropeptide Y receptor type 2 reconstituted into dimyristoylphosphatidylcholine (DMPC) membranes was investigated by means of solid-state NMR spectroscopy. Static (15) N NMR spectra show that the receptor performs axially symmetric motions in the membrane, and several residues undergo large amplitude fluctuations. This was confirmed by quantitative measurements of the motional (1) H,(13) C order parameter of the CH, CH2 , and CH3 groups. In directly polarized (13) C NMR experiments, these order parameters showed astonishingly low values of SCH =0.55, S CH 2=0.33, and S CH 3=0.17, which corresponds to segmental amplitudes of approximately 50° in the backbone and approximately 50-60° in the side chain. At physiological temperature, (2) H NMR spectra of the deuterated receptor showed a narrow component that is indicative of molecular order parameters of S≤0.3 superimposed with a very broad spectrum that could stem from the transmembrane α-helices. These results suggest that the crystal structures of GPCRs only represent a static snapshot of these highly mobile molecules, which undergo significant structural fluctuations with relatively large amplitudes in a liquid-crystalline membrane at physiological temperature.

Advances in solid-state relaxation methodology for probing site-specific protein dynamics

Dynamics are intimately linked to protein stability and play a crucial role in important biological processes, such as ligand binding, allosteric regulation, protein folding, signaling, and enzymatic catalysis. Solid-state NMR relaxation measurements allow researchers to determine the amplitudes, time scales, and under favorable conditions, directionality of motions at atomic resolution over the entire range of dynamic processes from picoseconds to milliseconds. Because this method allows researchers to examine both the amplitudes and time scales of motions in this range, they can link different tiers of protein motions in protein energy landscapes. As a result, scientists can better understand the relationships between protein motions and functions. Such studies are possible both with the primary targets of solid-state NMR studies, such as amyloid fibrils, membrane proteins, or other heterogeneous systems, and others that researchers typically study by solution NMR and X-ray crystallography. In addition, solid-state NMR, with the absence of tumbling in solution, eliminates the intrinsic size limitation imposed by slow tumbling of large proteins. Thus, this technique allows researchers to characterize interdomain and intermolecular interactions in large complexes at the atomic scale. In this Account, we discuss recent advances in solid-state relaxation methodology for studying widespread site-specific protein dynamics. We focus on applications involving magic angle spinning, one of the primary methods used in high-resolution solid-state NMR. We give an overview of challenges and solutions for measuring (15)N and (13)C spin-lattice relaxation (R1) to characterize fast picosecond-nanosecond motions, spin-lattice in the rotating frame (R1ρ), and other related relaxation rates for characterization of picosecond-millisecond protein motions. In particular, we discuss the problem of separating incoherent effects caused by random motions from coherent effects arising from incomplete averaging of orientation-dependent NMR interactions. We mention a number of quantitative studies of protein dynamics based on solid-state relaxation measurements. Finally, we discuss the potential use of relaxation measurements for extracting the directionality of motions. Using the (15)N and (13)C R1 and R1ρ measurements, we illustrate the backbone and side-chain dynamics in the protein GB1 and comment on this emerging dynamic picture within the context of data from solution NMR measurements and simulations.

Solid-state NMR approaches to internal dynamics of proteins: from picoseconds to microseconds and seconds

Solid-state nuclear magnetic resonance (NMR) spectroscopy has matured to the point that it is possible to determine the structure of proteins in immobilized states, such as within microcrystals or embedded in membranes. Currently, researchers continue to develop and apply NMR techniques that can deliver site-resolved dynamic information toward the goal of understanding protein function at the atomic scale. As a widely-used, natural approach, researchers have mostly measured longitudinal (T1) relaxation times, which, like in solution-state NMR, are sensitive to picosecond and nanosecond motions, and motionally averaged dipolar couplings, which provide an integral amplitude of all motions with a correlation time of up to a few microseconds. While overall Brownian tumbling in solution mostly precludes access to slower internal dynamics, dedicated solid-state NMR approaches are now emerging as powerful new options. In this Account, we give an overview of the classes of solid-state NMR experiments that have expanded the accessible range correlation times from microseconds to many milliseconds. The measurement of relaxation times in the rotating frame, T1ρ, now allows researchers to access the microsecond range. Using our recent theoretical work, researchers can now quantitatively analyze this data to distinguish relaxation due to chemical-shift anisotropy (CSA) from that due to dipole-dipole couplings. Off-resonance irradiation allows researchers to extend the frequency range of such experiments. We have built multidimensional analogues of T2-type or line shape experiments using variants of the dipolar-chemical shift correlation (DIPSHIFT) experiment that are particularly suited to extract intermediate time scale motions in the millisecond range. In addition, we have continuously improved variants of exchange experiments, mostly relying on the recoupling of anisotropic interactions to address ultraslow motions in the ms to s ranges. The NH dipolar coupling offers a useful probe of local dynamics, especially with proton-depleted samples that suppress the adverse effect of strong proton dipolar couplings. We demonstrate how these techniques have provided a concise picture of the internal dynamics in a popular model system, the SH3 domain of α-spectrin. T1-based methods have shown that large-amplitude bond orientation fluctuations in the picosecond range and slower 10 ns low-amplitude motions coexist in these structures. When we include T1ρ data, we observe that many residues undergo low amplitude motions slower than 100 ns. On the millisecond to second scale, mostly localized but potentially cooperative motions occur. Comparing different exchange experiments, we found that terminal NH2 groups in side chains can even undergo a combination of ultraslow large-angle two-site jumps accompanied by small-angle fluctuations that occur 10 times more quickly.

Windowed R-PDLF recoupling: a flexible and reliable tool to characterize molecular dynamics

This work focuses on the improvement of the R-PDLF heteronuclear recoupling scheme, a method that allows quantification of molecular dynamics up to the microsecond timescale in heterogeneous materials. We show how the stability of the sequence towards rf-imperfections, one of the main sources of error of this technique, can be improved by the insertion of windows without irradiation into the basic elements of the symmetry-based recoupling sequence. The impact of this modification on the overall performance of the sequence in terms of scaling factor and homonuclear decoupling efficiency is evaluated. This study indicates the experimental conditions for which precise and reliable measurement of dipolar couplings can be obtained using the popular R18(1)(7) recoupling sequence, as well as alternative symmetry-based R sequences suited for fast MAS conditions. An analytical expression for the recoupled dipolar modulation has been derived that applies to a whole class of sequences with similar recoupling properties as R18(1)(7). This analytical expression provides an efficient and precise way to extract dipolar couplings from the experimental dipolar modulation curves. We hereby provide helpful tools and information for tailoring R-PDLF recoupling schemes to specific sample properties and hardware capabilities. This approach is particularly well suited for the study of materials with strong and heterogeneous molecular dynamics where a precise measurement of dipolar couplings is crucial.

Atomic-Resolution Structural Dynamics in Crystalline Proteins from NMR and Molecular Simulation

Solid-state NMR can provide atomic-resolution information about protein motions occurring on a vast range of time scales under similar conditions to those of X-ray diffraction studies and therefore offers a highly complementary approach to characterizing the dynamic fluctuations occurring in the crystal. We compare experimentally determined dynamic parameters, spin relaxation, chemical shifts, and dipolar couplings, to values calculated from a 200 ns MD simulation of protein GB1 in its crystalline form, providing insight into the nature of structural dynamics occurring within the crystalline lattice. This simulation allows us to test the accuracy of commonly applied procedures for the interpretation of experimental solid-state relaxation data in terms of dynamic modes and time scales. We discover that the potential complexity of relaxation-active motion can lead to significant under- or overestimation of dynamic amplitudes if different components are not taken into consideration.

Site-resolved measurement of microsecond-to-millisecond conformational-exchange processes in proteins by solid-state NMR spectroscopy

We demonstrate that conformational exchange processes in proteins on microsecond-to-millisecond time scales can be detected and quantified by solid-state NMR spectroscopy. We show two independent approaches that measure the effect of conformational exchange on transverse relaxation parameters, namely Carr-Purcell-Meiboom-Gill relaxation-dispersion experiments and measurement of differential multiple-quantum coherence decay. Long coherence lifetimes, as required for these experiments, are achieved by the use of highly deuterated samples and fast magic-angle spinning. The usefulness of the approaches is demonstrated by application to microcrystalline ubiquitin. We detect a conformational exchange process in a region of the protein for which dynamics have also been observed in solution. Interestingly, quantitative analysis of the data reveals that the exchange process is more than 1 order of magnitude slower than in solution, and this points to the impact of the crystalline environment on free energy barriers.

Quantifying conformational dynamics using solid-state R₁ρ experiments

We demonstrate the determination of quantitative rates of molecular reorientation in the solid state with rotating frame (R(1ρ)) relaxation measurements. Reorientation of the carbon chemical shift anisotropy (CSA) tensor was used to probe site-specific conformational exchange in a model system, d(6)-dimethyl sulfone (d(6)-DMS). The CSA as a probe of exchange has the advantage that it can still be utilized when there is no dipolar mechanism (i.e. no protons attached to the site of interest). Other works have presented R(1ρ) measurements as a general indicator of dynamics, but this study extracts quantitative rates of molecular reorientation from the R(1ρ) values. Some challenges of this technique include precise knowledge of sample temperature and determining the R(2)(0) contribution to the observed relaxation rate from interactions other than molecular reorientation, such as residual dipolar couplings or fast timescale dynamics; determination of this term is necessary in order to quantify the exchange rate due to covariance between the 2 terms. Low-temperature experiments measured an R(2)(0) value of 1.8±0.2s(-1) Allowing for an additional relaxation term (R(2)(0)), which was modeled as both temperature-dependent and temperature-independent, rates of molecular reorientation were extracted from field strength-dependent R(1ρ) measurements at four different temperatures and the activation energy was determined from these exchange rates. The activation energies determined were 74.7±4.3kJ/mol and 71.7±2.9kJ/mol for the temperature-independent and temperature-dependent R(2)(0) models respectively, in excellent agreement with literature values. The results of this study suggest important methodological considerations for the application of the method to more complicated systems such as proteins, such as the importance of deuterating samples and the need to make assumptions regarding the R(2)(0) contribution to relaxation.

Ultra-high resolution in MAS solid-state NMR of perdeuterated proteins: implications for structure and dynamics

High resolution proton spectra are obtained in MAS solid-state NMR in case samples are prepared using perdeuterated protein and D(2)O in the recrystallization buffer. Deuteration reduces drastically (1)H, (1)H dipolar interactions and allows to obtain amide proton line widths on the order of 20 Hz. Similarly, high-resolution proton spectra of aliphatic groups can be obtained if specifically labeled precursors for biosynthesis of methyl containing side chains are used, or if limited amounts of H(2)O in the bacterial growth medium is employed. This review summarizes recent spectroscopic developments to access structure and dynamics of biomacromolecules in the solid-state, and shows a number of applications to amyloid fibrils and membrane proteins.

Deuterated peptides and proteins: structure and dynamics studies by MAS solid-state NMR

Perdeuteration and back substitution of exchangeable protons in microcrystalline proteins, in combination with recrystallization from D(2)O-containing buffers, significantly reduce (1)H, (1)H dipolar interactions. This way, amide proton line widths on the order of 20 Hz are obtained. Aliphatic protons are accessible either via specifically protonated precursors or by using low amounts of H(2)O in the bacterial growth medium. The labeling scheme enables characterization of structure and dynamics in the solid-state without dipolar truncation artifacts.

Solid-state NMR spectroscopy of protein complexes

Protein-protein interactions are vital for many biological processes. These interactions often result in the formation of protein assemblies that are large in size, insoluble, and difficult to crystallize, and therefore are challenging to study by structure biology techniques, such as single crystal X-ray diffraction and solution NMR spectroscopy. Solid-state NMR (SSNMR) spectroscopy is emerging as a promising technique for studies of such protein assemblies because it is not limited by molecular size, solubility, or lack of long-range order. In the past several years, we have applied magic angle spinning SSNMR-based methods to study several protein complexes. In this chapter, we discuss the general SSNMR methodologies employed for structural and dynamics analyses of protein complexes with specific examples from our work on thioredoxin reassemblies, HIV-1 capsid protein assemblies, and microtubule-associated protein assemblies. We present protocols for sample preparation and characterization, pulse sequences, SSNMR spectra collection, and data analysis.

Progress in correlation spectroscopy at ultra-fast magic-angle spinning: basic building blocks and complex experiments for the study of protein structure and dynamics

Recent progress in multi-dimensional solid-state NMR correlation spectroscopy at high static magnetic fields and ultra-fast magic-angle spinning is discussed. A focus of the review is on applications to protein resonance assignment and structure determination as well as on the characterization of protein dynamics in the solid state. First, the consequences of ultra-fast spinning on sensitivity and sample heating are considered. Recoupling and decoupling techniques at ultra-fast MAS are then presented, as well as more complex experiments assembled from these basic building blocks. Furthermore, we discuss new avenues in biomolecular solid-state NMR spectroscopy that become feasible in the ultra-fast spinning regime, such as sensitivity enhancement based on paramagnetic doping, and the prospect of direct proton detection.