Accurate determination of order parameters from 1H,15N dipolar couplings in MAS solid-state NMR experiments

5D solid-state NMR spectroscopy for facilitated resonance assignment

1H-detected solid-state NMR spectroscopy has been becoming increasingly popular for the characterization of protein structure, dynamics, and function. Recently, we showed that higher-dimensionality solid-state NMR spectroscopy can aid resonance assignments in large micro-crystalline protein targets to combat ambiguity (Klein et al., Proc. Natl. Acad. Sci. U.S.A. 2022). However, assignments represent both, a time-limiting factor and one of the major practical disadvantages within solid-state NMR studies compared to other structural-biology techniques from a very general perspective. Here, we show that 5D solid-state NMR spectroscopy is not only justified for high-molecular-weight targets but will also be a realistic and practicable method to streamline resonance assignment in small to medium-sized protein targets, which such methodology might not have been expected to be of advantage for. Using a combination of non-uniform sampling and the signal separating algorithm for spectral reconstruction on a deuterated and proton back-exchanged micro-crystalline protein at fast magic-angle spinning, direct amide-to-amide correlations in five dimensions are obtained with competitive sensitivity compatible with common hardware and measurement time commitments. The self-sufficient backbone walks enable efficient assignment with very high confidence and can be combined with higher-dimensionality sidechain-to-backbone correlations from protonated preparations into minimal sets of experiments to be acquired for simultaneous backbone and sidechain assignment. The strategies present themselves as potent alternatives for efficient assignment compared to the traditional assignment approaches in 3D, avoiding user misassignments derived from ambiguity or loss of overview and facilitating automation. This will ease future access to NMR-based characterization for the typical solid-state NMR targets at fast MAS.

Time-domain proton-detected local-field NMR for molecular structure determination in complex lipid membranes

Proton-detected local-field (PDLF) NMR spectroscopy, using magic-angle spinning and dipolar recoupling, is presently the most powerful experimental technique for obtaining atomistic structural information from small molecules undergoing anisotropic motion. Common examples include peptides, drugs, or lipids in model membranes and molecules that form liquid crystals. The measurements on complex systems are however compromised by the larger number of transients required. Retaining sufficient spectral quality in the direct dimension requires that the indirect time-domain modulation becomes too short for yielding dipolar splittings in the frequency domain. In such cases, the dipolar couplings can be obtained by fitting the experimental data; however ideal models often fail to fit PDLF data properly due to effects of radiofrequency field (RF) spatial inhomogeneity. Here, we demonstrate that by accounting for RF spatial inhomogeneity in the modeling of R-symmetry-based PDLF NMR experiments, the fitting accuracy is improved, facilitating the analysis of the experimental data. In comparison to the analysis of dipolar splittings without any fitting procedure, the accurate modeling of PDLF measurements makes possible three important improvements: the use of shorter experiments that enable the investigation of samples with a higher level of complexity, the measurement of C-H bond order parameters with smaller magnitudes | S CH | and of smaller variations of | S CH | caused by perturbations of the system, and the determination of | S CH | values with small differences from distinct sites having the same chemical shift. The increase in fitting accuracy is demonstrated by comparison with 2 H NMR quadrupolar echo experiments on mixtures of deuterated and non-deuterated dimyristoylphosphatidylcholine (DMPC) and with 1-palmitoyl-2-oleoyl-s n -glycero-3-phosphoethanolamine (POPE) membranes. Accurate modeling of PDLF NMR experiments is highly useful for investigating complex membrane systems. This is exemplified by application of the proposed fitting procedure for the characterization of membranes composed of a brain lipid extract with many distinct lipid types.

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

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

Accurate Determination of Motional Amplitudes in Biomolecules by Solid-State NMR

Protein dynamics are an intrinsically important factor when considering a protein's biological function. Understanding these motions is often limited through the use of static structure determination methods, namely, X-ray crystallography and cryo-EM. Molecular simulations have allowed for the prediction of global and local motions of proteins from these static structures. Nevertheless, determining local dynamics at residue-specific resolution through direct measurement remains crucial. Solid-state nuclear magnetic resonance (NMR) is a powerful tool for studying dynamics in rigid or membrane-bound biomolecules without prior structural knowledge with the help of relaxation parameters such as T ₁ and T _1ρ. However, these provide only a combined result of amplitude and correlation times in the nanosecond-millisecond frequency range. Thus, direct and independent determination of the amplitude of motions might considerably improve the accuracy of dynamics studies. In an ideal situation, the use of cross-polarization would be the optimal method for measuring the dipolar couplings between chemically bound heterologous nuclei. This would unambiguously provide the amplitude of motion per residue. In practice, however, the inhomogeneity of the applied radio-frequency fields across the sample leads to significant errors. Here, we present a novel method to eliminate this issue through including the radio-frequency distribution map in the analysis. This allows for direct and accurate measurement of residue-specific amplitudes of motion. Our approach has been applied to the cytoskeletal protein BacA in filamentous form, as well as to the intramembrane protease GlpG in lipid bilayers.

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

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

1H-Detected Biomolecular NMR under Fast Magic-Angle Spinning

Since the first pioneering studies on small deuterated peptides dating more than 20 years ago, 1H detection has evolved into the most efficient approach for investigation of biomolecular structure, dynamics, and interactions by solid-state NMR. The development of faster and faster magic-angle spinning (MAS) rates (up to 150 kHz today) at ultrahigh magnetic fields has triggered a real revolution in the field. This new spinning regime reduces the 1H-1H dipolar couplings, so that a direct detection of 1H signals, for long impossible without proton dilution, has become possible at high resolution. The switch from the traditional MAS NMR approaches with 13C and 15N detection to 1H boosts the signal by more than an order of magnitude, accelerating the site-specific analysis and opening the way to more complex immobilized biological systems of higher molecular weight and available in limited amounts. This paper reviews the concepts underlying this recent leap forward in sensitivity and resolution, presents a detailed description of the experimental aspects of acquisition of multidimensional correlation spectra with fast MAS, and summarizes the most successful strategies for the assignment of the resonances and for the elucidation of protein structure and conformational dynamics. It finally outlines the many examples where 1H-detected MAS NMR has contributed to the detailed characterization of a variety of crystalline and noncrystalline biomolecular targets involved in biological processes ranging from catalysis through drug binding, viral infectivity, amyloid fibril formation, to transport across lipid membranes.

Solid-State NMR: Methods for Biological Solids

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

Unambiguous Side-Chain Assignments for Solid-State NMR Structure Elucidation of Nondeuterated Proteins via a Combined 5D/4D Side-Chain-to-Backbone Experiment

Owing to fast-magic-angle-spinning technology, proton-detected solid-state NMR has been facilitating the analysis of insoluble, crystalline, sedimented, and membrane proteins. However, potential applications have been largely restricted by limited access to side-chain resonances. The recent availability of spinning frequencies exceeding 100 kHz in principle now allows direct probing of all protons without the need for partial deuteration. This potentiates both the number of accessible target proteins and possibilities to exploit side-chain protons as reporters on distances and interactions. Their low dispersion, however, has severely compromised their chemical-shift assignment, which is a prerequisite for their use in downstream applications. Herein, we show that unambiguous correlations are obtained from 5D methodology by which the side-chain resonances are directly connected with the backbone. When further concatenated with simultaneous 4D intra-side-chain correlations, this yields comprehensive assignments in the side chains and hence allows a high density of distance restraints for high-resolution structure calculation from minimal amounts of protein.

Backbone Torsion Angle Determination Using Proton Detected Magic-Angle Spinning Nuclear Magnetic Resonance

Protein torsion angles define the backbone secondary structure of proteins. Magic-angle spinning (MAS) NMR methods using carbon detection have been developed to measure torsion angles by determining the relative orientation between two anisotropic interactions─dipolar coupling or chemical shift anisotropy. Here we report a new proton-detection based method to determine the backbone torsion angle by recoupling NH and CH dipolar couplings within the HCANH pulse sequence, for protonated or partly deuterated samples. We demonstrate the efficiency and precision of the method with microcrystalline chicken α spectrin SH3 protein and the influenza A matrix 2 (M2) membrane protein, using 55 or 90 kHz MAS. For M2, pseudo-4D data detect a turn between transmembrane and amphipathic helices.

Dipolar Order Parameters in Large Systems With Fast Spinning

Order parameters are a useful tool for quantifying amplitudes of molecular motions. Here we measure dipolar order parameters by recoupling heteronuclear dipole-dipole couplings under fast spinning. We apply symmetry based recoupling methods to samples spinning under magic angle at 60 kHz by employing a variable flip angle compound inversion pulse. We validate the methods by measuring site-specific ¹⁵N-¹H order parameters of a microcrystalline protein over a small temperature range and the same protein in a large, precipitated complex with antibody. The measurements of the order parameters in the complex are consistent with the observed protein undergoing overall motion within the assembly.

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.

Selective 1H-14N Distance Measurements by 14N Overtone Solid-State NMR Spectroscopy at Fast MAS

Accurate distance measurements between proton and nitrogen can provide detailed information on the structures and dynamics of various molecules. The combination of broadband phase-modulated (PM) pulse and rotational-echo saturation-pulse double-resonance (RESPDOR) sequence at fast magic-angle spinning (MAS) has enabled the measurement of multiple 1H-14N distances with high accuracy. However, complications may arise when applying this sequence to systems with multiple inequivalent 14N nuclei, especially a single 1H sitting close to multiple 14N atoms. Due to its broadband characteristics, the PM pulse saturates all 14N atoms; hence, the single 1H simultaneously experiences the RESPDOR effect from multiple 1H-14N couplings. Consequently, no reliable H-N distances are obtained. To overcome the problem, selective 14N saturation is desired, but it is difficult because 14N is an integer quadrupolar nucleus. Alternatively, 14N overtone (OT) NMR spectroscopy can be employed owing to its narrow bandwidth for selectivity. Moreover, owing to the sole presence of two energy levels (m = ± 1), the 14N OT spin dynamics behaves similarly to that of spin-1/2. This allows the interchangeability between RESPDOR and rotational-echo double-resonance (REDOR) since their principles are the same except the degree of 14N OT population transfer; saturation for the former whereas inversion for the latter. As the ideal saturation/inversion is impractical due to the slow and orientation-dependent effective nutation of 14N OT, the working condition is usually an intermediate between REDOR and RESPDOR. The degree of 14N OT population transfer can be determined from the results of protons with short distances to 14N and then can be used to obtain long-distance determination of other protons to the same 14N site. Herein, we combine the 14N OT and REDOR/RESPDOR to explore the feasibility of selective 1H-14N distance measurements. Experimental demonstrations on simple biological compounds of L-tyrosine.HCl, N-acetyl-L-alanine, and L-alanyl-L-alanine were performed at 14.1 T and MAS frequency of 62.5 kHz. The former two consist of a single 14N site, whereas the latter consists of two 14N sites. The experimental optimizations and reliable fittings by the universal curves are described. The extracted 1H-14N distances by OT-REDOR are in good agreement with those determined by PM-RESPDOR and diffraction techniques.

Solid-state NMR spectroscopy

Solid-state nuclear magnetic resonance (NMR) spectroscopy is an atomic-level method used to determine the chemical structure, three-dimensional structure, and dynamics of solids and semi-solids. This Primer summarizes the basic principles of NMR as applied to the wide range of solid systems. The fundamental nuclear spin interactions and the effects of magnetic fields and radiofrequency pulses on nuclear spins are the same as in liquid-state NMR. However, because of the anisotropy of the interactions in the solid state, the majority of high-resolution solid-state NMR spectra is measured under magic-angle spinning (MAS), which has profound effects on the types of radiofrequency pulse sequences required to extract structural and dynamical information. We describe the most common MAS NMR experiments and data analysis approaches for investigating biological macromolecules, organic materials, and inorganic solids. Continuing development of sensitivity-enhancement approaches, including 1H-detected fast MAS experiments, dynamic nuclear polarization, and experiments tailored to ultrahigh magnetic fields, is described. We highlight recent applications of solid-state NMR to biological and materials chemistry. The Primer ends with a discussion of current limitations of NMR to study solids, and points to future avenues of development to further enhance the capabilities of this sophisticated spectroscopy for new applications.

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.

Protein Motional Details Revealed by Complementary Structural Biology Techniques

Proteins depend on defined molecular plasticity for their functionality. How to comprehensively capture dynamics correctly is of ubiquitous biological importance. Approaches commonly used to probe protein dynamics include model-free elucidation of site-specific motion by NMR relaxation, molecular dynamics (MD)-based approaches, and capturing the substates within a dynamic ensemble by recent eNOE-based multiple-structure approaches. Even though MD is sometimes combined with ensemble-averaged NMR restraints, these approaches have largely been developed and used individually. Owing to the different underlying concepts and practical requirements, it has remained unclear how they compare, and how they cross-validate and complement each other. Here, we extract and compare the differential information contents of MD simulations, NMR relaxation measurements, and eNOE-based multi-state structures for the SH3 domain of chicken α-spectrin. The data show that a validated, consistent, and detailed picture is feasible both for timescales and actual conformational states sampled in the dynamic ensemble. This includes the biologically important side-chain plasticity, for which experimentally cross-validated assessment is a significant challenge.

Accurate 1H-14N distance measurements by phase-modulated RESPDOR at ultra-fast MAS

The combination of a phase-modulated (PM) saturation pulse and symmetry-based dipolar recoupling into a rotational-echo saturation-pulse double-resonance (RESPDOR) sequence has been employed to measure ¹H-¹⁴N distances. Such a measurement is challenging owing to the quadrupolar interaction of ¹⁴N nucleus and the intense ¹H-¹H homonuclear dipolar interactions. Thanks to the recent advances in probe technology, the homonuclear dipolar interaction can be sufficiently suppressed at a fast MAS frequency (ν_R ≥ 60 kHz). PM pulse is robust to large variations of parameters on quadrupolar spins, but it has not been demonstrated under very fast MAS conditions. On the other hand, the RESPDOR sequence is applicable to such condition when it employs symmetry-based pulses during the recoupling period, but a prior knowledge on the system is required. In this article, we demonstrated the PM-RESPDOR combination for providing accurate ¹H-¹⁴N distances at a very fast MAS frequency of 70 kHz on two samples, namely L-tyrosine⋅HCl and N-acetyl-L-alanine. This sequence, supported by simulations and experiments, has shown its feasibility at ν_R = 70 kHz as well as the robustness to the ¹⁴N quadrupolar interaction. It is applicable to a wide range of ¹H-¹⁴N dipolar coupling constants when a radio frequency field on the ¹⁴N channel is approximately 80 kHz or more, while the PM pulse length lasts 10 rotor periods. For the first time, multiple ¹H-¹⁴N heteronuclear dipolar couplings, thus multiple quantitative distances, are simultaneously and reliably extracted by fitting the experimental fraction curves with the analytical expression. The size of the ¹H-¹⁴N dipolar interaction is solely used as a fitting parameter. These determined distances are in excellent agreement with those derived from diffraction techniques.

Determination of methyl order parameters using solid state NMR under off magic angle spinning

Quantification of dipolar couplings in biological solids is important for the understanding of dynamic processes. Under Magic Angle Spinning (MAS), order parameters are normally obtained by recoupling of anisotropic interactions involving the application of radio frequency pulses. We have recently shown that amide backbone order parameters can be estimated accurately in a spin-echo experiment in case the rotor spinning angle is slightly mis-calibrated. In this work, we apply this method to determine methyl order parameters in a deuterated sample of the SH3 domain of chicken α-spectrin in which the methyl containing side chains valine and leucine are selectively protonated.

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

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

Accurate Determination of 1 H-15 N Dipolar Couplings Using Inaccurate Settings of the Magic Angle in Solid-State NMR Spectroscopy

Magic-angle spinning (MAS) is an essential ingredient in a wide variety of solid-state NMR experiments. The standard procedures to adjust the rotor angle are not highly accurate, resulting in a slight misadjustment of the rotor from the magic angle ( θ R L = tan - 1 2 ) on the order of a few millidegrees. This small missetting has no significant impact on the overall spectral resolution, but is sufficient to reintroduce anisotropic interactions. Shown here is that site-specific ¹ H-¹⁵ N dipolar couplings can be accurately measured in a heavily deuterated protein. This method can be applied at arbitrarily high MAS frequencies, since neither rotor synchronization nor particularly high radiofrequency field strengths are required. The off-MAS method allows the quantification of order parameters for very dynamic residues, which often escape an analysis using existing methods.

Polarization inversion applied to proton MAS-NMR spectroscopy - Methylene and methine free proton NMR spectra

Polarization-inversion (PI) has been applied to proton magic angle spinning (MAS) NMR spectra recorded under fast MAS conditions. The combination of cross-polarization (CP) from carbon to proton and subsequent polarization-inversion produces strong oscillatory behavior in the proton signal intensities at high MAS speeds of 60 kHz. It is observed that by a suitable choice of the polarization-inversion time, a proton spectrum free of methylene and methine protons can be obtained. Such a spectrum, on the one hand, increases the resolution of the crowded proton spectrum and on the other hand provides exclusively chemical shifts of protons such as NH, OH and SH which might otherwise overlap with carbon attached protons. The oscillations observed during PI can also be used to estimate the dipolar coupling between proton and carbon by Fourier transformation of data acquired at equally incremented time periods. The utility of the above ideas has been demonstrated on a set of molecules with both ¹³C labeled and ¹³C in natural abundance.

Simple and Robust Study of Backbone Dynamics of Crystalline Proteins Employing 1H-15N Dipolar Coupling Dispersion

We report a new solid-state multidimensional NMR approach based on the cross-polarization with variable-contact pulse sequence [ Paluch , P. ; Pawlak , T. ; Amoureux , J.-P. ; Potrzebowski , M. J. J. Magn. Reson. 233 , 2013 , 56 ], with ¹H inverse detection and very fast magic angle spinning (ν_R = 60 kHz), dedicated to the measurement of local molecular motions of ¹H-¹⁵N vectors. The introduced three-dimensional experiments, ¹H-¹⁵N-¹H and hCA(N)H, are particularly useful for the study of molecular dynamics of proteins and other complex structures. The applicability and power of this methodology have been revealed by employing as a model sample the GB-1 small protein doped with Na₂CuEDTA. The results clearly prove that the dispersion of ¹H-¹⁵N dipolar coupling constants well correlates with higher order structure of the protein. Our approach complements the conventional studies and offers a fast and reasonably simple method.

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

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

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.

Solid-state NMR spectroscopic trends for supramolecular assemblies and protein aggregates

Solid-state NMR is able to generate structural data on sample preparations that are explicitly non-crystalline. In particular, for amyloid fibril samples, which can comprise significant degrees of sample disorder, solid-state NMR has been used very successfully. But also solid-state NMR studies of other supramolecular assemblies that have resisted assessment by more standard methods are being performed with increasing ease and biological impact, many of which are briefly reviewed here. New technical trends with respect to structure calculation, protein dynamics and smaller sample amounts have reshaped the field of solid-state NMR recently. In particular, proton-detected approaches based on fast Magic-Angle Spinning (MAS) were demonstrated for crystalline systems initially. Currently, such approaches are being expanded to the above-mentioned non-crystalline targets, the characterization of which can now be pursued with sample amounts on the order of a milligram. In this Trends article, I am giving a brief overview about achievements of the last years as well as the directions that the field has been heading into and delineate some satisfactory perspectives for solid-state NMR's future striving.

Solid-State NMR Provides Evidence for Small-Amplitude Slow Domain Motions in a Multispanning Transmembrane α-Helical Protein

Proteins are dynamic entities and populate ensembles of conformations. Transitions between states within a conformational ensemble occur over a broad spectrum of amplitude and time scales, and are often related to biological function. Whereas solid-state NMR (SSNMR) spectroscopy has recently been used to characterize conformational ensembles of proteins in the microcrystalline states, its applications to membrane proteins remain limited. Here we use SSNMR to study conformational dynamics of a seven-helical transmembrane (TM) protein, Anabaena Sensory Rhodopsin (ASR) reconstituted in lipids. We report on site-specific measurements of the 15N longitudinal R1 and rotating frame R1ρ relaxation rates at two fields of 600 and 800 MHz and at two temperatures of 7 and 30 °C. Quantitative analysis of the R1 and R1ρ values and of their field and temperature dependencies provides evidence of motions on at least two time scales. We modeled these motions as fast local motions and slower collective motions of TM helices and of structured loops, and used the simple model-free and extended model-free analyses to fit the data and estimate the amplitudes, time scales and activation energies. Faster picosecond (tens to hundreds of picoseconds) local motions occur throughout the protein and are dominant in the middle portions of the TM helices. In contrast, the amplitudes of the slower collective motions occurring on the nanosecond (tens to hundreds of nanoseconds) time scales, are smaller in the central parts of helices, but increase toward their cytoplasmic sides as well as in the interhelical loops. ASR interacts with a soluble transducer protein on its cytoplasmic surface, and its binding affinity is modulated by light. The larger amplitude of motions on the cytoplasmic side of the TM helices correlates with the ability of ASR to undergo large conformational changes in the process of binding/unbinding the transducer.

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.

Non-equilibrium hydrogen exchange for determination of H-bond strength and water accessibility in solid proteins

We demonstrate measurement of non-equilibrium backbone amide hydrogen-deuterium exchange rates (HDX) for solid proteins. The target of this study are the slowly exchanging residues in solid samples, which are associated with stable secondary-structural elements of proteins. These hydrogen exchange processes escape methods measuring equilibrium exchange rates of faster processes. The method was applied to a micro-crystalline preparation of the SH3 domain of chicken α-spectrin. Therefore, from a 100% back-exchanged micro-crystalline protein preparation, the supernatant buffer was exchanged by a partially deuterated buffer to reach a final protonation level of approximately 20% before packing the sample in a 1.3 mm rotor. Tracking of the HN peak intensities for 2 weeks reports on site-specific hydrogen bond strength and also likely reflects water accessibility in a qualitative manner. H/D exchange can be directly determined for hydrogen-bonded amides using ¹H detection under fast magic angle spinning. This approach complements existing methods and provides the means to elucidate interesting site-specific characteristics for protein functionality in the solid state.

Access to aliphatic protons as reporters in non-deuterated proteins by solid-state NMR

Interactions within proteins, with their surrounding, and with other molecules are mediated mostly by hydrogen atoms. In fully protonated, inhomogeneous, or larger proteins, however, aliphatic proton shifts tend to show little dispersion despite fast Magic-Angle Spinning. 3D correlations dispersing aliphatic proton shifts by their better resolved amide N/H shifts can alleviate this problem. Using inverse second-order cross-polarization (iSOCP), we here introduce dedicated and improved means to sensitively link site-specific chemical shift information from aliphatic protons with a backbone amide resolution. Thus, even in cases where protein deuteration is impossible, this approach may enable access to various aspects of protein functions that are reported on by protons.

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

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

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

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

Accurate NMR determination of C-H or N-H distances for unlabeled molecules

Cross-Polarization with Variable Contact-time (CP-VC) is very efficient at ultra-fast MAS (νR ≥ 60 kHz) to measure accurately the dipolar interactions corresponding to C-H or N-H short distances, which are very useful for resonance assignment and for analysis of dynamics. Here, we demonstrate the CP-VC experiment with (1)H detection. In the case of C-H distances, we compare the CP-VC signals with direct ((13)C) and indirect ((1)H) detection and find that the latter allows a S/N gain of ca. 2.5, which means a gain of ca. 6 in experimental time. The main powerful characteristics of CP-VC methods are related to the ultra-fast spinning speed and to the fact that most of the time only the value of the dipolar peak separation has to be used to obtain the information. As a result, CP-VC methods are: (i) easy to set up and to use, and robust with respect to (ii) rf-inhomogeneity thus allowing the use of full rotor samples, (iii) rf mismatch, and (iv) offsets and chemical shift anisotropies. It must be noted that the CP-VC 2D method with indirect (1)H detection requires the proton resolution and is thus mainly applicable to small or perdeuterated molecules. We also show that an analysis of the dynamics can even be performed, with a reasonable experimental time, on unlabeled samples with (13)C or even (15)N natural abundance.

Backbone assignment for minimal protein amounts of low structural homogeneity in the absence of deuteration

A set of higher-dimensionality ¹H-detected experiments is introduced for assigning non-deuterated proteins with low sample homogeneity at fast MAS.

Asynchronous through-bond homonuclear isotropic mixing: application to carbon-carbon transfer in perdeuterated proteins under MAS

Multiple-bond carbon-carbon homonuclear mixing is a hurdle in extensively deuterated proteins and under fast MAS due to the absence of an effective proton dipolar-coupling network. Such conditions are now commonly employed in solid-state NMR spectroscopy. Here, we introduce an isotropic homonuclear (13)C-(13)C through-bond mixing sequence, MOCCA, for the solid state. Even though applied under MAS, this scheme performs without rotor synchronization and thus does not pose the usual hurdles in terms of power dissipation for fast spinning. We compare its performance with existing homonuclear (13)C-(13)C mixing schemes using a perdeuterated and partially proton-backexchanged protein. Based on the analysis of side chain carbon-carbon correlations, we show that particularly MOCCA with standard 180-degree pulses and delays leading to non-rotor-synchronized spacing performs exceptionally well. This method provides high magnetization transfer efficiency for multiple-bond transfer in the aliphatic region compared with other tested mixing sequences. In addition, we show that this sequence can also be tailor-made for recoupling within a selected spectral region using band-selective pulses.

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.

(15)N CSA tensors and (15)N-(1)H dipolar couplings of protein hydrophobic core residues investigated by static solid-state NMR

In this work, we assess the usefulness of static (15)N NMR techniques for the determination of the (15)N chemical shift anisotropy (CSA) tensor parameters and (15)N-(1)H dipolar splittings in powder protein samples. By using five single labeled samples of the villin headpiece subdomain protein in a hydrated lyophilized powder state, we determine the backbone (15)N CSA tensors at two temperatures, 22 and -35 °C, in order to get a snapshot of the variability across the residues and as a function of temperature. All sites probed belonged to the hydrophobic core and most of them were part of α-helical regions. The values of the anisotropy (which include the effect of the dynamics) varied between 130 and 156 ppm at 22 °C, while the values of the asymmetry were in the 0.32-0.082 range. The Leu-75 and Leu-61 backbone sites exhibited high mobility based on the values of their temperature-dependent anisotropy parameters. Under the assumption that most differences stem from dynamics, we obtained the values of the motional order parameters for the (15)N backbone sites. While a simple one-dimensional line shape experiment was used for the determination of the (15)N CSA parameters, a more advanced approach based on the "magic sandwich" SAMMY pulse sequence (Nevzorov and Opella, 2003) was employed for the determination of the (15)N-(1)H dipolar patterns, which yielded estimates of the dipolar couplings. Accordingly, the motional order parameters for the dipolar interaction were obtained. It was found that the order parameters from the CSA and dipolar measurements are highly correlated, validating that the variability between the residues is governed by the differences in dynamics. The values of the parameters obtained in this work can serve as reference values for developing more advanced magic-angle spinning recoupling techniques for multiple labeled samples.

Sequential backbone assignment based on dipolar amide-to-amide correlation experiments

Proton detection in solid-state NMR has seen a tremendous increase in popularity in the last years. New experimental techniques allow to exploit protons as an additional source of information on structure, dynamics, and protein interactions with their surroundings. In addition, sensitivity is mostly improved and ambiguity in assignment experiments reduced. We show here that, in the solid state, sequential amide-to-amide correlations turn out to be an excellent, complementary way to exploit amide shifts for unambiguous backbone assignment. For a general assessment, we compare amide-to-amide experiments with the more common (13)C-shift-based methods. Exploiting efficient CP magnetization transfers rather than less efficient INEPT periods, our results suggest that the approach is very feasible for solid-state NMR.

Magic angle spinning NMR of viruses

Viruses, relatively simple pathogens, are able to replicate in many living organisms and to adapt to various environments. Conventional atomic-resolution structural biology techniques, X-ray crystallography and solution NMR spectroscopy provided abundant information on the structures of individual proteins and nucleic acids comprising viruses; however, viral assemblies are not amenable to analysis by these techniques because of their large size, insolubility, and inherent lack of long-range order. In this article, we review the recent advances in magic angle spinning NMR spectroscopy that enabled atomic-resolution analysis of structure and dynamics of large viral systems and give examples of several exciting case studies.

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.

Atomic model of a cell-wall cross-linking enzyme in complex with an intact bacterial peptidoglycan

The maintenance of bacterial cell shape and integrity is largely attributed to peptidoglycan, a highly cross-linked biopolymer. The transpeptidases that perform this cross-linking are important targets for antibiotics. Despite this biomedical importance, to date no structure of a protein in complex with an intact bacterial peptidoglycan has been resolved, primarily due to the large size and flexibility of peptidoglycan sacculi. Here we use solid-state NMR spectroscopy to derive for the first time an atomic model of an l,d-transpeptidase from Bacillus subtilis bound to its natural substrate, the intact B. subtilis peptidoglycan. Importantly, the model obtained from protein chemical shift perturbation data shows that both domains-the catalytic domain as well as the proposed peptidoglycan recognition domain-are important for the interaction and reveals a novel binding motif that involves residues outside of the classical enzymatic pocket. Experiments on mutants and truncated protein constructs independently confirm the binding site and the implication of both domains. Through measurements of dipolar-coupling derived order parameters of bond motion we show that protein binding reduces the flexibility of peptidoglycan. This first report of an atomic model of a protein-peptidoglycan complex paves the way for the design of new antibiotic drugs targeting l,d-transpeptidases. The strategy developed here can be extended to the study of a large variety of enzymes involved in peptidoglycan morphogenesis.

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.

Proton-detected MAS NMR experiments based on dipolar transfers for backbone assignment of highly deuterated proteins

Proton-detected solid-state NMR was applied to a highly deuterated insoluble, non-crystalline biological assembly, the Salmonella typhimurium type iii secretion system (T3SS) needle. Spectra of very high resolution and sensitivity were obtained at a low protonation level of 10-20% at exchangeable amide positions. We developed efficient experimental protocols for resonance assignment tailored for this system and the employed experimental conditions. Using exclusively dipolar-based interspin magnetization transfers, we recorded two sets of 3D spectra allowing for an almost complete backbone resonance assignment of the needle subunit PrgI. The additional information provided by the well-resolved proton dimension revealed the presence of two sets of resonances in the N-terminal helix of PrgI, while in previous studies employing (13)C detection only a single set of resonances was observed.

Dynamics in the solid-state: perspectives for the investigation of amyloid aggregates, membrane proteins and soluble protein complexes

Aggregates formed by amyloidogenic peptides and proteins and reconstituted membrane protein preparations differ significantly in terms of the spectral quality that they display in solid-state NMR experiments. Structural heterogeneity and dynamics can both in principle account for that observation. This perspectives article aims to point out challenges and limitations, but also potential opportunities in the investigation of these systems.

Restricted diffusion of methyl groups in proteins revealed by deuteron NMR: manifestation of intra-well dynamics

The three-site hops of methyl groups are usually used as an approximation of the mechanistic description of motions responsible for the longitudinal NMR relaxation. Distinguishing between three-site hops and a more realistic mechanism of diffusion in a potential requires extended experimental and computational analysis. In order to achieve this goal, in this work the restricted diffusion is decomposed into two independent modes, namely, the jumps between potential wells and intra-well fluctuations, assuming time scale separation between these modes. This approach allows us to explain the rise in the theoretical value of T1 minimum for the restricted diffusion mechanism compared with the three-site hops mechanism via rescaling the three-site hops correlation function by the order parameter of intra-well motions. The main result of the paper is that, in general, intra-well dynamics can be visible in NMR even in the limit of large barrier heights in contrast to the common view that this limit converges to the three-site hops mechanism. Based on a previously collected detailed set of deuteron NMR relaxation and spectral data in the villin headpiece subdomain protein over a wide temperature range of 300-31 K, we are then able to conclude that the mechanism of diffusion in the threefold potential is likely to be the main source of the dynamics in this system.