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

Internal protein dynamics on ps to μs timescales as studied by multi-frequency (15)N solid-state NMR relaxation

A comprehensive analysis of the dynamics of the SH3 domain of chicken alpha-spectrin is presented, based upon (15)N T1 and on- and off-resonance T1ρ relaxation times obtained on deuterated samples with a partial back-exchange of labile protons under a variety of the experimental conditions, taking explicitly into account the dipolar order parameters calculated from (15)N-(1)H dipole-dipole couplings. It is demonstrated that such a multi-frequency approach enables access to motional correlation times spanning about 6 orders of magnitude. We asses the validity of different motional models based upon orientation autocorrelation functions with a different number of motional components. We find that for many residues a "two components" model is not sufficient for a good description of the data and more complicated fitting models must be considered. We show that slow motions with correlation times on the order of 1-10 μs can be determined reliably in spite of rather low apparent amplitudes (below 1 %), and demonstrate that the distribution of the protein backbone mobility along the time scale axis is pronouncedly non-uniform and non-monotonic: two domains of fast (τ < 10(-10) s) and intermediate (10(-9) s < τ < 10(-7) s) motions are separated by a gap of one order of magnitude in time with almost no motions. For slower motions (τ > 10(-6) s) we observe a sharp ~1 order of magnitude decrease of the apparent motional amplitudes. Such a distribution obviously reflects different nature of backbone motions on different time scales, where the slow end may be attributed to weakly populated "excited states." Surprisingly, our data reveal no clearly evident correlations between secondary structure of the protein and motional parameters. We also could not notice any unambiguous correlations between motions in different time scales along the protein backbone emphasizing the importance of the inter-residue interactions and the cooperative nature of protein dynamics.

Amplitudes and time scales of picosecond-to-microsecond motion in proteins studied by solid-state NMR: a critical evaluation of experimental approaches and application to crystalline ubiquitin

Solid-state NMR provides insight into protein motion over time scales ranging from picoseconds to seconds. While in solution state the methodology to measure protein dynamics is well established, there is currently no such consensus protocol for measuring dynamics in solids. In this article, we perform a detailed investigation of measurement protocols for fast motions, i.e. motions ranging from picoseconds to a few microseconds, which is the range covered by dipolar coupling and relaxation experiments. We perform a detailed theoretical investigation how dipolar couplings and relaxation data can provide information about amplitudes and time scales of local motion. We show that the measurement of dipolar couplings is crucial for obtaining accurate motional parameters, while systematic errors are found when only relaxation data are used. Based on this realization, we investigate how the REDOR experiment can provide such data in a very accurate manner. We identify that with accurate rf calibration, and explicit consideration of rf field inhomogeneities, one can obtain highly accurate absolute order parameters. We then perform joint model-free analyses of 6 relaxation data sets and dipolar couplings, based on previously existing, as well as new data sets on microcrystalline ubiquitin. We show that nanosecond motion can be detected primarily in loop regions, and compare solid-state data to solution-state relaxation and RDC analyses. The protocols investigated here will serve as a useful basis towards the establishment of a routine protocol for the characterization of ps-μs motions in proteins by solid-state NMR.

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.

Proton-detected solid-state NMR spectroscopy at aliphatic sites: application to crystalline systems

When applied to biomolecules, solid-state NMR suffers from low sensitivity and resolution. The major obstacle to applying proton detection in the solid state is the proton dipolar network, and deuteration can help avoid this problem. In the past, researchers had primarily focused on the investigation of exchangeable protons in these systems. In this Account, we review NMR spectroscopic strategies that allow researchers to observe aliphatic non-exchangeable proton resonances in proteins with high sensitivity and resolution. Our labeling scheme is based on u-[(2)H,(13)C]-glucose and 5-25% H2O (95-75% D2O) in the M9 bacterial growth medium, known as RAP (reduced adjoining protonation). We highlight spectroscopic approaches for obtaining resonance assignments, a prerequisite for any study of structure and dynamics of a protein by NMR spectroscopy. Because of the dilution of the proton spin system in the solid state, solution-state NMR (1)HCC(1)H type strategies cannot easily be transferred to these experiments. Instead, we needed to pursue ((1)H)CC(1)H, CC(1)H, (1)HCC or ((2)H)CC(1)H type experiments. In protonated samples, we obtained distance restraints for structure calculations from samples grown in bacteria in media containing [1,3]-(13)C-glycerol, [2]-(13)C-glycerol, or selectively enriched glucose to dilute the (13)C spin system. In RAP-labeled samples, we obtained a similar dilution effect by randomly introducing protons into an otherwise deuterated matrix. This isotopic labeling scheme allows us to measure the long-range contacts among aliphatic protons, which can then serve as restraints for the three-dimensional structure calculation of a protein. Due to the high gyromagnetic ratio of protons, longer range contacts are more easily accessible for these nuclei than for carbon nuclei in homologous experiments. Finally, the RAP labeling scheme allows access to dynamic parameters, such as longitudinal relaxation times T1, and order parameters S(2) for backbone and side chain carbon resonances. We expect that these measurements will open up new opportunities to obtain a more detailed description of protein backbone and side chain dynamics.

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.

Avoiding bias effects in NMR experiments for heteronuclear dipole-dipole coupling determinations: principles and application to organic semiconductor materials

Carbon-proton dipole-dipole couplings between bonded atoms represent a popular probe of molecular dynamics in soft materials or biomolecules. Their site-resolved determination, for example, by using the popular DIPSHIFT experiment, can be challenged by spectral overlap with nonbonded carbon atoms. The problem can be solved by using very short cross-polarization (CP) contact times, however, the measured modulation curves then deviate strongly from the theoretically predicted shape, which is caused by the dependence of the CP efficiency on the orientation of the CH vector, leading to an anisotropic magnetization distribution even for isotropic samples. Herein, we present a detailed demonstration and explanation of this problem, as well as providing a solution. We combine DIPSHIFT experiments with the rotor-directed exchange of orientations (RODEO) method, and modifications of it, to redistribute the magnetization and obtain undistorted modulation curves. Our strategy is general in that it can also be applied to other types of experiments for heteronuclear dipole-dipole coupling determinations that rely on dipolar polarization transfer. It is demonstrated with perylene-bisimide-based organic semiconductor materials, as an example, in which measurements of dynamic order parameters reveal correlations of the molecular dynamics with the phase structure and functional properties.

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.

Very large residual dipolar couplings from deuterated ubiquitin

Main-chain (1)H(N)-(15)N residual dipolar couplings (RDCs) ranging from approximately -200 to 200 Hz have been measured for ubiquitin under strong alignment conditions in Pf1 phage. This represents a ten-fold increase in the degree of alignment over the typical weakly aligned samples. The measurements are made possible by extensive proton-dilution of the sample, achieved by deuteration of the protein with partial back-substitution of labile protons from 25 % H(2)O / 75 % D(2)O buffer. The spectral quality is further improved by application of deuterium decoupling. Since standard experiments using fixed-delay INEPT elements cannot accommodate a broad range of couplings, the measurements were conducted using J-resolved and J-modulated versions of the HSQC and TROSY sequences. Due to unusually large variations in dipolar couplings, the trosy (sharp) and anti-trosy (broad) signals are often found to be interchanged in the TROSY spectra. To distinguish between the two, we have relied on their respective (15)N linewidths. This strategy ultimately allowed us to determine the signs of RDCs. The fitting of the measured RDC values to the crystallographic coordinates of ubiquitin yields the quality factor Q = 0.16, which confirms the perturbation-free character of the Pf1 alignment. Our results demonstrate that RDC data can be successfully acquired not only in dilute liquid crystals, but also in more concentrated ones. As a general rule, the increase in liquid crystal concentration improves the stability of alignment media and makes them more tolerant to variations in sample conditions. The technical ability to measure RDCs under moderately strong alignment conditions may open the door for development of alternative alignment media, including new types of media that mimic biologically relevant systems.

The relation of the X-ray B-factor to protein dynamics: insights from recent dynamic solid-state NMR data

In addressing the potential use of B-factors derived from X-ray scattering data of proteins for the understanding the (functional) dynamics of proteins, we present a comparison of B-factors of five different proteins (SH3 domain, Crh, GB1, ubiquitin and thioredoxin) with data from recent solid-state nuclear magnetic resonance experiments reflecting true (rotational) dynamics on well-defined timescales. Apart from trivial correlations involving mobile loop regions and chain termini, we find no significant correlation of B-factors with the dynamic data on any of the investigated timescales, concluding that there is no unique and general correlation of B-factors with the internal reorientational dynamics of proteins.

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.

Side-chain to backbone correlations from solid-state NMR of perdeuterated proteins through combined excitation and long-range magnetization transfers

Proteins with excessive deuteration give access to proton detected solid-state NMR spectra of extraordinary resolution and sensitivity. The high spectral quality achieved after partial proton back-exchange has been shown to start a new era for backbone assignment, protein structure elucidation, characterization of protein dynamics, and access to protein parts undergoing motion. The large absence of protons at non-exchangeable sites, however, poses a serious hurdle for characterization of side chains, which play an important role especially for structural understanding of the protein core and the investigation of protein-protein and protein-ligand interactions, e.g. This has caused the perdeuteration approach to almost exclusively be amenable to backbone characterization only. In this work it is shown that a combination of isotropic (13)C mixing with long-range (1)H/(13)C magnetization transfers can be used effectively to also access complete sets of side-chain chemical shifts in perdeuterated proteins and correlate these with the protein backbone with high unambiguity and resolution. COmbined POlarization from long-Range transfers And Direct Excitation (COPORADE) allows this strategy to yield complete sets of aliphatic amino acid resonances with reasonable sensitivity.

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.

Dynamics of biomolecules from picoseconds to seconds at atomic resolution

Although biomolecular dynamics has been investigated using NMR for at least 40 years, only in the past 20 years have internal motions been characterized at atomic resolution throughout proteins and nucleic acids. This development was made possible by multidimensional heteronuclear NMR approaches that provide near complete sequential signal assignments of uniformly labeled biomolecules. Recent methodological advances have enabled characterization of internal dynamics on timescales ranging from picoseconds to seconds, both in solution and in the solid state. The size, complexity and functional significance of biomolecules investigated by NMR continue to grow, as do the insights that have been obtained about function. In this article I review a number of recent advances that have made such studies possible, and provide a few examples of where NMR either by itself or in combination with other approaches has paved the way to a better understanding of the complex relationship between dynamics and biomolecular function. Finally, I discuss prospects for further advances in this field.

Accurate measurement of one-bond H-X heteronuclear dipolar couplings in MAS solid-state NMR

The accurate experimental determination of dipolar-coupling constants for one-bond heteronuclear dipolar couplings in solids is a key for the quantification of the amplitudes of motional processes. Averaging of the dipolar coupling reports on motions on time scales up to the inverse of the coupling constant, in our case tens of microseconds. Combining dipolar-coupling derived order parameters that characterize the amplitudes of the motion with relaxation data leads to a more precise characterization of the dynamical parameters and helps to disentangle the amplitudes and the time scales of the motional processes, which impact relaxation rates in a highly correlated way. Here. we describe and characterize an improved experimental protocol--based on REDOR--to measure these couplings in perdeuterated proteins with a reduced sensitivity to experimental missettings. Because such effects are presently the dominant source of systematic errors in experimental dipolar-coupling measurements, these compensated experiments should help to significantly improve the precision of such data. A detailed comparison with other commonly used pulse sequences (T-MREV, phase-inverted CP, R18(2)(5), and R18(1)(7)) is provided.

Comparison of solid-state dipolar couplings and solution relaxation data provides insight into protein backbone dynamics

Analyses of solution (15)N relaxation data and solid-state (1)H(N)-(15)N dipolar couplings from a small globular protein, alpha-spectrin SH3 domain, produce a surprisingly similar pattern of order parameters. This result suggests that there is little or no ns-mus dynamics throughout most of the sequence and, in particular, in the structured portion of the backbone. At the same time, evidence of ns-mus motions is found in the flexible loops and termini. These findings, corroborated by the MD simulations of alpha-spectrin SH3 in a hydrated crystalline environment and in solution, are consistent with the picture of protein dynamics that has recently emerged from the solution studies employing residual dipolar couplings.

Conformational flexibility of Y145Stop human prion protein amyloid fibrils probed by solid-state nuclear magnetic resonance spectroscopy

Amyloid aggregates of a C-truncated Y145Stop mutant of human prion protein, huPrP23-144, associated with a heritable amyloid angiopathy, have previously been shown to contain a compact, relatively rigid, and beta-sheet-rich approximately 30-residue amyloid core near the C-terminus under physiologically relevant conditions. In contrast, the remaining huPrP23-144 residues display considerable conformational dynamics, as evidenced by the absence of corresponding signals in cross-polarization (CP)-based solid-state NMR (SSNMR) spectra under ambient conditions and their emergence in analogous spectra recorded at low temperature on frozen fibril samples. Here, we present the direct observation of residues comprising the flexible N-terminal domain of huPrP23-144 amyloid by using 2D J-coupling-based magic-angle spinning (MAS) SSNMR techniques. Chemical shifts for these residues indicate that the N-terminal domain is effectively an ensemble of protein chains with random-coil-like conformations. Interestingly, a detailed analysis of signal intensities in CP-based 3D SSNMR spectra suggests that non-negligible molecular motions may also be occurring on the NMR time scale within the relatively rigid core of huPrP23-144 amyloid. To further investigate this hypothesis, quantitative measurements of backbone dipolar order parameters and transverse spin relaxation rates were performed for the core residues. The observed order parameters indicate that, on the submicrosecond time scale, these residues are effectively rigid and experience only highly restricted and relatively uniform motions similar to those characteristic for well-structured regions of microcrystalline proteins. On the other hand, significant variations in magnitude of transverse spin relaxation rates were noted for residues present at different locations within the core region and correlated with observed differences in spectral intensities. While interpreted only qualitatively at the present time, the extent of the observed variations in transverse relaxation rates is consistent with the presence of relatively slow, microsecond-millisecond time scale chemical exchange type phenomena within the huPrP23-144 amyloid core.

(1)H-(13)C Hetero-nuclear dipole-dipole couplings of methyl groups in stationary and magic angle spinning solid-state NMR experiments of peptides and proteins

(13)C NMR of isotopically labeled methyl groups has the potential to combine spectroscopic simplicity with ease of labeling for protein NMR studies. However, in most high resolution separated local field experiments, such as polarization inversion spin exchange at the magic angle (PISEMA), that are used to measure (1)H-(13)C hetero-nuclear dipolar couplings, the four-spin system of the methyl group presents complications. In this study, the properties of the (1)H-(13)C hetero-nuclear dipolar interactions of (13)C-labeled methyl groups are revealed through solid-state NMR experiments on a range of samples, including single crystals, stationary powders, and magic angle spinning of powders, of (13)C(3) labeled alanine alone and incorporated into a protein. The spectral simplifications resulting from proton detected local field (PDLF) experiments are shown to enhance resolution and simplify the interpretation of results on single crystals, magnetically aligned samples, and powders. The complementarity of stationary sample and magic angle spinning (MAS) measurements of dipolar couplings is demonstrated by applying polarization inversion spin exchange at the magic angle and magic angle spinning (PISEMAMAS) to unoriented samples.

Quantitative analysis of backbone motion in proteins using MAS solid-state NMR spectroscopy

We present a comprehensive analysis of protein dynamics for a micro-crystallin protein in the solid-state. Experimental data include (15)N T (1) relaxation times measured at two different magnetic fields as well as (1)H-(15)N dipole, (15)N CSA cross correlated relaxation rates which are sensitive to the spectral density function J(0) and are thus a measure of T (2) in the solid-state. In addition, global order parameters are included from a (1)H,(15)N dipolar recoupling experiment. The data are analyzed within the framework of the extended model-free Clore-Lipari-Szabo theory. We find slow motional correlation times in the range of 5 and 150 ns. Assuming a wobbling in a cone motion, the amplitude of motion of the respective amide moiety is on the order of 10 degrees for the half-opening angle of the cone in most of the cases. The experiments are demonstrated using a perdeuterated sample of the chicken alpha-spectrin SH3 domain.