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.     

Separated local field NMR experiments on oriented samples rotating at the magic angle

Biophysical studies on membrane proteins by solid state NMR (SSNMR) can be carried out directly in a membrane environment. Samples are usually prepared in form of multi-lamellar dispersions for magic angle sample spinning or as aligned multi-layers for orientation dependent NMR experiments without sample rotation. A new development is the application of MAS NMR to aligned samples (MAOSS; Magic Angle Oriented Sample Spinning). In combination with separated local field (SLF) experiments, size and orientation of heteronuclear dipolar couplings may be extracted from two-dimensional experiments which correlate dipolar couplings with isotropic chemical shifts. The orientation of these ¹H–X dipolar couplings can be directly related to the orientation of molecular groups in the sample. Here, we demonstrate the feasibility of these experiments on highly ordered polyethylene fibers which serve as model compound. Based on these data, the experiment is also applied to ordered multi-layers of bacteriorhodopsin (purple membrane) which is used as a model for aligned membrane proteins. We present a detailed analysis of different experimental designs with respect to angular sensitivity and the influence of residual sample disorder (“mosaic spread”). The results of the MAOSS-SLF experiment are discussed within the context of established solid state NMR experiments which are usually performed without sample rotation and we compare the data to orientation information obtained from X-ray diffraction.     

Characterization of polyacrylamide-stabilized Pf1 phage liquid crystals for protein NMR spectroscopy

A new polymer-stabilized nematic liquid crystal has been characterized for the measurement of biomolecular residual dipolar couplings. Filamentous Pf1 phage were embedded in a polyacrylamide matrix that fixes the orientation of the particles. The alignment was characterized by the quadrupolar splitting of the ²H NMR water signal and by the measurement of ¹H-¹⁵N residual dipolar couplings (RDC) in the archeal translation elongation factor 1. Protein dissolved in the polymer-stabilized medium orients quantitatively as in media without polyacrylamide. We show that the quadrupolar splitting and RDCs are zero in media in which the Pf1 phage particles are aligned at the magic angle. This allows measurement of J and dipolar couplings in a single sample.     

Interference between Cross-correlated Relaxation and the Measurement of Scalar and Dipolar Couplings by Quantitative J

The effects of cross-correlated relaxation in Quantitative J methods are analyzed. One-bond ¹H–¹³C scalar and dipolar couplings of protein methine and methylene sites are obtained by monitoring proton and carbon magnetization in Quantitative J experiments. We find that scalar and dipolar couplings of the same pair of nuclei vary depending on the type of magnetization involved. These discrepancies can be as large as several Hz for methylene moieties. The contribution of dynamic frequency shifts, which are known to affect J couplings, is too small to explain the observed differences. We show that processes of magnetization transfer originated by cross-correlated relaxation are largely responsible for these discrepancies. We estimate the error transferred to methylene J values by cross-correlation interference, and show that is close to the experimentally observed one. Furthermore, this analysis indicates that cross-correlated relaxation effects under isotropic and anisotropic media differ, indicating that errors are not cancelled in residual dipolar coupling measurements.     

Measuring the magnitude of internal motion in a complex hexasaccharide

For the development of a scheme for quantitative experimental estimation of internal motion in the complex human milk hexasaccharide lacto‐N‐di‐fuco hexose I (LNDFH I), we measured a large number of experimental residual dipolar couplings in liquid crystal orienting media. We present a total of 40 ¹³C? ¹H and ¹H? ¹H dipolar coupling values, each representing distinct directions of internuclear vectors. The NMR data were interpreted with established methods for analysis of rigid subdomains of the oligosaccharide as well as a novel method in which dipolar couplings were calculated over an ensemble of conformers from a solvent Molecular Dynamics trajectory using multiple linear regression analysis. The Lewis^b epitope region of LNDFH I assumed a single unique conformation with internal motion described by fluctuations of 5–10° in glycosidic dihedral angles consistent with previous studies. Greater flexibility was observed for the remaining GlcNAc1→3‐β‐D ‐Gal and β‐D ‐Gal1→4Glc linkages, with the former glycosidic linkage existing in a conformational exchange among three states. The results were also supported by similar results of calculations carried out with conformers obtained from a simple Monte Carlo simulation without explicit solvent. © 2010 Wiley Periodicals, Inc. Biopolymers 95: 39–50, 2011.     

Structural characterization of a mannose-binding protein-trimannoside complex using residual dipolar couplings

The ligand-binding properties of a 53 kDa homomultimeric trimer from mannose-binding protein (MBP) have been investigated using residual dipolar couplings (RDCs) that are easily measured from NMR spectra of the ligand and isotopically labeled protein. Using a limited set of 1H-15N backbone amide NMR assignments for MBP and orientational information derived from the RDC measurements in aligned media, an order tensor for MBP has been determined that is consistent with symmetry-based predictions of an axially symmetric system. 13C-1H couplings for a bound trisaccharide ligand, methyl 3,6-di-O-(alpha-D-mannopyranosyl)-alpha-D-mannopyranoside (trimannoside) have been determined at natural abundance and used as orientational constraints. The bound ligand geometry and orientational constraints allowed docking of the trimannoside ligand in the binding site of MBP to produce a structural model for MBP-oligosaccharide interactions.     

Application of Correlated Residual Dipolar Couplings to the Determination of the Molecular Alignment Tensor Magnitude of Oriented Proteins and Nucleic Acids

Residual dipolar couplings (RDC) between nuclear spins in partially aligned samples offer unique insights into biomacromolecular structure and dynamics. To fully benefit from the RDC data, accurate knowledge of the magnitude ( D (a)) and rhombicity ( R ) of the molecular alignment tensor, A, is important. An extended histogram method (EHM) is presented which extracts these parameters more effectively from dipolar coupling data. The method exploits the correlated nature of RDCs for structural elements of planar geometry, such as the one-bond (13)C'(i)-(13)C(i)(alpha), (13)C'(i)-(15)N(i+1), and (15)N(i+1)-(1)H(N)(i+1) couplings in peptide bonds of proteins, or suitably chosen combinations of (1) D (C1'H1'), (1) D (C2'H2'), (1) D (C1'C2'), (2) D (C2'H1'), (2) D (C1'H2'), and (3) D (H1'H2') couplings in nucleic acids, to generate an arbitrarily large number of synthetic RDCs. These synthetic couplings result in substantially improved histograms and resulting values of D (a) and R, compared with histograms generated solely from the original sets of correlated RDCs, particularly when the number of planar fragments for which couplings are available is small. An alternative method, complementary to the EHM, is also described, which uses a systematic grid search procedure, based on least-squares fitting of sets of correlated RDCs to structural elements of known geometry, and provides an unambiguous lower limit for the degree of molecular alignment.     

The global conformation of the hammerhead ribozyme determined using residual dipolar couplings

The global structure of the hammerhead ribozyme was determined in the absence of Mg(2+) by solution NMR experiments. The hammerhead ribozyme motif forms a branched structure consisting of three helical stems connected to a catalytic core. The (1)H-(15)N and (1)H-(13)C residual dipolar couplings were measured in a set of differentially (15)N/(13)C-labeled ribozymes complexed with an unlabeled noncleavable substrate. The residual dipolar couplings provide orientation information on both the local and the global structure of the molecule. Analysis of the residual dipolar couplings demonstrated that the local structure of the three helical stems in solution is well modeled by an A-form conformation. However, the global structure of the hammerhead in solution in the absence of Mg(2+) is not consistent with the Y-shaped conformation observed in crystal structures of the hammerhead. The residual dipolar couplings for the helical stems were combined with standard NOE and J coupling constant NMR data from the catalytic core. The NOE data show formation of sheared G-A base pairs in domain 2. These NMR data were used to determine the global orientation of the three helical stems in the hammerhead. The hammerhead forms a rather extended structure under these conditions with a large angle between stems I and II ( approximately 153 degrees ), a smaller angle between stems II and III ( approximately 100 degrees ), and the smallest angle between stems I and III ( approximately 77 degrees ). The residual dipolar coupling data also contain information on the dynamics of the molecule and were used here to provide qualitative information on the flexibility of the helical domains in the hammerhead ribozyme-substrate complex.     

The utility of residual dipolar couplings in detecting motion in carbohydrates: application to sucrose

The solution structure and dynamics of sucrose are examined using a combination of NMR residual dipolar coupling and molecular mechanics force fields. It is found that the alignment tensors of the individual rings are different, and that fitting 35 measured residual dipolar couplings to structures with specific phi, psi values indicates the presence of three major conformations: phi, psi=(120 degrees ,270 degrees), (45 degrees, 300 degrees) and (90 degrees ,180 degrees). Furthermore, fitting two structures simultaneously to the 35 residual dipolar couplings results in a substantial improvement in the fits. The existence of multiple conformations having similar stabilities is a strong indication of motion, due to the interconversion among these states. Results from four molecular mechanics force fields are in general agreement with the experimental results. However, there are major disagreements between force fields. Because fits of residual dipolar couplings to structures are dependent on the force field used to calculate the structures, multiple force fields were used to interpret NMR data. It is demonstrated that the pucker of the fructofuranosyl ring affects the calculated potential energy surface, and the fit to the residual dipolar couplings data. Previously published 13C nuclear relaxation results suggesting that sucrose is rigid are not inconsistent with the present results when motional timescales are considered.     

Spatially encoded strategies in the execution of biomolecular-oriented 3D NMR experiments

Three-dimensional nuclear magnetic resonance (3D NMR) provides one of the foremost analytical tools available for the elucidation of biomolecular structure, function and dynamics. Executing a 3D NMR experiment generally involves scanning a series of time-domain signals S(t ₃), as a function of two time variables (t ₁, t ₂) which need to undergo parametric incrementations throughout independent experiments. Recent years have witnessed extensive efforts towards the acceleration of this kind of experiments. Among the different approaches that have been proposed counts an “ultrafast” scheme, which distinguishes itself from other propositions by enabling—at least in principle—the acquisition of the complete multidimensional NMR data set within a single transient. 2D protein NMR implementations of this single-scan method have been demonstrated, yet its potential for 3D acquisitions has only been exemplified on model organic compounds. This publication discusses a number of strategies that could make these spatial encoding protocols compatible with 3D biomolecular NMR applications. These include a merging of 2D ultrafast NMR principles with temporal 2D encoding schemes, which can yield 3D HNCO spectra from peptides and proteins within ≈100 s timescales. New processing issues that facilitate the collection of 3D NMR spectra by relying fully on spatial encoding principles are also assessed, and shown capable of delivering HNCO spectra within 1 s timescales. Limitations and prospects of these various schemes are briefly addressed.     

Enhancement of bound-state residual dipolar couplings: conformational analysis of lactose bound to Galectin-3

Residual dipolar couplings (RDCs) have proven to be a valuable NMR tool that can provide long-range constraints for molecular structure determination. The constraints are orientational in nature and are, thus, highly complementary to conventional distance constraints from NOE data. This complementarity would seem to extend to the study of the geometry of ligands bound to proteins. However, unlike transferred NOEs, where collection, even with a large excess of free ligand, results in measurements dominated by bound contributions, RDCs of exchanging ligands can be dominated by free-state contributions. Here we present a strategy for enhancement of RDCs from bound states that is based on specifically enhancing the alignment of the protein to which a ligand will bind. The protein is modified by addition of a hydrophobic alkyl tail that anchors it to the bicelles that are a part of the ordering medium needed for RDC measurement. As an illustration, we have added a propyl chain to the C terminus of the carbohydrate recognition domain of the protein, Galectin-3, and report enhanced RDCs that prove consistent with known bound-ligand geometries for this protein.     

Quantification of H/D Isotope Effects on Protein Hydrogen-bonds by h3JNC′ and 1JNC′ Couplings and Peptide Group 15N and 13C′ Chemical Shifts

The effect of hydrogen/deuterium exchange on protein hydrogen bond coupling constants (h3)J(NC') has been investigated in the small globular protein ubiquitin. The couplings across deuterated or protonated hydrogen bonds were measured by a long-range quantitative HA(CACO)NCO experiment. The analysis is combined with a determination of the H(N)/D(N) isotope effect on the amide group (1)J(NC') couplings and the (15)N and (13)C' chemical shifts. On average, H-bond deuteration exchange weakens (h3)J(NC') and strengthens (1)J(NC') couplings. A correlation is found between the size of the (15)N isotope shift, the (15)N chemical shift, and the (h3)J(NC') coupling constants. The data are consistent with a reduction of donor-acceptor overlap as expected from the classical Ubbelohde effect and the common understanding that H(N)/D(N) exchange leads to a shortening of the N-hydron bond length.     

Sign determination of dipolar couplings in field-oriented bicelles by variable angle sample spinning (VASS)

Residual dipolar couplings are being increasingly used as structural constraints for NMR studies of biomolecules. A problem arises when dipolar coupling contributions are larger than scalar contributions for a given spin pair, as is commonly observed in solid state NMR studies, in that signs of dipolar couplings cannot easily be determined. Here the sign ambiguities of dipolar couplings in field-oriented bicelles are resolved by variable angle sample spinning (VASS) techniques. The director behavior of field-oriented bicelles (DMPC/DHPC, DMPC/CHAPSO) in VASS is studied by ³¹P NMR. A stable configuration occurs when the spinning angle is smaller than the magic angle, 54.7°, and the director (or bicelle normal) of the disks is mainly distributed in a plane perpendicular to the rotation axis. Since the dipolar couplings depend on how the bicelles are oriented with respect to the magnetic field, it is shown that the dipolar interaction can be scaled to the same order as the J-coupling by moving the spinning axis from 0° toward 54.7°. Thus the relative sign of dipolar and scalar couplings can be determined.     

Backbone dynamics of bacteriorhodopsin as studied by <Superscript>13</Superscript>C solid-state NMR spectroscopy

The surface dynamics of bacteriorhodopsin was examined by measurements of site-specific ¹³C–¹H dipolar couplings in [3-¹³C]Ala-labeled bacteriorhodopsin. Motions of slow or intermediate frequency (correlation time <50 µs) scale down ¹³C–¹H dipolar couplings according to the motional amplitude. The two-dimensional dipolar and chemical shift (DIPSHIFT) correlation technique was utilized to obtain the dipolar coupling strength for each resolved peak in the ¹³C MAS solid-state NMR spectrum, providing the molecular order parameter of the respective site. In addition to the rotation of the Ala methyl group, which scales the dipolar coupling to 1/3 of the rigid limit value, fluctuations of the C–C vector result in additional motional averaging. Typical order parameters measured for mobile sites in bacteriorhodopsin are between 0.25 and 0.29. These can be assigned to Ala103 of the C–D loop and Ala235 at the C-terminal -helix protruded from the membrane surface, and Ala196 of the F–G loop, as well as to Ala228 and Ala233 of the C-terminal -helix and Ala51 from the transmembrane -helix. Such order parameters departing significantly from the value of 0.33 for rotating methyl groups are obviously direct evidence for the presence of fluctuation motions of the Ala C–C vectors of intact preparations of fully hydrated, wild-type bacteriorhodopsin at ambient temperature. The order parameter for Ala160 from the expectantly more flexible E–F loop, however, is unavailable under highest-field NMR conditions, probably because increased chemical shift anisotropy together with intrinsic fluctuation motions result in an unresolved ¹³C NMR signal.     

Top-down approach in protein RDC data analysis: <Emphasis Type="Italic">de novo</Emphasis> estimation of the alignment tensor

In solution NMR spectroscopy the residual dipolar coupling (RDC) is invaluable in improving both the precision and accuracy of NMR structures during their structural refinement. The RDC also provides a potential to determine protein structure de novo. These procedures are only effective when an accurate estimate of the alignment tensor has already been made. Here we present a top–down approach, starting from the secondary structure elements and finishing at the residue level, for RDC data analysis in order to obtain a better estimate of the alignment tensor. Using only the RDCs from N–H bonds of residues in α-helices and CA–CO bonds in β-strands, we are able to determine the offset and the approximate amplitude of the RDC modulation-curve for each secondary structure element, which are subsequently used as targets for global minimization. The alignment order parameters and the orientation of the major principal axis of individual helix or strand, with respect to the alignment frame, can be determined in each of the eight quadrants of a sphere. The following minimization against RDC of all residues within the helix or strand segment can be carried out with fixed alignment order parameters to improve the accuracy of the orientation. For a helical protein Bax, the three components A _xx , A _yy and A _zz , of the alignment order can be determined with this method in average to within 2.3% deviation from the values calculated with the available atomic coordinates. Similarly for β-sheet protein Ubiquitin they agree in average to within 8.5%. The larger discrepancy in β-strand parameters comes from both the diversity of the β-sheet structure and the lower precision of CA–CO RDCs. This top-down approach is a robust method for alignment tensor estimation and also holds a promise for providing a protein topological fold using limited sets of RDCs.     

Visualization of the phosphorylated active site loop of the cytoplasmic B domain of the mannitol transporter II(Mannitol) of the Escherichia coli phosphotransferase system by NMR spectroscopy and residual dipolar couplings

The solution structure of a stably phosphorylated form of the cytoplasmic B domain of the mannitol-specific transporter (IIB(Mtl)) of the Escherichia coli phosphotransferase system, containing a mutation of the active site Cys384 to Ser, has been solved by NMR. The strategy employed relies principally on backbone residual dipolar couplings recorded in three different alignment media, supplemented by nuclear Overhauser enhancement data and torsion angle restraints related specifically to the active site loop (residues 383-393). As judged from the dipolar coupling data, the remainder of the structure is unchanged upon phosphorylation within the errors of the coordinates of the previously determined solution structure of unphosphorylated wild-type IIB(Mtl). Thus, only the active site loop was refined. Phosphorylation results in a backbone atomic rms shift of approximately 0.7 angstroms in the active site loop. The resulting conformation is less than 0.5 angstroms away from the equivalent P-loop in both the low and high molecular mass eukaryotic tyrosine phosphatases. 3J(NP) coupling constant measurements using quantitative J-correlation spectroscopy provide a direct demonstration of a hydrogen bond between the phosphoryl group and the backbone amide of Ser391 at position i + 7 from phospho-Ser384, with an approximately linear P-O-H(N) bond angle. The structure also reveals additional hydrogen bonding interactions involving the backbone amides of residues at positions i + 4 and i + 5, and the hydroxyl groups of two serine residues at positions i + 6 and i + 7 that stabilize the phosphoryl group.     

A novel interactive tool for rigid-body modeling of multi-domain macromolecules using residual dipolar couplings

Residual dipolar couplings (RDC), measured by dissolving proteins in dilute liquid crystal media, or by studying naturally paramagnetic molecules, have rapidly become established as routine measurements in the investigation of the structure of macromolecules by NMR. One of the most obvious applications of the previously inaccessible long-range angular information afforded by RDC is the accurate definition of domain orientation in multi-module macromolecules or complexes. In this paper we describe a novel program developed to allow the determination of alignment tensor parameters for individual or multiple domains in macromolecules from residual dipolar couplings and to facilitate their manipulation to construct low-resolution models of macromolecular structure. For multi-domain systems the program determines the relative orientation of individual structured domains, and provides graphical user-driven rigid-body modeling of the different modules relative to the common tensorial frame. Translational freedom in the common frame, and equivalent rotations about the diagonalized (x,y,z) axes are used to position the different modules in the common frame to find a model in best agreement with experimentally measured couplings alone or in combination with additional experimental or covalent information.     

A Thorough Dynamic Interpretation of Residual Dipolar Couplings in Ubiquitin

The presence of slow motions with large amplitudes, as detected by measurements based on residual dipolar couplings [Peti, W., Meiler, J., Brueschweiler, R. and Griesinger, C. (2002) J. Am. Chem. Soc., 124, 5822–5833], has stirred up much discussion in recent years. Based on ubiquitin NH residual dipolar couplings (rdcs) measured in 31 different alignment conditions, a model-free analysis of structure and dynamics [Meiler, J., Peti, W., Prompers, J., Griesinger, C. and Brueschweiler, R. (2001) J. Am. Chem. Soc., 123, 6098–6107] is presented. Starting from this broad experimental basis, rdc-based order parameters with so far unattained accuracy were determined. These rdc-based order parameters underpin the presence of new modes of motion slower than the inverse overall tumbling correlation time. Amplitudes and anisotropies of the motion were derived. The effect of structural noise on the results was proven to be negligible. Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Experimentally restrained molecular dynamics simulations for characterizing the open states of cytochrome P450cam

Residual dipolar couplings (RDCs) were used as restraints in fully solvated molecular dynamics simulations of reduced substrate- and carbonmonoxy-bound cytochrome P450(cam) (CYP101A1), a 414-residue soluble monomeric heme-containing camphor monooxygenase from the soil bacterium Pseudomonas putida. The (1)D(NH) residual dipolar couplings used as restraints were measured in two independent alignment media. A soft annealing protocol was used to heat the starting structures while incorporating the RDC restraints. After production dynamics, structures with the lowest total violation energies for RDC restraints were extracted to identify ensembles of conformers accessible to the enzyme in solution. The simulations result in substrate orientations different from that seen in crystallographic structures and a more open and accessible enzyme active site and largely support previously reported differences between the open and closed states of CYP101A1.