Simultaneous definition of high resolution protein structure and backbone conformational dynamics using NMR residual dipolar couplings

REDCRAFT: A computational platform using residual dipolar coupling NMR data for determining structures of perdeuterated proteins in solution

Nuclear Magnetic Resonance (NMR) spectroscopy is one of the three primary experimental means of characterizing macromolecular structures, including protein structures. Structure determination by solution NMR spectroscopy has traditionally relied heavily on distance restraints derived from nuclear Overhauser effect (NOE) measurements. While structure determination of proteins from NOE-based restraints is well understood and broadly used, structure determination from Residual Dipolar Couplings (RDCs) is relatively less well developed. Here, we describe the new features of the protein structure modeling program REDCRAFT and focus on the new Adaptive Decimation (AD) feature. The AD plays a critical role in improving the robustness of REDCRAFT to missing or noisy data, while allowing structure determination of larger proteins from less data. In this report we demonstrate the successful application of REDCRAFT in structure determination of proteins ranging in size from 50 to 145 residues using experimentally collected data, and of larger proteins (145 to 573 residues) using simulated RDC data. In both cases, REDCRAFT uses only RDC data that can be collected from perdeuterated proteins. Finally, we compare the accuracy of structure determination from RDCs alone with traditional NOE-based methods for the structurally novel PF.2048.1 protein. The RDC-based structure of PF.2048.1 exhibited 1.0 Å BB-RMSD with respect to a high-quality NOE-based structure. Although optimal strategies would include using RDC data together with chemical shift, NOE, and other NMR data, these studies provide proof-of-principle for robust structure determination of largely-perdeuterated proteins from RDC data alone using REDCRAFT.

Residual Dipolar Couplings have the potential to improve the accuracy and reduce the time needed to characterize protein structures. In addition, RDC data have been demonstrated to concurrently elucidate structure of proteins, provide assignment of resonances, and characterize the internal dynamics of proteins. Given all the advantages associated with the study of proteins from RDC data, based on the statistics provided by the Protein Databank (PDB), surprisingly only 124 proteins (out of nearly 150,000 proteins) have utilized RDCs as part of their structure determination. Even a smaller subset of these proteins (approximately 7) have utilized RDCs as the primary source of data for structure determination. One key factor in the use of RDCs is the challenging computational and analytical aspects of this source of data. In this report, we demonstrate the success of the REDCRAFT software package in structure determination of proteins using RDC data that can be collected from small and large proteins in a routine fashion. REDCRAFT accomplishes the challenging task of structure determination from RDCs by introducing a unique search and optimization technique that is both robust and computationally tractable. Structure determination from routinely collectable RDC data using REDCRAFT can complement existing methods to provide faster and more accurate studies of larger and more complex protein structures by NMR spectroscopy in solution state.

Increased usability, algorithmic improvements and incorporation of data mining for structure calculation of proteins with REDCRAFT software package

Background

Traditional approaches to elucidation of protein structures by Nuclear Magnetic Resonance spectroscopy (NMR) rely on distance restraints also known as Nuclear Overhauser effects (NOEs). The use of NOEs as the primary source of structure determination by NMR spectroscopy is time consuming and expensive. Residual Dipolar Couplings (RDCs) have become an alternate approach for structure calculation by NMR spectroscopy. In previous works, the software package REDCRAFT has been presented as a means of harnessing the information containing in RDCs for structure calculation of proteins. However, to meet its full potential, several improvements to REDCRAFT must be made.

Results

In this work, we present improvements to REDCRAFT that include increased usability, better interoperability, and a more robust core algorithm. We have demonstrated the impact of the improved core algorithm in the successful folding of the protein 1A1Z with as high as ±4 Hz of added error. The REDCRAFT computed structure from the highly corrupted data exhibited less than 1.0 Å with respect to the X-ray structure. We have also demonstrated the interoperability of REDCRAFT in a few instances including with PDBMine to reduce the amount of required data in successful folding of proteins to unprecedented levels. Here we have demonstrated the successful folding of the protein 1D3Z (to within 2.4 Å of the X-ray structure) using only N-H RDCs from one alignment medium.

Conclusions

The additional GUI features of REDCRAFT combined with the NEF compliance have significantly increased the flexibility and usability of this software package. The improvements of the core algorithm have substantially improved the robustness of REDCRAFT in utilizing less experimental data both in quality and quantity.

Remarkable Rigidity of the Single α-Helical Domain of Myosin-VI As Revealed by NMR Spectroscopy

Although the α-helix has long been recognized as an all-important element of secondary structure, it generally requires stabilization by tertiary interactions with other parts of a protein's structure. Highly charged single α-helical (SAH) domains, consisting of a high percentage (>75%) of Arg, Lys, and Glu residues, are exceptions to this rule but have been difficult to characterize structurally. Our study focuses on the 68-residue medial tail domain of myosin-VI, which is found to contain a highly ordered α-helical structure extending from Glu-6 to Lys-63. High hydrogen exchange protection factors (15-150), small (ca. 4 Hz) 3 JHNHα couplings, and a near-perfect fit to an ideal model α-helix for its residual dipolar couplings (RDCs), measured in a filamentous phage medium, support the high regularity of this helix. Remarkably, the hydrogen exchange rates are far more homogeneous than the protection factors derived from them, suggesting that for these transiently broken helices the intrinsic exchange rates derived from the amino acid sequence are not appropriate reference values. 15N relaxation data indicate a very high degree of rotational diffusion anisotropy ( D∥/ D⊥ ≈ 7.6), consistent with the hydrodynamic behavior predicted for such a long, nearly straight α-helix. Alignment of the helix by a paramagnetic lanthanide ion attached to its N-terminal region shows a decrease in alignment as the distance from the tagging site increases. This decrease yields a precise measure for the persistence length of 224 ± 10 Å at 20 °C, supporting the idea that the role of the SAH helix is to act as an extension of the myosin-VI lever arm.

Molecular modeling of biomolecules by paramagnetic NMR and computational hybrid methods

The 3D atomic structures of biomolecules and their complexes are key to our understanding of biomolecular function, recognition, and mechanism. However, it is often difficult to obtain structures, particularly for systems that are complex, dynamic, disordered, or exist in environments like cell membranes. In such cases sparse data from a variety of paramagnetic NMR experiments offers one possible source of structural information. These restraints can be incorporated in computer modeling algorithms that can accurately translate the sparse experimental data into full 3D atomic structures. In this review, we discuss various types of paramagnetic NMR/computational hybrid modeling techniques that can be applied to successful modeling of not only the atomic structure of proteins but also their interacting partners. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

Applications of NMR and computational methodologies to study protein dynamics

Overwhelming evidence now illustrates the defining role of atomic-scale protein flexibility in biological events such as allostery, cell signaling, and enzyme catalysis. Over the years, spin relaxation nuclear magnetic resonance (NMR) has provided significant insights on the structural motions occurring on multiple time frames over the course of a protein life span. The present review article aims to illustrate to the broader community how this technique continues to shape many areas of protein science and engineering, in addition to being an indispensable tool for studying atomic-scale motions and functional characterization. Continuing developments in underlying NMR technology alongside software and hardware developments for complementary computational approaches now enable methodologies to routinely provide spatial directionality and structural representations traditionally harder to achieve solely using NMR spectroscopy. In addition to its well-established role in structural elucidation, we present recent examples that illustrate the combined power of selective isotope labeling, relaxation dispersion experiments, chemical shift analyses, and computational approaches for the characterization of conformational sub-states in proteins and enzymes.

Protein dynamics and function from solution state NMR spectroscopy

It is well-established that dynamics are central to protein function; their importance is implicitly acknowledged in the principles of the Monod, Wyman and Changeux model of binding cooperativity, which was originally proposed in 1965. Nowadays the concept of protein dynamics is formulated in terms of the energy landscape theory, which can be used to understand protein folding and conformational changes in proteins. Because protein dynamics are so important, a key to understanding protein function at the molecular level is to design experiments that allow their quantitative analysis. Nuclear magnetic resonance (NMR) spectroscopy is uniquely suited for this purpose because major advances in theory, hardware, and experimental methods have made it possible to characterize protein dynamics at an unprecedented level of detail. Unique features of NMR include the ability to quantify dynamics (i) under equilibrium conditions without external perturbations, (ii) using many probes simultaneously, and (iii) over large time intervals. Here we review NMR techniques for quantifying protein dynamics on fast (ps-ns), slow (μs-ms), and very slow (s-min) time scales. These techniques are discussed with reference to some major discoveries in protein science that have been made possible by NMR spectroscopy.

Structure Calculation and Reconstruction of Discrete-State Dynamics from Residual Dipolar Couplings

Residual dipolar couplings (RDCs) acquired by nuclear magnetic resonance (NMR) spectroscopy are an indispensable source of information in investigation of molecular structures and dynamics. Here, we present a comprehensive strategy for structure calculation and reconstruction of discrete-state dynamics from RDC data that is based on the singular value decomposition (SVD) method of order tensor estimation. In addition to structure determination, we provide a mechanism of producing an ensemble of conformations for the dynamical regions of a protein from RDC data. The developed methodology has been tested on simulated RDC data with ±1 Hz of error from an 83 residue α protein (PDB ID 1A1Z ) and a 213 residue α/β protein DGCR8 (PDB ID 2YT4 ). In nearly all instances, our method reproduced the structure of the protein including the conformational ensemble to within less than 2 Å. On the basis of our investigations, arc motions with more than 30° of rotation are identified as internal dynamics and are reconstructed with sufficient accuracy. Furthermore, states with relative occupancies above 20% are consistently recognized and reconstructed successfully. Arc motions with a magnitude of 15° or relative occupancy of less than 10% are consistently unrecognizable as dynamical regions within the context of ±1 Hz of error.

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

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

A rigid lanthanide binding tag to aid NMR studies of a 70 kDa homodimeric coat protein of human norovirus

Attachment of human noroviruses to histo blood group antigens is thought to be essential for infection of host cells. Molecular details of the attachment process can be studied in vitro using a variety of NMR experiments. The use of protein NMR based experiments requires assignments of backbone NMR signals. Using uniformly (2)H,(15)N-labeled protruding domains (P-dimers) of a prevalent epidemic human norovirus strain (GII.4 Saga) we have studied the potential of α-l-fucose covalently linked to a rigid lanthanide binding tag to aid backbone assignments using the paramagnetic properties of lanthanide ions. The synthesis of tagged α-l-fucose is reported. Notably, the metal chelating unit connects to the carbohydrate via a triazole linker constructed using click chemistry.

High-resolution NMR spectroscopy of encapsulated proteins dissolved in low-viscosity fluids

High-resolution multi-dimensional solution NMR is unique as a biophysical and biochemical tool in its ability to examine both the structure and dynamics of macromolecules at atomic resolution. Conventional solution NMR approaches, however, are largely limited to examinations of relatively small (<25kDa) molecules, mostly due to the spectroscopic consequences of slow rotational diffusion. Encapsulation of macromolecules within the protective nanoscale aqueous interior of reverse micelles dissolved in low viscosity fluids has been developed as a means through which the 'slow tumbling problem' can be overcome. This approach has been successfully applied to diverse proteins and nucleic acids ranging up to 100kDa, considerably widening the range of biological macromolecules to which conventional solution NMR methodologies may be applied. Recent advances in methodology have significantly broadened the utility of this approach in structural biology and molecular biophysics.

Structural characterization of intrinsically disordered proteins by NMR spectroscopy

Recent advances in NMR methodology and techniques allow the structural investigation of biomolecules of increasing size with atomic resolution. NMR spectroscopy is especially well-suited for the study of intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs) which are in general highly flexible and do not have a well-defined secondary or tertiary structure under functional conditions. In the last decade, the important role of IDPs in many essential cellular processes has become more evident as the lack of a stable tertiary structure of many protagonists in signal transduction, transcription regulation and cell-cycle regulation has been discovered. The growing demand for structural data of IDPs required the development and adaption of methods such as ¹³C-direct detected experiments, paramagnetic relaxation enhancements (PREs) or residual dipolar couplings (RDCs) for the study of ‘unstructured’ molecules in vitro and in-cell. The information obtained by NMR can be processed with novel computational tools to generate conformational ensembles that visualize the conformations IDPs sample under functional conditions. Here, we address NMR experiments and strategies that enable the generation of detailed structural models of IDPs.

Perspectives in biological physics: the nDDB project for a neutron Dynamics Data Bank for biological macromolecules

Neutron spectroscopy provides experimental data on time-dependent trajectories, which can be directly compared to molecular dynamics simulations. Its importance in helping us to understand biological macromolecules at a molecular level is demonstrated by the results of a literature survey over the last two to three decades. Around 300 articles in refereed journals relate to neutron scattering studies of biological macromolecular dynamics, and the results of the survey are presented here. The scope of the publications ranges from the general physics of protein and solvent dynamics, to the biologically relevant dynamics-function relationships in live cells. As a result of the survey we are currently setting up a neutron Dynamics Data Bank (nDDB) with the aim to make the neutron data on biological systems widely available. This will benefit, in particular, the MD simulation community to validate and improve their force fields. The aim of the database is to expose and give easy access to a body of experimental data to the scientific community. The database will be populated with as much of the existing data as possible. In the future it will give value, as part of a bigger whole, to high throughput data, as well as more detailed studies. A range and volume of experimental data will be of interest in determining how quantitatively MD simulations can reproduce trends across a range of systems and to what extent such trends may depend on sample preparation and data reduction and analysis methods. In this context, we strongly encourage researchers in the field to deposit their data in the nDDB.

Three-dimensional protein fold determination from backbone amide pseudocontact shifts generated by lanthanide tags at multiple sites

Site-specific attachment of paramagnetic lanthanide ions to a protein generates pseudocontact shifts (PCS) in the nuclear magnetic resonance (NMR) spectra of the protein that are easily measured as changes in chemical shifts. By labeling the protein with lanthanide tags at four different sites, PCSs are observed for most amide protons and accurate information is obtained about their coordinates in three-dimensional space. The approach is demonstrated with the chaperone ERp29, for which large differences have been reported between X-ray and NMR structures of the C-terminal domain, ERp29-C. The results unambiguously show that the structure of rat ERp29-C in solution is similar to the crystal structure of human ERp29-C. PCSs of backbone amides were the only structural restraints required. Because these can be measured for more dilute protein solutions than other NMR restraints, the approach greatly widens the range of proteins amenable to structural studies in solution.

An improved algorithm for MFR fragment assembly

A method for generating protein backbone models from backbone only NMR data is presented, which is based on molecular fragment replacement (MFR). In a first step, the PDB database is mined for homologous peptide fragments using experimental backbone-only data i.e. backbone chemical shifts (CS) and residual dipolar couplings (RDC). Second, this fragment library is refined against the experimental restraints. Finally, the fragments are assembled into a protein backbone fold using a rigid body docking algorithm using the RDCs as restraints. For improved performance, backbone nuclear Overhauser effects (NOEs) may be included at that stage. Compared to previous implementations of MFR-derived structure determination protocols this model-building algorithm offers improved stability and reliability. Furthermore, relative to CS-ROSETTA based methods, it provides faster performance and straightforward implementation with the option to easily include further types of restraints and additional energy terms.

Advances in automated NMR protein structure determination

Around half of all protein structures solved nowadays using solution-state nuclear magnetic resonance (NMR) spectroscopy have been because of automated data analysis. The pervasiveness of computational approaches in general hides, however, a more nuanced view in which the full variety and richness of the field appears. This review is structured around a comparison of methods associated with three NMR observables: classical nuclear Overhauser effect (NOE) constraint gathering in contrast with more recent chemical shift and residual dipole coupling (RDC) based protocols. In each case, the emphasis is placed on the latest research, covering mainly the past 5 years. By describing both general concepts and representative programs, the objective is to map out a field in which--through the very profusion of approaches--it is all too easy to lose one's bearings.

Scrutinizing molecular mechanics force fields on the submicrosecond timescale with NMR data

Protein dynamics on the atomic level and on the microsecond timescale has recently become accessible from both computation and experiment. To validate molecular dynamics (MD) at the submicrosecond timescale against experiment we present microsecond MD simulations in 10 different force-field configurations for two globular proteins, ubiquitin and the gb3 domain of protein G, for which extensive NMR data is available. We find that the reproduction of the measured NMR data strongly depends on the chosen force field and electrostatics treatment. Generally, particle-mesh Ewald outperforms cut-off and reaction-field approaches. A comparison to measured J-couplings across hydrogen bonds suggests that there is room for improvement in the force-field description of hydrogen bonds in most modern force fields. Our results show that with current force fields, simulations beyond hundreds of nanoseconds run an increased risk of undergoing transitions to nonnative conformational states or will persist within states of high free energy for too long, thus skewing the obtained population frequencies. Only for the AMBER99sb force field have such transitions not been observed. Thus, our results have significance for the interpretation of data obtained with long MD simulations, for the selection of force fields for MD studies and for force-field development. We hope that this comprehensive benchmark based on NMR data applied to many popular MD force fields will serve as a useful resource to the MD community. Finally, we find that for gb3, the force-field AMBER99sb reaches comparable accuracy in back-calculated residual dipolar couplings and J-couplings across hydrogen bonds to ensembles obtained by refinement against NMR data.

MQ-HNCO-TROSY for the measurement of scalar and residual dipolar couplings in larger proteins: application to a 557-residue IgFLNa16-21

We describe a novel pulse sequence, MQ-HNCO-TROSY, for the measurement of scalar and residual dipolar couplings between amide proton and nitrogen in larger proteins. The experiment utilizes the whole 2T(N) polarization transfer delay for labeling of (15)N chemical shift in a constant time manner, which efficiently doubles the attainable resolution in (15)N dimension with respect to the conventional HNCO-TROSY experiment. In addition, the accordion principle is employed for measuring (J + D)(NH)s, and the multiplet components are selected with the generalized version of the TROSY scheme introduced by Nietlispach (J Biomol NMR 31:161-166, 2005). Therefore, cross peak overlap is diminished while the time period during which the (15)N spin is susceptible to fast transverse relaxation associated with the anti-TROSY transition is minimized per attainable resolution unit. The proposed MQ-HNCO-TROSY scheme was employed for measuring RDCs in high molecular weight protein IgFLNa16-21 of 557 residues, resulting in 431 experimental RDCs. Correlations between experimental and back-calculated RDCs in individual domains gave relatively low Q-factors (0.19-0.39), indicative of sufficient accuracy that can be obtained with the proposed MQ-HNCO-TROSY experiment in high molecular weight proteins.

Site-specific backbone amide (15)N chemical shift anisotropy tensors in a small protein from liquid crystal and cross-correlated relaxation measurements

Site-specific (15)N chemical shift anisotropy (CSA) tensors have been derived for the well-ordered backbone amide (15)N nuclei in the B3 domain of protein G (GB3) from residual chemical shift anisotropy (RCSA) measured in six different mutants that retain the native structure but align differently relative to the static magnetic field when dissolved in a liquid crystalline Pf1 suspension. This information is complemented by measurement of cross-correlated relaxation rates between the (15)N CSA tensor and either the (15)N-(1)H or (15)N-(13)C' dipolar interaction. In agreement with recent solid state NMR measurements, the (15)N CSA tensors exhibit only a moderate degree of variation from averaged values, but have larger magnitudes in alpha-helical (-173 +/- 7 ppm) than in beta-sheet (-162 +/- 6 ppm) residues, a finding also confirmed by quantum computations. The orientations of the least shielded tensor component cluster tightly around an in-peptide-plane vector that makes an angle of 19.6 +/- 2.5 degrees with the N-H bond, with the asymmetry of the (15)N CSA tensor being slightly smaller in alpha-helix (eta = 0.23 +/- 0.17) than in beta-sheet (eta = 0.31 +/- 0.11). The residue-specific (15)N CSA values are validated by improved agreement between computed and experimental (15)N R(1rho) relaxation rates measured for (15)N-{(2)H} sites in GB3, which are dominated by the CSA mechanism. Use of residue-specific (15)N CSA values also results in more uniform generalized order parameters, S(2), and predicts considerable residue-by-residue variations in the magnetic field strengths where TROSY line narrowing is most effective.

Toward a unified representation of protein structural dynamics in solution

An atomic resolution description of protein flexibility is essential for understanding the role that structural dynamics play in biological processes. Despite the unique dependence of nuclear magnetic resonance (NMR) to motional averaging on different time scales, NMR-based protein structure determination often ignores the presence of dynamics, representing rapidly exchanging conformational equilibria in terms of a single static structure. In this study, we use the rich dynamic information encoded in experimental NMR parameters to develop a molecular and statistical mechanical characterization of the conformational behavior of proteins in solution. Critically, and in contrast to previously proposed techniques, we do not use empirical energy terms to restrain a conformational search, a procedure that can strongly perturb simulated dynamics in a nonpredictable way. Rather, we use accelerated molecular dynamic simulation to gradually increase the level of conformational sampling and to identify the appropriate level of sampling via direct comparison of unrestrained simulation with experimental data. This constraint-free approach thereby provides an atomic resolution free-energy weighted Boltzmann description of protein dynamics occurring on time scales over many orders of magnitude in the protein ubiquitin.

Variable helix elongation as a tool to modulate RNA alignment and motional couplings

The application of residual dipolar couplings (RDCs) in studies of RNA structure and dynamics can be complicated by the presence of couplings between collective helix motions and overall alignment and by the inability to modulate overall alignment of the molecule by changing the ordering medium. Here, we show for a 27-nt TAR RNA construct that variable levels of helix elongation can be used to alter both overall alignment and couplings to collective helix motions in a semi-predictable manner. In the absence of elongation, a four base-pair helix II capped by a UUCG apical loop exhibits a higher degree of order compared to a six base-pair helix I (theta(I)/theta(II)=0.56+/-0.1). The principal S(zz) direction is nearly parallel to the axis of helix II but deviates by approximately 40 degrees relative to the axis of helix I. Elongating helix I by three base-pairs equalizes the alignment of the two helices and pushes the RNA into the motional coupling limit such that the two helices have comparable degrees of order (theta(I)/theta(II)=0.92+/-0.04) and orientations relative to S(zz) ( approximately 17 degrees ). Increasing the length of elongation further to 22 base-pairs pushes the RNA into the motional decoupling limit in which helix I dominates alignment (theta(II)/theta(I)=0.45+/-0.05), with S(zz) orientated nearly parallel to its helix axis. Many of these trends can be rationalized using PALES simulations that employ a previously proposed three-state dynamic ensemble of TAR. Our results provide new insights into motional couplings, offer guidelines for assessing their extent, and suggest that variable degrees of helix elongation can allow access to independent sets of RDCs for characterizing RNA structural dynamics.

NMR resonance assignments of sparsely labeled proteins: amide proton exchange correlations in native and denatured states

Protein NMR assignments of large proteins using traditional triple resonance techniques depends on double or triple labeling of samples with (15)N, (13)C, and (2)H. This is not always practical with proteins that require expression in nonbacterial hosts. Labeling with isotopically labeled versions of single amino acids (sparse labeling) often is possible; however, resonance assignment then requires a new strategy. Here a procedure for the assignment of cross-peaks in (15)N-(1)H correlation spectra of sparsely labeled proteins is presented. It relies on the correlation of proton-deuterium amide exchange rates in native and denatured spectra of the intact protein, followed by correlation of chemical shifts in the spectra of the denatured protein with chemical shifts of sequenced peptides derived from the protein. The procedure is successfully demonstrated on a sample of a protein, Galectin-3, selectively labeled with (15)N at all alanine residues.

Ultrahigh resolution characterization of domain motions and correlations by multialignment and multireference residual dipolar coupling NMR

Nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) provide a unique opportunity for spatially characterizing complex motions in biomolecules with time scale sensitivity extending up to milliseconds. Up to five motionally averaged Wigner rotation elements, (D(0k)2(alphaalpha)), can be determined experimentally using RDCs measured in five linearly independent alignment conditions and applied to define motions of axially symmetric bond vectors. Here, we show that up to 25 motionally averaged Wigner rotation elements, (D(mk)2(alphabetagamma)), can be determined experimentally from multialignment RDCs and used to characterize rigid-body motions of chiral domains. The 25 (D(mk)2(alphabetagamma)) elements form a basis set that allows one to measure motions of a domain relative to an isotropic distribution of reference frames anchored on a second domain (and vice versa), thus expanding the 3D spatial resolution with which motions can be characterized. The 25 (D(mk)2(alphabetagamma)) elements can also be used to fit an ensemble consisting of up to eight equally or six unequally populated states. For more than two domains, changing the identity of the domain governing alignment allows access to new information regarding the correlated nature of the domain fluctuations. Example simulations are provided that validate the theoretical derivation and illustrate the high spatial resolution with which rigid-body domain motions can be characterized using multialignment and multireference RDCs. Our results further motivate the development of experimental approaches for both modulating alignment and anchoring it on specifically targeted domains.

Structural biology by NMR: structure, dynamics, and interactions

The function of bio-macromolecules is determined by both their 3D structure and conformational dynamics. These molecules are inherently flexible systems displaying a broad range of dynamics on time-scales from picoseconds to seconds. Nuclear Magnetic Resonance (NMR) spectroscopy has emerged as the method of choice for studying both protein structure and dynamics in solution. Typically, NMR experiments are sensitive both to structural features and to dynamics, and hence the measured data contain information on both. Despite major progress in both experimental approaches and computational methods, obtaining a consistent view of structure and dynamics from experimental NMR data remains a challenge. Molecular dynamics simulations have emerged as an indispensable tool in the analysis of NMR data.

Self-consistent residual dipolar coupling based model-free analysis for the robust determination of nanosecond to microsecond protein dynamics

Residual dipolar couplings (RDCs) provide information about the dynamic average orientation of inter-nuclear vectors and amplitudes of motion up to milliseconds. They complement relaxation methods, especially on a time-scale window that we have called supra-tau(c) (tau(c) < supra-tau(c) < 50 micros). Here we present a robust approach called Self-Consistent RDC-based Model-free analysis (SCRM) that delivers RDC-based order parameters-independent of the details of the structure used for alignment tensor calculation-as well as the dynamic average orientation of the inter-nuclear vectors in the protein structure in a self-consistent manner. For ubiquitin, the SCRM analysis yields an average RDC-derived order parameter of the NH vectors <S2(rdc)>0.72 +/- 0.02 compared to <S2(LS)> = 0.778 +/- 0.003 for the Lipari-Szabo order parameters, indicating that the inclusion of the supra-tau(c) window increases the averaged amplitude of mobility observed in the sub-supra-tau(c) window by about 34%. For the beta-strand spanned by residues Lys48 to Leu50, an alternating pattern of backbone NH RDC order parameter S2(rdc)(NH) = (0.59, 0.72, 0.59) was extracted. The backbone of Lys48, whose side chain is known to be involved in the poly-ubiquitylation process that leads to protein degradation, is very mobile on the supra-tau(c) time scale (S2(rdc)(NH) = 0.59 +/- 0.03), while it is inconspicuous (S2(LS)(NH)= 0.82) on the sub-tau(c) as well as on micros-ms relaxation dispersion time scales. The results of this work differ from previous RDC dynamics studies of ubiquitin in the sense that the results are essentially independent of structural noise providing a much more robust assessment of dynamic effects that underlie the RDC data.

De novo determination of internuclear vector orientations from residual dipolar couplings measured in three independent alignment media

The straightforward interpretation of solution state residual dipolar couplings (RDCs) in terms of internuclear vector orientations generally requires prior knowledge of the alignment tensor, which in turn is normally estimated using a structural model. We have developed a protocol which allows the requirement for prior structural knowledge to be dispensed with as long as RDC measurements can be made in three independent alignment media. This approach, called Rigid Structure from Dipolar Couplings (RSDC), allows vector orientations and alignment tensors to be determined de novo from just three independent sets of RDCs. It is shown that complications arising from the existence of multiple solutions can be overcome by careful consideration of alignment tensor magnitudes in addition to the agreement between measured and calculated RDCs. Extensive simulations as well applications to the proteins ubiquitin and Staphylococcal protein GB1 demonstrate that this method can provide robust determinations of alignment tensors and amide N-H bond orientations often with better than 10 degrees accuracy, even in the presence of modest levels of internal dynamics.