Model-free approach to the dynamic interpretation of residual dipolar couplings in globular proteins

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

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

Synergism between x-ray crystallography and NMR residual dipolar couplings in characterizing protein dynamics

The important role of structural dynamics in protein function is widely recognized. Thermal or B-factors and their anisotropy, seen in x-ray analysis of protein structures, report on the presence of atomic coordinate heterogeneity that can be attributed to motion. However, their quantitative evaluation in terms of protein dynamics by x-ray ensemble refinement remains challenging. NMR spectroscopy provides quantitative information on the amplitudes and time scales of motional processes. Unfortunately, with a few exceptions, the NMR data do not provide direct insights into the atomic details of dynamic trajectories. Residual dipolar couplings, measured by solution NMR, are very precise parameters reporting on the time-averaged bond-vector orientations and may offer the opportunity to derive correctly weighted dynamic ensembles of structures for cases where multiple high-resolution x-ray structures are available. Applications to the SARS-CoV-2 main protease, M^pro, and ubiquitin highlight this complementarity of NMR and crystallography for quantitative assessment of internal motions.

Programmable alignment media from self-assembled oligopeptide amphiphiles for the measurement of independent sets of residual dipolar couplings in organic solvents

NMR spectroscopy in anisotropic media has emerged as a powerful technique for the structural elucidation of organic molecules. Its application requires weak alignment of analytes by means of suitable alignment media. Although a number of alignment media, that are compatible with organic solvents, have been introduced in the last 20 years, acquiring a number of independent, non-linearly related sets of anisotropic NMR data from the same organic solvent system remains a formidable challenge, which is however crucial for the alignment simulations and deriving dynamic and structural information of organic molecules unambiguously. Herein, we introduce a programmable strategy to construct several distinct peptide-based alignment media by adjusting the amino acid sequence, which allows us to measure independent sets of residual dipolar couplings (RDCs) in a highly efficient and accurate manner. This study opens a new avenue for de novo structure determination of organic compounds without requiring prior structural information.

We report a programmable strategy to construct multi-alignment media via peptide self-assembly for the measurement of independent sets of residual dipolar couplings (RDCs).

Concurrent Identification and Characterization of Protein Structure and Continuous Internal Dynamics with REDCRAFT

Internal dynamics of proteins can play a critical role in the biological function of some proteins. Several well documented instances have been reported such as MBP, DHFR, hTS, DGCR8, and NSP1 of the SARS-CoV family of viruses. Despite the importance of internal dynamics of proteins, there currently are very few approaches that allow for meaningful separation of internal dynamics from structural aspects using experimental data. Here we present a computational approach named REDCRAFT that allows for concurrent characterization of protein structure and dynamics. Here, we have subjected DHFR (PDB-ID 1RX2), a 159-residue protein, to a fictitious, mixed mode model of internal dynamics. In this simulation, DHFR was segmented into 7 regions where 4 of the fragments were fixed with respect to each other, two regions underwent rigid-body dynamics, and one region experienced uncorrelated and melting event. The two dynamical and rigid-body segments experienced an average orientational modification of 7° and 12° respectively. Observable RDC data for backbone C′-N, N-HN, and C′-HN were generated from 102 uniformly sampled frames that described the molecular trajectory. The structure calculation of DHFR with REDCRAFT by using traditional Ramachandran restraint produced a structure with 29 Å of structural difference measured over the backbone atoms (bb-rmsd) over the entire length of the protein and an average bb-rmsd of more than 4.7 Å over each of the dynamical fragments. The same exercise repeated with context-specific dihedral restraints generated by PDBMine produced a structure with bb-rmsd of 21 Å over the entire length of the protein but with bb-rmsd of less than 3 Å over each of the fragments. Finally, utilization of the Dynamic Profile generated by REDCRAFT allowed for the identification of different dynamical regions of the protein and the recovery of individual fragments with bb-rmsd of less than 1 Å. Following the recovery of the fragments, our assembly procedure of domains (larger segments consisting of multiple fragments with a common dynamical profile) correctly assembled the four fragments that are rigid with respect to each other, categorized the two domains that underwent rigid-body dynamics, and identified one dynamical region for which no conserved structure could be defined. In conclusion, our approach was successful in identifying the dynamical domains, recovery of structure where it is meaningful, and relative assembly of the domains when possible.

NMR Relaxation Dispersion Methods for the Structural and Dynamic Analysis of Quickly Interconverting, Low-Populated Conformational Substates

Most biomolecular processes involve proteins shuttling among different conformational states, particularly from highly populated ground states to the lowly populated excited states that determine the interconversion rates and biological function, and which are invisible to most structural biology techniques. These structural transitions are rare and relatively fast: happen in the millisecond-microsecond timescale (ms-μs). NMR spectroscopy can access these timescales via relaxation dispersion techniques (RD-NMR). The exchange parameters extracted from RD-NMR experiments provide pivotal information on these otherwise invisible states that reports on key properties of the high free energy, reactive regions of the protein's energy landscape, including the mechanisms of folding/unfolding and of the interconversion between active and inactive states. Here, we describe a simple, step-by-step protocol to carry out RD-NMR experiments on proteins to detect the existence of such conformational substates and characterize their structural properties (chemical shifts).

Model free analysis of experimental residual dipolar couplings in small organic compounds

Residual dipolar couplings (RDCs) contain information on the relative arrangement and dynamics of internuclear spin vectors in chemical compounds. Classically, RDC data is analyzed by fitting to structure models, while model-free approaches (MFA) directly relate RDCs to the corresponding internuclear vectors. The recently introduced software TITANIA implements the MFA and extracts structure and dynamics parameters directly from RDCs to facilitate de novo structure refinement for small organic compounds. Encouraged by our previous results on simulated data, we herein focus on the prerequisites and challenges faced when using purely experimental data for this approach. These concern mainly the fact that not all couplings are accessible in all media, leading to voids in the RDC matrix and the concomitant effects on the structure refinement. It is shown that RDC data sets obtained experimentally from currently available alignment media and measurement methods are of sufficient quality to allow relative configuration determination even when the relative configuration of the analyte is completely unknown.

TITANIA: Model-Free Interpretation of Residual Dipolar Couplings in the Context of Organic Compounds

Residual dipolar couplings (RDCs) become increasingly important as additional NMR parameters in the structure elucidation of organic compounds but are usually used in fitting procedures to discriminate between (computed) structures that are in accordance with RDCs and others that can be ruled out. Thus, the determination of configurations requires prior structural information. The direct use of RDCs as restraints to construct structures based on RDCs has only recently begun also in organic compounds. No protocol has been published though that uses the vector and dynamics information available in multialignment data sets directly for the joint determination of conformation and configuration of organic compounds. This is proposed in the current study. We show that by employing these data, even a flat or random start structure converges into the correctly configured structure when employing multiple alignment data sets in our iterative procedure. The requirements in terms of the number of RDCs and alignment media necessary are discussed in detail.

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.

The Role of Conformational Dynamics in the Recognition and Regulation of Ubiquitination

The ubiquitination pathway is central to many cell signaling and regulatory events. One of the intriguing aspects of the pathway is the combinatorial sophistication of substrate recognition and ubiquitin chain building determinations. The abundant structural and biological data portray several characteristic protein folds among E2 and E3 proteins, and the understanding of the combinatorial complexity that enables interaction with much of the human proteome is a major goal to developing targeted and selective manipulation of the pathway. With the commonality of some folds, there are likely other aspects that can provide differentiation and recognition. These aspects involve allosteric effects and conformational dynamics that can direct recognition and chain building processes. In this review, we will describe the current state of the knowledge for conformational dynamics across a wide timescale, address the limitations of present approaches, and illustrate the potential to make new advances in connecting dynamics with ubiquitination regulation.

Generating Five Independent Molecular Alignments for Simultaneous Protein Structure and Dynamics Determination Using Nuclear Magnetic Resonance Spectroscopy

Residual dipolar couplings (RDCs) are commonly used in NMR for protein structure and dynamics studies, but it is challenging to generate five independent RDC data sets (required for simultaneous structure and dynamics determination) for most protein molecules in the magnetic field. In this work, a reporter protein with a lanthanide tag is introduced to create five independent alignments. This reporter protein is then attached to target proteins where five independent sets of RDCs are also obtained for the target proteins. The fitting of RDCs provides important information about the structure and dynamics of the target proteins. The method is simple and effective and, in principle, can be used to generate complete sets of RDCs for different protein molecules.

Determination of Configuration and Conformation of a Reserpine Derivative with Seven Stereogenic Centers Using Molecular Dynamics with RDC-Derived Tensorial Constraints*

NMR-based determination of the configuration of complex molecules containing many stereocenters is often not possible using traditional NOE data and coupling patterns. Making use of residual dipolar couplings (RDCs), we were able to determine the relative configuration of a natural product containing seven stereocenters, including a chiral amine lacking direct RDC data. To identify the correct relative configuration out of 32 possible ones, experimental RDCs were used in three different approaches for data interpretation: by fitting experimental data based singular value decomposition (SVD) using a single alignment tensor and either (i) a single conformer or (ii) multiple conformers, or alternatively (iii) using molecular dynamics simulations with tensorial orientational constraints (MDOC). Even though in all three approaches one and the same configuration could be selected and clear discrimination between possible configurations was achieved, the experimental data was not fully satisfied by the methods based on single tensor approaches. While these two approaches are faster, only MDOC is able to fully reproduce experimental results, as the obtained conformational ensemble adequately covers the conformational space necessary to describe the molecule with inherent flexibility.

Design and applications of lanthanide chelating tags for pseudocontact shift NMR spectroscopy with biomacromolecules

In this review, lanthanide chelating tags and their applications to pseudocontact shift NMR spectroscopy as well as analysis of residual dipolar couplings are covered. A complete overview is presented of DOTA-derived and non-DOTA-derived lanthanide chelating tags, critical points in the design of lanthanide chelating tags as appropriate linker moieties, their stability under reductive conditions, e.g., for in-cell applications, the magnitude of the anisotropy transferred from the lanthanide chelating tag to the biomacromolecule under investigation and structural properties, as well as conformational bias of the lanthanide chelating tags are discussed. Furthermore, all DOTA-derived lanthanide chelating tags used for PCS NMR spectroscopy published to date are displayed in tabular form, including their anisotropy parameters, with all employed lanthanide ions, C_B-Ln distances and tagging reaction conditions, i.e., the stoichiometry of lanthanide chelating tags, pH, buffer composition, temperature and reaction time. Additionally, applications of lanthanide chelating tags for pseudocontact shifts and residual dipolar couplings that have been reported for proteins, protein-protein and protein-ligand complexes, carbohydrates, carbohydrate-protein complexes, nucleic acids and nucleic acid-protein complexes are presented and critically reviewed. The vast and impressive range of applications of lanthanide chelating tags to structural investigations of biomacromolecules in solution clearly illustrates the significance of this particular field of research. The extension of the repertoire of lanthanide chelating tags from proteins to nucleic acids holds great promise for the determination of valuable structural parameters and further developments in characterizing intermolecular interactions.

Protein NMR: Boundless opportunities

Over the past approximately three decades, isotope-directed NMR spectroscopy has become a powerful method for determining 3D structures of biological macromolecules and their complexes in solution. From a structural perspective NMR provides an invaluable tool for studying systems that are not amenable to crystallization, including intrinsically disordered proteins and weak complexes. In contrast to both X-ray crystallography and cryo-electron microscopy which afford a largely static view of the systems under consideration, the great power of NMR lies in its ability to quantitatively probe exchange dynamics between interconverting states, and to reveal and characterize at atomic resolution the existence of transient states that may be populated at levels as low as 1%. Such "excited" states play a key role in macromolecular recognition, allostery, signal transduction and macromolecular assembly, including the initial events involved in aggregation and amyloid formation. Optimal application of NMR to such systems of fundamental biological interest requires a sound footing of the physical underpinnings of today's and tomorrow's sophisticated NMR experiments.

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.

Companion Simulations and Modeling to NMR-Based Dynamical Studies of Proteins

NMR-based studies of protein dynamics and molecular simulations have a synergistic relationship. Molecular simulations, in combination with interpretative theoretical models, leverage the dynamical information obtained from NMR. They provide the concrete physical schema underlying the quantities measured by NMR, and help extend the range of applications beyond the strictly dynamic properties. NMR data in turn provide concrete data to test and improve the potential functions used for simulation of dynamics of proteins. The concept of time correlation functions is central to the understanding of many dynamical processes. Their evaluation through atomistic simulations is discussed, with application to different dynamical quantities measured by NMR. While advances in computers have made such atomistic simulations almost routine, the companion use of simple interpretive models is stressed, to provide not just numbers but physical insight.

Solution NMR views of dynamical ordering of biomacromolecules

BACKGROUND

To understand the mechanisms related to the 'dynamical ordering' of macromolecules and biological systems, it is crucial to monitor, in detail, molecular interactions and their dynamics across multiple timescales. Solution nuclear magnetic resonance (NMR) spectroscopy is an ideal tool that can investigate biophysical events at the atomic level, in near-physiological buffer solutions, or even inside cells.

SCOPE OF REVIEW

In the past several decades, progress in solution NMR has significantly contributed to the elucidation of three-dimensional structures, the understanding of conformational motions, and the underlying thermodynamic and kinetic properties of biomacromolecules. This review discusses recent methodological development of NMR, their applications and some of the remaining challenges.

MAJOR CONCLUSIONS

Although a major drawback of NMR is its difficulty in studying the dynamical ordering of larger biomolecular systems, current technologies have achieved considerable success in the structural analysis of substantially large proteins and biomolecular complexes over 1MDa and have characterised a wide range of timescales across which biomolecular motion exists. While NMR is well suited to obtain local structure information in detail, it contributes valuable and unique information within hybrid approaches that combine complementary methodologies, including solution scattering and microscopic techniques.

GENERAL SIGNIFICANCE

For living systems, the dynamic assembly and disassembly of macromolecular complexes is of utmost importance for cellular homeostasis and, if dysregulated, implied in human disease. It is thus instructive for the advancement of the study of the dynamical ordering to discuss the potential possibilities of solution NMR spectroscopy and its applications. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

Block-restraining of residual dipolar couplings to allow fluctuating relative alignments of molecular subdomains

Residual dipolar couplings (RDCs), unlike most other types of NMR observables, provide orientational information, reporting on the alignment of inter-spin vectors (ISVs) relative to the magnetic field. A great challenge in using experimental RDCs to restrain molecular dynamics (MD) simulations is how to represent this alignment. An alignment tensor is often used to parameterise the contribution of molecular alignment to the angular dependence of RDCs. All ISVs that share the same tensor have fixed relative alignment, i.e. if just one tensor is used, the molecule is internally rigid. Here we propose and illustrate a method for subdividing molecules into individually aligned blocks during MD simulations restrained to fit RDCs. This allows the relative orientation of each block to vary during the simulation, which in turn ensures that the internal structure of each block is more realistically reproduced.

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.

The Exact NOE as an Alternative in Ensemble Structure Determination

The structure-function paradigm is increasingly replaced by the structure-dynamics-function paradigm. All protein activity is steered by the interplay between enthalpy and entropy. Conformational dynamics serves as a proxy of conformational entropy. Therefore, it is essential to study not only the average conformation but also the spatial sampling of a protein on all timescales. To this purpose, we have established a protocol for determining multiple-state ensembles of proteins based on exact nuclear Overhauser effects (eNOEs). We have recently extended our previously reported eNOE data set for the protein GB3 by a very large set of backbone and side-chain residual dipolar couplings and three-bond J couplings. Here, we demonstrate that at least four structural states are required to represent the complete data set by dissecting the contributions to the CYANA target function, which quantifies restraint violations in structure calculation. We present a four-state ensemble of GB3, which largely preserves the characteristics obtained from eNOEs only. Due to the abundance of the input data, the ensemble and χ(1) angles in particular are well suited for cross-validation of the input data and comparison to x-ray structures. Principal component analysis is used to automatically identify and validate relevant states of the ensembles. Overall, our findings suggest that eNOEs are a valuable alternative to traditional NMR probes in spatial elucidation of proteins.

Improved Accuracy from Joint X-ray and NMR Refinement of a Protein-RNA Complex Structure

Integrated experimental approaches play an increasingly important role in structural biology, taking advantage of the complementary information provided by different techniques. In particular, the combination of NMR data with X-ray diffraction patterns may provide accurate and precise information about local conformations not available from average-resolution X-ray structures alone. Here, we refined the structure of a ternary protein-protein-RNA complex comprising three domains, Sxl and Unr, bound to a single-stranded region derived in the msl2 mRNA. The joint X-ray and NMR refinement reveals that-despite the poor quality of the fit found for the original structural model-the NMR data can be largely accommodated within the uncertainty in the atom positioning (structural noise) from the primary X-ray data and that the overall domain arrangements and binding interfaces are preserved on passing from the crystalline state to the solution. The refinement highlights local conformational differences, which provide additional information on specific features of the structure. For example, conformational dynamics and heterogeneity observed at the interface between the CSD1 and the Sxl protein components in the ternary complex are revealed by the combination of NMR and crystallographic data. The joint refinement protocol offers unique opportunities to detect structural differences arising from various experimental conditions and reveals static or dynamic differences in the conformation of the biomolecule between the solution and the crystals.

Validation of Molecular Dynamics Simulations of Biomolecules Using NMR Spin Relaxation as Benchmarks: Application to the AMBER99SB Force Field

Biological function of biomolecules is accompanied by a wide range of motional behavior. Accurate modeling of dynamics by molecular dynamics (MD) computer simulations is therefore a useful approach toward the understanding of biomolecular function. NMR spin relaxation measurements provide rigorous benchmarks for assessing important aspects of MD simulations, such as the amount and time scales of conformational space sampling, which are intimately related to the underlying molecular mechanics force field. Until recently, most simulations produced trajectories that exhibited too much dynamics particularly in flexible loop regions. Recent modifications made to the backbone φ and ψ torsion angle potentials of the AMBER and CHARMM force fields indicate that these changes produce more realistic molecular dynamics behavior. To assess the consequences of these changes, we performed a series of 5-20 ns molecular dynamics trajectories of human ubiquitin using the AMBER99 and AMBER99SB force fields for different conditions and water models and compare the results with NMR experimental backbone N-H S(2) order parameters. A quantitative analysis of the trajectories shows significantly improved agreement with experimental NMR data for the AMBER99SB force field as compared to AMBER99. Because NMR spin relaxation data (T1, T2, NOE) reflect the combined effects of spatial and temporal fluctuations of bond vectors, it is found that comparison of experimental and back-calculated NMR spin-relaxation data provides a more objective way of assessing the quality of the trajectory than order parameters alone. Analysis of a key mobile β-hairpin in ubiquitin demonstrates that the dynamics of mobile sites are not only reduced by the modified force field, but the extent of motional correlations between amino acids is also markedly diminished.

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.

Starting-Condition Dependence of Order Parameters Derived from Molecular Dynamics Simulations

We have studied how backbone N-H S(2) order parameters calculated from molecular dynamics simulations depend on the method used to calculate them, the starting conditions, and the length of the simulations. Using the carbohydrate binding domain of galectin-3 in the free and lactose-bound states as a test case, we compared the calculated order parameters with experimental data from NMR relaxation. The results indicate that the sampling can be improved by using several starting structures, taking into account conformational heterogeneity reported in crystal structures. However, the improvement is rather limited, and for 93% of the dihedrals that have alternative conformations in the crystal structures, the conformational space is well sampled even if a single conformation is used as the starting structure. Moreover, the agreement with experimental data is improved when using several short simulations, rather than a single long simulation. In the present case, we find that ∼10 independent simulations provide sufficient sampling, and the ideal length of the simulations is ∼10 ns, which is ∼25% longer than the global correlation time for rotational diffusion. On the other hand, the equilibration time appears to be less important, and our results suggest that an equilibration time of 0.25 ns is sufficient. We have also compared four different methods to extract the order parameters from the simulations, namely, the autocorrelation function and isotropic reorientational eigenmode dynamics using three different window sizes. Overall, the four methods yield comparable results, but large differences between the methods may serve to pinpoint cases for which the calculated parameters are unreliable.

Side Chain Conformational Distributions of a Small Protein Derived from Model-Free Analysis of a Large Set of Residual Dipolar Couplings

Accurate quantitative measurement of structural dispersion in proteins remains a prime challenge to both X-ray crystallography and NMR spectroscopy. Here we use a model-free approach based on measurement of many residual dipolar couplings (RDCs) in differentially orienting aqueous liquid crystalline solutions to obtain the side chain χ₁ distribution sampled by each residue in solution. Applied to the small well-ordered model protein GB3, our approach reveals that the RDC data are compatible with a single narrow distribution of side chain χ₁ angles for only about 40% of the residues. For more than half of the residues, populations greater than 10% for a second rotamer are observed, and four residues require sampling of three rotameric states to fit the RDC data. In virtually all cases, sampled χ₁ values are found to center closely around ideal g^–, g⁺ and t rotameric angles, even though no rotamer restraint is used when deriving the sampled angles. The root-mean-square difference between experimental ³J_HαHβ couplings and those predicted by the Haasnoot-parametrized, motion-adjusted Karplus equation reduces from 2.05 to 0.75 Hz when using the new rotamer analysis instead of the 1.1-Å X-ray structure as input for the dihedral angles. A comparison between observed and predicted ³J_HαHβ values suggests that the root-mean-square amplitude of χ₁ angle fluctuations within a given rotamer well is ca. 20°. The quantitatively defined side chain rotamer equilibria obtained from our study set new benchmarks for evaluating improved molecular dynamics force fields, and also will enable further development of quantitative relations between side chain chemical shift and structure.

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

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

Unveiling Inherent Degeneracies in Determining Population-Weighted Ensembles of Interdomain Orientational Distributions Using NMR Residual Dipolar Couplings: Application to RNA Helix Junction Helix Motifs

A growing number of studies employ time-averaged experimental data to determine dynamic ensembles of biomolecules. While it is well-known that different ensembles can satisfy experimental data to within error, the extent and nature of these degeneracies, and their impact on the accuracy of the ensemble determination remains poorly understood. Here, we use simulations and a recently introduced metric for assessing ensemble similarity to explore degeneracies in determining ensembles using NMR residual dipolar couplings (RDCs) with specific application to A-form helices in RNA. Various target ensembles were constructed representing different domain-domain orientational distributions that are confined to a topologically restricted (<10%) conformational space. Five independent sets of ensemble averaged RDCs were then computed for each target ensemble and a "sample and select" scheme used to identify degenerate ensembles that satisfy RDCs to within experimental uncertainty. We find that ensembles with different ensemble sizes and that can differ significantly from the target ensemble (by as much as ∑Ω ∼ 0.4 where ∑Ω varies between 0 and 1 for maximum and minimum ensemble similarity, respectively) can satisfy the ensemble averaged RDCs. These deviations increase with the number of unique conformers and breadth of the target distribution, and result in significant uncertainty in determining conformational entropy (as large as 5 kcal/mol at T = 298 K). Nevertheless, the RDC-degenerate ensembles are biased toward populated regions of the target ensemble, and capture other essential features of the distribution, including the shape. Our results identify ensemble size as a major source of uncertainty in determining ensembles and suggest that NMR interactions such as RDCs and spin relaxation, on their own, do not carry the necessary information needed to determine conformational entropy at a useful level of precision. The framework introduced here provides a general approach for exploring degeneracies in ensemble determination for different types of experimental data.

Assessing the potential of atomistic molecular dynamics simulations to probe reversible protein-protein recognition and binding

Protein-protein recognition and binding are governed by diffusion, noncovalent forces and conformational flexibility, entangled in a way that only molecular dynamics simulations can dissect at high resolution. Here we exploited ubiquitin's noncovalent dimerization equilibrium to assess the potential of atomistic simulations to reproduce reversible protein-protein binding, by running submicrosecond simulations of systems with multiple copies of the protein at millimolar concentrations. The simulations essentially fail because they lead to aggregates, yet they reproduce some specificity in the binding interfaces as observed in known covalent and noncovalent ubiquitin dimers. Following similar observations in literature we hint at electrostatics and water descriptions as the main liable force field elements, and propose that their optimization should consider observables relevant to multi-protein systems and unfolded proteins. Within limitations, analysis of binding events suggests salient features of protein-protein recognition and binding, to be retested with improved force fields. Among them, that specific configurations of relative direction and orientation seem to trigger fast binding of two molecules, even over 50 Å distances; that conformational selection can take place within surface-to-surface distances of 10 to 40 Å i.e. well before actual intermolecular contact; and that establishment of contacts between molecules further locks their conformations and relative orientations.

NMR studies of dynamic biomolecular conformational ensembles

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

Towards understanding the molecular recognition process in prokaryotic zinc-finger domain

Eukaryotic Cys2His2 zinc finger domain is one of the most common and important structural motifs involved in protein-DNA interaction. The recognition motif is characterized by the tetrahedral coordination of a zinc ion by conserved cysteine and histidine residues. We have characterized the prokaryotic Cys2His2 zinc finger motif, included in the DNA binding region (Ros87) of Ros protein from Agrobacterium tumefaciens, demonstrating that, although possessing a similar zinc coordination sphere, this domain presents significant differences from its eukaryotic counterpart. Furthermore, basic residues flanking the zinc binding region on either side have been demonstrated, by Electrophoretic Mobility Shift Assay (EMSA) experiments, to be essential for Ros DNA binding. In spite of this wealth of knowledge, the structural details of the mechanism through which the prokaryotic zinc fingers recognize their target genes are still unclear. Here, to gain insights into the molecular DNA recognition process of prokaryotic zinc finger domains we applied a strategy in which we performed molecular docking studies using a combination of Nuclear Magnetic Resonance (NMR) and Molecular Dynamics (MD) simulations data. The results demonstrate that the MD ensemble provides a reasonable picture of Ros87 backbone dynamics in solution. The Ros87-DNA model indicates that the interaction involves the first two residue of the first α-helix, and several residues located in the basic regions flanking the zinc finger domain. Interestingly, the prokaryotic zinc finger domain, mainly with the C-terminal tail that is wrapped around the DNA, binds a more extended recognition site than the eukaryotic counterpart. Our analysis demonstrates that the introduction of the protein flexibility in docking studies can improve, in terms of accuracy, the quality of the obtained models and could be particularly useful for protein showing high conformational heterogeneity as well as for computational drug design applications.

Correlated inter-domain motions in adenylate kinase

Correlated inter-domain motions in proteins can mediate fundamental biochemical processes such as signal transduction and allostery. Here we characterize at structural level the inter-domain coupling in a multidomain enzyme, Adenylate Kinase (AK), using computational methods that exploit the shape information encoded in residual dipolar couplings (RDCs) measured under steric alignment by nuclear magnetic resonance (NMR). We find experimental evidence for a multi-state equilibrium distribution along the opening/closing pathway of Adenylate Kinase, previously proposed from computational work, in which inter-domain interactions disfavour states where only the AMP binding domain is closed. In summary, we provide a robust experimental technique for study of allosteric regulation in AK and other enzymes.

NMR approaches for structural analysis of multidomain proteins and complexes in solution

NMR spectroscopy is a key method for studying the structure and dynamics of (large) multidomain proteins and complexes in solution. It plays a unique role in integrated structural biology approaches as especially information about conformational dynamics can be readily obtained at residue resolution. Here, we review NMR techniques for such studies focusing on state-of-the-art tools and practical aspects. An efficient approach for determining the quaternary structure of multidomain complexes starts from the structures of individual domains or subunits. The arrangement of the domains/subunits within the complex is then defined based on NMR measurements that provide information about the domain interfaces combined with (long-range) distance and orientational restraints. Aspects discussed include sample preparation, specific isotope labeling and spin labeling; determination of binding interfaces and domain/subunit arrangements from chemical shift perturbations (CSP), nuclear Overhauser effects (NOEs), isotope editing/filtering, cross-saturation, and differential line broadening; and based on paramagnetic relaxation enhancements (PRE) using covalent and soluble spin labels. Finally, the utility of complementary methods such as small-angle X-ray or neutron scattering (SAXS, SANS), electron paramagnetic resonance (EPR) or fluorescence spectroscopy techniques is discussed. The applications of NMR techniques are illustrated with studies of challenging (high molecular weight) protein complexes.

A tensor-free method for the structural and dynamical refinement of proteins using residual dipolar couplings

Residual dipolar couplings (RDCs) are parameters measured in nuclear magnetic resonance spectroscopy that can provide exquisitely detailed information about the structure and dynamics of biological macromolecules. We describe here a method of using RDCs for the structural and dynamical refinement of proteins that is based on the observation that the RDC between two atomic nuclei depends directly on the angle ϑ between the internuclear vector and the external magnetic field. For every pair of nuclei for which an RDC is available experimentally, we introduce a structural restraint to minimize the deviation from the value of the angle ϑ derived from the measured RDC and that calculated in the refinement protocol. As each restraint involves only the calculation of the angle ϑ of the corresponding internuclear vector, the method does not require the definition of an overall alignment tensor to describe the preferred orientation of the protein with respect to the alignment medium. Application to the case of ubiquitin demonstrates that this method enables an accurate refinement of the structure and dynamics of this protein to be obtained.

ORIUM: optimized RDC-based Iterative and Unified Model-free analysis

Residual dipolar couplings (RDCs) are NMR parameters that provide both structural and dynamic information concerning inter-nuclear vectors, such as N-H(N) and Cα-Hα bonds within the protein backbone. Two approaches for extracting this information from RDCs are the model free analysis (MFA) (Meiler et al. in J Am Chem Soc 123:6098-6107, 2001; Peti et al. in J Am Chem Soc 124:5822-5833, 2002) and the direct interpretation of dipolar couplings (DIDCs) (Tolman in J Am Chem Soc 124:12020-12030, 2002). Both methods have been incorporated into iterative schemes, namely the self-consistent RDC based MFA (SCRM) (Lakomek et al. in J Biomol NMR 41:139-155, 2008) and iterative DIDC (Yao et al. in J Phys Chem B 112:6045-6056, 2008), with the goal of removing the influence of structural noise in the MFA and DIDC formulations. Here, we report a new iterative procedure entitled Optimized RDC-based Iterative and Unified Model-free analysis (ORIUM). ORIUM unifies theoretical concepts developed in the MFA, SCRM, and DIDC methods to construct a computationally less demanding approach to determine these structural and dynamic parameters. In all schemes, dynamic averaging reduces the actual magnitude of the alignment tensors complicating the determination of the absolute values for the generalized order parameters. To readdress this scaling issue that has been previously investigated (Lakomek et al. in J Biomol NMR 41:139-155, 2008; Salmon et al. in Angew Chem Int Edit 48:4154-4157, 2009), a new method is presented using only RDC data to establish a lower bound on protein motion, bypassing the requirement of Lipari-Szabo order parameters. ORIUM and the new scaling procedure are applied to the proteins ubiquitin and the third immunoglobulin domain of protein G (GB3). Our results indicate good agreement with the SCRM and iterative DIDC approaches and signify the general applicability of ORIUM and the proposed scaling for the extraction of inter-nuclear vector structural and dynamic content.

New opportunities for tensor-free calculations of residual dipolar couplings for the study of protein dynamics

Residual dipolar couplings (RDCs) can provide exquisitely detailed information about the structure and dynamics of proteins. It is challenging, however, to extract such information from RDC measurements in conformationally heterogeneous states of proteins because of the complex relationship between RDCs and protein structures. To obtain new insights into this problem, we discuss methods of calculating the RDCs that do not require the definition of an alignment tensor. These methods can help in particular in the search of effective ways to use RDCs to characterise disordered or partially disordered states of proteins.

Improved cross validation of a static ubiquitin structure derived from high precision residual dipolar couplings measured in a drug-based liquid crystalline phase

The antibiotic squalamine forms a lyotropic liquid crystal at very low concentrations in water (0.3-3.5% w/v), which remains stable over a wide range of temperature (1-40 °C) and pH (4-8). Squalamine is positively charged, and comparison of the alignment of ubiquitin relative to 36 previously reported alignment conditions shows that it differs substantially from most of these, but is closest to liquid crystalline cetyl pyridinium bromide. High precision residual dipolar couplings (RDCs) measured for the backbone (1)H-(15)N, (15)N-(13)C', (1)H(α)-(13)C(α), and (13)C'-(13)C(α) one-bond interactions in the squalamine medium fit well to the static structural model previously derived from NMR data. Inclusion into the structure refinement procedure of these RDCs, together with (1)H-(15)N and (1)H(α)-(13)C(α) RDCs newly measured in Pf1, results in improved agreement between alignment-induced changes in (13)C' chemical shift, (3)JHNHα values, and (13)C(α)-(13)C(β) RDCs and corresponding values predicted by the structure, thereby validating the high quality of the single-conformer structural model. This result indicates that fitting of a single model to experimental data provides a better description of the average conformation than does averaging over previously reported NMR-derived ensemble representations. The latter can capture dynamic aspects of a protein, thus making the two representations valuable complements to one another.

NMR studies of nucleic acid dynamics

Nucleic acid structures have to satisfy two diametrically opposite requirements; on one hand they have to adopt well-defined 3D structures that can be specifically recognized by proteins; on the other hand, their structures must be sufficiently flexible to undergo very large conformational changes that are required during key biochemical processes, including replication, transcription, and translation. How do nucleic acids introduce flexibility into their 3D structure without losing biological specificity? Here, I describe the development and application of NMR spectroscopic techniques in my laboratory for characterizing the dynamic properties of nucleic acids that tightly integrate a broad set of NMR measurements, including residual dipolar couplings, spin relaxation, and relaxation dispersion with sample engineering and computational approaches. This approach allowed us to obtain fundamental new insights into directional flexibility in nucleic acids that enable their structures to change in a very specific functional manner.

Interdomain dynamics explored by paramagnetic NMR

An ensemble-based approach is presented to explore the conformational space sampled by a multidomain protein showing moderate interdomain dynamics in terms of translational and rotational motions. The strategy was applied on a complex of calmodulin (CaM) with the IQ-recognition motif from the voltage-gated calcium channel Ca(v)1.2 (IQ), which adopts three different interdomain orientations in the crystal. The N60D mutant of calmodulin was used to collect pseudocontact shifts and paramagnetically induced residual dipolar couplings for six different lanthanide ions. Then, starting from the crystal structure, pools of conformations were generated by free MD. We found the three crystal conformations in solution, but four additional MD-derived conformations had to be included into the ensemble to fulfill all the paramagnetic data and cross-validate optimally against unused paramagnetic data. Alternative approaches led to similar ensembles. Our "ensemble" approach is a simple and efficient tool to probe and describe the interdomain dynamics and represents a general method that can be used to provide a proper ensemble description of multidomain proteins.

Measuring dynamic and kinetic information in the previously inaccessible supra-τ(c) window of nanoseconds to microseconds by solution NMR spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful tool that has enabled experimentalists to characterize molecular dynamics and kinetics spanning a wide range of time-scales from picoseconds to days. This review focuses on addressing the previously inaccessible supra-tc window (defined as τ(c) < supra-τ(c) < 40 μs; in which tc is the overall tumbling time of a molecule) from the perspective of local inter-nuclear vector dynamics extracted from residual dipolar couplings (RDCs) and from the perspective of conformational exchange captured by relaxation dispersion measurements (RD). The goal of the first section is to present a detailed analysis of how to extract protein dynamics encoded in RDCs and how to relate this information to protein functionality within the previously inaccessible supra-τ(c) window. In the second section, the current state of the art for RD is analyzed, as well as the considerable progress toward pushing the sensitivity of RD further into the supra-τ(c) scale by up to a factor of two (motion up to 25 μs). From the data obtained with these techniques and methodology, the importance of the supra-τ(c) scale for protein function and molecular recognition is becoming increasingly clearer as the connection between motion on the supra-τ(c) scale and protein functionality from the experimental side is further strengthened with results from molecular dynamics simulations.

Characterization of the interdomain motions in hen lysozyme using residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations

Hen lysozyme is an enzyme characterized by the presence of two domains whose relative motions are involved in the mechanism of binding and release of the substrates. By using residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations, we characterize the breathing motions describing the interdomain fluctuations of this protein. We found that the ensemble of conformations that we determined spans the entire range of structures of hen lysozyme deposited in the Protein Data Bank, including both the free and bound states, suggesting that the thermal motions in the free state provide access to the structures populated upon binding. The approach that we present illustrates how the use of residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations makes it possible to explore conformational fluctuations of a relatively large amplitude in proteins.

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.

Modulating alignment of membrane proteins in liquid-crystalline and oriented gel media by changing the size and charge of phospholipid bicelles

We demonstrate that alignment of a structured peptide or small protein solubilized in mixed phospholipid:detergent micelles or bicelles, when embedded in a compressed gel or liquid crystalline medium, can be altered by either changing the phospholipid aggregate shape, charge, or both together. For the hemagglutinin fusion peptide solubilized in bicelles, we show that bicelle shape and charge do not change its helical hairpin structure but impact its alignment relative to the alignment medium, both in charged compressed acrylamide gel and in liquid crystalline d(GpG). The method can be used to generate sets of residual dipolar couplings that correspond to orthogonal alignment tensors, and holds promise for high-resolution structural refinement and dynamic mapping of membrane proteins.

A general method for constructing atomic-resolution RNA ensembles using NMR residual dipolar couplings: the basis for interhelical motions revealed

The ability to modulate alignment and measure multiple independent sets of NMR residual dipolar couplings (RDCs) has made it possible to characterize internal motions in proteins at atomic resolution and with time scale sensitivity ranging from picoseconds up to milliseconds. The application of such methods to the study of RNA dynamics, however, remains fundamentally limited by the inability to modulate alignment and by strong couplings between internal and overall motions that complicate the quantitative interpretation of RDCs. Here, we address this problem by showing that RNA alignment can be generally modulated, in a controlled manner, by variable elongation of A-form helices and that the information contained within the measured RDCs can be extracted even in the presence of strong couplings between motions and overall alignment via structure-based prediction of alignment. Using this approach, four RDC data sets, and a broad conformational pool obtained from a 8.2 μs molecular dynamics simulation, we successfully construct and validate an atomic resolution ensemble of human immunodeficiency virus type I transactivation response element RNA. This ensemble reveals local motions in and around the bulge involving changes in stacking and hydrogen-bonding interactions, which are undetectable by traditional spin relaxation and drive global changes in interhelical orientation. This new approach broadens the scope of using RDCs in characterizing the dynamics of nucleic acids.