Influence of the fluctuations of the alignment tensor on the analysis of the structure and dynamics of proteins using residual dipolar couplings

It has been suggested that the fluctuations of the alignment tensor can affect the results of procedures for characterizing the structure and the dynamics of proteins using residual dipolar couplings. We show here that the very significant fluctuations of the steric alignment tensor caused by the dynamics of proteins can be safely ignored when they do not correlate with those of the bond vectors. A detailed analysis of these correlations in the protein ubiquitin reveals that their effects are negligible for the analysis of backbone motions within secondary structure elements, but also that they may be significant in turns, loops and side chains, especially for bond vectors that have small residual dipolar couplings. Our results suggest that methods that explicitly consider the motions of the alignment tensor will be needed to study the large-scale structural fluctuations that take place on the millisecond timescale, which are often important for the biological function of proteins, from residual dipolar coupling measurements.     

Principal component method for assessing structural heterogeneity across multiple alignment media

The recent availability of residual dipolar coupling measurements in a variety of different alignment media raises the question to what extent biomolecular structure and dynamics are differentially affected by their presence. A computational method is presented that allows the sensitive assessment of such changes using dipolar couplings measured in six or more alignment media. The method is based on a principal component analysis of the covariance matrix of the dipolar couplings. It does not require a priori structural or dynamic information nor knowledge of the alignment tensors and their orientations. In the absence of experimental errors, the covariance matrix has at most five nonzero eigenvalues if the structure and dynamics of the biomolecule is the same in all media. In contrast, differential structural and dynamic changes lead to additional nonzero eigenvalues. Characteristic features of the eigenvalue distribution in the absence and presence of noise are discussed using dipolar coupling data calculated from conformational ensembles taken from a molecular dynamics trajectory of native ubiquitin.     

Structural characterization of unfolded states of apomyoglobin using residual dipolar couplings

The conformational propensities of unfolded states of apomyoglobin have been investigated by measurement of residual dipolar couplings between (15)N and (1)H in backbone amide groups. Weak alignment of apomyoglobin in acid and urea-unfolded states was induced with both stretched and compressed polyacrylamide gels. In 8 M urea solution at pH 2.3, conditions under which apomyoglobin contains no detectable secondary or tertiary structure, significant residual dipolar couplings of uniform sign were observed for all residues. At pH 2.3 in the absence of urea, a change in the magnitude and/or sign of the residual dipolar couplings occurs in local regions of the polypeptide where there is a high propensity for helical secondary structure. These results are interpreted on the basis of the statistical properties of the unfolded polypeptide chain, viewed as a polymer of statistical segments. For a folded protein, the magnitude and sign of the residual dipolar couplings depend on the orientation of each bond vector relative to the alignment tensor of the entire molecule, which reorients as a single entity. For unfolded proteins, there is no global alignment tensor; instead, residual dipolar couplings are attributed to alignment of the statistical segments or of transient elements of secondary structure. For apomyoglobin in 8 M urea, the backbone is highly extended, with phi and psi dihedral angles favoring the beta or P(II) regions. Each statistical segment has a highly anisotropic shape, with the N-H bond vectors approximately perpendicular to the long axis, and becomes weakly aligned in the anisotropic environment of the strained acrylamide gels. Local regions of enhanced flexibility or chain compaction are characterized by a decrease in the magnitude of the residual dipolar couplings. The formation of a small population of helical structure in the acid-denatured state of apomyoglobin leads to a change in sign of the residual dipolar couplings in local regions of the polypeptide; the population of helix estimated from the residual dipolar couplings is in excellent agreement with that determined from chemical shifts. The alignment model described here for apomyoglobin can also explain the pattern of residual dipolar couplings reported previously for denatured states of staphylococcal nuclease and other proteins. In conjunction with other NMR experiments, residual dipolar couplings can provide valuable insights into the dynamic conformational propensities of unfolded and partly folded states of proteins and thereby help to chart the upper reaches of the folding landscape.     

Evaluation of uncertainty in alignment tensors obtained from dipolar couplings

Residual dipolar couplings and their corresponding alignment tensors are useful for structural analysis of macromolecules. The error in an alignment tensor, derived from residual dipolar couplings on the basis of a known structure, is determined not only by the accuracy of the measured couplings but also by the uncertainty in the structure (structural noise). This dependence is evaluated quantitatively on the basis of simulated structures using Monte-Carlo type analyses. When large numbers of dipolar couplings are available, structural noise is found to result in a systematic underestimate of the magnitude of the alignment tensor. Particularly in cases where only few dipolar couplings are available, structural noise can cause significant errors in best-fitted alignment tensor values, making determination of the relative orientation of small fragments and evaluation of local backbone mobility from dipolar couplings difficult. An example for the protein ubiquitin demonstrates the inherent limitations in characterizing motions on the basis of local alignment tensor magnitudes.     

Molecular alignment of denatured states of staphylococcal nuclease with strained polyacrylamide gels and surfactant liquid crystalline phases

Residual dipolar couplings reflect the orientation of vectors between pairs of magnetic nuclei relative to a unique set of molecular axes. Thus, unlike NOEs and scalar couplings, dipolar couplings provide access to long-range structural information. A prerequisite for measurement of these NMR parameters is imposition of a weak net alignment, most simply by forcing the macromolecules to tumble in an asymmetric environment that restricts some orientations more than others. In this report, several denatured forms of staphylococcal nuclease are aligned by using compressed and stretched polyacrylamide gels, a nonionic type of lipid bilayer disk or bicelle, and a liquid crystalline phase formed by a cationic lipid. All three types of media can be used at high urea concentrations. While polyacrylamide gels and bicelles produce similar alignment tensors through steric interactions, a liquid crystalline phase of cetylpyridinium bromide aligns denatured nuclease along a different set of axes, presumably through electrostatic effects. The analysis of residual dipolar couplings collected with two different alignment tensors may permit the calculation of ensembles of conformations. The dipolar couplings observed for staphylococcal nuclease denatured with urea, by low pH or by deletion of residues from both termini, suggest that all denatured forms share a common "topology", one which has been shown previously to be native-like. Although SDS/nuclease complexes give sharp and disperse (1)H-(15)N correlation spectra, only small couplings are observed in strained polyacrylamide gels.     

The importance of being ordered: improving NMR structures using residual dipolar couplings

Residual dipolar couplings arise from small degrees of alignment of molecules in a magnetic field. Most biomolecules lack sufficient intrinsic magnetic susceptibility anisotropies for practical purposes; however, alignment can be achieved using dilute aqueous phospholipid mixtures, colloidal suspensions of rod-shaped viruses, complex phases of surfactant systems and strained gels. The stability of the liquid crystalline phases varies with respect to temperature range, pH variation and time and is critically dependent on sample composition and experimental conditions. The magnitude of the residual dipolar couplings depends upon the degree of ordering and allows the determination of the corresponding inter-nuclear vectors with respect to the molecule's alignment frame. Inclusion of dipolar constraints into NMR structure calculations leads to improved precision and accuracy of the resulting structures, especially in cases where the information content provided by traditional NOE constraints is limited. In addition, rapid evaluation of backbone protein folds and determination of the relative orientations of individual components in multi-molecular complexes have become feasible. Dipolar coupling based strategies may well emerge as the most critical developments, in establishing NMR as a valuable and competitive methodology in the structural genomics initiative.     

A unifying probabilistic framework for analyzing residual dipolar couplings

Residual dipolar couplings provide complementary information to the nuclear Overhauser effect measurements that are traditionally used in biomolecular structure determination by NMR. In a de novo structure determination, however, lack of knowledge about the degree and orientation of molecular alignment complicates the analysis of dipolar coupling data. We present a probabilistic framework for analyzing residual dipolar couplings and demonstrate that it is possible to estimate the atomic coordinates, the complete molecular alignment tensor, and the error of the couplings simultaneously. As a by-product, we also obtain estimates of the uncertainty in the coordinates and the alignment tensor. We show that our approach encompasses existing methods for determining the alignment tensor as special cases, including least squares estimation, histogram fitting, and elimination of an explicit alignment tensor in the restraint energy.     

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.     

Dipolar couplings as a probe of molecular dynamics and structure in solution.

The introduction of residual dipolar coupling methodology has increased the scope of structural biological problems that can be addressed by NMR spectroscopy. Conformational changes, the relative orientation of domains, and intermolecular complexes can now be characterized accurately and rapidly using NMR. The development of residual dipolar coupling methodology for the rapid recognition of homologous protein folds and for studies of submillisecond timescale dynamics has also seen considerable progress.     

Incorporating residual dipolar couplings into the NMR solution structure determination of nucleic acids

NMR solution structures of nucleic acids are generally less well defined than similar-sized proteins. Most NMR structures of nucleic acids are defined only by short-range interactions, such as intrabase-pair or sequential nuclear Overhauser effects (NOEs), and J-coupling constants, and there are no long-range structural data on the tertiary structure. Residual dipolar couplings represent an extremely valuable source of distance and angle information for macromolecules but they average to zero in isotropic solutions. With the recent advent of general methods for partial alignment of macromolecules in solution, residual dipolar couplings are rapidly becoming indispensable constraints for solution NMR structural studies. These residual dipolar couplings give long-range global structural information and thus complement the strictly local structural data obtained from standard NOE and torsion angle constraints. Such global structural data are especially important in nucleic acids due to the more elongated, less-globular structure of many DNAs and RNAs. Here we review recent progress in application of residual dipolar couplings to structural studies of nucleic acids. We also present results showing how refinement procedures affect the final solution structures of nucleic acids.Copyright 2001 John Wiley & Sons, Inc.     

Induced alignment and measurement of dipolar couplings of an SH2 domain through direct binding with filamentous phage

Large residual ¹⁵N-¹H dipolar couplings have been measured in a Src homology II domain aligned at Pf1 bacteriophage concentrations an order of magnitude lower than used for induction of a similar degree of alignment of nucleic acids and highly acidic proteins. An increase in ¹ H and ¹⁵N protein linewidths and a decrease in T₂ and T₁ relaxation time constants implicates a binding interaction between the protein and phage as the mechanism of alignment. However, the associated increased linewidth does not preclude the accurate measurement of large dipolar couplings in the aligned protein. A good correlation is observed between measured dipolar couplings and predicted values based on the high resolution NMR structure of the SH2 domain. The observation of binding-induced protein alignment promises to broaden the scope of alignment techniques by extending their applicability to proteins that are able to interact weakly with the alignment medium.     

Pressure‐induced structural transition of mature HIV‐1 protease from a combined NMR/MD simulation approach

We investigate the pressure‐induced structural changes in the mature human immunodeficiency virus type 1 protease dimer, using residual dipolar coupling (RDC) measurements in a weakly oriented solution. ¹D_NH RDCs were measured under high‐pressure conditions for an inhibitor‐free PR and an inhibitor‐bound complex, as well as for an inhibitor‐free multidrug resistant protease bearing 20 mutations (PR20). While PR20 and the inhibitor‐bound PR were little affected by pressure, inhibitor‐free PR showed significant differences in the RDCs measured at 600 bar compared with 1 bar. The structural basis of such changes was investigated by MD simulations using the experimental RDC restraints, revealing substantial conformational perturbations, specifically a partial opening of the flaps and the penetration of water molecules into the hydrophobic core of the subunits at high pressure. This study highlights the exquisite sensitivity of RDCs to pressure‐induced conformational changes and illustrates how RDCs combined with MD simulations can be used to determine the structural properties of metastable intermediate states on the folding energy landscape. Proteins 2015; 83:2117–2123. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.     

NMR approaches for monitoring domain orientations in calcium-binding proteins in solution using partial replacement of Ca2+ by Tb3+.

This work shows that the partial replacement of diamagnetic Ca2+ by paramagnetic Tb3+ in Ca2+/calmodulin systems in solution allows the measurement of interdomain NMR pseudocontact shifts and leads to magnetic alignment of the molecule such that significant residual dipolar couplings can be measured. Both these parameters can be used to provide structural information. Species in which Tb3+ ions are bound to only one domain of calmodulin (the N-domain) and Ca2+ ions to the other (the C-domain) provide convenient systems for measuring these parameters. The nuclei in the C-domain experience the local magnetic field induced by the paramagnetic Tb3+ ions bound to the other domain at distances of over 40 A from the Tb3+ ion, shifting the resonances for these nuclei. In addition, the Tb3+ ions bound to the N-domain of calmodulin greatly enhance the magnetic susceptibility anisotropy of the molecule so that a certain degree of alignment is produced due to interaction with the external magnetic field. In this way, dipolar couplings between nuclear spins are not averaged to zero due to solution molecular tumbling and yield dipolar coupling contributions to, for example, the one-bond 15N-1H splittings of up to 17 Hz in magnitude. The degree of alignment of the C-domain will also depend on the degree of orientational freedom of this domain with respect to the N-domain containing the Tb3+ ions. Pseudocontact shifts for NH groups and 1H-15N residual dipolar couplings for the directly bonded atoms have been measured for calmodulin itself, where the domains have orientational freedom, and for the complex of calmodulin with a target peptide from skeletal muscle myosin light chain kinase, where the domains have fixed orientations with respect to each other. The simultaneous measurements of these parameters for systems with domains in fixed orientations show great potential for the determination of the relative orientation of the domains.     

Complete protein structure determination using backbone residual dipolar couplings and sidechain rotamer prediction

Residual dipolar couplings provide significant structural information for proteins in the solution state, which makes them attractive for the rapid determination of protein structures. While dipolar couplings contain inherent structural ambiguities, these can be reduced via an overlap similarity measure that insists that protein fragments assigned to overlapping regions of the sequence must have self-consistent structures. This allows us to determine a backbone fold (including the correct C–C bond orientations) using only residual dipolar coupling data from one ordering medium. The resulting backbone structures are of sufficient quality to allow for modeling of sidechain rotamer states using a rotamer prediction algorithm and a force field employing the Surface Generalized Born continuum solvation model. We demonstrate the applicability of the method using experimental data for ubiquitin. These results illustrate the synergies that are possible between protein structural database and molecular modeling methods and NMR spectroscopy, and we expect that the further development of these methods will lead to the extraction of high resolution structural information from minimal NMR data.     

NMR approaches for monitoring domain orientations in calcium-binding proteins in solution using partial replacement of Ca by Tb

This work shows that the partial replacement of diamagnetic Ca²⁺ by paramagnetic Tb³⁺ in Ca²⁺/calmodulin systems in solution allows the measurement of interdomain NMR pseudocontact shifts and leads to magnetic alignment of the molecule such that significant residual dipolar couplings can be measured. Both these parameters can be used to provide structural information. Species in which Tb³⁺ ions are bound to only one domain of calmodulin (the N-domain) and Ca²⁺ ions to the other (the C-domain) provide convenient systems for measuring these parameters. The nuclei in the C-domain experience the local magnetic field induced by the paramagnetic Tb³⁺ ions bound to the other domain at distances of over 40 Å from the Tb³⁺ ion, shifting the resonances for these nuclei. In addition, the Tb³⁺ ions bound to the N-domain of calmodulin greatly enhance the magnetic susceptibility anisotropy of the molecule so that a certain degree of alignment is produced due to interaction with the external magnetic field. In this way, dipolar couplings between nuclear spins are not averaged to zero due to solution molecular tumbling and yield dipolar coupling contributions to, for example, the one-bond ¹⁵N-¹H splittings of up to 17 Hz in magnitude. The degree of alignment of the C-domain will also depend on the degree of orientational freedom of this domain with respect to the N-domain containing the Tb³⁺ ions. Pseudocontact shifts for NH groups and ¹H-¹⁵N residual dipolar couplings for the directly bonded atoms have been measured for calmodulin itself, where the domains have orientational freedom, and for the complex of calmodulin with a target peptide from skeletal muscle myosin light chain kinase, where the domains have fixed orientations with respect to each other. The simultaneous measurements of these parameters for systems with domains in fixed orientations show great potential for the determination of the relative orientation of the domains.     

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

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

Determination of residual dipolar couplings in homonuclear MOCCA-SIAM experiments

In solutions with partial molecular alignment, anisotropic magnetic interactions such as the chemical shift anisotropy, the electric quadrupole interaction, and the magnetic dipole-dipole interaction are no longer averaged out to zero in contrast to isotropic solutions. The resulting residual anisotropic magnetic interactions are increasingly used in biological NMR studies for the determination of 3D structures of proteins and other biomolecules. In the present paper we propose a new approach allowing the measurement of residual H^N-H dipolar couplings of non-isotope enriched proteins based on the application of the MOCCA-SIAM experiment. This experiment allows the measurement of homonuclear coupling constants with an accuracy of ca. ±0.2 Hz and is therefore particularly well suited to determine residual dipolar couplings at relatively low degrees of molecular orientation. The agreement between experimentally determined residual H^N-H couplings and calculated values is demonstrated for BPTI.     

Lanthanide induced residual dipolar couplings for the conformational investigation of peripheral 15NH2 moieties

The Ca₂ calbindin protein in which one calcium has been substituted with Ce(III), Yb(III) and Dy(III) displays substantial alignment in high magnetic fields due to the high anisotropy of the metal magnetic susceptibility. This property has allowed the measurement of residual dipolar coupling contributions to ¹ J _HNand ² J _HH couplings of asparagine and glutamine NH₂ moieties. Such data have been used to aid structural characterization of these groups. The exploitation of auto-orientation of magnetic anisotropic metalloproteins represents a step ahead in the investigation of the conformational space of peripheral residues that are not fixed by the protein folding.