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.     

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.     

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.     

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.     

NMR: prediction of molecular alignment from structure using the PALES software

Orientational restraints such as residual dipolar couplings promise to overcome many of the problems that traditionally limited liquid-state nuclear magnetic resonance spectroscopy. Recently, we developed methods to predict a molecular alignment tensor and thus residual dipolar couplings for a given molecular structure. This provides many new opportunities for the study of the structure and dynamics of proteins, nucleic acids, oligosaccharides and small molecules. This protocol details the use of the software PALES (Prediction of AlignmEnt from Structure) for prediction of an alignment tensor from a known three-dimensional (3D) coordinate file of a solute. The method is applicable to alignment of molecules in many neutral and charged orienting media and takes into account the molecular shape and 3D charge distribution of the molecule.     

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.     

Recognition of protein folds via dipolar couplings

Alignment of proteins in dilute liquid crystalline medium gives rise to residual dipolar couplings which provide orientational information of vectors connecting the interacting nuclei. Considering that proteins are mainly composed of regular secondary structures in a finite number of different mutual orientations, main chain dipolar couplings appear sufficient to reveal structural resemblance. Similarity between dipolar couplings measured from a protein and corresponding values computed from a known structure imply homologous structures. For dissimilar structures the agreement between experimental and calculated dipolar couplings remains poor. In this way protein folds can be readily recognized prior to a comprehensive structure determination. This approach has been demonstrated by showing the similarity in fold between the hitherto unknown structure of calerythrin and sarcoplasmic calcium-binding proteins from Nereis diversicolor and Branchiostoma lanceolatum with known crystal structures.     

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.     

Solution structure of calcium-saturated cardiac troponin C bound to cardiac troponin I

Cardiac troponin C (TnC) is composed of two globular domains connected by a flexible linker. In solution, linker flexibility results in an ill defined orientation of the two globular domains relative to one another. We have previously shown a decrease in linker flexibility in response to cardiac troponin I (cTnI) binding. To investigate the relative orientation of calcium-saturated TnC domains when bound to cTnI, (1)H-(15)N residual dipolar couplings were measured in two different alignment media. Similarity in alignment tensor orientation for the two TnC domains supports restriction of domain motion in the presence of cTnI. The relative spatial orientation of TnC domains bound to TnI was calculated from measured residual dipolar couplings and long-range distance restraints utilizing a rigid body molecular dynamics protocol. The relative domain orientation is such that hydrophobic pockets face each other, forming a latch to constrain separate helical segments of TnI. We have utilized this structure to successfully explain the observed functional consequences of linker region deletion mutants. Together, these studies suggest that, although linker plasticity is important, the ability of TnC to function in muscle contraction can be correlated with a preferred domain orientation and interdomain distance.     

Observation of residual dipolar couplings in short peptides

Residual dipolar couplings provide information on the orientation of individual bond vectors with respect to a unique set of molecular axes. We report that short peptides from 2 to 15 amino acids in length of arbitrary sequence exhibit a modest range of residual dipolar couplings when aligned in either strained polyacrylamide gels or alkyl-PEG bicelles. The absence of significant line broadening in gels suggests peptides align predominantly through steric interactions with the polyacrylamide matrix. However, broadening of NMR lines for a subset of residues aligned in bicelles indicates some peptides bind weakly to these lipid disks, yet a weak negative correlation between the couplings measured in gels and bicelles is consistent with steric hindrance playing a role in both media. The observation of dipolar couplings for peptides of length 10-15 suggests the statistical segment lengths of polypeptide chains must often be >10-15 residues, with data from denatured proteins indicating even larger values. Presumably, local side-chain backbone interactions severely restrict chain flexibility, with the cumulative effect of many such restrictions giving rise to biases in chain direction that may persist for the entire length of a protein chain. Comparison of experimental dipolar couplings for peptides with couplings calculated for ensembles of conformations generated by molecular dynamics should permit evaluation of the accuracy of molecular mechanics potentials in reproducing sequence-specific preferences for phi and psi angles.     

Simple multidimensional NMR experiments to obtain different types of one-bond dipolar couplings simultaneously

In order to measure residual dipolar couplings, the molecule under study has to be partially oriented in the presence of the magnetic field. It has been observed that some protein samples are not stable under the conditions imposed by the orienting media. If different types of dipolar couplings are measured sequentially, their values will not agree with a unique alignment tensor that is changing slowly over time. This could bias the structure calculation. It would be more appropriate to obtain different types of dipolar couplings simultaneously, such that all the data correspond to one effective alignment tensor. We describe here a general NMR strategy designed to do so, that can be adapted to various existing pulse sequences.     

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.     

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.     

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.     

Rapid determination of protein folds using residual dipolar couplings

Over the next few years, various genome projects will sequence many new genes and yield many new gene products. Many of these products will have no known function and little, if any, sequence homology to existing proteins. There is reason to believe that a rapid determination of a protein fold, even at low resolution, can aid in the identification of function and expedite the determination of structure at higher resolution. Recently devised NMR methods of measuring residual dipolar couplings provide one route to the determination of a fold. They do this by allowing the alignment of previously identified secondary structural elements with respect to each other. When combined with constraints involving loops connecting elements or other short-range experimental distance information, a fold is produced. We illustrate this approach to protein fold determination on (15)N-labeled Eschericia coli acyl carrier protein using a limited set of (15)N-(1)H and (1)H-(1)H dipolar couplings. We also illustrate an approach using a more extended set of heteronuclear couplings on a related protein, (13)C, (15)N-labeled NodF protein from Rhizobium leguminosarum.     

Improving the Accuracy of NMR Structures of Large Proteins Using Pseudocontact Shifts as Long-Range Restraints

We demonstrate improved accuracy in protein structure determination for large (>/=30 kDa), deuterated proteins (e.g. STAT4(NT)) via the combination of pseudocontact shifts for amide and methyl protons with the available NOEs in methyl-protonated proteins. The improved accuracy is cross validated by Q-factors determined from residual dipolar couplings measured as a result of magnetic susceptibility alignment. The paramagnet is introduced via binding to thiol-reactive EDTA, and multiple sites can be serially engineered to obtain data from alternative orientations of the paramagnetic anisotropic susceptibility tensor. The technique is advantageous for systems where the target protein has strong interactions with known alignment media.     

Theoretical framework for NMR residual dipolar couplings in unfolded proteins

A theoretical framework for the prediction of nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) in unfolded proteins under weakly aligning conditions is presented. The unfolded polypeptide chain is modeled as a random flight chain while the alignment medium is represented by a set of regularly arranged obstacles. For the case of bicelles oriented perpendicular to the magnetic field, a closed-form analytical result is derived. With the obtained analytical expression the RDCs are readily accessible for any locus along the chain, for chains of differing length, and for varying bicelle concentrations. The two general features predicted by the model are (i) RDCs in the center segments of a polypeptide chain are larger than RDCs in the end segments, resulting in a bell-shaped sequential distribution of RDCs, and (ii) couplings are larger for shorter chains than for longer chains at a given bicelle concentration. Experimental data available from the literature confirm the first prediction of the model, providing a tool for recognizing fully unfolded polypeptide chains. With less certainty experimental data appear to support the second prediction as well. However, more systematic experimental studies are needed in order to validate or disprove the predictions of the model. The presented framework is an important step towards a solid theoretical foundation for the analysis of experimentally measured RDCs in unfolded proteins in the case of alignment media such as polyacrylamide gels and neutral bicelle systems which align biomacromolecules by a steric mechanism. Various improvements and generalizations are possible within the suggested approach.     

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.     

Improvement of hydrogen bond geometry in protein NMR structures by residual dipolar couplings – an assessment of the interrelation of NMR restraints

We have examined how the hydrogen bond geometry in three different proteins is affected when structural restraints based on measurements of residual dipolar couplings are included in the structure calculations. The study shows, that including restraints based solely on (1)H(N)-(15)N residual dipolar couplings has pronounced impact on the backbone rmsd and Ramachandran plot but does not improve the hydrogen bond geometry. In the case of chymotrypsin inhibitor 2 the addition of (13)CO-(13)C(alpha) and (15)N-(13)CO one bond dipolar couplings as restraints in the structure calculations improved the hydrogen bond geometry to a quality comparable to that obtained in the 1.8 A resolution X-ray structure of this protein. A systematic restraint study was performed, in which four types of restraints, residual dipolar couplings, hydrogen bonds, TALOS angles and NOEs, were allowed in two states. This study revealed the importance of using several types of residual dipolar couplings to get good hydrogen bond geometry. The study also showed that using a small set of NOEs derived only from the amide protons, together with a full set of residual dipolar couplings resulted in structures of very high quality. When reducing the NOE set, it is mainly the side-chain to side-chain NOEs that are removed. Despite of this the effect on the side-chain packing is very small when a reduced NOE set is used, which implies that the over all fold of a protein structure is mainly determined by correct folding of the backbone.     

Novel Techniques for Weak Alignment of Proteins in Solution Using Chemical Tags Coordinating Lanthanide Ions

A molecule with an anisotropic magnetic susceptibility is spontaneously aligned in a static magnetic field. Alignment of such a molecule yields residual dipolar couplings and pseudocontact shifts. Lanthanide ions have recently been successfully used to provide an anisotropic magnetic susceptibility in target molecules either by replacing a calcium ion with a lanthanide ion in calcium-binding proteins or by attaching an EDTA derivative to a cysteine residue via a disulfide bond. Here we describe a novel enantiomerically pure EDTA derived tag that aligns stronger due to its shorter linker and does not suffer from stereochemical diversity upon lanthanide complexation. We observed residual (15)N,(1)H-dipolar couplings of up to 8 Hz at 800 MHz induced by a single alignment tensor from this tag.