One-bond and two-bond J couplings help annotate protein secondary-structure motifs: J-coupling indexing applied to human endoplasmic reticulum protein ERp18

NMR coupling constants, both direct one‐bond (¹J) and geminal two‐bond (²J), are employed to analyze the protein secondary structure of human oxidized ERp18. Coupling constants collected and evaluated for the 18 kDa protein comprise 1268 values of ¹J_CαHα, ¹J_CαCβ, ¹J_CαC′, ¹J_C′N′, ¹J_N′Cα, ¹J_N′HN, ²J_CαN′, ²J_HNCα, ²J_C′HN, and ²J_HαC′. Comparison with ¹J and ²J data from reference proteins and pattern analysis on a per‐residue basis permitted main‐chain φ,ψ torsion‐angle combinations of many of the 149 amino‐acid residues in ERp18 to be narrowed to particular secondary‐structure motifs. J‐coupling indexing is here being developed on statistical criteria and used to devise a ternary grid for interpreting patterns of relative values of J. To account for the influence of the varying substituent pattern in different amino‐acid sidechains, a table of residue‐type specific threshold values was compiled for discriminating small, medium, and large categories of J. For the 15‐residue insertion that distinguishes the ERp18 fold from that of thioredoxin, the J‐coupling data hint at a succession of five isolated Type‐I β turns at progressively shorter sequence intervals, in agreement with the crystal structure. Proteins 2011. © 2010 Wiley‐Liss, Inc.     

Structural dependencies of protein backbone 2JNC' couplings

Protein folding can introduce strain in peptide covalent geometry, including deviations from planarity that are difficult to detect, especially for a protein in solution. We have found dependencies in protein backbone (2)J(NC') couplings on the planarity and the relative orientation of the sequential peptide planes. These dependences were observed in experimental (2)J(NC') couplings from seven proteins, and also were supported by DFT calculations for a model tripeptide. Findings indicate that elevated (2)J(NC') couplings may serve as reporters of structural strain in the protein backbone imposed by protein folds. Such information, supplemented with the H-bond strengths derived from (h3)J(NC') couplings, provides useful insight into the overall energy profile of the protein backbone in solution.     

Direct structure refinement of high molecular weight proteins against residual dipolar couplings and carbonyl chemical shift changes upon alignment: an application to maltose binding protein

The global fold of maltose binding protein in complex with -cyclodextrin has been determined using a CNS-based torsion angle molecular dynamics protocol involving direct refinement against dipolar couplings and carbonyl chemical shift changes that occur upon alignment. The shift changes have been included as structural restraints using a new module, CANI, that has been incorporated into CNS. Force constants and timesteps have been determined that are particularly effective in structure refinement applications involving high molecular weight proteins with small to moderate numbers of NOE restraints. Solution structures of the N- and C-domains of MBP calculated with this new protocol are within 2 Å of the X-ray conformation.     

Rapid and accurate structure determination of coiled-coil domains using NMR dipolar couplings: application to cGMP-dependent protein kinase Ialpha

Coiled-coil motifs play essential roles in protein assembly and molecular recognition, and are therefore the targets of many ongoing structural and functional studies. However, owing to the dynamic nature of many of the smaller coiled-coil domains, crystallization for X-ray studies is very challenging. Determination of elongated structures using standard NMR approaches is inefficient and usually yields low-resolution structures due to accumulation of small errors over long distances. Here we describe a solution NMR approach based on residual dipolar couplings (RDCs) for rapid and accurate structure determination of coiled-coil dimers. Using this approach, we were able to determine the high-resolution structure of the coiled-coil domain of cGMP-dependent protein kinase Ialpha, a protein of previously unknown structure that is critical for physiological relaxation of vascular smooth muscle. This approach can be extended to solve coiled-coil structures with higher order assemblies.     

Knowledge-based protein secondary structure assignment

We have developed an automatic algorithm STRIDE for protein secondary structure assignment from atomic coordinates based on the combined use of hydrogen bond energy and statistically derived backbone torsional angle information. Parameters of the pattern recognition procedure were optimized using designations provided by the crystallographers as a standard-of-truth. Comparison to the currently most widely used technique DSSP by Kabsch and Sander (Biopolymers 22:2577-2637, 1983) shows that STRIDE and DSSP assign secondary structural states in 58 and 31% of 226 protein chains in our data sample, respectively, in greater agreement with the specific residue-by-residue definitions provided by the discoverers of the structures while in 11% of the chains, the assignments are the same. STRIDE delineates every 11th helix and every 32nd strand more in accord with published assignments. © 1995 Wiley-Liss, Inc.     

Asymmetric Karplus curves for the protein side-chain <Superscript>3</Superscript><Emphasis Type="Italic">J</Emphasis> couplings

The standard Karplus equation for calculating ³ J coupling constants from any given dihedral angle requires three empirical coefficients be determined that relate to the magnitudes of three modes of the angle dependency of ³ J. Considering cosine modes only (bimodal, unimodal and baseline component), Karplus curves are generally symmetric with respect to the sign of the angle argument. Typically, their primary and secondary maxima differ in amplitude, whereas the two minima are of equal depth. However, chiral molecular topologies, such as those surrounding the main-chain and side-chain torsions in amino-acid residues, preclude, as regards substituent positioning, exact mirror-image conformations from being formed—for any given torsion-angle value. It is therefore unlikely that ³ J couplings assume identical values for the corresponding positive and negative dihedral angles. This suggests that a better empirical fit of the torsion-angle dependency of ³ J could be obtained when removing the constraint of symmetrically identical coupling constants. A sine term added to the Karplus equation allows independent modelling of both curve minima typically located near dihedral-angle values of +90° and −90°. Revisiting an extensive ³ J coupling dataset previously recorded to determine the side-chain torsions χ₁ in the protein flavodoxin, the asymmetric Karplus model accomplishes a more accurate fit to the experimental data. Asymmetries revealed in the angle dependencies exceed the experimental precision in determining ³ J. Accounting for these effects helps improve molecular models. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Accurate and automated classification of protein secondary structure with PsiCSI

PsiCSI is a highly accurate and automated method of assigning secondary structure from NMR data, which is a useful intermediate step in the determination of tertiary structures. The method combines information from chemical shifts and protein sequence using three layers of neural networks. Training and testing was performed on a suite of 92 proteins (9437 residues) with known secondary and tertiary structure. Using a stringent cross-validation procedure in which the target and homologous proteins were removed from the databases used for training the neural networks, an average 89% Q3 accuracy (per residue) was observed. This is an increase of 6.2% and 5.5% (representing 36% and 33% fewer errors) over methods that use chemical shifts (CSI) or sequence information (Psipred) alone. In addition, PsiCSI improves upon the translation of chemical shift information to secondary structure (Q3 = 87.4%) and is able to use sequence information as an effective substitute for sparse NMR data (Q3 = 86.9% without (13)C shifts and Q3 = 86.8% with only H(alpha) shifts available). Finally, errors made by PsiCSI almost exclusively involve the interchange of helix or strand with coil and not helix with strand (<2.5 occurrences per 10000 residues). The automation, increased accuracy, absence of gross errors, and robustness with regards to sparse data make PsiCSI ideal for high-throughput applications, and should improve the effectiveness of hybrid NMR/de novo structure determination methods. A Web server is available for users to submit data and have the assignment returned.     

Conformational analysis of protein and nucleic acid fragments with the new grid search algorithm FOUND

The new computer algorithm FOUND, which is implemented as an integrated module of the DYANA structure calculation program, is capable of performing systematic local conformation analyses by exhaustive grid searches for arbitrary contiguous fragments of proteins and nucleic acids. It uses torsion angles as the only degrees of freedom to identify all conformations that fulfill the steric and NMR-derived conformational restraints within a contiguous molecular fragment, as defined either by limits on the maximal restraint violations or by the fragment-based DYANA target function value. Sets of mutually dependent torsion angles, for example in ribose rings, are treated as a single degree of freedom. The results of the local conformation analysis include allowed torsion angle ranges and stereospecific assignments for diastereotopic substituents, which are then included in the input of a subsequent structure calculation. FOUND can be used for grid searches comprising up to 13 torsion angles, such as the backbone of a complete -helical turn or dinucleotide fragments in nucleic acids, and yields a significantly higher number of stereospecific assignments than the precursor grid search algorithm HABAS.     

Description and recognition of regular and distorted secondary structures in proteins using the automated protein structure analysis method

The Automated Protein Structure Analysis (APSA) method, which describes the protein backbone as a smooth line in three‐dimensional space and characterizes it by curvature κ and torsion τ as a function of arc length s, was applied on 77 proteins to determine all secondary structural units via specific κ(s) and τ(s) patterns. A total of 533 α‐helices and 644 β‐strands were recognized by APSA, whereas DSSP gives 536 and 651 units, respectively. Kinks and distortions were quantified and the boundaries (entry and exit) of secondary structures were classified. Similarity between proteins can be easily quantified using APSA, as was demonstrated for the roll architecture of proteins ubiquitin and spinach ferridoxin. A twenty‐by‐twenty comparison of all α domains showed that the curvature‐torsion patterns generated by APSA provide an accurate and meaningful similarity measurement for secondary, super secondary, and tertiary protein structure. APSA is shown to accurately reflect the conformation of the backbone effectively reducing three‐dimensional structure information to two‐dimensional representations that are easy to interpret and understand. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Structural analysis and prediction of protein mutant stability using distance and torsion potentials: role of secondary structure and solvent accessibility

Platelet-activating factor receptor (PAFR) is a member of G-protein coupled receptor (GPCR) superfamily. Understanding the regulation mechanisms of PAFR by its agonists and antagonists at the atomic level is essential for designing PAFR antagonists as drug candidates for treating PAF-mediated diseases. In this study, a 3D model of PAFR was constructed by a hierarchical approach integrating homology modeling, molecular docking and molecular dynamics (MD) simulations. Based on the 3D model, regulation mechanisms of PAFR by agonists and antagonists were investigated via three 8-ns MD simulations on the systems of apo-PAFR, PAFR-PAF and PAFR-GB. The simulations revealed that binding of PAF to PAFR triggers the straightening process of the kinked helix VI, leading to its activated state. In contrast, binding of GB to PAFR locks PAFR in its inactive state.     

Efficient Multiple-Trait Association and Estimation of Genetic Correlation Using the Matrix-Variate Linear Mixed Model

Multiple-trait association mapping, in which multiple traits are used simultaneously in the identification of genetic variants affecting those traits, has recently attracted interest. One class of approaches for this problem builds on classical variance component methodology, utilizing a multitrait version of a linear mixed model. These approaches both increase power and provide insights into the genetic architecture of multiple traits. In particular, it is possible to estimate the genetic correlation, which is a measure of the portion of the total correlation between traits that is due to additive genetic effects. Unfortunately, the practical utility of these methods is limited since they are computationally intractable for large sample sizes. In this article, we introduce a reformulation of the multiple-trait association mapping approach by defining the matrix-variate linear mixed model. Our approach reduces the computational time necessary to perform maximum-likelihood inference in a multiple-trait model by utilizing a data transformation. By utilizing a well-studied human cohort, we show that our approach provides more than a 10-fold speedup, making multiple-trait association feasible in a large population cohort on the genome-wide scale. We take advantage of the efficiency of our approach to analyze gene expression data. By decomposing gene coexpression into a genetic and environmental component, we show that our method provides fundamental insights into the nature of coexpressed genes. An implementation of this method is available at http://genetics.cs.ucla.edu/mvLMM.     

Use of residual dipolar couplings as restraints in ab initio protein structure prediction

NMR residual dipolar couplings (RDCs), in the form of the projection angles between the respective internuclear bond vectors, are used as structural restraints in the ab initio structure prediction of a test set of six proteins. The restraints are applied using a recently developed SICHO (SIde-CHain-Only) lattice protein model that employs a replica exchange Monte Carlo (MC) algorithm to search conformational space. Using a small number of RDC restraints, the quality of the predicted structures is improved as reflected by lower RMSD/dRMSD (root mean square deviation/distance root mean square deviation) values from the corresponding native structures and by the higher correlation of the most cooperative mode of motion of each predicted structure with that of the native structure. The latter, in particular, has possible implications for the structure-based functional analysis of predicted structures.     

HIFI-C: a robust and fast method for determining NMR couplings from adaptive 3D to 2D projections

We describe a novel method for the robust, rapid, and reliable determination of J couplings in multi-dimensional NMR coupling data, including small couplings from larger proteins. The method, “High-resolution Iterative Frequency Identification of Couplings” (HIFI-C) is an extension of the adaptive and intelligent data collection approach introduced earlier in HIFI-NMR. HIFI-C collects one or more optimally tilted two-dimensional (2D) planes of a 3D experiment, identifies peaks, and determines couplings with high resolution and precision. The HIFI-C approach, demonstrated here for the 3D quantitative J method, offers vital features that advance the goal of rapid and robust collection of NMR coupling data. (1) Tilted plane residual dipolar couplings (RDC) data are collected adaptively in order to offer an intelligent trade off between data collection time and accuracy. (2) Data from independent planes can provide a statistical measure of reliability for each measured coupling. (3) Fast data collection enables measurements in cases where sample stability is a limiting factor (for example in the presence of an orienting medium required for residual dipolar coupling measurements). (4) For samples that are stable, or in experiments involving relatively stronger couplings, robust data collection enables more reliable determinations of couplings in shorter time, particularly for larger biomolecules. As a proof of principle, we have applied the HIFI-C approach to the 3D quantitative J experiment to determine N-C′ RDC values for three proteins ranging from 56 to 159 residues (including a homodimer with 111 residues in each subunit). A number of factors influence the robustness and speed of data collection. These factors include the size of the protein, the experimental set up, and the coupling being measured, among others. To exhibit a lower bound on robustness and the potential for time saving, the measurement of dipolar couplings for the N-C′ vector represents a realistic “worst case analysis”. These couplings are among the smallest currently measured, and their determination in both isotropic and anisotropic media demands the highest measurement precision. The new approach yielded excellent quantitative agreement with values determined independently by the conventional 3D quantitative J NMR method (in cases where sample stability in oriented media permitted these measurements) but with a factor of 2–5 in time savings. The statistical measure of reliability, measuring the quality of each RDC value, offers valuable adjunct information even in cases where modest time savings may be realized. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

B3LYP/6-311++G* * study of structure and spin-spin coupling constant in heparin disaccharide

Structures of heparin disaccharide have been analyzed by DFT using the B3LYP/6-311++G( * *) method. The optimized geometries of two forms of this disaccharide, differing in the conformation ((1)C(4) and (2)S(0)) of the IdoA2S residue, confirmed considerable influences of the sulfate and the carboxylate groups upon the pyranose ring geometries. The computed energies showed that disaccharide having the (1)C(4) form of the IdoA2S residue is more stable than that with the (2)S(0) form. Interatomic distances, bond and torsion angles showed that interconversion of the IdoA2S residue results in geometry changes in the GlcN,6S residue as well. Three-bond proton-proton and proton-carbon spin-spin coupling constants computed for both forms agree with the experimental data and indicate that only two chair forms contribute to the conformational equilibrium in disaccharide. Influences of the charged groups upon the magnitudes of spin-spin coupling constants are also discussed.     

Improved efficiency of protein structure calculations from NMR data using the program DIANA with redundant dihedral angle constraints

Summary A new strategy for NMR structure calculations of proteins with the variable target function method (Braun, W. and Go, N. (1985)J. Mol. Biol.,186, 611) is described, which makes use of redundant dihedral angle constraints (REDAC) derived from preliminary calculations of the complete structure. The REDAC approach reduces the computation time for obtaining a group of acceptable conformers with the program DIANA 5-100-fold, depending on the complexity of the protein structure, and retains good sampling of conformation space.Dedicated to the memory of Professor V.F. Bystrov     

Spin-state-selective coherence transfer via intermediate states of two-spin coherence in IS spin systems: Application to E.COSY-type measurement of J coupling constants

It is demonstrated that a new pulse sequence element, Spin-State-SelectiveCoherence Transfer (S³CT), via an intermediate state ofheteronuclear IS zero- or double-quantum coherence can transfer the twosingle-quantum coherences on one of the spins exclusively to any one of thetwo single-quantum coherences on the other spin. This fact is used for editinginto two subspectra that are most suitable for extraction of homo- orheteronuclear J coupling constants when S³CT is combined withhomonuclear coherence transfer during a mixing period. Experimentalconfirmation is obtained using a ¹⁵N-labeled 58-residue protein,the C-terminal Kunitz domain from human type VI collagen. The J coupling con-stants determined include ³J_HN-H and³J_N-H related to the and¹ angles, respectively.     

NMR secondary structure of the plasminogen activator protein staphylokinase

Staphylokinase (Sak) is a 15.5 kDa protein secreted by several strains of Staphylococcusaureus. Due to its ability to convert plasminogen, the inactive proenzyme of the fibrinolyticsystem, into plasmin, Sak is presently undergoing clinical trials for blood clot lysis in thetreatment of thrombovascular disorders. With a view to developing a better understanding ofthe mode of action of Sak, we have initiated a structural investigation of Sak viamultidimensional heteronuclear NMR spectroscopy employing uniformly 15N- and 15N,13C-labelled Sak. Sequence-specific resonance assignments have been made employing 15N-editedTOCSY and NOE experiments and from HNCACB, CBCA(CO)NH, HBHA(CBCACO)NHand CC(CO)NH sets of experiments. From an analysis of the chemical shifts,3JHNH scalar coupling constants, NOEs and HN exchange data, the secondary structural elements of Sakhave been characterized.     

Overcoming the problems associated with poor spectra quality of the protein kinase Byr2 using residual dipolar couplings

For the Ras-binding domain of the protein kinase Byr2, only a limited number of NOE contacts could be initially assigned unambiguously, as the quality of the NOESY spectra was too poor. However, the use of residual (1)H-(15)N dipolar couplings in the beginning of the structure determination process allows to overcome this problem. We used a three-step recipe for this procedure. A previously unknown structure could be calculated reasonably well with only a limited number of unambiguously assigned NOE contacts.     

Hypothesis testing in comparative and experimental studies of function-valued traits

Many traits of evolutionary interest, when placed in their developmental, physiological, or environmental contexts, are function-valued. For instance, gene expression during development is typically a function of the age of an organism and physiological processes are often a function of environment. In comparative and experimental studies, a fundamental question is whether the function-valued trait of one group is different from another. To address this question, evolutionary biologists have several statistical methods available. These methods can be classified into one of two types: multivariate and functional. Multivariate methods, including univariate repeated-measures analysis of variance (ANOVA), treat each trait as a finite list of data. Functional methods, such as repeated-measures regression, view the data as a sample of points drawn from an underlying function. A key difference between multivariate and functional methods is that functional methods retain information about the ordering and spacing of a set of data values, information that is discarded by multivariate methods. In this study, we evaluated the importance of that discarded information in statistical analyses of function-valued traits. Our results indicate that functional methods tend to have substantially greater statistical power than multivariate approaches to detect differences in a function-valued trait between groups.     

TOUCHSTONEX: protein structure prediction with sparse NMR data

TOUCHSTONEX, a new method for folding proteins that uses a small number of long-range contact restraints derived from NMR experimental NOE (nuclear Overhauser enhancement) data, is described. The method employs a new lattice-based, reduced model of proteins that explicitly represents C(alpha), C(beta), and the sidechain centers of mass. The force field consists of knowledge-based terms to produce protein-like behavior, including various short-range interactions, hydrogen bonding, and one-body, pairwise, and multibody long-range interactions. Contact restraints were incorporated into the force field as an NOE-specific pairwise potential. We evaluated the algorithm using a set of 125 proteins of various secondary structure types and lengths up to 174 residues. Using N/8 simulated, long-range sidechain contact restraints, where N is the number of residues, 108 proteins were folded to a C(alpha)-root-mean-square deviation (RMSD) from native below 6.5 A. The average RMSD of the lowest RMSD structures for all 125 proteins (folded and unfolded) was 4.4 A. The algorithm was also applied to limited experimental NOE data generated for three proteins. Using very few experimental sidechain contact restraints, and a small number of sidechain-main chain and main chain-main chain contact restraints, we folded all three proteins to low-to-medium resolution structures. The algorithm can be applied to the NMR structure determination process or other experimental methods that can provide tertiary restraint information, especially in the early stage of structure determination, when only limited data are available.