Analytical solution to the coupled evolution of multidimensional NMR data

A substantial time savings in the collection of multidimensional NMR data can be achieved by coupling the evolution of nuclei in the indirect dimensions. In order to save time, the sampling of the indirect dimensions is inherently incomplete. Therefore, many algorithms and samplings schemes have been developed aimed at separating the coevolved frequencies into analyzable data with limited artifacts. This paper extends the use of circulant matrices to describe coupled evolution with convolutions. By understanding the data in terms of convolutions, there is an exact solution to the inversion problem of extracting the orthogonal vectors from the coupled dimensions. Previously, this inversion problem has been solved using peak coordinates extracted from spectra. In contrast, the method described here uses spectra directly. This solution suggests a simple sampling scheme of collecting N orthogonal spectra, and N + 1 projections at specific projection angles, however, the theory developed can be extended generally to arbitrary projection angles. The circulant matrix methodology is demonstrated for simulated and real data. Further, an algorithm for separating overlapped signals in the detected dimension is presented. The algorithm involves the forward calculation of the coupled spectra from the orthogonal spectra, followed by back calculation of the orthogonal spectra from the coupled spectra, thus permitting rigorous cross-validation. This algorithm is shown to be robust in that erroneous solutions give rise to large artifacts. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Tools for the automated assignment of high-resolution three-dimensional protein NMR spectra based on pattern recognition techniques

One of the major bottlenecks in the determination of proteinstructures by NMR is in the evaluation of the data produced by theexperiments. An important step in this process is assignment, where thepeaks in the spectra are assigned to specific spins within specificresidues. In this paper, we discuss a spin system assignment tool based onpattern recognition techniques. This tool employs user-specified templatesto search for patterns of peaks in the original spectra; these patterns maycorrespond to side-chain or backbone fragments. Multiple spectra willnormally be searched simultaneously to reduce the impact of noise. Thesearch generates a preliminary list of putative assignments, which arefiltered by a set of heuristic algorithms to produce the final results list.Each result contains a set of chemical shift values plus information aboutthe peaks found. The results may be used as input for combinatorialroutines, such as sequential assignment procedures, in place of peak lists.Two examples are presented, in which (i) HCCH-COSY and -TOCSY spectra arescanned for side-chain spin systems; and (ii) backbone spin systems aredetected in a set of spectra comprising HNCA, HN(CO)CA, HNCO, HN(CA)CO,CBCANH and CBCA(CO)NH.     

ORB, a homology-based program for the prediction of protein NMR chemical shifts

A computer program (ORB) has been developed to predict ¹H,¹³C and ¹⁵N NMR chemical shifts of previouslyunassigned proteins. The program makes use of the information contained in achemical shift database of previously assigned proteins supplemented by astatistically derived averaged chemical shift database in which the shifts arecategorized according to their residue, atom and secondary structure type[Wishart et al. (1991) J. Mol. Biol., 222, 311–333]. The predictionprocess starts with a multiple alignment of all previously assigned proteinswith the unassigned query protein. ORB uses the sequence and secondarystructure alignment program XALIGN for this task [Wishart et al. (1994)CABIOS, 10, 121–132; 687–688]. The prediction algorithm in ORB isbased on a scoring of the known shifts for each sequence. The scores dependon global sequence similarity, local sequence similarity, structuralsimilarity and residue similarity and determine how much weight one particularshift is given in the prediction process. In situations where no applicablepreviously assigned chemical shifts are available, the shifts derived from theaveraged database are used. In addition to supplying the user with predictedchemical shifts, ORB calculates a confidence value for every prediction. Theseconfidence values enable the user to judge which predictions are the mostaccurate and they are particularly useful when ORB is incorporated into acomplete autoassignment package. The usefulness of ORB was tested on threemedium-sized proteins: an interleukin-8 analog, a troponin C synthetic peptideheterodimer and cardiac troponin C. Excellent results are obtained if ORB isable to use the chemical shifts of at least one highly homologous sequence.ORB performs well as long as the sequence identity between proteins with knownchemical shifts and the new sequence is not less than 30%.     

Assignment of amide proton signals by combined evaluation of HN,NN and HNCA MAS-NMR correlation spectra

In this paper, we present a strategy for the ¹H^N resonance assignment in solid-state magic-angle spinning (MAS) NMR, using the -spectrin SH3 domain as an example. A novel 3D triple resonance experiment is presented that yields intraresidue H^N-N-C correlations, which was essential for the proton assignment. For the observable residues, 52 out of the 54 amide proton resonances were assigned from 2D (¹H-¹⁵N) and 3D (¹H-¹⁵N-¹³C) heteronuclear correlation spectra. It is demonstrated that proton-driven spin diffusion (PDSD) experiments recorded with long mixing times (4 s) are helpful for confirming the assignment of the protein backbone ¹⁵N resonances and as an aid in the amide proton assignment.     

A modified strategy for sequence specific assignment of protein NMR spectra based on amino acid type selective experiments

The determination of the three-dimensional structure of a protein or the study of protein–ligand interactions requires the assignment of all relevant nuclei as an initial step. This is nowadays almost exclusively performed using triple-resonance experiments. The conventional strategy utilizes one or more pairs of three dimensional spectra to obtain redundant information and thus reliable assignments. Here, a modified strategy for obtaining sequence specific assignments based on two dimensional amino acid type selective triple-resonance experiments is proposed. These experiments can be recorded with good resolution in a relatively short time. They provide very specific and redundant information, in particular on sequential connectivities, that drastically increases the ease and reliability of the assignment procedure, done either manually or in an automated fashion. The new strategy is demonstrated with the protein domain PB1 from yeast CDC24p. Dedicated to Rüdiger Winter ( 06.04.2004)     

Ansig for Windows: An interactive computer program for semiautomatic assignment of protein NMR spectra

Assignment of NMR spectra is a prerequisite for structure determination of proteins using NMR. The time spent on the assignment is comparatively long compared to that spent on other parts in the protein structure determination process, but it can be shortened by using either interactive or fully automated computer programs. To benefit from the advantages of both types of program we have developed a version of the interactive assignment program ANSIG to include automatized, yet user-supervised, routines. The new program includes tools for (i) semiautomatic sequential assignment, (ii) plotting of distances from PDB structure files directly in NMR spectra and (iii) statistical analysis of distance restraint violations with the possibility to directly zoom to violated NOEs in NOESY spectra.     

Sorting signals from protein NMR spectra: SPI,a Bayesian protocol for uncovering spin systems

Grouping of spectral peaks into J-connected spin systems is essential in the analysis of macromolecular NMR data as it provides the basis for disentangling chemical shift degeneracies. It is a mandatory step before resonance and NOESY cross-peak identities can be established. We have developed SPI, a computational protocol that scrutinizes peak lists from homo- and hetero-nuclear multidimensional NMR spectra and progressively assembles sets of resonances into consensus J- and/or NOE-connected spin systems. SPI estimates the likelihood of nuclear spin resonances appearing at defined frequencies given sets of cross-peaks measured from multi-dimensional experiments. It quantifies spin system matching probabilities via Bayesian inference. The protocol takes advantage of redundancies in the number of connectivities revealed by suites of diverse NMR experiments, systematically tracking the adequacy of each grouping hypothesis. SPI was tested on 2D homonuclear and 2D/3D¹⁵N-edited data recorded from two protein modules, the col 2 domain of matrix metalloproteinase-2 (MMP-2) and the kringle 2 domain of plasminogen, of 60 and 83 amino acid residues, respectively. For these protein domains SPI identifies 95% unambiguous resonance frequencies, a relatively good performance vis-à-vis the reported `manual' (interactive) analyses. Abbreviations and Acronyms: SPI, SPin Identification; BMRB, BioMagResBank (Madison, WI).     

Automated error-tolerant macromolecular structure determination from multidimensional nuclear Overhauser enhancement spectra and chemical shift assignments: improved robustness and performance of the PASD algorithm

We report substantial improvements to the previously introduced automated NOE assignment and structure determination protocol known as PASD (Kuszewski et al. (2004) J Am Chem Soc 26:6258-6273). The improved protocol includes extensive analysis of input spectral data to create a low-resolution contact map of residues expected to be close in space. This map is used to obtain reasonable initial guesses of NOE assignment likelihoods which are refined during subsequent structure calculations. Information in the contact map about which residues are predicted to not be close in space is applied via conservative repulsive distance restraints which are used in early phases of the structure calculations. In comparison with the previous protocol, the new protocol requires significantly less computation time. We show results of running the new PASD protocol on six proteins and demonstrate that useful assignment and structural information is extracted on proteins of more than 220 residues. We show that useful assignment information can be obtained even in the case in which a unique structure cannot be determined.     

Combined frequency- and time-domain NMR spectroscopy. Application to fast protein resonance assignment

A simple and general method is presented to simplify multi-dimensional NMR spectra of isotope-labeled bio-molecules. The approach is based on band-selective Hadamard-type frequency encoding, which disperses the correlation peaks into different sub-spectra. This makes it possible to apply low-dimensionality-based NMR techniques to larger molecular systems. Here we demonstrate the use of band-selective Hadamard frequency labeling for fast protein resonance assignment, based on our recently proposed suite of 2D experiments (Bersch et al., 2003).     

Performance of a neural-network-based determination of amino acid class and secondary structure from 1H-15N NMR data

A neural network which can determine both amino acid class andsecondary structure using NMR data from ¹⁵N-labeled proteinsis described. We have included nitrogen chemical shifts,³J_HN_H coupling constants, -protonchemical shifts, and side-chain proton chemical shifts as input to athree-layer feed-forward network. The network was trained with 456 spinsystems from several proteins containing various types of secondarystructure, and tested on human ubiquitin, which has no sequence homologywith any of the proteins in the training set. A very limited set of data,representative of those from a TOCSY-HSQC and HNHA experiment, was used.Nevertheless, in 60% of the spin systems the correct amino acid classwas among the top two choices given by the network, while in 96% ofthe spin systems the secondary structure was correctly identified. Theperformance of this network clearly shows the potential of the neuralnetwork algorithm in the automation of NMR spectral analysis.     

Efficient analysis of protein 2D NMR spectra using the software packageEASY

Summary The programEASY supports the spectral analysis of biomacromolecular two-dimensional (2D) nuclear magnetic resonance (NMR) data. It provides a user-friendly, window-based environment in which to view spectra for interactive interpretation. In addition, it includes a number of automated routines for peakpicking, spin-system identification, sequential resonance assignment in polypeptide chains, and cross peak integration. In this uniform environment, all resulting parameter lists can be recorded on disk, so that the paper plots and handwritten notes which normally accompany manual assignment of spectra can be largely eliminated. For example, in a protein structure determination by 2D¹H NMR,EASY accepts the frequency domain datasets as input, and after combined use of the automated and interactive routines it can yield a listing of conformational constraints in the format required as input for the calculation of the 3D structure. The program was extensively tested with current protein structure determinations in our laboratory. In this paper, its main features are illustrated with data on the protein basic pancreatic trypsin inhibitor.     

Computer-assisted assignment of multidimensional NMR spectra of proteins: Application to 3D NOESY-HMQC and TOCSY-HMQC spectra

Summary An algorithm based on the technique of combinatorial minimization is used for the semi-automated assignment of multidimensional heteronuclear spectra. The program (ALFA) produces the best assignment compatible with the available input data. Even partially misleading or missing data do not seriously corrupt the final assignment. Ambiguous sequences of the possible assignment and all alternatives are indicated. The program can also use additional non-spectroscopic data to assist in the assignment procedure. For example, information from the X-ray structure of the protein and/or information about the secondary structure can be used. The assignment procedure was tested on spectra of mucous trypsin inhibitor, a protein of 107 residues.     

Double quantum filtering homonuclear MAS NMR correlation spectra: a tool for membrane protein studies

13C homonuclear correlation spectra based on proton driven spin diffusion (PDSD) are becoming increasingly important for obtaining distance constraints from multiply labeled biomolecules by MAS NMR. One particular challenging situation arises when such constraints are to be obtained from spectra with a large natural abundance signal background which causes detrimental diagonal peak intensities. They obscure cross peaks, and furthermore impede the calculation of a buildup rates matrix which may be used to derive distance constraints, as carried out in "NMR crystallography". Here, we combine double quantum (DQ) filtering with 13C-13C dipolar assisted rotational resonance (DARR) experiments to yield correlation spectra free of natural abundance contributions. Two experimental schemes, using DQ filtering prior to evolution (DOPE), and after mixing (DOAM), have been evaluated. Diagonal peak intensities along the spectrum diagonal are removed completely, and crosspeaks close to the diagonal are easily identifiable. For DOAM spectra with negligible mixing times, it is possible to carry out 'assignment walks' which simplify peak identification substantially. The method is demonstrated on 13C-cys labeled proteorhodopsin, a 27 kDa membrane protein. The magnetization transfer characteristics were studied using buildup curves obtained on uniformly 13C labelled crystalline tripeptide MLF. Our data show that DQ filtered DARR experiments pave the way for obtaining through space constraints for structural studies on ligands, bound to membrane receptors, or on small fragments within large proteins.     

On the NMR structure determination of a 44n RNA pseudoknot: Assignment strategies and derivation of torsion angle restraints

The complete T- and pseudoknotted acceptor arm of the tRNA-like structure of turnip yellow mosaic virus (TYMV) genomic RNA has been studied by NMR spectroscopy. Resonance assignment and the gathering of restraints of the 44-mer are impeded by spectral complexity as well as by line broadening. The latter is caused by local dynamical effects in the pseudoknot domain in the molecule. These specific problems could be solved by using different field strengths and selectively ¹³C/¹⁵ labeled samples. Experiments for assigning the sugar spin systems were adjusted to satisfy the requirements of this system. Furthermore, the quality of the structure could be improved by determining the backbone torsion angles , and , using new approaches that were tailored for use in large RNA molecules.     

Graph-theoretical assignment of secondary structure in multidimensional protein NMR spectra: Application to the lac repressor headpiece

Summary A novel procedure is presented for the automatic identification of secondary structures in proteins from their corresponding NOE data. The method uses a branch of mathematics known as graph theory to identify prescribed NOE connectivity patterns characteristic of the regular secondary structures. Resonance assignment is achieved by connecting these patterns of secondary structure together, thereby matching the connected spin systems to specific segments of the protein sequence. The method known as SERENDIPITY refers to a set of routines developed in a modular fashion, where each program has one or several well-defined tasks. NOE templates for several secondary structure motifs have been developed and the method has been successfully applied to data obtained from NOESY-type spectra. The present report describes the application of the SERENDIPITY protocol to a 3D NOESY-HMQC spectrum of the ¹⁵N-labelled lac repressor headpiece protein. The application demonstrates that, under favourable conditions, fully automated identification of secondary structures and semi-automated assignment are feasible.Abbreviations 2D, 3D two-, three-dimensional - NOESY nuclear Overhauser enhancement spectroscopy - HMQC heteronuclear multiple quantum coherence - SSE secondary structure element - SERENDIPITY SEcondary structuRE ideNtification in multiDImensional ProteIn specTra analYsis Supplementary Material available from the authors: Two tables containing the total number of mappings resulting from the graph search procedure for simulated and experimental NOE data.     

NMR assignment of PN2-3, a tubulin interaction subdomain of the CPAP protein

We report the NMR assignment of the PN2-3 subdomain of the CPAP protein. It has been previously shown that this motif interacts with tubulin, inhibits microtubule nucleation from the centrosome and depolymerizes taxol-stabilized microtubules. Marie-Jeanne Clément and Philippe Savarin contributed equally.     

A novel approach to the detection of synchronisation in EEG based on empirical mode decomposition

Transient neural assemblies mediated by synchrony in particular frequency ranges are thought to underlie cognition. We propose a new approach to their detection, using empirical mode decomposition (EMD), a data-driven approach removing the need for arbitrary bandpass filter cut-offs. Phase locking is sought between modes. We explore the features of EMD, including making a quantitative assessment of its ability to preserve phase content of signals, and proceed to develop a statistical framework with which to assess synchrony episodes. Furthermore, we propose a new approach to ensure signal decomposition using EMD. We adapt the Hilbert spectrum to a time-frequency representation of phase locking and are able to locate synchrony successfully in time and frequency between synthetic signals reminiscent of EEG. We compare our approach, which we call EMD phase locking analysis (EMDPL) with existing methods and show it to offer improved time-frequency localisation of synchrony. Action Editor: Carson C. Chow     

Assignment of polar states for protein amino acid residues using an interaction cluster decomposition algorithm and its application to high resolution protein structure modeling

We have developed a new method (Independent Cluster Decomposition Algorithm, ICDA) for creating all-atom models of proteins given the heavy-atom coordinates, provided by X-ray crystallography, and the pH. In our method the ionization states of titratable residues, the crystallographic mis-assignment of amide orientations in Asn/Gln, and the orientations of OH/SH groups are addressed under the unified framework of polar states assignment. To address the large number of combinatorial possibilities for the polar hydrogen states of the protein, we have devised a novel algorithm to decompose the system into independent interacting clusters, based on the observation of the crucial interdependence between the short range hydrogen bonding network and polar residue states, thus significantly reducing the computational complexity of the problem and making our algorithm tractable using relatively modest computational resources. We utilize an all atom protein force field (OPLS) and a Generalized Born continuum solvation model, in contrast to the various empirical force fields adopted in most previous studies. We have compared our prediction results with a few well-documented methods in the literature (WHATIF, REDUCE). In addition, as a preliminary attempt to couple our polar state assignment method with real structure predictions, we further validate our method using single side chain prediction, which has been demonstrated to be an effective way of validating structure prediction methods without incurring sampling problems. Comparisons of single side chain prediction results after the application of our polar state prediction method with previous results with default polar state assignments indicate a significant improvement in the single side chain predictions for polar residues.