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

Maximal clique method for the automated analysis of NMR TOCSY spectra of complex mixtures

Characterization of the chemical components of complex mixtures in solution is important in many areas of biochemistry and chemical biology, including metabolomics. The use of 2D NMR total correlation spectroscopy (TOCSY) experiments has proven very useful for the identification of known metabolites as well as for the characterization of metabolites that are unknown by taking advantage of the good resolution and high sensitivity of this homonuclear experiment. Due to the complexity of the resulting spectra, automation is critical to facilitate and speed-up their analysis and enable high-throughput applications. To better meet these emerging needs, an automated spin-system identification algorithm of TOCSY spectra is introduced that represents the cross-peaks and their connectivities as a mathematical graph, for which all subgraphs are determined that are maximal cliques. Each maximal clique can be assigned to an individual spin system thereby providing a robust deconvolution of the original spectrum for the easy extraction of critical spin system information. The approach is demonstrated for a complex metabolite mixture consisting of 20 compounds and for E. coli cell lysate.

Network representation of protein interactions: Theory of graph description and analysis

A methodological framework is presented for the graph theoretical interpretation of NMR data of protein interactions. The proposed analysis generalizes the idea of network representations of protein structures by expanding it to protein interactions. This approach is based on regularization of residue-resolved NMR relaxation times and chemical shift data and subsequent construction of an adjacency matrix that represents the underlying protein interaction as a graph or network. The network nodes represent protein residues. Two nodes are connected if two residues are functionally correlated during the protein interaction event. The analysis of the resulting network enables the quantification of the importance of each amino acid of a protein for its interactions. Furthermore, the determination of the pattern of correlations between residues yields insights into the functional architecture of an interaction. This is of special interest for intrinsically disordered proteins, since the structural (three-dimensional) architecture of these proteins and their complexes is difficult to determine. The power of the proposed methodology is demonstrated at the example of the interaction between the intrinsically disordered protein osteopontin and its natural ligand heparin.

Use of graph theory for secondary structure recognition and sequential assignment in heteronuclear (13C, 15N) NMR spectra: application to HU protein from Bacillus stearothermophilus

A computer-assisted procedure, based upon a branch of mathematics known as graph theory, has been developed to recognize secondary structure elements in proteins from their corresponding nuclear Overhauser effect spectroscopy (NOESY)-type spectra and to carry out their sequential assignment. In the method, NOE connectivity templates characteristic of regular secondary structures are identified in the spectra. Resonance assignment is then achieved by connecting these NOE patterns of secondary structure together, and thereby matching connected spin systems to specific parts of the primary sequence. The range of NOE-graph templates of secondary structure motifs, incorporating alpha-helices and beta-strand motifs, has been examined for reliability and extent of secondary structure identification in a data base composed of the high resolution structures of 20 proteins. The analysis identified several robust NOE-graph templates and supports the implementation of an ordered search strategy. The method, known as SERENDIPITY, has been applied to the analysis of nuclear Overhauser effect data from a three-dimensional time-shared nuclear Overhauser effect spectroscopy (13C, 15N) heteronuclear single quantum correlation spectrum of the (alpha + beta) type protein HU from Bacillus stearothermophilus. The arrangement of the elucidated elements of secondary structure is very similar to that of the x-ray and nmr structures of HU. In addition, our analysis revealed a pattern of interstrand nuclear Overhauser effect in the beta-arm region (residues 53-76) of HU, which suggest irregularities, not reported in the x-ray structure, in both strands of the beta-arm at Ala57 and Pro72, respectively. At these residues, both strands of the beta-arm appear to flip inside out before continuing as a regular antiparallel beta-sheet.