Wavelets and molecular structure

Multiscale denoising of biological data: a comparative analysis

Measured microarray genomic and metabolic data are a rich source of information about the biological systems they represent. For example, time-series biological data can be used to construct dynamic genetic regulatory network models, which can be used to design intervention strategies to cure or manage major diseases. Also, copy number data can be used to determine the locations and extent of aberrations in chromosome sequences. Unfortunately, measured biological data are usually contaminated with errors that mask the important features in the data. Therefore, these noisy measurements need to be filtered to enhance their usefulness in practice. Wavelet-based multiscale filtering has been shown to be a powerful denoising tool. In this work, different batch as well as online multiscale filtering techniques are used to denoise biological data contaminated with white or colored noise. The performances of these techniques are demonstrated and compared to those of some conventional low-pass filters using two case studies. The first case study uses simulated dynamic metabolic data, while the second case study uses real copy number data. Simulation results show that significant improvement can be achieved using multiscale filtering over conventional filtering techniques.

Wavelet Analysis of Protein Motion

As high-throughput molecular dynamics simulations of proteins become more common and the databases housing the results become larger and more prevalent, more sophisticated methods to quickly and accurately mine large numbers of trajectories for relevant information will have to be developed. One such method, which is only recently gaining popularity in molecular biology, is the continuous wavelet transform, which is especially well-suited for time course data such as molecular dynamics simulations. We describe techniques for the calculation and analysis of wavelet transforms of molecular dynamics trajectories in detail and present examples of how these techniques can be useful in data mining. We demonstrate that wavelets are sensitive to structural rearrangements in proteins and that they can be used to quickly detect physically relevant events. Finally, as an example of the use of this approach, we show how wavelet data mining has led to a novel hypothesis related to the mechanism of the protein γδ resolvase.

A WAVELET APPROACH FOR THE ANALYSIS OF FOLDING TRAJECTORY OF PROTEIN TRP-CAGE

Understanding how protein folds into a functional native structure is arguably one of the most challenging problems remaining in computational biology. Currently, the protein folding mechanism is often characterized by calculating the free energy landscape in terms of various reaction coordinates such as the fraction of native contacts, the radius of gyration, the RMS deviation from the native and so on. In this paper, we present a wavelet approach towards understanding the global state changes during protein folding. The approach is based on the wavelet analysis on the trajectories of various reaction coordinates to identify the significant intermediate states or structural motifs in the folding process. We demonstrate through an example protein Trp-cage that this approach extracts crucial information about protein folding intermediate states as well as the time correlation among these states. Furthermore, the current approach reveals a meaningful structural pattern that had been overlooked in previous works, which provides a better understanding of the folding mechanism as well as the limitation of the current force fields.

Wavelet Approximation of GRID Fields: Application to Quantitative Structure-Activity Relationships

Molecular interaction fields such as those computed by the GRID program are widely used in applications such as virtual screening, molecular docking and 3D-QSAR modelling. They characterise molecules according to their favourable interaction sites and therefore enable predictions to be made on how molecules might interact. The fields are, however, comprised of a very large number of data points which presents difficulties for many applications. For example, there are likely to be high degrees of correlation between the variables which can lead to misleading results in 3D-QSAR. We describe the use of wavelet methods for approximating such data into a much smaller number of variables. We present a number of validation experiments, including use of the approximated GRIDs in 3D-QSAR, and demonstrate that wavelet approximation at high levels of data compression preserves the information content in GRID fields while significantly reducing computational requirements.

Atomic resolution structures of rieske iron-sulfur protein: role of hydrogen bonds in tuning the redox potential of iron-sulfur clusters

The Rieske [2Fe-2S] iron-sulfur protein of cytochrome bc(1) functions as the initial electron acceptor in the rate-limiting step of the catalytic reaction. Prior studies have established roles for a number of conserved residues that hydrogen bond to ligands of the [2Fe-2S] cluster. We have constructed site-specific variants at two of these residues, measured their thermodynamic and functional properties, and determined atomic resolution X-ray crystal structures for the native protein at 1.2 A resolution and for five variants (Ser-154-->Ala, Ser-154-->Thr, Ser-154-->Cys, Tyr-156-->Phe, and Tyr-156-->Trp) to resolutions between 1.5 A and 1.1 A. These structures and complementary biophysical data provide a molecular framework for understanding the role hydrogen bonds to the cluster play in tuning thermodynamic properties, and hence the rate of this bioenergetic reaction. These studies provide a detailed structure-function dissection of the role of hydrogen bonds in tuning the redox potentials of [2Fe-2S] clusters.

Essential role of the B23/NPM core domain in regulating ARF binding and B23 stability

How cells coordinate inhibition of growth and division during genotoxic events is fundamental to our understanding of the origin of cancer. Despite increasing interest and extensive study, the mechanisms that link regulation of DNA synthesis and ribosomal biogenesis remain elusive. Recently, the tumor suppressor p14(ARF) (ARF) has been shown to interact functionally with the nucleolar protein B23/NPM (B23) and inhibit rRNA biogenesis. However, the molecular basis of the ARF-B23 interaction is hitherto unclear. Here we show that a highly conserved motif in the B23 oligomerization domain is essential for mediating ARF binding in vivo. Mutagenesis of conserved B23 core residues (L102A, G105A, G107A) prevented B23 from interacting with ARF. Modeling of the B23 core indicated that substitutions in the GSGP loop motif could trigger conformational changes in B23 thereby obstructing ARF binding. Interestingly, the GSGP loop mutants were unstable, defective for oligomerization, and delocalized from the nucleolus to the nucleoplasm. B23 core mutants displayed increased ubiquitination and proteasomal degradation. We conclude that the functional integrity of the B23 core motif is required for stability, efficient nucleolar localization as well as ARF binding.

Statistical mechanics of protein folding with separable energy functions

We have initiated an entirely new approach to statistical mechanical models of strongly interacting systems where the configurational parameters and the potential energy function are both constructed so that the canonical partition function can be evaluated analytically. For a simplified model of proteins consisting of a single, fairly short polypeptide chain without cross-links, we can adjust the energy parameters to favor the experimentally determined native state of seven proteins having diverse types of folds. Then 497 test proteins are predicted to have stable native folds, even though they are also structurally diverse, and 480 of them have no significant sequence similarity to any of the training proteins.

Investigating the evolution and structure of chemokine receptors

Chemokine receptors represent a prime target for the development of novel therapeutic strategies in a variety of disease processes, including inflammation, allergy and neoplasia. Here we use maximum likelihood methods and bootstrap methods to investigate both the phylogenetic relationships in a large set of human chemokine receptor sequences and the relationships between chemokine receptors and their nearest neighbors. We found that CCR and CXCR families are not homogeneous. We also provide evidences that angiotensin receptors are the closest neighbors. Other close neighbors include opioid, somatostatin and melanin-concentrating hormone receptors. The phylogenetic analysis suggests ancient paralogous relationships and establishes a link between immune, metabolic and neural systems modulation. We complement our findings with a structural analysis based on wavelet methods of the major branches of chemokine receptors phylogeny. We hypothesize that receptors very close in the tree can form heterodimers. Our analyses reveal different characteristics of amino acid hydrophobicity and volume propensity in the different subfamilies. We also found that the second extra-cytoplasmic loop has higher rates of evolution than the internal loops and transmembrane segments, suggesting that selection, shifting, reassignments and broadening of receptor binding specificities involve mainly this loop.

Crystal structure of the SarS protein from Staphylococcus aureus

The expression of virulence determinants in Staphylococcus aureus is controlled by global regulatory loci (e.g., sarA and agr). One of these determinants, protein A (spa), is activated by sarS, which encodes a 250-residue DNA-binding protein. Genetic analysis indicated that the agr locus likely mediates spa repression by suppressing the transcription of sarS. Contrary to SarA and SarR, which require homodimer formation for proper function, SarS is unusual within the SarA protein family in that it contains two homologous halves, with each half sharing sequence similarity to SarA and SarR. Here we report the 2.2 A resolution X-ray crystal structure of the SarS protein. SarS has folds similar to those of SarR and, quite plausibly, the native SarA structure. Two typical winged-helix DNA-binding domains are connected by a well-ordered loop. The interactions between the two domains are extensive and conserved. The putative DNA-binding surface is highly positively charged. In contrast, negatively charged patches are located opposite to the DNA-binding surface. Furthermore, sequence alignment and structural comparison revealed that MarR has folds similar to those of SarR and SarS. Members of the MarR protein family have previously been implicated in the negative regulation of an efflux pump involved in multiple antibiotic resistance in many gram-negative species. We propose that MarR also belongs to the winged-helix protein family and has a similar mode of DNA binding as SarR and SarS and possibly the entire SarA protein family member. Based on the structural differences of SarR, SarS, and MarR, we further classified these winged-helix proteins to three subfamilies, SarA, SarS, and MarR. Finally, a possible transcription regulation mechanism is proposed.

Structures of apolipoprotein A-II and a lipid-surrogate complex provide insights into apolipoprotein-lipid interactions

Apolipoproteins A-I and A-II form the major protein constituents of high-density lipid particles (HDL), the concentration of which is inversely correlated with the frequency of heart disease in humans. Although the physiological role of apolipoprotein A-II is unclear, evidence for its involvement in free fatty acid metabolism in mice has recently been obtained. Currently, the best characterized activity of apolipoprotein A-II is its potent antagonism of the anti-atherogenic and anti-inflammatory activities of apolipoprotein A-I, probably due to its competition with the latter for lipid acyl side chains in HDL. Many interactions of apolipoprotein A-I with enzymes and proteins involved in reverse cholesterol transport and HDL maturation are mediated by lipid-bound protein. The structural bases of interaction with lipids are expected to be common to exchangeable apolipoproteins and attributable to amphipathic alpha-helices present in each of them. Thus, characterization of apolipoprotein-lipid interactions in any apolipoprotein is likely to provide information that is applicable to the entire class. We report structures of human apolipoprotein A-II and its complex with beta-octyl glucoside, a widely used lipid surrogate. The former shows that disulfide-linked dimers of apolipoprotein A-II form amphipathic alpha-helices which aggregate into tetramers. Dramatic changes, observed in the presence of beta-octyl glucoside, might provide clues to the structural basis for its antagonism of apolipoprotein A-I. Additionally, excursions of individual molecules of apolipoprotein A-II from a common helical architecture in both structures indicate that lipid-bound apolipoproteins are likely to have an ensemble of related conformations. These structures provide the first experimental paradigm for description of apolipoprotein-lipid interactions at the atomic level.

Quadratic shape descriptors. 1. Rapid superposition of dissimilar molecules using geometrically invariant surface descriptors

In this paper, we present a novel approach to shape-based molecular similarity searching. The method that we introduce is able to superimpose dissimilar molecules by using geometrically invariant molecular surface descriptors. The shape descriptors are calculated by least-squares fitting of a quadratic function to small sections of the molecular surface of a ligand. Invariant geometric properties of the approximated surface patch are then extracted from the fitted quadratic function. The extracted properties are used to quantify the shape and to obtain a canonical orientation for this section of surface. The superimposition algorithm uses these geometric invariants to recognize similar regions of surface shape existing on two molecules and to bring these regions (and consequently the molecules) into registration. Because these geometric descriptors are based upon local surface shape, the superimposing algorithm is insensitive to the connectivity and the relative sizes of the molecules being matched. The capabilities of our algorithm are demonstrated by superimposing dissimilar ligands known to inhibit the same enzyme system. In all cases examined the algorithm generates superpositions that are in agreement with crystallographic results. The algorithm is also applied to align the two different proteins on the basis of the shape of their active sites.

Deviant trafficking of I-Ad mutant molecules is reflected in their peptide binding properties

I-Ad molecules harboring single amino acid changes in the conserved 80-82 region of the beta-chain show altered trafficking in invariant chain (Ii)-negative cell lines. Since residues beta81 and beta82 form hydrogen bonds with the backbone of bound peptide, alterations in this region may result in distinct MHC class II conformers that are targeted aberrantly. We examined the assembly and peptide binding properties of the mutant I-Ad molecules generated by in vitro translation. Indeed, loss of a single hydrogen bond at beta81, or of two hydrogen bonds at beta82, is sufficient to render I-Ad incapable of stable interaction with CLIP and other antigenic peptides, despite normal assembly with intact invariant chain. These results suggest that stable interaction of MHC class II molecules with peptide requires the integrity of the H-bond network between residues in the MHC class II alpha-helices and bound peptide, and that conformational features revealed by stable peptide binding are critical for MHC class II intracellular transport.