Visible Volume: a Robust Measure for Protein Structure Characterization

We propose a new characterization of protein structure based on the natural tetrahedral geometry of the β carbon and a new geometric measure of structural similarity, called visible volume. In our model, the side-chains are replaced by an ideal tetrahedron, the orientation of which is fixed with respect to the backbone and corresponds to the preferred rotamer directions. Visible volume is a measure of the non-occluded empty space surrounding each residue position after the side-chains have been removed. It is a robust, parameter-free, locally-computed quantity that accounts for many of the spatial constraints that are of relevance to the corresponding position in the native structure. When computing visible volume, we ignore the nature of both the residue observed at each site and the ones surrounding it. We focus instead on the space that, together, these residues could occupy. By doing so, we are able to quantify a new kind of invariance beyond the apparent variations in protein families, namely, the conservation of the physical space available at structurally equivalent positions for side-chain packing. Corresponding positions in native structures are likely to be of interest in protein structure prediction, protein design, and homology modeling. Visible volume is related to the degree of exposure of a residue position and to the actual rotamers in native proteins. In this article, we discuss the properties of this new measure, namely, its robustness with respect to both crystallographic uncertainties and naturally occurring variations in atomic coordinates, and the remarkable fact that it is essentially independent of the choice of the parameters used in calculating it. We also show how visible volume can be used to align protein structures, to identify structurally equivalent positions that are conserved in a family of proteins, and to single out positions in a protein that are likely to be of biological interest. These properties qualify visible volume as a powerful tool in a variety of applications, from the detailed analysis of protein structure to homology modeling, protein structural alignment, and the definition of better scoring functions for threading purposes.National Library of Medicine (LM05205-13

Exploration of the Disambiguation of Amino Acid Types to Chi-1 Rotamer Types in Protein Structure Prediction and Design

A protein’s global fold provide insight into function; however, function specificity is often detailed in sidechain orientation. Thus, determining the rotamer conformations is often crucial in the contexts of protein structure/function prediction and design. For all non-glycine and non-alanine types, chi-1 rotamers occupy a small number of discrete number of states. Herein, we explore the possibility of describing evolution from the perspective of the sidechains’ structure versus the traditional twenty amino acid types. To validate our hypothesis that this perspective is more crucial to our understanding of evolutionary relationships, we investigate its uses as evolutionary, substitution matrices for sequence alignments for fold recognition purposes and computational protein design with specific focus in designing beta sheet environments, where previous studies have been done on amino acid-types alone. Throughout this study, we also propose the concept of the “chi-1 rotamer sequence” that describes the chi-1 rotamer composition of a protein. We also present attempts to predict these sequences and real-value torsion angles from amino acid sequence information. First, we describe our developments of log-odds scoring matrices for sequence alignments. Log-odds substitution matrices are widely used in sequence alignments for their ability to determine evolutionary relationship between proteins. Traditionally, databases of sequence information guide the construction of these matrices which illustrates its power in discovering distant or weak homologs. Weak homologs, typically those that share low sequence identity (< 30%), are often difficult to identify when only using basic amino acid sequence alignment. While protein threading approaches have addressed this issue, many of these approaches include sequenced-based information or profiles guided by amino acid-based substitution matrices, namely BLOSUM62. Here, we generated a structural-based substitution matrix born by TM-align structural alignments that captures both the sequence mutation rate within same protein family folds and the chi-1 rotamer that represents each amino acid. These rotamer substitution matrices (ROTSUMs) discover new homologs and improved alignments in the PDB that traditional substitution matrices, based solely on sequence information, cannot identify. Certain tools and algorithms to estimate rotamer torsions angles have been developed but typically require either knowledge of backbone coordinates and/or experimental data to help guide the prediction. Herein, we developed a fragment-based algorithm, Rot1Pred, to determine the chi-1 states in each position of a given amino acid sequence, yielding a chi-1 rotamer sequence. This approach employs fragment matching of the query sequence to sequence-structure fragment pairs in the PDB to predict the query’s sidechain structure information. Real-value torsion angles were also predicted and compared against SCWRL4. Results show that overall and for most amino-acid types, Rot1Pred can calculate chi-1 torsion angles significantly closer to native angles compared to SCWRL4 when evaluated on I-TASSER generated model backbones. Finally, we’ve developed and explored chi-1-rotamer-based statistical potentials and evolutionary profiles constructed for de novo computational protein design. Previous analyses which aim to energetically describe the preference of amino acid types in beta sheet environments (parallel vs antiparallel packing or n- and c-terminal beta strand capping) have been performed with amino acid types although no explicit rotamer representation is given in their scoring functions. In our study, we construct statistical functions which describes chi-1 rotamer preferences in these environments and illustrate their improvement over previous methods. These specialized knowledge-based energy functions have generated sequences whose I-TASSER predicted models are structurally-alike to their input structures yet consist of low sequence identity.PHDChemical BiologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145951/1/jarrettj_1.pd

Multiple structure alignment and consensus identification for proteins

<p>Abstract</p> <p>Background</p> <p>An algorithm is presented to compute a multiple structure alignment for a set of proteins and to generate a consensus (pseudo) protein which captures common substructures present in the given proteins. The algorithm represents each protein as a sequence of triples of coordinates of the alpha-carbon atoms along the backbone. It then computes iteratively a sequence of transformation matrices (i.e., translations and rotations) to align the proteins in space and generate the consensus. The algorithm is a heuristic in that it computes an approximation to the optimal alignment that minimizes the sum of the pairwise distances between the consensus and the transformed proteins.</p> <p>Results</p> <p>Experimental results show that the algorithm converges quite rapidly and generates consensus structures that are visually similar to the input proteins. A comparison with other coordinate-based alignment algorithms (MAMMOTH and MATT) shows that the proposed algorithm is competitive in terms of speed and the sizes of the conserved regions discovered in an extensive benchmark dataset derived from the HOMSTRAD and SABmark databases.</p> <p>The algorithm has been implemented in C++ and can be downloaded from the project's web page. Alternatively, the algorithm can be used via a web server which makes it possible to align protein structures by uploading files from local disk or by downloading protein data from the RCSB Protein Data Bank.</p> <p>Conclusions</p> <p>An algorithm is presented to compute a multiple structure alignment for a set of proteins, together with their consensus structure. Experimental results show its effectiveness in terms of the quality of the alignment and computational cost.</p

Mass & secondary structure propensity of amino acids explain their mutability and evolutionary replacements

Why is an amino acid replacement in a protein accepted during evolution? The answer given by bioinformatics relies on the frequency of change of each amino acid by another one and the propensity of each to remain unchanged. We propose that these replacement rules are recoverable from the secondary structural trends of amino acids. A distance measure between high-resolution Ramachandran distributions reveals that structurally similar residues coincide with those found in substitution matrices such as BLOSUM: Asn Asp, Phe Tyr, Lys Arg, Gln Glu, Ile Val, Met → Leu; with Ala, Cys, His, Gly, Ser, Pro, and Thr, as structurally idiosyncratic residues. We also found a high average correlation (\overline{R} R = 0.85) between thirty amino acid mutability scales and the mutational inertia (I X ), which measures the energetic cost weighted by the number of observations at the most probable amino acid conformation. These results indicate that amino acid substitutions follow two optimally-efficient principles: (a) amino acids interchangeability privileges their secondary structural similarity, and (b) the amino acid mutability depends directly on its biosynthetic energy cost, and inversely with its frequency. These two principles are the underlying rules governing the observed amino acid substitutions. © 2017 The Author(s)

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe

Reduced representation of protein structure: implications on efficiency and scope of detection of structural similarity

<p>Abstract</p> <p>Background</p> <p>Computational comparison of two protein structures is the starting point of many methods that build on existing knowledge, such as structure modeling (including modeling of protein complexes and conformational changes), molecular replacement, or annotation by structural similarity. In a commonly used strategy, significant effort is invested in matching two sets of atoms. In a complementary approach, a global descriptor is assigned to the overall structure, thus losing track of the substructures within.</p> <p>Results</p> <p>Using a small set of geometric features, we define a reduced representation of protein structure, together with an optimizing function for matching two representations, to provide a pre-filtering stage in a database search. We show that, in a straightforward implementation, the representation performs well in terms of resolution in the space of protein structures, and its ability to make new predictions.</p> <p>Conclusions</p> <p>Perhaps unexpectedly, a substantial discriminating power already exists at the level of main features of protein structure, such as directions of secondary structural elements, possibly constrained by their sequential order. This can be used toward efficient comparison of protein (sub)structures, allowing for various degrees of conformational flexibility within the compared pair, which in turn can be used for modeling by homology of protein structure and dynamics.</p