Similarity and symmetry measures for convex sets based on Minkowski addition

This paper discusses similarity and symmetry measures for convex shapes. Their definition is based on Minkowski addition and the Brunn-Minkowski inequality. All measures considered are invariant under translations; furthermore, they may also be invariant under rotations, multiplications, reflections, or the class of all affine transformations. The examples discussed in this paper allow efficient algorithms if one restricts oneselves to convex polygons. Although it deals exclusively with the 2-dimensional case, many of the theoretical results carry over almost directly to higher-dimensional spaces. Some results obtained in this paper are illustrated by experimental data

Side-chain conformational changes upon protein-protein association

Conformational changes upon protein-protein association are the key element of the binding mechanism. The study presents a systematic large-scale analysis of such conformational changes in the side chains. The results indicate that short and long side chains have different propensities for the conformational changes. Long side chains with three or more dihedral angles are often subject to large conformational transition. Shorter residues with one or two dihedral angles typically undergo local conformational changes not leading to a conformational transition. The relationship between the local readjustments and the equilibrium fluctuations of a side chain around its unbound conformation is suggested. Most of the side chains undergo larger changes in the dihedral angle most distant from the backbone. The amino acids with symmetric aromatic (Phe and Tyr) and charged (Asp and Glu) groups show the opposite trend where the near-backbone dihedral angles change the most. The frequencies of the core-to-surface interface transitions of six nonpolar residues and Tyr exceed the frequencies of the opposite, surface-to-core transitions. The binding increases both polar and nonpolar interface areas. However, the increase of the nonpolar area is larger for all considered classes of protein complexes. The results suggest that the protein association perturbs the unbound interfaces to increase the hydrophobic forces. The results facilitate better understanding of the conformational changes in proteins and suggest directions for efficient conformational sampling in docking protocols.Comment: 21 pages, 6 figure

Structure Fluctuations and Conformational Changes in Protein Binding

Structure fluctuations and conformational changes accompany all biological processes involving macromolecules. The paper presents a classification of protein residues based on the normalized equilibrium fluctuations of the residue centers of mass in proteins and a statistical analysis of conformation changes in the side-chains upon binding. Normal mode analysis and an elastic network model were applied to a set of protein complexes to calculate the residue fluctuations and develop the residue classification. Comparison with a classification based on normalized B-factors suggests that the B-factors may underestimate protein flexibility in solvent. Our classification shows that protein loops and disordered fragments are enriched with highly fluctuating residues and depleted with weakly fluctuating residues. Strategies for engineering thermostable proteins are discussed. To calculate the dihedral angles distribution functions, the configuration space was divided into cells by a cubic grid. The effect of protein association on the distribution functions depends on the amino acid type and a grid step in the dihedral angles space. The changes in the dihedral angles increase from the near-backbone dihedral angle to the most distant one, for most residues. On average, one fifth of the interface residues change the rotamer state upon binding, whereas the rest of the interface residues undergo local readjustments within the same rotamer

Rotamer libraries and probabilities of transition between rotamers for the side chains in protein-protein binding

Author's Pre-print: green tick author can archive pre-print (ie pre-refereeing) Author's Post-print: grey tick subject to Restrictions below, author can archive post-print (ie final draft post-refereeing) Restrictions: 12 months embargo Publisher's Version/PDF: cross author cannot archive publisher's version/PDF General Conditions: Some journals have separate policies, please check with each journal directly On author's personal website, institutional repositories, arXiv, AgEcon, PhilPapers, PubMed Central, RePEc or Social Science Research Network Author's pre-print may not be updated with Publisher's Version/PDF Author's pre-print must acknowledge acceptance for publication Non-Commercial Publisher's version/PDF cannot be used Publisher source must be acknowledged with citation Must link to publisher version with set statement (see policy) If OnlineOpen is available, BBSRC, EPSRC, MRC, NERC and STFC authors, may self-archive after 12 month

Correlation analysis of the side-chains conformational distribution in bound and unbound proteins

Background: Protein interactions play a key role in life processes. Characterization of conformational properties of protein-protein interactions is important for understanding the mechanisms of protein association. The rapidly increasing amount of experimentally determined structures of proteins and protein-protein complexes provides foundation for research on protein interactions and complex formation. The knowledge of the conformations of the surface side chains is essential for modeling of protein complexes. The purpose of this study was to analyze and compare dihedral angle distribution functions of the side chains at the interface and non-interface areas in bound and unbound proteins. Results: To calculate the dihedral angle distribution functions, the configuration space was divided into grid cells. Statistical analysis showed that the similarity between bound and unbound interface and non-interface surface depends on the amino acid type and the grid resolution. The correlation coefficients between the distribution functions increased with the grid spacing increase for all amino acid types. The Manhattan distance showing the degree of dissimilarity between the distribution functions decreased accordingly. Short residues with one or two dihedral angles had higher correlations and smaller Manhattan distances than the longer residues. Met and Arg had the slowest growth of the correlation coefficient with the grid spacing increase. The correlations between the interface and non-interface distribution functions had a similar dependence on the grid resolution in both bound and unbound states. The interface and non-interface differences between bound and unbound distribution functions, caused by biological protein-protein interactions or crystal contacts, disappeared at the 70° grid spacing for interfaces and 30° for non-interface surface, which agrees with an average span of the side-chain rotamers. Conclusions: The two-fold difference in the critical grid spacing indicates larger conformational changes upon binding at the interface than at the rest of the surface. At the same time, transitions between rotamers induced by interactions across the interface or the crystal packing are rare, with most side chains having local readjustments that do not change the rotameric state. The analysis is important for better understanding of protein interactions and development of flexible docking approaches. Keywords: Protein interactions; Protein docking; Molecular recognition; Conformational analysi

Ultra-fast Glyco-coating of Non-biological Surfaces

The ability to glycosylate surfaces has medical and diagnostic applications, but there is no technology currently recognized as being able to coat any surface without the need for prior chemical modification of the surface. Recently, a family of constructs called function-spacer-lipids (FSL) has been used to glycosylate cells. Because it is known that lipid-based material can adsorb onto surfaces, we explored the potential and performance of cell-labelling FSL constructs to “glycosylate” non-biological surfaces. Using blood group A antigen as an indicator, the performance of a several variations of FSL constructs to modify a large variety of non-biological surfaces was evaluated. It was found the FSL constructs when optimised could in a few seconds glycosylate almost any non-biological surface including metals, glass, plastics, rubbers and other polymers. Although the FSL glycan coating was non-covalent, and therefore temporary, it was sufficiently robust with appropriate selection of spacer and surface that it could capture anti-glycan antibodies, immobilize cells (via antibody), and withstand incubation in serum and extensive buffer washing, making it suitable for diagnostic and research applications

Structure fluctuations and conformational changes in protein binding

Structure fluctuations and conformational changes accompany all biological processes involving macromolecules. The paper presents a classification of protein residues based on the normalized equilibrium fluctuations of the residue centers of mass in proteins and a statistical analysis of conformation changes in the side-chains upon binding. Normal mode analysis and an elastic network model were applied to a set of protein complexes to calculate the residue fluctuations and develop the residue classification. Comparison with a classification based on normalized B-factors suggests that the B-factors may underestimate protein flexibility in solvent. Our classification shows that protein loops and disordered fragments are enriched with highly fluctuating residues and depleted with weakly fluctuating residues. To calculate the dihedral angles distribution functions, the configuration space was divided into cells by a cubic grid. The effect of protein association on the distribution functions depends on the amino acid type and a grid step in the dihedral angles space. The changes in the dihedral angles increase from the near-backbone dihedral angle to the most distant one, for most residues. On average, one fifth of the interface residues change the rotamer state upon binding, whereas the rest of the interface residues undergo local readjustments within the same rotamer.Comment: 13 pages, 6 figure

Protein Model Docking Benchmark 2

Structural characterization of protein-protein interactions is essential for our ability to understand life processes. However, only a fraction of known proteins have experimentally determined structures. Such structures provide templates for modeling of a large part of the proteome, where individual proteins can be docked by template-free or template-based techniques. Still, the sensitivity of the docking methods to the inherent inaccuracies of protein models, as opposed to the experimentally determined high-resolution structures, remains largely untested, primarily due to the absence of appropriate benchmark set(s). Structures in such a set should have pre-defined inaccuracy levels and, at the same time, resemble actual protein models in terms of structural motifs/packing. The set should also be large enough to ensure statistical reliability of the benchmarking results. We present a major update of the previously developed benchmark set of protein models. For each interactor, six models were generated with the model-to-native Cα RMSD in the 1 to 6 Å range. The models in the set were generated by a new approach, which corresponds to the actual modeling of new protein structures in the “real case scenario,” as opposed to the previous set, where a significant number of structures were model-like only. In addition, the larger number of complexes (165 vs. 63 in the previous set) increases the statistical reliability of the benchmarking. We estimated the highest accuracy of the predicted complexes (according to CAPRI criteria), which can be attained using the benchmark structures. The set is available at http://dockground.bioinformatics.ku.edu