2D Zernike polynomial expansion: finding the protein-protein binding regions

We present a method for efficiently and effectively assessing whether and where two proteins can interact with each other to form a complex. This is still largely an open problem, even for those relatively few cases where the 3D structure of both proteins is known. In fact, even if much of the information about the interaction is encoded in the chemical and geometric features of the structures, the set of possible contact patches and of their relative orientations are too large to be computationally affordable in a reasonable time, thus preventing the compilation of reliable interactome. Our method is able to rapidly and quantitatively measure the geometrical shape complementarity between interacting proteins, comparing their molecular iso-electron density surfaces expanding the surface patches in term of 2D Zernike polynomials. We first test the method against the real binding region of a large dataset of known protein complexes, reaching a success rate of 0.72. We then apply the method for the blind recognition of binding sites, identifying the real region of interaction in about 60% of the analyzed cases. Finally, we investigate how the efficiency in finding the right binding region depends on the surface roughness as a function of the expansion order

Relating the shape of protein binding sites to binding affinity profiles: is there an association?

<p>Abstract</p> <p>Background</p> <p>Various pattern-based methods exist that use <it>in vitro </it>or <it>in silico </it>affinity profiles for classification and functional examination of proteins. Nevertheless, the connection between the protein affinity profiles and the structural characteristics of the binding sites is still unclear. Our aim was to investigate the association between virtual drug screening results (calculated binding free energy values) and the geometry of protein binding sites. Molecular Affinity Fingerprints (MAFs) were determined for 154 proteins based on their molecular docking energy results for 1,255 FDA-approved drugs. Protein binding site geometries were characterized by 420 PocketPicker descriptors. The basic underlying component structure of MAFs and binding site geometries, respectively, were examined by principal component analysis; association between principal components extracted from these two sets of variables was then investigated by canonical correlation and redundancy analyses.</p> <p>Results</p> <p>PCA analysis of the MAF variables provided 30 factors which explained 71.4% of the total variance of the energy values while 13 factors were obtained from the PocketPicker descriptors which cumulatively explained 94.1% of the total variance. Canonical correlation analysis resulted in 3 statistically significant canonical factor pairs with correlation values of 0.87, 0.84 and 0.77, respectively. Redundancy analysis indicated that PocketPicker descriptor factors explain 6.9% of the variance of the MAF factor set while MAF factors explain 15.9% of the total variance of PocketPicker descriptor factors. Based on the salient structures of the factor pairs, we identified a clear-cut association between the shape and bulkiness of the drug molecules and the protein binding site descriptors.</p> <p>Conclusions</p> <p>This is the first study to investigate complex multivariate associations between affinity profiles and the geometric properties of protein binding sites. We found that, except for few specific cases, the shapes of the binding pockets have relatively low weights in the determination of the affinity profiles of proteins. Since the MAF profile is closely related to the target specificity of ligand binding sites we can conclude that the shape of the binding site is not a pivotal factor in selecting drug targets. Nonetheless, based on strong specific associations between certain MAF profiles and specific geometric descriptors we identified, the shapes of the binding sites do have a crucial role in virtual drug design for certain drug categories, including morphine derivatives, benzodiazepines, barbiturates and antihistamines.</p

Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening

This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. Multicomponent persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for chemical and biological problems. Extensive numerical experiments involving more than 4,000 protein-ligand complexes from the PDBBind database and near 100,000 ligands and decoys in the DUD database are performed to test respectively the scoring power and the virtual screening power of the proposed topological approaches. It is demonstrated that the present approaches outperform the modern machine learning based methods in protein-ligand binding affinity predictions and ligand-decoy discrimination

Using diffusion distances for flexible molecular shape comparison

<p>Abstract</p> <p>Background</p> <p>Many molecules are flexible and undergo significant shape deformation as part of their function, and yet most existing molecular shape comparison (MSC) methods treat them as rigid bodies, which may lead to incorrect shape recognition.</p> <p>Results</p> <p>In this paper, we present a new shape descriptor, named Diffusion Distance Shape Descriptor (DDSD), for comparing 3D shapes of flexible molecules. The diffusion distance in our work is considered as an average length of paths connecting two landmark points on the molecular shape in a sense of inner distances. The diffusion distance is robust to flexible shape deformation, in particular to topological changes, and it reflects well the molecular structure and deformation without explicit decomposition. Our DDSD is stored as a histogram which is a probability distribution of diffusion distances between all sample point pairs on the molecular surface. Finally, the problem of flexible MSC is reduced to comparison of DDSD histograms.</p> <p>Conclusions</p> <p>We illustrate that DDSD is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. The presented algorithm is robust and does not require any prior knowledge of the flexible regions.</p

Multipolar representation of protein structure

BACKGROUND: That the structure determines the function of proteins is a central paradigm in biology. However, protein functions are more directly related to cooperative effects at the residue and multi-residue scales. As such, current representations based on atomic coordinates can be considered inadequate. Bridging the gap between atomic-level structure and overall protein-level functionality requires parameterizations of the protein structure (and other physicochemical properties) in a quasi-continuous range, from a simple collection of unrelated amino acids coordinates to the highly synergistic organization of the whole protein entity, from a microscopic view in which each atom is completely resolved to a "macroscopic" description such as the one encoded in the three-dimensional protein shape. RESULTS: Here we propose such a parameterization and study its relationship to the standard Euclidian description based on amino acid representative coordinates. The representation uses multipoles associated with residue Cα coordinates as shape descriptors. We demonstrate that the multipoles can be used for the quantitative description of the protein shape and for the comparison of protein structures at various levels of detail. Specifically, we construct a (dis)similarity measure in multipolar configuration space, and show how such a function can be used for the comparison of a pair of proteins. We then test the parameterization on a benchmark set of the protein kinase-like superfamily. We prove that, when the biologically relevant portions of the proteins are retained, it can robustly discriminate between the various families in the set in a way not possible through sequence or conventional structural representations alone. We then compare our representation with the Cartesian coordinate description and show that, as expected, the correlation with that representation increases as the level of detail, measured by the highest rank of multipoles used in the representation, approaches the dimensionality of the fold space. CONCLUSION: The results described here demonstrate how a granular description of the protein structure can be achieved using multipolar coefficients. The description has the additional advantage of being immediately generalizable for any residue-specific property therefore providing a unitary framework for the study and comparison of the spatial profile of various protein properties

Protein Surface Characterization Using an Invariant Descriptor

Aim. To develop a new invariant descriptor for the characterization of protein surfaces, suitable for various analysis tasks, such as protein functional classification, and search and retrieval of protein surfaces over a large database. Methods. We start with a local descriptor of selected circular patches on the protein surface. The descriptor records the distance distribution between the central residue and the residues within the patch, keeping track of the number of particular pairwise residue cooccurrences in the patch. A global descriptor for the entire protein surface is then constructed by combining information from the local descriptors. Our method is novel in its focus on residue-specific distance distributions, and the use of residue-distance co-occurrences as the basis for the proposed protein surface descriptors. Results. Results are presented for protein classification and for retrieval for three protein families. For the three families, we obtained an area under the curve for precision and recall ranging from 0.6494 (without residue co-occurrences) to 0.6683 (with residue co-occurrences). Large-scale screening using two other protein families placed related family members at the top of the rank, with a number of uncharacterized proteins also retrieved. Comparative results with other proposed methods are included