The application of 3D Zernike moments for the description of "model-free" molecular structure, functional motion, and structural reliability

Binding site identification of G protein-coupled receptors through a 3D Zernike polynomials-based method: application to C. elegans olfactory receptors

Studying the binding processes of G protein-coupled receptors (GPCRs) proteins is of particular interest both to better understand the molecular mechanisms that regulate the signaling between the extracellular and intracellular environment and for drug design purposes. In this study, we propose a new computational approach for the identification of the binding site for a specific ligand on a GPCR. The method is based on the Zernike polynomials and performs the ligand-GPCR association through a shape complementarity analysis of the local molecular surfaces. The method is parameter-free and it can distinguish, working on hundreds of experimentally GPCR-ligand complexes, binding pockets from randomly sampled regions on the receptor surface, obtaining an Area Under ROC curve of 0.77. Given its importance both as a model organism and in terms of applications, we thus investigated the olfactory receptors of the C. elegans, building a list of associations between 21 GPCRs belonging to its olfactory neurons and a set of possible ligands. Thus, we can not only carry out rapid and efficient screenings of drugs proposed for GPCRs, key targets in many pathologies, but also we laid the groundwork for computational mutagenesis processes, aimed at increasing or decreasing the binding affinity between ligands and receptors.

Comprehensive analysis of lectin-glycan interactions reveals determinants of lectin specificity

Lectin-glycan interactions facilitate inter- and intracellular communication in many processes including protein trafficking, host-pathogen recognition, and tumorigenesis promotion. Specific recognition of glycans by lectins is also the basis for a wide range of applications in areas including glycobiology research, cancer screening, and antiviral therapeutics. To provide a better understanding of the determinants of lectin-glycan interaction specificity and support such applications, this study comprehensively investigates specificity-conferring features of all available lectin-glycan complex structures. Systematic characterization, comparison, and predictive modeling of a set of 221 complementary physicochemical and geometric features representing these interactions highlighted specificity-conferring features with potential mechanistic insight. Univariable comparative analyses with weighted Wilcoxon-Mann-Whitney tests revealed strong statistical associations between binding site features and specificity that are conserved across unrelated lectin binding sites. Multivariable modeling with random forests demonstrated the utility of these features for predicting the identity of bound glycans based on generalized patterns learned from non-homologous lectins. These analyses revealed global determinants of lectin specificity, such as sialic acid glycan recognition in deep, concave binding sites enriched for positively charged residues, in contrast to high mannose glycan recognition in fairly shallow but well-defined pockets enriched for non-polar residues. Focused fine specificity analysis of hemagglutinin interactions with human-like and avian-like glycans uncovered features representing both known and novel mutations related to shifts in influenza tropism from avian to human tissues. As the approach presented here relies on co-crystallized lectin-glycan pairs for studying specificity, it is limited in its inferences by the quantity, quality, and diversity of the structural data available. Regardless, the systematic characterization of lectin binding sites presented here provides a novel approach to studying lectin specificity and is a step towards confidently predicting new lectin-glycan interactions.

Quantitative Description of Surface Complementarity of Antibody-Antigen Interfaces

Antibodies have the remarkable ability to recognise their cognate antigens with extraordinary affinity and specificity. Discerning the rules that define antibody-antigen recognition is a fundamental step in the rational design and engineering of functional antibodies with desired properties. In this study we apply the 3D Zernike formalism to the analysis of the surface properties of the antibody complementary determining regions (CDRs). Our results show that shape and electrostatic 3DZD descriptors of the surface of the CDRs are predictive of antigen specificity, with classification accuracy of 81% and area under the receiver operating characteristic curve (AUC) of 0.85. Additionally, while in terms of surface size, solvent accessibility and amino acid composition, antibody epitopes are typically not distinguishable from non-epitope, solvent-exposed regions of the antigen, the 3DZD descriptors detect significantly higher surface complementarity to the paratope, and are able to predict correct paratope-epitope interaction with an AUC = 0.75.

ZEAL: protein structure alignment based on shape similarity

MOTIVATION

Most protein-structure superimposition tools consider only Cartesian coordinates. Yet, much of biology happens on the surface of proteins, which is why proteins with shared ancestry and similar function often have comparable surface shapes. Superposition of proteins based on surface shape can enable comparison of highly divergent proteins, identify convergent evolution and enable detailed comparison of surface features and binding sites.

RESULTS

We present ZEAL, an interactive tool to superpose global and local protein structures based on their shape resemblance using 3D (Zernike-Canterakis) functions to represent the molecular surface. In a benchmark study of structures with the same fold, we show that ZEAL outperforms two other methods for shape-based superposition. In addition, alignments from ZEAL were of comparable quality to the coordinate-based superpositions provided by TM-align. For comparisons of proteins with limited sequence and backbone-fold similarity, where coordinate-based methods typically fail, ZEAL can often find alignments with substantial surface-shape correspondence. In combination with shape-based matching, ZEAL can be used as a general tool to study relationships between shape and protein function. We identify several categories of protein functions where global shape similarity is significantly more likely than expected by random chance, when comparing proteins with little similarity on the fold level. In particular, we find that global surface shape similarity is particular common among DNA binding proteins.

AVAILABILITY AND IMPLEMENTATION

ZEAL can be used online at https://andrelab.org/zeal or as a standalone program with command line or graphical user interface. Source files and installers are available at https://github.com/Andre-lab/ZEAL.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A novel strategy for molecular interfaces optimization: The case of Ferritin-Transferrin receptor interaction

Protein-protein interactions regulate almost all cellular functions and rely on a fine tune of surface amino acids properties involved on both molecular partners. The disruption of a molecular association can be caused even by a single residue mutation, often leading to a pathological modification of a biochemical pathway. Therefore the evaluation of the effects of amino acid substitutions on binding, and the ad hoc design of protein-protein interfaces, is one of the biggest challenges in computational biology. Here, we present a novel strategy for computational mutation and optimization of protein-protein interfaces. Modeling the interaction surface properties using the Zernike polynomials, we describe the shape and electrostatics of binding sites with an ordered set of descriptors, making possible the evaluation of complementarity between interacting surfaces. With a Monte Carlo approach, we obtain protein mutants with controlled molecular complementarities. Applying this strategy to the relevant case of the interaction between Ferritin and Transferrin Receptor, we obtain a set of Ferritin mutants with increased or decreased complementarity. The extensive molecular dynamics validation of the method results confirms its efficacy, showing that this strategy represents a very promising approach in designing correct molecular interfaces.

Quantitative Characterization of Binding Pockets and Binding Complementarity by Means of Zernike Descriptors

In this work, we describe the application of the Zernike formalism to quantitatively characterize the binding pockets of two sets of biologically relevant systems. Such an approach, when applied to molecular dynamics trajectories, is able to pinpoint the subtle differences between very similar molecular regions and their impact on the local propensity to ligand binding, allowing us to quantify such differences. The statistical robustness of our procedure suggests that it is very suitable to describe protein binding sites and protein-ligand interactions within a rigorous and well-defined framework.

Antibody Specific B-Cell Epitope Predictions: Leveraging Information From Antibody-Antigen Protein Complexes

B-cells can neutralize pathogenic molecules by targeting them with extreme specificity using receptors secreted or expressed on their surface (antibodies). This is achieved via molecular interactions between the paratope (i.e., the antibody residues involved in the binding) and the interacting region (epitope) of its target molecule (antigen). Discerning the rules that define this specificity would have profound implications for our understanding of humoral immunogenicity and its applications. The aim of this work is to produce improved, antibody-specific epitope predictions by exploiting features derived from the antigens and their cognate antibodies structures, and combining them using statistical and machine learning algorithms. We have identified several geometric and physicochemical features that are correlated in interacting paratopes and epitopes, used them to develop a Monte Carlo algorithm to generate putative epitopes-paratope pairs, and train a machine-learning model to score them. We show that, by including the structural and physicochemical properties of the paratope, we improve the prediction of the target of a given B-cell receptor. Moreover, we demonstrate a gain in predictive power both in terms of identifying the cognate antigen target for a given antibody and the antibody target for a given antigen, exceeding the results of other available tools.

Efficient algorithm for expanding theoretical electron densities in canterakis-zernike functions

An algorithm for the efficient computation of Canterakis-Zernike moments of theoretically computed molecular electron densities and rotationally invariant Fingerprint indices derived from them is reported. The algorithm is suitable for any density expressed in terms of Gaussian- or Slater-type functions within the Linear Combination of Atomic Orbitals framework at any level of computation. Electron density is expressed as a one-center expansion of real regular spherical harmonics times radial factors by means of translation techniques, which facilitates the efficient computation of the moments in terms of a single one-dimension numerical integration. The performance of the algorithm is analyzed showing that the computation of radial factors in the quadrature points is responsible for almost all computational time. The procedure is applicable to any density obtained with standard packages for molecular structure calculations. © 2018 Wiley Periodicals, Inc.

Superposition-free comparison and clustering of antibody binding sites: implications for the prediction of the nature of their antigen

We describe here a superposition free method for comparing the surfaces of antibody binding sites based on the Zernike moments and show that they can be used to quickly compare and cluster sets of antibodies. The clusters provide information about the nature of the bound antigen that, when combined with a method for predicting the number of direct antibody antigen contacts, allows the discrimination between protein and non-protein binding antibodies with an accuracy of 76%. This is of relevance in several aspects of antibody science, for example to select the framework to be used for a combinatorial antibody library.

Comparison of organs' shapes with geometric and Zernike 3D moments

The morphological similarity of organs is studied with feature vectors based on geometric and Zernike 3D moments. It is particularly investigated if outliers and average models can be identified. For this purpose, the relative proximity to the mean feature vector is defined, principal coordinate and clustering analyses are also performed. To study the consistency and usefulness of this approach, 17 livers and 76 hearts voxel models from several sources are considered. In the liver case, models with similar morphological feature are identified. For the limited amount of studied cases, the liver of the ICRP male voxel model is identified as a better surrogate than the female one. For hearts, the clustering analysis shows that three heart shapes represent about 80% of the morphological variations. The relative proximity and clustering analysis rather consistently identify outliers and average models. For the two cases, identification of outliers and surrogate of average models is rather robust. However, deeper classification of morphological feature is subject to caution and can only be performed after cross analysis of at least two kinds of feature vectors. Finally, the Zernike moments contain all the information needed to re-construct the studied objects and thus appear as a promising tool to derive statistical organ shapes.

Fragmentation-tree density representation for crystallographic modelling of bound ligands

The identification and modelling of ligands into macromolecular models is important for understanding molecule's function and for designing inhibitors to modulate its activities. We describe new algorithms for the automated building of ligands into electron density maps in crystal structure determination. Location of the ligand-binding site is achieved by matching numerical shape features describing the ligand to those of density clusters using a "fragmentation-tree" density representation. The ligand molecule is built using two distinct algorithms exploiting free atoms with inter-atomic connectivity and Metropolis-based optimisation of the conformational state of the ligand, producing an ensemble of structures from which the final model is derived. The method was validated on several thousand entries from the Protein Data Bank. In the majority of cases, the ligand-binding site could be correctly located and the ligand model built with a coordinate accuracy of better than 1 Å. We anticipate that the method will be of routine use to anyone modelling ligands, lead compounds or even compound fragments as part of protein functional analyses or drug design efforts.

Fingerprint-based structure retrieval using electron density

We present a computational approach that can quickly search a large protein structural database to identify structures that fit a given electron density, such as determined by cryo-electron microscopy. We use geometric invariants (fingerprints) constructed using 3D Zernike moments to describe the electron density, and reduce the problem of fitting of the structure to the electron density to simple fingerprint comparison. Using this approach, we are able to screen the entire Protein Data Bank and identify structures that fit two experimental electron densities determined by cryo-electron microscopy.

Using diffusion distances for flexible molecular shape comparison

Background

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.

Results

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.

Conclusions

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.