3D Zernike Descriptors Research Articles

Efficient protein structure search using indexing methods

Understanding functions of proteins is one of the most important challenges in many studies of biological processes. The function of a protein can be predicted by analyzing the functions of structurally similar proteins, thus finding structurally similar proteins accurately and efficiently from a large set of proteins is crucial. A protein structure can be represented as a vector by 3D-Zernike Descriptor (3DZD) which compactly represents the surface shape of the protein tertiary structure. This simplified representation accelerates the searching process. However, computing the similarity of two protein structures is still computationally expensive, thus it is hard to efficiently process many simultaneous requests of structurally similar protein search. This paper proposes indexing techniques which substantially reduce the search time to find structurally similar proteins. In particular, we first exploit two indexing techniques, i.e., iDistance and iKernel, on the 3DZDs. After that, we extend the techniques to further improve the search speed for protein structures. The extended indexing techniques build and utilize an reduced index constructed from the first few attributes of 3DZDs of protein structures. To retrieve top-k similar structures, top-10 × k similar structures are first found using the reduced index, and top-k structures are selected among them. We also modify the indexing techniques to support θ-based nearest neighbor search, which returns data points less than θ to the query point. The results show that both iDistance and iKernel significantly enhance the searching speed. In top-k nearest neighbor search, the searching time is reduced 69.6%, 77%, 77.4% and 87.9%, respectively using iDistance, iKernel, the extended iDistance, and the extended iKernel. In θ-based nearest neighbor serach, the searching time is reduced 80%, 81%, 95.6% and 95.6% using iDistance, iKernel, the extended iDistance, and the extended iKernel, respectively.

Macromolecular Structure Modeling and Electron Microscopy Fitting using 3D Zernike Descriptors

A novel computational method for fitting high-resolution structures of multiple proteins into a cryoelectron microscopy (EM) map is presented. The method named EMLZerD generates a pool of candidate complex conformations of component proteins using a novel multiple protein docking method, Multi-LZerD, which are later compared with a provided EM map to select the ones that fit well into the EM map (Esquivel-Rodriguez & Kihara, J. Phys Chem B, 2012). Multi-LZerD (Esquivel-Rodriguez & Kihara, Proteins, 2012) builds models of multimeric protein complexes by effectively reusing pairwise docking predictions of component proteins. The comparison of docking conformations and the EM map is performed using the 3D Zernike descriptor (3DZD), a mathematical series expansion of three-dimensional functions. The 3DZD provides a unified representation of the surface shape of multimeric protein complex models and EM maps, which allows a convenient, fast quantitative comparison of the three-dimensional structural data. Out of 19 multimeric complexes tested, near native complex structures with a RMSD of less than 2.5 A were obtained for 14 cases while medium range resolution structures with correct topology were computed for the additional 5 cases.View Large Image | View Hi-Res Image | Download PowerPoint Slide

SVM Prediction of Ligand-binding Sites in Bacterial Lipoproteins Employing Shape and Physio-chemical Descriptors

Bacterial lipoproteins play critical roles in various physiological processes including the maintenance of pathogenicity and numbers of them are being considered as potential candidates for generating novel vaccines. In this work, we put forth an algorithm to identify and predict ligand-binding sites in bacterial lipoproteins. The method uses three types of pocket descriptors, namely fpocket descriptors, 3D Zernike descriptors and shell descriptors, and combines them with Support Vector Machine (SVM) method for the classification. The three types of descriptors represent shape-based properties of the pocket as well as its local physio-chemical features. All three types of descriptors, along with their hybrid combinations are evaluated with SVM and to improve classification performance, WEKA-InfoGain feature selection is applied. Results obtained in the study show that the classifier successfully differentiates between ligand-binding and non-binding pockets. For the combination of three types of descriptors, 10 fold cross-validation accuracy of 86.83% is obtained for training while the selected model achieved test Matthews Correlation Coefficient (MCC) of 0.534. Individually or in combination with new and existing methods, our model can be a very useful tool for the prediction of potential ligand-binding sites in bacterial lipoproteins.

Alignment-Independent Comparison of Binding Sites Based on DrugScore Potential Fields Encoded by 3D Zernike Descriptors

Analyzing protein binding sites provides detailed insights into the biological processes proteins are involved in, e.g., into drug-target interactions, and so is of crucial importance in drug discovery. Herein, we present novel alignment-independent binding site descriptors based on DrugScore potential fields. The potential fields are transformed to a set of information-rich descriptors using a series expansion in 3D Zernike polynomials. The resulting Zernike descriptors show a promising performance in detecting similarities among proteins with low pairwise sequence identities that bind identical ligands, as well as within subfamilies of one target class. Furthermore, the Zernike descriptors are robust against structural variations among protein binding sites. Finally, the Zernike descriptors show a high data compression power, and computing similarities between binding sites based on these descriptors is highly efficient. Consequently, the Zernike descriptors are a useful tool for computational binding site analysis, e.g., to predict the function of novel proteins, off-targets for drug candidates, or novel targets for known drugs.

Novel binding pocket descriptors based on DrugScore potential fields encoded by 3D Zernike descriptors

Proteins interact with other molecules, e.g. ligands or other proteins, in specific binding sites. Key factors for these interactions are the shape, size, and buriedness of the binding site, as well as its physicochemical composition. Since all these properties usually significantly vary among different proteins, up to now there is no standard definition what constitutes a binding site [1]. Thus, novel pocket descriptors allowing an in-depth characterization of binding sites are highly desired. Hence, we developed novel binding pocket descriptors based on 3D molecular interaction fields. The binding pocket of a protein is characterized using the distance dependent, knowledge-based pair potentials of the DrugScore scoring function [2] in combination with multiple ligand atom probes. To allow an efficient comparison of the resulting potential fields, the 3D grids are encoded using 3D Zernike descriptors. The 3D Zernike polynomials Znlm are orthonormal basis functions on the unit sphere. Thus, any 3D object can be represented as: using a 3D Zernike function expansion. We utilized the resulting function expansion coefficients cnlm, i.e. the 3D Zernike moments, to describe the 3D molecular potential fields characterizing a protein's binding pocket. The resulting descriptors are invariant under rotation, scaling, and translation and enable a fast comparison and an efficient characterization of protein binding pockets. Thus, these novel pocket descriptors can be used to predict target druggability or to calculate similarities between binding pockets, e.g. to predict potential off-targets or to perform protein function de-orphanization.

Fitting multimeric protein complexes into electron microscopy maps using 3D Zernike descriptors.

A novel computational method for fitting high-resolution structures of multiple proteins into a cryoelectron microscopy map is presented. The method named EMLZerD generates a pool of candidate multiple protein docking conformations of component proteins, which are later compared with a provided electron microscopy (EM) density map to select the ones that fit well into the EM map. The comparison of docking conformations and the EM map is performed using the 3D Zernike descriptor (3DZD), a mathematical series expansion of three-dimensional functions. The 3DZD provides a unified representation of the surface shape of multimeric protein complex models and EM maps, which allows a convenient, fast quantitative comparison of the three-dimensional structural data. Out of 19 multimeric complexes tested, near native complex structures with a root-mean-square deviation of less than 2.5 Å were obtained for 14 cases while medium range resolution structures with correct topology were computed for the additional 5 cases.

Detecting local ligand‐binding site similarity in nonhomologous proteins by surface patch comparison

Functional elucidation of proteins is one of the essential tasks in biology. Function of a protein, specifically, small ligand molecules that bind to a protein, can be predicted by finding similar local surface regions in binding sites of known proteins. Here, we developed an alignment free local surface comparison method for predicting a ligand molecule which binds to a query protein. The algorithm, named Patch-Surfer, represents a binding pocket as a combination of segmented surface patches, each of which is characterized by its geometrical shape, the electrostatic potential, the hydrophobicity, and the concaveness. Representing a pocket by a set of patches is effective to absorb difference of global pocket shape while capturing local similarity of pockets. The shape and the physicochemical properties of surface patches are represented using the 3D Zernike descriptor, which is a series expansion of mathematical 3D function. Two pockets are compared using a modified weighted bipartite matching algorithm, which matches similar patches from the two pockets. Patch-Surfer was benchmarked on three datasets, which consist in total of 390 proteins that bind to one of 21 ligands. Patch-Surfer showed superior performance to existing methods including a global pocket comparison method, Pocket-Surfer, which we have previously introduced. Particularly, as intended, the accuracy showed large improvement for flexible ligand molecules, which bind to pockets in different conformations.

Molecular Surface Representation Using 3D Zernike Descriptors for Protein Shape Comparison and Docking

The tertiary structures of proteins have been solved in an increasing pace in recent years. To capitalize the enormous efforts paid for accumulating the structure data, efficient and effective computational methods need to be developed for comparing, searching, and investigating interactions of protein structures. We introduce the 3D Zernike descriptor (3DZD), an emerging technique to describe molecular surfaces. The 3DZD is a series expansion of mathematical three-dimensional function, and thus a tertiary structure is represented compactly by a vector of coefficients of terms in the series. A strong advantage of the 3DZD is that it is invariant to rotation of target object to be represented. These two characteristics of the 3DZD allow rapid comparison of surface shapes, which is sufficient for real-time structure database screening. In this article, we review various applications of the 3DZD, which have been recently proposed.

Novel Methods for Rapid Comparison and Multimeric Protein Complex Fitting for Low-Resolution Electron Microscopy Data

Recent advancements of experimental techniques for determining protein tertiary structures raise significant challenges for protein bioinformatics. Previously, we have introduced a method for protein surface shape representation using the 3D Zernike descriptors (3DZDs). The 3DZD enables fast structure database searches, taking advantage of its rotation invariance and compact representation. The 3DZD has been successfully applied for global protein surface shape comparison, local pocket shape comparison, protein docking prediction, and rapid small ligand molecule search. Here, we apply the 3DZD for comparing low-resolution structure data from the electron microscopy (EM). Two applications are presented. First, we use the 3DZD for rapid comparison for an EM density map of a protein structure to a database of EM data. We examined EM maps of varying resolutions and found that the method has good performance in identifying the structures of the same fold even for EM maps at a resolution of 15 Angstroms (Sael, Kihara , BMC Bioinformatics, in press). Next, we applied the 3DZD for fitting multiple component proteins into an EM map. The method integrates a multiple protein docking procedure and the 3DZD, which compares surface shape of docking conformation to the EM map. The multiple docking is performed by the Multi-LZerD algorithm, which starts by computing pairwise docking prediction of component chains by using the LZerD docking program, which our group have developed recently (Venkatraman et al., BMC Bioinformatics, 2010). Multi-LZerD combines the pairwise docking results generating a couple of hundreds solutions. Then the fitness of the multiple docking decoys and the EM map is quantified by using the 3DZD. Overall, we show that the 3DZD is powerful in comparing low-resolution structure data for comparison and multiple-docking guided by the low-resolution data.

Local Protein Surface Patch Method for Protein-Ligand Binding Prediction

Characterizing the protein structures of an unknown function is an important task in bioinformatics. Function of a protein, specifically, the type of ligand that bind to a protein, can be predicted by finding similar local surface regions of known proteins. Unlike existing methods that compare the global characteristics of a protein fold, we propose a local surface-based approach which can find functional similarity between non-homologous proteins. In the proposed pocket comparison method, the pockets are segmented to surface patches, which are then compared using a modified weighted bipartite matching algorithm. The 3D Zernike descriptors, which have been found to be successful in representing protein global surface properties (Sael L, Li B et al. Proteins, 2008; Sael L, La D et al. Proteins, 2008) and global pockets shape comparison (Chikhi R et al. Proteins, 2010), are used to encode the geometric and physicochemical properties of the surface patches. By representing a pocket by a set of local patches, local similarity of binding pockets can be captured. This is effective when pocket shapes are slightly different due to flexibility of ligand molecules. The binding ligand prediction performance was evaluated on a data set of 100 non-homologous proteins that bind to either one of nine types of ligands. 84.0% of the binding ligands were predicted correctly within the top three scores using the shape and pocket size information, which is better than the previous method which uses the surface of whole pocket. The performance was further improved to 87.0% when surface properties, i.e. electrostatic potential and hydrophobicity, were added. Overall, we show that proposed method is powerful in predicting the type of ligand a protein binds even in the absence of homologous proteins in the database.

Binding ligand prediction for proteins using partial matching of local surface patches.

Functional elucidation of uncharacterized protein structures is an important task in bioinformatics. We report our new approach for structure-based function prediction which captures local surface features of ligand binding pockets. Function of proteins, specifically, binding ligands of proteins, can be predicted by finding similar local surface regions of known proteins. To enable partial comparison of binding sites in proteins, a weighted bipartite matching algorithm is used to match pairs of surface patches. The surface patches are encoded with the 3D Zernike descriptors. Unlike the existing methods which compare global characteristics of the protein fold or the global pocket shape, the local surface patch method can find functional similarity between non-homologous proteins and binding pockets for flexible ligand molecules. The proposed method improves prediction results over global pocket shape-based method which was previously developed by our group.

Improved protein surface comparison and application to low-resolution protein structure data

BackgroundRecent advancements of experimental techniques for determining protein tertiary structures raise significant challenges for protein bioinformatics. With the number of known structures of unknown function expanding at a rapid pace, an urgent task is to provide reliable clues to their biological function on a large scale. Conventional approaches for structure comparison are not suitable for a real-time database search due to their slow speed. Moreover, a new challenge has arisen from recent techniques such as electron microscopy (EM), which provide low-resolution structure data. Previously, we have introduced a method for protein surface shape representation using the 3D Zernike descriptors (3DZDs). The 3DZD enables fast structure database searches, taking advantage of its rotation invariance and compact representation. The search results of protein surface represented with the 3DZD has showngood agreement with the existing structure classifications, but some discrepancies were also observed.ResultsThe three new surface representations of backbone atoms, originally devised all-atom-surface representation, and the combination of all-atom surface with the backbone representation are examined. All representations are encoded with the 3DZD. Also, we have investigated the applicability of the 3DZD for searching protein EM density maps of varying resolutions. The surface representations are evaluated on structure retrieval using two existing classifications, SCOP and the CE-based classification.ConclusionsOverall, the 3DZDs representing backbone atoms show better retrieval performance than the original all-atom surface representation. The performance further improved when the two representations are combined. Moreover, we observed that the 3DZD is also powerful in comparing low-resolution structures obtained by electron microscopy.

Characterization and Classification of Local Protein Surfaces Using Self-Organizing Map

Annotating protein structures is an urgent task as increasing number of protein structures of unknown function is being solved. To achieve this goal, it is critical to establish computational methods for characterizing and classifying protein local structures. The authors analyzed the similarity of local surface patches from 609 representative proteins considering shape and the electrostatic potential, which are represented by the 3D Zernike descriptors. Classification of local patches is done with the emergent self-organizing map (ESOM). They mapped patches at ligand binding-sites to investigate how they distribute and cluster among the ESOM map. They obtained 30-50 clusters of local surfaces of different characteristics, which will be useful for annotating surface of proteins.

A Unified Protein Docking Procedure with a Shape Complementarity Screening using 3D Zernike Descriptors

Protein-protein interactions are a pivotal component of many biological processes. Knowing the tertiary structure of a protein complex is therefore essential for understanding the interaction mechanism. Experimental techniques to solve the structure of the complex are, however, often difficult. To this end, computational protein-protein docking approaches can provide a useful alternative to address this issue. We present a novel protein docking algorithm, VDOCK, based on the use of 3D Zernike descriptors (3DZD) as regional features of molecular shape. The key motivation of using these descriptors is their invariance to transformation, in addition to a compact representation of local surface shape characteristics. In our previous works we have shown that 3DZD are suitable for comparing global/local protein surface shape and surface physicochemical properties to quantify their similarity. Here we apply 3DZD for quantifying surface complementarity. Docking decoys are generated using geometric hashing, which are then initially screened by a shape-based scoring function that incorporates buried surface area and 3DZD. The benchmark studies show that 3DZD are not only efficient in identifying shape complementarity for bound docking cases but superior to other existing methods in accommodating a certain level of flexibility of the protein surface in unbound docking cases, taking advantage of 3DZD's controlable resolution of the surface description. In the next stage, generated docking decoys are evaluated using a physics-based scoring function. The weighting factors to combine these terms are trained using several different target metrics on a large dataset of docking decoys. Additional information and steps for selecting models are also employed, which include protein-protein interaction site predictions and optimization of global and side-chain conformations.

Protein-protein docking using region-based 3D Zernike descriptors

BackgroundProtein-protein interactions are a pivotal component of many biological processes and mediate a variety of functions. Knowing the tertiary structure of a protein complex is therefore essential for understanding the interaction mechanism. However, experimental techniques to solve the structure of the complex are often found to be difficult. To this end, computational protein-protein docking approaches can provide a useful alternative to address this issue. Prediction of docking conformations relies on methods that effectively capture shape features of the participating proteins while giving due consideration to conformational changes that may occur.ResultsWe present a novel protein docking algorithm based on the use of 3D Zernike descriptors as regional features of molecular shape. The key motivation of using these descriptors is their invariance to transformation, in addition to a compact representation of local surface shape characteristics. Docking decoys are generated using geometric hashing, which are then ranked by a scoring function that incorporates a buried surface area and a novel geometric complementarity term based on normals associated with the 3D Zernike shape description. Our docking algorithm was tested on both bound and unbound cases in the ZDOCK benchmark 2.0 dataset. In 74% of the bound docking predictions, our method was able to find a near-native solution (interface C-αRMSD ≤ 2.5 Å) within the top 1000 ranks. For unbound docking, among the 60 complexes for which our algorithm returned at least one hit, 60% of the cases were ranked within the top 2000. Comparison with existing shape-based docking algorithms shows that our method has a better performance than the others in unbound docking while remaining competitive for bound docking cases.ConclusionWe show for the first time that the 3D Zernike descriptors are adept in capturing shape complementarity at the protein-protein interface and useful for protein docking prediction. Rigorous benchmark studies show that our docking approach has a superior performance compared to existing methods.

Application of 3D Zernike descriptors to shape-based ligand similarity searching

BackgroundThe identification of promising drug leads from a large database of compounds is an important step in the preliminary stages of drug design. Although shape is known to play a key role in the molecular recognition process, its application to virtual screening poses significant hurdles both in terms of the encoding scheme and speed.ResultsIn this study, we have examined the efficacy of the alignment independent three-dimensional Zernike descriptor (3DZD) for fast shape based similarity searching. Performance of this approach was compared with several other methods including the statistical moments based ultrafast shape recognition scheme (USR) and SIMCOMP, a graph matching algorithm that compares atom environments. Three benchmark datasets are used to thoroughly test the methods in terms of their ability for molecular classification, retrieval rate, and performance under the situation that simulates actual virtual screening tasks over a large pharmaceutical database. The 3DZD performed better than or comparable to the other methods examined, depending on the datasets and evaluation metrics used. Reasons for the success and the failure of the shape based methods for specific cases are investigated. Based on the results for the three datasets, general conclusions are drawn with regard to their efficiency and applicability.ConclusionThe 3DZD has unique ability for fast comparison of three-dimensional shape of compounds. Examples analyzed illustrate the advantages and the room for improvements for the 3DZD.

3D-SURFER: software for high-throughput protein surface comparison and analysis

We present 3D-SURFER, a web-based tool designed to facilitate high-throughput comparison and characterization of proteins based on their surface shape. As each protein is effectively represented by a vector of 3D Zernike descriptors, comparison times for a query protein against the entire PDB take, on an average, only a couple of seconds. The web interface has been designed to be as interactive as possible with displays showing animated protein rotations, CATH codes and structural alignments using the CE program. In addition, geometrically interesting local features of the protein surface, such as pockets that often correspond to ligand binding sites as well as protrusions and flat regions can also be identified and visualized. 3D-SURFER is a web application that can be freely accessed from: http://dragon.bio.purdue.edu/3d-surfer dkihara@purdue.edu Supplementary data are available at Bioinformatics online.

Potential for Protein Surface Shape Analysis Using Spherical Harmonics and 3D Zernike Descriptors

With structure databases expanding at a rapid rate, the task at hand is to provide reliable clues to their molecular function and to be able to do so on a large scale. This, however, requires suitable encodings of the molecular structure which are amenable to fast screening. To this end, moment-based representations provide a compact and nonredundant description of molecular shape and other associated properties. In this article, we present an overview of some commonly used representations with specific focus on two schemes namely spherical harmonics and their extension, the 3D Zernike descriptors. Key features and differences of the two are reviewed and selected applications are highlighted. We further discuss recent advances covering aspects of shape and property-based comparison at both global and local levels and demonstrate their applicability through some of our studies.

Local surface shape-based protein function prediction using Zernike descriptors

Structural genomics projects have been solving an increasing number of protein structures with unknown function. As the number of uncharacterized protein structures continues to grow, there is increasing need for effective computational strategies for structure-based protein function prediction. As of now, there are more than 2400 protein structures in the PDB database, which are categorized as unknown function and thus are awaiting functional characterization. Previously, we have reported a fast global protein surface shape comparison method based on 3D Zernike descriptors.

Rapid comparison of properties on protein surface

The mapping of physicochemical characteristics onto the surface of a protein provides crucial insights into its function and evolution. This information can be further used in the characterization and identification of similarities within protein surface regions. We propose a novel method which quantitatively compares global and local properties on the protein surface. We have tested the method on comparison of electrostatic potentials and hydrophobicity. The method is based on 3D Zernike descriptors, which provides a compact representation of a given property defined on a protein surface. Compactness and rotational invariance of this descriptor enable fast comparison suitable for database searches. The usefulness of this method is exemplified by studying several protein families including globins, thermophilic and mesophilic proteins, and active sites of TIM beta/alpha barrel proteins. In all the cases studied, the descriptor is able to cluster proteins into functionally relevant groups. The proposed approach can also be easily extended to other surface properties. This protein surface-based approach will add a new way of viewing and comparing proteins to conventional methods, which compare proteins in terms of their primary sequence or tertiary structure.