Zernike Descriptors Research Articles

FP-Zernike: An Open-source Structural Database Construction Toolkit for Fast Structure Retrieval.

The release of AlphaFold2 has sparked a rapid expansion in protein model databases. Efficient protein structure retrieval is crucial for the analysis of structure models, while measuring the similarity between structures is the key challenge in structural retrieval. Although existing structure alignment algorithms can address this challenge, they are often time-consuming. Currently, the state-of-the-art approach involves converting protein structures into three-dimensional (3D) Zernike descriptors and assessing similarity using Euclidean distance. However, the methods for computing 3D Zernike descriptors mainly rely on structural surfaces and are predominantly web-based, thus limiting their application in studying custom datasets. To overcome this limitation, we developed FP-Zernike, a user-friendly toolkit for computing different types of Zernike descriptors based on feature points. Users simply need to enter a single line of command to calculate the Zernike descriptors of all structures in customized datasets. FP-Zernike outperforms the leading method in terms of retrieval accuracy and binary classification accuracy across diverse benchmark datasets. In addition, we showed the application of FP-Zernike in the construction of the descriptor database and the protocol used for the Protein Data Bank (PDB) dataset to facilitate the local deployment of this tool for interested readers. Our demonstration contained 590,685 structures, and at this scale, our system required only 4-9 s to complete a retrieval. The experiments confirmed that it achieved the state-of-the-art accuracy level. FP-Zernike is an open-source toolkit, with the source code and related data accessible at https://ngdc.cncb.ac.cn/biocode/tools/BT007365/releases/0.1, as well as through a webserver at http://www.structbioinfo.cn/.

Machine learning and similar image-based techniques based on Nash game theory

The use of computer vision techniques to address the task of image retrieval is known as a Content-Based Image Retrieval (CBIR) system. It is a system designed to locate and retrieve the appropriate digital image from a large database by utilizing a query image. Over the last few years, machine learning algorithms have achieved impressive results in image retrieval tasks due to their ability to learn from large amounts of diverse data and improve their accuracy in image recognition and retrieval. Our team has developed a CBIR system that is reinforced by two machine learning algorithms and employs multiple clustering and low-level image feature extraction, such as color, shape, and texture, to formulate a Nash game. Consequently, we are faced with a multicriteria optimization problem. To solve this problem, we have formulated a three-player static Nash game, where each player utilizes a different strategy (color descriptor, Zernike descriptor, and SFTA descriptor) based on their objective function. The Nash equilibrium is defined as the membership classes of the query image.

Exploiting the Role of Features for Antigens-Antibodies Interaction Site Prediction.

Antibodies are a class of proteins that recognize and neutralize pathogens by binding to their antigens. They are the most significant category of biopharmaceuticals for both diagnostic and therapeutic applications. Understanding how antibodies interact with their antigens plays a fundamental role in drug and vaccine design and helps to comprise the complex antigen binding mechanisms. Computational methods for predicting interaction sites of antibody-antigen are of great value due to the overall cost of experimental methods. Machine learning methods and deep learning techniques obtained promising results.In this work, we predict antibody interaction interface sites by applying HSS-PPI, a hybrid method defined to predict the interface sites of general proteins. The approach abstracts the proteins in terms of hierarchical representation and uses a graph convolutional network to classify the amino acids between interface and non-interface. Moreover, we also equipped the amino acids with different sets of physicochemical features together with structural ones to describe the residues. Analyzing the results, we observe that the structural features play a fundamental role in the amino acid descriptions. We compare the obtained performances, evaluated using standard metrics, with the ones obtained with SVM with 3D Zernike descriptors, Parapred, Paratome, and Antibody i-Patch.

Quantitative comparison of protein-protein interaction interface using physicochemical feature-based descriptors of surface patches.

Driving mechanisms of many biological functions in a cell include physical interactions of proteins. As protein-protein interactions (PPIs) are also important in disease development, protein-protein interactions are highlighted in the pharmaceutical industry as possible therapeutic targets in recent years. To understand the variety of protein-protein interactions in a proteome, it is essential to establish a method that can identify similarity and dissimilarity between protein-protein interactions for inferring the binding of similar molecules, including drugs and other proteins. In this study, we developed a novel method, protein-protein interaction-Surfer, which compares and quantifies similarity of local surface regions of protein-protein interactions. protein-protein interaction-Surfer represents a protein-protein interaction surface with overlapping surface patches, each of which is described with a three-dimensional Zernike descriptor (3DZD), a compact mathematical representation of 3D function. 3DZD captures both the 3D shape and physicochemical properties of the protein surface. The performance of protein-protein interaction-Surfer was benchmarked on datasets of protein-protein interactions, where we were able to show that protein-protein interaction-Surfer finds similar potential drug binding regions that do not share sequence and structure similarity. protein-protein interaction-Surfer is available at https://kiharalab.org/ppi-surfer.

Machine learning algorithms for classifying corneas by Zernike descriptors

Keratoconus is the most common primary ectasia, as the treatment is not easy, its early diagnosis is essential. The main goal of this study is to develop a method for classification of specific types of corneal shapes where 55 Zernike coefficients (angular index m = 9) are used as inputs. We describe and apply six Machine Learning (ML) classification methods and an ensemble of them to objectively discriminate between keratoconic and non-keratoconic corneal shapes. Earlier attempts by other authors have successfully implemented several Machine Learning models using different parameters (usually, indirect measurements) and have obtained positive results. Given the importance and ubiquity of Zernike polynomials in the eye care community, our proposal should be a suitable choice to incorporate to current methods which might serve as a prescreening test. In this project we work with 475 corneas, classified by experts in two groups, 50 keratoconics and 425 non-keratoconics. All six models yield high rated results with accuracies above 98%, precisions above 97%, or sensitivities above 93%. Also, by building an assembly with the models, we further improve the accuracy of our classification, for example we found an accuracy of 99.7%, a precision of 99.8% and sensitivity of 98.3%. The model can be easily implemented in any system, being very simple to use, thus providing ophthalmologists with a effortless and powerful tool to make a first diagnosis.

Shape Complementarity Optimization of Antibody-Antigen Interfaces: The Application to SARS-CoV-2 Spike Protein.

Many factors influence biomolecule binding, and its assessment constitutes an elusive challenge in computational structural biology. In this aspect, the evaluation of shape complementarity at molecular interfaces is one of the main factors to be considered. We focus on the particular case of antibody–antigen complexes to quantify the complementarities occurring at molecular interfaces. We relied on a method we recently developed, which employs the 2D Zernike descriptors, to characterize the investigated regions with an ordered set of numbers summarizing the local shape properties. Collecting a structural dataset of antibody–antigen complexes, we applied this method and we statistically distinguished, in terms of shape complementarity, pairs of the interacting regions from the non-interacting ones. Thus, we set up a novel computational strategy based on in silico mutagenesis of antibody-binding site residues. We developed a Monte Carlo procedure to increase the shape complementarity between the antibody paratope and a given epitope on a target protein surface. We applied our protocol against several molecular targets in SARS-CoV-2 spike protein, known to be indispensable for viral cell invasion. We, therefore, optimized the shape of template antibodies for the interaction with such regions. As the last step of our procedure, we performed an independent molecular docking validation of the results of our Monte Carlo simulations.

Real-time structure search and structure classification for AlphaFold protein models

Last year saw a breakthrough in protein structure prediction, where the AlphaFold2 method showed a substantial improvement in the modeling accuracy. Following the software release of AlphaFold2, predicted structures by AlphaFold2 for proteins in 21 species were made publicly available via the AlphaFold Database. Here, to facilitate structural analysis and application of AlphaFold2 models, we provide the infrastructure, 3D-AF-Surfer, which allows real-time structure-based search for the AlphaFold2 models. In 3D-AF-Surfer, structures are represented with 3D Zernike descriptors (3DZD), which is a rotationally invariant, mathematical representation of 3D shapes. We developed a neural network that takes 3DZDs of proteins as input and retrieves proteins of the same fold more accurately than direct comparison of 3DZDs. Using 3D-AF-Surfer, we report structure classifications of AlphaFold2 models and discuss the correlation between confidence levels of AlphaFold2 models and intrinsic disordered regions.

LZerD webserver for pairwise and multiple protein-protein docking.

Protein complexes are involved in many important processes in living cells. To understand the mechanisms of these processes, it is necessary to solve the 3D structures of the protein complexes. When protein complex structures have not yet been determined by experiment, protein-protein docking tools can be used to computationally model the structures of these complexes. Here, we present a webserver which provides access to LZerD and Multi-LZerD protein docking tools. The protocol provided by the server have performed consistently among the top in the CAPRI blind evaluation. LZerD docks pairs of structures, while Multi-LZerD can dock three or more structures simultaneously. LZerD uses a soft protein surface representation with 3D Zernike descriptors and explores the binding pose space using geometric hashing. Multi-LZerD performs multi-chain docking by combining pairwise solutions by LZerD. Both methods output full-atom docked models of the input proteins. Users can also input distance constraints between interacting or non-interacting residues as well as residues that locate at the interface or far from the interface. The webserver is equipped with a user-friendly panel that visualizes the distribution and structures of binding poses of top scoring models. The LZerD webserver is available at https://lzerd.kiharalab.org.

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.

FTIP: an accurate and efficient method for global protein surface comparison

Global protein surface comparison (GPSC) studies have been limited compared to other research works on protein structure alignment/comparison due to lack of real applications associated with GPSC. However, the technology advances in cryo-electron tomography (CET) have made methods to identify proteins from their surface shapes extremely useful. In this study, we developed a new method called Farthest point sampling (FPS)-enhanced Triangulation-based Iterative-closest-Point (ICP) (FTIP) for GPSC. We applied it to protein classification using only surface shape information. Our method first extracts a set of feature points from protein surfaces using FPS and then uses a triangulation-based efficient ICP algorithm to align the feature points of the two proteins to be compared. Tested on a benchmark dataset with 2329 proteins using nearest-neighbor classification, FTIP outperformed the state-of-the-art method for GPSC based on 3D Zernike descriptors. Using real and simulated cryo-EM data, we show that FTIP could be applied in the future to address problems in protein identification in CET experiments. Programs/scripts we developed/used in the study are available at http://ani.stat.fsu.edu/∼yuan/index.fld/FTIP.tar.bz2. Supplementary data are available at Bioinformatics online.

FTIP - An Accurate and Efficient Method for Global Protein Surface Comparison

Motivation Global protein surface comparison (GPSC) studies have been limited compared to other research works on protein structure alignment/comparison due to lack of real applications associated with GPSC. However, the technology advances in cryo-electron tomography (CET) have made methods to identify proteins from their surface shapes extremely useful. Results In this study, we developed a new method called Farthest point sampling (FPS)-enhanced Triangulation-based Iterative-closest-Point (ICP) (FTIP) for GPSC. We applied it to protein classification using only surface shape information. Our method first extracts a set of feature points from protein surfaces using FPS and then uses a triangulation-based efficient ICP algorithm to align the feature points of the two proteins to be compared. Tested on a benchmark dataset with 2329 proteins using nearest-neighbor classification, FTIP outperformed the state-of-the-art method for GPSC based on 3D Zernike descriptors. Using real and simulated cryo-EM data, we show that FTIP could be applied in the future to address problems in protein identification in CET experiments. Availability and implementation Programs/scripts we developed/used in the study are available at http://ani.stat.fsu.edu/∼yuan/index.fld/FTIP.tar.bz2. Supplementary information Supplementary data are available at Bioinformatics online.

Continuous and optimally complete description of chemical environments using Spherical Bessel descriptors

Recently, machine learning potentials have been advanced as candidates to combine the high-accuracy of electronic structure methods with the speed of classical interatomic potentials. A crucial component of a machine learning potential is the description of local atomic environments by some set of descriptors. These should ideally be invariant to the symmetries of the physical system, twice-differentiable with respect to atomic positions (including when an atom leaves the environment), and complete to allow the atomic environment to be reconstructed up to symmetry. The stronger condition of optimal completeness requires that the condition for completeness be satisfied with the minimum possible number of descriptors. Evidence is provided that an updated version of the recently proposed Spherical Bessel (SB) descriptors satisfies the first two properties and a necessary condition for optimal completeness. The Smooth Overlap of Atomic Position (SOAP) descriptors and the Zernike descriptors are natural counterparts of the SB descriptors and are included for comparison. The standard construction of the SOAP descriptors is shown to not satisfy the condition for optimal completeness and, moreover, is found to be an order of magnitude slower to compute than that of the SB descriptors.

Predicting binding poses and affinity ranking in D3R Grand Challenge using PL-PatchSurfer2.0.

Computational prediction of protein-ligand interactions is a useful approach that aids the drug discovery process. Two major tasks of computational approaches are to predict the docking pose of a compound in a known binding pocket and to rank compounds in a library according to their predicted binding affinities. There are many computational tools developed in the past decades both in academia and industry. To objectively assess the performance of existing tools, the community has held a blind assessment of computational predictions, the Drug Design Data Resource Grand Challenge. This round, Grand Challenge 4 (GC4), focused on two targets, protein beta-secretase 1 (BACE-1) and cathepsin S (CatS). We participated in GC4 in both BACE-1 and CatS challenges using our molecular surface-based virtual screening method, PL-PatchSurfer2.0. A unique feature of PL-PatchSurfer2.0 is that it uses the three-dimensional Zernike descriptor, a mathematical moment-based shape descriptor, to quantify local shape complementarity between a ligand and a receptor, which properly incorporates molecular flexibility and provides stable affinity assessment for a bound ligand-receptor complex. Since PL-PatchSurfer2.0 does not explicitly build a bound pose of a ligand, we used an external docking program, such as AutoDock Vina, to provide an ensemble of poses, which were then evaluated by PL-PatchSurfer2.0. Here, we provide an overview of our method and report the performance in GC4.

A global map of the protein shape universe.

Proteins are involved in almost all functions in a living cell, and functions of proteins are realized by their tertiary structures. Obtaining a global perspective of the variety and distribution of protein structures lays a foundation for our understanding of the building principle of protein structures. In light of the rapid accumulation of low-resolution structure data from electron tomography and cryo-electron microscopy, here we map and classify three-dimensional (3D) surface shapes of proteins into a similarity space. Surface shapes of proteins were represented with 3D Zernike descriptors, mathematical moment-based invariants, which have previously been demonstrated effective for biomolecular structure similarity search. In addition to single chains of proteins, we have also analyzed the shape space occupied by protein complexes. From the mapping, we have obtained various new insights into the relationship between shapes, main-chain folds, and complex formation. The unique view obtained from shape mapping opens up new ways to understand design principles, functions, and evolution of proteins.

Efficient Terrain Matching With 3-D Zernike Moments

The 3-D Zernike descriptors are investigated for an efficient terrain matching algorithm. The maximum order of the 3-D Zernike moments and the template size are determined. The odd-order descriptors are compared with the even-order ones in sensitivity to terrain elevation fluctuation and robustness to noise and rotation. Numerical experiments show that the matching with the odd-order descriptors can achieve as good as or better than that with both the odd-order and the even-order descriptors.

Antibody interface prediction with 3D Zernike descriptors and SVM.

Antibodies are a class of proteins capable of specifically recognizing and binding to a virtually infinite number of antigens. This binding malleability makes them the most valuable category of biopharmaceuticals for both diagnostic and therapeutic applications. The correct identification of the antigen-binding residues in the antibody is crucial for all antibody design and engineering techniques and could also help to understand the complex antigen binding mechanisms. However, the antibody-binding interface prediction field appears to be still rather underdeveloped. We present a novel method for antibody interface prediction from their experimentally solved structures based on 3D Zernike Descriptors. Roto-translationally invariant descriptors are computed from circular patches of the antibody surface enriched with a chosen subset of physico-chemical properties from the AAindex1 amino acid index set, and are used as samples for a binary classification problem. An SVM classifier is used to distinguish interface surface patches from non-interface ones. The proposed method was shown to outperform other antigen-binding interface prediction software. Linux binaries and Python scripts are available at https://github.com/sebastiandaberdaku/AntibodyInterfacePrediction. The datasets generated and/or analyzed during the current study are available at https://doi.org/10.6084/m9.figshare.5442229. Supplementary data are available at Bioinformatics online.

Advances in the Development of Shape Similarity Methods and Their Application in Drug Discovery.

Molecular similarity is a key concept in drug discovery. It is based on the assumption that structurally similar molecules frequently have similar properties. Assessment of similarity between small molecules has been highly effective in the discovery and development of various drugs. Especially, two-dimensional (2D) similarity approaches have been quite popular due to their simplicity, accuracy and efficiency. Recently, the focus has been shifted toward the development of methods involving the representation and comparison of three-dimensional (3D) conformation of small molecules. Among the 3D similarity methods, evaluation of shape similarity is now gaining attention for its application not only in virtual screening but also in molecular target prediction, drug repurposing and scaffold hopping. A wide range of methods have been developed to describe molecular shape and to determine the shape similarity between small molecules. The most widely used methods include atom distance-based methods, surface-based approaches such as spherical harmonics and 3D Zernike descriptors, atom-centered Gaussian overlay based representations. Several of these methods demonstrated excellent virtual screening performance not only retrospectively but also prospectively. In addition to methods assessing the similarity between small molecules, shape similarity approaches have been developed to compare shapes of protein structures and binding pockets. Additionally, shape comparisons between atomic models and 3D density maps allowed the fitting of atomic models into cryo-electron microscopy maps. This review aims to summarize the methodological advances in shape similarity assessment highlighting advantages, disadvantages and their application in drug discovery.

Exploring the potential of 3D Zernike descriptors and SVM for protein\u2013protein interface prediction

BackgroundThe correct determination of protein–protein interaction interfaces is important for understanding disease mechanisms and for rational drug design. To date, several computational methods for the prediction of protein interfaces have been developed, but the interface prediction problem is still not fully understood. Experimental evidence suggests that the location of binding sites is imprinted in the protein structure, but there are major differences among the interfaces of the various protein types: the characterising properties can vary a lot depending on the interaction type and function. The selection of an optimal set of features characterising the protein interface and the development of an effective method to represent and capture the complex protein recognition patterns are of paramount importance for this task.ResultsIn this work we investigate the potential of a novel local surface descriptor based on 3D Zernike moments for the interface prediction task. Descriptors invariant to roto-translations are extracted from circular patches of the protein surface enriched with physico-chemical properties from the HQI8 amino acid index set, and are used as samples for a binary classification problem. Support Vector Machines are used as a classifier to distinguish interface local surface patches from non-interface ones. The proposed method was validated on 16 classes of proteins extracted from the Protein–Protein Docking Benchmark 5.0 and compared to other state-of-the-art protein interface predictors (SPPIDER, PrISE and NPS-HomPPI).ConclusionsThe 3D Zernike descriptors are able to capture the similarity among patterns of physico-chemical and biochemical properties mapped on the protein surface arising from the various spatial arrangements of the underlying residues, and their usage can be easily extended to other sets of amino acid properties. The results suggest that the choice of a proper set of features characterising the protein interface is crucial for the interface prediction task, and that optimality strongly depends on the class of proteins whose interface we want to characterise. We postulate that different protein classes should be treated separately and that it is necessary to identify an optimal set of features for each protein class.

A unified protein docking procedure with a shape complementarity screening using 3D Zernike descriptors

A unified protein docking procedure with a shape complementarity screening using 3D Zernike descriptors

Virtual Ligand Screening Using PL-PatchSurfer2, a Molecular Surface-Based Protein-Ligand Docking Method.

Virtual screening is a computational technique for predicting a potent binding compound for a receptor protein from a ligand library. It has been a widely used in the drug discovery field to reduce the efforts of medicinal chemists to find hit compounds by experiments.Here, we introduce our novel structure-based virtual screening program, PL-PatchSurfer, which uses molecular surface representation with the three-dimensional Zernike descriptors, which is an effective mathematical representation for identifying physicochemical complementarities between local surfaces of a target protein and a ligand. The advantage of the surface-patch description is its tolerance on a receptor and compound structure variation. PL-PatchSurfer2 achieves higher accuracy on apo form and computationally modeled receptor structures than conventional structure-based virtual screening programs. Thus, PL-PatchSurfer2 opens up an opportunity for targets that do not have their crystal structures. The program is provided as a stand-alone program at http://kiharalab.org/plps2 . We also provide files for two ligand libraries, ChEMBL and ZINC Drug-like.