Molecular Graph Research Articles

Hierarchical multimodal self-attention-based graph neural network for DTI prediction.

Drug-target interactions (DTIs) are a key part of drug development process and their accurate and efficient prediction can significantly boost development efficiency and reduce development time. Recent years have witnessed the rapid advancement of deep learning, resulting in an abundance of deep learning-based models for DTI prediction. However, most of these models used a single representation of drugs and proteins, making it difficult to comprehensively represent their characteristics. Multimodal data fusion can effectively compensate for the limitations of single-modal data. However, existing multimodal models for DTI prediction do not take into account both intra- and inter-modal interactions simultaneously, resulting in limited presentation capabilities of fused features and a reduction in DTI prediction accuracy. A hierarchical multimodal self-attention-based graph neural network for DTI prediction, called HMSA-DTI, is proposed to address multimodal feature fusion. Our proposed HMSA-DTI takes drug SMILES, drug molecular graphs, protein sequences and protein 2-mer sequences as inputs, and utilizes a hierarchical multimodal self-attention mechanism to achieve deep fusion of multimodal features of drugs and proteins, enabling the capture of intra- and inter-modal interactions between drugs and proteins. It is demonstrated that our proposed HMSA-DTI has significant advantages over other baseline methods on multiple evaluation metrics across five benchmark datasets.

MvMRL: a multi-view molecular representation learning method for molecular property prediction.

Effective molecular representation learning is very important for Artificial Intelligence-driven Drug Design because it affects the accuracy and efficiency of molecular property prediction and other molecular modeling relevant tasks. However, previous molecular representation learning studies often suffer from limitations, such as over-reliance on a single molecular representation, failure to fully capture both local and global information in molecular structure, and ineffective integration of multiscale features from different molecular representations. These limitations restrict the complete and accurate representation of molecular structure and properties, ultimately impacting the accuracy of predicting molecular properties. To this end, we propose a novel multi-view molecular representation learning method called MvMRL, which can incorporate feature information from multiple molecular representations and capture both local and global information from different views well, thus improving molecular property prediction. Specifically, MvMRL consists of four parts: a multiscale CNN-SE Simplified Molecular Input Line Entry System (SMILES) learning component and a multiscale Graph Neural Network encoder to extract local feature information and global feature information from the SMILES view and the molecular graph view, respectively; a Multi-Layer Perceptron network to capture complex non-linear relationship features from the molecular fingerprint view; and a dual cross-attention component to fuse feature information on the multi-views deeply for predicting molecular properties. We evaluate the performance of MvMRL on 11 benchmark datasets, and experimental results show that MvMRL outperforms state-of-the-art methods, indicating its rationality and effectiveness in molecular property prediction. The source code of MvMRL was released in https://github.com/jedison-github/MvMRL.

QSPR analysis for physiochemical properties of new potential antimalarial compounds involving topological indices

AbstractMalaria has a wide impact on the healthcare system, affecting everyone from hyperendemic areas who dearth access to medical treatment to international tourists returning to nonendemic regions with tertiary referral care. Implementing timely and accurate diagnosis is necessary to stop malaria's growing global effect, which is attributed to the development of antimalarial medication resistance. In this research, potential antimalarial compounds, including quinine, primaquine, artemether, artelinic acid, triazoles‐modified, and so forth are examined with topological indices (TI) and linear regression modeling of said compounds. Some degree based topological indices are assembled for these drugs' chemical graphs. We compute the topological descriptors with the limiting behaviors associated with these pharmaceutical drugs. Moreover, in this study some of the physicochemical features of the drugs are estimated using these TIs in the QSPR models. These indices better reflect chemical properties such as boiling point, complexity, polarity, and so forth and the outcomes of regression technique acquired QSPR studies may aid in the creation of fresh medicines for the treatment of malaria. These indices and antimalarial activity were discovered to be related. Other compound series do very well with this relationship. The TIs could be a key component in creating and synthesizing new antimalarial drugs.

MASMDDI: multi-layer adaptive soft-mask graph neural network for drug-drug interaction prediction.

Accurately predicting Drug-Drug Interaction (DDI) is a critical and challenging aspect of the drug discovery process, particularly in preventing adverse reactions in patients undergoing combination therapy. However, current DDI prediction methods often overlook the interaction information between chemical substructures of drugs, focusing solely on the interaction information between drugs and failing to capture sufficient chemical substructure details. To address this limitation, we introduce a novel DDI prediction method: Multi-layer Adaptive Soft Mask Graph Neural Network (MASMDDI). Specifically, we first design a multi-layer adaptive soft mask graph neural network to extract substructures from molecular graphs. Second, we employ an attention mechanism to mine substructure feature information and update latent features. In this process, to optimize the final feature representation, we decompose drug-drug interactions into pairwise interaction correlations between the core substructures of each drug. Third, we use these features to predict the interaction probabilities of DDI tuples and evaluate the model using real-world datasets. Experimental results demonstrate that the proposed model outperforms state-of-the-art methods in DDI prediction. Furthermore, MASMDDI exhibits excellent performance in predicting DDIs of unknown drugs in two tasks that are more aligned with real-world scenarios. In particular, in the transductive scenario using the DrugBank dataset, the ACC and AUROC and AUPRC scores of MASMDDI are 0.9596, 0.9903, and 0.9894, which are 2% higher than the best performing baseline.

HMMF: a hybrid multi-modal fusion framework for predicting drug side effect frequencies

BackgroundThe identification of drug side effects plays a critical role in drug repositioning and drug screening. While clinical experiments yield accurate and reliable information about drug-related side effects, they are costly and time-consuming. Computational models have emerged as a promising alternative to predict the frequency of drug-side effects. However, earlier research has primarily centered on extracting and utilizing representations of drugs, like molecular structure or interaction graphs, often neglecting the inherent biomedical semantics of drugs and side effects.ResultsTo address the previously mentioned issue, we introduce a hybrid multi-modal fusion framework (HMMF) for predicting drug side effect frequencies. Considering the wealth of biological and chemical semantic information related to drugs and side effects, incorporating multi-modal information offers additional, complementary semantics. HMMF utilizes various encoders to understand molecular structures, biomedical textual representations, and attribute similarities of both drugs and side effects. It then models drug-side effect interactions using both coarse and fine-grained fusion strategies, effectively integrating these multi-modal features.ConclusionsHMMF exhibits the ability to successfully detect previously unrecognized potential side effects, demonstrating superior performance over existing state-of-the-art methods across various evaluation metrics, including root mean squared error and area under receiver operating characteristic curve, and shows remarkable performance in cold-start scenarios.

Computation of molecular description of supramolecular Fuchsine model useful in medical data

Supramolecular chemistry is a fascinating field that explores the interactions between molecules to create higher-order structures. In the case of the supramolecular chain of Fuchsine acid, which is a type of dye molecule, several chemical applications are possible. Fuchsine acid helps to make better medicine carriers that deliver drugs where they’re needed in the body, making treatments more effective and reducing side effects. It also helps create smart materials like sensors and self-fixing plastics, which are useful in electronics, keeping our environment clean, and making new materials. In sensing and detection, the supramolecular chain of Fuchsine acid utilizes as a sensor or detector for specific analyzes. In drug delivery, the supramolecular chains of Fuchsine acid incorporated into drug delivery systems. In recent years, a common method is linking a graph to a chemical structure and using topological descriptors to study it. This technique is becoming increasingly important over time. Topological descriptors gives very useful information while studying the topology of chemical graph. In this paper, we have computed the 3D structure of supramolecular graph of Fuchsine acid. We have computed an explicit expressions of ABC index, GA index, General Randic´\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\acute{c}$$\\end{document} index, first and second Zagreb index, hyper Zagreb index, H-index and F-index of supramolecular structure of Fushine acid.

Distance plus attention for binding affinity prediction

Protein-ligand binding affinity plays a pivotal role in drug development, particularly in identifying potential ligands for target disease-related proteins. Accurate affinity predictions can significantly reduce both the time and cost involved in drug development. However, highly precise affinity prediction remains a research challenge. A key to improve affinity prediction is to capture interactions between proteins and ligands effectively. Existing deep-learning-based computational approaches use 3D grids, 4D tensors, molecular graphs, or proximity-based adjacency matrices, which are either resource-intensive or do not directly represent potential interactions. In this paper, we propose atomic-level distance features and attention mechanisms to capture better specific protein-ligand interactions based on donor-acceptor relations, hydrophobicity, and π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi $$\\end{document}-stacking atoms. We argue that distances encompass both short-range direct and long-range indirect interaction effects while attention mechanisms capture levels of interaction effects. On the very well-known CASF-2016 dataset, our proposed method, named Distance plus Attention for Affinity Prediction (DAAP), significantly outperforms existing methods by achieving Correlation Coefficient (R) 0.909, Root Mean Squared Error (RMSE) 0.987, Mean Absolute Error (MAE) 0.745, Standard Deviation (SD) 0.988, and Concordance Index (CI) 0.876. The proposed method also shows substantial improvement, around 2% to 37%, on five other benchmark datasets. The program and data are publicly available on the website https://gitlab.com/mahnewton/daap.Scientific Contribution StatementThis study innovatively introducesdistance-based features to predict protein-ligand binding affinity, capitalizing onunique molecular interactions. Furthermore, the incorporation of protein sequencefeatures of specific residues enhances the model’s proficiency in capturing intricatebinding patterns. The predictive capabilities are further strengthened through theuse of a deep learning architecture with attention mechanisms, and an ensembleapproach, averaging the outputs of five models, is implemented to ensure robustand reliable predictions.

PointGAT: A Quantum Chemical Property Prediction Model Integrating Graph Attention and 3D Geometry.

Predicting quantum chemical properties is a fundamental challenge for computational chemistry. While the development of graph neural networks has advanced molecular representation learning and property prediction, their performance could be further enhanced by incorporating three-dimensional (3D) structural geometry into two-dimensional (2D) molecular graph representation. In this study, we introduce the PointGAT model for quantum molecular property prediction, which integrates 3D molecular coordinates with graph-attention modeling. Comparison with other current models in molecular prediction tasks showed that PointGAT could provide higher predictive accuracy in various benchmark data sets from MoleculeNet, including ESOL, FreeSolv, Lipop, HIV, and 6 out of 12 tasks of the QM9 data set. To further examine PointGAT prediction of quantum mechanical (QM) energies, we constructed a C10 data set comprising 11,841 charged and chiral carbocation intermediates with QM energies calculated at the DM21/6-31G*//B3LYP/6-31G* levels. Notably, PointGAT achieved an R2 value of 0.950 and an MAE of 1.616 kcal/mol, outperforming even the best-performing graph neural network model with a reduction of 0.216 kcal/mol in MAE and an improvement of 0.050 in R2. Additional ablation studies indicated that incorporating molecular geometry into the model resulted in markedly higher predictive accuracy, reducing the MAE value from 1.802 to 1.616 kcal/mol. Moreover, visualization of PointGAT atomic attention weights suggested its predictions were interpretable. Findings in this study support the application of PointGAT as a powerful and versatile tool for quantum chemical property prediction that can facilitate high-accuracy modeling for fundamental exploration of chemical space as well as drug design and molecular engineering.

Predicting drug-Protein interaction with deep learning framework for molecular graphs and sequences: Potential candidates against SAR-CoV-2.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) caused the COVID-19 disease, which represents a new life-threatening disaster. Regarding viral infection, many therapeutics have been investigated to alleviate the epidemiology such as vaccines and receptor decoys. However, the continuous mutating coronavirus, especially the variants of Delta and Omicron, are tended to invalidate the therapeutic biological product. Thus, it is necessary to develop molecular entities as broad-spectrum antiviral drugs. Coronavirus replication is controlled by the viral 3-chymotrypsin-like cysteine protease (3CLpro) enzyme, which is required for the virus's life cycle. In the cases of severe acute respiratory syndrome coronavirus (SARS-CoV) and middle east respiratory syndrome coronavirus (MERS-CoV), 3CLpro has been shown to be a promising therapeutic development target. Here we proposed an attention-based deep learning framework for molecular graphs and sequences, training from the BindingDB 3CLpro dataset (114,555 compounds). After construction of such model, we conducted large-scale screening the in vivo/vitro dataset (276,003 compounds) from Zinc Database and visualize the candidate compounds with attention score. geometric-based affinity prediction was employed for validation. Finally, we established a 3CLpro-specific deep learning framework, namely GraphDPI-3CL (AUROC: 0.958) achieved superior performance beyond the existing state of the art model and discovered 10 molecules with a high binding affinity of 3CLpro and superior binding mode.

GraphEGFR: Multi-task and transfer learning based on molecular graph attention mechanism and fingerprints improving inhibitor bioactivity prediction for EGFR family proteins on data scarcity.

The proteins within the human epidermal growth factor receptor (EGFR) family, members of the tyrosine kinase receptor family, play a pivotal role in the molecular mechanisms driving the development of various tumors. Tyrosine kinase inhibitors, key compounds in targeted therapy, encounter challenges in cancer treatment due to emerging drug resistance mutations. Consequently, machine learning has undergone significant evolution to address the challenges of cancer drug discovery related to EGFR family proteins. However, the application of deep learning in this area is hindered by inherent difficulties associated with small-scale data, particularly the risk of overfitting. Moreover, the design of a model architecture that facilitates learning through multi-task and transfer learning, coupled with appropriate molecular representation, poses substantial challenges. In this study, we introduce GraphEGFR, a deep learning regression model designed to enhance molecular representation and model architecture for predicting the bioactivity of inhibitors against both wild-type and mutant EGFR family proteins. GraphEGFR integrates a graph attention mechanism for molecular graphs with deep and convolutional neural networks for molecular fingerprints. We observed that GraphEGFR models employing multi-task and transfer learning strategies generally achieve predictive performance comparable to existing competitive methods. The integration of molecular graphs and fingerprints adeptly captures relationships between atoms and enables both global and local pattern recognition. We further validated potential multi-targeted inhibitors for wild-type and mutant HER1 kinases, exploring key amino acid residues through molecular dynamics simulations to understand molecular interactions. This predictive model offers a robust strategy that could significantly contribute to overcoming the challenges of developing deep learning models for drug discovery with limited data and exploring new frontiers in multi-targeted kinase drug discovery for EGFR family proteins.

Rethinking the Masking Strategy for Pretraining Molecular Graphs from a Data-Centric View.

Node-level self-supervised learning has been widely applied for pretraining molecular graphs. Attribute Masking (AttrMask) is pioneering work in this field, and its improved methods focus on enhancing the capacity of the backbone models by incorporating additional modules. However, these methods overlook the imbalanced atom distribution due to employing only the random masking strategy to mask atoms for pretraining. According to the properties of molecules, we propose a weighted masking strategy to enhance the capacity of pretrained models by more effective utilization of molecular information while pretraining. Our experimental results demonstrate that AttrMask combined with our proposed weighted masking strategy yields superior performance compared to the random masking strategy, even surpassing the model-centric improvement methods without increasing the parameters. Additionally, our weighted masking strategy can be extended to other pretraining methods to achieve enhanced performance.

Molecular property prediction based on graph structure learning.

Molecular property prediction (MPP) is a fundamental but challenging task in the computer-aided drug discovery process. More and more recent works employ different graph-based models for MPP, which have achieved considerable progress in improving prediction performance. However, current models often ignore relationships between molecules, which could be also helpful for MPP. For this sake, in this article we propose a graph structure learning (GSL) based MPP approach, called GSL-MPP. Specifically, we first apply graph neural network (GNN) over molecular graphs to extract molecular representations. Then, with molecular fingerprints, we construct a molecule similarity graph (MSG). Following that, we conduct GSL on the MSG, i.e. molecule-level GSL, to get the final molecular embeddings, which are the results of fuzing both GNN encoded molecular representations and the relationships among molecules. That is, combining both intra-molecule and inter-molecule information. Finally, we use these molecular embeddings to perform MPP. Extensive experiments on 10 various benchmark datasets show that our method could achieve state-of-the-art performance in most cases, especially on classification tasks. Further visualization studies also demonstrate the good molecular representations of our method. Source code is available at https://github.com/zby961104/GSL-MPP.

Exploring expected values of topological indices of random cyclodecane chains for chemical insights

Chemical graph theory has made a significant contribution to understand the chemical compound properties in the modern era of chemical science. At present, calculation of the topological indices is one of most important area of research in the field of chemical graph theory. Cyclodecane is a cyclic hydrocarbon with the chemical formula C10H20\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{10}H_{20}$$\\end{document}. It consists of a ring of ten carbon atoms bonded together in a cyclical structure. Cyclodecane chains can be part of larger molecules or polymers, where multiple cyclodecane rings are connected together. These molecules can have various applications in chemistry, materials science, and pharmaceuticals. This article aims to determine expected values of some connectivity based topological indices of random cyclodecane chains, containing saturated hydrocarbons with at least two rings. It also compares these descriptors using explicit formulae, numerical tables and present graphical profiles of these comparisons.

Structure-property modeling of coumarins and coumarin-related compounds in pharmacotherapy of cancer by employing graphical topological indices.

Coumarins, a subgroup of colorless and crystalline oxygenated heterocyclic compounds originally discovered in the plant Dipteryx odorata, were the subject of a recent study investigating their quantitative structure-activity relationship (QSAR) in cancer pharmacotherapy. This study utilized graph theoretical molecular descriptors, also known as topological indices, as a numerical representation method for the chemical structures embedded in molecular graphs. These descriptors, derived from molecular graphs, play a pivotal role in quantitative structure-property relationship (QSPR) analysis. In this paper, intercorrelation between the Balban index, connective eccentric index, eccentricity connectivity index, harmonic index, hyper Zagreb index, first path Zagreb index, second path Zagreb index, Randic index, sum connectivity index, graph energy and Laplacian energy is studied on the set of molecular graphs of coumarins. It is found that the pairs of degree-based indices are highly intercorrelated. The use of these molecular descriptors in structure-boiling point modeling was analyzed. Finally, the curve-linear regression between considered molecular descriptors with physicochemical properties of coumarins and coumarin-related compounds is obtained.

The Second Omega Index

Background: The omega index has been recently introduced to identify a variety of topological and combinatorial aspects of a graph with a new viewpoint. As a continuing study of the omega index, by considering the incidence of edges and vertices to the adjacency of the vertices, in this paper, we have introduced the second omega index Ω2 and then computed it over some well-known graph classes. Methods: Many combinatorial counting methods have been utilized in the proofs. The edge partition is frequently used throughout the work. Naturally, some graph theoretical lemmas are also used. Results: In particular, trees having the smallest and largest Ω2 have been constructed. Finally, the second omega index of some derived graphs, such as line graphs, subdivision graphs, and vertex-semitotal graphs, has been presented. Conclusion: Omega invariant has already been explored in many papers. It has been defined in terms of vertex degrees. Vertices correspond to the atoms in a molecule and a calculation, which only depends on the atomic parameters, is not even comparable with a calculation containing both atoms and chemical bonds between them. With this idea in mind, we have evaluated some mathematical properties of the second omega index, which has great potential in chemical applications related to the number of cycles in the molecular graph.

Predicting equilibrium distributions for molecular systems with deep learning

Advances in deep learning have greatly improved structure prediction of molecules. However, many macroscopic observations that are important for real-world applications are not functions of a single molecular structure but rather determined from the equilibrium distribution of structures. Conventional methods for obtaining these distributions, such as molecular dynamics simulation, are computationally expensive and often intractable. Here we introduce a deep learning framework, called Distributional Graphormer (DiG), in an attempt to predict the equilibrium distribution of molecular systems. Inspired by the annealing process in thermodynamics, DiG uses deep neural networks to transform a simple distribution towards the equilibrium distribution, conditioned on a descriptor of a molecular system such as a chemical graph or a protein sequence. This framework enables the efficient generation of diverse conformations and provides estimations of state densities, orders of magnitude faster than conventional methods. We demonstrate applications of DiG on several molecular tasks, including protein conformation sampling, ligand structure sampling, catalyst–adsorbate sampling and property-guided structure generation. DiG presents a substantial advancement in methodology for statistically understanding molecular systems, opening up new research opportunities in the molecular sciences.

Forgotten Topological and Wiener Indices of Prime Ideal Sum Graph of Zn.

Chemical graph theory is a sub-branch of mathematical chemistry, assuming each atom of a molecule is a vertex and each bond between atoms as an edge. Owing to this theory, it is possible to avoid the difficulties of chemical analysis because many of the chemical properties of molecules can be determined and analyzed via topological indices. Due to these parameters, it is possible to determine the physicochemical properties, biological activities, environmental behaviours and spectral properties of molecules. Nowadays, studies on the zero divisor graph of Z_n via topological indices is a trending field in spectral graph theory. For a commutative ring R with identity, the prime ideal sum graph of R is a graph whose vertices are nonzero proper ideals of R and two distinctvertices I and J are adjacent if and only if I+J is a prime ideal of R. In this study the forgotten topological index and Wiener index of the prime ideal sum graph of Z_n are calculated for n=p^α,pq,p^2 q,p^2 q^2,pqr,p^3 q,p^2 qr,pqrs where p,q,r and s are distinct primes and a Sage math code is developed for designing graph and computing the indices. In the light of this study, it is possible to handle the other topological descriptors for computing and developing new algorithms for next studies and to study some spectrum and graph energies of certain finite rings with respect to PIS-graph easily.

Zagreb Topological Properties of Hexa Organic Molecular Structures.

In connection with the study of chemical graph theory, it has been explored that a single number can capture the numerical representation of a molecular structure, and this number is known as a topological property (index). This study aimed to explore a few Zagreb topological properties for four hexa organic molecular structures (hexagonal, honeycomb, silicate, and oxide) based on the valency and valency sum of atoms in the structure. We employed the technique of partitioning the set of bonds according to the valency and valency-sum of end atoms of each bond and then performed the computation by using combinatorial rules of counting (that is, the rule of sum and the rule of product). The obtained results were also compared numerically and graphically. Exact values of five valencies based and five valency-sum-based Zagreb topological properties were found for the underline chemical structures.

Weighted Mostar invariants of chemical compounds: An analysis of structural stability

The concept of the weighted Mostar invariant is a mathematical tool used in chemical graph theory to study the stability of chemical compounds. Several recent studies have explored the weighted Mostar invariant of various chemical structures, including hydrocarbons, alcohols, and other organic compounds. One of the key advantages of the weighted Mostar invariant is that it can be easily computed for large and complex chemical structures, making it a valuable tool for studying the stability of a wide range of chemical compounds. This notion has been utilized to build novel approaches for forecasting chemical compound stability, such as machine learning algorithms. The focus of the paper is to demonstrate the weighted Mostar indices of three specific nanostructures: silicon dioxide (SIO2, poly-methyl methacrylate network (PMMA(s)), and melem chains (MC(h)). The authors seek to provide the findings of their investigation of these nanostructures using the weighted Mostar invariant.

Degree Descriptors and Graph Entropy Quantities of Zeolite ACO.

Cheminformatics is a fascinating emerging subfield of chemical graph theory that studies quantitative structure-activity and property relationships of molecules and, in turn, uses these to predict the physical and chemical properties, which are extremely useful in drug discovery and optimization. Knowledge discovery can be put to use in pharmaceutical data matching to help in finding promising lead compounds. Topological descriptors are numerical quantities corresponding to the chemical structures that are used in the study of these phenomena. This paper is concerned with developing the generalized analytical expression of topological descriptors for zeolite ACO structures with underlying degree and degree-sum parameters. To demonstrate improved discrimination power between the topological descriptors, we have further modified Shannon's entropy approach and used it to calculate the entropy measures of zeolite ACO structures.