Molecular Graph Research Articles

Graph neural processes for molecules: an evaluation on docking scores and strategies to improve generalization

Neural processes (NPs) are models for meta-learning which output uncertainty estimates. So far, most studies of NPs have focused on low-dimensional datasets of highly-correlated tasks. While these homogeneous datasets are useful for benchmarking, they may not be representative of realistic transfer learning. In particular, applications in scientific research may prove especially challenging due to the potential novelty of meta-testing tasks. Molecular property prediction is one such research area that is characterized by sparse datasets of many functions on a shared molecular space. In this paper, we study the application of graph NPs to molecular property prediction with DOCKSTRING, a diverse dataset of docking scores. Graph NPs show competitive performance in few-shot learning tasks relative to supervised learning baselines common in chemoinformatics, as well as alternative techniques for transfer learning and meta-learning. In order to increase meta-generalization to divergent test functions, we propose fine-tuning strategies that adapt the parameters of NPs. We find that adaptation can substantially increase NPs' regression performance while maintaining good calibration of uncertainty estimates. Finally, we present a Bayesian optimization experiment which showcases the potential advantages of NPs over Gaussian processes in iterative screening. Overall, our results suggest that NPs on molecular graphs hold great potential for molecular property prediction in the low-data setting.Scientific contributionNeural processes are a family of meta-learning algorithms which deal with data scarcity by transferring information across tasks and making probabilistic predictions. We evaluate their performance on regression and optimization molecular tasks using docking scores, finding them to outperform classical single-task and transfer-learning models. We examine the issue of generalization to divergent test tasks, which is a general concern of meta-learning algorithms in science, and propose strategies to alleviate it.

Counting Polynomials in Chemistry II

Some polynomials find their way into chemical graph theory less often than others. They could provide new ways of understanding the origins of regularities in the chemistry of specific classes of compounds. This study’s objective is to depict the place of polynomials in chemical graph theory. Different approaches and notations are explained and levelled. The mathematical aspects of a series of such polynomials are put into the context of recent research. The directions in which this project was intended to proceed and where it stands right now are presented.

A new spectral-based index for graphs and its application to polyaromatic compounds

In this study, we introduce a novel index called the modified inverse sum indeg (MISI) energy as an extension of the traditional inverse sum indeg (ISI) energy and neighbor degree sum energy. We devised an algorithm that employs the simplified molecular input line entry system (SMILES) formula of compounds to compute the MISI energy of polycyclic aromatic hydrocarbon (PAH). Additionally, we established the bounds of the MISI energy for certain classes of graphs with fixed number of vertices. A strong correlation between the MISI energy and the total [Formula: see text]-electron energy of PAHs is observed through regression analysis. Remarkably, this correlation outperforms that achieved by the classical ISI energy. These findings highlight the enhanced effectiveness of the MISI energy as a descriptor for capturing significant molecular properties. Moreover, our study establishes a foundation for further theoretical extensions and practical applications in the field of chemical graph theory.

Multimodal Representation Learning via Graph Isomorphism Network for Toxicity Multitask Learning.

Toxicity is paramount for comprehending compound properties, particularly in the early stages of drug design. Due to the diversity and complexity of toxic effects, it became a challenge to compute compound toxicity tasks. To address this issue, we propose a multimodal representation learning model, termed multimodal graph isomorphism network (MMGIN), to address this challenge for compound toxicity multitask learning. Based on fingerprints and molecular graphs of compounds, our MMGIN model incorporates a multimodal representation learning model to acquire a comprehensive compound representation. This model adopts a two-channel structure to independently learn fingerprint representation and molecular graph representation. Subsequently, two feedforward neural networks utilize the learned multimodal compound representation to perform multitask learning, encompassing compound toxicity classification and multiple compound category classification simultaneously. To test the effectiveness of our model, we constructed a novel data set, termed the compound toxicity multitask learning (CTMTL) data set, derived from the TOXRIC data set. We compare our MMGIN model with other representative machine learning and deep learning models on the CTMTL and Tox21 data sets. The experimental results demonstrate significant advancements achieved by our MMGIN model. Furthermore, the ablation study underscores the effectiveness of the introduced fingerprints, molecular graphs, the multimodal representation learning model, and the multitask learning model, showcasing the model's superior predictive capability and robustness.

GCLmf: A Novel Molecular Graph Contrastive Learning Framework Based on Hard Negatives and Application in Toxicity Prediction.

In silico methods for prediction of chemical toxicity can decrease the cost and increase the efficiency in the early stage of drug discovery. However, due to low accessibility of sufficient and reliable toxicity data, constructing robust and accurate prediction models is challenging. Contrastive learning, a type of self-supervised learning, leverages large unlabeled data to obtain more expressive molecular representations, which can boost the prediction performance on downstream tasks. While molecular graph contrastive learning has gathered growing attentions, current models neglect the quality of negative data set. Here, we proposed a self-supervised pretraining deep learning framework named GCLmf. We first utilized molecular fragments that meet specific conditions as hard negative samples to boost the quality of the negative set and thus increase the difficulty of the proxy tasks during pre-training to learn informative representations. GCLmf has shown excellent predictive power on various molecular property benchmarks and demonstrates high performance in 33 toxicity tasks in comparison with multiple baselines. In addition, we further investigated the necessity of introducing hard negatives in model building and the impact of the proportion of hard negatives on the model.

Cocrystal screening of benznidazole based on electronic transition, molecular reactivity, hydrogen bonding, and stability.

Screening of cocrystals of active pharmaceutical ingredients is important in the development of pharmaceutical compounds because it improves bioavailability, stability, solubility, and many other physicochemical properties. In this work, quantum chemical calculations were utilized for the computational evaluation of the cocrystal screening of benznidazole (BZN) API via hydrogen bonding with four coformers (maleic acid, malonic acid, oxalic acid, and salicylic acid), and they contain carboxylic groups. The nitrogen of the imidazole ring in benznidazole and the carboxylic group of the coformer form a hetero-synthon connected by a strong hydrogen bond. The strength of the hydrogen bonding interaction O-H…N was measured using various tools. It was found that in comparison to BZN cocrystals with malonic acid, oxalic acid, and salicylic acid, the O-H…N interaction in the BZN-maleic acid cocrystal had higher interaction energy, indicating it had stronger hydrogen bonding. The strength of the hydrogen bond O-H…N for synthons was discovered to be more beneficial than the C-H…O interaction, as confirmed by ESP analysis. The BZN-salicylic acid cocrystal was found to be more reactive and polarizable, whereas the BZN-malonic acid cocrystal was more stable. Cocrystals of benznidazole exhibited better physicochemical characteristics than API benznidazole, as indicated by electron transition properties between the most significant orbitals. The computational evaluation for the screening of benznidazole cocrystals was performed in Gaussian 16 software using density functional theory (DFT) with the hybrid functional B3LYP and the basis set 6-311 + + G(d,p). The UV-Vis absorption spectrum in solvent water was analyzed using the TD-DFT/6-311 + + G(d,p) method to determine the influence of the solvent in cocrystals using a polarizable continuum model. The strength of the hydrogen bonding interactions O-H…N in each of those mentioned cocrystals was used to screen the cocrystals using tools such as thermodynamic probability, ESP analysis, QTAIM analysis, and NBO analysis. The pairing energy of interaction was measured by determining H-bond donor ( ) and H-bond acceptor ) parameters for hydrogen bonds from maxima and minima on the ESP surface. GaussView 06 software was used to create, visualize, and plot the optimized structure of the cocrystal and HOMO-LUMO orbitals. The AIMALL (10.05.04) software package generated the molecular graph for intra- and intermolecular interactions. The RDG-scatter plot, MEP map, and ELF plot were rendered from Multiwfn 8.0 and VMD 1.9.1 software.

Chain-aware graph neural networks for molecular property prediction.

Predicting the properties of molecules is a fundamental problem in drug design and discovery, while how to learn effective feature representations lies at the core of modern deep-learning-based prediction methods. Recent progress shows expressive power of graph neural networks (GNNs) in capturing structural information for molecular graphs. However, we find that most molecular graphs exhibit low clustering along with dominating chains. Such topological characteristics can induce feature squashing during message passing and thus impair the expressivity of conventional GNNs. Aiming at improving node features' expressiveness, we develop a novel chain-aware graph neural network model, wherein the chain structures are captured by learning the representation of the center node along the shortest paths starting from it, and the redundancy between layers are mitigated via initial residual difference connection (IRDC). Then the molecular graph is represented by attentive pooling of all node representations. Compared to standard graph convolution, our chain-aware learning scheme offers a more straightforward feature interaction between distant nodes, thus it is able to capture the information about long-range dependency. We provide extensive empirical analysis on real-world datasets to show the outperformance of the proposed method. The MolPath code is publicly available at https://github.com/Assassinswhh/Molpath.

Computational analysis of diameter eccentricity based and hyper diameter eccentricity based indices for linear saturated monocarboxylic acids

Chemical graph theory deals with chemical graphs, which are used to represent chemical systems. Topological indices of molecular graphs are an important area of research in chemical graph theory. These indices are numerical values associated with compounds that aim to establish connections between chemical structures and physical attributes, chemical reactivity, and biological activity. Many graph polynomials have been proposed to compute various topological indices. Quantitative structure-property relationship (QSPR) analysis of chemical compounds involves several regression methods that rely on these topological indices. In this article, we utilize the newly introduced DƐ-polynomial to calculate the eccentricitybased indices such as the diameter eccentricity based and hyper diameter eccentricity based index values for nineteen linear saturated monocarboxylic acids. Quantitative structureproperty relationship (QSPR) analysis is also performed for the seven thermodynamic properties of monocarboxylic acids. The relationship between thermodynamic properties and topological indices is explored using linear, quadratic and cubic regression models. The best fit curvilinear regression models were determined based on the R2 and RMSE values of the models. To further investigate the statistical significance of our models, we also conducted chi-square goodness-of-fit tests to identify the best fit models.

Electron Density and Molecular Orbital Analyses of the Nature of Bonding in the η3-CCH Agostic Rhodium Complexes Preceding the C-C and C-H Bond Cleavages.

In our recent work, we revisited C-H and C-C bond activation in rhodium (I) complexes of pincer ligands PCP, PCN, PCO, POCOP, and SCS. Our findings indicated that an η3-Csp2Csp3H agostic intermediate acts as a common precursor to both C-C and C-H bond activation in these systems. We explore the electronic structure and bonding nature of these precleavage complexes using electron density and molecular orbital analyses. Using NBO, IBO, and ESI-3D methods, the bonding in the η3-CCH agostic moiety is depicted by two three-center agostic bonds: Rh-Csp2-Csp3 and Rh-Csp3-H, with all three atoms datively bound to Rh(I). IBO analysis specifically highlights the involvement of three orbitals (CC→Rh and CH→Rh σ donation, plus Rh→CCH π backdonation) in both C-C and C-H bond cleavages. NCIPLOT and QTAIM analyses highlight anagostic (Rh-H) or β-agostic (Rh-Csp2-H) interactions and the absence of Rh-Csp3 interactions. QTAIM molecular graphs suggest bond path instability under dynamic conditions due to the nearness of line and ring critical points. Several low-frequency and low-force vibrational modes interconvert various bonding patterns, reinforcing the dynamic η3-CCH agostic nature. The kinetic preference for C-H bond breaking is attributed to the smaller reduced mass of C-H vibrations compared to C-C vibrations.

A Molecular Fragment Representation Learning Framework for Drug-Drug Interaction Prediction.

The concurrent use of multiple drugs may result in drug-drug interactions, increasing the risk of adverse reactions. Hence, it is particularly crucial to propose computational methods for precisely identifying unknown drug-drug interactions, which is of great significance for drug development and health. However, most recent studies have limited the drug-drug interaction prediction task to identifying interactions between substructures, overlooking molecular hierarchical information. Moreover, the extracted substructures in these methods are always restricted to have the same number of atoms as contained in the molecular graph, which does not align with real-world facts. In this study, a molecular fragment representation learning framework for drug-drug interaction prediction is introduced. Initially, a fragment extraction module is designed to acquire a series of molecular fragments. Subsequently, to capture more comprehensive features, molecular hierarchical information is effectively integrated, enabling drug-drug interaction prediction by identifying pairwise interactions between molecular fragments of each drug. Comprehensive evaluations demonstrate that the proposed method achieved state-of-the-art performance in both DrugBank and Twosides datasets, particularly achieving an improved accuracy of over 20% for unseen drugs in both two datasets. Furthermore, case studies and visual analysis confirm that the proposed method can accurately identify crucial substructures influencing the interactions, which are basically consistent with functional group structures in reality. In conclusion, this method not only enhances the performance of drug-drug interaction prediction but also offers high interpretability. Source code is freely available at https://github.com/kennysyp/MFR-DDI .

Some Reverse Topological Indices of Comet and Double Comet Graphs

Introduction: Chemical Graph Theory or CGT for short, is a transdisciplinary field of Mathematics wherein graphs are used to represent chemical compounds. Under this representation, the atoms of a chemical compound are expressed as vertices, while the bonds connecting these atoms are expressed as edges. Once the graph representation of a chemical compound has been determined, graph-theoretic techniques can now be used to determine various topological indices associated with the chemical compound. Topological indices are invariants of a graph that have predictive power for the chemical properties of a chemical compound. In CGT, trees, being connected and acyclic, have been an essential class of graphs. This is because, most compounds have acyclic molecular structures. In the 2023 study by Gowtham and Husin, various reverse topological indices of a family of trees called bistar graphs have been determined. Objectives: Motivated by the work of Gowtham and Husin, we determine some reverse topological indices of another family of trees called comets and double comets. Double comets are natural extension of bistar graphs. We also give a certain computational application of our results on double comet graphs. Finally, we investigate the relationship between the reverse topological indices of bistar graphs and double comets. Methods: Several important graph-theoretic concepts were used to analyze some important properties of comets and double comets, leading to the computation of their reverse vertex degree based topological indices. Results: The following reverse vertex degree-based topological indices for comets and double comets were determined: Reverse sum-connectivity, First reverse Zagreb, Second reverse Zagreb, Reverse arithmetic-geometric, Reverse geometric-arithmetic, Reverse Sombor, and Reverse Nirmala. A computational application of the results to a certain chemical compound (2,2,4,4-Tetramethylpentane) or C9H20 were also demonstrated. Conclusions: The results of the paper provided an extension to an existing result on the reverse vertex degree-based topological indices of bistar graphs by considering double comet graphs. Several topological reverse vertex degree-based topological indices were also computed for comet graphs. The computed topological indices were also applied in determining some invariants of a certain chemical compound. For future studies, we recommend that reverse vertex degree based topological indices of other family of trees will be considered.

Interpretable and Physicochemical-Intuitive Deep Learning Approach for the Design of Thermal Resistance of Energetic Compounds.

Thermal resistance of energetic materials is critical due to its impact on safety and sustainability. However, developing predictive models remains challenging because of data scarcity and limited insights into quantitative structure-property relationships. In this work, a deep learning framework, named EM-thermo, was proposed to address these challenges. A data set comprising 5029 CHNO compounds, including 976 energetic compounds, was constructed to facilitate this study. EM-thermo employs molecular graphs and direct message-passing neural networks to capture structural features and predict thermal resistance. Using transfer learning, the model achieves an accuracy of approximately 97% for predicting the thermal-resistance property (decomposition temperatures above 573.15 K) in energetic compounds. The involvement of molecular descriptors improved model prediction. These findings suggest that EM-thermo is effective for correlating thermal resistance from the atom and covalent bond level, offering a promising tool for advancing molecular design and discovery in the field of energetic compounds.

Compatibility analysis of waste polymer recycling in asphalt binder using molecular descriptor and graph neural network

Recycling of waste polymers for valuable use is important for circular economy and environmental sustainability. This study introduces a novel approach to evaluating the compatibility between waste polymers and asphalt binders using advanced molecular representation models. The solubility parameters of waste polymers were predicted using traditional machine learning (ML) models and geometry-enhanced graph neural network (GeoGNN), respectively. The compatibility index was then calculated based on the absolute difference between the solubility parameters of polymers and asphalt. Results indicate that GeoGNN outperforms traditional ML and other GNN models due to its superior ability to capture complex spatial structures. The study also identifies key molecular descriptors that significantly influence solubility parameters of waste polymers. Given the variability in asphalt binder composition, the most compatible waste polymers differ across binders, making the data-driven approach especially valuable. The GeoGNN model greatly enhances the ability to assess compatibility in the polymer-asphalt system. This complements experimental techniques by integrating geometric information to analyze molecular features uncovering the structure-property relationship of material.

Molecular descriptors of symmetrically configured carbon nanocones via quotient graph technique

Carbon nanocones, characterized by planar networks primarily consisting of hexagonal carbon faces and a few pentagons in the core, hold significant promise in various fields such as electronics, medicine, and material research due to their exceptional properties. This study exclusively investigates the topological descriptors of symmetrically configured carbon nanocones, specifically nanocones with two and three pentagonal core respectively. By modeling these structures as chemical graphs and employing molecular descriptors, we aim to provide a quantitative analysis of the structures without laboratory experimentation. The quotient graph approach is employed to determine the distance based descriptors, namely wiener, szeged and Padmakar-Ivan indices for these symmetrically configured carbon nanocones. The analytically closed formulas determined could be useful in quantitative structure-property-activity relationship studies, which helps in predicting the physico-chemical properties of the underlying structures. Thus the findings in this work not only deepen our understanding of symmetric carbon nanocones but also pave the way for significant advancements in nanotechnology and materials science.

Topology of quasi divisor graphs associated with non-associative algebra

The visualization of graphs representing algebraic structures has increasingly gained traction in chemical engineering research, emerging as a significant scientific challenge in contemporary studies. Due to their practical applications, graphs associated with groups and various algebraic systems have garnered significant interest in academic literature. Chemical graph theory employs graphs to illustrate molecular structures, where vertices symbolize atoms and edges represent bonds. The structure of quasi divisor graphs linked to non-associative algebra, including quasigroups and loops, presents numerous potential implications and wider applications. These applications span multiple disciplines, such as algebra, combinatorics, computer science, and network theory. Latin squares are tabular representations of quasigroups, generalizations of group structure. Numerous classifications of quasigroups exist in academic literature, such as Moufang quasigroups, Bol quasigroups, and alternative quasigroups. However, the structural characteristics of quasigroups exhibiting the weak inverse property closely resemble those of groups. The overall purpose of this study is to see the interrelationship between non-isomorphic quasi divisor graphs and a particular class of G-loops. To achieve our results, we employ a variety of methods, including a combinatorial approach, degree counting techniques, vertex and edge partitioning methods, as well as graph-theoretical tools and analytical procedures. In this paper, we compute a few topological indices based on degree, distance, and degree-distance using the structural aspects of quasi divisor graphs of orders 2φ,22ϕ,23ϕ and 4ϕ1ϕ2 where φ is a positive integer and ϕ1,ϕ2 are odd primes with ϕ1<ϕ2. This work also includes polynomial forms and their geometrical interpretations connected to linear, quadratic and higher degree topological indices of quasi divisor graphs associated with a class of non-commutative weak inverse property quasigroups.

On Detour Index of Join of Hamilton-connected Graphs

In this paper we contribute to the literature of computational chemistry by providing exact expressions for the detour index of joins of Hamilton-connected ( H C ) graphs. This improves upon existing results by loosening the requirement of a molecular graph being Hamilton-connected and only requirement certain subgraphs to be Hamilton-connected.

Predictive potential of distance-related spectral graphical descriptors for structure-property modeling of thermodynamic properties of polycyclic hydrocarbons with applications

A distance-related spectral descriptor is a graphical index with defining structure built on eigenvalues of chemical matrices relying on distances in graphs. This paper explores the predictive ability of both existing and new distance-related spectral descriptors for estimating thermodynamic characteristics of polycyclic hydrocarbons (PHs). As a standard choice, the entropy and heat capacity are selected to represent thermodynamic properties. Furthermore, 30 initial members of PHs are considered as test molecules for this study. Three new molecular matrices have been proposed and our research demonstrates that distance-spectral graphical indices built by these novel matrices surpass in efficiency relative to famous distance-spectral indices. First, a novel computational method is put forwarded to evaluate distance-spectral indices of molecular graphs. The proposed methodology is utilized to compute both pre-existing and novel distance-related spectral descriptors, with an aim to assess their predictive efficacy using experimental data pertaining to two selected thermodynamic properties. Subsequently, we identify the five most promising distance-related spectral descriptors, comprising the degree-distance and Harary energies, the recently introduced second geometric-arithmetic energy along with its associated Estrada invariant, and 2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {nd}$$\\end{document} atom-bond connectivity (ABC) Estrada index. Notably, the 2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {nd}$$\\end{document} ABC Estrada index and Harary energy demonstrate correlation coefficients exceeding 0.95, while certain conventional spectral indices including the distance energy as well as its associated Estrada index, display comparatively lower performance levels. Moreover, we illustrate the practical implications of our findings on specific classes of one-hexagonal nanocones and carbon polyhex nanotubes. These outcomes hold potential for enhancing the theoretical determination of certain thermodynamic attributes of these nanostructures, offering improved accuracy and minimal margin of error.

A multi-view feature representation for predicting drugs combination synergy based on ensemble and multi-task attention models

This paper proposes a novel multi-view ensemble predictor model that is designed to address the challenge of determining synergistic drug combinations by predicting both the synergy score value values and synergy class label of drug combinations with cancer cell lines. The proposed methodology involves representing drug features through four distinct views: Simplified Molecular-Input Line-Entry System (SMILES) features, molecular graph features, fingerprint features, and drug-target features. On the other hand, cell line features are captured through four views: gene expression features, copy number features, mutation features, and proteomics features. To prevent overfitting of the model, two techniques are employed. First, each view feature of a drug is paired with each corresponding cell line view and input into a multi-task attention deep learning model. This multi-task model is trained to simultaneously predict both the synergy score value and synergy class label. This process results in sixteen input view features being fed into the multi-task model, producing sixteen prediction values. Subsequently, these prediction values are utilized as inputs for an ensemble model, which outputs the final prediction value. The ‘MVME’ model is assessed using the O’Neil dataset, which includes 38 distinct drugs combined across 39 distinct cancer cell lines to output 22,737 drug combination pairs. For the synergy score value, the proposed model scores a mean square error (MSE) of 206.57, a root mean square error (RMSE) of 14.30, and a Pearson score of 0.76. For the synergy class label, the model scores 0.90 for accuracy, 0.96 for precision, 0.57 for kappa, 0.96 for the area under the ROC curve (ROC-AUC), and 0.88 for the area under the precision-recall curve (PR-AUC).

Combining graph neural networks and transformers for few-shot nuclear receptor binding activity prediction

Nuclear receptors (NRs) play a crucial role as biological targets in drug discovery. However, determining which compounds can act as endocrine disruptors and modulate the function of NRs with a reduced amount of candidate drugs is a challenging task. Moreover, the computational methods for NR-binding activity prediction mostly focus on a single receptor at a time, which may limit their effectiveness. Hence, the transfer of learned knowledge among multiple NRs can improve the performance of molecular predictors and lead to the development of more effective drugs. In this research, we integrate graph neural networks (GNNs) and Transformers to introduce a few-shot GNN-Transformer, Meta-GTNRP to predict the binding activity of compounds using the combined information of different NRs and identify potential NR-modulators with limited data. The Meta-GTNRP model captures the local information in graph-structured data and preserves the global-semantic structure of molecular graph embeddings for NR-binding activity prediction. Furthermore, a few-shot meta-learning approach is proposed to optimize model parameters for different NR-binding tasks and leverage the complementarity among multiple NR-specific tasks to predict binding activity of compounds for each NR with just a few labeled molecules. Experiments with a compound database containing annotations on the binding activity for 11 NRs shows that Meta-GTNRP outperforms other graph-based approaches. The data and code are available at: https://github.com/ltorres97/Meta-GTNRP.Scientific contributionThe proposed few-shot GNN-Transformer model, Meta-GTNRP captures the local structure of molecular graphs and preserves the global-semantic information of graph embeddings to predict the NR-binding activity of compounds with limited available data; A few-shot meta-learning framework adapts model parameters across NR-specific tasks for different NRs in a joint learning procedure to predict the binding activity of compounds for each NR with just a few labeled molecules in highly imbalanced data scenarios; Meta-GTNRP is a data-efficient approach that combines the strengths of GNNs and Transformers to predict the NR-binding properties of compounds through an optimized meta-learning procedure and deliver robust results valuable to identify potential NR-based drug candidates.

The Second Hyper-Zagreb Index and Coindex of Chemical Nanostructures in Drugs.

Various dendrimer nanoparticles have properties like multivalency, controlled size, and surface functionality that make them promising nanocarriers for targeted drug delivery and other applications in pharmaceutical sciences. The precise tunability of dendrimers is an advantage over other nanoparticles. The topological descriptors can be used to predict the physicochemical properties of dendrimers and optimize their branching pattern for specific applications. The second hyper-Zagreb index and co-index are computed for various chemical structures, including dendrimers, to facilitate the correlation between their structure and biological activity. In this study, the second Hyper-Zagreb index and second Hyper-Zagreb polynomials were calculated for various chemical structures, such as the molecular graph of poly(propyl) ether imine dendrimer PETIM, nanostar dendrimer (D3[p]), polypropylenimine octaamine dendrimer (NS1[p]) and (NS2[p]), polymer dendrimer (NS3[p]) and NS5[p]), fullerene dendrimer (NS4[p]), and other classes of dendrimers. By computing formulae and analyzing data and figures, we obtained new insights into the features of structure-property connections for these types of compounds of nanostar dendrimers. The results can be used to optimize the properties of dendrimers for specific applications.