Molecular Graph Research Articles

MolE: a foundation model for molecular graphs using disentangled attention.

Models that accurately predict properties based on chemical structure are valuable tools in the chemical sciences. However, for many properties, public and private training sets are typically small, making it difficult for models to generalize well outside of the training data. Recently, this lack of generalization has been mitigated by using self-supervised pretraining on large unlabeled datasets, followed by finetuning on smaller, labeled datasets. Inspired by these advances, we report MolE, a Transformer architecture adapted for molecular graphs together with a two-step pretraining strategy. The first step of pretraining is a self-supervised approach focused on learning chemical structures trained on ~842 million molecular graphs, and the second step is a massive multi-task approach to learn biological information. We show that finetuning models that were pretrained in this way perform better than the best published results on 10 of the 22 ADMET (absorption, distribution, metabolism, excretion and toxicity) tasks included in the Therapeutic Data Commons leaderboard (c. September 2023).

Drug Sensitivity Prediction Based on Multi-stage Multi-modal Drug Representation Learning.

Accurate prediction of anticancer drug responses is essential for developing personalized treatment plans in order to improve cancer patient survival rates and reduce healthcare costs. To this end, we propose a drug sensitivity prediction model based on multi-stage multi-modal drug representations (ModDRDSP) to reflect the properties of drugs more comprehensively, and to better model the complex interactions between cells and drugs. Specifically, we adopt the SMILES representation learning method based on the deep hierarchical bi-directional GRU network (DSBiGRU) and the molecular graph representation learning method based on the deep message-crossing network (DMCN) for the multi-modal information of drugs. Additionally, we integrate the multi-omics information of cell lines based on a convolutional neural network (CNN). Finally, we use an ensemble deep forest algorithm for the prediction of drug sensitivity. After validation, the ModDRDSP shows impressive performance which outperforms the four current industry-leading models. More importantly, ablation experiments demonstrate the validity of each module of the proposed model, and case studies show the good results of ModDRDSP for predicting drug sensitivity, further establishing the superiority of ModDRDSP in terms of performance.

DigFrag as a digital fragmentation method used for artificial intelligence-based drug design.

Fragment-Based Drug Design (FBDD) plays a pivotal role in the field of drug discovery and development. The construction of high-quality fragment libraries is a critical step in FBDD. Conventional fragmentation approaches often rely on rigid rules and chemical intuition, limiting their adaptability to diverse molecular structures. The rapid development of Artificial Intelligence (AI) technology offers a transformative opportunity to rethink traditional methods. Here, we present DigFrag, a digital fragmentation method that highlights important substructures by focusing locally within the molecular graph. In addition, we feed the fragments segmented by machine intelligence and human expertise into the deep generative model to compare the preference for data from different sources. Experimental results show that the structural diversity of fragments segmented by DigFrag is higher, and more desirable compounds are generated based on these fragments. These results also demonstrate that data generated based on AI methods may be more suitable for AI models. Moreover, a user-friendly platform called MolFrag ( https://dpai.ccnu.edu.cn/MolFrag/ ) is developed based on various fragmentation techniques to support molecular segmentation.

Exponential Wiener index of some silicate networks

Any graph that depicts a particular molecular structure can be given a topological graph index, also known as a molecular descriptor. This index can be used to examine numerical data and discover more about specific physical properties of molecules. Silicates are hard crystals that can be sliced into little pieces. Therefore, silicon play a vital role in many real time applications. It is the authentic material to make microchips which run in PDA, PC and other game tools. In the current study, we have determined the new topological index for a few silicate structures, including cyclic, single-chain, and Pyro silicates by grouping the vertices of the corresponding molecular graphs based on their distance sums. This index is known as the exponential Wiener index. It is expanded to include their line graphs as well. The numerical values of exponential Wiener index and multiplicative exponential Wiener index for the molecular graphs of cyclic silicates, single chain silicates and their line graphs with n vertices where n = 3, 4, 5 are explored.

Analysis of octane isomer properties via topological descriptors of line graphs

Currently, graph-based molecular structure descriptors are frequently used in QSAR (Quantitative Structure-Activity Relationship) and QSPR (Quantitative Structure-Property Relationship) modeling of the properties of chemical compounds. Octane isomers have an important role in the testing of such relationships. In this study, we compute some well-known topological descriptors of the molecular graphs of isomeric octanes and their line graphs, both indices and coindices. Then we analyze the correlation coefficients between the physicochemical properties of the octane isomers and some well-known topological indices and their coindices of the molecular graphs and the line molecular graphs of the octane isomers, to find the particular topological descriptors that have the best predictive values.

A Comparative Study: Domination Parameters and Physico-Chemical Properties of Benzenoid Hydrocarbons

In graph theory, a graph is a mathematical structure that consists of a set of vertices and a set of edges connecting those pairs of vertices. Let G = ( V , E ) be a graph, a dominating set for G is a subset D ⊆ V of vertices such that every vertex in V ∖ D has at least one neighbor in D. The domination number of G, denoted by γ ( G ) , is the minimum cardinality of a dominating set in G. Recently, Khan (2023) performed a comparative study of seven important domination parameters with the π -electronic energy of benzenoid hydrocarbons, with a new theoretical approach. Physico-chemical properties are crucial for understanding the physical and chemical behavior of a molecule. In this paper, we perform a comparative study of those seven domination parameters with the physico-chemical properties of benzenoid hydrocarbons. We find the values of those domination parameters for the 22 lower benzenoid hydrocarbons and follow the statistical approach described by Khan (2023). The two physico-chemical properties to be chosen are the normal boiling point T b , a representative for intermolecular and van-der-Waals type interactions, whereas, the standard enthalpy/heat of formation Δ H f o is referred to represent the thermal properties of a molecular graph. This study further enhances that the performance of paired domination number is exceptional among all other parameters and highly correlated with both of the physico-chemical properties. Its correlation coefficient is 0.9981 (respectively, 0.9726) with T b (respectively, Δ H f o ). The outstanding correlation coefficient of paired domination number ensures further usage in quantitative structure-property relationship (QSPR) models.

Analyzing boron oxide networks through Shannon entropy and Pearson correlation coefficient

In the current age of chemical science, chemical graph theory has significantly advanced our understanding of the characteristics of chemical compounds. To simulate the mathematical, chemical, and physical aspects of networks, a topological index, a numerical measure obtained from the graph of a chemical network, employed. Recent work has explored the topological properties of boron oxide using chemical graph theory. In this work, we conduct a Pearson correlation analysis of boron oxide to assess the correlations between the Van and S indices and entropy metrics. We analyze the Pearson correlation coefficients between the entropy values and the calculated indices using a heatmap. In this article, a significant positive correlation between the Van, and S indices, and entropy values, which is represented by the heatmap of the strong linear correlations. To avoid duplication, a dimensionality reduction technique should be used for highly connected variables. Additionally, this study gives a detailed explanation of the link between the indices and entropy, which will form the basis of further statistical investigations.

Comparative study of various molecular feature representations for solvation free energy predictions of neutral species

Predicting molecular properties with the help of Neural Networks is a common way to substitute or enhance comprehensive quantum-chemical calculations. One of the problems facing researchers is the choice of vectorization approach to representing the solvent and the solute for the estimator model. In this work, 10 different approaches have been investigated for both organic solute and solvent including vectorizers that relied on macroscopic parameters, functional groups classification, molecular graphs, or atomic coordinates. A variation of the Bag of Bonds approach called JustBonds, trained on the MNSol database, showed the best overall performance resulting in RMSD < 2 kcal/mol for the blind dataset that contains the solutes not presented in the training subset and < 1 kcal/mol on records from Solv@TUM database, which is close to contemporary continuum models. We have also demonstrated that the most important bags usually contain heteroatom and play a key role in the solvation process. Furthermore, the small role of solvent vectorization was demonstrated and revealed that approaches based on functional groups or macroscopic solvent parameters are often enough to efficiently represent solvent media.

Application of the Nirmala Index in Nanotechnology: Optimizing Molecular Structures for Advanced Nanomaterials

Abstract Chemical graph theory has played a key role in advancing our understanding of molecular structure by producing degree-based topological indices that forecast crucial physical and chemical properties. In this paper we attempt to investigate this recently defined Nirmala index as an invariant from different topological angles and applications on multiple molecular graph structures such as triangular, double, and alternate quadrilateral snake structures. This index offers a more profound comprehension of the connections between molecular structures and attributes. The next generation of ground breaking developments in nanotechnology, where the creation of devices and functional nanomaterials hinges on molecular interaction at the nanoscale, may also be greatly influenced by this index. These indices have potential applications in drug delivery systems and in molecular structure optimization related to nanotechnological fields like nanophotonics and nanoelectronics. Consequently, the Nirmala index will pave the way for the development of more sophisticated tools for the production of high-performing nanoscale materials.

Distance and Degree Based Topological Indices of Cog-Wheel Graph, n-Barbell Graph and Boron Kagome Lattice

Abstract Let G = (V, E), be a graph with vertex and edge set, say V(G) and E(G). In chemical graphs the vertices and edges of the graphs represents atoms and chemical bond of the molecule. Since the distance based topological indices having high degree of predictability of pharmacological properties. In this paper we compute Eccentricity connectivity polynomial, Total eccentricity polynomial of Barbell graph and Cog wheel graph and degree based topological indices of Boron kagome lattice chemical structure.

Analyzing Single-Valued Neutrosophic Fuzzy Graphs Through Matroid Perspectives

We hope to present this paper on the emergence of a novel category of matroids derived from single-valued neutrosophic (SVN) fuzzy-graphs. The findings of this study make a substantial contribution to both matroid theory and the field of neutrosophic systems. In this study, we aim to introduce the concept of SVN-matroids and conduct a thorough investigation into their fundamental properties. Additionally, we explore the essential requirements for establishing duality within the realm of matroids formed from neutrosophic fuzzy-networks. This investigation encompasses co-weak isomorphism, weak isomorphism, and isomorphism between two matroids. Furthermore, our research proposes the expansion of other graph products and the creation of a SVN-graph to utilize the Greedy and Kruskal algorithms for determining optimal productivity in an information flow of a single-source network within a SVN-network. The application of neutronosophic graph theory offers a paradigm for addressing optimization problems in chemical graph theory, such as identifying the maximal independent set and a minimum spanning tree. When faced with uncertainty, neutrosophic optimization provides more reliable solutions by considering the uncertainties associated with the objective function or constraints.

Site Selection for Thermal Power Plant Based on Sombor Index in Neutrosophic Graph

A graph or molecular graph’s overall resilience and connectedness are gauged by the Sombor Index (SOI). It is an improved version of the conventional SOI that is designed to capture ambiguity in the relationships between nodes or atoms. This indicator aids in assessing the network’s resilience and stability in erratic circumstances. We have investigated the charac-teristics of the SOI of neutrosophic graphs (N Gs) in this study. The association between the neutrosophic first Zagreb Index (N FZI) of N Gs and the neutrosophic Sombor Index (N SI) was revealed in the study. The application of SOI based on Site Selection for Thermal Power Plants in N Gs is finally covered.

Integrated Knowledge Graph and Drug Molecular Graph Fusion via Adversarial Networks for Drug-Drug Interaction Prediction.

The Co-administration of multiple drugs can enhance the efficacy of disease treatment by reducing drug resistance and side effects. However, it also raises the risk of adverse drug interactions, presenting a challenging problem in healthcare. Various approaches have been developed to predict drug-drug interactions (DDIs) by leveraging both knowledge graphs and drug attribute information. While these methods have shown promise, they often fail to effectively capture correlations between biomedical information in the knowledge graph and drug properties. This work introduces a novel end-to-end DDI predictor framework based on generative adversarial networks. This framework utilizes a message-passing neural network to capture molecular structure information while employing the knowledge-aware graph attention network to capture the representation of drugs in the knowledge graph through considering the importance of different multihop neighbor nodes and relationships. The dual generative adversarial networks employ two generators and two discriminators in knowledge graph embedding and molecular topology embedding for adversarial training to capture the interrelations and complementary knowledge between molecular structure information and semantic information from the knowledge graph. comprehensive experiments have demonstrated that the proposed method outperforms state-of-the-art algorithms in binary classification, with improvements of 1.0% in accuracy, 0.45% in area under the receiver operating characteristic curve (AUC), 0.24% in area under the precision-recall curve (AUPR), and 0.98% in F1 score. Furthermore, for multiclass classification tasks, improvements were observed across various evaluation metrics, including 0.9% in accuracy, 0.25% in macro precision, 0.2% in macro recall, and 0.28% in macro F1. Additionally, ablation studies were conducted to showcase the effectiveness and robustness of our method in DDI prediction tasks.

Weighted Asymmetry Index: A New Graph-Theoretic Measure for Network Analysis and Optimization

Graph theory is a crucial branch of mathematics in fields like network analysis, molecular chemistry, and computer science, where it models complex relationships and structures. Many indices are used to capture the specific nuances in these structures. In this paper, we propose a new index, the weighted asymmetry index, a graph-theoretic metric quantifying the asymmetry in a network using the distances of the vertices connected by an edge. This index measures how uneven the distances from each vertex to the rest of the graph are when considering the contribution of each edge. We show how the index can capture the intrinsic asymmetries in diverse networks and is an important tool for applications in network analysis, optimization problems, social networks, chemical graph theory, and modeling complex systems. We first identify its extreme values and describe the corresponding extremal trees. We also give explicit formulas for the weighted asymmetry index for path, star, complete bipartite, complete tripartite, generalized star, and wheel graphs. At the end, we propose some open problems.

Predicting variable-length ACE inhibitory peptides based on graph convolutional network

Traditional molecular descriptors have contributed to the prediction of angiotensin I-converting enzyme (ACE) inhibitory peptides, but they often fall short in capturing the complex structure of the molecule. To address these limitations, this study introduces molecular graphs as an advanced method for peptide characterization. Peptides containing 2–10 amino acids were represented using molecular graphs, and a graph convolutional network (GCN) model was constructed to predict variable-length peptides. This model was compared with machine learning (ML) models based on molecular descriptors, including Random Forest (RF), Support Vector Machine (SVM), and k-Nearest Neighbor (kNN), under the same benchmark. Notably, the GCN model outperformed the other models with an accuracy of 0.78, effectively identifying ACE inhibitory potential. Furthermore, the GCN model also demonstrated superior performance, exceeding existing methods with an accuracy rate of over 98 % on an independent test set. To validate our predictions, we synthesized peptides VAPE and AQQKEP with high predicted probabilities, and their IC50 values of 2.25 ± 0.11 and 3.75 ± 0.17 μM, respectively, indicating potent ACE inhibitory activity. The developed GCN model presents a powerful tool for the rapid screening and identification of ACE inhibitory peptides, offering promising opportunities for developing antihypertensive components in functional foods.

GTransCYPs: an improved graph transformer neural network with attention pooling for reliably predicting CYP450 inhibitors

State‑of‑the‑art medical studies proved that predicting CYP450 enzyme inhibitors is beneficial in the early stage of drug discovery. However, accurate machine learning-based (ML) in silico methods for predicting CYP450 inhibitors remains challenging. Here, we introduce GTransCYPs, an improved graph neural network (GNN) with a transformer mechanism for predicting CYP450 inhibitors. This model significantly enhances the discrimination between inhibitors and non-inhibitors for five major CYP450 isozymes: 1A2, 2C9, 2C19, 2D6, and 3A4. GTransCYPs learns information patterns from molecular graphs by aggregating node and edge representations using a transformer. The GTransCYPs model utilizes transformer convolution layers to process features, followed by a global attention-pooling technique to synthesize the graph-level information. This information is then fed through successive linear layers for final output generation. Experimental results demonstrate that the GTransCYPs model achieved high performance, outperforming other state-of-the-art methods in CYP450 prediction.Scientific contributionThe prediction of CYP450 inhibition via computational techniques utilizing biological information has emerged as a cost-effective and highly efficient approach. Here, we presented a deep learning (DL) architecture based on GNN with transformer mechanism and attention pooling (GTransCYPs) to predict CYP450 inhibitors. Four GTransCYPs of different pooling technique were tested on an experimental tasks on the CYP450 prediction problem for the first time. Graph transformer with attention pooling algorithm achieved the best performances. Comparative and ablation experiments provide evidence of the efficacy of our proposed method in predicting CYP450 inhibitors. The source code is publicly available at https://github.com/zonwoo/GTransCYPs.

Analyzing the modified symmetric division deg index: mathematical bounds and chemical relevance

Abstract The modified symmetric division deg (MSD) index of a graph G is precisely defined as MSD ( G ) = ∑ j ∼ k 1 2 d j d k + d k d j , where d j and d k represent the degrees of j and k respectively. In this paper, we present precise bounds for the modified symmetric division deg index, expressed in the relation to the minimum and maximum degrees, the order and size of the graph, the number of pendant vertices and the minimum degree of a non-pendant vertex, the forgotten topological index, the modified second Zagreb index. We determine the upper bounds for the modified symmetric division deg index of unicyclic, bicyclic and k-cyclic graphs. Moreover, upon analyzing the modified symmetric division deg index, we observe its correlation with other well-known indices and its chemical applicability on the molecular graphs of octane isomers. At the end, we find the chemical applicability of the modified symmetric division deg index on benzenoid hydrocarbons and observe that the modified symmetric division deg index has a very strong correlation with the physical properties of benzenoid hydrocarbons.

Optimizing predictive models for evaluating the F-temperature index in predicting the π-electron energy of polycyclic hydrocarbons, applicable to carbon nanocones

In the fields of mathematics, chemistry, and the physical sciences, graph theory plays a substantial role. Using modern mathematical techniques, quantitative structure-property relationship (QSPR) modeling predicts the physical, synthetic, and natural properties of substances based only on their chemical composition. For a chemical graph, the temperature of a vertex is a local property introduced by Fajtlowicz (1988). A temperature-based graphical descriptor is structured based on temperatures of vertices. Involving a non-zero real parameter β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}, the general F-temperature index Tβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\beta }$$\\end{document} is a temperature index having strong efficacy. In this paper, we employ discrete optimization and regression analysis to find optimal value(s) of β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} for which the prediction potential of Tβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\beta }$$\\end{document} and the total 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}-electron energy Eπ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\pi }$$\\end{document} of polycyclic hydrocarbons is the strongest. This, in turn, answers an open problem proposed by Hayat & Liu (2024). Applications of the optimal values for Tβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\beta }$$\\end{document} are presented a two-parametric family of carbon nanocones in predicting their Eπ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\pi }$$\\end{document} with significantly higher accuracy.

GDMol: Generative Double-Masking Self-Supervised Learning for Molecular Property Prediction.

Effective molecular feature representation is crucial for drug property prediction. Recent years have seen increased attention on graph neural networks (GNNs) that are pre-trained using self-supervised learning techniques, aiming to overcome the scarcity of labeled data in molecular property prediction. Traditional GNNs in self-supervised molecular property prediction typically perform a single masking operation on the nodes and edges of the input molecular graph, masking only local information and insufficient for thorough self-supervised training. Hence, we propose a model for molecular property prediction based on generative double-masking self-supervised learning, termed as GDMol. This integrates generative learning into the self-supervised learning framework for latent representation, and applies a second round of masking to these latent representations, enabling the model to better capture global information and semantic knowledge of the molecules for a richer, more informative representation, thereby achieving more accurate and robust molecular property prediction. Our experiments on 5 datasets demonstrated superior performance of GDMol in predicting molecular properties across different domains. Moreover, we used the masking operation to traverse through the gradient changes of each node, the magnitude and sign of which reflect the positive and negative contribution respectively of the local structure in the molecule to the prediction outcome. This in-depth interpretative analysis not only enhances the model's interpretability, but also provides more targeted insights and direction for optimizing drug molecules. In summary, this research offers novel insights on improving molecular property prediction tasks, and paves the way for further research on the application of generative learning and self-supervised learning in the field of chemistry.

σ Interference: Through-Space and Through-Bond Dichotomy.

Dividing orbital interactions into through-space (TS) and through-bond (TB) modes is valuable for understanding various molecular properties. In this paper, we elucidate how the quantum interference phenomenon known as σ interference in electron transport through σ systems arises from TS and TB interactions. We performed electron transport calculations using a combination of density functional theory and nonequilibrium Green's function methods, focusing on ethylenediamine, a classical molecule that effectively highlights the contrast between TS and TB interactions. Our results confirm that destructive σ interference occurs in the syn and gauche conformers of this molecule. To further investigate both TS and TB interactions, we employed two analytical methods: the fragment molecular orbital (FMO) method, which captures the effects of both TS and TB interactions, and the chemical graph theory method, which specializes in TB interactions. The FMO analysis demonstrated that TB interactions lead to the characteristic distribution and energy level alignment of the frontier orbitals. Additionally, it was clarified that a change in TS interaction, due to a variation in the dihedral angle of the molecule, alters the energy gap between these orbitals, resulting in the manifestation of σ interference in the syn and gauche conformers, but not in the trans conformer. The chemical graph theory analysis based on the ladder C model, aimed at exploring the topological origin of σ interference from the network of TB interactions, revealed that σ interference is caused by the cancellation between the walk associated with geminal interactions (σ-conjugation) and the one related to vicinal interaction (σ-hyperconjugation). Notably, it was found that the vicinal interaction, which changes sign with the dihedral angle, has a decisive influence on whether this cancellation occurs. These findings clarify that σ interference arises from the interplay between TS and TB interactions. This insight will be valuable for designing molecular systems that utilize σ interference.