Molecular Graph Research Articles

Role of GA, AG and R in Structure-Property Modelling

Molecular descriptors are essential tools that bridge the gap between chemical structures and their properties. Among these, the Randić index (R), geometric-arithmetic index (GA), and arithmetic-geometric index (AG) are well-established. However, the relationships between these descriptors, particularly the gaps GA − R and AG − R , have not been extensively explored. This study investigates the impact of these descriptor gaps on chemical graph theory. Our findings reveal that the differences GA − R and AG − R provide unique insights into the structure-property modeling of molecules, particularly outperforming AG, GA, R, and other known descriptors for alkanes. Polycyclic aromatic compounds (PACs) are organic molecules composed of multiple fused aromatic rings. PACs are of significant environmental concern due to their persistence and potential toxicity, including carcinogenic properties. The effectiveness of GA − R and AG − R is observed to be strong in structure-property modeling for some polycyclic aromatic compounds. Additionally, GA − R and AG − R are recognized as important descriptors for various pharmaceutical compounds employed in treating malignant diseases.

Two-Matchings with Respect to the General Sum-Connectivity Index of Trees

A vertex-degree-based topological index φ associates a real number to a graph G which is invariant under graph isomorphism. It is defined in terms of the degrees of the vertices of G and plays an important role in chemical graph theory, especially in QSPR/QSAR investigations. A subset of k edges in G with no common vertices is called a k-matching of G, and the number of such subsets is denoted by mG,k. Recently, this number was naturally extended to weighted graphs, where the weight function is induced by the topological index φ. This number was denoted by mkG,φ and called the k-matchings of G with respect to the topological index φ. It turns out that m1G,φ=φG, and so for k≥2, the k-matching numbers mkG,φ can be viewed as kth order topological indices which involve both the topological index φ and the k-matching numbers. In this work, we solve the extremal value problem for the number of 2-matchings with respect to general sum-connectivity indices SCα, over the set Tn of trees with n vertices, when α is a real number in the interval −1,0.

Protein language models are performant in structure-free virtual screening.

Hitherto virtual screening (VS) has been typically performed using a structure-based drug design paradigm. Such methods typically require the use of molecular docking on high-resolution three-dimensional structures of a target protein-a computationally-intensive and time-consuming exercise. This work demonstrates that by employing protein language models and molecular graphs as inputs to a novel graph-to-transformer cross-attention mechanism, a screening power comparable to state-of-the-art structure-based models can be achieved. The implications thereof include highly expedited VS due to the greatly reduced compute required to run this model, and the ability to perform early stages of computer-aided drug design in the complete absence of 3D protein structures.

GexMolGen: cross-modal generation of hit-like molecules via large language model encoding of gene expression signatures.

Designing de novo molecules with specific biological activity is an essential task since it holds the potential to bypass the exploration of target genes, which is an initial step in the modern drug discovery paradigm. However, traditional methods mainly screen molecules by comparing the desired molecular effects within the documented experimental results. The data set limits this process, and it is hard to conduct direct cross-modal comparisons. Therefore, we propose a solution based on cross-modal generation called GexMolGen (Gene Expression-based Molecule Generator), which generates hit-like molecules using gene expression signatures alone. These signatures are calculated by inputting control and desired gene expression states. Our model GexMolGen adopts a "first-align-then-generate" strategy, aligning the gene expression signatures and molecules within a mapping space, ensuring a smooth cross-modal transition. The transformed molecular embeddings are then decoded into molecular graphs. In addition, we employ an advanced single-cell large language model for input flexibility and pre-train a scaffold-based molecular model to ensure that all generated molecules are 100% valid. Empirical results show that our model can produce molecules highly similar to known references, whether feeding in- or out-of-domain transcriptome data. Furthermore, it can also serve as a reliable tool for cross-modal screening.

A multichannel graph neural network based on multisimilarity modality hypergraph contrastive learning for predicting unknown types of cancer biomarkers.

Identifying potential cancer biomarkers is a key task in biomedical research, providing a promising avenue for the diagnosis and treatment of human tumors and cancers. In recent years, several machine learning-based RNA-disease association prediction techniques have emerged. However, they primarily focus on modeling relationships of a single type, overlooking the importance of gaining insights into molecular behaviors from a complete regulatory network perspective and discovering biomarkers of unknown types. Furthermore, effectively handling local and global topological structural information of nodes in biological molecular regulatory graphs remains a challenge to improving biomarker prediction performance. To address these limitations, we propose a multichannel graph neural network based on multisimilarity modality hypergraph contrastive learning (MML-MGNN) for predicting unknown types of cancer biomarkers. MML-MGNN leverages multisimilarity modality hypergraph contrastive learning to delve into local associations in the regulatory network, learning diverse insights into the topological structures of multiple types of similarities, and then globally modeling the multisimilarity modalities through a multichannel graph autoencoder. By combining representations obtained from local-level associations and global-level regulatory graphs, MML-MGNN can acquire molecular feature descriptors benefiting from multitype association properties and the complete regulatory network. Experimental results on predicting three different types of cancer biomarkers demonstrate the outstanding performance of MML-MGNN. Furthermore, a case study on gastric cancer underscores the outstanding ability of MML-MGNN to gain deeper insights into molecular mechanisms in regulatory networks and prominent potential in cancer biomarker prediction.

Prototype-based contrastive substructure identification for molecular property prediction.

Substructure-based representation learning has emerged as a powerful approach to featurize complex attributed graphs, with promising results in molecular property prediction (MPP). However, existing MPP methods mainly rely on manually defined rules to extract substructures. It remains an open challenge to adaptively identify meaningful substructures from numerous molecular graphs to accommodate MPP tasks. To this end, this paper proposes Prototype-based cOntrastive Substructure IdentificaTion (POSIT), a self-supervised framework to autonomously discover substructural prototypes across graphs so as to guide end-to-end molecular fragmentation. During pre-training, POSIT emphasizes two key aspects of substructure identification: firstly, it imposes a soft connectivity constraint to encourage the generation of topologically meaningful substructures; secondly, it aligns resultant substructures with derived prototypes through a prototype-substructure contrastive clustering objective, ensuring attribute-based similarity within clusters. In the fine-tuning stage, a cross-scale attention mechanism is designed to integrate substructure-level information to enhance molecular representations. The effectiveness of the POSIT framework is demonstrated by experimental results from diverse real-world datasets, covering both classification and regression tasks. Moreover, visualization analysis validates the consistency of chemical priors with identified substructures. The source code is publicly available at https://github.com/VRPharmer/POSIT.

A graph theoretical study of porphyrin-cored dendrimers by means of Sombor indices:a computational approach

Topological indices are numerical parameters calculated on the molecular graph of chemical structures which do not depend on the method the molecular graph is labelled or depicted and have no need of energy minimisation of the molecular structure. The Sombor index is a recently established topological index possessing the ability to predict the enthalpy of vaporisation and entropy of octane isomers. Here, we apply the edge-partition technique to study the Sombor index and some of its variants namely delta Sombor index, reduced Sombor index, increased Sombor index, modified Sombor index, reverse Sombor index and Kulli-Gutman Sombor index for four types of dendrimers with porphyrin core. Our results could be helpful in better understanding the physico-chemical characteristics of this family of macromolecules.

Chemical Graph-Based Transformer Models for Yield Prediction of High-Throughput Cross-Coupling Reaction Datasets.

The chemical reaction yield is an important factor to determine the reaction conditions. Recently, many data-driven models for yield prediction using high-throughput experimentation datasets have been reported. In this study, we propose a neural network architecture based on the chemical graphs of the reaction components to predict the reaction yield. The proposed model is the sequential combination of a message-passing neural network and a transformer encoder (MPNN-Transformer). The reaction components are converted to molecular matrices by the first network, followed by the interplay of the reaction components in the second network after adding the embeddings of the compound roles in the chemical reaction. The predictive ability of the proposed models was compared with state-of-the-art yield prediction models using two high-throughput experimental datasets: the Buchwald-Hartwig cross-coupling (BHC) and Suzuki-Miyaura cross-coupling (SMC) reaction datasets. Overall, the MPNN-Transformer models showed high prediction accuracy for the BHC reaction datasets and some of the extrapolation-oriented SMC reaction datasets. These models also performed well when the training dataset size was relatively large. Furthermore, analyzing the poorly predicted reactions for the BHC reaction dataset revealed a limitation of the data-driven yield prediction approach based on the chemical structural similarity.

Chemical reaction enhanced graph learning for molecule representation.

Molecular representation learning (MRL) models molecules with low-dimensional vectors to support biological and chemical applications. Current methods primarily rely on intrinsic molecular information to learn molecular representations, but they often overlook effectively integrating domain knowledge into MRL. In this article, we develop a reaction-enhanced graph learning (RXGL) framework for MRL, utilizing chemical reactions as domain knowledge. RXGL introduces dual graph learning modules to model molecule representation. One module employs graph convolutions on molecular graphs to capture molecule structures. The other module constructs a reaction-aware graph from chemical reactions and designs a novel graph attention network on this graph to integrate reaction-level relations into molecular modeling. To refine molecule representations, we design a reaction-based relation learning task, which considers the relations between the reactant and product sides in reactions. In addition, we introduce a cross-view contrastive task to strengthen the cooperative associations between molecular and reaction-aware graph learning. Experiment results show that our RXGL achieves strong performance in various downstream tasks, including product prediction, reaction classification, and molecular property prediction. The code is publicly available at https://github.com/coder-ACAC/RLM.

GraphNABP: Identifying nucleic acid-binding proteins with protein graphs and protein language models

The computational identification of nucleic acid-binding proteins (NABP) is of great significance for understanding the mechanisms of these biological activities and drug discovery. Although a bunch of sequence-based methods have been proposed to predict NABP and achieved promising performance, the structure information is often overlooked. On the other hand, the power of popular protein language models (pLM) has seldom been harnessed for predicting NABPs. In this study, we propose a novel framework called GraphNABP, to predict NABP by integrating sequence and predicted 3D structure information. Specifically, sequence embeddings and protein molecular graphs were first obtained from ProtT5 protein language model and predicted 3D structures, respectively. Then, graph attention (GAT) and bidirectional long short-term memory (BiLSTM) neural networks were used to enhance feature representations. Finally, a fully connected layer is used to predict NABPs. To the best of our knowledge, this is the first time to integrate AlphaFold and protein language models for the prediction of NABPs. The performances on multiple independent test sets indicate that GraphNABP outperforms other state-of-the-art methods. Our results demonstrate the effectiveness of pLM embeddings and structural information for NABP prediction. The codes and data used in this study are available at https://github.com/lixiangli01/GraphNABP.

On statistical evaluation of reverse degree based topological indices for iron telluride networks

In the context of graph theory and chemical graph theory, this research conducts a detailed mathematical investigation of reverse topological indices as they relate to iron telluride networks, clarifying their complex interactions. Graph theory is a branch of abstract mathematics that carefully studies the connections and structural features of graphs made up of edges and vertices. These theoretical ideas are expanded upon in chemical graph theory, which models molecular architectures with atoms acting as vertices and chemical bonds as edges. By extending these concepts, this work investigates the reverse topological indices in the context of Iron Telluride networks and outlines their significant effects on chemical reactivity, molecular topology and statistical modeling. By navigating intricate mathematical formalisms and algorithmic approaches, the analysis provides profound insights into the reactivity patterns and structural dynamics of Iron Telluride compounds, enhancing our knowledge of solid-state chemistry and materials science.

MCMVDRP: a multi-channel multi-view deep learning framework for cancer drug response prediction.

Drug therapy remains the primary approach to treating tumours. Variability among cancer patients, including variations in genomic profiles, often results in divergent therapeutic responses to analogous anti-cancer drug treatments within the same cohort of cancer patients. Hence, predicting the drug response by analysing the genomic profile characteristics of individual patients holds significant research importance. With the notable progress in machine learning and deep learning, many effective methods have emerged for predicting drug responses utilizing features from both drugs and cell lines. However, these methods are inadequate in capturing a sufficient number of features inherent to drugs. Consequently, we propose a representational approach for drugs that incorporates three distinct types of features: the molecular graph, the SMILE strings, and the molecular fingerprints. In this study, a novel deep learning model, named MCMVDRP, is introduced for the prediction of cancer drug responses. In our proposed model, an amalgamation of these extracted features is performed, followed by the utilization of fully connected layers to predict the drug response based on the IC50 values. Experimental results demonstrate that the presented model outperforms current state-of-the-art models in performance.

Geometry-Augmented Molecular Representation Learning for Property Prediction.

Accurate molecular representation plays a crucial role in expediting the process of drug discovery. Graph neural networks (GNNs) have demonstrated robust capabilities in molecular representation learning, adept at capturing structural and spatial information in molecular graphs. For molecular representation learning, most previous GNN methods are specialized in dealing with 2D or 3D molecular data formats. By further fusing the geometric attributes and structural features of molecules, we can elevate the performance of molecular representation. To realize this, we present a novel geometry-augmented molecular representation learning model, designed to effectively encode both the 2D structural and 3D spatial information inherent in molecular graphs. By incorporating structural and spatial information as attention biases in the graph Transformer framework, our model offers a comprehensive architecture that introduces molecular structural details at both atom and bond levels. We further propose a geometry information fusion module to encode the geometry information within 3D molecular graphs. The experimental results show the efficacy of our model, demonstrating its ability to achieve competitive performance when compared to state-of-the-art (SOTA) models in various property prediction tasks.

Learning Joint 2-D and 3-D Graph Diffusion Models for Complete Molecule Generation.

Designing new molecules is essential for drug discovery and material science. Recently, deep generative models that aim to model molecule distribution have made promising progress in narrowing down the chemical research space and generating high-fidelity molecules. However, current generative models only focus on modeling 2-D bonding graphs or 3-D geometries, which are two complementary descriptors for molecules. The lack of ability to jointly model them limits the improvement of generation quality and further downstream applications. In this article, we propose a joint 2-D and 3-D graph diffusion model (JODO) that generates geometric graphs representing complete molecules with atom types, formal charges, bond information, and 3-D coordinates. To capture the correlation between 2-D molecular graphs and 3-D geometries in the diffusion process, we develop a diffusion graph transformer (DGT) to parameterize the data prediction model that recovers the original data from noisy data. The DGT uses a relational attention mechanism that enhances the interaction between node and edge representations. This mechanism operates concurrently with the propagation and update of scalar attributes and geometric vectors. Our model can also be extended for inverse molecular design targeting single or multiple quantum properties. In our comprehensive evaluation pipeline for unconditional joint generation, the experimental results show that JODO remarkably outperforms the baselines on the QM9 and GEOM-Drugs datasets. Furthermore, our model excels in few-step fast sampling, as well as in inverse molecule design and molecular graph generation. Our code is provided in https://github.com/GRAPH-0/JODO.

Quantitatively determining melting properties for energetic compounds via knowledge-infused molecular graphs and interpretable deep learning

The melting properties of energetic compounds are critical to their performances, but challenges persist in understanding the molecular features and design strategies that drive these properties. Integrating domain knowledge into data-driven approaches for predicting melting properties enhances the generation of comprehensive insights and enables the construction of interpretable prediction models. For this purpose, a knowledge-infused molecular graphs (KIMGs) were devised to describe the characters of energetic compounds, by which prediction models were developed in conjunction with the message passing neural networks. A melting-point dataset composed of around 30,000 melt-castable energetic compounds was constructed, and a collection of 29 key descriptors relevant to melting behaviors is integrated in KIMGs. The model achieved the best mean absolute error of 10.93 K for the melting point prediction. The model interpretability from both molecular graphs and feature importances offer insights for understanding the complex interplay that determine the melting properties of energetic compounds. This work enables researchers not only to predict melting behaviors with enhanced accuracy but also applicable to establishing other quantitively structure-property relationships.

CLigOpt: controllable ligand design through target-specific optimization.

A key challenge in deep generative models for molecular design is to navigate random sampling of the vast molecular space, and produce promising molecules that strike a balance across multiple chemical criteria. Fragment-based drug design (FBDD), using fragments as starting points, is an effective way to constrain chemical space and improve generation of biologically active molecules. Furthermore, optimization approaches are often implemented with generative models to search through chemical space, and identify promising samples which satisfy specific properties. Controllable FBDD has promising potential in efficient target-specific ligand design. We propose a controllable FBDD model, CLigOpt, which can generate molecules with desired properties from a given fragment pair. CLigOpt is a variational autoencoder-based model which utilizes co-embeddings of node and edge features to fully mine information from molecular graphs, as well as a multi-objective Controllable Generation Module to generate molecules under property controls. CLigOpt achieves consistently strong performance in generating structurally and chemically valid molecules, as evaluated across six metrics. Applicability is illustrated through ligand candidates for hDHFR and it is shown that the proportion of feasible active molecules from the generated set is increased by 10%. Molecular docking and synthesizability prediction tasks are conducted to prioritize generated molecules to derive potential lead compounds. The source code is available via https://github.com/yutongLi1997/CLigOpt-Controllable-Ligand-Design-through-Target-Specific-Optimisation.

Molecular Design Based on Integer Programming and Splitting Data Sets by Hyperplanes.

A novel framework for designing the molecular structure of chemical compounds with a desired chemical property has recently been proposed. The framework infers a desired chemical graph by solving a mixed integer linear program (MILP) that simulates the computation process of two functions: a feature function defined by a two-layered model on chemical graphs and a prediction function constructed by a machine learning method. To improve the learning performance of prediction functions in the framework, we design a method that splits a given data set C into two subsets C(i),i=1,2 by a hyperplane in a chemical space so that most compounds in the first (resp., second) subset have observed values lower (resp., higher) than a threshold θ. We construct a prediction function ψ to the data set C by combining prediction functions ψi,i=1,2 each of which is constructed on C(i) independently. The results of our computational experiments suggest that the proposed method improved the learning performance for several chemical properties to which a good prediction function has been difficult to construct.

Data-driven approaches to study the spectral properties of chemical structures

The molecular energy, which is the sum of all eigenvalues, is crucial in determining the total π-electron energy of conjugated hydrocarbon molecules. We used machine learning techniques to calculate the energy, inertia, nullity, signature, and Estrada index of molecular graphs for bismuth tri-iodide and benzene rings embedded in P-type surfaces within 2D networks. We applied MATLAB to extract the actual eigenvalues from the data and developed general equations for these molecular properties. We then used these equations to estimate the values and compared them to the actual values through graphical analysis. Our results demonstrate the potential of data-driven techniques in predicting molecular properties and enhancing our understanding of spectral theory.

Enumeration of the Hosoya index of pericondensed benzenoid system

In chemical graph theory, topological indices play an important role and have various uses in quantitative structure-property relationships (QSPR) as well as quantitative structure-activity relationships (QSARs). The Hosoya index is one of them, performing a molecular descriptor in mathematical chemistry. Therefore, progressing with investigations requires computing the Hosoya index of distinct molecular graphs. This research presents a computational method for determining the Hosoya index of pericondensed benzenoid systems using the transfer matrix approach and the Hosoya vector.

Prediction of cluster energy of lithium clusters from codescriptors with application in 2D porous graphene

A lithium metal anode has a high energy density, but its applications face numerous challenges, particularly the irregular deposition of lithium dendrites, which form due to the aggregation of lithium clusters, posing serious safety risks. Research has revealed that small lithium clusters have the potential to enhance the electrode potential in Lithium-ion batteries (LIBs), and cluster energy affects the stability of lithium clusters. Modern computational tools and DFT calculations of lithium clusters can provide invaluable insights into their chemical, physical, and structural properties. However, calculating structural properties through large-scale experiments can be time-consuming and expensive. To overcome the challenges inherent in studying lithium clusters, this study employs a novel approach. We construct molecular graphs for the most stable structures and leverage CoM Polynomial computations to generate codescriptors, enabling efficient and accurate predictions of cluster energy for diverse lithium cluster configurations. The curvilinear regression analysis filters out highly significant regression equations and highly predictive codescriptors. Additionally, we investigated two molecular structures of porous graphene, namely linear and triangular, and obtained topological codescriptors’ analytical expressions by utilizing the CoM Polynomial in each case. A deeper understanding of both lithium clusters and porous graphene properties is essential for optimizing LIBs’ performance and stability.