Molecular Graph Research Articles

Quantitative Structure–Property Relationship Analysis in Molecular Graphs of Some Anticancer Drugs with Temperature Indices Approach

The most important application of anticancer drugs in various forms (alkylating agents, hormones agents, and antimetabolites) is the treatment of malignant diseases. Topological indices are widely used in the field of chemical and medical sciences, especially in studying the chemical, biological, clinical, and therapeutic aspects of drugs. In this article, the temperature indices in anticancer drugs molecular graphs such as Carmustine, Convolutamine F, Raloxifene, Tambjamine K, and Pterocellin B were calculated and then analyzed based on physical and chemical properties. The analysis was performed by identifying the best regression models based on temperature indices for six physical and chemical features of anticancer drugs. The results indicated that temperature indices were essential topological indices that predict the properties of anticancer drugs, such as boiling point, flash point, enthalpy, molar refractivity, molar volume, and polarizability. It was also observed that the r value of the regression model was more than 0.6, and the p value was less than 0.05.

Forecasting the molecular interactions: A hypergraph-based neural network for molecular relational learning

Molecular relational learning refers to forecasting the interaction performance between pairs of molecules. Graph neural networks (GNNs) enables the effective modeling of chemical molecules by transferring them as abstract structures of graph, thus considering node-level interactions instead of atom’s. However, the abilities of modeling and predicting of classical GNN methods is restricted by edges’ redundancy and insufficient process of interaction modeling in a pair of molecular graphs. Therefore, based on the novel hypergraph convolutional neural network and bi-view cross interaction message passing and updating, we propose a hypergraph-based neural network method named IE-HGNN (Internal-External Bi-view Hypergraph Neural Network). We evaluate our method on two real-world molecular datasets, i.e., LEP and ZhangDDI, demonstrating IE-HGNN achieves excellent performance for both macro and micro molecules, while maintaining high training efficiency. We believe that this study introduces a novel approach for exploring the field of molecular relational learning and interaction prediction.

Double resolvability parameters of fosmidomycin anti-malaria drug and exchange property

The practical and theoretical significance of the resolvability parameter makes it an important factor, particularly in the context of network analysis. Its significance is seen in various applications and consequences: Network security, efficient routing, social network analysis, facility location, and site selection. This article finds the double resolvability parameters of the fosmidomycin anti-malaria drug. Resolvability parameters like double metric, double edge metric, and double mixed metric dimensions of fosmidomycin anti-malaria drug also hold exchange properties in the molecular graph of fosmidomycin. We convert the molecular structures of fosmidomycin into molecular graphs and then find some resolvability parameters.

Molecular sharing and molecular-specific representations for multimodal molecular property prediction

Molecular property prediction plays a crucial role in drug discovery and development. However, traditional experimental measurements and Quantitative Structure-Activity Relationship (QSAR) models are often expensive, time-consuming, and data acquisition is challenging. To overcome these limitations and challenges, this study innovatively proposes a fusion molecular property prediction method called molecular property prediction model (MSSP) to address the non-uniqueness of Simplified Molecular Input Line Entry System (SMILES) string representation and the difficulty of capturing global information in molecular graphs. This method extracts multiple fingerprint features and utilizes graph neural network encoding to map different modalities of molecules into molecular sharing and molecular-specific representation spaces, achieving modal alignment and fusion of molecules by combining molecular invariance and representation specificity. To enhance the interpretability and visualization capabilities of the model, graph attention mechanisms are introduced, enabling the identification and inference of important chemical fragments within molecules. Experimental results on publicly available cell line phenotype and kinase activity datasets demonstrate that MSSP outperforms the current state-of-the-art methods in molecular property prediction. Additionally, MSSP exhibits strong competitiveness across nine benchmark molecular property prediction datasets. Furthermore, in the task of predicting SRC kinase data properties, this study successfully screens promising therapeutic compounds from compound libraries by validating the predictions of the MSSP model and combining them with traditional methods such as molecular docking and molecular dynamics simulations. Multiple potential Lyn inhibitors have been discovered through this approach. The application of MSSP model is helpful to discover new molecules with new drug properties or functions, accelerate the process of drug discovery, save time and resources, and provide important guidance for drug discovery.

Graph Entropy of Some Special Chemical Graphs

لا غنى عن نظرية الرسم البياني الكيميائي لنمذجة الجزيئات، لا سيما في الألكانات، وهي فئة من الهيدروكربونات ذات الصيغة C_n H_(2n+2). تظهر أيزومرات الألكانات تنوعًا هيكليًا على الرغم من مشاركتها في نفس الصيغة الكيميائية، مما يؤدي إلى خصائص طيفية مميزة. تعتبر واصفات الرسوم البيانية محورية في كيمياء الكم، حيث توفر الأدوات الأساسية للتحليل. تلعب المعلمات الطيفية، بما في ذلك نصف القطر الطيفي، وثاني أكبر القيم الذاتية، والفجوة الطيفية، وطاقة الرسم البياني، دورًا حاسمًا في تقدير مستويات الطاقة والاستقرار الجزيئي. إنتروبيا الرسم البياني، مثل إنتروبيا المعامل القائم على القيمة الذاتية المستمدة من مصفوفة المجاورة، تحدد كمية عدم التجانس الجزيئي. تركز هذه الورقة على نوع معين من الألكانات وايزومراتها، وتحليل معاملاتها الطيفية والانتروبيا البيانية. وتستخدم الرسوم البيانية المقارنة لتوضيح طبيعة هذه المعلمات، وكشف تعقيدات السلوك الجزيئي. تؤكد الدراسة على أهمية نظرية الرسم البياني في كيمياء الكم، وخاصة في فهم الخصائص الطيفية والتعقيدات الهيكلية للألكانات وإيزومراتها. ويساهم هذا الفهم بشكل كبير في الفهم الشامل للخصائص الجزيئية والسلوك على المستوى الكمي، مما يؤكد الدور الحيوي لنظرية الرسم البياني الكيميائي في البحث العلمي الحديث.

New Formulas and New Bounds for the First and Second Zagreb Indices of Phenylenes

Graph theory is widely used to represent and analyze chemical structures. In addition, topological indices developed for graphs have a connection with the relationships of chemical structures such as physicochemical and bioactivity. Topological indices are widely used in QSPR-QSAR analysis and have found many applications in chemical graph theory. The oldest known degree-dependent topological indices are the first and second Zagreb indices. These indices have found wide application in chemical structures. Phenylenes containing aromatic and antiaromatic rings exhibit unique physicochemical properties and there is a wide variety of studies on phenylenes. In this article, we present some new formulas and lower bounds for the first and second Zagreb indices molecular structures of phenylenes. In addition, the BFS algorithm method, which is one of the graph algorithms, was used for the first time for the boundary study of chemical structures.

Composite Graph Neural Networks for Molecular Property Prediction.

Graph Neural Networks have proven to be very valuable models for the solution of a wide variety of problems on molecular graphs, as well as in many other research fields involving graph-structured data. Molecules are heterogeneous graphs composed of atoms of different species. Composite graph neural networks process heterogeneous graphs with multiple-state-updating networks, each one dedicated to a particular node type. This approach allows for the extraction of information from s graph more efficiently than standard graph neural networks that distinguish node types through a one-hot encoded type of vector. We carried out extensive experimentation on eight molecular graph datasets and on a large number of both classification and regression tasks. The results we obtained clearly show that composite graph neural networks are far more efficient in this setting than standard graph neural networks.

Advancing Force Fields Parameterization: A Directed Graph Attention Networks Approach.

Force fields (FFs) are an established tool for simulating large and complex molecular systems. However, parametrizing FFs is a challenging and time-consuming task that relies on empirical heuristics, experimental data, and computational data. Recent efforts aim to automate the assignment of FF parameters using pre-existing databases and on-the-fly ab initio data. In this study, we propose a graph-based force field (GB-FFs) model to directly derive parameters for the Generalized Amber Force Field (GAFF) from chemical environments and research into the influence of functional forms. Our end-to-end parametrization approach predicts parameters by aggregating the basic information in directed molecular graphs, eliminating the need for expert-defined procedures and enhances the accuracy and transferability of GAFF across a broader range of molecular complexes. Simulation results are compared to the original GAFF parametrization. In practice, our results demonstrate an improved transferability of the model, showcasing its improved accuracy in modeling intermolecular and torsional interactions, as well as improved solvation free energies. The optimization approach developed in this work is fully applicable to other nonpolarizable FFs as well as to polarizable ones.

Predicting Stroke Risk Based on ICD Codes Using Graph-Based Convolutional Neural Networks

In recent years, convolutional neural networks (CNNs) have emerged as highly efficient architectures for image and audio classification tasks, gaining widespread adoption in state-of-the-art methodologies. While CNNs excel in machine learning scenarios where the data representation exhibits a grid structure, they face challenges in generalizing to other data types. For instance, they struggle with data structured on 3D meshes (e.g., measurements from a network of meteorological stations) or data represented by graph structures (e.g., molecular graphs). To address such challenges, the scientific literature proposes novel graph-based convolutional network architectures, extending the classical convolution concept to data structures defined by graphs. In this paper, we use such a deep learning architecture to examine graphs defined using the ICD-10 codes appearing in the medical data of patients who suffered hemorrhagic stroke in Hungary in the period 2006–2012. The purpose of the analysis is to predict the risk of stroke by examining a patient’s ICD graph. Finally, we also compare the effectiveness of this method with classical machine learning classification methods. The results demonstrate that the graph-based method can predict the risk of stroke with an accuracy of over 73%, which is more than 10% higher than the classical methods.

Applications of magnesium iodide structure via modified-polynomials

A relatively recent approach in molecular graph theory for analyzing chemical networks and structures is called a modified polynomial. It emphasizes the characteristics of molecules through the use of a polynomial-based procedure and presents numerical descriptors in algebraic form. The Quantitative Structure-Property Relationship study makes use of Modified Polynomials (M-Polynomials) as a mathematical tool. M-Polynomials used to create connections between a material’s various properties and its structural characteristics. In this study, we calculated several modified polynomials and gave a polynomial description of the magnesium iodide structure. Particularly, we computed first, second and modified Zagreb indices based M-polynomials. Randić index, and inverse Randić indices based M-polynomials are also computed in this work.

T-SMILES: a fragment-based molecular representation framework for de novo ligand design

Effective representation of molecules is a crucial factor affecting the performance of artificial intelligence models. This study introduces a flexible, fragment-based, multiscale molecular representation framework called t-SMILES (tree-based SMILES) with three code algorithms: TSSA (t-SMILES with shared atom), TSDY (t-SMILES with dummy atom but without ID) and TSID (t-SMILES with ID and dummy atom). It describes molecules using SMILES-type strings obtained by performing a breadth-first search on a full binary tree formed from a fragmented molecular graph. Systematic evaluations using JTVAE, BRICS, MMPA, and Scaffold show the feasibility of constructing a multi-code molecular description system, where various descriptions complement each other, enhancing the overall performance. In addition, it can avoid overfitting and achieve higher novelty scores while maintaining reasonable similarity on labeled low-resource datasets, regardless of whether the model is original, data-augmented, or pre-trained then fine-tuned. Furthermore, it significantly outperforms classical SMILES, DeepSMILES, SELFIES and baseline models in goal-directed tasks. And it surpasses state-of-the-art fragment, graph and SMILES based approaches on ChEMBL, Zinc, and QM9.

Structure-property modeling of physicochemical properties of fractal trigonal triphenylenoids by means of novel degree-based topological indices.

Trigonal triphenylenoids (TTPs) are a fascinating class of organic molecules with unique structural and electronic properties. Their diverse applications, ranging from organic electronics to nonlinear optics, have spurred significant research interest in understanding their physicochemical behavior. Topological indices, mathematical descriptors derived from the molecular graph, offer valuable insights into the structural complexity and potential properties of TTPs. This work focuses on exploring the utility of degree-based topological indices in characterizing and predicting the properties of trigonal triphenylenoids. We systematically calculate various degree-based topological indices, for a diverse set of TTPs with varying substituents and topologies. The relationships between these indices and key physicochemical properties, such as HOMO-LUMO energy gap, thermodynamic stability, and reactivity are investigated using statistical and machine learning approaches. We identify significant correlations between specific degree-based indices and different properties, allowing for potential prediction of these properties based solely on the topological information.

Functional analysis on hypergraphs: Density and zeta functions – applications to molecular graphs and image analysis

This paper introduces new descriptors and invariants for hypergraphs. We develop a new type of Zeta functions and density functions, that are proved to have useful invariance and monotony properties. Links with hypergraph entropies are established as well. New matrices linked with hypergraphs are also proposed, from which a new type of Laplacian associated with hypergraphs is derived. Two applications are then suggested, molecular graphs in chemistry and image analysis, where the proposed functions and invariants are useful characterizations.

Computational Analysis of the Molecular Graph and the Line Graph of Glass by Studying Their M-Polynomial and Topological Indices

Computational Analysis of the Molecular Graph and the Line Graph of Glass by Studying Their M-Polynomial and Topological Indices

On topological indices and QSPR analysis of some drugs used for treating Coronavirus patients

A topological index is a real number obtained from the molecular graph structure. It can predict the physicochemical and biological properties of many anticoronavirus drugs. In this article, the topological index of some drugs for the treatment of coronavirus was computed using the Wiener-Hosoya eigenvalues of the molecular structure of hydroxychloroquine, chloroquine, camostat, nafamostat, remdesivir, and lopinavir compounds, and the Quantitative Structure Property Relationship (QSPR) study of some properties: Boiling point, Molar weight, Flash point and Enthalpy were investigated. It was observed that the regression model value r is more than 0.6 and p value shows less than 0.05.

Graph neural networks for CO[formula omitted] solubility predictions in Deep Eutectic Solvents

Deep Eutectic Solvents (DESs) are a promising class of solvents for CO2 capture. DESs are complex mixtures that can be designed to optimize CO2 solubility and overall capture process efficiency. However, the vast design landscape of DES mixtures makes experimental investigation prohibitive; as such, there is a need for computational models that can quickly and efficiently navigate the design space and inform data collection efforts. In this work, we propose Graph Neural Network (GNN) models for predicting CO2 solubility for DESs; the GNN leverages a mixture graph representation that captures the molecular structure of the DES components as well as their intermolecular interactions. We compare the GNN framework against alternative architectures (neural networks, graph convolution networks, and random forests) and data representations (molecular fingerprints, sigma profiles, and graphs). We show that the proposed approach offers superior predictive performance; specifically, we show that solubility can be predicted reliably directly from molecular structure (without the need of using sigma profiles as proposed in previous studies). This result is important, as obtaining sigma profiles requires expensive density functional theory computations. We also explored the ability of GNNs to predict solubility for new DES mixtures and operating conditions. We found that the model extrapolates across temperature reliably. However, we also found deficiencies in the ability of the model to predict solubility for DES mixtures, pressures, and molar ratio not included in the training sets; we show that this is due to an inherent lack of chemical diversity in datasets available in the literature. The proposed computational capabilities can thus help navigate the design space of DES and inform data collection efforts. Our models, data, and benchmarks are shared as Python code implemented in Jupyter notebooks.

A python based algorithmic approach to optimize sulfonamide drugs via mathematical modeling

This article explores the structural properties of eleven distinct chemical graphs that represent sulfonamide drugs using topological indices by developing python algorithm. To find significant relationships between the topological characteristics of these networks and the characteristics of the associated sulfonamide drugs. We use quantitative structure-property relationship (QSPR) approaches. In order to model and forecast these correlations and provide insights into the structure-activity relationships that are essential for drug design and optimization, linear regression is a vital tool. A thorough framework for comprehending the molecular characteristics and behavior of sulfonamide drugs is provided by the combination of topological indices, graph theory and statistical models which advances the field of pharmaceutical research and development.

On QSAR modeling with novel degree-based indices and thermodynamics properties of eye infection therapeutics.

Topological descriptors are numerical results generated from the structure of a chemical graph that are useful in identifying the physicochemical characteristics of a wide range of drugs. The introduction of molecular descriptors advances quantitative structure-property relationship research. This article focuses on the nine degree-based topological indices and the linear regression model of the eye infection drugs. We introduced two new indices, namely, the "first revised Randic index" and the "second revised Randic index, for the analysis of eye infection drugs. Topological indices are calculated by using edge partitioning, vertex degree counting, and vertex degree labeling. This analysis is done with a scientific calculator and then authenticated with Matlab, a potent tool for examining data. The experimental data and results of the topological indices serve as inputs for the statistical computations and provide the values of intercepts, slopes, and correlation coefficients. All the correlations for the eye-infection drugs are positive, indicating a direct relationship between the experimental and estimated results of the drugs. There are significant results of the p-test for all of the characteristics of eye infection, such as molecular weight, boiling point, enthalpy, flash point, molar refraction, and molar volume, that validate the accuracy of the computations. A significant link was determined in this study between the defined indices with two properties: molar weight and molar refraction. The molar weight and molar refraction have a correlation coefficient ranging from 0.9. These results demonstrate a strong association between the indices and the properties under investigation. The linear regression approach is a valuable tool for chemists and pharmacists to obtain data about different medicines quickly and cost-effectively.

Computing Topological Indices of Certain Networks

In mathematical chemistry, topological indices are molecular descriptors that are calculated on the molecular graph of a chemical compound. The molecular graph is a graph which is obtained from some chemical structures. The degree of every molecular graph cannot exceeds 4. Topological indices are numerical quantities of a graph that describe its topology. An atom represents a vertex and a bond between two atoms represents an edge in a molecular graph. Mainly there are three types of topological indices viz., degree-based, distance based and eigenvalue-based topological indices. The first degree-based topological indices are the first and second Zagreb indices. The first Zagreb index M_1 is defined as the sum of squares of degrees of each vertex in a graph G and the second Zagreb index M_2 is the product of degree of every adjacent vertices. In this case the summation goes on the set of edges of a graph G. The most studied topological indices are degree-based topological indices. Motivated by these topological indices in this paper, we introduce five new degree-based topological indices based on the neighborhood degree of a vertex. Further, we compute the values of various nanostructures like hexagonal parallelogram P(m,n) nanotube, triangular benzenoid G_n,zigzag-edge coronoid fused with starphene nanotubes ZCS(k,l,m), dominating derived networks D_1,D_2,D_3, Porphyrin Dendrimer, Zinc-Porphyrin Dendrimer, Propyl Ether Imine Dendrimer, Poly(Ethylene amido amine Dendrimer, PAMAM dendrimers(????????1,????????2,????????1), linear polyomino chain L_n,Z_n,B_n^1 (n≥3),B_n^2 (n≥3) and triangular, hourglass, and jagged-rectangle benzenoid systems of these indices. The standard computational techniques are used for the computation of topological indices of nanostructures. For the edge partition of the nanostructures the algebraic techniques are used. Using these techniques computation of topological indices became easy and also helped to get the more accurate results.

Complementary multi-modality molecular self-supervised learning via non-overlapping masking for property prediction.

Self-supervised learning plays an important role in molecular representation learning because labeled molecular data are usually limited in many tasks, such as chemical property prediction and virtual screening. However, most existing molecular pre-training methods focus on one modality of molecular data, and the complementary information of two important modalities, SMILES and graph, is not fully explored. In this study, we propose an effective multi-modality self-supervised learning framework for molecular SMILES and graph. Specifically, SMILES data and graph data are first tokenized so that they can be processed by a unified Transformer-based backbone network, which is trained by a masked reconstruction strategy. In addition, we introduce a specialized non-overlapping masking strategy to encourage fine-grained interaction between these two modalities. Experimental results show that our framework achieves state-of-the-art performance in a series of molecular property prediction tasks, and a detailed ablation study demonstrates efficacy of the multi-modality framework and the masking strategy.