The paper describes the use of topological indices in conjunction with high cholesterol drugs, specifically Fibrates, to predict their physicochemical properties and biological activities. Fibrates are known to lower high triglycerides, increase HDL cholesterol, and reduce the small dense fraction of LDL cholesterol. The study uses a quantitative structural-property relationships (QSPR) approach, which involves analyzing the relationships between physicochemical properties and topological indices using curvilinear regression. The QSPR model predicts the physicochemical properties of the drugs based on degrees and distances determined from topological indices. The study also conducted (DFT) calculations at the B3LYP/6-31G(d,p) level on the four investigated derivatives to gain insights into their optimized geometries, DOS plots, HOMO and LUMO orbital energies, and distribution. The theoretical results presented in the study suggest that the use of topological indices in QSPR models could provide a powerful tool for predicting the physicochemical properties and biological activities of molecules, including drugs. These findings could lead to the development of new cholesterol-lowering drugs with desirable properties.

Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: S degree. And also we define S indices of a simple connected graph by using the S degree concept. We compute the S indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.

As the rate of discovery of new antibacterial compounds towards multidrug resistant bacteria is declining, there is an urge for the search of molecules that could revert this tendency. Acinetobacter baumannii has emerged as a highly virulent Gram-negative bacterium that has acquired multiple mechanisms against antibiotics and is considered of critical priority. In this work we developed a quantitative structure-property relationship (QSPR) model with 592 compounds for the identification of structural parameters related to their property as antibacterial agents against A. baumannii. QSPR mathematical validation (R2 = 70.27, RN = -0.008, aR2 = 0.014 and δK = 0.021) and its prediction ability (Q2LMO= 67.89, Q2EXT = 67.75, a(Q2)= -0.068, δQ = 0.0, rm2 = 0.229, and ∆rm2 = 0.522) were obtained with different statistical parameters; additional validation jobs were done using three sets of external molecules (R2 = 72.89, 71.64 and 71.56). We used the QSPR model to perform a virtual screening on the BIOFACQUIM natural product database. From this screening our model showed that molecules 32 to 35 and 54 to 68, isolated from different extracts of plants of the Ipomoea sp., are potential antibacterial against A. baumannii. Furthermore, biological assays showed that molecules 56 and 60 to 64 have a wide antibacterial activity against clinical isolated strains of A. baumannii, as well as other multidrug resistant bacteria including Staphylococcus aureus, Escherichia coli, Klebsiella pneumonia, and Pseudomonas aeruginosa. Finally, we propose 60 as a potential lead compound due to its broad-spectrum activity and its structural simplicity. Therefore, our QSPR model can be used as a tool for the investigation and search of new antibacterial compounds against A. baumannii.

The dielectric constant (ε) reflects the ability of a material to align and orient electrical dipoles within its structure in response to an externally applied electric field; the greater the polarizability of molecules, the greater the value of dielectric constant. In this study a data set of 86 polymers was investigated to develop a structure-property quantitative relations (QSPR) model to predict the dielectric constant in polymers. An initial set of 1273 descriptors was used to select a best set of descriptors and to construct two machine learning models with Gradient Boosting Regressor (GB_A and GB_B). The best performing model (GB_A) with 8 descriptors, exhibited a performance of (R2train) = 0.938 and (R2test) = 0.802. The models were internally validated by 5 folds cross-validation, demonstrating robustness. Additionally, using the Accumulative Local Effect (ALE) technique, we analyzed the relationship between the 8 descriptors involved and the impact of these descriptors to dielectric constant of polymers.

Molecular descriptors are essential in mathematical chemistry for studying quantitative structure-property relationships (QSPR), and topological indices are a valuable source of information about molecular properties such as size, cyclicity, branching degree, and symmetry. Graph theory has played a crucial role in the development of topological indices and dominating parameters for molecular descriptors. The molecule graph, under graph isomorphism conditions, represents an invariant number, and the graph theory approach considers dominating sets, which are subsets of the vertex set where every vertex outside the set is adjacent to at least one vertex inside the set. The dominating sigma index, a topological index that incorporates the mathematical principles of domination topological indices and the sigma index, is applicable to some families of graphs, such as book graphs, windmill graphs, and some graph operations, which have exact values for this new index. To evaluate the effectiveness of the domination sigma index in QSPR studies, a comparative analysis was conducted to establish an appropriate domination index that correlates with the physicochemical properties of octane and its isomers. Linear and non-linear models were developed using the QSPR approach to predict the properties of interest, and the results showed that both the domination forgotten and domination first Zagreb indices exhibited satisfactory performance in comparison testing. Further research into QSAR/QSPR domination indices is required to build more robust models for predicting the physicochemical properties of organic compounds while maintaining the importance of symmetry.

In the realm of modern drug discovery, the integration of chemoinformatics and quantitative structure-activity relationship (QSAR) modeling has emerged as a formidable alliance, enabling researchers to harness the vast potential of machine learning (ML) techniques for predictive molecular design and analysis. This review delves into the fundamental aspects of chemoinformatics, elucidating the intricate nature of chemical data and the crucial role of molecular descriptors in unveiling the underlying molecular properties. Molecular descriptors, including 2D fingerprints and topological indices, in conjunction with the structural-activity relationships (SARs), play a pivotal role in unlocking the pathway to small-molecule drug discovery. Technical intricacies of developing robust ML-QSAR models, including feature selection, model validation, and performance evaluation, are discussed herewith. Various ML algorithms, such as regression analysis and support vector machines, are showcased in the text for their ability to predict and comprehend the relationships between molecular structures and biological activities. This review serves as a comprehensive guide for researchers, providing an understanding of the synergy between chemoinformatics, QSAR, and ML. By embracing these cutting-edge technologies, predictive molecular analysis holds promise for expediting the discovery of novel therapeutic agents in the pharmaceutical sciences.

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph. Recently novel two degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study we define ev-degree Zagreb index, ve-degree Zagreb indices and ve-degree Randić index by using these new graph invariants as parallel to their corresponding classical degree versions. We compare these new group ev-degree and ve-degree indices with the other well-known and most used topological indices in literature such as; Wiener, Zagreb and Randić indices by modelling some physicochemical properties of octane isomers. We show that the ev-degree Zagreb index, the ve-degree Zagreb and the ve-degree Randić indices give better correlation than Wiener, Zagreb and Randić indices to predict the some specific physicochemical properties of octanes. We investigate the relations between the second Zagreb index and ev-degree and ve-degree Zagreb indices and some mathematical properties of ev-degree and ve-degree Zagreb indices.