Quantitative Structure-Property Relationships Generated with Optimizable Even/Odd Wiener Polynomial Descriptors

QSAR for dihydrofolate reductase inhibitors with molecular graph structural descriptors

In the pharmaceutical industry, the virtual screening of combinatorial libraries is used to rationally select compounds for biological testing from databases of hundreds of thousands of compounds. In addition to structural descriptors, such as fingerprints and pharmacophores, the application of relatively simple structural descriptors traditionally used in quantitative structure-activity studies offers speed and efficiency for rapidly measuring the molecular diversity of such collections. We explore new topological indices computed from the molecular graph as potential structural descriptors for the characterization of molecular diversity. A database of 2000 compounds randomly selected from the National Cancer Institute AIDS database was used to measure the intercorrelation of the descriptors. The initial collection of 240 structural descriptors was reduced to several quasi-orthogonal sets of up to 9 descriptors, using different thresholds for the maximum intercorrelation coefficient.

Tuberculosis (TB) is one of the most contagious diseases that has a greater mortality rate than HIV/AIDS and the cases of TB are feared to rise as a repercussion of the COVID-19 pandemic. The pharmaceutical industry is constantly looking for ways to improve drug design processes in order to combat the growth of infections and cure newly identified syndromes or genetically based dysfunctions with the help of QSPR models. QSPR models are mathematical tools that establish relationships between a molecular structure and its physicochemical attributes using structural properties. Topological indices are such properties that are generated from the molecular graph without any empirically derived measurements. This work focuses on developing a QSPR model using distance-based topological indices for anti-tuberculosis medications and their diverse physicochemical features.

In the study of QSPR/QSAR, topological indices such as Zagreb index, Randic index, atom-bond connectivity index are exploited to estimate the bioactivity of chemical compounds. Inspired by many degree based topological indices, we propose here a new topological index, called the Atom Bond Connectivity temperature index ABCT(G) of a molecular graph G, which shows good correlation with entropy, acentric factor, enthalpy of vaporization and standard enthalpy of vaporization of an octane isomers. In this paper we compute the Atom Bond Connectivity temperature index ABCT(G) of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC_4 C_8 [p,q].

Molecular descriptors that influence the amount of drugs transfer into human breast milk

Read the full review for this Faculty Opinions recommended article: Virtual screening of combinatorial libraries across a gene family: in search of inhibitors of Giardia lamblia guanine phosphoribosyltransferase.

QSPR models are proposed that satisfactorily describe the relationships between standard enthalpies/ entropies of formation and topological indices in the form of Wiener and Randic indices and the sum of the squares of the eigenvalues from the adjacency matrix of a molecular graph. The models can be recommended for use in scientific and engineering calculations of thermodynamic functions.

Several bioactivities of chemical compounds in a molecular graph can be expected by using many topological descriptors. A topological descriptor is a numeric quantity which quantify the topology of a graph. By defining the metric on a graph related with a vector space, we consider this graph in the context of few topological descriptors, and quantify the Wiener index, hyper Wiener index, Reciprocal complimentary Wiener index, Schultz molecular topological index and Harary index. We also provide the graphical comparison of our results to describe the relationship and dependence of these descriptors on the involved parameters.

The QSAR method, using multivariate statistics, was developed by Hansch and Fujita, and it has been successfully applied to many drug and agrochemical design problems. As well as speed and simplicity QSAR has advantages of being capable of accounting for some transport and metabolic processes which occur once the compound is administered. Until recently QSAR analyses have used relatively simple molecular descriptors based on substituent constants (e.g., Hammett constants, π, or molar refractivities), physicochemical properties (e.g., partition coefficients), topological indices (e.g., Randic and Weiner indices). Recently several new representations have been devised: atomistic; molecular eigenvalues and BCUT indices derived therefrom; E-state fields; topological autocorrelation vectors; various molecular fragment-based hash codes. These representations have advantages in speed of computation, in more accurately representing molecular properties most relevant to activity, or in being more generally applicable to diverse chemical classes acting at a common receptor, than traditional representations. Historically, linear regression methods such as MLR (multiple linear regression) and PLS (partial least squares) have been used to develop QSAR models. Regression is an “ill-posed” problem in statistics, which sometimes results in QSAR models exhibiting instability when trained with noisy data. In addition traditional regression techniques often require subjective decisions to be made on the part of the investigator as to the likely non-linear relationship between structure and activity, and whether there are cross-terms. Regression methods based on neural networks offer some advantages over MLR methods as they can account for non-linear SARs, and can deal with linear dependencies which sometimes appear in real SAR problems. However, some problems still exist in the development of SAR models using conventional backpropagation neural networks. We have used a specific type of neural network, the Bayesian Regularized Artificial Neural Network (BRANN), in the development of SAR models. The advantage of BRANN is that the models are robust and the validation process, which scales as O(N2) in normal regression methods, is unnecessary. These networks have the potential to solve a number of problems which arise in QSAR modelling such as: choice of model; robustness of model; choice of validation set; size of validation effort; and optimization of network architecture. The application of the methods to QSAR of compounds active at the benzodiazepine and muscarinic receptors will be illustrated.

Polycyclic aromatic hydrocarbons (PAHs) exhibit complex relationships between molecular topology, π-electron delocalization, and thermodynamic stability. This study introduces a composite logarithmic descriptor, C_G = log₁₀W(G) + log₁₀H(G) + log₁₀MDP(G,2), integrating distance- and degree-connectivity-based topological indices—the Wiener index, Harary index, and Metric Degree Polynomial (MDP) index—to quantify structural complexity and stability across PAHs. Nine representative PAHs, from naphthalene to coronene, were modeled as molecular graphs using Python-based computation. The composite descriptor was correlated with energy per atom to identify patterns of aromatic stabilization and structural transitions. Distinct bifurcation points, notably Phenanthrene → Pyrene (−48.36%) and Tetracene → Pentacene (−40.10%), were detected, signifying angular-to-compact and linear-to-extended aromatic reorganizations. These nonlinear variations highlight the descriptor’s sensitivity to topological shifts and conjugation regimes. The C_G metric effectively distinguishes between progressive (linear acenes) and delocalized (compact aromatics) families, demonstrating strong correlation (r = 0.717) with thermodynamic stability indicators. By integrating bifurcation analysis with graph-theoretical modeling, the study establishes C_G as a unified, efficient, and predictive tool for assessing aromaticity, stability, and structure–property relationships in PAHs, with broad implications for QSPR/QSAR modeling and organic materials design.

A topological index is a numeric quantity that is mathematically derived in a direct and unambiguous manner from the structural graph of a molecule. It has been found that many properties of a chemical compound are closely related to some topological indices of its molecular graph. Among topological indices, the Wiener index is probably the most important one. This index was introduced by the chemist H. Wiener (1947) about 60 years ago to demonstrate correlations between physicochemical properties of organic compounds and the topological structure of their molecular graphs. He defined his index as the sum of distances between any two carbon atoms in the molecules, in terms of carbon‐carbon bonds. The aim of this paper is to prepare some algorithms for computing distance matrix and Wiener index of zig‐zag and armchair polyhex nanotubes.

Topological indices are graph invariants computed usually by means of the distances or degrees of vertices of a graph. In chemical graph theory, a molecule can be modeled by a graph by replacing atoms by the vertices and bonds by the edges of this graph. Topological graph indices have been successfully used in determining the structural properties and in predicting certain physicochemical properties of chemical compounds. Wiener index is the oldest topological index which can be used for analyzing intrinsic properties of a molecular structure in chemistry. The Wiener index of a graph $G$ is equal to the sum of distances between all pairs of vertices of $G$. Recently, the entire versions of several indices have been introduced and studied due to their applications. Here we introduce the entire Wiener index of a graph. Exact values of this index for trees and some graph families are obtained, some properties and bounds for the entire Wiener index are established. Exact values of this new index for subdivision and $k$-subdivision graphs and some graph operations are obtained.

Topological molecular descriptor is calculated by a mathematical procedure from the structure of chemical compounds represented by a molecular graph, containing information about their structural characteristics [1]. There are many defined topological descriptors in literature which transform specific chemical information into useful numerical values that have been used for correlation of structure-descriptors with various physico-chemical properties [2]. Among the first topological descriptors that accelerate further development of the field are M1 and M2 indices introduced by Gutman and Trinajstić in 1972 [3] (later named Zagreb indices). Vertices of a molecular graph represent atoms and edges connecting vertices of a graph represent carbon-carbon (or non-hydrogen) chemical bonds. The total number of edges connecting one vertex with its (first) neighbour carbon vertices corresponds to valence of that atom with other carbons within a molecule. One of the largest classes of topological descriptors is the one based on the analysis of vertex degrees of a molecular graph [4]. Starting from electronic version of chemical structures we will develop and optimize an application for calculation of different vertex-degree-based topological descriptors, which is made available for free use to the research community at http://meteo2.irb.hr/indexer.

PM_{2.5}, a major air pollutant, often carries toxic components such as polycyclic aromatic hydrocarbons (PAHs), which pose potential health risks. This study investigated the relationships between five physicochemical properties-boiling point, molecular mass, enthalpy of vaporization, molar volume, and surface tension-of 15 PAHs and seven molecular topological indices (including the Wiener, Hyper-Wiener, Distance-degree, and Gutman indices) using regression analysis. Results indicated that the selected topological indices were strongly correlated with the properties of PAHs, with correlation coefficients generally exceeding 0.7. In particular, quadratic regression models based on the Distance-degree and Gutman indices showed a very high correlation with enthalpy of vaporization ($R = 0.998$). This work provides quantitative insights into the structure–property relationships of PAHs and may support further theoretical developments in the risk assessment and source control of PM_{2.5}-bound PAHs.

A topological index W (Wiener index), which is the sum of all the edges between all pairs of vertices in a chemical graph, is used for characterizing branching in random-flight chains. The chains are composed of statistical bonds (or edges) of a length b jointing N beads (or vertices). The mean square radius of gyration 〈S2〉 of random-flight chains is shown to be given by 〈S2〉=(b/N)2W. On the other hand, the set of partial differential equations describing the motion of the chains, whether linear or with any mode of branching, can be expressed by a connectivity matrix (K). We demonstrate that a relationship between the matrix (K) and the Wiener index is given by W=N Tr (K)−1. It follows that the whole of linear chain theory can be generalized to include any form of branching by replacing the molecular weight or N with the Wiener index W.