Topological models for the prediction of HIV-protease inhibitory activity of tetrahydropyrimidin-2-ones

On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers

Topological indices (TIs) assign a numeric value to a graph or a molecular structure. Due to their ability to predict the physiochemical properties of a molecular graph, several TIs have been introduced and studied, mainly based on degree and distance. For a vertex $v$ , the maximum distance of $v$ from any other vertex in a graph $G$ is called the eccentricity of $v$ , which is denoted by $\sigma \left(v\right)$ , in $G$ . The eccentricity of vertices gained special attention among the distance-based or degree-distance based TIs. An important TI in the class of eccentricity-dependent TIs is an eccentricity-entropy index. Furthermore, other eccentricity-dependent TIs such as eccentric-connectivity index, total-eccentricity index, and the first Zagreb index have also been extensively studied. On the other hand, dendrimers came out as unique polymeric macromolecules because of extensively branched three-dimensional architectural characteristics. This structure design prepares for various unique properties of dendrimers, including monodispersity, multivalency, uniform size, globular shape, water solubility with hydrophobic internal cavities, and a high degree of branching. These properties make them attractive candidates for different applications. PAMAM (polyamidoamine) dendrimers are promising polymers that can be successfully used in various biomedical applications. The PAMAM dendrimers having different structures such as a primary amine as the end group or porphyrin core have been studied through graph-theoretic parameters. This paper studies these two types of PAMAM dendrimers through eccentricity-dependent parameters. In particular, we establish formulae of eccentricity entropy for two types of PAMAM dendrimers. Moreover, we also derive analytic formulae of some other significant TIs from the class of eccentricity-dependent TIs. Furthermore, we apply graphical tools to demonstrate the trends of the values in the obtained results.

Zagreb Polynomials and redefined Zagreb indices of Dendrimers and Polyomino Chains

Dendrimers have an incredibly strong potential because their structure allows multivalent frameworks, i.e. one dendrimer molecule has many possible destinations to couple to a functioning species. Researchers expected to utilize the hydrophobic conditions of the dendritic media to lead photochemical responses that make the things that are artificially tested. Carboxylic acid and phenol- terminated water-dissolvable dendrimers were joined to set up their utility in tranquilize conveyance and furthermore driving compound reactions in their inner parts. This may empower scientists to associate both concentrating on atoms and medication particles to the equivalent dendrimer, which could diminish negative manifestations of prescriptions on sound and health cells. Topological indices are numerical numbers associated with the graphs of dendrimers and are invariant up to graph isomorphism. These numbers compare certain physicochemical properties like boiling point, strain energy, stability, etc. of a synthetic compound. There are three main types of topological indices, i.e degree-based, distance-based and spectrum-based. In this paper, our aim is to compute some degree-based indices and polynomials for some dendrimers and polyomino chains. We computed redefined first, second and third Zagreb indices of PAMAM dendrimers PD1, PD2, and DS1 and linear Polyomino chain Ln , Zigzag Polyomino chain Zn, polyomino chain with n squares and of m segments $B_{n}^{1}$and $B_{n}^{2}$We also computed some Zagreb polynomials of understudy dendrimers and chains.

Some Eccentricity-Based Topological Indices and Polynomials of Poly(EThyleneAmidoAmine) (PETAA) Dendrimers

Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with molecular structures and are helpful in featuring many properties. Among these molecular descriptors, the eccentricity connectivity index has a dynamic role due to its ability of estimating pharmaceutical properties. In this article, eccentric connectivity, total eccentricity connectivity, augmented eccentric connectivity, first Zagreb eccentricity, modified eccentric connectivity, second Zagreb eccentricity, and the edge version of eccentric connectivity indices, are computed for the molecular graph of a PolyEThyleneAmidoAmine (PETAA) dendrimer. Moreover, the explicit representations of the polynomials associated with some of these indices are also computed.

APPLICATIONS OF A NEW TOPOLOGICAL INDEX EDm IN SOME ALIPHATIC HYDROCARBONS

A novel index EDm based on ionicity index matrix, improved distance matrix, and branching degree matrix is used to describe the structural information of the molecule and realizes unique characterization of the molecular structures. The quantitative structure–property relationship (QSPR) models, with correlation coefficients (R) in the range of 0.99–1.00 for standard enthalpy of formation ([Formula: see text]), standard entropy ([Formula: see text]), molar volume (V m ), and molar refraction (R m ) of alkanes, alkenes, and alkynes, are subsequently developed using the index EDm. The leave-one-out (LOO) method and random sampling prediction (RSP) method demonstrate the models to be statistically significant and reliable. Compared with other published topological descriptors, the index EDm has many advantages such as zero degeneracy, better simulation, and so on. Furthermore, the models of solubility and octanol–water partition coefficient are built with satisfied results, which further manifests the superiority and wide application of this index.

Prediction of h5-HT2A receptor antagonistic activity of arylindoles: Computational approach using topochemical descriptors

Relationship between the topochemical indices and h5-HT2A receptor antagonistic activity of arylindoles has been investigated. Three topochemical indices, Wiener's topochemical index--a distance-based topochemical descriptor, molecular connectivity topochemical index--an adjacency-based topochemical descriptor and eccentric connectivity topochemical index--an adjacency-cum-distance based topochemical descriptor, were used for the present investigation. A data set comprising 31 differently substituted arylindoles was selected for the present study. The values of the Wiener's topochemical index, molecular connectivity topochemical index and eccentric connectivity topochemical index were computed for all the analogues involved in the data set using an in-house computer program. Resultant data was analyzed and suitable models were developed after identification of the active ranges. Subsequently, a biological activity was assigned to each analogue using these models, which was then compared with the reported h5-HT2A receptor antagonistic activity. Accuracy of prediction was found to vary from a minimum of approximately 81% to a maximum of approximately 84%.

Topochemical models for the prediction of voltage-gated sodium channel binding activity of hydantoins and related non-hydantoins

The relationship of Wiener's topochemical index-a distance based topochemical index, molecular connectivity topochemical index-an adjacency based topochemical index and eccentric connectivity topochemical index-an adjacency-cum-distance based topochemical index with sodium channel binding activity has been investigated. A dataset comprising 50 hydantoins and related non-hydantoins was selected. The dataset was divided equally into training and test sets. The values of the three topochemical indices for all the compounds present in both the training and test sets were computed using an in-house computer program. The resulting data was analyzed and suitable models were developed after identification of the active ranges in the training set. Subsequently, a biological activity was assigned to each compound involved in the training set using these models, which was then compared with the reported sodium channel binding activity. An accuracy of prediction of the order of >99% was observed using the proposed models. Cross-validation of these models using the test set revealed an exceptionally high accuracy of approximately 95%.