Iterative procedure for the generalized graph center in polycyclic graphs

Terpenic Constituents of Essential Oils with Larvicidal Activity against Aedes Aegypti: A QSAR and Docking Molecular Study

Aedes aegypti is a vector for the arbovirus responsible for yellow fever, Zika and Chikungunya virus. Essential oils and their constituents are known for their larvicidal properties and are strong candidates for mosquito control. This work aimed to develop a quantitative structure-activity study and molecular screening for the search and design of new larvicidal agents. Twenty-five monoterpenes with previously evaluated larvicidal activity were built and optimized using computational tools. QSAR models were constructed through genetic algorithms from the larvicidal activity and the calculation of theoretical descriptors for each molecule. Docking studies on acetylcholinesterase (AChE) and sterol carrier protein (SCP-2) were also carried out. Results demonstrate that the epoxide groups in the structure of terpenes hinder larvicidal activity, while lipophilicity plays an important role in enhancing biological activity. Larvicidal activity correlates with the interaction of the sterol-carrier protein. Of the 25 compounds evaluated, carvacrol showed the highest larvicidal activity with an LC₅₀ of 8.8 µg/mL. The information included in this work contributes to describing the molecular, topological, and quantum mechanical properties related to the larvicidal activity of monoterpenes and their derivatives.

From Molecular to Biological Structure and Back

A comparative analysis of the topological structure of molecules and molecular biology networks revealed both similarity and differences in the methods used, as well as in the essential features of the two types of systems. Molecular graphs are static and, due to the limitations in atomic valence, show neither power distribution of vertex degrees nor "small-world" properties, which are typical for dynamic evolutionary networks. Areas of mutual benefits from an exchange of methods and ideas are outlined for the two fields. More specifically, chemical graph theory might make use of some new descriptors of network structure. Of interest for quantitative structure-property relationship/quantitative structure-activity relationship and drug design might be the conclusion that descriptors based on distributions of vertex degrees, distances, and subgraphs seem to be more relevant to biological information than the single-number descriptors. The network concepts of centrality, clustering, and cliques provide a basis for similar studies in theoretical chemistry. The need of dynamic theory of molecular topology is advocated.

Structural Interpretation of a Topological Index. 1. External Factor Variable Connectivity Index (EFVCI)

The external factor variable connectivity index (EFVCI) is interpreted by mining out the structural features hidden in the space spanned by the EFVCI indices through projection pursuit combining with number-theory net (NT-net) on the unit sphere U(Us). Projection pursuit is concerned with "interesting" projections of high-dimensional data sets to machine-pick "interesting" low-dimensional projections of a high-dimensional point cloud by numerically maximizing a certain objective function or projection index. At first, the optimal EFVCI index reaches to -0.80 in the correlation with a retention index of 207 hydrocarbons produced by insects. The EFVCI indices, with regression results of R = 0.99998, s = 3.49, RMSECV = 3.90, and F = 7.9560e+005, obtain high regression quality. The model is proven valid by leave-one-out cross validation. Second, the EFVCI index is interpreted by the structure information, that is, size, branch number, graph center, and branching position of topological structures, which is searched out on the unit sphere U(Us) by projection pursuit. Finally, the interpretation information is used to discover some chemical knowledge concerning the variation of the retention index with the change in chemical structures.

External factor variable connectivity index

A new variable index, external factor variable connectivity index (EFVCI), is proposed, in which the atomic attribute is divided into two parts. The innate part is denoted as outer-shell electrons and external part or perturbation by other atoms is represented as summation, multiplied by a variable x, of squared reciprocal matrix of i row (corresponds to atom A(i)). The division of atomic attribute in EFVCI is interpreted by using topological structure. In the correlation of boiling point of 149 acyclic alkanes, the optimal values will approach to a constant at -0.29 by using the zero to higher order indices of the same series. The new index, with high regression quality (R = 0.9986, s = 2.26, and F = 7088.4), is compared favorably with variable connectivity index and molecular connectivity index.