Gordon G. Cash

Predicting genotoxicity of aromatic and heteroaromatic amines using electrotopological state indices

A quantitative structure-activity relationship (QSAR) model relating electrotopological state (E-state) indices and mutagenic potency was previously described by Cash [Mutat. Res. 491 (2001) 31-37] using a data set of 95 aromatic amines published by Debnath et al. [Environ. Mol. Mutagen. 19 (1992) 37-52]. Mutagenic potency was expressed as the number of Salmonella typhimurium TA98 revertants per nmol (LogR). Earlier work on the development of QSARs for the prediction of genotoxicity indicated that numerous methods could be effectively employed to model the same aromatic amines data set, namely, Debnath et al.; Maran et al. [Quant. Struct.-Act. Relat. 18 (1999) 3-10]; Basak et al. [J. Chem. Inf. Comput. Sci. 41 (2001) 671-678]; Gramatica et al. [SAR QSAR Environ. Res. 14 (2003) 237-250]. However, results obtained from external validations of those models revealed that the effective predictivity of the QSARs was well below the potential indicated by internal validation statistics (Debnath et al., Gramatica et al.). The purpose of the current research is to externally validate the model published by Cash using a data set of 29 aromatic amines reported by Glende et al. [Mutat. Res. 498 (2001) 19-37; Mutat. Res. 515 (2002) 15-38] and to further explore the potential utility of using E-state sums for the prediction of mutagenic potency of aromatic amines.

The Permanental Polynomial

This study identifies properties and uses of the permanental polynomial of adjacency matrixes of unweighted chemical graphs. Coefficients and zeroes of the polynomial for several representative structures are provided, and their properties are discussed. A computer program for calculating the permanental polynomial from the adjacency matrix is also described.

Relationship between the Hosoya polynomial and the hyper-Wiener index

Abstract The Hosoya polynomial of a graph, H ( G, x ), has the property that its first derivative, evaluated at x = 1, equals the Wiener index, i.e., W ( G ) = H ′( G , 1). In this paper, an equation is presented that gives the hyper-Wiener index, WW ( G ), in terms of the first and second derivatives of H ( G, x ). Also defined here is a hyper-Hosoya polynomial, HH ( G, x ), which has the property WW ( G ) = HH ′( G , 1), analogous to W ( G ) = H ′( G , 1). Uses of higher derivatives of HH ( G, x ) are proposed, analogous to published uses of higher derivatives of H ( G, x ).

A SIMPLE MEANS OF COMPUTING THE KEKULE STRUCTURE COUNT FOR TOROIDAL POLYHEX FULLERENES

A simple method is presented for determining the Kekule structure count of toroidal polyhex fullerenes, along with the computer source code used. Toroidal fullerenes, unlike spherical fullerenes, can consist entirely of hexagonal faces, and those that do are alternant hydrocarbons (with zero hydrogens). For alternant hydrocarbons, the square of the Kekule structure count is equal to the permanent of the adjacency matrix. Also, for alternant structures, the adjacency matrix for n atoms can be written in such a way that only an n/2 × n/2 matrix need be evaluated.

Three methods for calculation of the hyper-wiener index of molecular graphs

The hyper-Wiener index WW of a graph G is defined as WW(G) = (summation operator d (u, v)(2) + summation operator d (u, v))/2, where d (u, v) denotes the distance between the vertices u and v in the graph G and the summations run over all (unordered) pairs of vertices of G. We consider three different methods for calculating the hyper-Wiener index of molecular graphs: the cut method, the method of Hosoya polynomials, and the interpolation method. Along the way we obtain new closed-form expressions for the WW of linear phenylenes, cyclic phenylenes, poly(azulenes), and several families of periodic hexagonal chains. We also verify some previously known (but not mathematically proved) formulas.

Permanental polynomials of the smaller fullerenes.

Using a general computer code developed previously, permanental polynomials were computed for all fullerenes C< or =36. Mathematical properties of the coefficients and zeroes were investigated. For a given isomer series of constant n, the n/2 independent zeroes appear to consist of a set of 10 that are nearly constant within the series and a set of n/2-10 that differ greatly with structure.

Permanents of Adjacency Matrices of Fullerenes

Abstract This study examines the relationships between structural parameters for 28 fullerenes and the permanents of their adjacency matrices, per(A). In particular, the structural parameters examined were related to the adjoining of pentagons. A new parameter, r, was introduced which counts contiguous pentagon triplets that have no single vertex in common. The quantity well-correlated with structure was not per(A) itself, but In(per(A))/lnK, where K is the Kekule structure count. For all 28 fullernes, ln(per(A))/lnK > 2, contrary to expectations.

Polynomial expressions for the hyper-Wiener index of extended hydrocarbon networks.

General expressions are derived for the hyper-Wiener index (WW) for several series of hydrocarbons, both benzenoid and non-benzenoid, including some two-dimensional networks. Indeed, such expressions were found for all but one series studied. Methods are also described for eliminating the register overflow problem that besets computer-based approaches to calculating WW for large structures by means of the distance matrix.

Prediction of physicochemical properties from euclidean distance methods based on electrotopological state indices

Abstract This paper describes predictions of log K OW , Henrys Law constant, vapor pressure, and OH-radical bimolecular rate constant from two Euclidean distance methods, using electrotopological state indices as input. The quality of the predictions is highly dependent on the size of the experimental dataset, i. e. , the density of experimental data points in the Euclidean space. The Euclidean distance results are compared with predictions made by commercial software products for the same sets of compounds.

A FAST COMPUTER ALGORITHM FOR FINDING THE PERMANENT OF ADJACENCY MATRICES

A fast computer algorithm is described which brings computation of the permanents of sparse matrices, specifically, chemical adjacency matrices, within the reach of a desktop computer. Examples and results are presented, along with a discussion of the relationship of the permanent to the Kekulé structure count. Also presented is a C-language implementation which was deliberately written for ease of translation into other high-level languages.