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.

Minimum cross-sectional diameter: calculating when molecules may not fit through a biological membrane.

Some compounds that are predicted to be toxic to aquatic organisms instead show no toxicity. In some cases, this phenomenon occurs because the molecules are too large physically to pass through biological membranes, at least by passive transport. The size of the smallest circle through which a molecule can pass is called its minimum effective cross-sectional diameter. Until now, no method has been generally available for determining this parameter. Here, we present such a method, based on vector analysis, that produces results in seconds or minutes, even for relatively large molecules, on a desktop computer. The only input required is the Cartesian coordinates and van der Waals radii of the constituent atoms. The gas-phase, energy-minimized structure is used as an approximation, because to our knowledge, no practical means of experimentally measuring an effective diameter in solution is currently available.

A differential-operator approach to the permanental polynomial.

A recently published computational approach to the permanental polynomial scales very badly (approximately 2(n)) with problem size, relying as it does on examining the entire augmented adjacency matrix for nonzero products. The present study presents an entirely different algorithm that relies on symbolic computation of second partial derivatives. This approach has previously been applied to the matching polynomial but not the permanental polynomial. The differential-operator algorithm scales much better with problem size. For fullerene-type structures without perimeters, the two algorithms take about the same time to compute n = 32. On one n = 40 structure, the new algorithm was >45 times faster. Relative performance is even better for polycyclic aromatic hydrocarbon structures, which have perimeters.

Immanants and immanantal polynomials of chemical graphs.

The much-studied determinant and characteristic polynomial and the less well-known permanent and permanental polynomial are special cases of a large class of objects, the immanants and immanantal polynomials. These have received some attention in the mathematical literature, but very little has appeared on their applications to chemical graphs. The present study focuses on these and also generalizes the acyclic or matching polynomial to an equally large class of acyclic immanantal polynomials, generalizes the Sachs theorem to immanantal polynomials, and sets forth relationships between the immanants and other graph properties, namely, Kekulé structure count, number of Hamiltonian cycles, Clar covering polynomial, and Hosoya sextet polynomial.