QSAR models for Daphnia toxicity of pesticides based on combinations of topological parameters of molecular structures

Abstract

A topological parameter is defined as an integer value of a given local or global invariant of a molecular graph. We examined three types of local graph invariants, the vertex degrees ( 0EC), the extended connectivity of first order ( 1EC), and the numbers of paths of length two (P2), as elementary invariants for construction of quantitative structure–activity relationships (QSAR). We also examined combined invariants, obtained by multiplying one of these three elementary types with another (i.e., [ 0EC · 1EC], [ 0EC · P2], and [ 1EC · P2]), as graph invariants. Finally, global invariants were used in the QSAR analyses, codifying the presence and nature of cycles in the molecular structures under consideration. We used the correlation weights of these invariants to obtain optimal descriptors. These descriptors have been used in one-variable models to predict toxicity toward Daphnia magna for a set of pesticides. Statistical characteristics of the best model, based on the correlation weight of local topological parameters (the [ 0EC · P2]) together with the global topological parameters, are the following: n = 220, r 2 = 0.7822, s = 0.849, F = 783 (training set); n = 42, r 2 = 0.7388, s = 0.941, F = 113 (test set). The role of these topological parameters is discussed.