A natural graph-theory model for partition and kinetic coefficients

Abstract

A model of six partition coefficients and two metabolic kinetic parameters of a class of halogenated compounds has been performed with the aid of molecular connectivity concepts, which are based on complete graphs and general graphs. The complete graphs are used to encode the core electrons into the main parameter of molecular connectivity theory, the valence delta number, δ^v. The present model, which is solely based on graph concepts, confirms the central importance of a complete graph conjecture, which is based on an odd number of vertices for the core electrons. Two slightly different algorithms for δ^v, both centered on this conjecture, compete in deriving an optimal model for the six sets of partition coefficients. An algorithm, the K_p-(p-odd) algorithm, is valid for a model based on a linear combination of four connectivity and pseudoconnectivity basis indices. This linear combination is able to model, in a satisfactory way, all the six sets of partition coefficients. The other algorithm, the K_p-(pp-odd) algorithm, is, instead, able to derive a molecular connectivity term, which is able to adequately model four sets of partition coefficients, and in a less satisfactory way another set of partition coefficients. The two metabolic kinetic constants are, instead, optimally modeled by different basis indices based on the K_p-(pp-odd) algorithm. Underlying are also (i) the importance, in nearly all cases, of the ¹χ^v basis index as best single descriptor, and (ii) the overall improvement the model undergoes when the only cis-compound of the class of chemicals is deleted form the class. Preliminary results show the possibility of improving the model with a δ^v algorithm, which encodes also the bonded hydrogens.