Simple stochastic fingerprints towards mathematical modelling in biology and medicine. 1. The treatment of coccidiosis.

We have developed a classification function that is capable of discriminating between anticoccidial and nonanticoccidial compounds with different structural patterns. For this purpose, we calculated the Markovian electron delocalization negentropies of several compounds. These molecular descriptors, which act as molecular fingerprints, are derived from an electronegativity-weighted stochastic matrix (1Pi). The method attempts to describe the delocalization of electrons with time during the process of molecule formation by considering the 3D environment of the atoms. Accordingly, the entropies of this random process are used as molecular descriptors. The present study involves a stochastic generalization of the original idea described by Kier, which concerned the use of molecular negentropies in QSAR. Linear discriminant analysis allowed us to fit the discriminant function. This function has given rise to a good classification of 82.35% (28 anticoccidials out of 34) and 91.8% of inactive compounds (56/61) in training series. An overall classification of 88.42% (84/95) was achieved. Validation of the model was carried out by means of an external predicting series and this gave a global predictability of 93.1%. Finally, we report the experimental assay (more than 95% of lesion control) of two compounds selected from a large data set through virtual screening. We conclude that the approach described here seems to be a promising 3D-QSAR tool based on the mathematical theory of stochastic processes.