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

Abstract

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.

Markovian chemicals “in silico” design (MARCH-INSIDE), a promising approach for computer-aided molecular design III: 2.5D indices for the discovery of antibacterials

“…The symbols R, S refers to the chirality of the atom. Alternatively, Z-E regards to the 3D characteristic for atoms involved in double bonds [12,13,19,20]. The first step on calculating 1 Π may be deriving an electronegativity matrix χ which elements are isomer-indicator exponential functions coinciding with the numerators of expression like (1) [12,13,19].…”

“…Alternatively, Z-E regards to the 3D characteristic for atoms involved in double bonds [12,13,19,20]. The first step on calculating 1 Π may be deriving an electronegativity matrix χ which elements are isomer-indicator exponential functions coinciding with the numerators of expression like (1) [12,13,19]. In the short-term scale of time (t 1 = 1) the movement of electrons is described here by 1 Π, whilst the probabilities of long-term movements are the elements of k Π, (t k = k > 0) described herein by the Chapman-Kolgomorov equations [10][11][12][13]23]:…”

“…In the present context, they are the probabilities with which electrons return to the original atoms at different times. That is to say, these numbers encode the distribution of electrons after the formation of the molecule as governed by EEP [10][11][12][13]. The calculation of SR π k for any organic or inorganic molecule was carried out using the MARCH-INSIDE software, being Tr the trace operator [24]:…”

“…Consequently, our research group has introduced a Markov chain (MC) approach based on the idea of EEP [10][11][12][13][14][15][16][17][18][19]. As a consequence, we were able to derive new molecular descriptors encoding the distribution of electrons in the molecule.…”

“…As a consequence, we were able to derive new molecular descriptors encoding the distribution of electrons in the molecule. The approach termed as Markovian-Chemicals-In silico-Design (MARCH-INSIDE) has shown to be very useful in drug design, toxicology, proteomics, and bioinformatics [10][11][12][13][14][15][16][17][18][19]. MARCH-INSIDE presents also interesting skills to codify 3D structural features such chirality and Z-E isomerism [12,13,19].…”