Simple stochastic fingerprints towards mathematical modeling in biology and medicine 2. Unifying Markov model for drugs side effects.

Most of present mathematical models for biological activity consider just the molecular structure. In the present article we pretend extending the use of Markov chain models to define novel molecular descriptors, which consider in addition other parameters like target site or biological effect. Specifically, this mathematical model takes into consideration not only the molecular structure but the specific biological system the drug affects too. Herein, a general Markov model is developed that describes 19 different drugs side effects grouped in eight affected biological systems for 178 drugs, being 270 cases finally. The data was processed by linear discriminant analysis (LDA) classifying drugs according to their specific side effects, forward stepwise was fixed as strategy for variables selection. The average percentage of good classification and number of compounds used in the training/predicting sets were 100/95.8% for endocrine manifestations, (18 out of 18)/(13 out of 14); 90.5/92.3% for gastrointestinal manifestations, (38 out of 42)/(30 out of 32); 88.5/86.5% for systemic phenomena, (23 out of 26)/(17 out of 20); 81.8/77.3% for neurological manifestations, (27 out of 33)/(19 out of 25); 81.6/86.2% for dermal manifestations, (31 out of 38)/(25 out of 29); 78.4/85.1% for cardiovascular manifestation, (29 out of 37)/(24 out of 28); 77.1/75.7% for breathing manifestations, (27 out of 35)/(20 out of 26) and 75.6/75% for psychiatric manifestations, (31 out of 41)/(23 out of 31). Additionally a back-projection analysis (BPA) was carried out for two ulcerogenic drugs to prove in structural terms the physical interpretation of the models obtained. This article develops a mathematical model that encompasses a large number of drugs side effects grouped in specifics biological systems using stochastic absolute probabilities of interaction ((A)pi(k)(j)) by the first time.