Influence of the Stochasticity in the Model on the Certain Drugs Pharmacodynamics

Abstract

In this paper I analyze the impact of the stochasticity on the three different levels (genes, mRNA and protein) on the of drug pharmacodynamics of a large class of drugs. I focus on the basic mechanisms underlying the dose-response curves considering two elementary molecular circuits. Both consist in the gene activation/deactivation, then gene transcription and following translation into the corresponding protein. In the first circuit gene activation and deactivation are spontaneous whereas gene deactivation rate in the second circuit depends on the protein level introducing negative feedback. In both cases drug is assumed to enhance the protein degradation level and the success of the therapy is considered as lowering the protein level below given threshold for given time. My numerical simulation shows that the level on which the stochasticity is introduced to the model (none, genes, mRNA, protein) influences not only the shape of dose-response curves but also the value of the critical dose i.e. the dose which causes of the positive response to the therapy in at least half of the cells.