[Mathematical modeling of the relationship between the cytogenetic effect and the concentration of the mutagen]

Abstract

The effect of different concentrations of thiophosphamide on the culture of human leucocytes was investigated. Three mathematical models were studied, one of which, being satisfactory for describing the experimental data, was chosen. According to this model a quantity of aberrant cells changes with the concentration of thiophosphamide non-linearly and can be described according to the equation A=exp[-(KC+alpha)2], where A is a portion of normal cells, C - a concentration of a mutagen, K and alpha - the coefficients, while exp[-alpha2] is the control level of normal metaphases. The quantity of chromosome breaks per cell is described according to the equation X= exp [KC + +alpha)2]-1. The general view of the equation is constant for different phases of the cell cycle. It follows from the suggested model that the action of two molecules of an alkylating agent is necessary for the formation of a chromosome break. This is indicative of double-stranded structure of a chromosome in its section. It also follows from the suggested model that the action of thiophosphamide has no cut-off. Thiophosphamide induced chromatid aberrations during the G2 phase, therefore it is not a mutagen of the check action.