A stochastic model for the induction of heritable translocation in spermatozoa by exposure to environmental agents

Abstract

In this paper we develop a stochastic model for the induction of heritable translocation in spermatozoa by exposure to some environmental agents by following the biological mechanism for the generation of spermatozoa in mice and human beings. By using Kolmogorov forward equation, it is shown that the probability generating functions (PGF) of the numbers of some normal and translocation carrying spermatid cells satisfy some partial differential equations. Using these results, a procedure for computing the probability distribution of the number of translocation carrying spermatid cells is derived under some important cases. These results will be applied to some dose- response data available on the induction of reciprocal translocations by exposure to some environmental agents in male mice.