Mathematical modeling of the generation of radiation-induced DNA double strand breaks by stochastic approach

Abstract

The present study proposed a stochastic model for the randomly generated DNA double strand breaks, under the assumption that double strand breaks (dsbs) result from a pair of closely located single strand breaks (ssbs) produced in the opposite strands. By introducing probability variables corresponding to the number and the location of ssbs, mathematical formulation was presented to give the ratio of dsbs to the total number of ssbs. In the case of Poisson distribution for randomly produced ssbs, when the number of dsbs and those of ssbs in both stands is represented by q, q₁ and q₂, respectively, the ratio q/(q₁+q₂) was found to be proportional to (d/t)[λexp(-2λ)+λ²exp(-λ)+λ³], where d, t and λ is the distance between two ssbs to form dsb, the length of each strand, the average number of ssbs produced in each strand, respectively. In order to compare these results with the existing model based on the similar assumption to ours, q/(q₁+q₂) was calculated following the formulation of ssbs presented by Aspen's textbook on Radiation Biophysics. The result was simply expressed as [1-exp(-λ)]. Although the detailed comparison has not been achieved yet, the ratio becomes approximately proportional to radiation dose in both cases under the realistic assumption that λ is small. In addition, we also considered a binomial distribution model and compared with the Poisson distribution case.