Mathematical models of the generation of radiation-induced DNA double-strand breaks

The double-strand break (dsb) is one of the most critical lesions leading to a variety of radiobiological effects. In this paper, we reconsider the previously constructed and generally accepted mathematical models for dsb generation, and give a concrete mathematical basis for the generation of dsbs and the calculation of the number of induced dsbs, under the assumption of randomness in the break location in DNA and in the number of breaks. Using these models based on the Poisson distribution and the binomial distribution, we calculate the dose dependence of dsb generation. We deduced from our models that the dose dependence of the number of dsbs is described approximately as a quadratic form in both distribution models where dsb generation is accounted for by two ssbs. Previously reported experimental data on the dsb generation in phage DNA was found to be in good agreement with our models. Though the widely used model, the linear quadratic (LQ) model or the molecular theory of dsb formation based on the Poisson distribution, also gives the quadratic term, in spite of rough estimates or some mathematical incompleteness, a marked feature of our formulation is the absence of a parameter like the [Formula: see text] in the quadratic term that requires experimental data to determine. Thus in this study we provide mathematical validity to the generally accepted models of the number of dsb.