Singular Perturbation Theory Applied to Markov Models for DNA Damage Caused by Ionizing Radiation

The induction of DNA double strand breaks by ionizing radiation, and enzymatic double strand break repair or misrepair, are modeled as continuous time Markov chains. Systems of partial differential equations for appropriate probability generating functions are solved by singular perturbation theory with scaling. The zero-th order singular perturbation result coincides with a model recently suggested in a biological literature. Higher order terms correct for various effects including "overkill". The results are applicable to both sparsely ionizing and densely ionizing radiation.