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DNA double strand breaks (DSBs) are the most lethal lesions of DNA induced by ionizing radiation, industrial chemicals and a wide variety of drugs used in chemotherapy. In the context of DNA damage response system modelling, uncertainty may arise in several ways such as number of induced DSBs, kinetic rates and measurement error in observable quantities. Therefore, using the stochastic approaches is imperative to gain further insight into the dynamic behaviour of DSBs repair process. In this article, a continuous-time Markov chain (CTMC) model of the non-homologous end joining (NHEJ) mechanism is formulated according to the DSB complexity. Additionally, a Metropolis Monte Carlo method is used to perform maximum likelihood estimation of the kinetic rate constants. Here, the effects of fluctuating kinetic rates and DSBs induction rate of the NHEJ mechanism are investigated. The stochastic realizations of the total yield of simple and complex DSBs ligation are simulated to compare their asymptotic dynamics. Furthermore, it has been proved that the total yield of DSBs has a normal distribution for sufficiently large number of DSBs. In order to estimate the expected duration of repairing DSBs, the probability distribution of DSBs lifetime is calculated based on the CTMC NHEJ model. Moreover, the variability of total yield of DSBs during constant low-dose radiation is evaluated in the presented model. The findings indicate that in stochastic NHEJ model, when there is no new DSBs induction through the repair process, all DSBs are eventually repaired. However, when DSBs are induced by constant low-dose radiation, a number of DSBs remains un-repaired.
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