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.

中文翻译：

---

在整个非同源末端连接途径中，随机性对DNA双链断裂修复的影响。

DNA双链断裂（DSB）是电离辐射，工业化学品和化学疗法中使用的多种药物引起的最致命的DNA损伤。在DNA损伤反应系统建模的背景下，不确定性可能会以几种方式出现，例如，诱导DSB的数量，动力学速率和可观察量的测量误差。因此，必须使用随机方法来进一步了解DSB修复过程的动态行为。在本文中，根据DSB复杂度，建立了非同源末端连接（NHEJ）机制的连续时间马尔可夫链（CTMC）模型。另外，大都会蒙特卡罗方法用于执行动力学速率常数的最大似然估计。这里，研究了NHEJ机理的波动动力学速率和DSBs诱导速率的影响。模拟了简单和复杂DSB结扎的总产量的随机实现，以比较它们的渐近动力学。此外，已经证明，对于足够大量的DSB，DSB的总产量具有正态分布。为了估计修复DSB的预期持续时间，基于CTMC NHEJ模型计算DSB寿命的概率分布。此外，在恒定的低剂量辐射过程中，在所提出的模型中评估了DSB的总产率的可变性。研究结果表明，在随机NHEJ模型中，当在修复过程中没有新的DSB诱导时，所有DSB最终都将被修复。但是，当持续不断的低剂量辐射诱导DSB时，