The presence of DNA double-stranded breaks in a mammalian cell typically activates the Non-Homologous End Joining (NHEJ) pathway to repair the damage and signal to downstream systems that govern cellular decisions such as apoptosis or senescence. The signalling system also stimulates effects such as the generation of reactive oxygen species (ROS) which in turn feed back into the damage response. Although the overall process of NHEJ is well documented, we know little of the dynamics and how the system operates as a whole. We have developed a computational model which includes DNA Protein Kinase (DNA-PK) dependent NHEJ (D-NHEJ) and back-up NHEJ mechanisms (B-NHEJ) and use it to explain the dynamic response to damage induced by different levels of gamma irradiation in human fibroblasts. Our work suggests that the observed shift from fast to slow repair of DNA damage foci at higher levels of damage cannot be explained solely by inherent stochasticity in the NHEJ system. Instead, our model highlights the importance of Ku oxidation which leads to increased Ku dissociation rates from DNA damage foci and shifts repair in favour of the less efficient B-NHEJ system.