A Model of Photon Cell Killing Based on the Spatio-Temporal Clustering of DNA Damage in Higher Order Chromatin Structures

We present a new approach to model dose rate effects on cell killing after photon radiation based on the spatio-temporal clustering of DNA double strand breaks (DSBs) within higher order chromatin structures of approximately 1-2 Mbp size, so called giant loops. The main concept of this approach consists of a distinction of two classes of lesions, isolated and clustered DSBs, characterized by the number of double strand breaks induced in a giant loop. We assume a low lethality and fast component of repair for isolated DSBs and a high lethality and slow component of repair for clustered DSBs. With appropriate rates, the temporal transition between the different lesion classes is expressed in terms of five differential equations. These allow formulating the dynamics involved in the competition of damage induction and repair for arbitrary dose rates and fractionation schemes. Final cell survival probabilities are computable with a cell line specific set of three parameters: The lethality for isolated DSBs, the lethality for clustered DSBs and the half-life time of isolated DSBs. By comparison with larger sets of published experimental data it is demonstrated that the model describes the cell line dependent response to treatments using either continuous irradiation at a constant dose rate or to split dose irradiation well. Furthermore, an analytic investigation of the formulation concerning single fraction treatments with constant dose rates in the limiting cases of extremely high or low dose rates is presented. The approach is consistent with the Linear-Quadratic model extended by the Lea-Catcheside factor up to the second moment in dose. Finally, it is shown that the model correctly predicts empirical findings about the dose rate dependence of incidence probabilities for deterministic radiation effects like pneumonitis and the bone marrow syndrome. These findings further support the general concepts on which the approach is based.