Reaction kinetics for the development of radiation-induced chromosome aberrations

The formation of chromosome aberrations from DNA double-strand breaks (dsb) following ionizing irradiation of cells is analysed using a stochastic, continuous-time Markov chain formalism. A restitution/complete exchange model is proposed which incorporates kinetic competition between dsb restitution and chromosome exchange; it applies primarily to those dsb whose broken ends are held in close proximity by proteins. Some additional pathways for damage evolution are also considered. The calculations are compared in detail to the experiments on dicentric yield and variance in human lymphocytes following acute low-LET irradiation summarized by Lloyd and Edwards (1983) and Lloyd et al. (1987). It was found that dicentric formation by pairwise dsb interactions can lead to a dicentric yield/dose curve with a significant linear component even if one-track action is neglected. In other words a dicentric formation rate quadratic in the dsb number does not automatically imply a dicentric yield quadratic in the dose. However, the data indicate that at least in some experiments there could have been a significant one-track contribution to the dicentric yield in addition to the intertrack contributions analysed in the present paper. From the data the order of magnitude of the dsb interaction rate constant is estimated to be at most approximately 3 x 10(-3) exchanges per dsb pair per hour. It was found that for the reaction pathways considered, a initial Poisson distribution of dsb leads to an underdispersed distribution of dicentrics; the amount of underdispersion is strongly model-dependent and the variance data are consistent with the restitution/complete exchange model. Finally, a general mathematical theorem on Markov models is presented. It implies that assays performed after repair and exchange are completed cannot determine absolute repair or exchange rates, only their ratio (which may depend on lesion number).