Pairwise lesion interaction in competition with first-order repair kinetics: A mathematical theory of cell survival

Lea's 40-year-old theory that radiation-induced reparable chromatin lesions interact pairwise to form irreparable products has been re-evaluated assuming (a) first-order kinetics of enzymatic lesion repair, (b) Poisson statistics for the molecular contacts of lesions, and (c) Poisson statistics for a contact to result in an interaction. Survival rate, as the probability for a cell to remain free from unrepaired chromatin lesions (potentially lethal damage) and from the products of pairwise lesion interaction (sublethal damage interaction), has been analytically derived for acute, fractionated and protracted irradiations. Calculated survival curves are nonlinear due to the second-order kinetics imposed by pairwise lesion interaction, and have exponential tails in the dose region where the first-order kinetics of lesion repair is slow in comparison with the second-order kinetics of lesion interaction