The repair rate of radiation-induced DNA damage: a stochastic interpretation based on the gamma function

There is a large body of evidence that stress-induced DNA damage may be responsible for cell lethality, cancer proneness and/or immune reaction. However, statistical features of their repair rate remain poorly documented. In order to interpret the shape of the radiation-induced DNA damage repair curves with a minimum of biological assumptions, we introduced the concept of repair probability, specific to any individual radiation-induced DNA damage, whatever its biochemical type. We strengthened the apparent paradox that the repair rate of a population of DNA damage is time-dependent even if the repair rate of the individual DNA damage is constant. Hence, the existing models, based on a dual approach of the DNA repair may be insufficient for describing the DNA repair rate over a large range of repair times. Since the repair probability of DNA damage cannot be assessed individually, the measurement of the DNA repair rate is assumed to consist in determining the instantaneous mean of all repair probabilities. The relevance of this model was examined with different endpoints: cell species, genotypes, radiation type and chromatin condensation. The Euler's Gamma function was shown to provide the distribution the most consistent with such hypotheses. Furthermore, formulas, deduced from the Gamma distribution, were found to be compatible with our previous model, empirically defined but based on a variable repair half-time.