This work studies the first and second order mechanisms for the induction of lethal lesions in DNA after irradiation with protons and -particles. The purpose is to numerically study the mechanisms behind the Dual Radiation Action Theory (DRAT) for these heavy particles. A genetic material geometrical model with atomic resolution is used. It accounts for the explicit position of 5.47 × 109 base pairs, organized up to the chromatin level. The GEANT4-DNA Monte Carlo code was employed to simulate the interaction of these ions with the genetic material model. The number of lethal lesions induced by one- and two-track mechanisms was determined as a function of dose. Values of the ratio were estimated as well as corresponding relative biological effectiveness (RBE). The number of lethal lesions produced by one-track and two-track mechanisms depends on the dose and squared dose, respectively, as predicted by the DRAT. RBE values consistent with experimental results were found, at least for LET below ∼100 keV/μm. Double strand break spatial distributions are qualitatively analyzed. According to this work, the parameter determined from cellular surviving curves depends on both the physical and parameters introduced here, and on the specific energy deposited by a single track into the region of interest. We found an increment of the parameter with LET, yet at a slower rate than so that the ratio increases with LET. In addition, we observed and explained the saturation of the parameter as the dose increases above ∼6 Gy.< Réduire