A branching process model for the analysis of abortive colony size distributions in carbon ion-irradiated normal human fibroblasts

A single cell can form a colony, and ionizing irradiation has long been known to reduce such a cellular clonogenic potential. Analysis of abortive colonies unable to continue to grow should provide important information on the reproductive cell death (RCD) following irradiation. Our previous analysis with a branching process model showed that the RCD in normal human fibroblasts can persist over 16 generations following irradiation with low linear energy transfer (LET) γ-rays. Here we further set out to evaluate the RCD persistency in abortive colonies arising from normal human fibroblasts exposed to high-LET carbon ions (18.3 MeV/u, 108 keV/µm). We found that the abortive colony size distribution determined by biological experiments follows a linear relationship on the log-log plot, and that the Monte Carlo simulation using the RCD probability estimated from such a linear relationship well simulates the experimentally determined surviving fraction and the relative biological effectiveness (RBE). We identified the short-term phase and long-term phase for the persistent RCD following carbon-ion irradiation, which were similar to those previously identified following γ-irradiation. Taken together, our results suggest that subsequent secondary or tertiary colony formation would be invaluable for understanding the long-lasting RCD. All together, our framework for analysis with a branching process model and a colony formation assay is applicable to determination of cellular responses to low- and high-LET radiation, and suggests that the long-lasting RCD is a pivotal determinant of the surviving fraction and the RBE.