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A mathematical model is used to analyze mutant spectra for large mutations induced by low-LET radiation. The model equations are based mainly on two-break misrejoining that leads to deletions or translocations. It is assumed, as a working hypothesis, that the initial damage induced by low-LET radiation is located randomly in the genome. Specifically, we analyzed data for two hemizygous loci: CD59- mutants, mainly very large-scale deletions (>3 Mbp), in human-hamster hybrid cells, and data from the literature on those HPRT- mutants which involve at least deletion of the whole gene, and often of additional flanking markers (approximately 50-kbp to approximately 4.4-Mbp deletions). For five data sets, we estimated f, the probability that two given breaks on the same chromosome will misrejoin to make a deletion, as a function of the separation between the breaks. We found that f is larger for nearby breaks than for breaks that are more widely separated; i.e., there is a "proximity effect". For acute irradiation, the values of f determined from the data are consistent with the corresponding break misrejoining parameters found previously in quantitative modeling of chromosome aberrations. The value of f was somewhat smaller for protracted irradiation than for acute irradiation at a given total dose; i.e., the mutation data show a decrease that was smaller than expected for dose protraction by fractionation or low dose rate.

DNA double-strand breaks (DSBs) produced by densely ionizing radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. Stochastic DSB clustering at large scales, from > 100 Mbp down to < 0.01 Mbp, is modeled using computer simulations and analytic equations. A random-walk, coarse-grained polymer model for chromatin is combined with a simple track structure model in Monte Carlo software called DNAbreak and is applied to data on alpha-particle irradiation of V-79 cells. The chromatin model neglects molecular details but systematically incorporates an increase in average spatial separation between two DNA loci as the number of base-pairs between the loci increases. Fragment-size distributions obtained using DNAbreak match data on large fragments about as well as distributions previously obtained with a less mechanistic approach. Dose-response relations, linear at small doses of high linear energy transfer (LET) radiation, are obtained. They are found to be non-linear when the dose becomes so large that there is a significant probability of overlapping or close juxtaposition, along one chromosome, for different DSB clusters from different tracks. The non-linearity is more evident for large fragments than for small. The DNAbreak results furnish an example of the RLC (randomly located clusters) analytic formalism, which generalizes the broken-stick fragment-size distribution of the random-breakage model that is often applied to low-LET data.