Results

Preview. For the one-colour data sets, we first apply the breakage-and-reunion model to the 4 Gy fibroblast data (Simpson and Savage 1996), then the recombinational-repair model. Thereafter somewhat smaller fibroblast data sets, for 2 Gy and 6 Gy, and the very large lymphocyte data set of Barquinero et al. (1998) will be analyzed similarly. Finally, other data, for multi-colour painting, is briefly discussed.

Fibroblast data. Table 1 shows fibroblast data (Simpson and Savage 1996) at 4 Gy for 6 different chromosome homologue pairs painted (effectively one pair at a time), and for a number of different aberration types. In the table, the data is compared with the breakage-and-reunion model predictions, calculated as described in the Methods section, using the parameters $S$ and $\delta$ shown in Table 2. It was found that only the apparently simple centric rings depend sensitively on site number $S$ in the range 8-12 sites; predicted frequencies for the other aberration categories listed remain roughly fixed if $S$ is varied holding $\delta ^2 / S$ constant (i.e. $\delta$ proportional to $S ^{1/2}$).

[Insert Tables 1 and 2 and captions about here]

The participation of different chromosomes in aberrations was further analyzed by determining correlation coefficients. For example, in Figure 3A, CAS model predictions for apparently simple interchanges are shown in a scatter plot with the experimental results. Figure 3B gives corresponding results for total visibly complex aberrations. The correlation coefficients for these and other aberration types are shown in Table 3. For the most part strong correlations are seen.

[Insert Fig. 3 + table 3 + captions about here]

A similar analysis was carried out for the recombinational-repair model. The best parameters for this model, considering all three doses, were found to be $S = 10$ sites and $\delta$=0.45/Gy (Table 2). Summary results, for totals over all chromosomes, are shown in Table 4. It is seen that the model drastically underpredicts aberration patterns 2F and 2G (Table 4). The model also drastically underpredicts insertions, which are included among the TVC category in Table 4. However, the chromosome participation correlations remain high (Table 3).

[Insert table 4 + caption about here]

Similar, but less detailed, analyses were carried out at 2 Gy and at 6 Gy, using the same parameters. The main results are shown in Tables 3 and 4. It is again seen that the random breakage-and-reunion model gives reasonably accurate results, that the correlations are high, and that the recombinational-repair model drastically underpredicts 2F and 2G patterns. One additional detail of interest is that at 6 Gy, for very complex aberrations involving 6 or more breaks, the observed:predicted numbers for the breakage-and-reunion model are 38:10, i.e. there is substantial underprediction of very complex aberrations, as was previously also found at 4 Gy (Chen et al. 1997).

Theoretical dose-response curves for simple and complex aberrations, incorporating the effects of distortion and saturation, are compared to data at three doses in Figure 4.

The data of Barquinero et al. This experiment has results for all 23 homologue pairs, painted one pair at a time. Table 5 gives the experimental data, with one-way exchange types I-VI reallocated via method (ii), described in the Methods section. The table also gives the predictions of the breakage-and-reunion model with the parameters shown in Table 2. Table 3 gives some correlations for chromosome participation. The breakage-and-reunion model predictions are reasonably accurate. Their weakest feature is a systematic tendency to overpredict visibly complex aberrations other than 2F and 2G patterns (contrasting with the underpredictions found for the fibroblast data in this category).

Some corresponding results for the recombinational-repair model are given in Tables 3 and 4. Once more it is seen that the recombinational-repair model drastically underpredicts 2F and 2G frequencies. For method (i) of reclassifying apparently incomplete aberration patterns, discussed in the Methods section, the predictions for 2F and 2G are somewhat improved, being about 1/5 of the observed values rather than about 1/10, but for method (iii) the discrepancy is somewhat worse (details not shown).

[Insert Table 5 and caption about here]

Multicolour painting. Assuming completeness and negligible DSB clustering along chromosomes, the recombinational-repair pathway cannot lead to an odd number of junctions between any two colours, since each of its complete reciprocal exchanges makes either two or zero colour junctions; the breakage-and-reunion model, however, allows odd numbers of colour junctions. In view of the theorem that for one FISH color all patterns allowed by the breakage-and-reunion model are also allowed by the recombinational-repair model (Sachs et al. 1999) distinguishing between the models by looking for odd numbers of color junctions is relevant only for painting with two or more FISH colours. Three low-LET two-colour data sets give the following respective numbers of patterns recorded as having just one junction between the two FISH colours (rather than having an even number): Lucas and Sachs (1993), 18; Chen et al. (1995), 3; Simpson et al. (1999), 14. A three-colour data set (Knehr et al. 1999) gives additional examples, including some for low LET irradiation.