It is sometimes assumed that for apparently simple aberrations the breakage-and-reunion model predicts a quadratic (or, because of the admixture of complex aberrations, faster than quadratic) increase with dose. We showed that at doses above a few Gy, distortion and saturation can set in and then the dose-response curve grows less rapidly than quadratically instead (Figure 4). Correspondingly the recombinational-repair dose-response curve does not increase linearly at higher doses; it tends to level off, due to distortion (Figure 4). The excellent dose-response fit in Fig. 4B for the breakage-and-reunion model should be regarded with some skepticism because it is a fit of just three empirical points with a two-parameter model, and because the detailed effects of saturation depend on our assumption (Methods section) that reactive DSB are Poisson-distributed with average proportional to dose. However, Fig. 4B does show that even if visibly complex aberrations are left out of the argument entirely, dose-response relations favor the breakage-and-reunion mechanism somewhat.
The strongest argument against the recombinational-repair model is that it underpredicts some common visibly complex aberrations by a factor of about 10 (Table 4). In addition, it predicts that the number of junctions between different FISH colours is always even, contradicting some low-LET data involving two or more FISH colours.
Loopholes. The data thus appear to exclude the recombinational-repair model, but there are some caveats. It could be that recombinational repair is responsible for an aberration subset, almost negligible for low LET doses of several Gy or more but dominant at sufficiently small doses. In fact, the low-dose linear portion of the dose-response curve for dicentrics (Edwards 1997), usually attributed to some single tracks making more than one DSB even at low LET, could instead be due to an admixture of the recombinational-repair pathway.
Another possibility would be that even at low LET DSBs typically do not occur singly, but rather in comparatively tight clusters of two or more, with different DSBs in one cluster capable of reacting independently of each other, and with intra-cluster chromosome segments too short to observe in the usual FISH assays. Then the discrepancies between the recombinational-repair model and the data on visibly complex aberrations would be mitigated (Sachs et al. 1999). Intuitively speaking, the situation is that the two free ends of a reactive DSB are, on the recombinational-repair model, forced to act in concert, whereas on the breakage-and-reunion model they can misrejoin independently. If there is enough clustering, the free ends at the extremes of each cluster act independently in any case, and the predictions of the two models become very similar (Sachs et al. 1999). However, direct pulsed-field gel-electrophoresis measurements do not seem to indicate enough clustering of DSBs at low LET.
Randomness. Analyzing randomness supplies coherence to otherwise almost overwhelmingly intricate data. Without some theoretical picture, a data set such as that shown in Table 5, with more than 100 prima facie independent entries, is opaque; the random breakage-and-reunion model gives an overall interpretation of Tables 1 or 5 in terms of just two parameters, which then also apply to other doses. The utility of randomness as a general guide is supported by chromosome participation correlations (Fig. 3, Table 3), dose-response curves (Fig. 4), and substantial evidence in the literature (Appendix).
Deviations from randomness, even apart from proximity effects here taken approximately into account by using interaction sites, probably do occur (Appendix) but then they typically involve factors considerably less than 2 and are not consistent for different cell cultures. For example, in Fig. 3C for simple interchanges, the fact that the intercept of the straight line on the vertical axis is positive indicates an over-all tendency, previously noted by Barquinero et al. in the same data (1998), for underparticipation of large chromosomes compared to smaller chromosomes. The corresponding positive intercept in Fig. 3D confirms this tendency for visibly complex aberrations in the same lymphocyte data set. But for the fibroblast data the intercepts (Figs. 3A and 3B) are negative, suggesting an over-all tendency for overparticipation of the larger chromosomes. Thus there is here no systematic trend valid for both lymphocytes and fibroblasts.
Many of the other suggested deviations from randomness (Appendix) seem to have a similarly individualistic character. The deviations may somewhat complicate the use of FISH for biological dosimetry, but do not alter the fact that randomness can be used as an organizing principle for the data. Thus the discrepancies for patterns 2F and 2G between the recombinational-repair model and the data (Table 4), being about 10-fold, are much more likely a failure of the model than a failure of randomness.
Site number. One peripheral, but puzzling, issue is that chromosome aberration data suggest about 5-25 interaction sites per nucleus (Table 2, Chen et al. 1997), whereas PFGE data on fragment rejoining and misrejoining (Radivoyevitch et al. 1998) and data on interaction distances (Sachs et al. 1997a) tend to suggest hundreds or thousands. These disparate estimates could perhaps be reconciled by considering scenarios where each chromosome can contribute chromatin to many different small interaction sites (Savage 1996), rather than to just one bigger interaction site as in the present version of CAS. This revision could also perhaps simultaneously account for extra intra-chromosomal proximity effects, biasing for small intrachanges relative to larger intrachanges, which are observed but are not incorporated into CAS (Appendix). For if one chromosome contributes chromatin to many interaction sites, then its chromatin within any one interaction site will tend, on average, to have DNA loci which are not separated by too many Mbp (Wu et al. 1997b, Sachs et al. 1997b), and this tendency will bias for small intrachanges relative to larger intrachanges, as observed.
However, this picture would require very extensive intermingling of different chromosomes, with many interaction sites having close jutaxpositions of a number of chromosomes, whereas direct geometric information on chromosome territories is often interpreted as showing segregation instead (Cremer et al. 1993). Moreover, no actual numerical implementation of the picture has yet been attempted; preliminary estimates suggest that the number of visibly complex aberrations would be underpredicted by such a model.
Conclusions. Observed frequencies of visibly complex aberrations are informative about aberration formation mechanisms. The random breakage-and-reunion model is a sufficiently good approximation to organize current FISH aberration data coherently. Results on visibly complex aberration patterns show that the recombinational-repair pathway cannot be a major contributor to aberration formation after low-LET doses of several Gy or more, unless there is unexpectedly frequent cryptic clustering of reactive breaks along chromosomes.
Acknowledgements. We are grateful to M. Bauchinger, D. Brenner, and M. Cornforth for discussions. Research supported by NIH grant GM 57245-01 (RKS and AMC), by NSF grants DMS 9532055 (AR and AMC), DMS-9707991 (PH), and BIR 9630735 (LRH), and by EU Contracts PL0095004 and F14PCT95001 (PS and JRKS).