Methods

Data. The two largest relevant experiments that use one-colour painting were analyzed. Both data sets are essentially for one homologue pair painted at a time. One data set is that of Simpson and Savage (1996), supplemented by some extra information on centric rings. It is for irradiation of human male fibroblasts with hard x-ray doses from 2-6 Gy. The other data set is that of Barquinero et al. (1998), on x-irradiation of human female lymphocytes at 3 Gy, extending data of Knehr et al. (1998). In addition, data sets which use two-colour painting (Lucas and Sachs 1993, Chen et al. 1995, Simpson et al. 1999) or three-colour painting (Knehr et al. 1999) were considered, in less detail.

Data processing. Most models of chromosome aberration formation, including those considered here, assume completeness, i.e. no excess chromosome fragments left over at the end of the exchange process. For chromosome aberrations, formed during G0/G1, true incompleteness is rare at low LET (Savage 1976, Boei et al. 1998b, Wu et al. 1998). However, FISH patterns are observed which are not visibly complete. Probably a common cause is an exchange involving a counterstained chromosome fragment too small to be scored in the assay (Kodama et al. 1997).

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Simpson and Savage (1996) divided the most frequently observed patterns which appear to be incomplete ('one-way exchanges') into six types, and suggested ways to reallocate some of the types to complete patterns. For `incomplete type I' (i.e. type `2BI' in the notation of Barquinero et al.), shown here in Figure 2B, they suggested that about 50% of the time the apparent incompleteness was due to a cryptic counterstained acentric segment attached to the acentric painted segment, the resulting pattern being 2F in the S&S classification. They suggested reclassifying the remaining 50% of the cases as if the `missing' counterstained piece were either centric or acentric, i.e. classifying as either a 2B or 2F pattern. The ratio between 2B and 2F was `in proportion', i.e. set equal to the ratio in the full data as a whole. Boei et al. (1998a) and Knehr et al. (1999) consider classifying all these type I one-way exchanges as S&S type 2F, in light of recent results (Kodama et al. 1997, Wu et al. 1998, Boei and Natarajan 1998, Boei et al. 1998a, 1998b) on completeness. Barquinero et al. consider counting them all as apparently simple translocations (S&S type 2B) instead, or excluding them from the data, or allocating them in a way similar to that suggested by Simpson and Savage. As in the case of type I, other one-way exchanges can also be reclassified into complete patterns, and the optimal reclassification method is somewhat problematical.

The fibroblast data set used here to test the models (Simpson and Savage 1996) already incorporates such reclassifications, and we shall continue to use the data in that form. For the lymphocyte data (Barqinero et al. 1998), one cannot do the reclassification in precisely the same form because the method used for fibroblasts depends on assuming that both `type III' and `type VI' are relatively rare, which does not hold for the lymphocyte data. We will here consider three different reclassification methods for the data of Barquinero et al., as follows.

1. Method (i). Types I, II, and III (i.e. 2BI, 2BII, and 2BIII respectively) are reclassified as S&S type 2B; types IV, V, VI (i.e. 2AIV, 2AV, and 2AVI respectively) are reclassified as S&S type 2A (i.e. apparently simple dicentrics).
2. Method (ii). Type I, allocated as suggested by Simpson and Savage (50% 2F, and 50% split between 2B and 2F in proportion); type II, 50% 2B and 50% split between 2B and 2G in proportion; type III, all split between 2B and 2F in proportion; type IV, 50% 2A and 50% split between 2A and 2G in proportion; type V, 50% 2F and 50% split between 2A and 2F in proportion; and type VI, all split between 2A and 2G in proportion.
3. Method (iii). Types I and V, 2F; type II, 2B; type IV 2A; types III and VI as in method (ii) (Boei et al. 1998a, Knehr et al. 1999).

Methods (i) and (iii) are extremes in the sense that the ratio of visibly complex to apparently simple aberrations, which is important in choosing model parameters, is smaller in method (i), larger in method (iii), and intermediate in other methods that have been proposed, such as method (ii) or excluding one-way exchanges from the data altogether. We shall here emphasize method (ii), because it is the method most nearly consistent with the way in which the fibroblast data was handled. When implementing method (ii) we worked iteratively, updating at each iteration the ratios (2F/2A, 2F/2B, 2G/2A, and 2G/2B) used in the calculation.

One other, comparatively minor, point regarding the paper of Barquinero et al. (1998) is that painted centric rings were not explicitly divided into apparently simple and visibly complex subcategories. We shall here consider apparently simple painted centric rings as being the category `other simple aberrations' from table 3 of Barquinero et al. minus the category `r(b)' (acentric rings) from their table 2. This procedure may result in a slight underestimate, since not all the r(b) are necessarily apparently simple, but gives results identical (apart from one ring) to a published subset of the data with apparently simple centric rings listed explicitly (Knehr et al. 1998).

CAS computer calculations. Monte Carlo algorithms, based on randomness (Appendix), were used to work out aberration frequencies. CAS software, described previously (Chen et al. 1995, 1996, 1997, 1998), was extended to incorporate the recombinational-repair model.

In CAS, proximity effects (i.e. effects due to the fact that DSBs initially formed close together are more likely to take part in an exchange than DSBs initially formed far apart) are taken into account by dividing the cell nucleus into interaction sites (Savage 1996, Sachs et al. 1997a). The site number $S$ is treated as an adjustable parameter, in our calculations usually found to be in the range 5-15 for low LET radiations. This way of handling proximity effects is oversimplified, but does incorporate them systematically into calculations for all different kinds of aberrations. For any one cell, chromosomes are assigned at random to the sites.

Radiation induction of `reactive' DSBs, i.e. of DSBs which participate in misrejoining or accidental restitution rather than being systematically restituted, is then simulated. The computer places reactive DSBs at random throughout the genome; the number in any particular portion of the genome (such as a chromosome arm) is determined by Poisson statistics, the average being proportional to DNA content. The average number of reactive DSBs per G1 genome per Gy is the second (and last) adjustable CAS parameter, $\delta$.³ The assumption that the reactive DSBs should be Poisson-distributed with average proportional to dose is almost automatic at low LET if the reactive DSBs constitute a biophysically defined subset of all DSBs. Otherwise the assumption is made plausible for the recombinational-repair model by the fact that the set of all DSBs presumably has these same properties; for the breakage-and-reunion model a particular kinetic scenario is also involved (Radivoyevitch 1997), with reactive DSBs the residual survivors of systematic DSB restitution.

After the computer simulates induction of reactive DSBs, the DSBs undergo simulated misrejoining or accidental restitution. For the breakage-and-reunion model, DSB free ends within each interaction site join pairwise at random. For the recombinational-repair model each radiation-induced reactive DSB chooses a locus at random on the DNA in its own interaction site. It interacts with the locus and a complete reciprocal exchange occurs, the two different possibilities for the complete reciprocal exchange being taken as equally probable.

After thus simulating interactions, the computer classifies the resulting aberration patterns, using the specific painting protocol and aberration classification system of the experiment being simulated. CAS can emulate conventional staining, one-colour whole-chromosome painting, or multi-colour whole-chromosome painting. Any number of different aberration categories can be distinguished, e.g. apparently simple dicentrics or translocations or centric rings, various three-way interchanges such as insertions or (in one-colour painting) S&S patterns 2F and 2G, tricentrics, centric rings or insertions accompanied by additional exchanges, and more complicated visibly complex aberrations.

Because the software can match the actual scoring in all particulars (apart from incomplete types, discussed above), direct predictions can be obtained for the categories actually observed. For example, it would be straightforward to correct the simulated frequency of apparently simple aberrations for simulated aberrations that are apparently simple but actually complex (Simpson and Savage 1996); however, it is also straightforward, and perhaps more informative, to simulate combining truly simple aberrations with apparently simple complex aberrations, in just the same way as observations using the microscope would combine them.

The entire simulation -- of DSB induction, DSB rejoining/misrejoining, chromosome painting, and aberration pattern classification -- is repeated for many cells, typically at least 100 times as many as in the experiment being simulated. Simulated aberration frequencies are thereby obtained. Cell by cell lists, corresponding to collections of photographs of specific metaphases in an actual experiment, can also be obtained.

In our calculations here we used one painted chromosome (instead of two painted homologues) for convenience, and doubled the results apart from correction factors of a few percent for aberrations involving both homologues. The numbers for what are called AG5 and AG6 by Simpson and Savage (1996) were obtained by linear combination from two corresponding categories.