Modelling the Formation of Polycentric Chromosome Aberrations

Abstract

Exchange-type chromosome aberrations produced by ionizing radiation or restriction enzymes are believed to result from pairwise interaction of DNA double-strand breaks (dsb). In addition to dicentrics, such aberrations may include higher-order polycentrics (tricentrics, tetracentrics, etc.). We have developed computer programs that calculate the probability of the various polycentrics for a given average number of pairwise interactions. Two models are used. Model I incorporates kinetic competition between restitution, complete exchanges (illegitimate recombination events), and incomplete exchanges. Model II allows unrestituted breaks even if there is no recombination. The models were applied to experimental observations of aberrations produced in G1 Chinese hamster ovary cells after electroporation with the restriction enzyme PvuII, which produces blunt-end dsb. We found, experimentally and theoretically, that there was a maximum in the number and multiplicity of polycentrics per cell: beyond a certain PvuII concentration no additional or higher-order polycentrics were produced. Computer-generated relationships, which were remarkably similar for both models and for all values of the adjustable parameters, were found between dicentrics per cell and higher-order polycentrics per cell. Excellent agreement was found between the experimental observations and the consensus theoretical curve relating tricentrics per cell to dicentrics per cell. The observed number of higher polycentrics per cell for a given number of dicentrics per cell was somewhat larger than the consensus theoretical prediction. The observed number of centric rings per cell was markedly larger than the consensus theoretical value, presumably owing to intrachromosomal localization ('proximity effects'). The computer models also provided estimates for the adjustable parameters; for example, in model I the fraction of incomplete exchanges was found to be about 35%.

Using three-color chromosome painting to test chromosome aberration models.

“…The exchange model, on the other hand, predicts no significant production of triplets at all (Table 1). This is true even if some of the exchanges are incomplete exchanges (3, 7), provided, as has hitherto been assumed (3,7,13,14), the nontelomeric ends formed in an incomplete exchange are "capped" (i.e., nonreactive), so that an excess acentric fragment at metaphase results from any incomplete exchange.…”

“…Using this discrete time chain reduces the computations by enabling use of recursion relations (19) rather than integration of the Kolmogorov forward equations of the continuous time chain. The models determine a Monte Carlo calculation, with the computer simulating the pairwise interaction of DSB, cell-by-cell, chromosome-by-chromosome, and step-by-step (14,19).…”

“…For y-ray irradiation, this Poisson assumption is the appropriate one (12). Both models, the classical and the exchange, were formulated probabilistically, as continuous time Markov chains (12,14,19). Spatial homogeneity and randomness of DSB-DSB interactions (19) were assumed.…”

“…Fully stochastic versions of the models were used because the per-cell average number of DSB-DSB interactions involving a particular chromosome is quite small, and the final chromosome rearrangements observed are thus heavily influenced by stochastic fluctuations. We used Monte Carlo computer simulations adapted from programs previously used to analyze cell killing after irradiation, dicentric yield and variance after irradiation, or polycentric chromosome derivative formation after restriction enzyme treatment (12,14).…”

“…One or both of these models (or some more complicated extension) are almost always assumed in any quantitative analysis of pairwise chromosome interactions (e.g., refs. [8][9][10][11][12][13][14]. For theoretical analyses of chromosome aberrations, and for understanding the general mechanisms of DNA recombination, it would be very useful to confirm either model, invalidate either, or invalidate both.…”