Modelling the probability distribution of the number of DNA double-strand breaks due to sporadic alkylation of nucleotide bases.

Metabolites and certain chemical agents (for example methyl methanesulfonate) can induce nucleotide bases on chromosomal strands to become alkylated. These alkylated sites have the potential to become single-strand chromosomal breaks, a form of DNA damage, if they are exposed to a sufficient temperature in vitro. It has been proposed that a single-strand break (SSB) sufficiently close to another SSB on the opposite chromosomal strand will form a double-strand break (DSB). DNA repair mechanisms are less able to repair DSBs compared to SSBs. Because of the complex three-dimensional structure of DNA, some chromosomal regions are more susceptible to alkylation than others. A question of interest is therefore whether these alkylated bases are randomly distributed or tend to be clustered. Pulsed-field gel electrophoresis allows the number of DNA fragments (and hence the number of DSBs) to be observed directly. The randomness of alkylation events can therefore be tested using the standard statistical hypothesis-testing framework. Under the null hypothesis, that the SSBs are randomly distributed on each of the strands, we can calculate the probability of observing a number of DSBs at least as large as that observed and hence the associated p-value. Previously, the probability distribution of the number of DSBs has been determined by Monte Carlo simulations; when considering the whole genome this can be very time consuming. In this paper, we theoretically derive an approximation to the distribution enabling appropriate probabilities to be calculated quickly. Based on previous findings we assume that the number of breaks on each strand is small compared to the number of nucleotide bases. We show that our method can give the correct probability distribution when alkylation events are relatively rare, discuss how rare these events have to be and suggest potential extensions to the model when a greater proportion of bases are alkylated.