The Effects of Unequal Sister Chromatid Exchange on Length of Arrays of Repeated Sequences

Models of homogenization of repeated sequences by unequal sister chromatid exchange (USCE) assume that no significant changes in array length occur. The effects of successive USCEs on the lengths of arrays of repeated sequences has been examined mathematically and by simulation, assuming misalignment to be greater in longer arrays, a condition necessary for homogenization. The series of duplications and deletions gives a wide, asymmetric variation in copy number. Frequencies follow a binomial distribution, but if misalignment increases with array length, lengths become logarithmically distributed, most arrays being shorter than the original, counterbalanced by a few very long arrays. The median length, which is also the modal length, decreases exponentially or asymptotically. Given a proportional misalignment of a, the median (mode) decreases by a2/2 per unequal crossover. Since drift is a random transmission of available alleles in the population, it follows that fixation of common short arrays is much more probable than fixation of rare long arrays. This process will continue inexorably until each array is too short to undergo further unequal crossing over, and no more variation is generated. The number of unequal crossovers required by some published models of homogenization would almost certainly cause dramatic reduction in number, or complete loss, of repeats. Frequent unequal sister chromatid exchanges are not compatible with survival of arrays unless counteracted by an independent amplification mechanism or selection, so are unlikely to be important as a long-term homogenization mechanism in non-essential repeated sequences.