A Comparison of Three Heuristic Methods for Solving the Parsing Problem for Tandem Repeats

Abstract

In many applications of tandem repeats the outcome depends critically on the choice of boundaries (beginning and end) of the repeated motif: for example, different choices of pattern boundaries can lead to different duplication history trees. However, the best choice of boundaries or parsing of the tandem repeat is often ambiguous, as the flanking regions before and after the tandem repeat often contain partial approximate copies of the motif, making it difficult to determine where the tandem repeat (and hence the motif) begins and ends. We define the parsing problem for tandem repeats to be the problem of discriminating among the possible choices of parsing.

In this paper we propose and compare three heuristic methods for solving the parsing problem, under the assumption that the parsing is fixed throughout the duplication history of the tandem repeat. The three methods are PAIR, which minimises the number of pairs of common adjacent mutations which span a boundary; VAR, which minimises the total number of variants of the motif; and MST, which minimises the length of the minimum spanning tree connecting the variants, where the weight of each edge is the Hamming distance of the pair of variants. We test the methods on simulated data over a range of motif lengths and relative rates of substitutions to duplications, and show that all three perform better than choosing the parsing arbitrarily. Of the three MST typically performs the best, followed by VAR then PAIR.