Assembling contigs in draft genomes using reversals and block-interchanges

The techniques of next generation sequencing allow an increasing number of draft genomes to be produced rapidly in a decreasing cost. However, these draft genomes usually are just partially sequenced as collections of unassembled contigs, which cannot be used directly by currently existing algorithms for studying their genome rearrangements and phylogeny reconstruction. In this work, we study the one-sided block (or contig) ordering problem with weighted reversal and block-interchange distance. Given a partially assembled genome pi and a completely assembled genome sigma, the problem is to find an optimal ordering to assemble (i.e., order and orient) the contigs of pi such that the rearrangement distance measured by reversals and block-interchanges (also called generalized transpositions) with the weight ratio 1: 2 between the assembled contigs of pi and sigma is minimized. In addition to genome rearrangements and phylogeny reconstruction, the one-sided block ordering problem particularly has a useful application in genome resequencing, because its algorithms can be used to assemble the contigs of a draft genome pi based on a reference genome sigma. By using permutation groups, we design an efficient algorithm to solve this one-sided block ordering problem in O(delta n) time, where n is the number of genes or markers and delta is the number of used reversals and block-interchanges. We also show that the assembly of the partially assembled genome can be done in O(n) time and its weighted rearrangement distance from the completely assembled genome can be calculated in advance in O(n) time. Finally, we have implemented our algorithm into a program and used some simulated datasets to compare its accuracy performance to a currently existing similar tool, called SIS that was implemented by a heuristic algorithm that considers only reversals, on assembling the contigs in draft genomes based on their reference genomes. Our experimental results have shown that the accuracy performance of our program is better than that of SIS, when the number of reversals and transpositions involved in the rearrangement events between the complete genomes of pi and sigma is increased. In particular, if there are more transpositions involved in the rearrangement events, then the gap of accuracy performance between our program and SIS is increasing.