Models and Algorithms for Genome Rearrangement with Positional Constraints

Abstract

Traditionally, the merit of a rearrangement scenario between two genomes has been measured based on a parsimony criteria alone; two scenarios with the same number of rearrangements are considered equally good. In this paper, we acknowledge that each rearrangement has a certain likelihood of occurring based on biological constraints, e.g. physical proximity of the DNA segments implicated, or repetitive sequences. Accordingly, we propose optimization problems with the objective of maximizing overall likelihood, by weighting the rearrangements. We study a binary weight function suitable to the representation of sets of genome positions that are most likely to have swapped adjacencies. We give a polynomial-time algorithm for the problem of finding a minimum weight double cut and join (DCJ) scenario among all minimum length scenarios. In the process, we solve an optimization problem on colored noncrossing partitions which is a generalization of the Maximum Independent Set problem on circle graphs.