A Path-Deformation Framework for Determining Weighted Genome Rearrangement Distance

An algebraic model for inversion and deletion in bacterial genome rearrangement

Inversions, also sometimes called reversals, are a major contributor to variation among bacterial genomes, with studies suggesting that those involving small numbers of regions are more likely than larger inversions. Deletions may arise in bacterial genomes through the same biological mechanism as inversions, and hence a model that incorporates both is desirable. However, while inversion distances between genomes have been well studied, there has yet to be a model which accounts for the combination of both deletions and inversions. To account for both of these operations, we introduce an algebraic model that utilises partial permutations. This leads to an algorithm for calculating the minimum distance to the most recent common ancestor of two bacterial genomes evolving by inversions (of adjacent regions) and deletions. The algebraic model makes the existing short inversion models more complete and realistic by including deletions, and also introduces new algebraic tools into evolutionary distance problems.

A mean first passage time genome rearrangement distance

This paper introduces a new way to define a genome rearrangement distance, using the concept of mean first passage time from probability theory. Crucially, this distance provides a genuine metric on genome space. We develop the theory and introduce a link to a graph-based zeta function. The approach is very general and can be applied to a wide variety of group-theoretic models of genome evolution.