An algebraic model for inversion and deletion in bacterial genome rearrangement

TL;DR

This paper introduces an algebraic model using partial permutations to analyze bacterial genome evolution, accounting for both inversions and deletions, and provides an algorithm to compute evolutionary distances.

Contribution

It presents the first algebraic framework combining inversions and deletions in bacterial genome rearrangement analysis.

Findings

Developed an algebraic model with partial permutations for genome rearrangements.

Created an algorithm to compute minimum evolutionary distance including deletions.

Enhanced existing inversion models by incorporating deletions for more realistic analysis.

Abstract

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.