A symmetry-inclusive algebraic approach to genome rearrangement

TL;DR

This paper introduces a theoretical algebraic framework that models genome rearrangements while incorporating structural symmetries, offering a flexible approach to understanding evolutionary distances.

Contribution

It presents a novel algebraic approach using genome algebras to include symmetries in genome rearrangement models, advancing theoretical understanding.

Findings

Framework allows modeling of genome symmetries

Enables comparison of different rearrangement models

Highlights computational challenges for practical implementation

Abstract

Of the many modern approaches to calculating evolutionary distance via models of genome rearrangement, most are tied to a particular set of genomic modelling assumptions and to a restricted class of allowed rearrangements. The "position paradigm", in which genomes are represented as permutations signifying the position (and orientation) of each region, enables a refined model-based approach, where one can select biologically plausible rearrangements and assign to them relative probabilities/costs. Here, one must further incorporate any underlying structural symmetry of the genomes into the calculations and ensure that this symmetry is reflected in the model. In our recently-introduced framework of {\em genome algebras}, each genome corresponds to an element that simultaneously incorporates all of its inherent physical symmetries. The representation theory of these algebras then provides a natural model of evolution via rearrangement as a Markov chain. Whilst the implementation of this framework to calculate distances for genomes with `practical' numbers of regions is currently computationally infeasible, we consider it to be a significant theoretical advance: one can incorporate different genomic modelling assumptions, calculate various genomic distances, and compare the results under different rearrangement models. The aim of this paper is to demonstrate some of these features.