A symmetry-inclusive algebraic approach to genome rearrangement

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 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. In this paper, we consider the relevant genome algebras for signed circular single-chromosome genomes with and without an origin of replication, and demonstrate the computation of genomic distance, as estimated via several distance measures, under various rearrangement models.