Graphs Associated With DNA Rearrangements and Their Polynomials

Abstract

DNA rearrangement is a process often found in biology on both developmental and evolutionary scale. While many models have considered abstract operations involved in the rearrangement, the process itself can be directly modeled through four-regular graphs, as presented here. We describe ways to explain DNA rearrangements through four-regular graphs and double occurrence words. These models are illustrated through the rearrangement processes in a well-studied ciliate species where DNA recombination is observed on a massive scale. The number of resulting molecules and the intermediate molecules throughout this process can be counted as terms in graph polynomials, closely related to the well-known Tutte polynomial. We present two such polynomials in the last section.