Invariants of graphs modeling nucleotide rearrangements

Abstract

Nucleotide rearrangements occur in many biological systems. These genome reorganisations are especially widespread in ciliates, making these protozoans an attractive model system for experimental, computational, and theoretical studies. Rearrangements of ciliate chromosomes are modeled by the so-called assembly graphs. Edges of these graphs represent double-stranded DNA molecules, while vertices correspond to DNA recombination sites. This work is an expository article in which we discuss topological and combinatorial invariants of assembly graphs. The topological invariant, called the genus range, gives information about possible spatial arrangement of the corresponding DNA molecule. The combinatorial invariant, called the assembly polynomial, is closely related to the possible products of the rearrangement modeled by the assembly graph.