Characterizing cancer chromosome aberration pathways using multigraphs

Exchange-type chromosome aberrations are the result of chromosome breaks and joining reactions that are commonly observed in evolution, in cancer cells and in cells that have been exposed to DNA damaging agents. Aberration multigraphs provide a complete description of chromosome aberrations, and describe pathways of aberration formation in terms of cyclic graphs or cycles. Experimentally, the complete structure of these cycles is often unknown and different imputation methods have been proposed. Characterizing different imputed cycle structures and relations between them remains an open question. We present theoretical and computational enumeration results addressing this question. Additionally, inspired by evolutionary studies, we propose the use of chromosome fragment inversions/reversals to establish a partial order relation between cycles. We provide sufficient conditions that determine the preservation of cycles by edge reversals and use this partial order and the theory of Young diagrams and partitions to build a lattice structure of cycles. We show how reversals and the lattice structure of cycles help analyze chromosome aberration pathways with missing data.