  Breakage-Fusion-Bridge (BFB) is a mechanism of genomic instability
characterized by the joining and subsequent tearing apart of sister chromatids.
When this process is repeated during multiple rounds of cell division, it leads
to patterns of copy number increases of chromosomal segments as well as
fold-back inversions where duplicated segments are arranged head-to-head. These
structural variations can then drive tumorigenesis.
  BFB can be observed in progress using cytogenetic techniques, but generally
BFB must be inferred from data like microarrays or sequencing collected after
BFB has ceased. Making correct inferences from this data is not
straightforward, particularly given the complexity of some cancer genomes and
BFB's ability to generate a wide range of rearrangement patterns.
  Here we present algorithms to aid the interpretation of evidence for BFB. We
first pose the BFB count vector problem: given a chromosome segmentation and
segment copy numbers, decide whether BFB can yield a chromosome with the given
segment counts. We present the first linear-time algorithm for the problem,
improving a previous exponential-time algorithm. We then combine this algorithm
with fold-back inversions to develop tests for BFB. We show that, contingent on
assumptions about cancer genome evolution, count vectors and fold-back
inversions are sufficient evidence for detecting BFB. We apply the presented
techniques to paired-end sequencing data from pancreatic tumors and confirm a
previous finding of BFB as well as identify a new chromosomal region likely
rearranged by BFB cycles, demonstrating the practicality of our approach.
