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 such as 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 countvector problem: given a chromosome segmentation and segment copy numbers, decide whether BFB can yield a chromosome with the given segment counts. We present a linear time algorithm for the problem, in contrast to 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 chromosomal region likely rearranged by BFB cycles, demonstrating the practicality of our approach.
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