Combinatorics of the breakage-fusion-bridge mechanism.

The breakage-fusion-bridge (BFB) mechanism was proposed over seven decades ago and is a source of genomic variability and gene amplification in cancer. Here we formally model and analyze the BFB mechanism, to our knowledge the first time this has been undertaken. We show that BFB can be modeled as successive inverted prefix duplications of a string. Using this model, we show that BFB can achieve a surprisingly broad range of amplification patterns. We find that a sequence of BFB operations can be found that nearly fits most patterns of copy number increases along a chromosome. We conclude that this limits the usefulness of methods like array CGH for detecting BFB.