  Breakage-Fusion-Bridge cycles in cancer arise when a broken segment of DNA is
duplicated and an end from each copy joined together. This structure then
`unfolds' into a new piece of palindromic DNA. This is one mechanism
responsible for the localised amplicons observed in cancer genome data. The
process has parallels with paper folding sequences that arise when a piece of
paper is folded several times and then unfolded. Here we adapt such methods to
study the breakage-fusion-bridge structures in detail. We firstly consider
discrete representations of this space with 2-d trees to demonstrate that there
are 2^(n(n-1)/2) qualitatively distinct evolutions involving n
breakage-fusion-bridge cycles. Secondly we consider the stochastic nature of
the fold positions, to determine evolution likelihoods, and also describe how
amplicons become localised. Finally we highlight these methods by inferring the
evolution of breakage-fusion-bridge cycles with data from primary tissue cancer
samples.
