This is a paper I wrote as a  sophomore for an REU program at IU Bloomington. As such, it is definitionally sophomoric. For many years, it has been hosted on their university website. However, I have fond memories of working with the biology and math departments to define the problem, learning probability and combinatorics over the summer, and working through the mathematics of compound probability distributions, pathways through the space of permutations of genes, and Monte Carlo simulations. I didn’t realize how valuable it was back then to be able to just sit and focus on a hard problem for an extended period of time.

Recent developments in LLM’s and protein folding make me feel like it might be worth revisiting this material at some point. The principal difficulties were the large number of genes involved and the size of permutation space. In any case, it is a fun trip down memory lane.