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I saw a paper on the preprint server BioRxiv which applies techniques from quantum theory to the problem of modeling the insertions and deletions that occur in the molecular sequences of all organisms during their evolution. Here's a brief description of the problem, vaguely aimed at mathematical physicists.
Most of the mutations that occur in DNA (and hence in RNA and proteins) are changes in single nucleotides. (These are called substitutions). Something like this happens:
ACTGTTACGGAGTATGT ACTGTTACGGAATATGT *
These are easy to model with a Markov process on 4 states. Insertions and deletions are also quite common, but much harder to model. There is a huge number of things which might happen, but each has a tiny probability.
In the study of evolution, we're looking backwards. We can observe molecular sequences in modern organisms (the final states) but don't know the initial state. But we are pretty sure that there was a single initial state from which all the final states evolved. So one molecular sequence tells you little, but a pair can tell you something, and a bunch of them can tell you a lot.
In both genetics and evolution, a lot of studies start with a 'pairwise alignment' or a 'multiple sequence alignment'. A three-sequence alignment might look like this.
rat: ACTGTTACGGA---GTATGT bat: ACTGTTACGGCCAAATATGT cat: ATTGTTACGGCCAAATATGT * *
Any insertions and deletions that may have occured are shown as gaps, thanks to a 'multiple sequence alignment program'. These are ad hoc 'engineering' solutions to the problem. One such is CLUSTAL W. The paper describing this software has over 40,000 citations. Other multiple sequence alignment programs are available. There are also statistical solutions to simplified versions of the problem. The preprint claims to be something new. In my words, not theirs, it seems to be a 'principled approximation'.