Re: [math-fun] nucleotide tetrahedron
Michael Kleber <michael.kleber@gmail.com> wrote:
David Kephart already mentioned the basic idea that what we really care about is strings over the alphabet {A,C,G,T}, and that the fundamental operation on this set is the self-inverse "reverse complement" action, the product of the double transposition (AT)(CG) with reversal of the entire string. This is the operation that really embodies Watson-Crick base pairing, because (again as David already said), DNA strands are oriented and the two strands in the double-helix are opposite to one another, so "reverse complement" takes one strand of your chromosome to the other.
It's worth noting that the Watson-Crick pairing is inherently meaningful in the DNA or RNA polymer context -- that is, as part of a string, not a single base -- since the fact that these guys pair with one another is a result of the precise alignment and separation enforced by the helical backbone of the polymer. In other words, the base pairing rules follow from the reverse- complement operation, not the other way around!
Back in the 70s, I did a lot of work with PDP-11s. They had this device called Dectape that was a magnetic tape storage medium, but designed for random access. The drives were very good at moving the tape in either direction, and reading it the direction of motion. Whenever the tape was being read in the 'backwards' direction, the tape driver did a reverse-and-complement operation on the data coming from the drive, because the bits were naturally in the wrong order, but their sense was also inverted. -- Mark D. Niemiec <mniemiec@interserv.com>
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Mark D. Niemiec