Summary

This project explores an application of equivalence relations to bioinformatics. RNA can be considered as a string over a four-letter alphabet. Cells use triples of these bases to regulate the production of protein by signaling the sequence of amino acids. But there are far fewer than 64 amino acids; is there a system behind the redundancy?

Students examine the equivalence classes arising from six difference equivalence relations on the set of codons, from simple to somewhat intricate. Then they research the actual genetic code; it is “closest” to one of the simpler relations, although it is far from an exact match.

Notes for the instructor

This project was motivated by student interest in bioinformatics and my difficulty finding engaging applications of equivalence relations and classes. The set of 64 codons is small enough to be tractable, but large enough to encourage labor-saving devices. While some of the relations have no biological motivation (e.g., number of A's), they do encourage the use of standard counting techniques. Students are instructed to “describe the equivalence classes” for each relation; this can prompt discussions of a good order for listing set elements and the proper use of ellipses.

I typically put the students in randomgroups of three (or two) for a project and give thema class period to get started, with the expectation that they will need to work outside class to complete the project and write it up.