Patterns in the genetic code

The origin and evolution of the genetic code remains an unsolved mystery. Genetic code defines how the genetic information in the DNA is translated into proteins, which are the building blocks of the cells. In particular, the genetic code maps the codons (triplets of bases) to amino acids. Since the very first days after the discovery of the genetic code it was observed that it contains several regularities. There have been many attempts to give a formal characterization of the particular structure of the code which would also have a justification from physico-chemical and/or evolutionary points of view.

We revisit the idea originally put forward by Rosemary Swanson to connect the genetic code to a type of codes called Gray codes. We show that cyclic arrangements of the codons which are different from the one proposed by Swanson, but which are still based on the principle of minimal change, yield a better grouping of the amino acids by similarity. We achieve we model the problem of finding generalized Gray codes (codon arrangements) as a Travelling Salesman Problem. Solutions of this problem lead to several Gray code arrangements of the codons. We consider the possible implications of the obtained results from evolutionary and physico-chemical point of views.