On dichotomic classes and bijections of the genetic code

Dichotomic classes arising from a recent mathematical model of the genetic code allow to uncover many symmetry properties of the code, and although theoretically derived, they permitted to build statistical classifiers able to retrieve the correct translational frame of coding sequences. Herein we formalize the mathematical properties of these classes, first focusing on all the possible decompositions of the 64 codons of the genetic code into two equally sized dichotomic subsets. Then the global framework of bijective transformations of the nucleotide bases is discussed and we clarify when dichotomic partitions can be generated. In addition, we show that the parity dichotomic classes of the mathematical model and complementarity dichotomic classes obtained in the present article can be formalized in the same algorithmic way the dichotomic Rumer's degeneracy classes. Interestingly, we find that the algorithm underlying dichotomic class definition mirrors biochemical features occurring at discrete base positions in the decoding center of the ribosome.