title: The fourfold way of the genetic code.
abstract: We describe a compact representation of the genetic code that factorizes the table in quartets. It represents a "least grammar" for the genetic language. It is justified by the Klein-4 group structure of RNA bases and codon doublets. The matrix of the outer product between the column-vector of bases and the corresponding row-vector V(T)=(C G U A), considered as signal vectors, has a block structure consisting of the four cosets of the KxK group of base transformations acting on doublet AA. This matrix, translated into weak/strong (W/S) and purine/pyrimidine (R/Y) nucleotide classes, leads to a code table with mixed and unmixed families in separate regions. A basic difference between them is the non-commuting (R/Y) doublets: AC/CA, GU/UG. We describe the degeneracy in the canonical code and the systematic changes in deviant codes in terms of the divisors of 24, employing modulo multiplication groups. We illustrate binary sub-codes characterizing mutations in the quartets. We introduce a decision-tree to predict the mode of tRNA recognition corresponding to each codon, and compare our result with related findings by Jestin and Soulé [Jestin, J.-L., Soulé, C., 2007. Symmetries by base substitutions in the genetic code predict 2' or 3' aminoacylation of tRNAs. J. Theor. Biol. 247, 391-394], and the rearrangements of the table by Delarue [Delarue, M., 2007. An asymmetric underlying rule in the assignment of codons: possible clue to a quick early evolution of the genetic code via successive binary choices. RNA 13, 161-169] and Rodin and Rodin [Rodin, S.N., Rodin, A.S., 2008. On the origin of the genetic code: signatures of its primordial complementarity in tRNAs and aminoacyl-tRNA synthetases. Heredity 100, 341-355], respectively.
authors: Division of Mathematics, Science, and Technology, Parker Building, Nova Southeastern University, Fort Lauderdale, FL 33314-7796, USA. ajimenez@uv.mx
authors: Miguel Angel
authors: MA
authors: Jiménez-Montaño
mesh_terms: D000465:Algorithms; D000596:Amino Acids / Q000235:genetics / Q000378:metabolism; D001483:Base Sequence; D003062:Codon / Q000235:genetics*; D003663:Decision Trees; D005815:Genetic Code / Q000235:genetics*; D008957:Models, Genetic; D012343:RNA, Transfer / Q000235:genetics / Q000378:metabolism; D046249:Transfer RNA Aminoacylation
chemical_list: D000596:Amino Acids; D003062:Codon; D012343:RNA, Transfer