title: Quaternionic representation of the genetic code.
abstract: A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin and evolution of the code as well as with the chronological order of appearance of the amino acids along the evolution as inferred from work that mixtures known experimental results with theoretical speculations. Suggested by the diagram we propose a Hamilton quaternions based mathematical representation of the code as it stands now-a-days. The central object in the description is a codon function that assigns to each amino acid an integer quaternion in such a way that the observed code degeneration is preserved. We emphasize the advantages of a quaternionic representation of amino acids taking as an example the folding of proteins. With this aim we propose an algorithm to go from the quaternions sequence to the protein three dimensional structure which can be compared with the corresponding experimental one stored at the Protein Data Bank. In our criterion the mathematical representation of the genetic code in terms of quaternions merits to be taken into account because it describes not only most of the known properties of the genetic code but also opens new perspectives that are mainly derived from the close relationship between quaternions and rotations.
authors.affiliation: Instituto de Física de Líquidos y Sistemas Biológicos, 59 Nro. 789, 1900 La Plata, Argentina; Universidad Tecnológica Nacional, Facultad Regional Buenos Aires, Mozart Nro. 2300, C14071VT Buenos Aires, Argentina. Electronic address: manuel@iflysib.unlp.edu.ar.
authors.forename: C Manuel
authors.initials: CM
authors.lastname: Carlevaro
authors.affiliation: Instituto de Física de Líquidos y Sistemas Biológicos, 59 Nro. 789, 1900 La Plata, Argentina; Instituto de Ingeniería y Agronomía, Universidad Nacional Arturo Jauretche, 1888 Florencio Varela, Buenos Aires, Argentina. Electronic address: rirastorza@iflysib.unlp.edu.ar.
authors.forename: Ramiro M
authors.initials: RM
authors.lastname: Irastorza
authors.affiliation: Instituto de Física de Líquidos y Sistemas Biológicos, 59 Nro. 789, 1900 La Plata, Argentina; Grupo de Aplicaciones Matemáticas y Estadísticas de la Facultad de Ingeniería (GAMEFI), Universidad Nacional de La Plata, Calle 115 y 48, 1900 La Plata, Argentina. Electronic address: vericat@iflysib.unlp.edu.ar.
authors.forename: Fernando
authors.initials: F
authors.lastname: Vericat
mesh_terms: D000465:Algorithms; D000595:Amino Acid Sequence; D000596:Amino Acids / Q000737:chemistry / Q000235:genetics*; D003062:Codon / Q000737:chemistry / Q000187:drug effects* / Q000235:genetics*; D019143:Evolution, Molecular; D005815:Genetic Code / Q000235:genetics; D008957:Models, Genetic; D008958:Models, Molecular; D017433:Protein Structure, Secondary; D011506:Proteins / Q000737:chemistry / Q000235:genetics
chemical_list: D000596:Amino Acids; D003062:Codon; D011506:Proteins
keywords: Broken symmetry; Genetic code evolution; Hamilton quaternions; Protein folding