Algebraic model for the evolution of the genetic code

Abstract

A search for symmetries based on the compact simple Lie algebras is performed to verify to what extent the genetic code is a manifestation of some underlying symmetry. An exact continuous symmetry group cannot be found to reproduce the present genetic code. However, a unique approximate symmetry group is compatible with codon assignment for the fundamental amino acids and the termination codon. In order to obtain the actual genetic code, the symmetry must be slightly broken.The storage of genetic information in a cell is governed by deoxyribonucleic acid (DNA). The DNA molecules are large polymers composed of deoxyribonucleotides which contain a base, a sugar (deoxyribose), and a phosphate. The sugar and the phosphate groups are responsible for the well known helical backbone of DNA, and the bases sequence carries the genetic information. In DNA there are only four bases derived from purine and pyrimidine. The purines, adenine {A) and guanine (G), and the pyrimidines, thymine iT) and cytosine (C), form the double helix through the base pairs C-G and A-T bonded, respectively, by 3 and 2 hydrogen bonds. This pairing rule manifests itself not only by the spatial conformation on DNA, but also by the equal rate of cytosine to guanine and adenine to thymine. It is this pairing rule that makes one of the helices the exact template of the other one, so replication can be understood.The transmission of information from DNA to protein building is a complex process of transcription and translation. In eucariotic cells DNA molecules are inside the nucleus of the cell and the proteins which they code are made outside of the nucleus in the citoplasma, more specifically in the ribosomes. The flow of information from DNA to the ribosomes requires another class of molecules, the ribonucleic acid (RNA) which are also constructed inside the nucleus. These molecules, rather than DNA, are the templates for protein synthesis; they leave the nucleus to the ribosomes to guide the synthesis.RNA are unbranched polymers, much smaller than DNA, and are also composed of a sugar (ribose), a phosphate group, and a base. Different from DNA's, RNA's subdivide into classes, messenger mRNA, transfer /RNA, and ribosomal rRNA. While /RNA and rRNA are part of the protein-synthesizing machinery, mRNA's are the information carrying intermediates in protein synthesis. The size of RNA varies from as few as 75 to many thousands of nucleotides. /RNA's are smaller and they carry amino acids (a.a.) in an active form to the ribosome for peptide-bond formation in a sequence determined by the mRNA template. Ribosomal RNA's are the major component of ribosomes, but their precise role in protein synthesis is not yet known. The concept of mRNA was formulated by Jacob and Monod 111 in 1961. The genetic information from DNA is transcripted by RNA polym-

An asymmetric underlying rule in the assignment of codons: Possible clue to a quick early evolution of the genetic code via successive binary choices

“…In this work, following others (Hornos and Hornos 1993;Bashford et al 1998;Balakrishnan 2002), the problem is revisited by searching for symmetries in the table of codons that might indicate whether or not this evolution could have been driven by an underlying mechanism (rule), thus converging much more rapidly than by random trial and error. As the clues to such a hypothetical mechanism are very scarce, it is common practice to look for patterns in either one of the key constituents of the codon identity, namely, tRNAs (Eigen et al 1989;Nicholas and McClain 1995) or aaRSs (Eriani et al 1990;Ribas de Pouplana and Schimmel 2001a), and their respective evolution deduced from phylogenetic methods (Nagel and Doolittle 1995;Woese et al 2000).…”

DNA, dichotomic classes and frame synchronization: a quasi-crystal framework

“…In any case, through the years, different approaches have shown that the genetic code is indeed a highly structured correspondence between codons and amino acids [20][21][22][23][24][25]. The most striking property of the genetic code is its degeneracy distribution-that is, the number of codons assigned to every amino acid.…”

Lie superalgebras and the multiplet structure of the genetic code. I. Codon representations

“…A new approach to the question was suggested in 1993 by Hornos & Hornos [1] who proposed to explain the degeneracy of the genetic code as the result of a symmetry breaking process. The demand of this approach can be compared to explaining the arrangement of the chemical elements in the periodic table as the result of an underlying dynamical symmetry which is reflected in the electronic shell structure of atoms.…”

“…They checked the tables of branching rules of McKay and Patera [2] for semisimple subalgebras of simple Lie algebras of rank ≤ 8. The most suitable multiplet structure found is derived from the codon representation of the symplectic algebra sp(6) by the following sequence of symmetry breakings: sp(6) ⊃ sp(4) ⊕ su(2) I ⊃ su(2) ⊕ su(2) ⊕ su(2) II ⊃ su(2) ⊕ u(1) ⊕ u (1) III/IV /V…”

“…

AbstractIt has been proposed [1] that the degeneracy of the genetic code, i.e., the phenomenon that different codons (base triplets) of DNA are transcribed into the same amino acid, may be interpreted as the result of a symmetry breaking process. In ref.

[1] this picture was developed in the framework of simple Lie algebras.

…”