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-

We give a comprehensive review of the algebraic approach to the genetic code originally proposed by two of the present authors, which aims at explaining the degeneracies encountered in the genetic code as the result of a sequence of symmetry breakings that have occurred during its evolution. We present the relevant background material from molecular biology and from mathematics, including the representation theory of (semi) simple Lie groups/algebras, together with considerations of general nature.

We study the structural properties, single-particle dynamics, and the charge transport in superionic and molten Ag2Se using the method of molecular dynamics. The calculations are based on a model of interionic potentials in which the ions interact through Coulomb interaction, steric repulsion, and charge–dipole interaction due to the large electronic polarizability of the selenium ions. In the superionic phase the Ag ions diffuse through a stable bcc lattice of Se atoms. Structural and dynamical correlations are studied at five temperatures in the superionic phase and three temperatures in the molten phase. Among the structural correlations the results are presented for partial pair distribution functions, coordination numbers, partial structure factors, bond angle distributions, and the wave vector and temperature dependence of the Bragg intensities. Detailed comparison with the neutron and x-ray single crystal diffraction results are made whenever possible. Diffuse neutron and x-ray scattering is calculated and investigated in detail in the vicinity of q0=(1.6,1,0). It is shown that the anisotropic disks of intensity arise entirely due to the collective motions of silver ions and that these correlations manifest in the q space at a point where the Se–Ag partial structure factor is nearly zero. The calculated temperature dependence of the self-diffusion constant of silver is in good agreement with the tracer diffusion measurements. The spectra of velocity autocorrelation functions and the frequency dependent ionic conductivity are calculated. The Haven’s ratio, derived both from the calculated self-diffusion and zero frequency limit of the ionic conductivity, is in good agreement with the experimental results of Okazaki. In the molten phase the calculated neutron structure factor is compared directly with the neutron diffraction experiments of Susman et al. The results for self-diffusion of silver and selenium ions in the molten phase and the frequency dependent ionic conductivity are also discussed.

The algebraic approach to the genetic code is further developed to incorporate global properties. As a result strong restrictions on the possibilities of assignment of amino acids and codons to representation vectors are found. Extending the search for symmetry breaking schemes to include nonconnected subgroups, a possibility is found based on the exceptional group G 2 .