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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. May 2004, Volume 3, Number 5, 247-270 |
Symmetry Groups for the Rumer-Konopel'chenko-Shcherbak
"Bisections" of the Genetic Code and Applications
Tidjani Négadi
Internet Electron. J. Mol. Des. 2004, 3, 247-270
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Abstract:
We derive, in a new way, the discrete symmetry groups for (i)
the 4-base set {U, C, A, G}, (ii) the 16-doublet set and (iii) the
64-codon set, as collections of adjacency matrices of selected
graphs on the Wittmann sub-sets of the above respective sets. In
the case of the genetic code 64 codons system, we re-derive the
chain of groups D8 ⊃ V ⊃ C2 and show that the last member of
the chain, C2, leaves 16 codons of type GNN invariant and this
invariance is maintained across all species with respect to their
"non-standard" use of the genetic code, including nuclear
genomes as well as mitochondrial genomes. Moreover, we show
that this symmetry is suited, in fact it fits, the "bisections" of the
set of 64 codons, used by Shcherbak to derive many striking
arithmetical regularities and balances, involving the nucleon
numbers in the amino acids. Besides the symmetry aspects, our
next new result concerns the derivation, using only the concept
of matrix-norms in traditional linear algebra, of some (striking)
numbers which appear to be characteristic of the genetic code.
Finally, by using only the RNA-components, i.e., the four
nitrogenous bases mentioned above, we introduce matrices
encoding the hydrogen-bond attribute and other matrices
encoding a certain "molecular size index" for the bases and
derive the ratio of their trace, and of their norms, which appear to
be equal in both cases to Shcherbak's "Prime Quantum" 037.
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