Symmetries of deoxyribonucleic acid (DNA) and related molecules

Abstract

The basic groups and some atomic groups in polynucleotide long-chains of deoxyribonucleic acid (DNA) and ribonucleic acid (RNA) have been used as the basic structural unit to analyze their molecular symmetry. The basic groups have been treated as the same structural unit in spite of the fact that they have very different intrinsic characteristics. In this paper, we developed bi-double-valued H- and P-representations to distinguish between the various structural units in DNA and RNA. We simulated their molecular symmetries based on our earlier work on the symmetry analysis of cylinder and torus carbon nanotubes. The symmetric and antisymmetric components of some gene segments with some transformations have been calculated in the bi-double-valued HP-representation space. By analyzing the genetic code table, we investigated the distributive features of codons in corresponding H- and P-representations. The results indicate that some characteristics of H- and P-representation carry messages of the corresponding genetic processes in DNA. In addition, we analyzed some topologic features and Mobius twists of torus groups for circular DNA.