A Symmetrical Theory of DNA Sequences and Its Applications
Chun-Ting Zhang
Journal of Theoretical Biology,
v 187, n 3, p297-306 (August 7, 1997)
Abstract
A unified symmetrical theory of DNA sequences has been
established based on the basic symmetry of the
DNA bases. It is shown that the symmetry of DNA
sequences is inherently related to that of a cube and its
inscribed regular tetrahedron. A DNA group is
defined as a particular alternating group of order 4, in which
the permuted objects are four bases. The symmetry of
DNA sequences is described by the DNA group which
is isomorphic to the tetrahedral group. The matrix
representation for the DNA group has been obtained, and
used to establish the relationships between the transforms
of bases and the rotations of the tetrahedron. It is
found that any DNA sequence can be uniquely described by
three independent distributions, i.e., the
distributions of the bases of purine/pyrimidine, of
amino group/keto group and of strong/weak hydrogen
bonds along the sequence. The three distributions are
invariant in some sense under the transforms of the
DNA group, indicating that the three distributions are
inherent for the sequence. The mathematical format
of the theory lays a foundation for further development.
The applications of the theory to analyse some
DNA sequences are presented.
