New 2-D graphical representation of DNA sequences

Abstract

In this paper we present a novel 2-D graphical representation of DNA sequences in the first quadrant of Cartesian coordinate system. This representation has been mathematically proved to have a zero length of circuit, i.e. without degeneracy. Given any point considered in a DNA sequence, the number of A, T, G, and C from the starting point could be calculated based upon an iterative comparison method. Furthermore, we deduced the fractal dimension of our graphical representation, which can be used to classify DNA sequences. Using the advantage of our novel graphical representation, a new graphical representation of protein sequence has been suggested, which may represent codon by codon or amino acid by amino acid. To apply this new representation to the genetic codons, we found the property of double stochastic matrix for genetic code based matrix can be achieved as long as A=U and C=G in spite of any assigned positive numbers beside A=U=2 and C=G=3.