Abstract
The Chaos Game is an algorithm that can allow one to produce pictures of fractal structures. Considering that the four bases A, G, C, and T of DNA sequences can be divided into three classes according to their chemical structure, we propose different kinds of CGR-walk sequences. Based on CGR coordinates of random sequences, we introduce some invariants for the DNA primary sequences. As an application, we can make the examination of similarity/dissimilarity among the first exon ofβ-globin gene of different species. The results indicate that our method is efficient and can get more biological information.
Highlights
A DNA sequence is comprised of four different nucleotides: adenine (A), cytosine (C), guanine (G), and thymine (T)
In order to numerically characterize a DNA sequence given by the Chaos Game Representation (CGR), we treat the hurst exponent as the efficient invariant that is sensitive to this kind of graphical representation
DNA sequences play an important role in modern biological research because all the information of the hereditary and species evolution is contained in these macromolecules
Summary
A DNA sequence is comprised of four different nucleotides: adenine (A), cytosine (C), guanine (G), and thymine (T). Zhang [15] considered a DNA primary sequence termed as Z-curve Several researchers in their recent studies have outlined different kinds of graphical representation of DNA sequences based on 2D [16,17,18,19,20,21], 3D [22,23,24,25], 4D [26], 5D [27], and 6D [28] spaces. Gao and Xu [29] pointed out that the CGR-walk model can generate a model sequence and can be fitted with a long-memory ARFIMA (p, d, q) model reasonably They treated the four bases and ignored the hidden chemical classification of nucleotides. Abstract and Applied Analysis we make a comparison of the similarity and dissimilarity of the first exon of β-globin gene sequences derived from nine species
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