On the similarity/dissimilarity of DNA sequences based on 4D graphical representation

Abstract

In this paper, we propose a new 4D graphical representation of DNA primary sequences based on the Z-curve theory. The advantage of our approach is that it has the similar biological significance with the Z-curve, and it does not lose any biological information of the sequence. The geometrical centers of the 4D graphical representation of DNA sequences are used as the numerical characterizations, and the examination of similarities/dissimilarities about the coding sequences of the first exon of β-globin genes of eleven different species shows that this approach can provide satisfactory results. DNA sequences, 4D graphical representation, similarities/dissimilarities Citation:Tang X C, Zhou P P, Qiu W Y. On the similarity/dissimilarity of DNA sequences based on 4D graphical representation.DNA has been known as the physical basis for the storage and delivery of genetic information, and the connection and arrangement of its constituent bases (adenine (A), guanine (G), thymine (T) and cytosine (C)), that is, DNA sequence, plays a crucial role in determining the characteristics of organism. The analysis of DNA sequence has attracted a lot of interest in recent years due to its significant importance in the realization of the functions gene takes on [1]. Graphical representation of DNA sequence has now been a powerful tool in the investigation of gene sequences [2-17], because it can offer visual inspection of data, and facilitate the analysis, comparison and recognition of DNA sequences as well as the differences in their structures. Several authors proposed different 2D or 3D graphical representations of DNA sequences [2][3][4][5][6][7]. However, both 2D and 3D graphical representations are accompanied with some loss of biological information due to overlapping and crossing of the curve representing DNA with itself and, an arbitrary decision with respect to the choice of the direction for the four bases [8][9][10][11][12][13][14][15]18]. Based on previous studies, Liao et al. [8][9][10][11][12][13][14][15] presented many graphical representations. These methods have overcome the aforementioned limitations. In addition, the concept of geometrical center is introduced into these nonsingular methods, and various similarity/dissimilarity matrices are constructed for the comparison of the similarity/dissimilarity of DNA sequence. Zhang et al. [16,17] created the Z-curve to describe DNA sequences. It can excellently characterize DNA sequence and not cause any loss of biological information of the sequence. Inspired by the idea of the Z-curve, we propose a new 4D graphical representation of DNA sequences in this work. It can also represent the biological characteristics of DNA sequences nicely, and more importantly, it avoids loss of information in the transfer from a DNA sequence to its geometrical representation.

Three 3D graphical representations of DNA primary sequences based on the classifications of DNA bases and their applications

“…The Z-curve is a 3D graphical representation and it has clear biological implication. However, as pointed out by Tang et al (2010), the Z-curve representation has a defeat that it might cause a loop in the resulting spatial curve if the frequencies of the four bases present in the sequence are the same. Randic et al (2000) presented another 3D graphical representation method, but the limitation in forms of crossing and overlapping of the spatial curve representing a DNA sequence still remains.…”

Analysis of Similarities/Dissimilarities of DNA Sequences Based on Segment of Triplets

“…Similar results have been obtained in other papers by different approaches. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] For testing the validity of our method, the existing results of the examination of the degree of similarity/dissimilarity of the coding sequences of -globin genes of several species with the coding sequence of the human -globin gene by means of approaches using alternative DNA sequence descriptors 7 10 12 14 are listed in Table III for comparison. And in Table III, to make comparison among the results of different methods easier, we utilize the results of "1 − Sim G H G S " as the final results of our work in Table III, where G H represents the DNA sequence of the Human -globin genes, and G S represents the DNA sequence of the -globin genes of species other than human.…”

“…Liao et al 16 Randic et al 17 and Aram et al 18 proposed different 3D graphical representation methods of DNA sequences respectively. Liao et al 19 Tang et al 20 and Chi et al 21 proposed different 4D graphical representation methods of DNA sequences respectively. And in addition, Liao et al 22 also proposed a kind of 5D representation method of DNA sequences, and so on.…”

A 2D Graphical Representation of the Sequences of DNA Based on Triplets and Its Application

“…Liao et al [20][21][22][23], Randic et al [24,25], Qi et al [26], Yu et al [27], and Aram et al [28] proposed different 3D graphical representation methods of DNA sequences, respectively. Liao et al [29], Tang et al [30], and Chi et al [31] proposed different 4D graphical representation methods of DNA sequences, respectively. In addition, Liao et al [32] also proposed a kind of 5D representation method of DNA sequences and so on.…”