New 2D graphical representation of DNA sequences

We consider a 2D graphical representations of DNA sequences, which avoids loss of information associated with crossing and overlapping of the corresponding curve. We outline an approach, which is based on the construction of a three-component vector whose components are the normalized leading eigenvalues of the L/L matrices associated with DNA. The examination of similarities/dissimilarities among the coding sequences of the first exon of beta-globin gene of different species illustrates the utility of the approach.     

A group of 3D graphical representation of DNA sequences based on dual nucleotides

Based on chemical properties of the neighboring dual nucleotides, we reduce a DNA sequence into four 3D graphical representations. Associating with the eigenvalues of the introduced covariance matrix and the introduced measure of similarity, we introduce an approach to make similarity analysis of DNA sequence. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Three‐unit semicircles curve: A compact 3D graphical representation of DNA sequences based on classifications of nucleotides

A new three‐dimensional graphical representation of DNA sequences, three‐unit semicircles (TUS)‐curve, which maps a given sequence into a dot sequences embedded in three‐unit semicircles, is proposed based on three biclassifications of nucleotides. TUS‐curve has the merit of compactness and could avoid the degeneracy and loss of information. The geometrical center of the curve, which indicates the distribution of base frequencies of the corresponding DNA sequence, is extracted and applied to analyze the similarity of various species. Phylogenetic tree of 11 species based on their first exons of β‐globin genes showed that the TUS‐curve is a powerful tool to get valuable biological information. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A class of 2D graphical representations of RNA secondary structures and the analysis of similarity based on them

Based on the concepts of cell and system of graphical representation, a class of 2D graphical representations of RNA secondary structures are given in terms of classifications of bases of nucleic acids. The representations can completely avoid loss of information associated with crossing and overlapping of the corresponding curve. As an application, we make quantitative comparisons for a set of RNA secondary structures at the 3'-terminus of different viruses based on the graphical representations. The examination of similarities/dissimilarities illustrates the utility of the approach.     

Coronavirus phylogeny based on 2D graphical representation of DNA sequence

A novel coronavirus has been identified as the cause of the outbreak of severe acute respiratory syndrome (SARS). Previous phylogenetic analyses based on sequence alignments show that SARS-CoVs form a new group distantly related to the other three groups of previously characterized coronaviruses. In this aritcle, a new approach based on the 2D graphical representation of the whole genome sequence is proposed to analyze the phylogenetic relationships of coronaviruses. The evolutionary distances are obtained through measuring the differences among the two-dimensional curves.     

On property of the invariant of graphical representations of DNA sequences

In this article, we consider the influence of variation of DNA sequence on the leading eigenvalue of graphical representation of the biological sequences. The research interpret the rationality of the graphical representation method that compare different DNA sequences. And we show the result on two different models that presented before.      

The graphical representation of protein sequences based on the physicochemical properties and its applications

Based on the chaos game representation, a 2D graphical representation of protein sequences was introduced in which the 20 amino acids are rearranged in a cyclic order according to their physicochemical properties. The Euclidean distances between the corresponding amino acids from the 2‐D graphical representations are computed to find matching (or conserved) fragments of amino acids between the two proteins. Again, the cumulative distance of the 2D‐graphical representations is defined to compare the similarity of protein. And, the examination of the similarity among sequences of the ND5 proteins of nine species shows the utility of our approach. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

A novel graphical representation of protein sequences and its application

On the basis of information on the evolution of the 20 amino acids and their physiochemical characteristics, we propose a new two-dimensional (2D) graphical representation of protein sequences in this article. By this representation method, we use 2D data to represent three-dimensional information constructed by the amino acids' evolution index, the class information of amino acid based on physiochemical characteristics, and the order of the amino acids appearing in the protein sequences. Then, using discrete Fourier transform, the sequence signals with different lengths can be transformed to the frequency domain, in which the sequences are with the same length. A new method is used to analyze the protein sequence similarity and to predict the protein structural class. The experiments indicate that our method is effective and useful.     

On 3D graphical representation of RNA secondary structures and their applications

In this article, we proposed a 3D representation of RNA secondary structures. Based on this representation, we outline an approach by constructing a 3-component vector whose components are the normalized leading eigenvalues of the L/L matrices associated with RNA secondary structure. The examination of similarities/dissimilarities among the secondary structure at the 3’-terminus of different viruses illustrates the utility of the approach.     

Analysis of similarity/dissimilarity of long DNA sequences based on three 2DD-curves

Some 2D graphical representations of DNA sequences have been reported by several authors, which give visual characterizations of DNA sequences. In this paper, we present a new 2D graphical representation of DNA sequences without degeneracy. Furthermore, we propose two methods for the visualization and analysis of long DNA sequences.     

RNA secondary structure 2D graphical representation without degeneracy

A two‐dimensional graphical representation (2DGRR) of RNA secondary structures using a two Cartesian coordinates system has been derived for mathematical denotation of RNA structure. The 2DGRR resolves structure degeneracy and avoids loss of information and the limitation that different structures correspond to the same curve. The RNA pseudo‐knots also can be represented as 2D graphical representations. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Novel numerical and graphical representation of DNA sequences and proteins

We have introduced novel numerical and graphical representations of DNA, which offer a simple and unique characterization of DNA sequences. The numerical representation of a DNA sequence is given as a sequence of real numbers derived from a unique graphical representation of the standard genetic code. There is no loss of information on the primary structure of a DNA sequence associated with this numerical representation. The novel representations are illustrated with the coding sequences of the first exon of β-globin gene of half a dozen species in addition to human. The method can be extended to proteins as is exemplified by humanin, a 24-aa peptide that has recently been identified as a specific inhibitor of neuronal cell death induced by familial Alzheimer's disease mutant genes.     

Highly compact 2D graphical representation of DNA sequences

Most 2D graphical representations of primary DNA sequences, while offering visual geometrical patterns for depicting sequences, do require considerable space if enough details of such representations are to be visible. In this contribution, we consider a highly compact graphical representation of DNA, which allows visual inspection and numerical characterization of DNA sequences having a large number of nucleic acid bases. The approach is illustrated on the DNA sequences of the first exon of human beta-globin. The same graphical approach not only allows one to depict differences in composition within a single DNA, but makes possible graphical representation of protein sequences, which have hitherto evaded similar 2D visual representations.     

Numerical characterization and similarity analysis of DNA sequences based on 2-D graphical representation of the characteristic sequences

Based on the classifications of the four nucleic acid bases, He and Wang reduced a DNA sequence to three binary sequences, which are called the characteristic sequences (J. Chem. Inf. Comput. Sci. 42 (2002) 1080). In this paper, we associate each characteristic sequence with a (b)L / (b)L matrix by giving a 2-D 'two horizontal lines' graphical representation, and thus obtain a 3-component vector with entries being the sums of the maximal and minimal eigenvalues of the (b)L / (b)L matrices. The introduced vector results in more simple characterizations and comparisons among the coding sequences of exon 1 of beta-globin gene of eleven different species.     

A 2D graphical representation of DNA sequence based on dual nucleotides and its application

From the perspective of the neighboring dual nucleotides, we introduce a novel 2D graphical representation of DNA sequences based on the magic circle, which correspond to 16 dual nucleotides. So, we can reduce a DNA sequence into a plot set in two‐dimensional space and get a two‐component vector relatively to the introduced covariance matrix. The utility of our approach can be illustrated by the examination of similarities/dissimilarities among the complete coding sequences of β‐globin gene belonging to 11 species. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009