Some notes on 2-D graphical representation of DNA sequence

Some 2-D and 3-D graphical representations of DNA sequences have been given by Nandy, Leong and Mogenthaler, and Randic et al., which give visual characterizations of DNA sequences. In this paper, we presented a novel graphical representation of DNA sequences by taking four special vectors in 2-D Cartesian coordinate system to represent the four nucleic acid bases in DNA sequences, so that a DNA sequence is denoted on a plane by a directed walk. It is shown that the new graphical representation of DNA sequences has lower or nondegeneracy.     

On a 3-D representation of DNA primary sequences

We introduce a graphical representation of DNA primary sequences by taking four special vectors in a 3-D space to represent the four nucleic acid bases in DNA sequences, so that a DNA primary sequence is denoted in a 3-D space by a successive vector sequence which is a directed walk on the space. It is demonstrated that this representation has no overlap and intersection and allows numerical characterization.     

A naturally logical representation for DNA primary sequences

In this paper, we (1) introduce a logical representation (LR) for DNA primary sequences; (2) show relations between LR and some other representations including the characteristic sequences of a DNA sequence, Randic's 2-D, 4-D representations, and Z-curve (a 3-D graphical representation); and (3) outline the constructions of the S/S matrix specific for a logical sequence and its 2*2 condensed matrix.     

On 3-D graphical representation of DNA primary sequences and their numerical characterization

In this article we (1) outline the construction of a 3-D "graphical" representation of DNA primary sequences, illustrated on a portion of the human beta globin gene; (2) describe a particular scheme that transforms the above 3-D spatial representation of DNA into a numerical matrix representation; (3) illustrate construction of matrix invariants for DNA sequences; and (4) suggest a data reduction based on statistical analysis of matrix invariants generated for DNA. Each of the four contributions represents a novel development that we hope will facilitate comparative studies of DNA and open new directions for representation and characterization of DNA primary sequences.     

On a four-dimensional representation of DNA primary sequences

We consider a four-dimensional representation of DNA primary sequences by assigning to each of the four basic amino acids A, T, G, C directions along the four orthogonal coordinate axes. Advantages and limitations of the novel representation of DNA primary sequences are discussed, and the use of the 4-D representation is illustrated by constructing novel sequence invariants. Comparisons with the similarity/dissimilarity results based on 2-D and 3-D representations for a set of eight short DNA sequences corresponding to the first exon of beta globin in eight species, including human, are considered to illustrate the use of our novel sequence invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.     

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.     

DB-Curve: a novel 2D method of DNA sequence visualization and representation

The large number of bases in a DNA sequence and the cryptic nature of the 4-alphabet representation make graphical visualization of DNA sequences useful for biologists. However, existing 3D graphical representations are complicated, whereas existing 2D graphical representations suffer from high degeneracy, and many features in a DNA sequence cannot be visualized clearly. This Letter introduces a novel 2D method of DNA representation: the DB-Curve (Dual-Base Curve), which overcomes some of the limitations in existing 2D graphical representations. Many properties of DNA sequences can be observed and visualized easily using a combination of DB-Curves. The new representation can avoid degeneracy completely compared to existing 2D graphical representations of DNA sequences. Unlike 3D graphical representations, no 2D projection is required for the DB-Curve, and this allows for easier analysis of DNA sequences. The DB-Curve provides a useful graphical tool for the visualization and study of DNA sequences.     

H–L curve: A novel 2D graphical representation for DNA sequences

By assigning to four kinds of basic nucleotide A, T, G and C, respectively, four different two-component vectors, in which the first elements are constant (equal to 1) and the second elements are different from each other, we presented a 2D graphical representation of DNA primary sequences, which is mathematically proven to be not any circuit and associated with DNA sequences in a one-to-one manner and whose advantage is that it helps in identifying major difference among similar DNA sequences. Making use of the presented graphical representation, we analyzed DNA mutations between sequences.     

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 beta-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.     

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.     

On the Similarity of DNA Primary Sequences Based on 5-D Representation

We propose a 5-D representation of DNA sequences based on the classifications of the four basic acid bases A,T,G, and C. The use of the 5-D representation is illustrated by constructing sequence invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal. As an application, we make a comparison for the first exon of β-globin gene sequences belonging to eleven different species based on the 5-D representation.     

Using Huffman coding method to visualize and analyze DNA sequences

On the basis of the Huffman coding method, we propose a new graphical representation of DNA sequence. The representation can avoid degeneracy and loss of information in the transfer of data from a DNA sequence to its graphical representation. Then a multicomponent vector from the representation is introduced to characterize quantitatively DNA sequences. The components of the vector are derived from the graphical representation of DNA primary sequence. The examination of similarities and dissimilarities among the complete coding sequences of β-globin gene of 11 species and six ND6 proteins shows the utility of the scheme.     

Similarity analysis of DNA sequences based on the generalized LZ complexity of (0,1)-sequences

Based on the permutation of a binary alphabet, four generalized LZ complexities of a (0,1)-sequence are introduced. Since the logical representation of a DNA primary sequence includes four logical sequences, a DNA primary sequence can be characterized by a 16-D vector whose entries are the complexities corresponding to the logical sequences. The utility of the new quantitative characterization of DNA sequences is illustrated by an examination of the similarity among the full β-globin genes of 11 different species.     

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.     

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.      

A graphical method to construct a phylogenetic tree

A 3D graphical representation of DNA sequences, which has no circuit or degeneracy, is derived for mathematical denotation of DNA sequence. Based on this graphical representation, we propose a new sequence distance measure. We make use of the corresponding similarity matrix to construct a phylogenic tree by virtue of the fuzzy theory. The examination of phylogenic tree belong to eight species illustrates the utility of our approach. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

TB-curve, a New 2-D Graphical Representation of DNA Sequences

Based on the classifications of the four nucleic acid bases, we introduce a new 2-D method of DNA representation: TB-curve, which avoids loss of information accompanying alternative 2-D representation in which the curve standing for DNA overlaps and intersects itself. The method is illustrated on the coding sequence of the first exon of human beta-globin gene.     

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.     

2-D graphical representation of proteins based on virtual genetic code

We consider a novel 2-D graphical representation of proteins in which individual nucleic acids are represented as "spots" within a square frame distributed according to specific construction rules. The resulting "images" of proteins can not only serve to facilitate visual comparison of similarities and dissimilarities between lengthy protein sequences, but also offer a way for mathematical characterization of protein sequences, analogous to similar considerations for lengthy DNA sequences. Basically the approach is based on the concept of virtual genetic code, which is a hypothetical string of RNA nucleic acid bases, A, C, U and G, which generates reported protein sequences, without the knowledge of the actual genetic code that produces the protein.     

On the similarity of DNA primary sequences

We consider numerical characterization of graphical representations of DNA primary sequences. In particular we consider graphical representation of DNA of beta-globins of several species, including human, on the basis of the approach of A. Nandy in which nucleic bases are associated with a walk over integral points of a Cartesian x, y-coordinate system. With a so-generated graphical representation of DNA, we associate a distance/distance matrix, the elements of which are given by the quotient of the Euclidean and the graph theoretical distances, that is, through the space and through the bond distances for pairs of bases of graphical representation of DNA. We use eigenvalues of so-constructed matrices to characterize individual DNA sequences. The eigenvalues are used to construct numerical sequences, which are subsequently used for similarity/dissimilarity analysis. The results of such analysis have been compared and combined with similarity tables based on the frequency of occurrence of pairs of bases.