DNA sequence representation without degeneracy

Graphical representation of DNA sequence provides a simple way of viewing, sorting and comparing various gene structures. A new two-dimensional graphical representation method using a two- quadrant Cartesian coordinates system has been derived for mathematical denotation of DNA sequence. The two-dimensional graphic representation resolves sequences’ degeneracy and is mathematically proven to eliminate circuit formation. Given x-projection and y-projection of any point on the graphical representation, the number of A, G, C and T from the beginning of the sequence to that point could be found. Compared with previous methods, this graphical representation is more in-line with the conventional recognition of linear sequences by molecular biologists, and also provides a metaphor in two dimensions for local and global DNA sequence comparison.     

Two Dimensional Yau-Hausdorff Distance with Applications on Comparison of DNA and Protein Sequences

Comparing DNA or protein sequences plays an important role in the functional analysis of genomes. Despite many methods available for sequences comparison, few methods retain the information content of sequences. We propose a new approach, the Yau-Hausdorff method, which considers all translations and rotations when seeking the best match of graphical curves of DNA or protein sequences. The complexity of this method is lower than that of any other two dimensional minimum Hausdorff algorithm. The Yau-Hausdorff method can be used for measuring the similarity of DNA sequences based on two important tools: the Yau-Hausdorff distance and graphical representation of DNA sequences. The graphical representations of DNA sequences conserve all sequence information and the Yau-Hausdorff distance is mathematically proved as a true metric. Therefore, the proposed distance can preciously measure the similarity of DNA sequences. The phylogenetic analyses of DNA sequences by the Yau-Hausdorff distance show the accuracy and stability of our approach in similarity comparison of DNA or protein sequences. This study demonstrates that Yau-Hausdorff distance is a natural metric for DNA and protein sequences with high level of stability. The approach can be also applied to similarity analysis of protein sequences by graphic representations, as well as general two dimensional shape matching.     

A new 2-D graphical representation of DNA sequences and their numerical characterization

We consider a novel 2-D graphical representation of DNA sequences according to chemical structures of bases, reflecting distribution of bases with different chemical structure, preserving information on sequential adjacency of bases, and allowing numerical characterization. The representation avoids loss of information accompanying alternative 2-D representations in which the curve standing for DNA overlaps and intersects itself. Based on this representation we present a numerical characterization approach by the leading eigenvalues of the matrices associated with the DNA sequences. The utility of the approach is illustrated on the coding sequences of the first exon of human beta-globin gene.     

Mapping the Space of Genomic Signatures

We propose a computational method to measure and visualize interrelationships among any number of DNA sequences allowing, for example, the examination of hundreds or thousands of complete mitochondrial genomes. An "image distance" is computed for each pair of graphical representations of DNA sequences, and the distances are visualized as a Molecular Distance Map: Each point on the map represents a DNA sequence, and the spatial proximity between any two points reflects the degree of structural similarity between the corresponding sequences. The graphical representation of DNA sequences utilized, Chaos Game Representation (CGR), is genome- and species-specific and can thus act as a genomic signature. Consequently, Molecular Distance Maps could inform species identification, taxonomic classifications and, to a certain extent, evolutionary history. The image distance employed, Structural Dissimilarity Index (DSSIM), implicitly compares the occurrences of oligomers of length up to k (herein k = 9) in DNA sequences. We computed DSSIM distances for more than 5 million pairs of complete mitochondrial genomes, and used Multi-Dimensional Scaling (MDS) to obtain Molecular Distance Maps that visually display the sequence relatedness in various subsets, at different taxonomic levels. This general-purpose method does not require DNA sequence alignment and can thus be used to compare similar or vastly different DNA sequences, genomic or computer-generated, of the same or different lengths. We illustrate potential uses of this approach by applying it to several taxonomic subsets: phylum Vertebrata, (super)kingdom Protista, classes Amphibia-Insecta-Mammalia, class Amphibia, and order Primates. This analysis of an extensive dataset confirms that the oligomer composition of full mtDNA sequences can be a source of taxonomic information. This method also correctly finds the mtDNA sequences most closely related to that of the anatomically modern human (the Neanderthal, the Denisovan, and the chimp), and that the sequence most different from it in this dataset belongs to a cucumber.     

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

In this article, we introduce three 3D graphical representations of DNA primary sequences, which we call RY-curve, MK-curve and SW-curve, based on three classifications of the DNA bases. The advantages of our representations are that (i) these 3D curves are strictly non-degenerate and there is no loss of information when transferring a DNA sequence to its mathematical representation and (ii) the coordinates of every node on these 3D curves have clear biological implication. Two applications of these 3D curves are presented: (a) a simple formula is derived to calculate the content of the four bases (A, G, C and T) from the coordinates of nodes on the curves; and (b) a 12-component characteristic vector is constructed to compare similarity among DNA sequences from different species based on the geometrical centers of the 3D curves. As examples, we examine similarity among the coding sequences of the first exon of beta-globin gene from eleven species and validate similarity of cDNA sequences of beta-globin gene from eight species.     

A graphical notation for biochemical networks

A solid definition and comprehensive graphical representation of biological networks is essential for efficient and accurate dissemination of information on biological models. Several proposals have already been made toward this aim. The most well known representation of this kind is a molecular interaction map, or ‘Kohn Map’. However, although the molecular interaction map is a well-defined and compact notation, there are several drawbacks, such as difficulties in intuitive understanding of temporal changes of reactions and additional complexities arising from particular graphical representations. This article proposes several improvements to the molecular interaction map, as well as the use of the ‘process diagram’ to help understand temporal sequences of reactions.     

2-D graphical representation for characteristic sequences of DNA and its application

DNA sequencing has resulted in an abundance of data on DNA sequences for various species. Hence, the characterization and comparison of sequences become more important but still difficult tasks. In this paper, we first give a 2-D ladderlike graphical representation for the characteristic sequences of a DNA sequence, and then construct a 3-component vector, in which the normalized ALE-indices extracted from such three 2-D graphs via D/D matrices are individual components, to characterize the DNA sequence. The examination of similarities/dissimilarities among sequences of the beta-globin genes of different species illustrates the utility of the approach.     

Computing distribution of scale independent motifs in biological sequences

The use of Chaos Game Representation (CGR) or its generalization, Universal Sequence Maps (USM), to describe the distribution of biological sequences has been found objectionable because of the fractal structure of that coordinate system. Consequently, the investigation of distribution of symbolic motifs at multiple scales is hampered by an inexact association between distance and sequence dissimilarity. A solution to this problem could unleash the use of iterative maps as phase-state representation of sequences where its statistical properties can be conveniently investigated. In this study a family of kernel density functions is described that accommodates the fractal nature of iterative function representations of symbolic sequences and, consequently, enables the exact investigation of sequence motifs of arbitrary lengths in that scale-independent representation. Furthermore, the proposed kernel density includes both Markovian succession and currently used alignment-free sequence dissimilarity metrics as special solutions. Therefore, the fractal kernel described is in fact a generalization that provides a common framework for a diverse suite of sequence analysis techniques.     

Two-dimensional graphical representation of DNA sequences and intron-exon discrimination in intron-rich sequences

We have shown earlier that analysis of DNA sequences using atwo-dimensional graphical representation provides considerableinformation on new global sequence patterns and homologies,repeated structures, relative base abundances, probable evolutionarypaths and evolutionary divergence. We have also reported thatat a more micro level the graphical representation reveals distinctdifferences in the features of intron and exon segments of eukaryoticsequences. In this paper, the distinguishing features of theintron and exon segments are exploited to show, through severalexamples of different gene structures, that an averaging procedureover the slopes of the representative maps provides an easytechnique to differentiate between probable in Iron and exonregions. We thus expect that this method will enable a rapidsearch and preliminary indication of possible locations of proteincoding regions in long eukaryotic sequences.     

C-curve: A novel 3D graphical representation of DNA sequence based on codons

In this paper, a novel 3D graphical representation of DNA sequence based on codons is proposed. Since there is not loss of information due to overlapping and containing loops, this representation will be useful for comparison of different DNA sequences. This 3D curve will be convenient for DNA mutations comparison specially. In continues we give a numerical characterization of DNA sequences based on the new 3D curve. This characterization facilitates quantitative comparisons of similarities/dissimilarities analysis of DNA sequences based on codons.     

Directed graphs of DNA sequences and their numerical characterization

In this paper we (1) introduce a directed graphical representation of DNA primary sequences; (2) describe a scheme that transforms the directed graph of a DNA sequence into an upper triangular matrix; (3) investigate whether or not the existing matrix-based invariants of DNA sequences are compatible for the upper triangular matrix representation. The utility of our method is illustrated by an examination of the similarity between human and other seven species.     

Alignment-free comparison of genome sequences by a new numerical characterization

In order to compare different genome sequences, an alignment-free method has proposed. First, we presented a new graphical representation of DNA sequences without degeneracy, which is conducive to intuitive comparison of sequences. Then, a new numerical characterization based on the representation was introduced to quantitatively depict the intrinsic nature of genome sequences, and considered as a 10-dimensional vector in the mathematical space. Alignment-free comparison of sequences was performed by computing the distances between vectors of the corresponding numerical characterizations, which define the evolutionary relationship. Two data sets of DNA sequences were constructed to assess the performance on sequence comparison. The results illustrate well validity of the method. The new numerical characterization provides a powerful tool for genome comparison.     

A simple method to analyze the similarity of biological sequences based on the fuzzy theory

In this paper, we propose a simple method to analyze the similarity of biological sequences. By taking the average contents of biological sequences and their information entropies as the variables, the fuzzy method is used to cluster them. From the results of application, it finds that the method is relatively easy and rapid. Unlike other methods such as the graphical representation methods, which is usually very complex to compute some invariants of matric derived from graphical representation, our method pays more attention to the information of biological sequences themselves. Especially with the help of the software (SPSS), it seems to be very convenient. Therefore, it may be used to study the new biological sequences such as their evolution relationship and structures.     

拓扑指数在生物序列相似性比较中的应用

在生物序列的二维图形表示的基础上,利用Balaban指数和信息分布指数比较生物序列的相似性,我们以包括人类等9种不同物种的DNA序列和yar029w等6种蛋白质为例来说明该方法的使用．     

A protein map and its application

Graphical representation of gene sequences provides a simple way of viewing, sorting, and comparing various gene structures. Here we first report a two-dimensional graphical representation for protein sequences. With this method, we constructed the moment vectors for protein sequences, and mathematically proved that the correspondence between moment vectors and protein sequences is one-to-one. Therefore, each protein sequence can be represented as a point in a map, which we call protein map, and cluster analysis can be used for comparison between the points. Sixty-six proteins from five protein families were analyzed using this method. Our data showed that for proteins in the same family, their corresponding points in the map are close to each other. We also illustrate the efficiency of this approach by performing an extensive cluster analysis of the protein kinase C family. These results indicate that this protein map could be used to mathematically specify the similarity of two proteins and predict properties of an unknown protein based on its amino acid sequence.     

Computer-drawn faces characterizing nucleic acid sequences

A brief introduction to a rather unorthodox computer graphics characterization of DNA sequences is presented. This visual method of data reduction is accomplished by computer-drawn faces which function as multivariate representations sensitive to regularities and irregularities of the statistical properties of the sequence of bases. Various graphical methods of representing multivariate data using icons, or symbols, have been discussed previously. The system presented here is special in that it has as its primary focus the rapid characterization of a multidimensional data series using an interactive graphics system with a variety of controlling parameters.