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 homology 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.Comment: 14 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1307.375

BOOL-AN: A method for comparative sequence analysis and phylogenetic reconstruction

A novel discrete mathematical approach is proposed as an additional tool for molecular systematics which does not require prior statistical assumptions concerning the evolutionary process. The method is based on algorithms generating mathematical representations directly from DNA/RNA or protein sequences, followed by the output of numerical (scalar or vector) and visual characteristics (graphs). The binary encoded sequence information is transformed into a compact analytical form, called the Iterative Canonical Form (or ICF) of Boolean functions, which can then be used as a generalized molecular descriptor. The method provides raw vector data for calculating different distance matrices, which in turn can be analyzed by neighbor-joining or UPGMA to derive a phylogenetic tree, or by principal coordinates analysis to get an ordination scattergram. The new method and the associated software for inferring phylogenetic trees are called the Boolean analysis or BOOL-AN

Graphical Representation of Biological Sequences

Sequence comparison is one of the most fundamental tasks in bioinformatics. For biological sequence comparison, alignment is the most profitable method when the sequence lengths are not so large. However, as the time complexity of the alignment is the square order of the sequence length, the alignment requires a large amount of computational time for comparison of sequences of large size. Therefore, so-called alignment-free sequence comparison methods are needed for comparison between such as whole genome sequences in practical time. In this chapter, we reviewed the graphical representation of biological sequences, which is one of the major alignment-free sequence comparison methods. The notable effects of weighting during the course of the graphical representation introduced first by the author and co-workers were also mentioned

Numerical characterization of protein sequences based on the generalized Chou\u27s pseudo amino acid composition

The technique of comparison and analysis of biological sequences is playing an increasingly important role in the field of Computational Biology and Bioinformatics. One of the key steps in developing the technique is to identify an appropriate manner to represent a biological sequence. In this paper, on the basis of three physical-chemical properties of amino acids, a protein primary sequence is reduced into a six-letter sequence, and then a set of elements which reflect the global and local sequence-order information is extracted. Combining these elements with the frequencies of 20 native amino acids, a (21+λ) dimensional vector is constructed to characterize the protein sequence. The utility of the proposed approach is illustrated by phylogenetic analysis and identification of DNA-binding proteins

Numerical Characterization of DNA Sequence Based on Dinucleotides

Sequence comparison is a primary technique for the analysis of DNA sequences. In order to make quantitative comparisons, one devises mathematical descriptors that capture the essence of the base composition and distribution of the sequence. Alignment methods and graphical techniques (where each sequence is represented by a curve in high-dimension Euclidean space) have been used popularly for a long time. In this contribution we will introduce a new nongraphical and nonalignment approach based on the frequencies of the dinucleotide XY in DNA sequences. The most important feature of this method is that it not only identifies adjacent XY pairs but also nonadjacent XY ones where X and Y are separated by some number of nucleotides. This methodology preserves information in DNA sequence that is ignored by other methods. We test our method on the coding regions of exon-1 of β–globin for 11 species, and the utility of this new method is demonstrated

A Novel Model for DNA Sequence Similarity Analysis Based on Graph Theory

Determination of sequence similarity is one of the major steps in computational phylogenetic studies. As we know, during evolutionary history, not only DNA mutations for individual nucleotide but also subsequent rearrangements occurred. It has been one of major tasks of computational biologists to develop novel mathematical descriptors for similarity analysis such that various mutation phenomena information would be involved simultaneously. In this paper, different from traditional methods (eg, nucleotide frequency, geometric representations) as bases for construction of mathematical descriptors, we construct novel mathematical descriptors based on graph theory. In particular, for each DNA sequence, we will set up a weighted directed graph. The adjacency matrix of the directed graph will be used to induce a representative vector for DNA sequence. This new approach measures similarity based on both ordering and frequency of nucleotides so that much more information is involved. As an application, the method is tested on a set of 0.9-kb mtDNA sequences of twelve different primate species. All output phylogenetic trees with various distance estimations have the same topology, and are generally consistent with the reported results from early studies, which proves the new method\u27s efficiency; we also test the new method on a simulated data set, which shows our new method performs better than traditional global alignment method when subsequent rearrangements happen frequently during evolutionary history

TI2BioP — Topological Indices to BioPolymers. A Graphical– Numerical Approach for Bioinformatics

We developed a new graphical–numerical method called TI2BioP (Topological Indices to BioPolymers) to estimate topological indices (TIs) from two-dimensional (2D) graphical approaches for the natural biopolymers DNA, RNA and proteins The methodology mainly turns long biopolymeric sequences into 2D artificial graphs such as Cartesian and four-color maps but also reads other 2D graphs from the thermodynamic folding of DNA/RNA strings inferred from other programs. The topology of such 2D graphs is either encoded by node or adjacency matrixes for the calculation of the spectral moments as TIs. These numerical indices were used to build up alignment-free models to the functional classification of biosequences and to calculate alignment-free distances for phylogenetic purposes. The performance of the method was evaluated in highly diverse gene/protein classes, which represents a challenge for current bioinformatics algorithms. TI2BioP generally outperformed classical bioinformatics algorithms in the functional classification of Bacteriocins, ribonucleases III (RNases III), genomic internal transcribed spacer II (ITS2) and adenylation domains (A-domains) of nonribosomal peptide synthetases (NRPS) allowing the detection of new members in these target gene/protein classes. TI2BioP classification performance was contrasted and supported by predictions with sensitive alignment-based algorithms and experimental outcomes, respectively. The new ITS2 sequence isolated from Petrakia sp. was used in our graphical–numerical approach to estimate alignment-free distances for phylogenetic inferences. Despite TI2BioP having been developed for application in bioinformatics, it can be extended to predict interesting features of other biopolymers than DNA and protein sequences. TI2BioP version 2.0 is freely available from http://ti2biop.sourceforge.net/

On Map Representations of DNA

We have constructed graphical (qualitative and visual) representations of DNA sequences as 2D maps and their numerical (quantitative and computational) analysis. The maps are obtained by transforming the four-letter sequences (where letters represent the four nucleic bases) via a spiral representation over triangular and square cells grids into a four-color map. The so constructed maps are then represented by distance matrices. We consider the use of several matrix invariants as DNA descriptors for determining the degree of similarity of a selection of DNA sequences. (doi: 10.5562/cca2338