A Novel Method for Comparative Analysis of DNA Sequences by Ramanujan-Fourier Transform

Use of 3D chaos game representation to quantify DNA sequence similarity with applications for hierarchical clustering

A 3D chaos game is shown to be a useful way for encoding DNA sequences. Since matching subsequences in DNA converge in space in 3D chaos game encoding, a DNA sequence's 3D chaos game representation can be used to compare DNA sequences without prior alignment and without truncating or padding any of the sequences. Two proposed methods inspired by shape-similarity comparison techniques show that this form of encoding can perform as well as alignment-based techniques for building phylogenetic trees. The first method uses the volume overlap of intersecting spheres and the second uses shape signatures by summarizing the coordinates, oriented angles, and oriented distances of the 3D chaos game trajectory. The methods are tested using: (1) the first exon of the beta-globin gene for 11 species, (2) mitochondrial DNA from four groups of primates, and (3) a set of synthetic DNA sequences. Simulations show that the proposed methods produce distances that reflect the number of mutation events; additionally, on average, distances resulting from deletion mutations are comparable to those produced by substitution mutations.

Encoding and Decoding DNA Sequences by Integer Chaos Game Representation

DNA sequences are fundamental for encoding genetic information. The genetic information may be understood not only from symbolic sequences but also from the hidden signals inside the sequences. The symbolic sequences need to be transformed into numerical sequences so the hidden signals can be revealed by signal processing techniques. All current transformation methods encode DNA sequences into numerical values of the same length. These representations have limitations in the applications of genomic signal compression, encryption, and steganography. We propose a novel integer chaos game representation (inter-CGR or iCGR) of DNA sequences and a lossless encoding method DNA sequences by the iCGR. In the iCGR method, a DNA sequence is represented by the iterated function of the nucleotides and their positions in the sequence. Then the DNA sequence can be uniquely encoded and recovered using three integers from iCGR. One integer is the sequence length and the other two integers represent the accumulated distributions of nucleotides in the sequence. The integer encoding scheme can compress a DNA sequence by 2 bits per nucleotide. The integer representation of DNA sequences provides a prospective tool for sequence analysis and operations.

Detecting Periodicities in Eukaryotic Genomes by Ramanujan Fourier Transform

Ramanujan Fourier transform (RFT) nowadays is becoming a popular signal processing method. RFT is used to detect periodicities in exons and introns of eukaryotic genomes in this article. Genomic sequences of nine species were analyzed. The highest peak in the spectrum amplitude corresponding to each exon or intron is regarded as the significant signal. Accordingly, the periodicity corresponding to the significant signal can be also regarded as a valuable periodicity. Exons and introns have different periodic phenomena. The computational results reveal that the 2-, 3-, 4-, and 6-base periodicities of exons and introns are four kinds of important periodicities based on RFT. It is the first time that the 2-base periodicity of introns is discovered through signal processing method. The frequencies of the 2-base periodicity and the 3-base periodicity occurrence are polar opposite between the exons and the introns. With regard to the cyclicality of the Ramanujan sums, which is the base function of the transformation, RFT is suggested for studying the periodic features of dinucleotides, trinucleotides, and q nucleotides.

One novel representation of DNA sequence based on the global and local position information

One novel representation of DNA sequence combining the global and local position information of the original sequence has been proposed to distinguish the different species. First, for the sufficient exploitation of global information, one graphical representation of DNA sequence has been formulated according to the curve of Fermat spiral. Then, for the consideration of local characteristics of DNA sequence, attaching each point in the curve of Fermat spiral with the related mass has been applied based on the relationships of neighboring four nucleotides. In this paper, the normalized moments of inertia of the curve of Fermat spiral which composed by the points with mass has been calculated as the numerical description of the corresponding DNA sequence on the first exons of beta-global genes. Choosing the Euclidean distance as the measurement of the numerical descriptions, the similarity between species has shown the performance of proposed method.

Genomic signal processing for DNA sequence clustering

Genomic signal processing (GSP) methods which convert DNA data to numerical values have recently been proposed, which would offer the opportunity of employing existing digital signal processing methods for genomic data. One of the most used methods for exploring data is cluster analysis which refers to the unsupervised classification of patterns in data. In this paper, we propose a novel approach for performing cluster analysis of DNA sequences that is based on the use of GSP methods and the K-means algorithm. We also propose a visualization method that facilitates the easy inspection and analysis of the results and possible hidden behaviors. Our results support the feasibility of employing the proposed method to find and easily visualize interesting features of sets of DNA data.

Spectral-dynamic representation of DNA sequences

A graphical representation of DNA sequences in which the distribution of a particular base B=A,C,G,T is represented by a set of discrete lines has been formulated. The methodology of this approach has been borrowed from two areas of physics: spectroscopy and dynamics. Consequently, the set of discrete lines is referred to as the B-spectrum. Next, the B-spectrum is transformed to a rigid body composed of material points. In this way a dynamic representation of the DNA sequence has been obtained. The centers of mass of these rigid bodies, divided by their moments of inertia, have been taken as the descriptors of the spectra and, thus, of the DNA sequences. The performance of this method on a standard set of data commonly applied by authors introducing new approaches to bioinformatics (the first exons of β-globin genes of different species) proved to be very good.

On DNA numerical representations for genomic similarity computation

Genomic signal processing (GSP) refers to the use of signal processing for the analysis of genomic data. GSP methods require the transformation or mapping of the genomic data to a numeric representation. To date, several DNA numeric representations (DNR) have been proposed; however, it is not clear what the properties of each DNR are and how the selection of one will affect the results when using a signal processing technique to analyze them. In this paper, we present an experimental study of the characteristics of nine of the most frequently-used DNR. The objective of this paper is to evaluate the behavior of each representation when used to measure the similarity of a given pair of DNA sequences.

Identification of repeats in DNA sequences using nucleotide distribution uniformity

Repetitive elements are important in genomic structures, functions and regulations, yet effective methods in precisely identifying repetitive elements in DNA sequences are not fully accessible, and the relationship between repetitive elements and periodicities of genomes is not clearly understood. We present an ab initio method to quantitatively detect repetitive elements and infer the consensus repeat pattern in repetitive elements. The method uses the measure of the distribution uniformity of nucleotides at periodic positions in DNA sequences or genomes. It can identify periodicities, consensus repeat patterns, copy numbers and perfect levels of repetitive elements. The results of using the method on different DNA sequences and genomes demonstrate efficacy and accuracy in identifying repeat patterns and periodicities. The complexity of the method is linear with respect to the lengths of the analyzed sequences. The Python programs in this study are freely available to the public upon request or at https://github.com/cyinbox/DNADU.

Periodic power spectrum with applications in detection of latent periodicities in DNA sequences

Periodic elements play important roles in genomic structures and functions, yet some complex periodic elements in genomes are difficult to detect by conventional methods such as digital signal processing and statistical analysis. We propose a periodic power spectrum (PPS) method for analyzing periodicities of DNA sequences. The PPS method employs periodic nucleotide distributions of DNA sequences and directly calculates power spectra at specific periodicities. The magnitude of a PPS reflects the strength of a signal on periodic positions. In comparison with Fourier transform, the PPS method avoids spectral leakage, and reduces background noise that appears high in Fourier power spectrum. Thus, the PPS method can effectively capture hidden periodicities in DNA sequences. Using a sliding window approach, the PPS method can precisely locate periodic regions in DNA sequences. We apply the PPS method for detection of hidden periodicities in different genome elements, including exons, microsatellite DNA sequences, and whole genomes. The results show that the PPS method can minimize the impact of spectral leakage and thus capture true hidden periodicities in genomes. In addition, performance tests indicate that the PPS method is more effective and efficient than a fast Fourier transform. The computational complexity of the PPS algorithm is [Formula: see text]. Therefore, the PPS method may have a broad range of applications in genomic analysis. The MATLAB programs for implementing the PPS method are available from MATLAB Central ( http://www.mathworks.com/matlabcentral/fileexchange/55298 ).