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.
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.
“…The most frequently used similarity measures for analyzing differences or similarities between DNA sequences based their corresponding graphical representation are Euclidean distances or correlation angles. For papers that adopt graphical representation for DNA similarity analysis, the reader is referred to references [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21].…”
Methods for analyzing similarities among DNA sequences play a fundamental role in computational biology, and have a variety of applications in public health, and in the field of genetics. In this paper, a novel geometric and topological method for analyzing similarities among DNA sequences is developed, based on persistent homology from algebraic topology, in combination with chaos geometry in 4-dimensional space as a graphical representation of DNA sequences. Our topological framework for DNA similarity analysis is general, alignment-free, and can deal with DNA sequences of various lengths, while proving first-of-the-kind visualization features for visual inspection of DNA sequences directly, based on topological features of point clouds that represent DNA sequences. As an application, we test our methods on three datasets including genome sequences of different types of Hantavirus, Influenza A viruses, and Human Papillomavirus.
“…In general, an alignment-free method based on graphical representations of DNA sequences consists of two step, the first of which embed each DNA sequence into an Euclidean space, and the second is to compute the similarity matrix based on certain distance-based methods such as Euclidean distances or correlation angles to realize differences or similarities among DNA sequences. For papers using graphical representation for DNA similarity analysis, see, for example, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20].…”
In this paper, we propose another topological approach for DNA similarity analysis. For each DNA sequence, we transform it into a collection of vectors in 5-dimensional space in which all nucleotides of the same type, say A, C, G, T are on the same line in this 5D space. Based on this special geometric property, we combine this representation with tools in persistent homology to obtain only zeroth persistence diagrams as a topological representation of DNA sequences. Similarities between DNA sequences are signified via how close the representing zeroth persistence diagrams of the DNA sequences are, based on the Wasserstein distance of order zero, which provides a new method for analyzing similarities between DNA sequences. We test our methods on the datasets of Human rhinovirus (HRV) and Influenza A virus.
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