A class of 2D graphical representations of RNA secondary structures and the analysis of similarity based on them

Abstract

Based on the concepts of cell and system of graphical representation, a class of 2D graphical representations of RNA secondary structures are given in terms of classifications of bases of nucleic acids. The representations can completely avoid loss of information associated with crossing and overlapping of the corresponding curve. As an application, we make quantitative comparisons for a set of RNA secondary structures at the 3'-terminus of different viruses based on the graphical representations. The examination of similarities/dissimilarities illustrates the utility of the approach.

Similarity of RNA secondary structures

“…While the relationships among AlMV-3, APMV-3, and PDV-3 are closer than that between them and other secondary structures. This is similar to the results reported by Liao et al, 23,24 Yao et al, 25 and Bai et al 26 To further check our result, we construct a relationship tree for the nine shadow sequences using Clustal X1.8 and NJplot (Fig. 2).…”

“…Recently, Randic et al proposed a sequence comparison approach that is grounded on characterization of biological sequences by ordered sets of invariants, rather than by a direct comparison of the sequences themselves. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] On the basis of this idea, Liao et al 23,24 and Yao et al 25 presented some graphical representations for RNA secondary structures, and used the leading eigenvalues of matrices constructed from the graphs as invariants to characterize and compare RNAs. Also, Bai et al 26 suggested a random walk representation and applied a numerical characterization of the graphical representation to compute the similarities of RNA secondary structures.…”

2D‐RNA‐coupling numbers: A new computational chemistry approach to link secondary structure topology with biological function

“…For instance one can cite the seminal works of Liao et al [38][39][40] in DNA sequences or Liu and Wang 41 in proteins. Yao et al 42 and Liao et al [43][44][45][46][47] also reported interesting representations for RNA although possibly because of the more branched nature of RNA secondary chemical structure topology representations of this kind are less common. However, in the case of RNAs accurate and timely methods can be applied to estimate folded secondary structure.…”

Use of statistical measures for analyzing RNA secondary structures

“…2 ) Hochsmann et al 8 RNAforester O (|F1||F2|deg(F1))deg(F2)) Liao et al 9 a selected width of a band O(n 2 1 + n 2 2 ) Yao et al 12 Leading eigenvalues of E matrix O(n 13 Leading eigenvalues of D/D matrix O(n 3 1 + n 3 2 + n 2 1 + n 2 2 ) Zhu et al 14 ; Bai and Wang 11 Leading eigenvalues of L/L matrix O(…”