Overview

Visualizing RNA secondary structures and pseudoknot structures is essential to bioinformatics systems that deal with RNA structures. However, many bioinformatics systems use heterogeneous data structures and incompatible software components, so integration of software components into a system can be hindered by incompatibilities between the components of the system. We developed a new XML web service and web application program for visualizing RNA secondary structures with pseudoknots. Experimental results show that the PseudoViewer web service and web application are useful for resolving many problems with incompatible software components as well as for visualizing large-scale RNA secondary structures with pseudoknots of any type.

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Representation

Representation of pseudoknots
A drawing of an RNA secondary structure with a pseudoknot is a graph with inner cycles within the pseudoknot, and possibly outer cycles formed between the pseudoknot and other structural elements. In the typical arc representation of an RNA structure, a base pair is represented by an arc (Figure 1A). Layout of a pseudoknot starts with the arc representation of the pseudoknot (Figure 1A). The arcs representing the stems are put into two halfplanes separated by the backbone (Figures 1A and 1B). We convert the arc representation into a planar graph by putting opening stems next to their closing half stems, as shown in Figure 1E. In the visualization of the RNA structure, the backbone direction (either up or down) at base i  is opposite to that of base j  for each base pair (i, j) (Figures 1C and 1D). Note that in the final visualization of a pseudoknot (Figure 4E), the backbone direction changes from up to down for the stems in the lower halfplane, whereas the backbone direction changes from down to up for the stems in the upper halfplane. If there are stems that cannot be embedded into a planar graph, the stems are represented as dotted lines (see the example of E. coli  alpha operon mRNA in Examples page).

(A)	(B)	(C)
(D) (E)
Fig. 1 Representation of a pseudoknotted RNA structure. (A) Arc repre-sentation of base pairs. (B) Simplified arc representation, in which an arc represents a stem. (C) Layout of the stems in the lower halfplane to ensure that their backbone direction change from up to down. The stems in the upper halfplane are simply marked with arcs without considering the backbone direction. (D) Layout of the stems in the upper halfplane to ensure that their backbone direction changes from down to up. (E) A final visualization of the pseudoknotted RNA structure.

Representation of loops
The loop in a pseudoknot makes a path with the convex hulls of the structural elements in the pseudoknot. It requires less space than for just a line path and produces a more compact and aesthetic structure drawing (Figure 2).

(A)	(B)	(C)
Fig. 2 Representation of a loop in a pseudoknot. (A) A loop represented by a line. (B) Finding the convex hull of the structural elements in the pseudoknot. (C) A loop represented by the convex hull.