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About Tree Graphs

Our RNA-As-Graphs (RAG) approach represents RNA secondary (2D) structures as undirected tree and dual graphs [5]. These coarse-grained representations reduce the complexity of the RNA 2D structure and offer an efficient, alternative method to study RNA structure.

Undirected tree graphs can be used to represent the 2D structure of an RNA molecule [6, 7]. All unpaired single stranded regions, such as hairpin loops, internal loops and bulges (with at least two nucleotides in either strand), junctions, and dangling ends are represented by a vertex (see images below). Dangling ends refer to exterior loop nucleotides adjacent to stems at the 5' and/or 3' end of an RNA sequence. An RNA stem with at least two canonical base pairs (AU, GC, and GU wobble) is represented by an edge connecting the vertices/loops. Single, isolated base pairs are ignored.

By defining additional vertices and edges, we convert the 2D tree graph into a 3D tree graph [1]. Besides adding two vertices to illustrate the 5' and 3' ends of each helix, vertices are also added to represent internal loops and bulges that contain less than two nucleotides in the strands. In contrast to a 2D tree graph, the edges of a 3D tree graph link two vertices representing each helix, or the loop vertices to the proximal end helical vertices. The length of an edge is scaled by the number of nucleotides in the corresponding helices and loops. The figure below shows the 2D and 3D tree graphs for a 57-nucleotide fragment of rRNA (PDB ID: 1DK1).

Representing RNA structure as 2D graphs allows us to use graph theory methods, such as graph-isomorphism, partitioning, and enumeration to analyze RNA structure [8]. We have used graph enumeration methods to generate tree graph topologies up to 13 vertices, and classified them into existing, RNA-like, and non RNA-like topologies by clustering techniques. [6, 9, 10].

Learn more about RNA tree graphs on the RAG Website