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Graph Applications to RNA Structure and Function

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Biophysics of RNA Folding

Part of the book series: Biophysics for the Life Sciences ((BIOPHYS,volume 3))

Abstract

RNA’s modular, hierarchical, and versatile structure makes possible diverse, essential regulatory and catalytic roles in the cell. It also invites systematic modeling and simulation approaches. Among the diverse computational and theoretical approaches to model RNA structures, graph theory has been applied in various contexts to study RNA structure and function. Here, we describe graph-theoretical approaches for predicting and designing novel RNA topologies using graphical representations of RNA secondary structure, clustering tools, and a build-up procedure. Recent applications to noncoding RNA classification, RNA structure analysis and prediction, and novel RNA design are also described. As evident from the work of many groups in the mathematical and biological sciences, graph-theoretical approaches offer a fruitful avenue for discovering novel RNA topologies and designing new structural classes of RNAs.

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Acknowledgments

This work is supported by the National Science Foundation (DMS-0201160, CCF-0727001) and the National Institutes of Health (GM081410, GM100469).

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Authors and Affiliations

  1. Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Namhee Kim, Katherine Niccole Fuhr & Tamar Schlick

Authors
  1. Namhee Kim
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  2. Katherine Niccole Fuhr
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  3. Tamar Schlick
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Corresponding author

Correspondence to Tamar Schlick .

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Editors and Affiliations

  1. , Dept. of Chemistry and Biochemistry, University of Texas, Austin, 78712, Texas, USA

    Rick Russell

Glossary of Graph Theory Terminologies

Adjacency

The position of two vertices connected by an edge.

Adjacency Matrix

A square matrix that represents connectivity of a graph.

Directed Graph

A graph that depicts direction by its edges.

Domination Number

A graphical invariant that is sensitive to minor changes of the structure of a tree graph

Edge

A line that connects vertices. It can also be a loop.

Gaussian Radial Basis Function

In a neural network, the weight of the input G is a Gauss function G(r)  =  exp {−r 2/2}.

Graph

A mathematical structure that models relationships and consists of vertices and edges.

Graph Invariant

A property of a graph that depends on the isomorphism.

Graph Merge

A binary operation in which two graphs G1 and G2 are merged to form a new graph Guv, where vertex u in G1 and vertex v in G2 are identified together.

Isomorphic Graphs

When two graphs have corresponding vertices.

Junction

A point of connection between three or more edges.

Kernel Function

A weighting function applied to nonparametric function estimation.

Knot-component

A representation of the general secondary structure of pseudoknots in an elementary building block (similar to Nussinov linked-graph).

Laplacian Eigenvalues

Values calculated from the Laplacian matrix. The second smallest Laplacian eigenvalues is also known as the Fiedler value, as specifies the degree of compactness.

Multilayer Perception Network

A predictive model inspired by the action of biological neurons. The multilayer perception network contains an output, an input, and a hidden layer.

Planar Dual Graph

A 2D depiction of RNA where a vertex, hairpin loops, internal loops, and junctions show the stem is shown as loop edge.

Planar Tree Graph

A 2D depiction of RNA, where bulges, internal loops, hairpin, loops, junctions, and 3´ and 5´ ends are shown as vertices, connected by edges which represent stems.

Rooted Plane Tree Graph

A tree that has a specified root vertex, where subtree graphs of any given vertex is ordered.

Support Vector Machine

A classification model that constructs an N-dimensional hyperplane that separates data into two categories

Vertex

Represented by a node or a dot. The number of vertices is the order of the graph.

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Kim, N., Fuhr, K.N., Schlick, T. (2013). Graph Applications to RNA Structure and Function. In: Russell, R. (eds) Biophysics of RNA Folding. Biophysics for the Life Sciences, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4954-6_3

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