Background

Ribonucleic acid (RNA) molecules are important in the performance of biological processes in the cell.  Some of their known roles include protein synthesis and transport, catalysis, and chromosome replication and regulation.  Studies have shown that there are different types of RNA that perform the different biological functions.  These RNA molecules have a vast number of structures.  Using graph theory, we aim to describe and analyze these structures and apply the fingings to many important problems such as RNA design.  Our graphical representations are limited to RNA secondary elements.  Still, graph representation allows enumeration of RNA's repertoire.  Since we find that only few RNAs have been found compared to the number of possible topologies, these graphs will help the search of missing RNA structures and stimulate the production of RNAs in the laboratory.
 

Purpose

Our purpose is to classify and analyze existing RNA's according to their topological characteristics and to discovery structure/function relationships between RNAs.  We will further apply the findings to RNA search, design, and structure prediction.
 

Process

Our tree database utilizes graph theory by transforming secondary RNA structures into tree graphs.  These tree graphs provide a simplified image of what the actual secondary structures look like and so allow us to apply the tools of graph theory to study these graphs in more depth.  By using computational methods we calculate the corresponding Laplacian matrices and their eigenvalues for each graph.  The next step is to analyze the various eigenvalues and to search for clusters and relationships between the eigenvalues of an RNA found in nature and those for the RNA that have not been found yet.  Finally, these data and information will be applied to the design of RNA as well as to the search of RNA.
 

Database Description

The trees for the existing and non-existing RNAs are distinguished by color in the database.   In addition, the tree graphs have been organized according to two different methods.  In one method, the graphs are ordered by the number of vertices (in ascending order).  In the other classification method, graphs are ordered according to the RNA type.  You may look at all of the graphs with a particular number of vertices or of certain type at any one time.  In each classification, graphs are ordered by the second eigenvalue of their corresponding Laplacian matrix (i.e., in order of increasing compactness).  More information about a particular structure may be obtained by clicking on the graph.  Links to different parts of the rest of this database have been provided as well as links to other useful databases and programs.