Expected degree for RNA secondary structure networks

TL;DR

This paper introduces RNAexpNumNbors, an algorithm to compute the expected degree of RNA secondary structure networks, revealing insights into structural diversity and differences from minimum free energy structures.

Contribution

The first algorithm to efficiently compute the expected number of neighbors in RNA secondary structure networks, applicable to various RNA sequences.

Findings

Expected degree is lower than the MFE structure for Rfam RNAs.

Structural RNAs have smaller expected degrees than random RNAs.

Expected degree does not correlate with standard structural diversity measures.

Abstract

Consider the network of all secondary structures of a given RNA sequence, where nodes are connected when the corresponding structures have base pair distance one. The expected degree of the network is the average number of neighbors, where average may be computed with respect to the either the uniform or Boltzmann probability. Here we describe the first algorithm, RNAexpNumNbors, that can compute the expected number of neighbors, or expected network degree, of an input sequence. For RNA sequences from the Rfam database, the expected degree is significantly less than the CMFE structure, defined to have minimum free energy over all structures consistent with the Rfam consensus structure. The expected degree of structural RNAs, such as purine riboswitches, paradoxically appears to be smaller than that of random RNA, yet the difference between the degree of the MFE structure and the expected degree is larger than that of random RNA. Expected degree does not seem to correlate with standard structural diversity measures of RNA, such as positional entropy, ensemble defect, etc. The program {\tt RNAexpNumNbors} is written in C, runs in cubic time and quadratic space, and is publicly available at http://bioinformatics.bc.edu/clotelab/RNAexpNumNbors.