Distribution of graph-distances in Boltzmann ensembles of RNA secondary structures

TL;DR

This paper develops a polynomial-time dynamic programming method to compute the distribution of graph-distances in RNA secondary structures, providing insights into RNA spatial organization and functional domain interactions.

Contribution

It introduces an efficient algorithm for calculating graph-distance distributions in RNA structures, advancing beyond naive high-complexity methods.

Findings

Polynomial-time algorithm for graph-distance distribution

Reduction of complexity from O(n^{11}) to O(n^{6}) in practical cases

Sampling approaches are recommended for large RNA molecules

Abstract

Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be separated by very long introns. Similar effects appear in the processing of RNA virus genomes. Albeit a crude measure, the distribution of spatial distances in thermodynamic equilibrium therefore provides useful information on the overall shape of the molecule can provide insights into the interplay of its functional domains. Spatial distance can be approximated by the graph-distance in RNA secondary structure. We show here that the equilibrium distribution of graph-distances between arbitrary nucleotides can be computed in polynomial time by means of dynamic programming. A naive implementation would yield recursions with a very high time complexity of O(n^11). Although we were able to reduce this to O(n^6) for many practical applications a further reduction seems difficult. We conclude, therefore, that sampling approaches, which are much easier to implement, are also theoretically favorable for most real-life applications, in particular since these primarily concern long-range interactions in very large RNA molecules.