On the scale-free nature of RNA secondary structure networks

TL;DR

This study investigates whether RNA secondary structure networks are scale-free by developing efficient algorithms to analyze their connectivity, finding that while they visually resemble power-law distributions, statistical tests reject a true power-law fit.

Contribution

The paper introduces the first efficient algorithm to compute the connectivity density function for RNA secondary structures and examines preferential attachment in network expansion.

Findings

Connectivity data visually resembles a power-law distribution.

Statistical tests reject the hypothesis that RNA networks are truly scale-free.

Preferential attachment appears to occur during network growth.

Abstract

A network is scale-free if its connectivity density function is proportional to a power-law distribution. Scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the presence of a few highly connected hub nodes and a large number of small- degree nodes may provide alternate paths between any two nodes on average -- such robustness has been suggested in studies of metabolic networks, gene interaction networks and protein folding. A theoretical justification for why biological networks are often found to be scale-free may lie in the well-known fact that expanding networks in which new nodes are preferentially attached to highly connected nodes tend to be scale-free. In this paper, we provide the first efficient algorithm to compute the connectivity density function for the ensemble of all secondary structures of a user-specified length, and show both by computational and theoretical arguments that preferential attachment holds when expanding the network from length n to length n + 1 structures. Since existent power-law fitting software, such as powerlaw, cannot be used to determine a power-law fit for our exponentially large RNA connectivity data, we also implement efficient code to compute the maximum likelihood estimate for the power-law scaling factor and associated Kolmogorov-Smirnov p-value. Statistical goodness-of-fit tests indicate that one must reject the hypothesis that RNA connectivity data follows a power-law distribution. Nevertheless, the power-law fit is visually a good approximation for the tail of connectivity data, and provides a rationale for investigation of preferential attachment in the context of macromolecular folding.