Abstract
A network is scale-free if its connectivity density function is proportional to a power-law distribution. It has been suggested that 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 many networks appear to be scale-free has been provided by Barabási and Albert, who argue 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 homopolymer secondary structures of a user-specified length—a highly nontrivial result, since the exponential size of such networks precludes their enumeration. 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. Hypothesis tests strongly indicate that homopolymer RNA secondary structure networks are not scale-free; moreover, this appears to be the case for real (non-homopolymer) RNA networks.
Highlights
The connectivity of a node v in a network is the number of nodes of s, connected to v by an edge
We use the algorithms described in previous sections to compute RNA secondary structure connectivity, determine optimal scaling factor α and minimum degree kmin for a power-law fit, perform Kolmogorov–Smirnov bootstrapping to determine the goodness-of-fit for parameters α, kmin
Since the pioneering work of Zipf on the scale-free nature of natural languages (Zipf 1949), various groups have found scale-free networks in diverse domains ranging from communication patterns of dolphins (McCowan et al 2002), metabolic networks (Jeong et al 2000), protein–protein interaction networks (Ito et al 2000; Schwikowski et al 2000), protein folding networks (Bowman and Pande 2010), genetic interaction networks (Tong et al 2004; Van Noort et al 2004) to multifractal time series (Budroni et al 2017)
Summary
The connectivity (or degree) of a node v in a network (or undirected graph) is the number of nodes (or neighbors) of s, connected to v by an edge. In Barabasi and Albert (1999), it was argued that preferential attachment of new nodes implies that the degree N (k) with which a node in the network interacts with k other nodes decays as a power-law, following N (k) ∝ k−α, for α > 1. This argument provides a plausible explanation for why diverse biological and physical networks appear to be scale-free. Various publications have suggested that the the following biological networks are scale-free: protein–protein interaction networks (Ito et al 2000; Schwikowski et al 2000), metabolic networks (Ma and Zeng 2003), gene interaction networks (Tong et al 2004), yeast co-expression networks (Van Noort et al 2004), and protein folding networks (Bowman and Pande 2010)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
