Self-similarity of rRNA secondary structures: A clue to RNA folding

In this paper, we analyze helices in the secondary structures of the 16S and 23S rRNAs from the statistical physics perspective. The results of the analysis lead to propose a possible mechanism of the RNA folding based on the premise that the structure of RNA may bear a trace of its folding. We show that the frequency distribution of the helix contact order approximately follows a power-law, which implies that helices of large contact orders should inevitably exist. Furthermore, the frequencies of helix contact orders can be characterized by the multifractal. Comprehending the multifractality and the power-law of the distribution of the helix contact orders, we suggest a nearest-preferred helix formation as a mechanism for RNA folding via a random binary multiplicative process. The proposed process was supported by reconstructing the multifractal spectrum based on the transfer matrix theory and the binary tree representation of helices in the secondary structures. This justifies, at least partially if not entirely, the relevance of the proposed process as the kinetics of RNA folding.