Contact statistics highlight distinct organizing principles of proteins and RNA

Although both RNA and proteins have densely packed native structures, chain organizations of these two biopolymers are fundamentally different. Motivated by the recent discoveries in chromatin folding that interphase chromosomes have territorial organization with signatures pointing to metastability, we analyzed the biomolecular structures deposited in the Protein Data Bank and found that the intrachain contact probabilities, $P(s)$ as a function of the arc length $s$, decay in power-law $\sim s^{-\gamma}$ over the intermediate range of $s$, $10\lesssim s\lesssim 110$. We found that the contact probability scaling exponent is $\gamma\approx 1.11$ for large RNA ($N>110$), $\gamma\approx 1.41$ for small sized RNA ($N<110$), and $\gamma\approx 1.65$ for proteins. Given that Gaussian statistics is expected for a fully equilibrated chain in polymer melts, the deviation of $\gamma$ value from $\gamma=1.5$ for the subchains of large RNA in the native state suggests that the chain configuration of RNA is not fully equilibrated. It is visually clear that folded structures of large sized RNA ($N\gtrsim 110$) adopt crumpled structures, partitioned into modular multi-domains assembled by proximal sequences along the chain, whereas the polypeptide chain of folded proteins looks better mixed with the rest of the structure. Our finding of $\gamma\approx 1$ for large RNA might be an ineluctable consequence of the hierarchical ordering of the secondary to tertiary elements in the folding process.