Assessing the Reliability of RNA folding Using Statistical Mechanics

We have analyzed the base-pair probability distribution of 16S and 16S-like and 23S and 23S-like ribosomal RNAs of Archaea, Bacteria, chloroplasts, mitochondria and Eukarya, as predicted by the partition function approach for RNA folding (McCaskill, 1990). A quantitative analysis of the reliability of RNA folding is done by comparing the base-pairing probability distributions with the structures predicted by comparative sequence analysis (comparative structure). We distinguish two factors that show a relationship to the reliability of RNA minimum free energy structure. The first factor is the dominance of one particular base-pair or the absence of base-pairing for a given base within the base-pairing probability distribution (BPPD): We characterize the BPPD per base, including the probability of not base-pairing, by its Shannon entropy (S). The S value indicates the uncertainty about the base-pairing of a base: low S values result from BPPDs that are strongly dominated by a single base-pair or by the absence of base-pairing. We show that bases with low S values have a relatively high probability that their Minimum Free Energy structure (MFE) corresponds to the comparative structure. The BPPDs of prokaryotes that live at high temperatures (thermophilic Archaea and Bacteria) have, calculated at 37 degrees C, lower S values, than the BPPDs or prokaryotes that live at lower temperatures (mesophilic and psychrophilic Archaea and Bacteria). This reflects an adaptation of the ribosomal RNAs to the environmental temperature. A second factor that is important to consider with regard to the reliability of MFE folding is a variable degree of applicability of the thermodynamic model of RNA folding for different groups of RNAs. Here we show that among the bases that show low S values, the Archaea and Bacteria have similar, high probabilities (.96 and .94 in 16S and .93 and .91 in 23S, respectively) that the MFE corresponds to the comparative structure. These probabilities are lower in the chloroplasts (16S .91, 23S .79), mitochondria (16S-like .89, 23S-like .69) and Eukarya (18S .81, 28S .86). Key words. RNA secondary structure, RNA folding, Boltzmann distribution, base-pairing probability distribution, ribosomal RNA