A method for assessing the statistical significance of RNA folding.

We have developed a statistical method that is designed for analyzing potential RNA folded substructures. The statistical significance of RNA folding is assessed by the segment score. The segment score is defined as the difference between the lowest free energy calculated for the real biological sequence and the mean of the lowest free energies from random permutations of the real segment sequence, divided by the standard deviation of the random sample. This procedure was applied to the well-studied Escherichia coli 16S rRNA and potato spindle tuber viroid (PSTV) RNA. The results showed that the predictions of the locally significant secondary structures in these two molecules are in accord with the universally conserved local secondary structure elements (Gutell, Weiser & Noller, 1985, Prog. Nucl. Acid Res. molec. Biol. 32, 155-216; Riesner & Gross, 1985, A. Rev. Biochem. 54, 531-564). In addition, a statistical analysis indicated that the lowest free energies of a random sample set follow an approximately normal distribution. A reasonable size for the random sample set was determined statistically. Moreover, the statistical evaluation has been carried out using three different sets of energy rules--two sets (Salser, 1977, Cold Spring Harb. Symp. Quant Biol. 42, 985-1002; Freier, Kierzek, Jaeger, Sugimoto, Caruthers, Neilson & Turner, 1986, Proc. natn. Acad. Sci. U.S.A. 83, 9373-9377) take into account stacking energies and are based on experimental data and their computational extension (Salser, 1977)--the third set is a simplistic "unitary matrix" approach, where any base-pair is given a weight of "minus one" and an unpaired based is "zero". The Freier energy rules usually yield the strongest indication of significant folding region. However, the results derived from paired comparisons test don't provide sufficient evidence for concluding that a different set of energy rules is effective in changing the segment score level for local stem-loop structures in the 16S rRNA.