Correlation of RNA Secondary Structure Statistics with Thermodynamic Stability and Applications to Folding

Abstract

The accurate prediction of the secondary and tertiary structure of an RNA with different folding algorithms are dependent on several factors, including the energy functions. However, an RNA higher-order structure cannot be accurately predicted from its sequence based on a limited set of energy parameters. The inter- and intra-molecular forces between this RNA and other small molecules and macromolecules, in addition to other factors in the cell such as pH, ionic strength, and temperature influence the complex dynamics associated with a single stranded RNA's transitioning to its secondary and tertiary structure. Since all of the factors that affect the formation of an RNAs three-dimensional structure cannot be determined experimentally, statistically derived potential energy has been used in the prediction of protein structure. In the current work, we evaluate the statistical free energy of various secondary structure motifs, including base-pair stacks, hairpin loops, and internal loops, using their statistical frequencies obtained from the comparative analysis of more than 50 000 RNA sequences stored in the RNA Comparative Analysis Database (rCAD) at the Comparative RNA Web (CRW) Site. Statistical energies were computed from the structural statistics for several datasets. While the statistical energies for base-pair stacks correlate with experimentally derived free energy values, suggesting a Boltzmann-like distribution, variation is observed between different molecules and their location on the phylogenetic tree of life. Our statistical energies for several structural elements were utilized in the Mfold RNA folding algorithm. The combined statistical energies for base-pair stacks, hairpins and internal loop flanks results in a significant improvement in the accuracy of secondary structure prediction; however, the hairpin flanks contribute the most.

Statistical Potentials for Hairpin and Internal Loops Improve the Accuracy of the Predicted RNA Structure

“…However, this approach has been used in the prediction of protein structure 23; 24; 25; 26; 27; 28; 29 , suggesting that Woese's idea could have the potential to reveal free-energy values for RNA that are not easily discernable with experimental methods. Within the past few years, statistical potentials determined with comparative analysis 30; 31 for a few RNA structural elements were similar to the free energy values determined with experimental methods. The replacement of base pair stacking energetic parameters with statistical potentials generated from an analysis of RNA crystal structures showed similar prediction accuracies 30 .…”

“…Similar to previous studies 21; 31 , sensitivity has been used to gauge prediction accuracy. Sensitivity is defined as the number of canonical base pairs in the predicted minimal free-energy structure present in the comparative model divided by the total number of comparative canonical base pairs.…”

“…Previously, the base pair stack statistical potentials created with comparative data, on average, only slightly improved the prediction accuracy demonstrating that statistical potentials can generate analogous energetic parameters 31 . This minor improvement in the accuracy from the base pair stack statistical potentials was not as much as we anticipated.…”

“…While the statistical potentials for canonical base pair stacks resulted in a very minimal improvement in the accuracy of the predicted secondary structure, a larger improvement was observed when statistical potentials were determined for the nucleotides immediately flanking the ends of the helix and in small internal loops (1×1, 1×2, 2×2) 31 and used in place of the equivalent experimentally determined energetic parameters.…”

rCAD: A Novel Database Schema for the Comparative Analysis of RNA

“…Visit the CRW Site (http://www.rna.ccbb.utexas.edu/SAE/2D) for more presentations on structural statistics. Computing statistical potentials for RNA folding programs is one specific application of our structural statistics[29, 30]. …”