Using an RNA secondary structure partition function to determine confidence in base pairs predicted by free energy minimization

Abstract

A partition function calculation for RNA secondary structure is presented that uses a current set of nearest neighbor parameters for conformational free energy at 37 degrees C, including coaxial stacking. For a diverse database of RNA sequences, base pairs in the predicted minimum free energy structure that are predicted by the partition function to have high base pairing probability have a significantly higher positive predictive value for known base pairs. For example, the average positive predictive value, 65.8%, is increased to 91.0% when only base pairs with probability of 0.99 or above are considered. The quality of base pair predictions can also be increased by the addition of experimentally determined constraints, including enzymatic cleavage, flavin mono-nucleotide cleavage, and chemical modification. Predicted secondary structures can be color annotated to demonstrate pairs with high probability that are therefore well determined as compared to base pairs with lower probability of pairing.

FIGURE 1.

Secondary structure prediction of E. coli 5S rRNA. The secondary structure predicted without (A) and with (B) constraints from chemical modification (Mathews et al. 2004) and enzymatic cleavage (Speek and Lind 1982). Base pairs in the structure determined by comparative sequence analysis (Szymanski et al. 2000) are shown with a heavy line. Structures are color annotated to indicate base pairing probabilities as shown in C. The structures were drawn using XRNA (http://rna.ucsc.edu/rnacenter/xrna/xrna.html). The predicted free energies are -53.0 and -46.4 kcal/mole for the nonconstrained structure (A) and the constrained structure (B), respectively.

FIGURE 2.

The structural requirements for the two-dimensional arrays W, WL, Wcoax, WMB, and WMBL. Branches are represented as a stem-loop, but any arrangement of nucleotides is allowed, that is, the stem-loop can be extended by a helix, internal loop, bulge loop, or multibranch loop. Shaded items are not required, but allowed. For example, WMBL(i,j) can be started with any number of branches and terminates with j as either a paired nucleotide, a 3′ dangling end, a terminal mismatch, or a mismatched nucleotide mediating a coaxial stack. W(i,j) can have any number of unpaired nucleotides 5′ or 3′ to a single helix. WL(i,j) can have any number of unpaired nucleotides 5′ to a single helix. WMB(i,j) can have any number of unpaired nucleotides 5′ or 3′ to two or more helices. WMBL(i,j) can have any number of unpaired nucleotides 5′ to two or more helices.