A two-length-scale polymer theory for RNA loop free energies and helix stacking

The reliability of RNA secondary structure predictions is subject to the accuracy of the underlying free energy model. Mfold and other RNA folding algorithms are based on the Turner model, whose weakest part is its formulation of loop free energies, particularly for multibranch loops. RNA loops contain single-strand and helix-crossing segments, so we develop an enhanced two-length freely jointed chain theory and revise it for self-avoidance. Our resulting universal formula for RNA loop entropy has fewer parameters than the Turner/Mfold model, and yet simulations show that the standard errors for multibranch loop free energies are reduced by an order of magnitude. We further note that coaxial stacking decreases the effective length of multibranch loops and provides, surprisingly, an entropic stabilization of the ordered configuration in addition to the enthalpic contribution of helix stacking. Our formula is in good agreement with measured hairpin free energies. We find that it also improves the accuracy of folding predictions.