Theory for RNA Folding, Stretching, and Melting Including Loops and Salt

Secondary structure formation of nucleic acids strongly depends on salt concentration and temperature. We develop a theory for RNA folding that correctly accounts for sequence effects, the entropic contributions associated with loop formation, and salt effects. Using an iterative expression for the partition function that neglects pseudoknots, we calculate folding free energies and minimum free energy configurations based on the experimentally derived basepairing free energies. The configurational entropy of loop formation is modeled by the asymptotic expression c In m, where m is the length of the loop and c the loop exponent, which is an adjustable constant. Salt effects enter in two ways: first, we derive salt-induced modifications of the free energy parameters for describing basepairing, and second, we include the electrostatic free energy for loop formation. Both effects are modeled on the Debye-Huckel level including counterion condensation. We validate our theory for two different RNA sequences. For tRNA-phe, the resultant heat capacity curves for thermal denaturation at various salt concentrations accurately reproduce experimental results. For the P5ab RNA hairpin, we derive the global phase diagram in the three-dimensional space spanned by temperature, stretching force, and salt concentration and obtain good agreement with the experimentally determined critical unfolding force. We show that for a proper description of RNA melting and stretching, both salt and loop entropy effects are needed.