Ions and RNAs: Free Energies of Counterion-Mediated RNA Fold Stabilities.

We present an implicit ion model fo the calculation of the electrostatic free energies of RNA conformations in the presence of divalent counterions such as Mg(2+). The model was applied to the native and several non-native structures of the hammerhead ribozyme and the group I intron in Tetrahymena to study the stability of candidate unfolding intermediates. Based on a rigorous statistical mechanical treatment of the counterions that are closely associated with the RNA while handling the rest of the ions in the solution via a mean field theory in the Grand Canonical ensemble, the implicit ion model accurately reproduces the ordering of their free energies, correctly identifying the native fold as the most stable structure out of the other alternatives. For RNA concentrations in the range below 0.1 μM, divalent concentrations of ∼0.5 mM or above, and over a wide range of solvent dielectric constants, the equilibrium number of divalent ions associated with the RNA remains close to what is needed to exactly neutralize the phosphate negative charges, but the stability of compact RNA folds can be reversed when the divalent ion concentration is lower than ∼0.1 mM, causing the number of associated ions to underneutralize the RNA. In addition to calculating counterion-mediated free energies, the model is also able to identify potential high-affinity electronegative ion binding pockets on the RNA. The model can be easily integrated into an all-atom Monte Carlo RNA simulation as an implicit counterion model.