Salt Effects on the Thermodynamics of a Frameshifting RNA Pseudoknot under Tension

Because of the potential link between -1 programmed ribosomal frameshifting and response of a pseudoknot (PK) RNA to force, a number of single molecule pulling experiments have been performed on PKs to decipher the mechanism of programmed ribosomal frameshifting. Motivated in part by these experiments, we performed simulations using a coarse-grained model of RNA to describe the response of a PK over a range of mechanical forces (fs) and monovalent salt concentrations (Cs). The coarse-grained simulations quantitatively reproduce the multistep thermal melting observed in experiments, thus validating our model. The free energy changes obtained in simulations are in excellent agreement with experiments. By varying f and C, we calculated the phase diagram that shows a sequence of structural transitions, populating distinct intermediate states. As f and C are changed, the stem-loop tertiary interactions rupture first, followed by unfolding of the 3-end hairpin (I{rightleftharpoons}F). Finally, the 5-end hairpin unravels, producing an extended state (E{rightleftharpoons}I). A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as (log Cm) with = 1 (0.5) for E{rightleftharpoons}I (I{rightleftharpoons}F) transition. This relation is used to obtain the preferential ion-RNA interaction coefficient, which can be quantitatively measured in single-molecule experiments, as done previously for DNA hairpins. A by-product of our work is the suggestion that the frameshift efficiency is likely determined by the stability of the 5 end hairpin that the ribosome first encounters during translation.