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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 ($f$s) and monovalent salt concentrations ($C$s). 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 $3^{\prime}$-end hairpin ($\textrm{I}\rightleftharpoons\textrm{F}$). Finally, the $5^{\prime}$-end hairpin unravels, producing an extended state ($\textrm{E}\rightleftharpoons\textrm{I}$). A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as $\left(\log C_{\textrm{m}}\right)^α$ with $α=1\,(0.5)$ for $\textrm{E}\rightleftharpoons\textrm{I}$ ($\textrm{I}\rightleftharpoons\textrm{F}$) 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 $5^{\prime}$-end hairpin that the ribosome first encounters during translation.