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

Abstract

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 \(\left(\log C_{\textrm{m}}\right)^{\alpha}\) with \(\alpha=1\,(0.5)\) 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.