Force Dependent Hopping Rates of RNA Hairpins can be Estimated from Accurate Measurement of the Folding Landscapes

TL;DR

This study demonstrates that accurate measurement of RNA hairpin folding landscapes and the use of Kramers' theory enable reliable estimation of force-dependent hopping rates, even with flexible handles in single-molecule experiments.

Contribution

The paper introduces a theoretical approach to estimate RNA hairpin hopping rates from equilibrium free energy profiles measured at specific forces, accounting for handle dynamics.

Findings

Accurate free energy profiles require stiff polymers.

Flexible handles can still yield reliable hopping rate estimates.

Using the equilibrium profile at the transition force allows force-dependent rate predictions.

Abstract

The sequence-dependent folding landscapes of nucleic acid hairpins reflect much of the complexity of biomolecular folding. Folding trajectories, generated using single molecule force clamp experiments by attaching semiflexible polymers to the ends of hairpins have been used to infer their folding landscapes. Using simulations and theory, we study the effect of the dynamics of the attached handles on the handle-free RNA free energy profile $F^o_{eq}(z_m)$, where $z_m$ is the molecular extension of the hairpin. Accurate measurements of $F^o_{eq}(z_m)$ requires stiff polymers with small $L/l_p$, where $L$ is the contour length of the handle, and $l_p$ is the persistence length. Paradoxically, reliable estimates of the hopping rates can only be made using flexible handles. Nevertheless, we show that the equilibrium free energy profile $F^o_{eq}(z_m)$ at an external tension $f_m$, the force ($f$) at which the folded and unfolded states are equally populated, in conjunction with Kramers' theory, can provide accurate estimates of the force-dependent hopping rates in the absence of handles at arbitrary values of $f$. Our theoretical framework shows that $z_m$ is a good reaction coordinate for nucleic acid hairpins under tension.