Force-dependent hopping rates of RNA hairpins can be estimated from accurate measurement of the folding landscapes

Abstract

The sequence-dependent folding landscapes of nucleic acid hairpins reflect much of the complexity of biomolecular folding. Folding trajectories, generated by 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 eqo(zm), where zm is the molecular extension of the hairpin. Accurate measurements of Feqo(zm) requires stiff polymers with small L/lp, where L is the contour length of the handle, and lp is the persistence length. Paradoxically, reliable estimates of the hopping rates can only be made by using flexible handles. Nevertheless, we show that the equilibrium freeenergy profile Feqo(zm) at an external tension fm, 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 zm is a good reaction coordinate for nucleic acid hairpins under tension. © 2008 by The National Academy of Sciences of the USA.