Effect of elastic energy on the folding of an RNA hairpin

We analyse the folding and unfolding of an RNA hairpin using a conventional zipping model that includes both the free energy for RNA binding and the elastic free energy of the system. Unfolding under isotonic conditions (where we control the applied load) is known to occur at a well-defined critical load. In marked contrast, we find that unfolding under isometric conditions (where we control the extension of the hairpin) produces a series of sharp peaks in the average load as the stem of the hairpin starts to unzip base by base. A peak occurs when the elastic energy stored in the unzipped arms of the hairpin becomes so large that it is energetically favourable for the next base pair to unzip: the consequent increase in the contour length of the unzipped arms reduces their elastic energy and causes the average load to fall abruptly. However, as the contour length of the unzipped arms increases, the peaks become less distinct. Moreover, when we include the long DNA/RNA handles that have been used in single-molecule experiments, the unzipping of individual base pairs cannot be resolved at all. Instead, with the hairpin in the folded state, the average load increases with extension until the elastic energy stored in the handles makes it energetically favourable for the hairpin to unzip over a narrow range of extensions. The resultant yield point produces a mechanical hysteresis loop with a negative slope, as observed experimentally. Unfolding of the hairpin is also affected by the elastic energy stored in a compliant force transducer. We find that short, stiff handles and a stiff force transducer could improve the resolution of mechanical experiments on single molecules.