Stem–loop formation drives RNA folding in mechanical unzipping experiments

Abstract

Accurate knowledge of RNA hybridization is essential for understanding RNA structure and function. Here we mechanically unzip and rezip a 2-kbp RNA hairpin and derive the 10 nearest-neighbor base pair (NNBP) RNA free energies in sodium and magnesium with 0.1 kcal/mol precision using optical tweezers. Notably, force–distance curves (FDCs) exhibit strong irreversible effects with hysteresis and several intermediates, precluding the extraction of the NNBP energies with currently available methods. The combination of a suitable RNA synthesis with a tailored pulling protocol allowed us to obtain the fully reversible FDCs necessary to derive the NNBP energies. We demonstrate the equivalence of sodium and magnesium free-energy salt corrections at the level of individual NNBP. To characterize the irreversibility of the unzipping–rezipping process, we introduce a barrier energy landscape of the stem–loop structures forming along the complementary strands, which compete against the formation of the native hairpin. This landscape correlates with the hysteresis observed along the FDCs. RNA sequence analysis shows that base stacking and base pairing stabilize the stem–loops that kinetically trap the long-lived intermediates observed in the FDC. Stem–loops formation appears as a general mechanism to explain a wide range of behaviors observed in RNA folding.

Folding Free Energy Determination of an RNA Three-Way Junction Using Fluctuation Theorems

“…In the presence of a misfolded state, the standard Crooks fluctuation theorem (CFT) [ 23 ] and its corollary, the Jarzynski equality (JE) [ 24 ], are not directly applicable. Instead, one must use the extended versions of the CFT and the JE (hereafter referred to as ECFT and EJE) that consider the formation of different competing structures besides the native one [ 21 , 27 , 28 ]. In addition, we have also used the Bennet’s acceptance ratio (BAR) method [ 29 ] to extract .…”

“…Instead, in pulling experiments, the force is ramped at a given rate and the unfolding/folding and binding/unbinding reactions are followed under nonequilibrium conditions. In pulling experiments, the barrier height is modulated with time, rendering the folding energy landscape accessible even for molecules with high kinetic barriers, such as long RNAs or proteins [ 18 , 19 , 20 , 21 , 22 ].…”

Nucleic Acid Thermodynamics Derived from Mechanical Unzipping Experiments

“…Unzipping data for long NA hairpins have been used to derive the formation free energies of the 10 NNBP motifs in DNA [ 33 , 34 ] and RNA [ 35 ]. To do this, we developed a Monte Carlo optimization algorithm that uses both the experimental data and the theoretical FDC prediction described in Section 3 [ 33 ].…”

“…Here, we briefly review the thermodynamics of DNA and RNA folding as obtained by developments in our lab over the past ten years that combine LOTs with suitable data analysis methods. In this way, it has been possible to measure DNA and RNA base-pair free-energies from mechanical unzipping experiments with high accuracy (0.1 kcal/mol) in different experimental conditions [ 33 , 34 , 35 ]. Unzipping consists of pulling apart the and ends on one side of a helical NA structure stabilized by complementary (Watson–Crick) base-pair interactions.…”

“…Therefore, thermodynamic measurements with force spectroscopy require accurate knowledge of the ideal elastic response of the NA chains, which can also be measured by pulling the individual single-strands [ 29 , 30 ]. Here, we discuss the experimental results obtained in our lab and interpret them in the framework of the barrier energy landscape (BEL) model recently introduced by us to explain the strong irreversibility observed in RNA unzipping experiments [ 35 ]. We also extend the BEL model to predict of the force–extension curves reported in studies of the non-specific secondary structure in single-stranded DNA [ 30 ].…”