Nanomechanical measurements of the sequence-dependent folding landscapes of single nucleic acid hairpins

Abstract

Nucleic acid hairpins provide a powerful model system for probing the formation of secondary structure. We report a systematic study of the kinetics and thermodynamics of the folding transition for individual DNA hairpins of varying stem length, loop length, and stem GC content. Folding was induced mechanically in a high-resolution optical trap using a unique force clamp arrangement with fast response times. We measured 20 different hairpin sequences with quasi-random stem sequences that were 6-30 bp long, polythymidine loops that were 3-30 nt long, and stem GC content that ranged from 0% to 100%. For all hairpins studied, folding and unfolding were characterized by a single transition. From the force dependence of these rates, we determined the position and height of the energy barrier, finding that the transition state for duplex formation involves the formation of 1-2 bp next to the loop. By measuring unfolding energies spanning one order of magnitude, transition rates covering six orders of magnitude, and hairpin opening distances with subnanometer precision, our results define the essential features of the energy landscape for folding. We find quantitative agreement over the entire range of measurements with a hybrid landscape model that combines thermodynamic nearest-neighbor free energies and nanomechanical DNA stretching energies.

Fig. 1.

Measurement of hairpin folding/unfolding. (A) Illustration of the experimental geometry: A hairpin is attached by means of dsDNA handles to beads held in two traps (not to scale). (B) FEC for hairpin 20R55/4T, displaying WLC behavior of handles at low F (dotted red line) followed by hairpin unfolding at ≈13 pN. WLC fit to the contour length increase after hairpin unfolding (dotted blue line) gives 17.5 ± 1 nm. (C) DNA extension vs. time at constant F reveals two-state behavior. Fit of extension histogram (black) to two Gaussian curves (red) gives an opening distance of 18.0 ± 0.5 nm. (D) Unfolded state probability (black) varies with F according to two-state Boltzmann relation (red). (E) Lifetimes of folded (blue) and unfolded (black) states vary exponentially with force.

Fig. 2.

Hairpin energy landscape model. (A) Computed free energy for sequential unzipping of base pairs in the stem for hairpin 20R55/T4 at F = 0 based on mfold. (B) Energy landscape at F_1/2 before (dotted green line) and after (solid black line) smoothing due to ssDNA elasticity. Barrier is close to the unfolded state; its height (ΔG_1/2^‡) is dominated by loop length. Hairpin extension probability density (blue line) is further smoothed by dsDNA handle elasticity to create bead position probability density (red line).

Fig. 3.

Summary of results for hairpins with varied stem length (A–F), loop length (G–L), and stem GC content (M–R). Error bars represent sum of standard and systematic errors (experiment) or standard deviation of predictions over the full parameter set (model). (A, G, and M) Hairpin opening distance rises linearly with stem and loop length but is little changed with GC content (experiment, black; model, red). (B, H, and N) Unfolding force rises nonlinearly with stem length to a plateau at ≈25 bp, falls with loop length, and rises linearly with GC content. (C, I, and O) Unfolding free energy rises linearly with stem length and GC content but is little changed with loop length. Open circles show free energy of helix stacking only. (D, J, and P) Unfolding rate extrapolated to F = 0 decreases exponentially with increasing stem length and GC content but is little changed with loop length. (E, K, and Q) Folding lifetime at F_1/2 rises exponentially with loop length but depends much less strongly on stem length and GC content. (F, L, and R) Distance to transition state from folded state (experiment, blue; model, purple) rises linearly with stem length, whereas distance from unfolded state (experiment, black; model, red) rises linearly with loop length, consistent with a transition state located 1–2 bp from loop.