Direct measurement of the full, sequence-dependent folding landscape of a nucleic acid

Abstract

Nucleic acid hairpins provide a powerful model system for understanding macromolecular folding, with free-energy landscapes that can be readily manipulated by changing the hairpin sequence. The full shapes of energy landscapes for the reversible folding of DNA hairpins under controlled loads exerted by an optical force clamp were obtained by deconvolution from high-resolution, single-molecule trajectories. The locations and heights of the energy barriers for hairpin folding could be tuned by adjusting the number and location of G:C base pairs, and the presence and position of folding intermediates were controlled by introducing single-nucleotide mismatches.

Fig. 1

(A) Cartoon of the experimental geometry, showing a DNA hairpin attached at each end to dsDNA handles bound to two optically trapped beads (not to scale). (B) Extension record of a hairpin designed with an energy barrier 6 bp from the base of the stem (sequence in inset) displays two states, folded (F) and unfolded (U). (C) Unfolding distance Δx (green) and distance to barrier from unfolded state Δx^‡_u (black) and folded state Δx^‡_f (blue), as a function of the expected transition state location. Data (shown with std. errs.) agree well with model predictions for Δx (yellow), Δx^‡_u (red), and Δx^‡_f (purple). (D) Lifetime of folded/unfolded states at F_1/2 as a function of the expected barrier height. The lifetime rises exponentially with the modeled barrier height, with slope (k_BT)⁻¹ (red line).

Fig. 2

(A) Extension record of hairpin with a T:T mismatch 7 bp from the base of the stem (sequence in inset). Fit of extension histogram to two Gaussian peaks reveals a third Gaussian residual (fits in red, residual in blue), indicating three states: unfolded (U), intermediate (I), and folded (F). (B) Blow-up of the extension record shows rapid, ∼5-nm fluctuations between F and I states. (C) Distance from F to U (black), F to I (red), and I to U (blue) plotted versus the mismatch location. The intermediate state location moves in concert with the mismatch, in good agreement with model predictions (light-colored solid circles in grey, orange, purple), indicating that the intermediate state consists of a hairpin folded up to the mismatch.

Fig. 3

Potential landscapes determined by deconvolution of the extension histograms based on thousands of folding transitions. Experimental probability distributions and associated free energy landscapes (black) were deconvolved to remove the effects of blurring caused by thermal motions of beads attached to the hairpin via elastic handles. Probability distributions (left column) and landscapes (right column) recovered by Gaussian deconvolution (red) have small residual errors (green), and agree well with energy landscapes predicted by the model (blue). (A) Hairpin with a transition state 18 bp from the base of the stem. (B) Hairpin with a transition state 6 bp from the base of the stem. (C) Hairpin with a T:T mismatch 7 bp from the base of the stem. (D) Hairpin with an unpatterned, 30-bp stem sequence.