Unfolding and melting of DNA (RNA) hairpins: the concept of structure-specific 2D dynamic landscapes

Abstract

A 2D free-energy landscape model is presented to describe the (un)folding transition of DNA/RNA hairpins, together with molecular dynamics simulations and experimental findings. The dependence of the (un)folding transition on the stem sequence and the loop length is shown in the enthalpic and entropic contributions to the free energy. Intermediate structures are well defined by the two coordinates of the landscape during (un)zipping. Both the free-energy landscape model and the extensive molecular dynamics simulations totaling over 10 mus predict the existence of temperature-dependent kinetic intermediate states during hairpin (un)zipping and provide the theoretical description of recent ultrafast temperature-jump studies which indicate that hairpin (un)zipping is, in general, not a two-state process. The model allows for lucid prediction of the collapsed state(s) in simple 2D space and we term it the kinetic intermediate structure (KIS) model.

Fig. 1

5′-ATCCTA-X_n-TAGGAT-3′ (n = 4; a), 5′-CCCCTT-X_n-AAGGGG-3′ (n = 5, 10, 13, 20, and 40; c), 5′-CCCCCC-X_n-GGGGGG-3′ (n = 13; d), 5′-TTCCTT-X_n-AAGGAA-3′ (n = 13; e), 5′-GCCCCG-X_n-CGGGGC-3′ (n = 13; f), and 5′-CGCCGT-X_n-ACGGCG-3′ (n = 13; g) hairpins and the (i, j)-coordinate space we used to parameterize their free energy landscapes (b). Native states of the hairpins reside at (0, 0) and (partially) unfolded states (i, j), i, j > 0, correspond to i broken base pairs on the loop end and j broken base pairs on the free end of the stem. Note that all of the points (i, 6 – i), i ≤ 6, situated on the diagonal of the grid are degenerate within the framework of our model as they represent the ensemble of totally unfolded states.

Fig. 2

free energy landscapes of the hairpin of Fig. 1a as obtained from the KIS model (note the dramatic temperature dependence of ΔG(i, j); a–d). At T = 350 K, likely dynamic trajectories visiting the intermediate state at (0, 2) are superimposed on the landscape (c). Most likely (un)folding pathways characteristic of the above landscapes are represented by 1D profiles with the adjacent (i, j)-states connected by dotted lines; note that the barrier for (un)zipping between the states, which may contribute to the overall barrier, is unknown (e). The behavior at T = 350 K is magnified in the lower right panel to illustrate the onset of the kinetic intermediate state (f).

Fig. 3

MD statistics of the hairpin of Fig. 1a. Time dependence of the fraction of remaining native contacts and probability of observing a kinetic intermediate state upon a T-jump as obtained from ensemble-convergent MD simulations are shown (a–d). The fraction of native contacts was least-squares fitted with double (a) and single (b–d) exponential functions. The fits were performed for t ≥ 100 ps to exclude the initial heating period, and the relaxation times obtained are given in each graph (note that horizontal time scales are different for all graphs). Also shown is the order in which native Watson-Crick contacts (labeled from 1 at the free end to 6 at the loop end of the stem) are first broken upon a T-jump as obtained from ensemble-convergent MD simulations (e,f). The symbol size is proportional to the fraction of each contact breaching (e). The mean and standard deviation of the distribution across the ensemble as obtained for T = 400, 500, 600, and 700 K using 60, 491, 492, and 500 MD trajectories, respectively, indicate that the unfolding order is temperature-independent to a good approximation (f).

Fig. 4

Effective free energy landscapes, ΔG_MD(i, j), of the hairpin of Fig. 1a as obtained from ensemble-convergent MD simulations for a variety of T-jumps (a–e). 1D profiles of ΔG_MD(i, j) along the most likely unfolding pathways are shown as well, and the magnitude of k_BT is indicated by the vertical bars for comparison (f).

Fig. 5

free energy landscapes of the hairpin of Fig. 1c (n = 13) as obtained from the KIS model (a–d). (Un)folding pathways characteristic of the above landscapes are represented by 1D profiles (e). The behavior at T = 360 K is magnified in the lower right panel to illustrate the onset of the kinetic intermediate state with a free energy of about −2 kJ· mol⁻¹ and a barrier for unzipping of about 5 kJ·mol⁻¹ (f).

Fig. 6

Effect of stem sequence permutations, Fig. 1d–g, of the hairpin of Fig. 1c (n = 13) on the free energy landscape as obtained from the KIS model (a–d). (Un)folding pathways characteristic of the above landscapes are represented by 1D profiles (e). The behavior for i + j < 6 is magnified in the lower right panel to illustrate the change in the unfolding barrier (f).

Fig. 7

Effect of the loop length on the free energy landscape of the hairpin of Fig. 1c (5 ≤ n ≤ 40) as obtained from the KIS model (a–d). (Un)folding pathways characteristic of the above landscapes are represented by 1D profiles (e). The behavior for i + j < 6 is magnified in the lower right panel to illustrate the change in the unfolding barrier (f).

Fig. 8

Spatiotemporal snapshots of an unfolding trajectory of the hairpin of Fig. 1a as obtained from MD simulations. The time elapsed and the (i, j)-assignment are presented for each snapshot. Notably, the stem end of the hairpin undergoes a repeated reversible (un)zipping during the course of unfolding, which is common among the MD trajectories for all temperatures reported here.