Temperature-dependent funnel-like DNA folding landscapes

Abstract

Nucleic acid hybridization in bimolecular and folding reactions is a fundamental kinetic process susceptible to water solvation, counterions, and chemical modifications with intricate enthalpy-entropy compensation effects. Such effects hinder the typically weak temperature dependencies of enthalpies and entropies quantified by the heat capacity change upon duplex formation. Using a temperature-jump optical trap, we investigate the folding thermodynamics and kinetics of DNA hairpins of varying stem sequences and loop sizes in the temperature range of 5-40○C. From a kinetic analysis and using a Clausius-Clapeyron equation in force, we derive the hybridization heat capacity changes ΔCp per GC and AT bp, finding 36 ± 3 and 29 ± 3 cal/(mol K), respectively. The almost equal values imply similar degrees of freedom arrest upon GC and AT bp formation during duplex formation. Folding kinetics on DNA hairpins of varying loop sizes show that the transition states (TS) in duplex formation have high free energies but low ΔCp values relative to the native state. Consequently, TS have low configurational entropy in agreement with the funnel-like energy landscape hypotheses. Our study underlines the validity of general principles in the hybridization and folding of nucleic acids determined by the TS's ΔCp values.

Graphical Abstract

Figure 1.

Single-molecule experimental setup. (A) Schematic for a hybridization and folding process. (B) Cartoon showing the studied DNA sequences. Dark (light) green circles denote guanine (cytosine) bases, and dark (light) squares denote adenine (thymine) bases. (C) The hairpin under study is tethered between two polystyrene beads with double-stranded DNA (dsDNA) handles. One bead is captured in the optical trap, while the other is fixed at the tip of a glass micro-pipette. (D) Hopping experiments. Force–time traces for the mixed-GA₃ hairpin at three selected temperatures: 6^○C (blue), 25^○C (green), and 45^○C (red). Notice the temperature dependence of the force and timescales of the two force levels (upper level, folded; lower level, unfolded). (E) Pulling experiments. Five illustrative force–distance curves for the mixed-GA₃ hairpin at three selected temperatures: 6^○C (blue), 25^○C (green), and 45^○C (red). Dark color curves are unfolding trajectories, while light color curves are folding trajectories. Notice the increase in hysteresis (shaded areas) upon decreasing temperature.

Figure 2.

Temperature-dependent kinetic rates. (A) Unfolding (k_→, solid symbols) and folding (k_←, empty symbols) kinetic rates for the poly(GC) (top), poly(AT) (middle), and mixed-GA₃ (bottom) hairpins measured at different temperatures. (B) Unfolding (top) and folding (bottom) kinetic rates of mixed-GA₃ (diamonds), mixed-GA₇ (circles), mixed-GA₁₉ (squares), and mixed-GT₁₉ (triangles) at 6^○C (dark blue), 8^○C (light blue), 16^○C (turquoise), 25^○C (green), 32^○C (khaki), and 37^○C (brown). Notice that k_→ overlap for all explored hairpins. In contrast, k_← for mixed-GA₇, mixed-GA₁₉, and mixed-GT₁₉ do not depend on temperature, while k_← for mixed-GA₃ is weakly T-dependent. (C) Coexistence force as a function of temperature for the poly(GC), poly(AT), and mixed-GA₃ (top) and for the mixed-GA₃, mixed-GA₇, mixed-GA₁₉, and mixed-GT₁₉ (bottom). The dashed lines are linear fits to determine ∂f_c/∂T, which, combined with equation (8) gives ΔS₀(T).

Figure 3.

Temperature-dependent folding free energy, entropy, and enthalpy. (A–C) ΔG₀(T), ΔS₀(T) and ΔH₀(T) for poly(GC) (green circles), poly(AT) (yellow square), and mixed-GA₃ (red diamonds). (D–F) ΔG₀(T), ΔS₀(T) and ΔH₀(T) for mixed-GA₃ (diamonds), mixed-GA₇ (circles), mixed-GA₁₉ (squares), and mixed-GT₁₉ (triangles) hairpins. The solid lines are fits to the Gibbs’s free energy definition [panels (A) and (D)] using the fits to equation (1b) [panels (B) and (E)] and equation (1a) [panels (C) and (F)].

Figure 4.

Temperature-dependent kinetic rates at zero force. (A) Schematics of a 1D folding free energy landscape highlighting the folding energy ΔG₀ and the energy difference at TS relative to N, ΔG^‡, and U, ΔG*. (B) Unfolding (left) and folding (right) kinetic rate at zero force for the poly(GC) (top) and poly(AT) (bottom) hairpins. The lines are fits to equations (11a) and (11b). (C) Unfolding kinetic rate at zero force considering the four mixed hairpins. The dashed line is a fit to equation (11a). (D) Folding kinetic rate at zero force for the mixed-GA₃ (top, left), mixed-GA₇ (top, right), mixed-GA₁₉ (bottom, left), and mixed-GT₁₉ (bottom, right) hairpins. Lines are fits to equation (11b). Notice that in all cases changes by >10 orders of magnitude, whereas changes over three orders of magnitude at most, in the same temperature range.

Figure 5.

Thermodynamic and kinetic fragilities and FEL. (A) Kinetic fragilities defined in equation (15) for the DNA hairpins and protein barnase for comparison (empty black circle). Note that μ_ΔS > 0 and μ_ΔH > 0 while , indicating a large configuration change between TS and U. (B) Thermodynamic fragility at T_m, equation (16), versus μ_ΔS. F ∼ 2–3 for all molecules, comparable to the values for glass-forming liquids, F ∼ 2 [73]. (C) 3D funnel free energy landscape highlighting N, TS, and U. The color palette grades the free energy difference from U (light color) to N (dark color). The distance relative to N in the orthogonal plane equals Δn (lower black double arrow).