Stacking correlation length in single-stranded DNA

Abstract

Base stacking is crucial in nucleic acid stabilization, from DNA duplex hybridization to single-stranded DNA (ssDNA) protein binding. While stacking energies are tiny in ssDNA, they are inextricably mixed with hydrogen bonding in DNA base pairing, making their measurement challenging. We conduct unzipping experiments with optical tweezers of short poly-purine (dA and alternating dG and dA) sequences of 20-40 bases. We introduce a helix-coil model of the stacking-unstacking transition that includes finite length effects and reproduces the force-extension curves. Fitting the model to the experimental data, we derive the stacking energy per base, finding the salt-independent value $\Delta G_0^{ST}=0.14(3)$ kcal/mol for poly-dA and $\Delta G_0^{ST}=0.07(3)$ kcal/mol for poly-dGdA. Stacking in these polymeric sequences is predominantly cooperative with a correlation length of ∼4 bases at zero force . The correlation length reaches a maximum of ∼10 and 5 bases at the stacking-unstacking transition force of ∼10 and 20 pN for poly-dA and poly-dGdA, respectively. The salt dependencies of the cooperativity parameter in ssDNA and the energy of DNA hybridization are in agreement, suggesting that double-helix stability is primarily due to stacking. Analysis of poly-rA and poly-rC RNA sequences shows a larger stacking stability but a lower stacking correlation length of ∼2 bases.

Graphical Abstract

Figure 1.

Hairpin sequences, molecular construct and experimental setup. (A) Schematic depictions of the four hairpins studied. Gray boxes show the poly-dA regions of the sequence. Hairpins are named by the number of purines in the loop: H₀ (20bp stem and 20b dT-loop); H₂₀ (20bp stem and 20b purine-loop -1dG, 19dA-); H₄₀ (15bp stem and 40b purine-loop -1dG, 39dA-). L₄₀ consists of a 40dA loop without stem. (B) Scheme of the folded (top) and unfolded (bottom) states of the hairpins with the 48b BSO. C. Sketch of the optical tweezers setup. Left: a DNA hairpin is attached to two beads using specific linkages, one is held by a micropipette and the other by the optical trap. Right: the trap distance λ is moved away from the micropipette, while the applied force on the DNA hairpin increases, until it unfolds, and a force rip is observed in the FDC (top left).

Figure 2.

Unstacked ssDNA elasticity. (A) A typical FDC for H₀. In light green (dark blue blue) are shown the unfolding (folding) branches, with λ_F (λ_U) being the trap position (trap-pipette distance). The elastic contributions to the trap position λ at the F(U) branches are schematically depicted on top (bottom). Arrows indicate the jump in force when the molecule unfolds or folds, changing from one branch to another. These forces dictate the limits for applicability of the two branches method. (B) FEC of H₀ for 10 mM MgCl₂ (light yellow dots) and 1M NaCl (dark brown dots). Black lines show the fit of the TC model to the NaCl data. The inset shows a schematic depiction of the Thick Chain (TC) model, with its three parameters: the disk radius Δ, the spacing a, and the total contour length, L_c. (C) FECs per base x_ssDNA/N, for H₀ (red filled circles) and 7kbp hairpin [(blue empty triangles, Ref. (9)] for different NaCl concentration, with their fits to the TC model (continuous lines). The inset of the central panel shows the salt dependence of the fitting TC model parameters. Shadowed areas are the statistical errors obtained by bootstrapping (N = 500). The right inset shows how the theoretical FECs change with salt concentration. The error bars are the standard errors of the molecules studied at each condition (Supplementary Figure S3, Supplementary Table S6).

Figure 3.

poly-dA stacking (A) FECs of H₀ (yellow circles), H₂₀ (orange triangles), H₄₀ (blue filled rhombi) and L₄₀ (blue empty rhombi). (B) Re-scaled FECs of the molecules shown in panel A. (C) Re-scaled FECs for varying lengths: H₀ (re-scaled over its total number of bases) and H₂₀ and an average of H₄₀ and L₄₀ (re-scaled extensions of their poly-dA loops) with their respective fits. Color code as in b. Inset shows the comparison of the theoretical re-scaled FECs for the unstacked state (dashed) and the predicted for the infinite ST-model, compared with magnetic tweezers data (32) for a polypyrimidine and poly-dA ssDNA sequences.

Figure 4.

Stacking (ST) model. (A) Schematic depiction of the model for N = 20 bases. The bases are in either a stacked (dark blue) or unstacked (light yellow) state. The former are favored energetically by ε_ST, while adjacent bases are energetically favored (penalized) with γ_ST if they do (not) share state. As force increases, the longer unstacked state is energetically favored. (B) Theoretical FECs for varying lengths (color lines). Dashed and dotted lines represent the completely unstacked and unstacked elasticity, respectively. The black continuous line shows the model prediction for a domain of N → ∞. The inset shows the fraction of bases in the stacked state, ϕ_S, as a function of the force (same color code as the main panel).

Figure 5.

Salt dependence of base stacking. (A) FECs of the poly-dA loop for the H₄₀ (black squares) and poly-dA from Ref. (32) (empty red circles) for 10, 100 and 1000mM NaCl concentration. The gray dashed and dotted lines represent the elasticity of the unstacked and stacked state using the TC and WLC models, respectively. Solid curves are the fitting ones using the finite (black) and infinite (red) model (50mM and 500mM curves for H₄₀ shown in Supplementary Figure S8). (B) (top) Schematic depiction of the cooperativity between adjacent domains for the ST-γ₂ model. (bottom) Salt dependence of the stacking energy per base, ε_ST and interaction energies between purines (γ_ST) and the purine-pyrimidine boundary one (γ₂). (C) Results for the few kb mixed sequence of Ref. (32) containing the repetitive 28 b motif (AAGAGTATGGAAAGT AAAAGAAATAAAG) with three poly-purine regions of 9,6 and 8 b (bold letters) for 10, 100 and 1000 mM NaCl (orange triangles). Solid orange and black lines correspond to the fits of the finite ST-model and the ST-γ₂ models, respectively. The gray dashed and dotted lines represent the elasticity of the unstacked and stacked state using the TC and WLC models, respectively. D Correlation lengthfrom the ST model, Eq. (5), as a function of the force for 10, 100 and 1000 mM NaCl concentration. Inset: Theoretical predictions for the infinite model of the maximum stacking correlation length (, magenta) and the force at which it peaks () as a function of the salt concentration, C. Statistical uncertainties are shown as shadowed areas.

Figure 6.

Stacking in ssRNA compared to ssDNA. (A) Schematic depictions of the two hairpins with poly-dGdA motifs in the loop. (B) Re-scaled FECs per base for the dGdA loops of H_20GA (dark green), H_40GA (light green). As a comparison, data for the 20b and 40b dA loops (orange triangles and gray squares) is shown. Dashed lines represent the elasticity of the stacked and unstacked conformations. Continuous lines are fits of the ST model to the experimental data. (C) Re-scaled FECs per base for poly-rA (blue) and poly-rC (red) sequences from Reference (33). Continuous lines are fits of the ST model to the experimental data. In contrast, dashed lines represent the elasticity of the stacked (blue for poly-rA and red for poly-rC) and unstacked (black) conformations. (D) Correlation length from the ST model, Eq. (5), as a function of the force for poly-dA, poly-dGdA, poly-rA and polyrC. Statistical uncertainties are shown as shadowed areas. Error bars are the statistical errors from averaging different molecules (Supplementary Table S6).