Single-molecule derivation of salt dependent base-pair free energies in DNA

Abstract

Accurate knowledge of the thermodynamic properties of nucleic acids is crucial to predicting their structure and stability. To date most measurements of base-pair free energies in DNA are obtained in thermal denaturation experiments, which depend on several assumptions. Here we report measurements of the DNA base-pair free energies based on a simplified system, the mechanical unzipping of single DNA molecules. By combining experimental data with a physical model and an optimization algorithm for analysis, we measure the 10 unique nearest-neighbor base-pair free energies with 0.1 kcal mol(-1) precision over two orders of magnitude of monovalent salt concentration. We find an improved set of standard energy values compared with Unified Oligonucleotide energies and a unique set of 10 base-pair-specific salt-correction values. The latter are found to be strongest for AA/TT and weakest for CC/GG. Our unique energy values and salt corrections improve predictions of DNA unzipping forces and are fully compatible with melting temperatures for oligos. The method should make it possible to obtain free energies, enthalpies, and entropies in conditions not accessible by bulk methodologies.

Fig. 1.

Experimental setup and results. (A) Molecular construct. A sequence of 6,838 bp obtained from λ-DNA is ligated to a tetraloop and two short handles of 29 bp each. (B) Experimental setup. The molecular construct is attached to two beads. The unzipping experiment is performed by moving the optical trap relative to the pipette. (C) Unfolfing (red) and refolding (green) curves filtered with a running average filter of 1 Hz bandwidth. There is always some hysteresis in the last rip. Pulling and relaxing are almost identical in the rest of the curve. Inset shows raw data (same color as before, blue curve is the average at bandwidth 1 Hz). (D) FDCs at various monovalent salt concentrations. (E) Elastic response of a 3 kb ssDNA molecule at various salts. Raw data of three molecules are shown (orange, green and blue curves). Red curve shows the best-fit to the elastic model.

Fig. 2.

Salt dependencies. (A, B) FDCs for the 6.8 kb sequence at 10 mM NaCl (A) and 1 M NaCl (B). Black curve, experimental measurements; blue curve, UO prediction; red curve, our fit; magenta curve, elastic response of the fully unzipped molecule. The theoretical FDC is calculated in equilibrium, which assumes that the bandwidth is 0 Hz and the experimental data is filtered at bandwidth 1 Hz. If data is filtered at higher frequencies (> 1 Hz), hopping between states is observed and the experimental FDC does not compare well with the theoretical FDC at equilibrium. If data is filtered at lower frequencies (< 1 Hz), the force rips are smoothed and hopping transitions are averaged out. (C) Dependence of mean unzipping force with salt concentration. Red points, experimental measurements for the 6.8 kb sequence; green curve, UO prediction for the 6.8 kb sequence; blue points, experimental measurements for the 2.2 kb sequence; orange curve, UO prediction for the 2.2 kb sequence. (D, E) NNBP energies and comparison with UO values at 10 mM NaCl (D) and 1 M NaCl (E). The following notation is used for NNBP: AG/TC denotes 5′-AG-3′ paired with 5′-CT-3′. Black points, UO values; red points, values for the 6.8 kb molecule; blue points, values for the 2.2 kb molecule. The values for the 6.8 kb and the 2.2 kb molecules have been obtained after averaging over six molecules. Error bars are determined from the standard error among different molecules.

Fig. 3.

Salt corrections of the NNBP energies. Figure shows the energy of all different NNBP parameters. Red (blue) points are the experimental results for the 6.8 kb (2.2 kb) sequence; green curve, UO nonspecific salt correction; black curve, fit to Eq. 3 with adjustable parameters m_i (i = 1,…,10, loop) and .

Fig. 4.

Melting temperatures prediction. Comparison with melting temperatures for the 92 oligos ranging from 10–30 bp reported in ref.  (data reported in SI Appendix: Table S2). (A) Predicted vs. experimentally measured melting temperatures at five salt conditions ([Na⁺] = 69, 119, 220, 621, and 1,020 mM). The values obtained from unzipping have less error at higher temperatures (corresponding to longer oligos). (B) Prediction at 69 mM (left) and 1.02 M NaCl (right). Black lines are the experimentally measured melting temperatures, green line is the UO prediction and red line our prediction from unzipping data.