Elastic properties and secondary structure formation of single-stranded DNA at monovalent and divalent salt conditions

Abstract

Single-stranded DNA (ssDNA) plays a major role in several biological processes. It is therefore of fundamental interest to understand how the elastic response and the formation of secondary structures are modulated by the interplay between base pairing and electrostatic interactions. Here we measure force-extension curves (FECs) of ssDNA molecules in optical tweezers set up over two orders of magnitude of monovalent and divalent salt conditions, and obtain its elastic parameters by fitting the FECs to semiflexible models of polymers. For both monovalent and divalent salts, we find that the electrostatic contribution to the persistence length is proportional to the Debye screening length, varying as the inverse of the square root of cation concentration. The intrinsic persistence length is equal to 0.7 nm for both types of salts, and the effectivity of divalent cations in screening electrostatic interactions appears to be 100-fold as compared with monovalent salt, in line with what has been recently reported for single-stranded RNA. Finally, we propose an analysis of the FECs using a model that accounts for the effective thickness of the filament at low salt condition and a simple phenomenological description that quantifies the formation of non-specific secondary structure at low forces.

Figure 1.

(A) Scheme illustrating the connections between a hairpin and the polystyrene beads. SA bead stands for streptavidin-coated bead, whereas AD bead stands for antidigoxigenin-coated bead. Beads and molecules are not in scale. (B) Steps of the protocol used in our experiments to obtain FECs of ssDNA.

Figure 2.

Cycle of pulling, showing the stretching (black) and releasing (red/light gray) parts of the cycle in a hairpin in TE with 100 mM of NaCl. The refolding of the hairpin is observed at low forces (1 pN) as a sudden jump-up in the force (highlighted with an asterisk). The re-pulling curve in the absence of blocking oligo is drawn in green/dark gray [black and green/dark gray curves nearly superimpose due to the quasi-reversibility of the unfolding-folding process, see [(25)].

Figure 3.

FEC of 13-kb ssDNA at varying NaCl concentration taken at constant pulling speed of ∼30 nm/s and filtered at 2-Hz bandwidth. Inset shows how the formation of secondary structure reduces the apparent contour length of the molecule (dashed lines).

Figure 4.

FEC of 13-kb ssDNA at varying MgCl₂ concentration taken at constant pulling speed of ∼30 nm/s and filtered at 2-Hz bandwidth.

Figure 5.

Comparison between an experimental FEC (black) and a fit to the WLC model in the range 10–40 pN (red/gray) at different NaCl concentrations. Results are shown for a representative molecule.

Figure 6.

Comparison between an experimental FEC (black) and a fit to the WLC model in the range 10–40 pN (red/gray) at different MgCl₂ concentrations. Results are shown for a representative molecule.

Figure 7.

Persistence length values for ssDNA at different salt conditions in NaCl (black squares) and MgCl₂ (red diamonds). In blue circles, we show data obtained from (25). Magnesium concentrations along the x-axis have been multiplied by a factor 100. Solid black and dashed red lines correspond to the linear fits to NaCl and MgCl₂ data. The parameters obtained from the fit =(0)+A* are: (0) = 0.68 0.04 and A = 2.19 0.10 ( = 0.666) in the case of NaCl; and (0)=0.70 0.04 and A = 1.59 0.57 (=0.701) in the case of MgCl₂.

Figure 8.

Kuhn length and stretching modulus values for ssDNA versus salt concentration (normal-log scale) for NaCl (black squares) and MgCl₂ (red diamonds). Magnesium concentrations have been multiplied by a factor 100.

Figure 9.

Fit of FECs to the TC model at low monovalent salt conditions. Experimental data (black) and fits to the TC model (red/gray) for low NaCl concentrations.

Figure 10.

Fraction of unpaired ssDNA bases as a function of force. Dashed lines are fits to experimental data using Equation (5).

Figure 11.

Fraction of the unpaired bases at 0 force at different salt concentrations. Logarithmic scale is used for both axes. Black squares stand for NaCl and red diamonds stand for MgCl₂. Magnesium concentrations have been multiplied by a factor 100. Lines are fits to the power law dependence, (see text for details).