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. 2001 Jul 17;98(15):8608-13.
doi: 10.1073/pnas.151257598. Epub 2001 Jul 10.

Force and kinetic barriers to unzipping of the DNA double helix

S Cocco  1 , R Monasson, J F Marko
Affiliations

Force and kinetic barriers to unzipping of the DNA double helix

S Cocco et al. Proc Natl Acad Sci U S A. .

Abstract

A theory of the unzipping of double-stranded DNA is presented and is compared to recent micromanipulation experiments. It is shown that the interactions that stabilize the double helix and the elastic rigidity of single strands simply determine the sequence-dependent approximately 12-pN force threshold for DNA strand separation. Using a semimicroscopic model of the binding between nucleotide strands, we show that the greater rigidity of the strands when formed into double-stranded DNA, relative to that of isolated strands, gives rise to a potential barrier to unzipping. The effects of this barrier are derived analytically. The force to keep the extremities of the molecule at a fixed distance, the kinetic rates for strand unpairing at fixed applied force, and the rupture force as a function of loading rate are calculated. The dependence of the kinetics and of the rupture force on molecule length is also analyzed.

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Figures

Figure 1
Figure 1
Sketches of some experiments referred to in the text. All experiments are at room temperature and in physiological liquid buffers (PBS or Tris). Arrows symbolize the applied forces. (A) Unzipping experiment of Essevaz-Roulet et al. (1, 2): the 3′–5′ extremities of a λ-phage DNA (49 kbp) are attached to a glass microscope slide (with translational velocity v = 40 nm/sec) and a polystyrene bead connected to a glass microneedle (with stiffness k = 1.7 pN/μm). The loading rate equals λ = kv = 0.06 pN/sec. When the force approaches 12 pN, the DNA starts to open. As unzipping proceeds, the distance between the two single-strand extremities is controlled, and the force varies between 10 and 15 pN depending on the sequence. (B) Parameters used in the theoretical description: force f, torque Γ, and distance 2r between the two single-strand extremities. (C) Stretching experiment of Strunz et al. (6): a short ssDNA (10, 20, or 30 bp, with about 60% GC content) is attached by one 5′-end to a surface, and the complementary ssDNA is attached by the other 5′-end to an AFM tip. On approach of the surface to the tip, a duplex may form that is loaded on retract until unbinding occurs. The distribution of the rupture forces is obtained for loading rates ranging from 16 to 4,000 pN/sec. (D) Stretching and unzipping experiment of Rief et al. (5): DNA of poly(dA-dT) (5,100 bp) or poly(dG-dC) (1,260 bp) are attached between a gold surface and an AFM tip and stretched. Through a melting transition, single DNA strands are prepared; these strands on relaxation reanneal into hairpins as a result of their self-complementary sequences. The forces of unzipping of these hairpins are 20 ± 3 pN for poly(dG-dC) and 9 ± 3 pN for poly(dA-dT). (E) Dissociation experiment of Bonnet et al. (8): The rate of unzipping, ν_, and closing, ν+, of a 5-bp DNA hairpin (CCCAA-TTGGG) is investigated by fluorescence energy transfer and correlation spectroscopy techniques. The hairpin is closed by a loop of 12–21 thymine (T) or adenine (A). The characteristic time of opening t_ = 1/ν_ is found to be largely independent of the loop length and equal to t_ ≃ 0.5 msec.
Figure 2
Figure 2
Base-pair potentials in unit of kBT as a function of the base radius r (in angstroms), without (Inset) and with (main picture) entropic contributions. (Inset) Morse potential U(r) accounting for the hydrogen bond interaction. Main picture: total potential V(r) for zero torque. When entropic contributions are considered, small r values are less favorable, and a barrier appears. The free-energy gdsDNA = g0 of the dsDNA is lower than the single-strand free-energy gssDNA = 0. Note the difference of scales on the horizontal axis between the two figures.
Figure 3
Figure 3
Force f(r) (in piconewtons) to be exerted on the DNA to keep extremities at a distance 2r apart (in angstroms). The peak force f ≃ 270 pN, reached at r ≃ 10.5 Å, is much larger than the asymptotic value ≃ 12 pN, equal to the equilibrium force fu (at zero torque, and in the Gaussian approximation) for unzipping a large portion of the molecule. (Inset): phase diagram, in the plane of torque Γ (kBT) and of force f (piconewtons). The lines shows the critical unzipping force fu as a function of Γ with formula 2 (full line) and formula 3 (dashed line) for the stretching free energy of the single strand. Below the line, dsDNA is the stable thermodynamical configuration, whereas for forces larger than fu(Γ), denaturation takes place. fu vanishes at the critical torque Γu ≃ −2.4 kBT and is equal to 11 pN (full line) and 12 pN (dashed line) at zero torque.
Figure 4
Figure 4
Transition states involved in the theoretical calculation of the kinetic rates. (A) Unzipping: opening of dsDNA is favorable at forces f > fu, and the unzipping rate ν_ is calculated directly. The nucleation bubble is of (≃4) base pairs, weakly depending on the force. (B) Annealing: when f < fu, dsDNA is thermodynamically stable; the dissociation rate ν_ is obtained indirectly through the calculation of the annealing rate ν+ of the metastable ssDNA, ν = ν+e−NΔg(f)/kBT, where Δg(f) > 0 is the excess of free energy per base pair of ssDNA with respect to dsDNA. The nucleation bubble is of (≃4) base pairs.
Figure 5
Figure 5
Time of dissociation t_ (in sec) as a function of the force f (in piconewtons). Three regimes can be distinguished. For f < fu = 12 pN, the dissociation times depend on the length N of the sequence (N = 10, 20, 30 bp from Lower to Upper). For fu < f < fb = 230 pN, the dissociation time is length independent and decreases as the energetic barrier to overcome lowers. For f > fb, no barrier is left, and dissociation is immediate. The slope of the logarithm of t_ near fu is d log t_/df = −8 Å (f > fu), −2duN + 31 Å with du = 5 Å (f < fu). (Inset) Time of thermal dissociation t_ (for zero force) as a function of the number of base pairs N.
Figure 6
Figure 6
Rupture force (piconewtons) as a function of the loading rate λ (piconewtons/sec) for five different molecule lengths N = 10, 20, 30, 50, and 100. Arrows indicate the different critical loading rates for N = 10. Below λ1 (=100.8 for N = 10), rupture occurs at essentially zero force through thermal dissociation. For loading rates ranging from λ1 to λ2 (=104.6 for N = 10), the rupture force is finite, and thermal tunneling is responsible for the strong dependence on N, until the force reaches the equilibrium value fu = 12 pN. For larger loading rates, the rupture force is length independent. It increases again as λ > λ3 = 105.5 pN/sec, because the molecule is unable to respond to the force before it becomes very large.
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