Inside the well, ψ 0( r) is the Morse ground state ( 27) outside the well, it can be computed by using the Wentzel, Kramers, Brillouin approximation ( 28). The fluctuations of r are confined to the Morse well, so g 0 is well approximated if we take V( r) = V( R 0) + U H( r) − U H( R 0) and m( r) = m( R 0), for which Eq.
#Double helix definition free#
When DNA is the thermodynamical favorable state, g 0 < 0 represents the free energy per base pair of a long dsDNA, relative to separated ssDNAs. For g ≥ 0, the eigenvalue spectrum becomes continuous, corresponding to the appearance of completely separated ssDNAs at g = 0. The lowest eigenvalue g 0 is the equilibrium free energy, and the corresponding ψ 0( r) describes thermal fluctuations of distance between the two strands. used a similar theory to analyze unzipping force dependence on sequence ( 1, 2). In the opposite case, where torque is zero (i.e., for dsDNA with no constraint of its strand-linking number), the critical unzipping force is f \(\begin\) ≃ 4 Å. 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. The hairpin is closed by a loop of 12–21 thymine (T) or adenine (A). ( 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. ( E) Dissociation experiment of Bonnet et al. The forces of unzipping of these hairpins are 20 ± 3 pN for poly(dG-dC) and 9 ± 3 pN for poly(dA-dT). Through a melting transition, single DNA strands are prepared these strands on relaxation reanneal into hairpins as a result of their self-complementary sequences. ( 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.
( D) Stretching and unzipping experiment of Rief et al. The distribution of the rupture forces is obtained for loading rates ranging from 16 to 4,000 pN/sec. On approach of the surface to the tip, a duplex may form that is loaded on retract until unbinding occurs. ( 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. ( C) Stretching experiment of Strunz et al. ( B) Parameters used in the theoretical description: force f, torque Γ, and distance 2 r between the two single-strand extremities. 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. When the force approaches 12 pN, the DNA starts to open. The loading rate equals λ = kv = 0.06 pN/sec. ( 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). ( A) Unzipping experiment of Essevaz-Roulet et al. All experiments are at room temperature and in physiological liquid buffers (PBS or Tris). Figure 1 Sketches of some experiments referred to in the text.
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