Single-molecule unzippering experiments on DNA and Peyrard-Bishop-Dauxois model

In this paper, we rely on a nonlinear Peyrard-Bishop-Dauxois (PBD) model. This mechanical model explains DNA dynamics assuming only transversal oscillations of nucleotides. The potential energy for the hydrogen bonds, connecting $AT$ or $CG$ base pairs, is modeled by a Morse potential. This potential is characterized by the depth $D$ and the inverse width $a$ of the Morse potential well. We discuss one type of single molecule manipulation experiments, which we call unzippering experiments. It is explained that the highest values of two essential parameters of the PBD model, the parameters $D$ and $a$, can be determined according to the results of those experiments. This statement is supported by theoretical calculations. We show that the inverse width of the Morse potential well $a$ has been overestimated so far. The smallest value for this parameter is determined according to the PBD model, which means that a rather narrow interval can be assumed. Also, we give an idea how to determine the optimal value of the parameter $a$.

Figure 1

Morse potential.

Figure 2

Elongation of the out-of-phase motion as a function of time ($k=24\mathrm{N}∕\mathrm{m}$, $K=4\mathrm{N}∕\mathrm{m}$, $D=0.1\mathrm{eV}$, $a=2{\mathrm{\AA }}^{-1}$).

Figure 3

Elongation of the out-of-phase motion as a function of time ($k=1\mathrm{N}∕\mathrm{m}$, $K=0.5\mathrm{N}∕\mathrm{m}$, $D=0.1\mathrm{eV}$, $a=2{\mathrm{\AA }}^{-1}$).

Figure 4

Elongation of the out-of-phase motion as a function of time ($k=1\mathrm{N}∕\mathrm{m}$, $K=0.5\mathrm{N}∕\mathrm{m}$, $D=0.1\mathrm{eV}$, $a=0.9{\mathrm{\AA }}^{-1}$).

Figure 5

Elongation of the out-of-phase motion as a function of time ($k=3\mathrm{N}∕\mathrm{m}$, $K=0.5\mathrm{N}∕\mathrm{m}$, $D=0.1\mathrm{eV}$, $a=0.9{\mathrm{\AA }}^{-1}$).

Figure 6

Elongation of the out-of-phase motion as a function of time ($k=15\mathrm{N}∕\mathrm{m}$, $K=0.5\mathrm{N}∕\mathrm{m}$, $D=0.1\mathrm{eV}$, $a=0.9{\mathrm{\AA }}^{-1}$).

Figure 7

Velocity $\epsilon u_e$ as a function of the inverse width ($a$: $k=24\mathrm{N}∕\mathrm{m}$, $K=0.5\mathrm{N}∕\mathrm{m}$, $b$: $k=6\mathrm{N}∕\mathrm{m}$, $K=0.5\mathrm{N}∕\mathrm{m}$, $c$: $k=3\mathrm{N}∕\mathrm{m}$, $K=0.5\mathrm{N}∕\mathrm{m}$, d: $k=1\mathrm{N}∕\mathrm{m}$, $K=0.3\mathrm{N}∕\mathrm{m}$).