Electronic properties of guanine traps in DNA

We report on our study of the electronic properties of guanine traps in the DNA surrounded by adenines. We have shown that for a typical range of DNA parameters, formation of the bound state of two holes at the same guanine trap is possible for the GGG and GGGG traps if the hole-hole interaction is weak, which can be achieved for the DNA in solutions. The origin of the two-hole bound state is the competition between the Coulomb repulsion and the phonon mediated attraction between the holes. For the hole-phonon coupling constant $\approx 1$ two holes will be at the same trap if the on-site hole-hole repulsion energy is $\lesssim 0.9\mathrm{eV}$.

Figure 1

(a) The ground state energy of a single hole in a trap containing $N_G$ guanines for $t=0.2\mathrm{eV}$ and ${\Delta }_{GA}=0.3\mathrm{eV}$ as a function of the hole-phonon coupling constant $\lambda$. The numbers next to the lines are the number of guanines in the trap. (b) The energy $E_{1,1}+E_{1,4}$ of two holes for ${\Delta }_{GA}=0.3\mathrm{eV}$ as a function of $\lambda$. The numbers next to the lines are the values of tunneling integral $t$.

Figure 2

Ground state energy of two holes in the trap containing $N_G=3$ guanines (a) and $N_G=4$ guanines (b) as a function of the interhole interaction strength $V_0$ for ${\Delta }_{GA}=0.1\mathrm{eV}$ (dashed line) and ${\Delta }_{GA}=0.3\mathrm{eV}$ (solid line).

Figure 3

The average number of holes (a) and the average number of phonons (b) for a two hole system in a GGGG trap are shown as a function of the base index. The tunneling integral is $t=0.3\mathrm{eV}$ and the hole-phonon coupling is $\lambda =1$. Dots and triangles corresponds to interhole interaction strength $V_0=0.8$ and $1.2\mathrm{eV}$, respectively.

Figure 4

Energies $E_{1,1}+E_{1,4}$ and $E_{2,4}$ of a two-hole system are shown as a function of hole-phonon coupling $\lambda$ by dashed and solid lines, respectively. Tunneling integral is $t=0.3\mathrm{eV}$ and ${\Delta }_{GA}=0.3\mathrm{eV}$.