Calculation of the hole mobilities of the three homopolynucleotides, poly(guanilic acid), poly(adenilic acid), and polythymidine in the presence of water and ${\mathrm{Na}}^{+}$ ions

Recent high resolution x-ray diffraction experiments have determined the structure of nucleosomes. In it 147 base pair long DNA B superhelix is wrapped around the eight nucleohistone proteins. They have found that there are many hydrogen-bonds (H-bonds) between the negative sites phosphate ($\mathrm{P}{\mathrm{O}}_4^{-}$) groups DNA, and first of all there is the positively charged lysine and arginine side chains of the histones. This means that there is a non-negligible charge transfer from DNA to the proteins causing a hole current in DNA and an electronic one in the proteins. If the relative positions of the two macromolecules change due to some external disturbances, the DNA moves away from the protein and can be read. If this happens simultaneously at several nucleosomes and at many places in chromatin (built up from the nucleosomes), undesired genetic information becomes readable. This final end can cause the occurrence of oncoproteins at an undesired time point which most probably disturbs the self-regulation of a differentiated cell. The connection of these chain of events with the initiation of cancer is obvious. To look into the details of these events we have used the detailed band structures of the four homopolynucleotides in the presence of water and natrium (${\mathrm{Na}}^{+}$) ions calculated previously with the help of the ab initio Hartree-Fock crystal orbital method. We have found that in the case of three homopolynucleotides the width of their valence band is broad enough ($\sim 10$ times broader than the thermal energy at $300\mathrm{K}$) for the application of the simple deformation potential approximation for transport calculations. With the help of this we have determined the hole mobilities at $300\mathrm{K}$ and $180\mathrm{K}$ of poly(guanilic acid), poly(adenilic acid), and polythimidine (polycytidine has a too narrow valence band for the application of the deformation potential method). The obtained mobilities are large enough to allow Bloch-type conduction in these systems. At the end of the paper we discuss briefly the possible mechanism of charge transport in aperiodic DNA as a combination of Bloch-type conduction, hopping, and tunneling.

Figure 1

(Color online) The unit cell of poly(guanilic acid) with water molecules and one ${\mathrm{Na}}^{+}$.

Figure 2

(Color online) The unit cell of poly(adenilic acid) with water molecules and one ${\mathrm{Na}}^{+}$.

Figure 3

(Color online) The unit cell of polythymidine with water molecules and one ${\mathrm{Na}}^{+}$.

Figure 4

(Color online) The structural formula of the $\mathrm{P}{\mathrm{O}}_4^{-}$ group. The bond distances, valence angles, and torsional angles are given in Table .