Inhomogeneous DNA: Conducting exons and insulating introns

Parts of DNA sequences known as exons and introns play very different roles in coding and storage of genetic information. Here we show that their conducting properties are also very different. Taking into account long-range correlations among four basic nucleotides that form double-stranded DNA sequence, we calculate electron localization length for exon and intron regions. Analyzing different DNA molecules, we obtain that the exons have narrow bands of extended states, unlike the introns where all the states are well localized. The band of extended states is due to a specific form of the binary correlation function of the sequence of basic DNA nucleotides.

Figure 1

(Color online) Binary correlation function of the sequence of nucleotides for human BCRA gene. The correlation function drops from 1 at $k=0$ to about 0.1 at $k\ge 1$, left inset. Correlations extend to distances of a few thousands of base pairs, decaying very slowly. An important feature of this correlation function is close to regular oscillations about zero, right inset.

Figure 2

(Color online) Localization length vs energy for the human BRCA gene measured in the number of base pairs. The length of the exon (intron) is $2120\left(10421\right)\text{bps}$. The results for exon and intron are shown by black and gray (red) lines, respectively. The values of the hopping parameters are $h=0.5\text{eV}$ and $t=1\text{eV}$. The two channels are propagating if $6.6<E<10.4\text{eV}$. One of the channels becomes evanescent in two symmetric regions, $10.4<E<11.4\text{eV}$ and $5.6<E<6.6\text{eV}$, of the width of $2h=1\text{eV}$.

Figure 3

(Color online) Localization length for the human ADAM10 gene. The length of the exon (intron) is $1030\left(31752\right)\text{bps}$. Inset shows the fine structure of one of the peaks.

Figure 4

(Color online) Localization length vs energy for the human SNAP29 gene. The length of the exon (intron) is $2141\left(21701\right)\text{bps}$.

Figure 5

(Color online) Localization length vs energy for the human SUHW1 gene. The length of the exon (intron) is 1963 (4405) bps.

Figure 6

(Color online) Binary correlator for the exon (left panel) and intron (right panel) regions of the human SNAP29 gene. Inserts show local behavior of the correlators within small intervals of $k$.