Hereditary information is encoded in the chemical language of DNA and reproduced in all cells of living organisms. The double-stranded helical structure of the DNA is a key to its use in self-assembly applications. Each strand of the DNA is about 2 nm wide and is composed of a linear chain of four possible bases, namely adenine (A), cytosine (C), guanine (G), and thymine (T), on a backbone of alternating sugar molecules (S) and phosphate ions (P). Each unit of a phosphate, a sugar molecule, and a base is called a nucleotide, and each nucleotide is about 0.34 nm long. The specific binding through hydrogen bonds between adenine and thymine, and cytosine and guanine can result in the joining of two complementary single-stranded DNA to form a double-stranded DNA.
With this aim in mind, we report here a numerical study of electronic conduction in n-stacked arrays of DNA double-strand segments, made up from the nucleotides guanine, adenine, cytosine, and thymine, forming a Rudin-Shapiro as well as a Fibonacci polyGC quasiperiodic sequences, both structures presenting long-range pair-correlation. They are constructed starting from a guanine nucleotide as seed and following their respective inflation rules. For comparison, we show also the electrical transport properties for a genomic DNA sequence considering a segment of the first sequenced human chromosome 22 (Ch 22). Unlike proteins, a π-stacked array of DNA base pairs made up from these nucleotides can provide the way to promote long range charge migration, which in turn gives important clues to mechanisms and biological functions of transport.
Our theoretical method uses Dyson equation together with a transfer-matrix treatment, within an electronic tight-binding model Hamiltonian, suitable to describe the DNA segments. The electronic density of states is calculated stressing the regions of frequency where the transfer function is complex. The long-range correlations presented in the sequences are responsible for the slow vanishing of some transmission peaks as the segment size is increased, which may promote an effective electronic transport at specific resonant energies of finite DNA segments.
We thank financial support from CNPq-Rede Nanobioestruturas, FAPEMA and FINEP (Brazilian Agencies).
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