Electronic density of states in sequence dependent DNA molecules

We report in this work a numerical study of the electronic density of states (DOS) in π-stacked arrays of DNA single-strand segments made up from the nucleotides guanine G, adenine A, cytosine C and thymine T, forming a Rudin-Shapiro (RS) as well as a Fibonacci (FB) polyGC quasiperiodic sequences. Both structures are constructed starting from a G nucleotide as seed and following their respective inflation rules. Our theoretical method uses Dyson's equation together with a transfer-matrix treatment, within an electronic tight-binding Hamiltonian model, suitable to describe the DNA segments modelled by the quasiperiodic chains. We compared the DOS spectra found for the quasiperiodic structure to those using a sequence of natural DNA, as part of the human chromosome Ch22, with a remarkable concordance, as far as the RS structure is concerned. The electronic spectrum shows several peaks, corresponding to localized states, as well as a striking self-similar aspect.