Investigação de propriedades de transporte eletrônico e caracterização multifractal de bandas de energias de sequências GA no DNA humano

Abstract

In this work, we analyze the location and fractal properties of the energy spectrum in a genomic system, formed by seven types of pure GA sequences (G-Guanine and A-Adenine) found on human chromosome 7. We use two methods to find the Hamiltonian solutions in the tight-binding approximation: transfer matrix and negative eigenvalue method developed by Dean. Through the transfer matrix method we obtained: Energy diagram, Electronic Transmittance Spectrum and Lyapunov Coefficient. By means of the negative eigenvalues method, we determined: Energy Diagram and Electronic Density of States. The investigation of the multifractal behavior of energy bands obtained by the transfer matrix method, took place through the singularity spectrum f(α), which was calculated using an algorithm based on the theorems of Shannon, Eggelston and Billingsley, in addition, we determined the power law associated with the distribution of energy bands for each sequence studied. In our results, the Energy Diagram revealed a fractal behavior similar to the Cantor random set. Comparing all the sequences studied here, the results of the multifractal analysis of energy band distributions showed typical behavior of multifractal systems.