DNA molecules possess high density genetic information in living beings, as well as selfassembly and self-recognition properties that make them excellent candidates for many scientific areas, from medicine to nanotechnology. The process of electron transport through DNA is important because DNA repair occurs spontaneously via the process that restores mismatches and lesions, and furthermore, DNA-based molecular electronics in nano-bioelectronics can be possible through the process. In this thesis, we study theoretically the transport properties through a one-dimensional one-channel DNA model, a quasi-one-dimensional one-channel DNA model, and a two-dimensional four-channel DNA model by using the Tight-Binding Hamiltonian method. We show graphical outputs of the transmission, overall contour plots of transmission, localization lengths, the Lyapunov exponent, and current-voltage characteristics as a function of incoming electron energy and magnetic flux which are obtained using Mathematica run on the CSH Beowulf Cluster. Our results show that the semiconductor behavior can be observed in the I-V characteristics. The current through a quasi-one-dimensional one-channel DNA model starts to flow after the breakdown voltage and remains constant after threshold voltage. The variations of the temperature make the fluctuations of the system. As the temperature increases, the sharp transmission resonances are smeared out and the localization lengths are also decreased. Due to a magnetic field penetrating at the center of the two-dimensional DNA model, the Aharonov- Bohm (AB) oscillations can be observed. / Sequence dependent electron transport through a one-dimensional, one-channel DNA model -- Backbone-induced effects on charge transport through a quasi one-dimensional DNA molecule -- Temperature and magnetic fields effects on the electron transport through two-dimensional and four-channel DNA model.

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In recent years, the electronic behavior of DNA molecules has received much interest ranging from interpreting experimental results to electronic based applications, including DNA sequencing and DNA-based nanotransistors. Here we study the electronic properties of poly(G)- poly(C) double stranded DNA molecules by means of the tight binding approximation to understand how the molecules act under different physical conditions. For instance, the effects of DNA tilting, stretching and compressing on the electronic properties are elucidated. Very interesting features such as a tunable energy band gap and a metal-semiconductor transition are disclosed for DNA under different conditions. / Second order tight binding model -- Tilted DNA molecule -- Strain-dependent DNA electronics.