Tight-Binding Modeling of Nucleic Acid Sequences: Interplay between Various Types of Order or Disorder and Charge Transport

This review is devoted to tight-binding (TB) modeling of nucleic acid sequences like DNA and RNA. It addresses how various types of order (periodic, quasiperiodic, fractal) or disorder (diagonal, non-diagonal, random, methylation et cetera) affect charge transport. We include an introduction to TB and a discussion of its various submodels [wire, ladder, extended ladder, fishbone (wire), fishbone ladder] and of the process of renormalization. We proceed to a discussion of aperiodicity, quasicrystals and the mathematics of aperiodic substitutional sequences: primitive substitutions, Perron-Frobenius eigenvalue, induced substitutions, and Pisot property. We discuss the energy structure of nucleic acid wires, the coupling to the leads, the transmission coefficients and the current-voltage curves. We also summarize efforts aiming to examine the potentiality to utilize the charge transport characteristics of nucleic acids as a tool to probe several diseases or disorders.