Aptamers are chemically produced oligonucleotides, able to bind a variety of targets such as drugs, proteins and pathogens with high sensitivity and selectivity. Therefore, aptamers are largely employed for producing label-free biosensors (aptasensors), with significant applications in diagnostics and drug delivery. In particular, the anti-thrombin aptamers are biomolecules of high interest for clinical use, because of their ability to recognize and bind the thrombin enzyme. Among them, the DNA 15-mer aptamer (TBA), has been widely explored around the possibility of using it in aptasensors. This paper proposes a microscopic model of the electrical properties of TBA and of the aptamer-thrombin complex, combining information from both structure and function, following the issues addressed in an emerging branch of electronics known as proteotronics. The theoretical results are compared and validated with measurements reported in the literature. Finally, the model suggests resistance measurements as a novel tool for testing aptamer-target affinity.