In the last 25 years, aptamers gained most attention in the scientific community by yielding over 7000 entries in the PubMed. In essence, aptamers are short RNA or single-stranded DNA oligonucleotides functionally used to bind specific ligands. Usually they are generated in vitro and, recently, computational approaches have been developed for optimizing the in silico selection and exploring the affinity performances. However, the mechanism of aptamer-ligand formation is still far from being understood, and not obvious to be predicted. To address this issue we propose a computational model that describes aptamer-ligand binding affinity, by studying: (i) the topological structure of the corresponding graphs through the rank-degree distribution (hierarchy) and the node assortativity; (ii) the linear response (impedance) of the equivalent electrical-circuit. Numerical calculations are applied to the thrombin binding aptamer (TBA), alone and complexed in the presence of sodium and potassium ions. Results are quite intriguing since they reveal the possibility of identifying different affinities of the complex, due to the presence of different ions when looking at the hierarchy-assortativity plot. Furthermore, the analysis of the electrical response of TBA in a specific state is performed by dressing the topological graph with elementary impedances that preserve the electrical features of the original macromolecule. The result reveals that the macromolecule resistance sensitively depends on the presence of sodium or potassium ions, thus indicating the value of the resistance as a crucial parameter for testing affinity.
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