Theoretical models for electrochemical impedance spectroscopy and local ζ-potential of unfolded proteins in nanopores.

Single solid-state nanopores find increasing use for electrical detection and/or manipulation of macromolecules. These applications exploit the changes in signals due to the geometry and electrical properties of the molecular species found within the nanopore. The sensitivity and resolution of such measurements are also influenced by the geometric and electrical properties of the nanopore. This paper continues the development of an analytical theory to predict the electrochemical impedance spectra of nanopores by including the influence of the presence of an unfolded protein using the variable topology finite Warburg impedance model previously published by the authors. The local excluded volume of, and charges present on, the segment of protein sampled by the nanopore are shown to influence the shape and peak frequency of the electrochemical impedance spectrum. An analytical theory is used to relate the capacitive response of the electrical double layer at the surface of the protein to both the charge density at the protein surface and the more commonly measured zeta potential. Illustrative examples show how the theory predicts that the varying sequential regions of surface charge density and excluded volume dictated by the protein primary structure may allow for an impedance-based approach to identifying unfolded proteins.