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.

Determining nanocapillary geometry from electrochemical impedance spectroscopy using a variable topology network circuit model.

Solid-state nanopores and nanocapillaries find increasing use in a variety of applications including DNA sequencing, synthetic nanopores, next-generation membranes for water purification, and other nanofluidic structures. This paper develops the use of electrochemical impedance spectroscopy to determine the geometry of nanocapillaries. A network equivalent circuit element is derived to include the effects of the capacitive double layer inside the nanocapillaries as well as the influence of varying nanocapillary radius. This variable topology function is similar to the finite Warburg impedance in certain limits. Analytical expressions for several different nanocapillary shapes are derived. The functions are evaluated to determine how the impedance signals will change with different nanocapillary aspect ratios and different degrees of constriction or inflation at the capillary center. Next, the complex impedance spectrum of a nanocapillary array membrane is measured at varying concentrations of electrolyte to separate the effects of nanocapillary double layer capacitance from those of nanocapillary geometry. The variable topology equivalent circuit element model of the nanocapillary is used in an equivalent circuit model that included contributions from the membrane and the measurement apparatus. The resulting values are consistent with the manufacturer's specified tolerances of the nanocapillary geometry. It is demonstrated that electrochemical impedance spectroscopy can be used as a tool for in situ determination of the geometry of nanocapillaries.