Electrochemical Impedance Spectroscopy of Tethered Bilayer Membranes: An Effect of Heterogeneous Distribution of Defects in Membranes

The study focuses of the electrochemical impedance spectroscopy (EIS) response of tethered bilayer membranes (tBLMs) populated with heterogeneously distributed defects (pores). Such defects are common and may form spontaneously, or they may be produced by pore-forming agents, proteins, protein toxins, and peptides. To model heterogeneity in the populations of defects we assumed a log-normal distribution probability function. We found that the presence of heterogeneity results in specific transformations of EIS spectra compared to the spectra observed in homogeneous systems. These transformations may serve as a qualitative diagnostic criteria for the identification of heterogeneous distribution of defects in the tBLMs. We describe two simple algorithms that allows a quantitative estimation of the parameters determining heterogeneity, the standard deviation of distribution, a. and the defect density N-def degrees exhibiting the highest probability of occurrence. The first algorithm can be applied for systems populated with small radial defects with the radius smaller than approximately 5 nm. In this case the position of the phase minimum in;the frequency domain of EIS (admittance) Bode plots is a measure of N-def degrees, while the phase value at the minimum is a measure of sigma. In the case of large defects such as pore-forming toxins e.g., the cholesterol dependent cytolysins, which exhibit radii larger than approximately 5 nm a more complex analysis is required. However, we demonstrate that if the assumption of linearity of the position of the admittance minimum and N-def degrees and sigma is applicable, then a simple algorithm allows assessing both N-def degrees and sigma. Finally, we critically assess the widely used term membrane conductance (membrane resistance), which is typically evaluated by measuring the magnitude of the electrochemical admittance (resistance). We demonstrate that in heterogeneous tBLM systems such a term is ill-defined, because the same number of the same defects (per area) depending on their mode of distribution results in different electrochemical impedance (admittance) magnitude values. (C) 2016 Elsevier Ltd. All rights reserved.