Clusters of protein pores in phospholipid bilayer membranes can be identified and characterized by electrochemical impedance spectroscopy

Cluster formation is a widely-observed phenomenon, which results in unique sets of properties both in physical, chemical and biological domains of nature. Here, we present a qualitative description of clustering of membrane defects, specifically ion-conducting protein pores in tethered phospholipid bilayers, a versatile biomimetic model of biological membranes accomplished on chemically modified gold films. By invoking the Voronoi tessellation concept we demonstrate the possibility to distinguish between random and sparsely clustered patterns both in computer generated and real-world systems using one single parameter sigma, the standard deviation of the normalized Voronoi sector areas distribution. For random systems, sigma approximate to 0.54, for sparsely clustered patterns sigma > 0.54. Because of a specific structure and dielectric properties of tethered bilayers, they can be characterized by an alternating current technique, electrochemical impedance spectroscopy (EIS). EIS measures macroscopic parameters of dielectric systems and it is not a structural technique per se. However, we found the EIS spectra-derived quantitative metric zeta to be a diagnostic parameter that allows assessment of the distribution type (homogeneous, random or clustered) of defects at nanometer level. One of the most interesting findings of the current study is the fact that the EIS derived zeta parameter is sensitive to an average size of the defects thus enabling a purely electrochemical methodology to access fine structural information such as size of incomplete protein pores in phospholipid bilayers. Overall, our results demonstrate a fundamental property of the macroscopic technique, electrochemical impedance spectroscopy, to probe structural arrangement of defects with sizes between 0.5 nm to 25.5 nm located in a thin, 2 nm thick phospholipid dielectric layer. Our findings can be utilized in designing precision electrochemical biosensors, and/or solving specific physical, biochemical or electrochemical problems related to other types of nanometer thick dielectric films on conducting surfaces. (C) 2020 Elsevier Ltd. All rights reserved.