Electrochemical impedance spectrum reveals structural details of distribution of pores and defects in supported phospholipid bilayers
Introduction
Solid supported phospholipid bilayers are biological models increasingly used for studies of membrane protein function and structure [1], biosensing [2], as well as biotechnology and biopharmaceutical applications [3], [4], [5], [6]. Robust and electrically highly insulating artificial membranes can be accomplished on solid surfaces using molecular anchors, onto which via precipitation [7] solvent exchange [8] or vesicle fusion [9] phospholipids self-assemble into bilayers. Such constructs, if accomplished on molecular anchors are called tethered bilayer lipid membranes (tBLMs). They contain liquid ion reservoir between the lipid bilayer and solid support. Thickness of such reservoir as experimentally determined by the neutron reflectometry is between 10 and 20 Angstroms [10], [11], [12]. The advantages of a liquid ion reservoir are: it cushions the phospholipid membrane and allows reconstitution of transmembrane proteins without jamming them against solid surface [12], [13]. The molecular level structure of such constructs can be accessed by neutron reflectometry, while the electrochemical impedance spectroscopy (EIS) is a method of choice to interrogate membrane integrity and for biosensing. Recently, we demonstrated the possibility to extend applications of EIS into the domain of structural methodologies[14], [15].
From the electrochemical perspective, an ideal phospholipid bilayer on a conducting solid surface acts as a planar insulating sheet. Thus, the response of an ideal bilayer under the electric perturbation is that of a planar capacitor, while a simple series RC equivalent circuit can represent the whole electrode system in contact with an electrolyte solution.
Real tethered bilayers always contain defects, either natural, which are due to imperfections of solid supported membranes, or artificial such as reconstituted water-filled protein/peptides pores or defects of other origin. The latter may be generated by the exposure of bilayers to the solutions of the membrane penetrating peptides or pore-forming proteins, or any other membrane damaging agents, such as detergents[8], [16].
Knowing the surface density of water filled pores in membranes is an essential precondition for the utility of tBLMs in precision biosensing. This information is also important if tBLMs are intended for quantitative assessment of protein membrane interactions [17]. Unfortunately, the surface density (concentration) of defects (proteins) in tethered lipid membranes is not easily accessible from the conductance measurements as is the case in black lipid membranes. The problem arises due to the asymmetry of the surface construct at the nanoscale: the few nanometer dielectric sheet is bathed by an essentially infinite reservoir of solution form one side, while the other side facing the solid surface comprise 1–2 nm liquid layer [12]. Such geometry results in a significant contribution of the submembrane reservoir resistance to the total impedance of an electrode, thus obstructing evaluation of the resistance of defects [18].
As showed earlier, in the case of homogeneous (regular hexagonal) distribution of defects the analytical solution describing EIS response exists and the density of defects in tBLMs can be estimated using both exact formulas or approximate empirical relations [18], [19]. Such analytical solution allows one assessing defect densities as well as other physical parameters of tBLMs through the solution of an inverse problem.
However, in practice, it is quite unlikely that defects in tBLMs are distributed in an ideal hexagonal array. Instead, random distribution is expected. For random distributions there is no analytical solution for the EIS response. The numerical finite element analysis (FEA) approach allows modelling and predicting EIS spectral properties in the case of random defect distribution in tBLMs. Such purely numerical algorithm is extremely costly in terms of computational time, therefore, it is highly unlikely to readily solve an inverse optimization problem to find physical parameters from the EIS spectra[15].
Recently, an approach to model EIS spectra using hybrid: analytical and numerical algorithms was described[19]. The algorithm was proposed assuming certain type of defect density distribution function. Specifically, the log normal distribution and truncated log-normal distributions were used for EIS modelling [19].
Both numerical FEA and hybrid analytical/numerical approaches demonstrate similar features in EIS spectra related to heterogeneity [14], [15], [19]. However, in real systems the type of distribution is not known a priori as was presumed in those studies. So, while modelling based on assumed defect density distribution might be useful in predicting EIS spectral features it is not applicable for solving the inverse problem.
This prompted us to formulate the following research question: “is it possible to solve an inverse problem and access density of defects in tBLMs without hypothesizing about the type of density distribution but rather deriving distribution function from the experimental data?” We hypothesize that such possibility exists because the impedance spectra should contain all information about the density distribution of defects in tBLMs. So the ultimate goal of the current work to present evidence that such hypothesis is justified [19] and one of the central problems in electrochemistry finding physical parameters from measured EIS spectra can be solved for tBLMs.
Section snippets
Impedance of tethered bilayer membranes populated with defects
We first briefly review the analytical solution for EIS response in the case of homogeneously distributed protein pores (defects) in tBLMs [18]. The analytical expression then is used to design the model describing heterogeneous distribution of defect with arbitrary density distribution function.
Following [18], here, we claim that the electrochemical response of tBLMs is determined by the capacitances of phospholipid bilayer - and Helmholtz layer - and by a special type of impedance,
Materials
Thio(oligoethyleneoxide) lipid, [Z-20-(Z-octadec-9-enyloxy)- 3,6,9,12,15,18,22-heptaoxatetracont-31-ene-1-thiol] (HC18) was a generous gift from dr. David J Vanderah (NIST, Gaithersburg, MD, USA) (synthesis of this compound described in ref [24]). The phospholipid DPhPC was from Avanti Polar Lipids (Birmingham, AL), β-mercaptoethanol (ME) was from Sigma-Aldrich (St. Louis, MO) was distilled before use. Pure water was obtained using a Millipore UHQ water purification system. The buffer contained
Testing algorithm with EIS synthetic data
To evaluate accuracy of the model we first fit synthetically generated EIS spectra with the known set of physical parameters and the defect density distribution functions. The admittance was calculated using eq. (2) with the predefined defect density distribution function (Fig. 2 C and F, open circles). Then, the random Gaussian noise with the magnitude proportional to 2% of absolute impedance value was added to both real and imaginary parts of impedance to generate the
Conclusions
Our novel approach extends capabilities of EIS methodology along with the tBLMs as model systems for lipid-protein interaction studies. We demonstrate that the EIS spectra contain information about lateral distribution of water-filled pores (defects) or reconstituted ion-channels in the dielectric sheet of phospholipid and such structural information can be retrieved by an appropriate EIS data analysis.
Application of the proposed data analysis algorithm to a synthetic data set
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This research was funded by Research Council of Lithuania (LMT), Agreement No. S-MIP-19-33
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