Background

Epithelial electrophysiology can provide insight into epithelial barrier function by measuring the electrical properties associated with the transport of ions, nutrients, and waste products [3,4]. Furthermore, transport across the tissue can be perturbed by blocking and activating ion channels or degrading tight junctions formed between the cells to isolate specific pathways or channels. This perturbation is useful for understanding healthy and diseased models, testing therapeutics, and characterizing quality control of in vitro cultures [1,5,6].

Transepithelial resistance (TER; also known as transepithelial electrical resistance, TEER) has become the gold standard over the last 30 years for quantifying epithelial tissue maturity and barrier integrity using commercial or custom electrodes and chambers [4,7,8]. Electrochemical impedance spectroscopy (EIS/ECIS), although not yet widely adopted, has been shown to offer insights into epithelial transport dynamics, membrane-specific properties, and more accurate measurements of membrane integrity. For example, Lewallen et al. showed the advantages of combining EIS with intracellular voltage recording to distinguish apical and basolateral transport function during adenosine triphosphate administration [1] in a custom Ussing chamber and automated electrode placement [9]. Cottrill et al. reported similar parameters without intracellular voltage recording, by making assumptions about relative permeability [10]. Linz et al. integrated EIS into existing commercial electrodes (STX, World Precision Instruments) to measure Caco-2 monolayer dynamics in response to stimuli: saponin, sonoporation, and calcium chelator ethyleneglycol-bis(beta-aminoethyl ether)-N, N’-tetraacetic acid (EGTA) [2].

Transepithelial resistance (TER) is a good indicator of tight junction development and membrane integrity. Tight junctions form between the cells, creating a paracellular pathway as shown in Figure 1A. The electrical resistance of the tissue is dominated, but not determined exclusively, by this paracellular pathway, compared to the flow of ions through the respective apical and basolateral membranes [11–13].

Figure 1. Circuit models for transport across an epithelial monolayer. Modified from Lewallen et al. [1]. (A) Physical model: cross-section schematic of an epithelial tissue showing the three pathways where transport is regulated: apical, basolateral, and paracellular pathways. (B) Three-parameter circuit model: a simple resistor-capacitor (RC) circuit that can be fit from extracellular electrodes alone, widely used to measure transepithelial resistance (TER) and transepithelial capacitance (TEC) despite its low fidelity. (C) Seven-parameter model with apical, basolateral, and paracellular pathways requires intracellular voltage measurement to fully solve [1,14]. (D) Five-parameter model, which we refer to as the RCRC model, with two resistors (R) and 2 capacitors (C) representing the cell layer, shown to model the apical and basolateral cell membranes of Caco-2 cells in Linz et al. [2].

TER measurement is typically performed at a single frequency (e.g., 12.5 or 75 Hz [7,15]), assuming resistance is independent of frequency (i.e., reactance is negligible). Yet, it has been observed that reactance is not negligible [1,2,16] and therefore, this assumption is not valid. As a result, the TER measured with a single frequency is erroneously low. For example, bronchiolar epithelia show a strong frequency-dependent change in resistance (see Figure 2). Mathematical models of epithelia that include reactance contributed by capacitance, as shown in Figure 1B–D, can more accurately fit the measurements across frequencies. Figure 2 shows an EIS data fit with the model from Figure 1D. In this figure, called a Nyquist plot, the resistance (R) and reactance (X) are the real and imaginary components of the complex impedance (Z), measured as a function of frequency.

Adding capacitive elements to the model (Figure 1B–D) can yield novel insights about the epithelial barrier. EIS measurements of TER from fitting a circuit model, as shown in Figure 2, inherently separate the electrical resistance of the tissue from the transwell and media, termed R_solution, shortened to R_sol. Thus, unlike traditional TER measurement, “background subtraction” from a blank is not necessary. The impedance measurements also capture capacitance, enabling one to model charge blockage or storage at the tissue surface, a frequency-dependent property [1,2,16]. In addition, transepithelial capacitance (TEC) shows promise in describing cell properties such as cell volume or surface area [17–20]. Although cell capacitance has been used for single cells to identify cell types in cytometry, rigorous biological studies have yet to be published correlating the TEC of a monolayer of cells to a specific cell property.

Figure 2. Nyquist plot of negative reactance (-X) vs. resistance (R) for frequencies of 2 Hz to 10 kHz on a measurement of bronchiolar epithelia (at day 7). Each point is the measured reactance and resistance for a given frequency; all measurements were taken on a single sample. TER measurements taken at a single frequency, such as 12.5 Hz and 75 Hz and shown in orange, underestimate TER [21] and require background subtraction. Each capacitance component can be estimated based on the approximate peak of each semicircular curve in the Nyquist plot, where at the peak, $\omega =2\pi f=\frac{1}{RC}$.

Figure 1B shows the simplest model that accounts for capacitance and lumps the apical and basal membrane, along with the paracellular properties, into single values of TER and TEC. While insightful and implemented in commercial devices (CellZscope, NanoAnalytics), we have shown that some epithelial tissues, like bronchiolar epithelia, require more detailed models to accurately calculate TER (e.g., Figure 1C, D [22]). Figure 1C, while modeling the apical, basolateral, and paracellular pathways separately, requires intracellular measurement to solve [1]; thus, the method we present here relies on the model of Figure 1D. This model can capture the different time constants observed in the data (τ = RC), yet can be measured with only extracellular electrodes. This model has been used in prior publications to analyze impedance data on Caco-2 cells changing in response to forskolin [2]. However, one of the shortcomings of the model of Figure 1D is that the paracellular resistance is lumped into R₁, R₂, C₁, C₂ and is therefore not resolvable.

With off-the-shelf electronic circuitry and software, we have developed a method for fitting an electronic model to measure the resistances and time constants associated with tissue changes. The cells are grown on the same transwells and tested in the same chambers used for conventional TER measurement. The electronic circuitry performs galvanostatic signal processing (e.g., analog to digital conversion, modulation) and conversion to impedance. The custom software performs mathematical and data analysis (e.g., fitting and error calculation). The electrical current is set to less than 10 μA to maintain linearity [16,20], and the frequency sweep is chosen such that the reactance is approximately zero at the bounds of the range, or approximately 2 Hz–50 kHz, with frequencies logarithmically spaced. We take these impedance measurements on retinal pigment epithelia (RPE) and bronchiolar epithelia (16HBE), and report transepithelial resistance (TER), transepithelial capacitance (TEC), membrane ratio (α), and a validated metric of reporting measurement error, the mean absolute error (MAE).

Prior to describing the method for epithelia, we will first discuss our validation of the EIS and fitting technique on electrical circuits that mimic the TER and TEC of living tissues. We soldered circuits with commonly observed TER and TEC values of mature tissues and lower TER and TEC values representing developing tissues, resulting in four electrical circuits: 16HBE1, 16HBE2, RPE1, and RPE2, as shown in Figure 3. The results show precise and accurate TER (< 7 Ω error, < 1 Ω SD), TEC [< 0.12 μF error (< 0.025 μF SD)], R_sol [< 4 Ω error (< 0.4 Ω SD)], and membrane ratio < 1.5 error (< 0.6 SD) for all four circuit models. Individual circuit parameters R_sol, R₁, R₂, C₁, C₂, and their errors are reported in Figure S2.

Figure 3. Electrochemical impedance spectroscopy (EIS) measurement and fitting to the RCRC model (Figure 1D) on four electrical circuits (16HBE1, 16HBE2, RPE1, RPE2) simulating bronchiolar epithelia (16HBE) and retinal pigment epithelia (RPE) cell layers. Six replicate EIS measurements were taken on each circuit, and all six measurements were fit six times to include fitting variability. Transepithelial resistance (TER) (< 7 Ω error, < 1 Ω SD), transepithelial capacitance (TEC) [< 0.12 μF error (< 0.025 μF SD)], R_sol [< 4 Ω error (< 0.4 Ω SD)], and membrane ratio < 1.5 error (< 0.6 SD) for all four circuit models. Signal 2 Hz–50 kHz, 2 freq/dec, 4 μA. Table inset: actual circuit values.