PETER-assay: Combined Impedimetric Detection of Permeability (PE) and Resistance (TER) of Barrier-Forming Cell Layers

Epithelial and endothelial barrier function is typically studied in vitro by growing the cells of interest on permeable supports that are sandwiched between two fluid compartments. This setup mimics the physiological situation with the cell layer as the diffusion barrier at the interface between two chemically distinct fluids. Routinely, the barrier function is quantitatively described by two key parameters: (i) the transepithelial or transendothelial electrical resistance (TER) as a measure of the permeability for small inorganic ions and (ii) the permeability coefficient (PE) as a descriptor of the permeability for molecular tracers. So far the two parameters have been determined in separate experiments. This study introduces a device that allows for simultaneous detection of PE and TER of the very same cell monolayer in one single experiment (PETER-assay). The novel approach is entirely based on AC impedance measurements in two different modes, so that TER and PE become available in real time. The new approach is demonstrated for three epithelial cell lines derived from the kidney (MDCK-I, MDCK-II, NRK) with very different barrier properties under stationary conditions and when challenged by barrier-breaking fungal toxin cytochalasin D. PETER provides an excellent time-resolution and completely automated data collection.

Solid knowledge about the structure, function and regulation of cellular barriers (e.g. skin, blood vessels, colon wall) is mandatory to understand many fundamental biomedical processes and pathologies. Cellular barriers are generally formed by monolayers of endothelial (blood vessels, lymph vessels) or epithelial cells (all other barriers). They share the expression of barrier-forming cell junctions (tight junctions) that occlude the intercellular space and avoid uncontrolled diffusion along the intercellular cleft from one side to the other [1][2][3] . There are three basic parameters to describe endothelial and epithelial barrier function: (i) the integral electrical resistance across the cell layer, (ii) the permeability for water and (iii) the permeability for tracer molecules 4 . In vitro, all three are determined by growing cells on permeable supports so that barrier tightness is accessible experimentally by (i) introducing electrodes on either side of the barrier or (ii + iii) establishing gradients of tracer compounds between both compartments. This model has been outstandingly successful and serves as a standard screening tool whenever targeting of drugs across cellular barriers or the cellular barriers themselves are addressed.
Transepithelial or transendothelial electrical resistances (TER in units of Ω·cm 2 ) have been traditionally measured by applying low amplitude current pulses through so-called chopstick electrodes across the cell layer and by recording the associated voltage drop. Following Ohm's law, the ratio of voltage to current normalized by the area provides the area-specific electrical resistance of the cell layer for small inorganic ions like Na + , Cl − , K + and HCO 3 − . The electrodes are referred to as chopsticks because they look like a two-armed fork with one current injecting electrode and one voltage sensing electrode on either arm. The two arms are dipped into the upper and lower compartment, respectively, measuring the resistance of the monolayer. However, due to the random placement of the electrodes at the periphery of the cell layer and due to the electrode geometry, the electric field is inhomogeneous leading to systematically overestimated TER values 5,6 . Using planar current injecting electrodes that are placed in parallel to the barrier-forming monolayer has solved this problem. Recently, a new approach has been described that is based on just two instead of four electrodes: one planar electrode forms the bottom of the well, and a planar dipping electrode reaches into the upper compartment 7 . With a two electrode setup, it is mandatory to determine the TER by recording the AC impedance along an extended range of AC frequencies and by fitting the transfer function of an appropriate equivalent circuit to the experimental data. This method does not only provide the TER but also the cell layer capacitance (C cl in units of µF/cm 2 ) as a measure for membrane topography. Moreover, it returns the resistance of the culture medium (R bulk in units of Ω) which may serve as an internal thermometer. Subtracting the impedance of an empty cell culture insert, as it is common with most other approaches, is typically not required.
A cell layer's water permeability is typically determined by inducing an osmotic pressure gradient across the cell layer grown on the permeable support. It is expressed as the osmotic water permeability coefficient (P OS in units of cm/s). The osmotically-induced water flux is detected from the dilution of a fluorophore in the acceptor compartment (fluorescence dilution assay 8 ) or simply by the corresponding change in fluid height in a specialized glass capillary 9 . The permeability of a labelled tracer molecule is commonly quantified by establishing a concentration gradient of the tracer across the cell layer and by detecting probe accumulation in the acceptor compartment over time. The time-dependent increase of the tracer concentration gives rise to the permeability coefficient (P E in units of cm/s). To date, mostly radio-or fluorescence-labelled probes have been used in these experiments 10,11 . When isotope labelling is applied, the permeation rate of the probe is only accessible as an integral descriptor of cellular barrier function. The permeation of fluorescence-labelled tracers has been followed integrally but also with spatial resolution to identify barrier heterogeneities or defects within the monolayer [12][13][14] . More recently, we reported the use of electrochemically active tracers for this purpose. The tracer was allowed to diffuse across the cell layer from below, while the upper surface was continuously scanned by an ultra-microelectrode to perform local quantification of probe concentration (scanning electrochemical microscopy; SECM). While permeability of the cell layer was accessible with subcellular lateral resolution, the technique suffered from low scan rates 15,16 .
This study describes a combination of two impedance-based approaches to measure TER and P E of epithelial and endothelial cell layers grown on permeable supports quasi simultaneously in one experimental setup. This new device allows studying several cell layers in parallel; it is highly automated and offers an excellent time-resolution. It is based on the established setup for impedance-based determination of TER values 7 but substitutes the single bottom electrode in the lower compartment by a co-planar arrangement of two differently sized electrodes. Whereas the dipping electrode (apical) and the larger of the two surface electrodes (basolateral) are used to record the transcellular impedance of the cell layer for TER assessment, the two co-planar electrodes in the lower compartment are used to quantify the time-dependent concentration of an electrochemically active permeability probe that was added to the upper compartment at the beginning of the experiment. Thus, the new device provides TER, the cell layer capacitance C cl and the permeability coefficient P E for the probe under study in one single experiment. We refer to this setup and the assay as P E TER which is the combination of the two established acronyms.

Results and Discussion
General experimental setup of the P e TER-device. The experimental setup of the new approach comprises a measurement chamber, an impedance analyser, a relay and an ordinary PC (Fig. 1A) that controls the measurement and stores the data. The impedance analyser applies a sinusoidal AC voltage of a pre-set frequency and amplitude to the electrodes and detects the resulting AC current. The relay is necessary to switch between the two electrode combinations needed for reading P E or TER. The measurement chamber which is the core component of the new setup is stored in an incubator to maintain physiological conditions. It contains three electrodes, two interdigitated gold-film electrodes on the bottom of the chamber and a stainless steel dipping electrode reaching into the fluid from above. The cell layer under study, grown on a standard permeable support, is sandwiched between the co-planar electrode arrangement in the basolateral compartment (1, 2, Fig. 1B) and the stamp-like dipping electrode in the apical compartment (3, Fig. 1C). This dipping electrode is mounted into the lid of a standard petri to ensure a constant working distance between electrode and the permeable support as well as to close the device and maintain sterility. The co-planar electrode structure in the basolateral compartment is composed of two differently sized interdigitated gold electrodes. The permeation of the redox tracer, added to the apical compartment at time zero, is followed by these two basolateral electrodes (P E -mode: 1 vs. 2) that sense the time-dependent concentration of the tracer in the basolateral fluid. TER and C cl of the same cell layer are recorded by the apical stainless steel electrode and the larger of the two gold-film electrodes in the basolateral compartment (TER-mode: 1 vs. 3). A crucial requirement to extract the permeability coefficient P E from the time course of tracer accumulation is exact knowledge of the volume in the receiver compartment. Therefore, a thin PTFE ring (Fig. 1D) is integrated into the basolateral chamber. Cell-covered permeable supports are placed onto the PTFE spacer creating a well-defined receiver volume.
TER-mode measurements using the P e TER setup. By using the larger of the two interdigitated basolateral electrodes (1 in Fig. 1) and the apical dipping electrode (3 in Fig. 1), the impedance across the barrier-forming cell layer was recorded over a broad frequency range (1-10 5 Hz). The resulting impedance spectra have been analysed with the help of an equivalent circuit that represents the electrical properties of the system under study. The corresponding equivalent circuit (inset in Fig. 2) has been developed before and is well established 7,17 . The parameters of its transfer function were fitted to the experimental data providing the electrical parameters of the system -most notably the cell layer resistance R cl (=TER) and its capacitance C cl (subscript "cl" stands for cell layer). Full description of the electrochemical system requires including (i) the electrolyte resistance of the bulk medium R bulk ; (ii) additional impedance contributions from the setup and the permeable  supports R ins and C ins (subscript "ins" stands for insert) as well as (iii) the impedance of the electrodes represented by a constant phase element (CPE) as the established electrochemical model for polarizable electrodes in physiological buffer 18 . Figure 2 presents typical impedance spectra recorded with the P E TER-device in TER-mode (1 vs. The frequency-dependent impedance as depicted in Fig. 2 may be divided in three frequency regimes: (i) At high frequencies (10 4 -10 5 Hz) the impedance magnitude |Z | remains almost frequency-independent since it is dominated by R bulk . (ii) In the mid frequency range (10 2 -10 4 Hz for MDCK-II, 10 3 -10 5 Hz for NRK, 10 -10 4 Hz for MDCK-I) the dielectric properties of the cell layer (R cl , C cl ) are reflected as a shoulder. (iii) The linear impedance increase towards low frequencies is due to the impedance of the electrode/electrolyte interface modelled as a CPE. The three cell lines are known to express barrier forming tight junctions to very different degrees that mirror their physiological origin from different sites of the collecting duct in the kidneys. NRK cells represent the class of rather leaky cell layers that are classified as epithelial-like. MDCK-II cells are considered moderately tight, whereas MDCK-I cells are known to build very tight barriers 19,20 . The differences in barrier function are expressed in their individual TER values ranging from 11 Ωcm 2 for the NRK cell layer, 88 Ωcm 2 for MDCK-II to 2978 Ωcm 2 for MDCK-I cells. From the pool of our data we determined average TER values of (14 ± 1) Ωcm 2 for epithelial-like NRK cells, (92 ± 4) Ωcm 2 for MDCK-II cells and (3000 ± 130) Ωcm 2 for MDCK-I cells. Accordingly, the order of barrier tightness NRK < MDCK-II < MDCK-I is clearly reproduced by the individual TER values which compare favourably with data taken from the literature (cf. Table 1). It is noteworthy when comparing TER values recorded in different labs for the same cell lines that they are readily affected by the external conditions and the medium composition 21 .
Cell layer capacitances C cl are only rarely reported despite their usefulness in epithelial biology as an indicator for plasma membrane topography. The spectra in Fig. 2 reveal cell layer capacitances C cl to be 0.8 µF/cm² for NRK cells, 1.3 µF/cm² for MDCK-II cells and 2.0 µF/cm² for MDCK-I cells. Pooling all experiments, the average C cl values are (0.88 ± 0.04) µF/cm² for NRK, (1.37 ± 0.09) µF/cm² for MDCK-II and (1.91 ± 0.06) µF/cm² for MDCK-I cells (mean ± SE). When apical and basal membranes are entirely flat and do not show any convolutions or microvilli, the cell layer capacitance would be close 0.5 µF/cm². This value corresponds to the serial arrangement of two unfolded membranes in series, with each of the two flat membranes showing a membrane capacitance C M of 1 µF/cm², as it is widely accepted. A cell-type dependent cell layer capacitance C cl significantly higher than 0.5 µF/ cm² reveals the expression of microvilli and other membrane convolutions that enlarge the plasma membrane surface area. The highest C cl values for MDCK-I cells indicates that their plasma membrane shows the highest level of microvilli decoration, a fact that becomes important when active epithelial transport across the plasma membranes is quantitatively compared between different epithelial cell lines. Comparison to literature values is difficult as C cl values are rarely reported. Table 1 compares the capacitances of NRK, MDCK-II and MDCK-I cell layers as determined in this work with C cl values of the three cell lines taken from a different study from our lab 22 , when the cells were grown on planar gold-film electrodes but not on porous supports. We are well aware that cell differentiation might be different on permeable rather than non-permeable supports. We only report these values as an orientation.
Quantifying TER values by means of impedance analysis provides several striking advantages: (i) Using two planar, parallel electrodes ensures a homogenous electric field across the cell layer. Thus, the entire monolayer contributes to the recorded impedance preventing a systematic overestimation of the resistance of the cell layer, as it has been reported for chopstick electrodes 5,6 . Moreover, planar parallel electrodes in a fixed position make TER readings independent of a manual positioning of the electrodes providing significantly improved reliability and reproducibility. (ii) The P E TER-setup or technically similar approaches provide time-resolved TER monitoring (time resolution better than 2 min per well) without breaking the physiological temperature or humidity. (iii) Besides TER, cell layer capacitance (C cl ), bulk resistance (R bulk ) and constant phase element (CPE) are recorded www.nature.com/scientificreports www.nature.com/scientificreports/ and documented simultaneously which makes correction for cell-free permeable supports dispensable in most cases. Since R bulk is strongly temperature-dependent, it provides an internal temperature control of the experiment. (iv) TER assays as performed here are highly automated and are conducted under sterile conditions. Thus, the approach ensures measurements under well-controlled external conditions. p e -mode measurements using the P e TER setup. The two co-planar interdigitated gold electrodes (1/2, cf. Fig. 1) on the bottom of the measurement chamber were used to quantify the accumulation of a redox tracer in the basolateral compartment after its permeation across the barrier forming cell layer. The electrochemical detection of the redox tracer is based on the fact that gold-film electrodes are almost ideally polarizable electrodes when bathed in physiological buffers, i.e. there is no charge-transfer across the electrode/electrolyte interface. However, when redox active species with a matching electrochemical potential are added to the bathing fluid, charge transfer across the electrode/electrolyte interface occurs. This phenomenon has been demonstrated repeatedly, for instance, when equimolar mixtures of ferri-and ferrocyanide [Fe(CN) 6 ] 3−/4− were used as well-behaved redox species. The associated impedance change is dependent on the concentration of the species and easily measured at low AC frequencies. Accordingly, it is the rationale of the P E TER approach to add an electrochemically active species to the apical compartment at time zero and measure its accumulation in the basolateral compartment by impedance measurements with the help of the interdigitated gold-film electrodes integrated in the bottom of the measurement chamber. In order to determine P E values, it is indispensable to establish the concentration dependence of the impedance changes that are associated with the accumulation of the probe. From impedance theory, the presence of electrochemically active species gives rise to a charge-transfer resistance R ct that represents the resistance associated with electron transfer from the metal electrode to the ionic species in solution and vice versa. In series to R ct there is the so-called Warburg impedance Z w that represents the impedance associated with the diffusion-limited mass transfer of the redox species to/from the electrode. These two impedance elements, which are sometimes bundled to a so-called faradaic impedance Z f , are aligned in parallel to the constant phase element that represents the impedance of the electrode in absence of redox species. The parallel arrangement of Z f and Z CPE is in series (insert in Fig. 3A) to the bulk resistance R bulk [23][24][25] . Both quantities, R ct and Z w are dependent on the concentration of the redox active species. To quantify both parameters individually, it is necessary to record full impedance spectra. In the interest of time resolution, we made use of an empirical approach instead that provides a linear correlation between concentration of redox active species and electrochemical measurand. As detailed in Fig. 3A for the model redox species [Fe(CN) 6 ] 3−/4− , the inverse impedance magnitude 1/|Z | at a frequency of 1 Hz changes by almost two orders of magnitude when the concentration of [Fe(CN) 6 ] 3−/4− was increased from zero to 1.0 mM whereas 1/|Z | is hardly affected for frequencies higher than 1 kHz. This is in perfect agreement with impedance theory and experimental reports on the impedance characteristics of [Fe(CN) 6 ] 3−/4− in physiological buffers. Plotting 1/|Z | as a function of [Fe(CN) 6 ] 3−/4− concentration (Fig. 3B) provides a strictly linear correlation (R² = 0.999) with a slope of (670 ± 7) µS/mM. The slope of this calibration curve quantifies the sensitivity of the measurement for a given redox probe in the P E TER assay, provided that they prove sufficient biocompatibility and no interference with TER readings. Equimolar mixtures of [Fe(CN) 6 ] 3−/4− were found to fulfil all requirements to serve as permeation probe in the P E TER assay. It is noteworthy that the charge-transfer reaction does not occur at the stainless-steel dipping electrode due to a mismatch of redox potentials for this material. Thus, the TER reading is unaffected by the presence of the electro-active species. www.nature.com/scientificreports www.nature.com/scientificreports/ For the impedimetric P E assay, 1 mM [Fe(CN) 6 ] 3−/4− dissolved in the experimental buffer is added to the apical compartment. Subsequently the P E probe penetrates the cell layer by passive diffusion along the concentration gradient with time. The permeation rate is dependent on the barrier function of the cell layer under study. Upon arrival in the basolateral compartment, the redox species induces a concentration dependent change of 1/|Z | at the basolateral electrodes. Using the calibration curve in Fig. 3B and exact knowledge of the receiver volume (V R = 9.85 • 10 −3 cm 3 ), the time-course of 1/|Z| 1Hz can be transformed into the time-dependent tracer accumulation in the receiver compartment n R (t). As detailed in the supplementary information, the molecular permeability coefficient (P E ) is then calculated from the rate of tracer accumulation dn R (t)/dt which corresponds to the slope of the curve n R (t). Only the initial linear phase of the time course of tracer accumulation was used for analysis (i.e. linear regression) to ensure proper sink-conditions. Complete equilibration between both compartments would lead to stationary values of 1/|Z | . We have experimentally ruled out any toxicity of the tracer for the concentrations and exposure times used here (cf. fig. SI1 in supplementary information) by biochemical cell viability assays (PrestoBlue ™ ). This electrochemical P E assay was conducted for the same three cell lines that have been studied for their individual TER values above: NRK, MDCK-II and MDCK-I. Table 2 summarizes the individual P E values that were corrected for the P E of the cell-free permeable support (cf. materials & methods).
The order of decreasing P E values NRK» MDCK-II > MDCK-I mirrors the tightness of the cell layers for the permeation of [Fe(CN) 6 ] 3−/4− and corresponds to the order of increasing TER values. The lowest tracer permeability is observed for MDCK-I cells which form extremely tight monolayers as already indicated by their TER values. A slightly higher P E value is obtained for MDCK-II cells that build moderate barriers. NRK monolayers grown on permeable supports are very leaky due to the lack of functional tight junctions. This low-barrier phenotype is mirrored by more than 500 times higher P E values in comparison to MDCK-I layers. Since [Fe(CN) 6 ] 3−/4− is slightly coloured, it was possible to quantify the time-dependent concentration of the probe in the basolateral compartment also by photometry at a wavelength of 405 nm as an independent control of the impedance-based approach. Optical concentration analysis returned very similar permeability coefficients of MDCK-II and MDCK-I cells that were determined to be (1 ± 3)·10 −6 cm/s. So the outcome of optical and impedance-based concentration analysis was essentially the same. P E values recorded for NRK cells were significantly smaller following optical analysis compared to the impedance-based readout. But with either readout, the P E value indicates that NRK cells form very leaky epithelial barriers compared to MDCK-II and MDCK-I cells. It is noteworthy that the impedance-based P E values show significantly better reproducibility as indicated by the standard error of the measurements (cf. Table 2). This is at least in part due to the fact that the impedance-based approach does not require any sampling from the basolateral compartment since the [Fe(CN) 6 ] 3−/4− concentration is determined in situ. Once the redox probe is added to the apical compartment, the assay runs completely automated without any interference by the operator or opening of the incubator door. This is very different from the optical readout as performed here and throughout the literature. It requires repeated opening of the incubator and liquid handling in the lower compartment raising severe constraints to the time resolution of the optical assay. Reducing the number of data points to a minimum is the only way to limit the invasiveness of these readout approaches 26-28 but makes the readout prone to artefacts.
To the best of our knowledge, no permeability studies using [Fe(CN) 6 ] 3−/4− as a permeability probe have been conducted and no P E values for this probe have been reported so that a direct comparison to other studies is currently impossible. However, we compared the P E TER-based permeability coefficients for [Fe(CN) 6 ] 3−/4− with data recorded for other commonly used probes and found meaningful agreement that strongly supports the feasibility of the new assay (Table 3). Commonly used P E probes differ with respect to their molecular mass and their charge. Whereas the dependence of P E -values on probe size has been systematically documented recently 10,21 , we are not aware of any study that addresses the dependence of permeation rates on the net charge of the probe even though it is very likely to play a role. In terms of mass and charge fluorescein is the probe that is closest to [Fe(CN) 6 ] 3−/4− and the individual P E values agree favourably within the limits of experimental errors. Fluorescein is supposed to pass cellular barriers predominantly across bicellular tight junctions 29 . In contrast, the paracellular permeation of macromolecules across MDCK-II layers is mainly provided by large tricellular tight junctions 30 . The question whether [Fe(CN) 6 ] 3−/4− is transported primarily via bicellular or tricellular tight junctions cannot be addressed by the entirely integral P E TER assay. Besides [Fe(CN) 6 ] 3−/4− we tested a second redox species for its performance in the P E TER-assay: ferrocene-methanol, or short FcMeOH. Our studies (cf. supplementary information) revealed that FcMeOH is biocompatible for concentrations used here ( fig. SI1 in supplementary information) and readily detected by the basolateral electrodes following the same experimental procedures and analysis formalism as   www.nature.com/scientificreports www.nature.com/scientificreports/ the cell layer exclusively on paracellular pathways so that P E values report on the tightness of barrier forming cell junctions. In contrast, FcMeOH is suspected to migrate at least partially across the membranes due to its lipophilic and uncharged character 15 . We are currently investigating whether or not a serial application of different probes to one cell layer or the parallel application of two probes to two cell layers provide additional information.
Taken together, the impedance-based permeability measurement provides reliable P E estimates that agree favourably with measurements reported by others using conventional approaches. Moreover, the P E values are supported by the parallel TER readings that provide consistent characterization of the individual epithelial barrier function. The impedance-based P E -assay excels the conventional approaches significantly in terms of time-resolution that can be pushed well below one minute. Thus, the novel technique provides online permeability monitoring and the extraction of time course data for the permeability coefficient that has not been reported before. One limitation of the new assay at the current stage of development is the limited number of tracers that have been identified so far. Fluorescence-based assays offer a pool of permeability probes with varying molecular mass from small molecules like fluorescein to macromolecules like FITC-dextran. This set of tracers enables systematic investigations of size-dependent molecular permeability across epithelial cell layers. Such a variety of probes is not yet available or identified for the impedance-based readout but a direction of future research. Currently, the P E TER assay is limited to study the permeation of low molecular weight tracers. Another problem of in vitro permeability measurements in general is the potential impact of unstirred water layers on either side of the cell layer that build a second barrier to permeability probes and hence, lead to an underestimation of P E values 31 . Mild agitation of the incubation fluid on either side of the permeable support may solve this issue but the current setup is not yet compatible with that like most established P E approaches. combined impedimetric Detection of p e and teR (p e TER-assay). The parallel use of P E -and TER-mode measurements in what we call a P E TER assay allows characterizing the epithelial barrier function of a single cell layer with time by two independent parameters. MDCK-II cells were grown to confluence on permeable supports and mounted in the P E TER setup (cf. Fig. 1) which was kept in an ordinary cell culture incubator. In TER-mode impedance spectra were recorded using electrodes 1 and 3 for subsequent TER determination using equivalent circuit modelling. In P E -mode the impedance was only recorded at one single frequency of 1 Hz to conclude on the accumulation of the permeability probe in the basolateral compartment. At time zero the MDCK-II cell layer was exposed to 1 mM [Fe(CN) 6 ] 3−/4− which was added to the apical fluid compartment (Fig. 4A). The time course of 1/|Z | indicates that significant permeation of the probe across the cell layer started soon after its introduction. The measured 1/|Z| 1Hz increases linearly by 17 µS within an observation time of 60 min. Parallel TER monitoring supports the non-invasiveness of the approach, since the electrical resistance of the cell layer remains almost constant during the entire measurement (maximum change between 82 -93 Ωcm 2 ). In a second experiment (Fig. 4B), a MDCK-II monolayer was again exposed to 1 mM [Fe(CN) 6 ] 3−/4− at t = 0 min from the apical side and baseline data were recorded for app. 75 min. The cell layer was then challenged by 5 µM cytochalasin-D (t = 72 min). After a short delay time the presence of cytochalasin-D causes a pronounced disruption of barrier function as indicated by the massive increase of 1/|Z| 1Hz that amounts to almost 80 µS within 30 min. Please note the different scales for 1/|Z | 1Hz in Fig. 4A,B. The time-course of TER is consistent with this significant reduction of barrier function after cytochalasin-D exposure started. Initially no significant changes in TER are visible when the redox tracer is introduced into the system, but the subsequent addition of cytochalasin-D after 72 min induces an exponential decay of TER. The breakdown in barrier function is due to the well-known inhibitory effect of membrane-permeable cytochalasin-D on g-actin polymerization without affecting f-actin depolymerisation leading to net actin disassembly 32 within several minutes. The impact of cytochalasin-D on the actin cytoskeleton has been visualised by confocal fluorescence microscopy after staining the actin cytoskeleton by fluorescence-labelled phalloidin ( figure SI3 in supplementary information). Microscopic analysis confirms the pronounced perforation of the actin belt that marks the cell-cell contact zone as a continuous staining under control conditions. The results of Fig. 4 demonstrate that the new approach enables a quasi-simultaneous determination of P E and TER in one experiment and within one experimental setup. This implicates a significant improvement of in vitro permeability studies, as the P E experiments contain automatically an internal TER control as well as information on plasma membrane topography provided by the cell layer capacitance. So far permeability assays are commonly performed with TER measurements in separate setups before and/or after the P E assays, mostly to ensure barrier integrity prior to the P E assay. Thus, dual mode P E TER-assays provide a significant saving of cost and time in addition to the improved information content provided by simultaneous TER and P E recordings.  Table 3. Permeability coefficients P E for different permeability probes that are commonly used to characterize epithelial barrier function. All P E -values have been recorded for confluent MDCK-II cells grown on permeable supports from different manufacturers.

Conclusion
The novel P E TER-approach allows for simultaneous observation of two key parameters of epithelial and endothelial barrier function -TER and P E -with a time-resolution of around one minute per cell layer. The purely electrical readout and the high level of automation require significantly less manual handling of the cell layers compared to established methods which improves reproducibility. The proof-of-concept study presented here with a maximum of two cell layers studied in parallel is scalable, providing the potential for screening for barrier function with reasonable throughput. Using multi-channel impedance meters will enable studies on epithelial and endothelial barrier function in 12-, 24-, 48-or even larger formats without sacrificing time-resolution. Feeding the calibration data into the software (e.g. by look-up tables or user input) will allow for a complete analysis of the experiment in situ. This study describes the use of two different redox tracers. A more extended screening for suitable permeability probes will identify further candidates and thereby broaden the information content of the measurement. It seems appealing to develop coupling chemistry to label biomolecules with electrochemically active moieties and to apply them in P E TER assays. A future direction of method development might look for combining different redox tracers with different permeation routes to further increase the information content of the assay.  www.nature.com/scientificreports www.nature.com/scientificreports/ Merck KGaA, Germany) and iodine (0.499 mM, Merck KGaA, Germany) under constant agitation. The etching process was stopped by a washing step with double distilled water. To get rid of the remaining photoresist, the substrate was exposed to UV light in absence of any mask and developed with sodium hydroxide as described above. A glass ring (height = 10 mm; diameter = 24 mm) was mounted on the bottom plate holding the interdigitated gold-film electrodes by a cyto-compatible silicon adhesive. The stamp-like dipping electrode was made from stainless steel. The shaft of the stamp had a thickness of 4 mm and was flattened at one end to a circular disk with a height of 1 mm and a diameter of 10 mm. In order to guarantee equal distances between the apical electrode and the permeable support as well as to close the device, the dipping electrode was integrated into a standard petri dish lid (Ø = 40 mm, TPP ® , Sigma Aldrich, Germany). The electrode was fixed 2 mm above the permeable support.

Material and Methods
All electrodes were electrically connected to an impedance analyser (Solartron Instruments, SI-1260, UK) via a relay that allows connecting different electrode combinations to the impedance meter. Relay and impedance analyser were controlled by a standard PC using data collection software written in LabView. The new device allowed two measuring modes with frequency settings and individual AC voltage amplitudes (rms): (i) P E -mode: 1 vs. 2, 1 Hz/10 Hz, 50 mV, (ii) TER-mode: 1 vs. 3, 1-10 5 Hz, 10 mV. The DC potential was clamped to zero to prevent any battery effect between the two different metals used as electrodes. p e TER-assay. All impedance measurements were conducted in a standard cell culture incubator at 37 °C and 0% (v/v) CO 2 . A PBS ++ buffer (Sigma Aldrich, Germany) containing 1 g/L D-glucose (denoted as PBS ++ /glucose (1 g/L)) served as the experimental buffer. A PTFE ring (thickness = 100 µm; inner diameter = 1.12 cm, fabricated by the machine shop at Regensburg University) was fixed to the bottom of the basolateral chamber. Cell-covered inserts were placed on the PTFE spacer creating a small cylindric buffer reservoir between the permeable support and the basolateral electrodes. This cylindric volume is referred to as receiver volume (V R ) and it was calculated from its geometric dimensions to be 9.85 • 10 −3 cm 3 . The basolateral compartment was filled with 700 µL and the apical compartment with 500 µL PBS ++ /glucose (1 g/L). The redox tracer was added to the apical compartment by replacing 250 µL of the experimental buffer with 250 µL of a double-concentrated tracer solution. The permeability coefficients were extracted from the experimental data recorded in P E -mode. Based on device calibration and knowledge of V R , the time-course of 1/|Z| 1Hz was transformed into the time-dependent accumulation of tracer in the receiver compartment n R (t). The linear phase of the n R (t) time course was analysed by linear regression providing the parameter dn R (t)/dt. With the other relevant parameters V D,0 (initial volume of the donor compartment, 0.5 cm 3 ), A (area of the porous support, 1.12 cm 2 ) and n D,0 (initial amount of tracer in the donor compartment, 5 • 10 −4 mmol) the apparent permeability coefficient P app was calculated according to Eq. (1) 31,33 : app D D R ,0 ,0 P app was corrected for the permeability of the cell-free support (insert) P ins according to Eq. (2) providing the permeability coefficient P E : = − P P P 1 1 1 (2)

E a pp ins
The transepithelial or transendothelial electrical resistances (TER) were obtained by equivalent circuit modelling of the raw data in TER-mode. A detailed description of the modelling procedure has been reported before 7 . The applied equivalent circuit is included in Fig. 2. The transfer function of this model is fitted to the measured impedance spectra. The minimization was carried out by non-linear least square optimization (Levenberg-Marquardt). The bulk resistance (R bulk ) represents the resistance of the bulk electrolyte and the resistive contributions arising from wiring and connectors. The constant phase element (CPE) describes the impedance of the electrode/electrolyte interface as Z CPE = A −1 (iω) −n with A and n as adjustable parameters, ω = 2πf as the angular frequency and i as the imaginary unit. The cell layer has both resistive and capacitive features which are expressed by a parallel combination of the two circuit elements R cl (resistance of the cell layer) and C cl (capacitance of the cell layer). R cl provides the integral resistance of the cell layer which is also denoted as TER. TER and C cl are normalized to the area of the permeable supports and are presented in units of Ω·cm 2 and µF/cm 2 , respectively. The contribution of the permeable supports to the recorded impedance is considered by a parallel combination of the two parameters R ins (resistance of the insert) and C ins (capacitance of the insert). The values of R ins and C ins were determined in separate experiments and were kept constant during the fitting procedure.