A microfluidic sucrose gap platform using trilaminar flow with on-chip switching and novel calibration: Challenges and limitations

Abstract

Gap junction connectivity is crucial to intercellular communication and plays a key role in many critical processes in developmental biology. However, direct analysis of gap junction connectivity in populations of developing cells has proven difficult due to the limitations of patch clamp and dye diffusion based technologies. We re-examine a microfluidic technique based on the principle of laminar flow, which aims to electrically measure gap junction connectivity. In the device, the trilaminar flow of a saline sheathed sucrose solution establishes distinct regions of electrical conductivity in the extracellular fluid spanning an NRK-49F cell monolayer. In theory, the sucrose gap created by laminar flow provides sufficient electrical isolation to detect electrical current flows through the gap junctional network. A novel calibration approach is introduced to account for stream width variation in the device, and elastomeric valves are integrated to improve the performance of gap junction blocker assays. Ultimately, however, this approach is shown to be ineffective in detecting changes in gap junction impedance due to the gap junction blocker, 2-APB. A number of challenges associated with the technique are identified and analyzed in depth and important improvements are described for future iterations.

I. INTRODUCTION

A. Importance of gap junction connectivity to developmental biology

Intercellular communication is mediated by cytoplasmic couplings called gap junctions. In vertebrates, these intercellular channels are formed from clusters of hemichannel connexin proteins located on the cell membrane that allow direct diffusion of signaling molecules.¹ As the most direct mediators of cell-to-cell communication, gap junctions play a crucial role in the network dynamics that appear to govern many important developmental processes, including embryogenesis, regeneration, and cancer suppression.²

In normal growth, gap junctions appear necessary to establish large scale patterns and to guide pluripotent cell fates toward the correct morphology. The gap junction expression has been shown to affect organ and limb patterning,^2,3 the establishment of left–right asymmetry,⁴ and the differentiation of many cell types, including lens cells,⁵ dental pulp stem cells,⁶ and neuronal precursors.⁷ Gap junctions also seem to serve a central role in regeneration⁸ and respecification. In planarian flatworms, disruption of gap junction communication during regeneration can lead to double-headed specimens or even worms with characteristics of different planarian species.^9,10 The importance of gap junction connectivity to developmental biology suggests potent applications in synthetic morphology and tissue engineering.

The aberrant gap junction expression is associated with various disease states, including tumorgenesis and cancer. Metastatic cell behavior models primitive unicellular activity disconnected from a larger computational network, which would direct its morphogenetic goals.^11,12 Thus, tumor tissue expresses less gap junctions, and lowered gap junction connectivity is correlated with tumorgenesis.^13–15 Restoring intercellular connectivity and normal bioelectric signaling is an emerging therapy approach for endogenous cancer suppression.

The importance of gap junction communication to so many fundamental processes in developmental biology motivates the development of a reliable and repeatable assay to quantitatively assess gap junction connectivity in cell networks. Further, to investigate functional roles, assays that can manipulate junction dynamics with agents such as chemical gap junction blockers are needed.

B. Approaches to gap junction measurement

Gap junction connectivity can be measured electrically through dual whole-cell patch clamping. This technique produces high fidelity measurements of the conductance between isolated cell pairs.¹⁶ However, the process is expensive, invasive (compromising the cell membrane to introduce patch pipets), and technically difficult to perform.¹⁷ Further, dual cell patch clamping measurements characterize only two cells, failing to capture larger network dynamics. While analysis of capacitive transients in single cell patch clamping has been shown to reflect a cell’s connectivity to its network,^18,19 throughput for patch clamping is extremely low, sampling only a few individual cells while requiring expensive equipment and specialized labor.

The diffusion of membrane impermeable fluorescent dyes can also be optically traced to measure gap junction connectivity.²⁰ Dye can be introduced to a tissue sample through invasive means, including microinjection²¹ and scrape loading,²² or can be pre-loaded into a cell population and then co-cultured with non-dyed cells.²³ New microfluidic approaches have also sought to use laminar flow to spatially confine membrane permeable dye and to monitor its intercellular diffusion beyond the laminar boundary.^24,25 These methods struggle to provide continuous real-time quantitative measurement of intercellular connectivity due to the difficulty of dye washout and reinjection. Redistribution techniques, such as fluorescent recovery after photobleaching (FRAP),²⁶ can offer near real-time measurements. However, dye transfer, in general, may not fully capture bioelectric signaling as junctions that are electrically coupled may not effectively transfer dye due to the molecular size or chemical properties.^27,28

Bathany et al. ²⁹ proposed an electrical measurement of gap junction connectivity through a microfluidic sucrose gap platform. The device established trilaminar flow, wherein two conductive saline streams act like a sheath for a non-conductive sucrose solution. The sucrose region provides electrical isolation over a cell monolayer, forcing electrical current through the gap junctions and yielding a measure of gap junction conductance in the cell network. Here, we attempt to replicate and improve upon the findings of Bathany et al.²⁹ Despite methodological improvements, we ultimately report that the approach may not be as reliable as once thought for electrical gap junction interrogation. However, important considerations for the design of electrical sucrose gap platforms based on trilaminar flow are explored and potential sources of error based on updated bioelectrical modeling are presented.

II. METHODS AND DESIGN

A. Trilaminar device design with integrated microvalves

The trilaminar sucrose gap design of Bathany et al.²⁹ used a compression design to seal rigid microfluidic channels against a glass backing at the time of the experiment. We have created a design for closed devices to increase repeatability and experimental control.

Transitioning to a closed design permits the “soft lithography” manufacturing approach that is ubiquitous in microfluidic devices.³⁰ Because soft lithography is a replica molding technique, many identical devices can be produced through relatively cheap, low temperature processes. Closed devices eliminate the risk of fluid leakage and reduce the risk of introducing bubbles or contaminants that compression devices can experience during assembly. Generally, closed devices should lead to better test-to-test repeatability as the channel geometry is fixed in place.

Most importantly, adopting a closed fabrication regime presents the opportunity to integrate elastomeric valves for on-chip fluid control. The sucrose solution is not a biologically relevant environment and prolonged exposure can lead to membrane potential depolarization and adverse cell health effects (see Sec. III E). Therefore, the sucrose gap conditions should be maintained for as short a time as possible between assays. If the perfusion switching junction for the sucrose solution is located off-chip, a macroscale dead volume of solution in the tubing must be flushed between each experimental condition. Flushing the dead volume either costs time (usually, several minutes) or compromises cell health due to excessive shear stress if the flow is too rapid. Integrating pneumatic microvalves into the chip results in microsecond solution exchange, eliminating this trade-off.

The primary disadvantage of the closed device approach is that it shifts the burden from troublesome device assembly to cell culture in the microfluidic chip. Cells must be seeded into the device and cultured over the electrodes until they form a connected monolayer, which is a lengthy process that potentially limits testing throughput. Further, cells seeded in this manner distribute throughout the device, including in the upstream saline side channels, which can be a source of flow instability. Additionally, the closed devices are fabricated using the elastomer, polydimethylsiloxane (PDMS), which is moderately gas permeable and has been shown to absorb small molecules.³¹ Finally, the closed device design a priori limits the number of different sucrose perfusions that can be used in the assay. In this work, we have opted to switch between two solutions, but more channels could easily be added in a future design.

Figure 1(a) shows the design for a closed trilaminar sucrose gap device with integrated microvalve switches. The saline solution (with membrane non-permeable dye for stream width tracking) is perfused into fluidic ports 3 and 4. Normally closed elastomeric valves (pneumatic ports a and b) control perfusion of sucrose solutions into the central inlet channel from either fluid port 1 or 2. Three fluidic inlet channels converge to form a sucrose gap region of trilaminar flow over the planar electrodes [Fig. 1(c)]. The central sucrose channel is approximately 250  $\mu$m by 7.5 mm and the side saline channels are 275  $\mu$m wide with a total length of 8.6 mm. These dimensions are designed such that the sucrose stream occupies 30% of the total 1200  $\mu$m width in the trilaminar flow region, where the inner electrode spacing is 600  $\mu$m. Sensing electrodes are 50 by 1350  $\mu$m, and source electrodes measure 100 by 900  $\mu$m. The effluent is divided into two channels to ensure electrical isolation by splitting the sucrose stream. The fluidic layer is made as deep as reasonable in the fabrication process (75  $\mu$m), both to maximize the available nutrient volume during culture and to reduce the impact of the cell layer on the hydrodynamic resistance of the channels.

FIG. 1.

Trilaminar flow sucrose gap device design. (a) Saline is perfused into fluidic ports 3 and 4, while sucrose solution feeds into ports 1 and 2, creating a region of trilaminar flow over planar microelectrodes. (b) Flow into the middle sucrose channel is controlled pneumatically by normally closed elastomeric valves, shown in the open position (4 $\times$, bright field). (c) Cells are cultured in the device and measured under the trilaminar sucrose gap. To monitor the laminar flow boundaries, rhodamine dye is added to the saline channels (10 $\times$, composite phase contrast/RFP (Red Fluorescent Protein filter), false color).

The switching valves associated with pneumatic ports a and b are left in their normally closed state during cell seeding, ensuring that no cells are trapped under the valve seat. This approach guarantees that the valves seal tightly against the substrate, preventing leakage and ensuring consistent switching. Integrating elastomeric valves into the design allows the sucrose solution to be switched and completely re-perfused within hundreds of microseconds, drastically reducing the run time of gap junction blocker assays.

B. Fabrication

Device fabrication, including selective bonding of the elastomeric valves by an oligomer stamping method, follows a protocol previously described.³²

Cr/Au electrodes were sputter coated onto glass microscope slides using a liftoff process. The substrates were cleaned by piranha etch and oxygen plasma treatment. Electrodes were photolithographically patterned using an Omnicoat (Kayaku) release layer (spin coated at 3000 rpm for 30 s) and positive photoresist AZ9260 at approximately 6.5  $\mu$m thickness. After oxygen plasma treatment (200 W, 30 s, 70 mT), Cr/Au electrodes were deposited by sputter coating to a depth of 30 nm and 210 nm depth, respectively. Liftoff was performed by Microposit Remover 1165 at 55  ${}^{°}$C for more than 8 h.

The microfluidic device is composed of two layers of replica molded PDMS (Sylgard 184) prepared at the standard 10:1 elastomeric base to curing agent ratio. Master molds for both layers were fabricated on silicon wafers using negative photoresist SU8-3050. The SU8 was deposited using standard lithographic techniques to a depth of 75  $\mu$m. Following silanization, the fluidic layer was spin coated with uncrosslinked PDMS for 60 s at 2000 rpm, while the pneumatic layer was cast molded to a depth of 5 mm.

The layers were bonded by oxygen plasma treatment (20 W, 30 s, 500 mT), and alignment was performed with a custom rig. First, the pneumatic layer was bonded over the thin membranes of the fluidic layer. The device was released from the wafer and cored to form inlet/outlet ports. After plasma treatment, valve seat areas were stamped with untreated PDMS to selectively remove the surface activation before bonding to the glass substrate.

C. Experimental setup

All experiments were driven by pressurized nitrogen gas (Airgas, Inc.), which was programmatically controlled by OB1 Mk3+ regulators (Elveflow). A portable laboratory pump provided vacuum at $-75$ Torr (N810FTP, Ideal Vacuum Products). Compact magnetically latching solenoid valves (LHLA1231111H, Lee Co.) were used to switch between vacuum and positive pressure. Electrical measurements were recorded using a Keithley 6221 alternating current source (Tekronixs, Inc.) in conjunction with a SR830 digital lock-in amplifier (Stanford Research Systems). All stimulus signals used 100 nA amplitude. The lock-amplifier was used in floating configuration with a 300 ms time constant. High resolution images were captured by an EVOS M7000 inverted fluorescence microscope. Devices were imaged through a transparent indium tin oxide coated heater, which was maintained at 37  ${}^{°}$C.

D. Cell culture protocols

In principle, any gap junction expressing cell line that forms adherent monolayers is suitable for use in the device. Strong expression of cadherins, which play an important role in cell-cell adhesion and cytoskeletal connection, is additionally advantageous. Indeed, cadherins in epithelial cells can enhance the formation of gap junctions by improving cell–cell contact.³³ However, because they do not directly transfer ions, cadherin junctions alone in the absence of gap junctions are unlikely to provide the physiological connectivity that we seek to measure. In general, however, this device should enable the study of functional gap junction connectivity in many different cell types, including epithelia.

In this work, the NRK-49F line is selected as it has been previously used to study gap junction connectivity.^24,34 This fibroblast cell line derived from normal rat kidney is known for dense expression of gap junctions (primarily Cx43).^35,36,18 NRK cultures were passaged a minimum of two times and a maximum of five times after being thawed from frozen stock and were maintained at 70%–85% confluence. Cells were dissociated from plated cultures by application of Accutase (Thermo Fisher Scientific) for 6 min and seeded into the microfluidic devices through direct pipetted injection of a volume of roughly 75  $\mu$l at a density of 15 000 cells/ $\mu$l.

Prior to seeding, microfluidic devices were treated with a 1:20 by volume dilution of Matrigel (Corning, Inc.) in Dulbecco’s Modified Eagle Medium (Gibco DMEM, Thermo Fisher Scientific) and incubated for more than 30 min. Matrigel treatment provides an extracellular matrix and a substrate to improve cell adhesion under flow. Throughout the static culture, liquid droplets were maintained over each port of the microfluidic device to ensure liquid/liquid contact for bubbleless media injection and microfluidic tubing connection. After Matrigel treatment, a single liquid droplet is formed on the device surface over all input and output ports to eliminate hydrostatic flow during cell sedimentation and adhesion. This large droplet is broken during the first media change to allow microflows and enhanced nutrient delivery. Media in the cultured devices was carefully exchanged every hour, and devices were connected to the perfusion system after more than 4 h of static incubation at 37  ${}^{°}$C.

E. Molecular biology and generation of a stable cell line

The CAG ArcLight construct was subcloned from the plasmid ArcLight Q239 using HindIII and HpaI and was a gift from Vincent Pieribone (Addgene plasmid #36856).³⁷ The subcloned fragment was cloned into a pENTR1A plasmid with a CAG promoter and multiple cloning site (MCS) followed by an SV40 poly(A) using the same sites as were used in excising the fragment from the parent plasmid. The resulting pENTR1A CAG ArcLight plasmid was then Gateway LR Clonase (11791020, ThermoFisher) into the hyperactive piggyBac transposase-based, helper-independent, and self-inactivating delivery system, pmhyGENIE-3, a gift from Stefan Moisyadi.^38,39 The pmhyGENIE-3 had a neomycin resistance gene in the backbone. The resulting plasmid HypG3 NeoBB ArcLight was purified using a ZymoPURE Plasmid Miniprep Kit (D4210, Zymo Research) and used for subsequent transfection.

The NRK-49F ArcLight cell line was made by transfecting the cells at 30% confluence with 500 ng of the transfection grade plasmid, 1  $\mu$l of Lipofectamine 3000 (L3000008, Thermo Fisher Scientific), and 1  $\mu$l of P3000 reagent in 50  $\mu$l of Opti-MEM I Reduced Serum Medium (31985062, Thermo Fisher Scientific) and then adding the complex to one well of a 24-well plate containing complete FluoroBrite DMEM media (Thermo Fisher Scientific). Fresh culture media was added after 24 h and replaced the reagent media. Cells were under selection with 1.2 mg/ml G418 (10131035, Thermo-Fisher) for two weeks before serial dilution into 96-well plates for clonal isolation. Only the clone showing robust growth and strong expression was chosen.

F. Chemicals and reagents

The stock sucrose solution was prepared at 300 mM concentration in de-ionized water and passed through a 0.22  $\mu$m filter. In experimentation, sucrose solution was balanced with dimethyl sulfoxide (DMSO, Thermo Fisher Scientific) to match the volume fraction in the 2-aminoethoxydiphenyl borate solution (0.1%). 2-APB (Sigma-Aldrich) was dissolved to 100 mM in DMSO and stored in aliquots at $-{20}^{°}$C. The saline solution consist of 75 mM NaCl, 15 mM KCl, 2 mM MgCl ${}_{\text{2}}$, 1 mM CaCl ${}_{\text{2}}$, 94 mM mannitol, and 10 mM 2-[4-(2-hydroxyethyl)piperazin-1-yl]ethanesulfonic acid (HEPES, Sigma-Aldrich) buffer. The solution was corrected to a pH of 7.4. Cell culture media consisted of FluoroBrite DMEM with 10% by volume fetal bovine serum, 100 U/ml penicillin–streptomycin, and $1\times$ GlutaMAX (Thermo Fisher Scientific, Inc.). Rhodamine B dye (Fisher Scientific, Inc.) was added to solutions at 1.5  $\mu$M concentration.

III. RESULTS

A. Stream width instability causes measurement error

Stream width stability and consistency are crucial to the operation of the laminar flow device. The width of the sucrose gap is sensitive to changes in the cross-sectional area of the upstream channels such as debris or bubbles, as well as to pressure imbalance (including hydrostatic pressure), viscosity differences in solutions, and temperature differentials (affecting the viscosity). To maintain constant stream width, all of these factors must be tightly controlled. (See Appendix A for an analytical characterization of stream width under trilaminar flow.)

To study the effect of stream width variation on electrical impedance in the trilaminar flow microfluidic device, we conducted a control experiment in which the middle stream width was varied via a ramp of the driving pressure applied to rhodamine-dyed sucrose in the middle stream. Figure 2 shows these results. At each driving pressure, the stream was captured through fluorescent microscopy and was spatially averaged to produce an intensity profile in the axis perpendicular to flow. The stream width was then extracted from each frame as the full width at half the maximum peak height [Fig. 2(c)]. Electrical impedance was simultaneously measured continuously and the average value corresponding to each pressure step was extracted [Fig. 2(b)]. The resulting plots of stream width vs measured impedance are shown for a 100 Hz electrical stimulus and a 1 kHz signal in Figs. 2(d) and 2(e). The resulting curves are fit to an error function which is used as a practical form here but may be a physically relevant model (see Appendix B).

FIG. 2.

Impedance dependence on stream width. (a) The stream width in the trilaminar flow device was monitored via fluorescence microscopy and rhodamine dye. (b) The center stream width was varied by ramping the driving pressure, while the electrical impedance was continuously monitored at 100 Hz. (c) For each step, the stream widths are extracted from fluorescence images and (d) plotted against the average impedance over that interval. The results show good agreement with an error function fitting. Widths are normalized against the sensing electrode separation. (e) The experiment was repeated at 1 kHz, resulting in a degradation of the phase characteristic.

At 100 Hz, the maximum magnitude sensitivity corresponds to $1.746\mathrm{k}\mathrm{\Omega }/\mu \mathrm{m}$, showing that small fluctuations in pressure or minuscule obstructions to flow that alter the stream width by only microns can have significant impact on the measurement. Perhaps, more importantly, small differences in viscosity, hydrostatic pressure in the reservoirs, or hydraulic resistance in delivery (i.e., bubbles, tubing lengths, etc.) between the sucrose test solutions can produce significant impedance mismatches even when stream widths appear matched under visual inspection. These results suggest that tests should not run unsupervised without stream width tracking. However, corrective calibration of stream width differences may be possible when following a procedure similar to the experiment in Fig. 2 (see Sec. III C).

At low frequency (100 Hz), there exists an operating region above roughly one third of the available channel width where the phase is resilient to stream width variation. Using the trilaminar device in this operating region is a promising option for robust operation, though phase results lack the direct physical interpretation of resistance values. Additionally, at higher frequency (1 kHz), the same operating region shows linear decay, so the phase dependency may not be a reliable marker for all assays.

B. Need for closely balanced control solutions

As a gap junction blocker assay, this measurement is fundamentally differential. Any effect of a chemical gap junction blocker on cellular network conductivity must be judged against an appropriate control solution. The control solution must be biologically inert, viscosity matched, and osmotically balanced. But crucially, the control solution must also be carefully balanced against the test solution conductivity to provide a fair means of comparison.

Additionally, the large polar molecules, such as 2-APB (pK ${}_a=9.6$⁴⁰), can significantly impact the electric double layer formed at electrode interfaces, leading to an altered frequency response. Figure 3 demonstrates this issue for the case of 2-APB. When the solutions were allowed to fill the full channel of the device (including covering the electrodes), the impedance sweep [Fig. 3(a)] for the 2-APB solution initially shows greater magnitude at low frequencies but crosses over the control solution at 339 Hz. However, under trilaminar flow, the same solutions have a consistent magnitude separation in the absence of electrode interactions [Fig. 3(b)]. Thus, each reagent in the assay requires a carefully balanced control formulation that is measured in stable trilaminar flow at the test frequency. Our testing found that the addition of 0.05% saline solution by volume to the sucrose control solution results in a good impedance magnitude match for a 100  $\mu$M 2-APB solution at low frequencies.

FIG. 3.

Test solutions must be carefully electrically balanced in the trilaminar device. (a) Impedance sweeps for sucrose solution and sucrose solution with 100  $\mu$M 2-APB filling the full channel (not trilaminar) allow electrode interactions that result in a magnitude crossover at 339 Hz. However, (b) impedance sweeps of the same solutions in trilaminar flow do not show the same frequency dependence. Adding 0.05% by volume saline to the sucrose solution results in a good impedance match, especially at low frequencies. Each sweep represents the aggregated data of three trials. Confidence intervals represent one standard deviation.

Because of electrode interactions, external conductivity meters are unlikely to be adequate to evaluate control solution formulations. These experiments should occur under trilaminar flow, which should be optically monitored for stable and repeatable flow as we have shown that micrometer deviations in stream width can result in kilohms of measurement errors. Even when a balanced formulation is reached, the repeatability of preparation and purity of stock solutions represent a significant source of error.

C. Novel calibration approach correct stream width variation

We propose a calibration scheme to correct electrical measurement error due to stream width variation in trilaminar flow devices. To verify the approach, two matching sucrose solutions were alternately perfused into the device as a control experiment shown in Fig. 4. In order to determine the dependency of measured impedance on stream width, two calibration experiments similar to that of Fig. 2 were first carried out. For each solution, the driving pressure on the middle sucrose channel was linearly ramped around the intended operating pressure. The stream width was monitored by fluorescence microscopy and electrical impedance was continuously measured, creating the “mid” calibration curves [Fig. 4(a), top]. These experiments were repeated, instead of varying the pressure on the side saline channels, to create the “side” calibration curves [Fig. 4(a), bottom]. Each dataset in Fig. 4(a) represents the extracted impedance magnitudes and stream widths from three independent pressure ramps. All four calibration datasets were fit to an error function by a least squares method.

FIG. 4.

Calibration scheme to correct for stream width variation. (a) For both solutions, calibration sweeps were performed to find an error function fit for the impedance vs stream width. For the“mid” sweeps, the middle sucrose solution pressure was varied to produce the width change, while pressure on the side saline channels was varied to produce the “side” curves. (b) A decision tree using the stream width and flow rate information was used to determine which of the four calibration curves should be applied to subsequent data. In switching experiments, the calibration approach was effective in correcting stream width differences in (c) a control experiment switching between two sucrose solutions but did not affect (d) a switching experiment where the solutions’ conductivity does not match (300 mM sucrose and 100  $\mu$M 2-APB at 410 Hz in this case).

During experimentation, the total flow rate and stream width were continuously monitored to determine which of the calibration curves were most appropriate to use to adjust the measured impedance. The decision tree in Fig. 4(b) shows how the proper calibration curve was selected. For each solution, when the average flow rate increased and the center stream width increased or when the flow rate decreased along with the stream width, the “mid” calibration associated with incident flow rate changes in the middle stream was used. Increase in total flow rate resulting in lowered middle stream width or decrease in the flow rate corresponding to increased stream width indicated a variation associated with the “side” calibration. For each perfusion phase, the impedance change associated with the stream width deviation from the initial width was calculated via the selected error function fit. This corrective delta was added to each segment.

Figure 4(c) shows the effect of the calibration scheme for the sucrose control experiment. Over the full experiment, the difference between the average values of the two sucrose solutions was 17.1 k $\mathrm{\Omega }$ in the raw data, which was reduced to 0.21 k $\mathrm{\Omega }$ in the calibrated result. The calibration scheme could, in theory, be run in real time and at higher optical sampling rates, after initial experiments to extract the correction curves. Additionally, a similar approach should prove effective in correcting phase measurements as well, so long as an appropriate fitting function can be determined.

Importantly, this calibration approach responded only to changes in the stream width. Because the test solutions were calibrated independently, impedance differences arising from gap junction connectivity or solution conductivity were not affected. Figure 4(d) demonstrates that for a case where the test solutions have mismatched conductivity (i.e., the two curves in each plot of Fig. 4(a) would not overlap), the calibration algorithm was ineffective at equalizing impedance results. The measured impedance of 300 mM sucrose and 300 mM sucrose solution with 100  $\mu$M 2-APB [see Fig. 3(a)] was still significantly different after correction.

While this approach has proven effective in mitigating the effect of width deviations, it may not be effective in all circumstances. The stream width is extracted only from fluorescent imaging of rhodamine dye. If conductive species were present with significantly different diffusion coefficient from the dye, a potential error might arise if the charge concentration was not well correlated with the distribution of the dye. Additionally, cell experiments increased background fluorescence and the uptake of the dye into damaged cells hamper width extractions. Further, for experiments involving sensitive or poorly adhered cell cultures, the flow rate range available for initial calibration sweeps may be significantly decreased.

D. Gap junction blocker assay results

2-APB dose dependently and reversibly blocks gap junctions in NRK cells, including prominent connexins Cx43 and Cx50 at concentrations over 51.6  $\mu$M.^41,19 2-APB has been employed previously as a gap junction blocker assay in trilaminar flow devices.²⁹

Over a number of tests, our trilaminar platform has failed to measure significant gap junctional resistance changes in NRK-49F cultures in response to the chemical gap junction blocker, 2-APB. Figure 5 shows a representative test in which the osmotically balanced control solution (300 mM sucrose, 0.1% DMSO, 0.05% conductive solution) is alternately perfused with a solution containing gap junction blocker (300 mM sucrose, 0.1% DMSO, 100  $\mu$M 2-APB) over NRK-49F cells in 240 s increments. Images from the beginning and end of the sample show consistent flow conditions and acceptable cell health. While the raw data show a minor increase in the measured impedance under flow of the 2-APB solution, applying correction technique described in Sec. III C to account for stream width and flow rate variation results in a reversal of the results. That is, the increase in impedance in the raw data was due to stream width variation that is difficult to perceive by eye, and no significant change in the cell impedance was due to the presence of the gap junction blocker.

FIG. 5.

A representative system verification test using the chemical gap junction blocker, 2-APB. The blocker was alternately perfused with a balanced sucrose control solution every 240 s. Flow rate and stream width based calibration of the electrical resistance measurements show that perceived impedance increases due to 2-APB are likely inaccurate. Composite fluorescence/phase contrast images (10 $\times$, phase contrast/RFP, false color) from the beginning and end of the sample show that cell integrity and flow control were consistent over the length of the test.

Across multiple samples, no significant impact of treatment with gap junction blocker is observed. Figure 6 shows the results of multiple trilaminar flow assays using 2-APB where the electrical impedance across the sucrose gap was measured continuously at 10Hz. 2-APB tests switched every 240 s between the control sucrose solution and the 300 mM sucrose containing 100  $\mu$ M 2-APB. Prior to each test calibration sweeps were performed to evaluate stream width dependence. The average value for both the control and test conditions in Fig. 6(a) appears to depend primarily on the stream width, though some variability is present due to the tightness of the cell layer formed over the electrodes. Notably, the average measured impedances are not significantly reduced as compared to the no-cell control experiments, indicating an intracellular access issue. Figure 6(b) shows the impedance magnitude difference between each successive pair of control and test conditions in the same switching experiments after calibration for stream width variation. (i.e., each data point is the result of an experimental condition measurement subtracted from a control condition measurement, so that a net increase due to the experiment conditions would yield a negatively biased distribution.) No dataset is significantly biased away from zero, meaning that exposure of the culture to 100 uM 2-APB had no meaningful effect on the measured impedances.

FIG. 6.

Results of trilaminar device testing with 2-APB on NRK-49F cultures. Confluent cell populations in the device were treated alternately with 100 uM 2-APB and the sucrose control for 4 min periods. (a) The average impedance values over these periods show no significant difference between the two conditions. (b) Results calibrated based on stream width additionally show no significant difference from control conditions. Box plots show standard quartiles.

E. Cell health concerns

The trilaminar flow device poses several inherent challenges to cell health. Stable flow rates must be maintained continuously, which exposes the cell layer to constant shear stress. Reducing flow rates presents a trade-off with the electrical isolation provided by the sucrose stream as lower flow results in increased diffusion at the flow boundary (see Appendix B).

Additionally, pure sucrose is an abiological extracellular condition and prolonged exposure to this environment is taxing on cell health. Figure 7 shows a culture that was exposed to sucrose gap conditions for greater than 80 min. Zeiosis (cell blebbing) is visible in cells in the central sucrose region. Further, unwanted cytoskeletal effects are visible, especially at the laminar flow boundaries. At the boundaries, cells retract and eventually become disaggregated from the rest of the monolayer. The cause of this disaggregation along the laminar boundary is not clear. The solutions are osmotically balanced and pH matched. Cells in this region may experience uneven shear stress across their membranes if the solutions have significant viscosity differences. The most likely cause of these cytoskeletal effects is that cells in the boundary region may experience a large fluctuations or gradients in their membrane potentials. Cell health concerns under sucrose flow make the system non-ideal for assays involving gap junction blockers with long uptake or washout times, such as meclofenamic acid, because interrogation times must be kept brief.

FIG. 7.

Poor cell health observed in NRK cultures exposed to trilaminar sucrose flow for greater than 80 min. In response to stress, the monolayer disaggregates especially at the laminar flow boundaries. Zeiosis is observed in the cells that were maintained in the sucrose stream (10 $\times$, phase contrast).

IV. DISCUSSION

A. Challenges and limitations of the trilaminar sucrose gap approach

The trilaminar flow sucrose gap approach is a promising means to isolate distinct regions of a cell layer in an attempt to force electrical signaling through the intercellular connections (gap junctions). However, the approach inherently incurs several sources of error and forces design trade-offs that make the signal through the gap junctions exceptionally difficult to recover. We review the sources of error previously described and discuss other fundamental issues with the approach, namely, the lack of intracellular access and assumptions about the electrical modeling of cells living in a sucrose environment.

Sources of error. We have already identified and characterized several inherent sources of error in the trilaminar sucrose gap approach. Stream width stability and repeatability are crucial to reliable operation. At 100 Hz, the potential error is high at 1.746 k $\mathrm{\Omega }/\mu$m. Width variation can result from differences in flow conditions and fluid viscosity. Additionally, for gap junction blocker assays, a suitable sucrose control solution must be established for any chemical blocker that changes the conductivity of a sucrose solution. Finding reliable control solutions requires a titration search, using an equivalent electrode configuration and test frequency as the microfluidic device. The conductivity of gap junction blockers directly reduces the signal quality in an assay because the sucrose solution impedance is seen in parallel with the gap junctional network impedance. Finally, maintaining cell health in the presence of continuous sucrose flow is a concern. Poor cell health could lead to lowered connectivity in the cell layer and decreased signal. Further, cell health concerns limit the variety of gap junction blockers that are suitable for the assay to those with rapid activation and washout times.

Intracellular access and shunting resistance. This trilaminar approach has no direct means of intracellular electrical access. Instead, electrical access to the cell layer has two primary pathways—through transmembrane protein structures and directly through the cell membrane. The former process relies on driving a drift flux of charged ions through ion channels, while the latter (in the absence of electroporation) must move charge through field effects. Neither pathway is well-suited for low frequency conduction, resulting in large total membrane impedances. In whole cell patch clamp recordings, the membrane resistance is usually found to be several hundred megaohms.⁴² In NRK cells specifically, the average total conductance of the ion channels in single cells was found to be 3.24 nS, corresponding to a membrane resistance of 309 M $\mathrm{\Omega }$, with a similar total of 2.01 nS for small cell clusters.³⁵ The membrane resistance is so large that single and double shell cell models used in dielectric spectroscopy often model the membrane only as a capacitance.⁴³ While the membrane can be capacitively bypassed at high frequencies ( $\gtrsim$ 50 kHz), at such frequencies, the dominant charge transport mechanism is likely dipolar relaxation rather than ionic transport through the gap junctions. In the end, the intracellular access resistance, R ${}_{\text{access}}$, must be considered in parallel with the sucrose resistance (which is especially problematic if sucrose conductivity is modified by a drug or control balance). Any change in network resistance due to a gap junction blocker will be significantly degraded if the sucrose resistance does not exceed the intracellular access resistance.

Problems with the electrical model. Genetically expressed voltage sensors can lend some insight into the electrodynamics in the trilaminar device. Fluorescent imaging of ArcLight expressing NRK cells in Fig. 8(a) shows that cells in sucrose are heavily depolarized (i.e., the net intracellular charge is positive relative to the normal resting membrane potential). This result poses a number of issues. Nearly all connexins are known to be voltage sensitive. Particularly, the junctional conductance in response to a potential difference between the adjoined cells (transjunctional voltage, V ${}_j$) has the characteristic shown in Fig. 8(b), where swings to hyperpolarized or depolarized states result in dramatic conduction loss.^1,44 Large resistances due to voltage-gating effects at the sucrose border serve to exacerbate the intracellular access problem, presenting an additional large impedance in parallel with the sucrose isolation resistance that obscures gap junction changes in the network.

FIG. 8.

Electrical modeling of cells under sucrose flow. (a) Fluorescent imaging of NRK cells expressing Arclight membrane potential reporter under laminar flow (10 $\times$, GFP (Green Fluorescent Protein filter), false color). Cells in the left are in the saline solution, while cells in the right appear heavily depolarized in the sucrose stream. (b) Typical response of gap junction conductance to transjunctional voltage, adapted from Harris.¹ (c) Diagram of electrophysiological mechanisms at the laminar flow boundary. (d) A simplified lumped circuit model showing the difficulty of recovering gap junction resistance values given the other significant impedances present.

Beyond membrane potential reporting, little information is available concerning the electrophysiology of NRK cells in a sucrose environment, making their behavior difficult to model electrically. For gap junction interrogation, the ideal cell response to extracellular sucrose would be the complete closing of all ion channels. Such a response would result in the membrane potential remaining at a resting level in the sucrose region and being maintained by saline contacted cells through gap junctional channels. However, Fig. 8(a) shows that this is clearly not the case in the trilaminar device. Rather, transmembrane structures to the extracellular sucrose appear to be active, and vertical transport of the charge carriers in the solution seems to dominate horizontal diffusion in the gap junctional network, resulting in clear depolarization. Active exchange with the sucrose solution produces a number of concerns including that the resistance of the sucrose may be further lowered by ion flux out of the cell layer. Additionally, conduction in the intracellular spaces (which is usually considered very high, with the fundamental Hodgkin and Huxley model assumes perfect conduction) may be significantly reduced. Because the charge carriers in the solution are ionic species and these ions are subject to drift and diffusion out of the cell layer, we arrive at a challenge similar to attempting to transmit a longitudinal wave in a lossy medium. Benchtop sucrose gap systems are typically used to examine electrically active tissue transmitting transverse waves. The technique may be better suited to these applications where the sucrose isolation acts similarly to myelination, rather than for impedance measurements where the sucrose environment seems to have a significant attenuating factor.

In summary, Fig. 8(d) provides a simplified lumped model of the significant impedances, which obfuscates a measure of gap junction impedance in the trilaminar device. The device establishes a sucrose isolation impedance (R ${}_{\text{sucrose}}$), which should appear in parallel with the total resistance through gap junctions in the network (R ${}_{\text{GJ}}$). However, R ${}_{\text{GJ}}$ appears in series with the intracellular access barrier into the cell layer (R ${}_{\text{access}}$), a significant impedance due to voltage gating of channels at the laminar flow barrier (R ${}_{j\text{, gated}}$) and increased resistance due to ionic depletion in the intracelluar fluid (R ${}_{\text{ICF}}$). In order to force a significant fraction of the current through gap junctions, R ${}_{\text{sucrose}}$ must be large comparable to the series resistances in the lower branch of Fig. 8(d). In control experiments in our devices, the sucrose impedance measured roughly 275 k $\mathrm{\Omega }$ at 100 Hz in normal operating conditions. Each element in the series branch could reasonably be expected to be of similar or greater magnitude to the sucrose isolation impedance, resulting in poor signal quality that largely reflects only the sucrose stream width.

B. Future work and device improvements

The problem of intracellular access can be overcome through engineering means. Three-dimensional electrode surface structures in combination with electroporation have succeeded in bringing electrodes into the intracellular space, but the fabrication processes are highly non-trivial.^45,46 Improving intracellular access is likely the most important opportunity for advancement as placing electrodes in the intracellular space would cause the membrane impedance to work in favor of signal integrity [shifting R ${}_{\text{access}}$ to the opposite side of the voltage divider in Fig. 8(d)].

The issues related to cell physiology in the sucrose solution, namely, cell health concerns, junctional voltage gating, and ion depleted intracellular fluid may require adjustments to the experimental approach. Rather than continuous flow, the full cell culture could be brought to normal resting equilibrium in media and then treated with chemical blockers (in media). Using integrated valves for rapid switching, a trilaminar sucrose bolus could be pulsed in and the electrodynamics of sucrose gap formation might be used to elucidate the gap junctional network connectivity though mechanosensitivity of ion channels would need to be closely considered in this approach.

Parallelization of the experimentation in the microfluidic chip should be considered to both improve testing throughput and to provide on-chip control sites. On-chip controls would allow the calibration approach to alleviate the control solution balancing issues discussed in Sec. III B. The integrated microvalves introduced in this work can support and simplify the automation of parallelized testing.

Finally, direct improvements to the control systems are still possible to further manage experimental variables. Improved flow stability through the development of feedback system⁴⁷ and improved time resolution of calibration through continuous electrical stream width monitoring⁴⁸ might be achieved. Electrical measurement of gap junction connectivity in microfluidic devices should be achievable if these engineering challenges can be met.

V. CONCLUSION

A trilaminar flow sucrose gap approach to in vitro electrical measurement of gap junction networks has been re-examined. However, the attempts replicate the results of Bathany et al.²⁹ have resulted in marginal results. Potential sources of error in the design have been identified including stream width instability, control solution matching, and cell health concerns under extended sucrose exposure. Despite engineering improvements (namely, on-chip perfusion switching and a novel stream width-based calibration approach) to address these potential sources of error, the approach proves unreliable in gap junction blocker assays on NRK-49F cells. Potential issues in the bioelectrical model leading to these results have been identified to be addressed in future systems. A reliable and accessible means of electrical gap junction connectivity examination remains an important goal toward gaining more fundamental understanding of how we develop, grow, and heal.

APPENDIX A: TRILAMINAR FLOW STREAM WIDTH

For Poiseuille flow, the width of streams in the trilaminar flow is proportional to their incident flow rates (after the entrance region⁴⁹). That is, for our trilaminar case, where $Q_{mid}$ and $Q_{side}$ represent the incident flow rates of the middle and side channels, respectively, the fractional stream width of the middle stream under laminar flow can be given as

$$W_{mid}/W=\frac{Q_{mid}}{Q_{mid}+2Q_{side}}.$$ (A1)

The incident flow rates are proportional to the driving pressure ( $P_d$) with the (inverse) constant of proportionality termed the hydrodynamic resistance, $R_{hyd}$. For rectangular channels of length, $L$, the formulation is

$$Q=\frac{P_d}{R_{hyd}}\approx P_d{\left(\frac{12\mu L}{w{h}^3(1-0.63h/w)}\right)}^{-1},$$ (A2)

where $w\times h$ is the cross-sectional area and $\mu$ is the fluid viscosity.⁵⁰ Additionally, resistance in the input tubing and interconnects may be significant if the on-chip resistance is relatively low.

APPENDIX B: ELECTRICAL RESISTANCE UNDER TRILAMINAR FLOW

Consider the simplified trilaminar flow model of Fig. 9(a), letting $d_0$ denote the horizontal position of the laminar flow boundary. To first order, the total resistance through the idealized sample then is given by

$$\begin{array}{rl}R& ={\displaystyle {\int }_0^W\frac{\rho (x)}{A}dx}\\ & =\frac{2}{A}{\displaystyle {\int }_0^{W/2}\rho (x)dx}\\ & =\frac{2}{A}{\displaystyle {\int }_0^{d_0}{\rho }_{sucrose}dx+\frac{2}{A}{\displaystyle {\int }_{d_0}^{W/2}{\rho }_{saline}dx}}\\ & =\frac{2}{A}{\rho }_{sucrose}{d}_0+\frac{2}{A}{\rho }_{saline}(W/2-d_0).\end{array}$$ (B1)

FIG. 9.

Model of electrical resistance resulting from trilaminar flow. (a) coordinate system and dimensions for the trilaminar flow model, (b) ion concentration in the channel cross section for different values of time/diffusivity and middle stream width [Eq. (B5)], and (c) the analytical model for measured electrical resistance as a function of sucrose stream width, which is closely approximated by the error function.

While laminar flow prevents chaotic mixing, transverse diffusion at the fluid boundary still affects the concentration of charge carriers at the boundary. For each ion species, the concentration due to diffusion at the laminar flow boundary is governed by the diffusion equation

$$\frac{\mathrm{\partial }c}{\mathrm{\partial }t}=D\frac{{\mathrm{\partial }}^{2}c}{\mathrm{\partial }{x}^2},$$ (B2)

where $c(x,t)$ is the ion concentration, $D$ is the diffusion constant, and $t$ is the simulation time. Alternately, the simulation time can be considered a measure of distance along the direction of flow (i.e., $t=y/Q$).

Using symmetry, the initial conditions that $c(x,t=0)$ $=c_0\text{ for }x\le d_0$, and the boundary condition of no flux at the channel wall (i.e., $\frac{\mathrm{\partial }c}{\mathrm{\partial }x}{|}_{x=0,W/2}=0$), the differential equation can be solved through separation of variables,

$$\begin{array}{r}c(x,t)=X(x)T(t),\\ T(t)=A{e}^{-{\lambda }^{2}Dt},\\ X(x)=B\cos \lambda x+C\sin \lambda x.\end{array}$$ (B3)

Applying the boundary condition, we find that $C=0$ and $0=\sin (\lambda W/2)$ or ${\lambda }_n=\frac{2\pi n}{W}$. Then,

$$c(x,t)=\sum _{n=0}^{\mathrm{\infty }}{D}_n\cos \left(\frac{2\pi n}{W}x\right)e^{-Dt{(\frac{2\pi n}{W})}^2}.$$ (B4)

Applying the initial conditions, we eventually arrive at

$$c(x,t)=c_0(1-\frac{2d_0}{W})-c_0\sum _{n=1}^{\mathrm{\infty }}\frac{2}{n\pi }\sin \left(\frac{2\pi n}{W}{d}_0\right)\cos \left(\frac{2\pi n}{W}x\right)e^{-Dt{(\frac{2\pi n}{W})}^2}.$$ (B5)

Figure 9(b) shows this solution for different values of $d_0$ and $Dt$.

Generally, the relationship between ionic concentration and solution resistivity is a non-linear function of the mobility of the ion species present.⁵¹ However, the relationship is roughly linear at low concentrations when mobility is high, so resistivity can be considered inversely proportional to the ion concentration ( $\rho (x){\propto }^{-1}c(x)$). Additionally assuming for simplicity that $Dt$ is a constant (i.e., flow is fast enough that diffusion is constant relative to the length of the laminar flow region), we can arrive at the analytical solution shown in Fig. 9(c) using the formulation

$$R(d_0)=\frac{2}{A}{\int }_0^{d_e}\frac{1}{{\lambda }_{saline}c(x)+{\lambda }_{sucrose}(1-c(x))}dx,$$ (B6)

where $d_e$ is the position of a sensing electrode at a distance $0<d_e<W/2$. ${\lambda }_{saline}$ and ${\lambda }_{sucrose}$ are constants of proportionality such that ${\lambda }_{saline}>>{\lambda }_{sucrose}$. The analytical solution can be closely fit with an error function.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

J. Dungan: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). J. Mathews: Conceptualization (equal); Investigation (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). M. Levin: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (supporting). V. Koomson: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (supporting).

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.