{"paper_id":"167a6c5d-76d9-4ade-8e0f-b7b862398faf","body_text":"1 \n \nMembrane Geometric Confinement Reshapes the Lateral Electric Field Distribution and \nIntracellular Cargo Transport in Nanopore Electroporation  \nEmily McCorkle1☨, Matthew Lee Manion1☨, Xiaoqian Wang1, Cheyenne Meeks1, Guanren Tao2, \nSasha Cai Lesher-Pérez1,3,4*, Albert Tianxiang Liu1,4,5* \n1 Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48105  \n2 Department of Electrical Engineering, University of Michigan, Ann Arbor, MI 48105  \n3 Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48105  \n4 Biointerfaces Institute, University of Michigan, Ann Arbor, MI, 48109 USA  \n5 Department of Material Science and Engineering, University of Michigan, Ann Arbor, MI 48105  \n* Corresponding Authors Email:  sashacai@umich.edu, atliu@umich.edu \n☨These authors contributed equally.   \nAbstract \n  \nNanopore electroporation (NanoEP) is an emerging transfection method that enables efficient and \nsafe intracellular delivery and removal of biomolecular cargo for applications in disease modeling, \ntissue engineering, and therapeutic biologics manufacturing. Conventional device designs assume \nuniform vertical cargo flux across nanoporous membranes; however, we demonstrate that the \nlateral electric field distributions introduce a pronounced edge effect, with enhanced cargo delivery \nand depletion along the memb rane perimeters. We identify and characterize the presence of this \nedge effect in NanoEP systems, and develop a modified Nernst–Planck model to guide the design \nof membrane geometries that either promote delivery uniformity or create prescribed spatial \ngradients within cell monolayers. By varying the internal angles formed by the membrane edges \n(60°, 90°, 120°), we create predictable intracellular cargo gradients, while concave “serpentine” \ngeometries with high perimeter -to-area ratios amplify delivery effi ciency and minimize spatial \nheterogeneity compared to circular membranes. These findings establish membrane geometry as \na tunable design parameter in NanoEP, enabling control over both uniform and patterned \nintracellular payload delivery or depletion. This  geometric design principle offers a scalable \nstrategy for next-generation transfection platforms and synthetic tissue constructs. \n \nKeywords \nNanopore electroporation, transfection, device design, dosage control \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n2 \nIntroduction \nIntracellular delivery of bioactive molecules such as nucleic acids, commonly referred to as \ntransfection, is essential for biomedical research and clinical applications, including gene therapy, \ntissue engineering, and disease modeling 1,2,3,4,5,6. While numerous transfection techniques exist, \nthey often face trade-offs between efficiency, throughput, and dosage control 7,8. Broadly, in vitro \nand ex situ transfection methods fall into two categories: substrate -free and substrate -based. \nAlthough substrate -free methods (e.g., viral, chemical, sonoporation, electroporation, etc.) are \ntypically high throughput, they can elicit concerns about cytotoxicity or mutagenicity7. Substrate-\nbased transfection techniques have attracted interest for their ability to enhance intracellular \ndelivery while maintaining cell viability through engineered cell –material \ninterfaces7,9,10,11,12,13,14,15,16,17. Despite these advantages, substrate -based approaches still struggle \nto deliver consistent, high-efficiency transfection across entire cell populations.  \nOne promising substrate-based transfection method, nanopore electroporation (NanoEP), employs \nan insulating membrane substrate (positioned in the horizontal x -y plane) with vertically aligned \nnanopores to localize the applied electric field along the z-axis (perpendicular to the cells cultured \non the membrane substrate) 14,15,18,19. This localized field forms transient electropores on the cell \nmembrane at the cell –nanopore interface, allowing for precise electrophoretic transport of cargo \ninto and out of cel ls14,15. Unlike bulk electroporation 20, NanoEP’s substrate -free analog, which \nexposes suspended cells to high electric potentials (>500 V/mm) and often causes extensive cell \ndamage21, NanoEP achieves high delivery efficiency (>60%) and high cell viability (>90%) at \nmuch lower voltages (<15 V/mm)14,15,22,23,24. \nLike most substrate-based transfection techniques, the throughput of NanoEP is thought to scale \nwith the 2 -dimensional (2D) area of the nanoporous substrate the target cells interface with ––at \nleast in principle. While NanoEP has been primarily studied in the context of its electric field \nfocusing effects along the z-axis, the role of lateral (x-y) electric field distributions in maximizing \nor controlling delivery remains underexplored. The efficiency and scalability of NanoEP are \ndirectly tied to the spati al uniformity of cargo delivery and depletion across a cell population. \nBecause charged cargo transport in NanoEP is dominated by electromigration rather than \ndiffusion14,24, non -uniform lateral electric field distribution can significantly impact the spatial \nuniformity of molecular delivery. Previous studies have shown that electrode geometry can \ninfluence field distribution and the associated downstream outcome in brain stimulation25, cardiac \npacing25, and electrodeposition 27. By increasing the number of edges in an electrode, the current \ndensity increases, which leads to a reduction of the electrode impedance 25. Indeed, the effect of \nelectrode geometry has been explored in the context of NanoEP 28,29, particularly when the \nelectrode dimensions are significantly smaller than the substrate area.  \nIn reality, as we will report herein, the lateral spatial uniformity of the z -focused electric field in \nNanoEP cannot be simply assumed, even for devices with large, planar electrodes. We demonstrate \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n3 \nthat large-area NanoEP systems suffer from a substrate dependent \"edge effect\", in which cells \nnear the perimeter of the nanoporous membrane exhibit enhanced delivery and faster cargo \ndepletion than those at the center. This non -uniformity is attributed to  a lateral electric field \nconfinement effect created by the geometries of the cell–membrane in tandem with the electrolyte–\nelectrode interfaces. Understanding and controlling these effects are essential for scaling NanoEP-\nbased systems and could enable the  creation of not only highly uniform but also intentionally \nheterogeneous cell populations, which is critical in tissue engineering where spatially controlled \ngene expression and protein loading is necessary for modeling complex biological systems30,31. \nIn this study, we systematically investigate how device geometry influences lateral electric field \ndistributions in NanoEP. Using both experiments and a theoretical model we developed based on \nthe Nernst–Planck equation, we quantify the observed edge effec ts and identify design rules to \npredict kinetic rates for cargo depletion and geometric trends in cargo delivery. Our results \ndemonstrate that by modifying membrane geometry, specifically by introducing angular variations \nin membrane edges and adjusting pe rimeter-to-area ratios, we can tune intracellular molecular \ndelivery and depletion gradients within 2D cell populations. These findings suggest that membrane \ngeometry can serve as a tunable design parameter in NanoEP systems to enable both uniform and \nintentionally patterned intracellular delivery or depletion, offering a scalable strategy for next -\ngeneration transfection platforms and synthetic tissue constructs. \nResults \n \nEdge Effects in NanoEP Devices with Circular Membranes: \n \nTo examine spatial variations in cargo delivery and depletion during NanoEP, we fabricated \ndevices comprising indium tin oxide (ITO) transparent electrodes, a polydimethylsiloxane \n(PDMS) chamber containing the cell media or electroporation buffer (which defined the membrane \ngeometry), and a nanoporous track-etched polycarbonate (PCTE) membrane substrate supporting \na cell monolayer ( Figure 1a). In devices with circular membranes, we consistently observed a \npronounced edge effect, where cargo transport (characterized by its vertical flux) was enhanced at \nthe periphery of the cell monolayer compared to the center, when a perpendicular electric field \nwas applied between the planar ITO electrodes ( Figure 1b-1d). This effect was evident in both \ndelivery and depletion contexts using HT1080 human epithelial fibrosarcoma cells. Cargo of \nvarious sizes, from small molecules (~700 Da) to larger plasmids (~5 MDa), exhibited similar \ntrends (Figure 1b). Under typical NanoEP delivery conditions, propidium iodide (~700 Da), a \nmembrane impermeable dye, showed greater cellular uptake at the membrane edge versus the \ncenter of the device, as did pLenti3.7-DsRed plasmid (~5 MDa) stained with YOYO-1 dye. Protein \ndelivery followed the same pattern: cells internalized fluorescently labeled bovine serum albumin \n(BSA-AF488) with intensities that declined progressively toward the membrane center ( Figure \n1b). BSA-AF488 edge enhanced delivery was also observed in other electroporation buffers such \nas media and phosphate -buffered saline (PBS) ( Supplemental S1). Depletion studies, where we \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n4 \ntracked calcein removal from HT1080 cells, corroborated these findings. In a 2 mm diameter \ndevice, calcein depletion initiated at the periphery and propagated inward, with cells at the edge \nexhibiting higher depletion rates (k) (Figure 1c). Because depletion flux measurements decouple \ncargo concentration gradients from electric field effects, they provide a more direct readout of the \nfield distribution (versus the delivery experiments) and reinforce the notion that electric field non-\nuniformity, driven by the membrane-edge, governs NanoEP performance. \n \nTo investigate the role length scale plays on the observed edge effect, we repeated depletion \nexperiments in a larger 6 mm diameter circular device using 15 V, 20 Hz square-wave pulses with \n1 ms pulse widths for 120 s (n = 3). To accommodate the lower imaging resolution (as a result of \nthe lower magnification used to fit the entire 6 mm device in one frame), we analyzed fluorescence \nintensity across six concentric radial zones (referred to as “bins”) to quantify spatial varia tions. \nFluorescence intensity ( If) in each bin was tracked over time until reaching a plateau ( b) and \ndepletion rate constants (k) were extracted by fitting the experimental data to Equation 128. A clear \ngradient emerged from the outermost edge bin (Bin 6) to the innermost center bin (Bin 1), \nconfirming the presence of NanoEP edge effects at larger device scales ( Figure 1d). Across all \ncircular geometries tested, we consistently observed heightened delivery or removal rates near the \nedge of the cell monolayer compared to the center, refle cting lateral non-uniformities parallel to \nthe planar ITO electrodes ( Supplemental S2 ). Control experiments without applied fields \n(Supplemental S3) verified that these edge effect patterns arose from the applied electric field \nrather than photobleaching or buffer exposure. \n𝐼𝑓(𝑡) = (𝐼𝑓,0 − 𝑏)𝑒−𝑘𝑡 + 𝑏 (1) \n \n𝐶(𝑡) = 𝐶0𝑒−𝑘𝑐𝑡 (2) \n \n𝑘𝑐 =\n𝐷𝑧𝑒\n𝑘𝑏𝑇\n1\n𝑙𝑒𝑓𝑓(𝜑)\n𝑑𝜑\n𝑑𝑧 (3) \n \n𝑙𝑒𝑓𝑓(𝜑) =\n𝑉\n𝐴𝑝(𝜑)𝑛𝑝(𝜑) (4) \n \nWe hypothesized that the observed edge effects stem from lateral non-uniformities in the focused \nelectric field across the nanoporous membrane. To model the observed trends in the cargo transport \nrate as a function of voltage, we derived Equation 2 , describing the electrophoretic -driven \nexponential decay of intracellular calcein concentration (see Methods). Molecular diffusion was \nneglected since the calculated electrophoretic species flux across the nanoporous membrane was \n~1350× greater than that of diffu sion (Supplemental S4) and dominates cargo transport. Under \nthis theoretical framework ( Equation 3 ), the measured rate constant ( kc) scales linearly with \nelectric field strength (\n𝑑𝜑\n𝑑𝑧), diffusion coefficient (D), effective molecular charge ( ze), electropore \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n5 \narea (Ap), number of electropores ( np), and inversely with cell volume ( V) and thermal energy \n(kbT). Due to the presence of a complex, nonlinear dependence of Ap and np on the local voltage \n𝜑15, several of these hard-to-estimate parameters were consolidated into a single fitting parameter, \nleff, with units of length (Equation 4). This term represents an effective transport length for charged \nintracellular cargo exiting through electropores, and its derivation is detailed in Supplemental S5.  \n \nUsing this model, we compared normalized experimental k (knorm) values to model kc,norm \npredictions across applied voltages (Figure 1e), using physically relevant parameters summarized \nin Supplemental S4 . Consistent with prior reports 15, leff exhibits a sigmoidal dependence on \nvoltage, and scales linearly with the number of membrane nanopores contacting each cell, itself a \nfunction of the commercial membrane’s nanopore diameter. We found that a ~2 –2.5 V voltage \ndifferential between the edge and center regions of the cell–membrane monolayer would give rise \nto a gradient in cargo flux that coincides with the measured normalized rate constants (1 at the \nedge vs. ~0.6 at the center, Figure 1e), and therefore hypothesized that the enhanced cargo flux at \nthe membrane perimeter stems from a lateral variation in vertical voltage drop across the \nmembrane nanopores ( Figure 1f). Together, these findings suggest that spatial variation in the \nelectrophoretic driving force, governed by the geometric shape confinement of th e nanoporous \nmembrane, could underlie the observed edge effect. This spatial heterogeneity offers a means to \ncreate predictable gradients in cargo flux or enhance delivery uniformity by tailoring membrane \ngeometry.  \n \nFig. 1: Experimental evidence of edge effects in NanoEP. \n \na, Schematic illustration of the NanoEP device used for cargo delivery and depletion experiments. \nb, Left to middle right: representative fluorescent micrographs of HT1080 cells showing NanoEP \ndelivery of: (left) propidium iodide (PI; 1:3 (v/v) PI:electroporation buffer, 20 V, 20 Hz, 1 ms \nsquare-wave pulse width, 10 s duration; scale bar, 430 𝜇m), (middle left) YOYO -1–labeled \nplasmid (1:10 YOYO-1:base pairs, 20 V, 1 Hz, 10 ms square-wave pulse width, 8 s duration; scale \nbar, 430 𝜇m), and (middle right) Alexa Fluor™ 488–conjugated BSA (BSA-AF488, 1 𝜇g/𝜇L, 25 \nV, 1 Hz, 10 ms square-wave pulse width, 4 s duration; scale bar, 300 𝜇m). Right: radial decrease \nin BSA-AF488 fluorescence intensity with distance from membrane edge, n = 3 devices. c, Left: \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n6 \nrepresentative fluorescent micrographs of HT1080 cells showing calcein depletion in a 2 mm \ndiameter circular device before (top) and after (bottom) NanoEP (15 V, 20 Hz, 0.2 ms pulse width, \n90 s duration; scale bars, 500 𝜇m). Right: heat map of calcein depletion rate constants across the \ndevice (scale bar, 500 𝜇m). d, Radial bin analysis of calcein depletion in a 6 mm circular device \n(15 V, 20 Hz, 1 ms square -wave pulse width, 120 s duration; n = 3). Left: normalized intensity \ndecay over time across six co ncentric bins (Bin 1 = center; Bin 6 = edge). Insets: before/after \nfluorescent micrographs and schematic of bin regions (scale bars, 1.5 mm). e, Normalized rate \nconstants from experimental data across binned regions (points) compared with simulated \ntransport rates across applied voltages (line), capturing the nonlinear dependence of cargo transport \non voltage drop.  f, Schematic illustration of lateral voltage distribution across the PCTE \nnanoporous membrane during cargo delivery (top) and depletion (bottom) , illustrating enhanced \ncargo flux at the membrane edge. \n \nElectrode-Based Evidence of Radial Electric Field Heterogeneity: \n \nTo link radial heterogeneity in NanoEP flux with anisotropy in electric field strength, we exploited \na well-characterized electrochemical reaction that induces voltage-dependent changes in electrode \noptical properties, enabling visualization of the lateral  field distribution across the device. \nSpecifically, we measured changes in light transmission through the ITO cathodes, which \nexperience reduction currents during NanoEP experiments (Figure 2a). At the cathode–electrolyte \ninterface, electrochemical reduction of ITO decomposes its atomic complexes into indium and tin \nnanoparticles (Figure 2a), substantially decreasing optical transparency32,33. Because the rate and \nextent of the ITO reduction, and the corresponding decrease in optical transparency, are known to \nscale with the local voltage magnitude (i.e., electrochemical overpotential) 32, changes in \ntransmitted light provide a convenient proxy for mapping electric field distribution across the \nNanoEP device. To enhance contrast for image analysis, a voltage higher than usual was used. We \nsubjected 2 mm devices with PCTE membranes to 30 V,  20 Hz square-wave pulses (1 ms pulse \nwidth) for 40 s (Figure 2b). Under these conditions, regions of the ITO near the device perimeter \nconsistently darkened more rapidly than central regions, indicating stronger local electric fields at \nthe edge. \n \nWe note that the edge effect associated with this electrode reaction persisted in the absence of the \nPCTE membrane. Using a 6 mm device, we simulated the voltage drop across the electrolyte and \nassessed the rate and extent of reaction experimentally. Both approaches revealed stronger electric \nfields near the device perimeter. A 3D finite element (COMSOL) simulation of cylindrical \nNanoEP devices mapped the z -directional voltage drop at each x –y position under a 30 V bias, \nshowing enhanced voltage gradients at device edge compared to the center ( Figure 2c) . \nExperimentally, applying 30 V, 20 Hz square -wave pulses (1 ms pulse width, 60 s duration) \nproduced greater optical transparency changes and faster electrode reactions at the edge, consistent \nwith locally elevated field strengths (Figure 2d, 2e). Elemental mapping by energy dispersive X-\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n7 \nray spectroscopy (EDX) also confirmed these trends: post -NanoEP EDX maps showed a lower \noxygen signal at electrode edges ( Supplemental S6), consistent with more extensive local ITO \nreduction. Incorporating the simulated x–y electric field distribution (Figure 2c) into our modified \nNernst–Planck model ( Equation 3 ) predicted higher calcein depletion rate constants at the \nperiphery than the center ( Figure 2f), in agreement with the cargo flux observed experimentally \n(Figure 1c).  \n \nWe attribute the emergence of this edge effect to the interplay between the geometry of both the \ncell–membrane and the electrolyte –electrode interfaces (EEI). Conventional equivalent circuit \nmodels of the NanoEP device ( Supplemental S7) collapse the x –y dimensions into singular \nlumped elements from electrode to electrode, yielding only one effective voltage drop across the \nPCTE membrane and cell monolayer 34. By contrast, finite element simulations of 3D NanoEP \ndevices reveal that when both the EEI extends laterally beyond the cell–membrane interfacial area \nand when the finite EEI resistance is above a critical threshold (R ct > Rcritical), the vertical voltage \ndrop is amplified at the edges, an effect that disappears when the R ct becomes negligible (R ct < \nRcritical) (Supplemental S7). Here, Rct represents a lumped interfacial charge transfer resistance (or \nEEI impedance) to electron transfer and charge storage 35,36, which depends on factors including \nvoltage, buffer composition, electrode material, and electro de area35,36. From these simulations, \nwe infer that charge accumulation in electrode regions not directly contacting the electrolyte drives \nelectronic current along the EEI perimeter and ionic current toward the edge of the nanoporous \nmembrane, which represents the pa ths of least resistance. These combined currents elevate local \nvoltages across the cell –membrane interface, thereby enhancing cargo flux during NanoEP, \nassuming a laterally-uniform vertical transport resistance. Therefore, accounting for latera l non-\nuniformities is necessary in NanoEP models. Additional considerations of spatial resistance \nvariations are provided in Supplemental S8 . Taken together, these modeling, optical, and \nchemical data provide compelling evidence that membrane geometry induces lateral (radial) \ngradients in the electric field during NanoEP, in situations where the electrode surface area extends \nbeyond the membra ne edges. These field gradients, in turn, explain the observed non -uniform \nNanoEP cargo flux and support the idea that the observed edge effect is controlled by the geometry \nof both the cell–membrane and electrolyte–electrode interfaces. \n \n \n \n \n \n \n \n \n \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n8 \nFig. 2: Electrolyte –electrode interfacial reactions reveal lateral voltage heterogeneity in \nNanoEP devices. \n \na, Left: schematic illustration of the device setup for cathodic ITO reduction experiments. Top: \npristine ITO film (scale bar, 500 nm). Top right: reduced ITO film post-NanoEP (scale bar, 1 𝜇m). \nBottom right: bright field optical micrograph showing darkened cathode following electric \nstimulation of 2 mm device with PCTE membrane (scale bar, 750 𝜇m). b, Transmitted light \nintensity decreases over time across six concentric radial bins in a 2 mm circular device with PCTE \nmembrane (30 V, 20 Hz, 1 ms square -wave pulse width, 40 s duration; scale bar, 750 𝜇m). c, \nCOMSOL-simulated lateral distribution of vertical voltage drop across the electrolyte in a 6 mm \ncircular device with no PCTE membrane under 30 V cathode -to-anode bias. d, Heat map of ITO \nreduction rate constants in a 6 mm circular device with no PCTE membrane under 30 V cathode -\nto-anode bias (30 V, 20 Hz, 1 ms square -wave pulse width, 40 s duration). e, Bright field optical \nmicrograph showing the darkened cathode under 30 V cathode-to-anode bias (same device as 2d). \nf, Heat map of normalized depletion rate constants predicted using the modified Nernst –Planck \nmodel. The line profiles above panels c–f represent cross-sections through each 2D heat map, taken \nalong a ~6 mm slice indicated on the corresponding map. \n \nCreating Distinct Gradient Profiles with Angled Membrane Geometry:  \n \nBuilding on our theoretical framework, we explored how deviations from circular geometries, \nspecifically the introduction of membrane corners (i.e., locations where two edges meet), affect \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n9 \nspatial distribution of cargo flux during NanoEP. We hypothesized that electric field amplification \nat corners would generate distinct transport profiles compared to smooth circular boundaries. To \ntest this, we designed membrane geometries with varying int ernal angles between two adjacent \nedges (60°, 90°, 120°).  \n \nCalcein depletion experiments were performed under identical square-wave pulsing (15 V, 20 Hz, \n1 ms pulse width, 120 s duration) to evaluate the spatial dependence in field -driven molecular \ntransport, with device height and membrane surface area matched to  the 6 mm circular control \n(Figure 1d ). This ensures comparable impedances between the two electrodes, which is the \nsummed contribution of EEI charge transfer resistance, solution resistance, and membrane ion \ntransport resistance across the nanopores ( Supplemental S7). Depletion was imaged in real time \nthrough the anode to avoid optical interference from the cathode reduction ( Figure 3a ), and \ndepletion rate constants from the cell monolayers were extracted from the exponential fluorescence \ndecay kinetics for each geometry (Figure 3b). Representative fluorescent micrographs before and \nafter NanoEP for each device geometry can be found in Supplemental S9. COMSOL simulations \nof the x–y electric field distribution were performed for each geometry, and the result ing voltage \nprofiles were inputted into our modified Nernst–Planck model to calculate depletion rate patterns \n(Figure 3c). Our simulations predicted that the sharpest corner (60°) would exhibit the highest \nlocal depletion rates, with the highest gradient extending inward from the corner. Experimental \ncalcein depletion data validated these predictions, as shown in representa tive rate constant \nheatmaps for each geometry (Figure 3d).  \n \nTo quantify lateral gradients in cargo transport, we compared simulated and experimental ( n = 3) \ncalcein depletion rate constants as a function of distance from membrane corners. The Nernst –\nPlanck model predictions showed strong quantitative agreement with experimental results when \nmapped to the simulated voltage profile for each geometry (Figure 3e, refer to Supplemental S10 \nfor 90° and 120°). Our model was calibrated using independent datasets collected from corner and \ncenter regions, corresponding to the line plot endpoints ( Figure 3e), with training and evaluation \ndata acquired on different d ays. Calcein depletion rates were measured at each lateral spatial \nlocation and fit to an exponential decay function (Equation 1). With rate constants expressed as a \nfunction of distance from the corner, we defined a characteristic length (Char. Length, Figure 3e): \nthe distance at which the change in normalized rate constants (Δknorm = kcorner – kcenter) decayed to \n1/e of its initial value ((Δknorm)/e + kcenter), where kcorner is the depletion rate constant evaluated at \nthe device corner, kcenter is the asymptote rate constant, and e is Euler’s number). Both simulations \nand experiments revealed that sharper angles produced longer characteristic lengths ( Figure 3f). \nThis trend is intuitive: acute angles (e.g., 60°) keep cells in close proximity to one or more device \nedges, thereby sustaining an enhanced “edge effect” over a greater distance from the corner. In \ncontrast, wider angles (e.g., 120°) more closely resemble circular geometries, resulting in a shorter \nrange over which the enhanced electric field persists, hence a shorter characteristic length. We also \ncompared the Δknorm across geometries. While our model predicted larger differences in sharper \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n10 \nangles, experimental data showed no significant variation in Δ knorm between angles. Importantly, \nsimulated rate constants at all lateral positions fell within the 95% confidence interval of \nexperimental values, indicating strong overall agreement ( ≤ 12% average error, Figure 3g , \nSupplemental S10). Positive mean percent error ( 𝑀𝑃𝐸 =\n100%\n𝑁𝑠𝑎𝑚𝑝𝑙𝑒𝑠\n∑𝑁\n𝑖=1\n𝑦𝑖,𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑−𝑦𝑖,𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑\n𝑦𝑖,𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑\n) \nindicated model underprediction for large -angle geometries, whereas negative MPE values for \nacute angles (≤ 90°) suggested overestimation of the lateral electric field enhancement. Overall, \nthese results demonstrate that our model can capture cytoplasmic calcein transport driven by \nNanoEP across a range of confined membrane geometries, while also highlighting subtle \ndeviations in how lateral field enhancement scales with the corner angle. \n \nTo extend these findings to delivery applications, we conducted analogous geometric studies using \nAlexa Fluor™ 647–conjugated bovine serum albumin (BSA-AF647) as a model protein cargo. We \nensured uniform cargo distribution beneath the nanoporous membrane during NanoEP delivery, \nby incorporating 200 µm -tall PDMS pillars to elevate the membrane from the bottom electrode \n(Supplemental S11). Similar to the depletion experiments, fluorescent intensity was enhanced in \ncells near the corner of the triangular (60°) devices and decayed nonlinearly toward the center \n(Figure 3h, Supplemental S12 ). The shape of the normalized BSA -AF647 fluorescence closely \nmatched that of normalized calcein depletion in the same geometry ( Supplemental S1 3), \nunderscoring the generality of geometry -induced transport gradients across both delivery and \ndepletion modalities. However, their characteristic lengths differed (0.275 mm for BSA delivery \nvs. 0.520 mm for calcein depletion), as did Δknorm (0.78 for BSA vs. 0.69 for calcein). The shorter \ncharacteristic length and larger Δ knorm for BSA likely reflect second -order effects of its larger \nmolecular size (67 kDa for BSA vs. 0.6 kDa for calcein), though direct comparison is complicated \nby differences in how cargo transport was quantified (rate vs. amount). \n \nWe next examined how electrode polarity influenced calcein depletion across geometries. As \nbefore, imaging was always performed through the anode to avoid issues associated with cathodic \nreaction (Figure 3a and 3i). As expected for a (negatively) charged molecule, calcein exhibited \nfaster average depletion rates in the electrophoretic (anode -downward, Figure 3a) configuration \nthan when polarity was reversed (anti -electrophoretic, Figure 3i ). Importantly, the edge effect \npersisted in angled devices for both configurations, with corners consistently showing faster \ndepletion than centers ( Supplemental S10 ). We attribute this to elevated transmembrane \npotentials (across the cell –membrane interface) at the edges, which promote more and larger \nelectropores on cells within the applied voltage range 5. Both the transmembrane potential \n(governing electropore formation) and the potential across the PCTE membrane (driving cargo \nflux) contribute to the observed edge effect. Together, these findings validate that the heightened \nelectric field at the edge of  the EEI interface accurately translates into predictable spatial flux \npatterns for both cargo depletion and delivery. \n \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n11 \nFig. 3: Validation of the NanoEP transport model across membrane geometries. \n \na, Schematic illustration of NanoEP device setup and imaging orientation for electrophoretically \ndriven cargo transport. b, Full-device fluorescence micrographs of Calcein AM –stained HT1080 \ncells in triangular (60°), square (90°), and obtuse (120°) geometries (scale bars, 1 mm). c, \nNormalized model rate constant heat maps for 60°, 90°, and 120° NanoEP devices. d, \nRepresentative experimental rate constant heat maps of calcein depletion for 60°, 90°, 120° \nNanoEP devices (scale bars, 430 𝜇m). e, Comparison of simulated and experimental normalized \nrate constants as a function of distance from corner for 60° NanoEP devices (n = 3; scale bar, 430 \n𝜇m). f, Experimental Δknorm (left) and characteristic length (right) for each device geometry tested \n(n =3). g, Spatial mean percent error between model and experiment for each geometry, where \neach point i is a distance coordinate from the device corner.  h, Fluorescence intensity profiles of \nBSA-AF647 (2.5 mg/mL) delivery as a function of distance from a 60° device corner under 20 V, \n20 Hz, 1 ms square -wave pulse width, 10 s duration ( n = 3; scale bar, 430 𝜇m). i, Schematic \nillustration of NanoEP device setup and imaging orientation for anti -electrophoretically driven \ncargo transport. j, Average calcein depletion rate constants under electrophoretic vs. anti -\nelectrophoretic device configurations (n = 3 per device geometry).  \n \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n12 \nIncreasing Device Perimeter -to-Area Ratio to Enhance NanoEP Delivery Efficiency and \nReduce Lateral Variation:  \n \nBeyond creating device geometries for heterogeneous cell cargo manipulations, we sought to \ndesign a membrane shape that minimizes lateral variations in NanoEP -mediated delivery while \nenhancing overall flux, guided by our theoretical model. Conventional Nan oEP devices typically \nemploy circular wells14,15,24,28,29,34,37,38,39, which are convex and characterized by low perimeter-to-\narea ratios. In such designs, most cells reside far from the membrane edge and thus do not benefit \nfrom edge -enhanced field -driven transport, a limitation that becomes more pronounced when \nscaling up NanoEP systems for larger cell populations.  \n \nTo overcome this, we developed a concave, “serpentine” membrane geometry (Figure 4a) with a \nperimeter-to-area ratio of 2.03, compared to 0.67 for a 6 mm circular device of equal area. By \npositioning more cells in proximity to the membrane edge, we hypothesized that the serpentine \ndesign would amplify the edge effect, thereby boosting int racellular depletion and delivery \nefficiency while reducing lateral heterogeneity across the cell monolayer.  \n \nWe compared experimental calcein depletion rates in serpentine versus 6 mm circular geometries \n(Figure 4a, 4b ; n = 3, Supplemental S14 ). The serpentine rate constant profile followed a \nsymmetric U -shaped curve, with a maximum normalized rate difference (Δ knorm) of ~0.47, \nrepresenting the most uniform depletion observed across all geometries tested. This improvement \nis attributed to the serpentine’s parallel dual -edge configuration, which places more cells near \nregions of elevated electric field by minimizin g the distance of a cell to an edge. By contrast, \ncircular geometries showed a monotonic decrease in rate constants with distance from the edge. \nMoreover, serpentine devices exhibited higher overall depletion rates, consistent with stronger \nlocal electric fields. \n \nWe next assessed BSA-AF647 protein delivery across circular and serpentine devices (Figure 4c). \nPopulation-level fluorescence analysis revealed higher overall intensity in the serpentine geometry \ncompared to the circle ( Figure 4d, Supplemental S15 ). Variability in the serpentine device was \nattributed to local differences in cell adhesion and confluency on the PCTE nanoporous membrane, \nwhereas circular devices displayed a systemic radial gradient of decreasing fluorescence \n(indicative of amount of cargo delivered) with distance from the edge ( Supplemental S16, S17). \nHistogram analysis of single -cell fluorescence intensities ( Figure 4d, Supplemental S15 ) \nconfirmed a > 3-fold higher mean fluorescence intensity in serpentine devices compared to circles \n(15,128 vs. 3,787 a.u.). These results demonstrate that employing concave geometries with high \nperimeter-to-area ratios effectively amplifies edge -enhanced NanoEP flux, thereby improving \nprotein delivery efficiency while minimizing spatial heterogeneity at the device level.   \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n13 \nTo evaluate edge-enhanced delivery of larger molecular cargos, we delivered a plasmid encoding \nDsRed fluorescent protein (pLenti3.7-DsRed plasmid, ~5 MDa, 100 ng/𝜇L) labelled with YOYO-\n1 (Figure 4e, Supplemental S15, S16, S18). A PCR purification kit was used to remove unbound \nYOYO-1, ensuring that virtually all measured fluorescence came from the plasmid -bound dye \n(Supplemental S19). Under these conditions, the serpentine geometry showed markedly higher \nsingle-cell fluorescent intensity and a greater number of transfected cells to the circular geometry \n(Figure 4f, Supplemental S15 ). The spatial distribution again followed a U -shaped delivery \nprofile (Supplemental S16, S18), with random local fluctuations likely driven by differences in \ncell coverage, consistent with trends observed for the BSA-AF647 protein cargo. The high plasmid \ndose used in these experiments facilitated visualization but precluded assessment of protein \nexpression due to plasmid-induced toxicity14,40. For functional delivery, we repeated the pLenti3.7-\nDsRed plasmid delivery experiments at a lower plasmid concentration (5 ng/ 𝜇L) and assessed \nDsRed expression 48 hours post -transfection ( Figure 4g). Single -cell fluorescent analysis \nconfirmed both a greater proportion of DsRed expressing cells and higher mean expression levels \nin the serpentine devices (Figure 4h, Supplemental S15). Cell viability remained > 95% after 48 \nhours at this lower dose and was comparable to untreated controls ( Figure 4k ). At higher \nconcentrations (100 ng/ 𝜇L), cells began to come off the nanoporous membrane 24 hours post \ntransfection, so viability was taken at 24 hours rather than 48 hours post transfection to minimize \nthe extent of cell loss.  \n \nAggregated data across different cargos show a consistent trend of higher delivery or depletion in \nthe serpentine compared to the circular devices ( Figure 4i, j ): ~2-fold higher calcein depletion \nrates, ~4-fold higher BSA -AF647 fluorescent protein delivery, ~7 -fold higher plasmid delivery, \nand ~1.2-fold higher DsRed expression. These findings further support the hypothesis that devices \nemploying concave membrane shapes with higher perimeter -to-area ratios substantially improve \nNanoEP-mediated macromolecular transport efficiency and spatial uniformity.  \n \n \n \n \n \n \n \n \n \n \n \n \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n14 \nFig. 4:  Increasing device perimeter -to-area ratio enhances NanoEP-mediated cargo \ndepletion and delivery. \n \na, Left: full-device fluorescent micrograph of Calcein AM –stained HT1080 cells in serpentine \ndevice geometry (scale bar, 1 mm). Right: rate constant heat maps of calcein depletion in circular \n(top) vs. serpentine (bottom) geometries at 15 V, 20 Hz, 1 ms square-wave pulses, 120 s duration \n(scale bars, 430 𝜇m). b, Comparison of depletion rate constant as a function of distance from the \nedge for serpentine vs. circular devices ( n = 3 per geometry). c, Left: full -device fluorescent \nmicrograph of a serpentine device following BSA-AF647 delivery (2.5 mg/mL; scale bar, 1 mm). \nRight: representative fluorescent micrographs for BSA -AF647 delivery (2.5 mg/mL) in circular \n(top) and serpentine (bottom) devices at 20 V, 20 Hz, 1 ms square-wave pulse width, 10 s duration \n(n = 3 per geometry; scale bars, 200 𝜇m).  d, Histogram of single-cell BSA-AF647 fluorescence \nintensities in circular vs. serpentine geometries. e, Left: full-device fluorescent micrograph of a \nserpentine device following plasmid (pLenti3.7 -DsRed, ~5 MDa, 100 ng/ 𝜇L, YOYO-1 labeled) \ndelivery (scale bar, 1 mm).  Right: representative fluorescent micrographs in circular (top) vs. \nserpentine (bottom) devices at 25 V, 1Hz, 10 ms square-wave pulse width, 4 s duration (scale bars, \n200 𝜇m).  f, Histogram of single-cell plasmid+YOYO-1 fluorescence intensities per cell in circular \nvs. serpentine geometries. g,  Left: full -device fluorescent micrograph of a serpentine device \nshowing DsRed protein expression 48 h after plasmid delivery (pLenti3.7 -DsRed, 5 ng/𝜇L; scale \nbar, 1 mm). Right: representative fluorescent micrographs for DsRed expression in circular (top) \nvs. serpentine (bottom) devices at 25 V, 1 Hz, 10 ms square-wave pulse width, 4 s duration (scale \nbars, 200 𝜇m). h, Histogram of single-cell DsRed fluorescence intensities in circular vs. serpentine \ngeometries. i, Summary of fold -changes in fluorescent intensity per cell for BSA -AF647, \nplasmid+YOYO-1, and DsRed expression in circular vs. serpentine geometries. j, Average \ndepletion rate constant for electrophoretically vs. anti-electrophoretically driven cargo transport in \ncircular vs. serpentine geometries. k, Cell viability 24 h (100 ng/ 𝜇L samples) and 48 h (5 ng/ 𝜇L \nand control samples) post-transfection for plasmid+YOYO-1 delivery experiments. \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n15 \nUnderstanding the Role of Membrane Geometry in Electric Field Distribution and Cargo \nTransport Control: \n \nThrough combined experimental and simulation -based studies, we demonstrated that lateral \nnanoporous membrane geometry directly influences vertical NanoEP flux (along the z -axis) by \nreshaping the in -plane (x -y) electric field distribution across the membran e nanopores. By \ncontrolling this lateral field distribution, we can in turn modulate the spatial uniformity of \nintracellular cargo delivery and depletion across a cell monolayer. Using a modified Nernst–Planck \nmolecular flux model, we accurately predicted cargo transport rates (e.g., depletion kinetics) from \ndevice-specific lateral voltage profiles by introducing an effective transport length (leff), defined as \nthe ratio of cell volume to total electropore area, which is a function of local electric fields. \nConceptually, leff represents an ensemble -averaged path length for cargo molecules leaving the \ncell: smaller leff values correspond to faster depletion rates. This modeling framework enables \nrational design of membrane geometries to achieve targeted intra cellular delivery or depletion \nprofiles.  \n \nWe found that leff must be tuned for different sub -regions of the cell –membrane interface to \naccurately model cargo transport. Subdividing the nanoporous membrane into lateral “corner” and \n“center” zones substantially improved model fidelity. As expected from the sigmoidal dependence \nof leff on local voltage (𝜑), which reflects the voltage -driven increase in the electropore number \n(np) and area ( Ap) in cells during NanoEP, leff was lowest at device corners. Specifically, we \ncalculated leff values of 2.33 mm (center) and 0.92 mm (corner), confirming substantially enhanced \nfield-driven cargo transport near corners of the nanoporous membrane. While these values exceed \nthe dimension of a single cell, they are empirical measures that likely include transport retardation \neffects fr om thermal fluctuation (molecular random walk) and electropore cycling \n(opening/closing). Cells were pulsed with a 2 –4% duty cycle at 20 Hz (50 ms period), and prior \nstudies suggest large electropores close within ~100 µs 15. Thus, because 𝑙𝑖𝑚\n𝐴𝑝𝑛𝑝→0\n𝑙𝑒𝑓𝑓 = ∞, and the \nfield is “off” more than “on”, measured leff values are higher than physically intuitive. Using the \nexpression leff = \n𝑉\n𝐴𝑝(𝜑)𝑛𝑝(𝜑), with an estimated HT1080 cell volume V = 2 × 10-15 m3, electropore \nradius rp = 15 nm (Ap = 706 nm2), we estimated 1212–3065 electropores per cell, with the highest \ndensity near corners. Given ~ 3500 nanopores underneath each cell (nanopore diameter = 200 nm), \nthese estimates suggest 35–88% of the nanopores within the PCTE membrane actively contribute \nto intracellular cargo transport in a confluent cell monolayer, assuming one cell electropore per \nmembrane nanopore. In practice, a single nanopore may host multiple electropores of varying \nradii15.  \n \nOptimizing plasmid delivery via NanoEP has been a major focus of research over the past \ndecade8,14,15,24,28,29,39,41. Compared to protein delivery, plasmid transfection presents unique \nchallenges because successful gene expression requires uptake and an optimal intracellular copy \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n16 \nnumber, enough to enable detectable expression without inducing toxic overexpression. Here, we \nshow that membrane geometry, an often -overlooked aspect of NanoEP device design, can \nprofoundly influence both delivery and expression outcomes, introducing a hi dden layer of \nvariability unless carefully controlled. Designing patterned PCTE substrates that enhance \nuniformity of cargo delivery while promoting scalable transfection is therefore of critical \nimportance. While our serpentine geometry highlighted the im pact of edge -enhancing device \nstructures, its complex shape is not readily scalable for manufacturing. Interestingly, several prior \nreports have inadvertently validated our edge effect hypothesis using single -cell NanoEP devices \nwith patterned silicon membranes42 or photoresist-patterned PCTE substrates43. In both cases, as \nin our serpentine design, cells are positioned adjacent to an “edge”, which acts as a high-resistance \nbarrier to the electric field and mass transport. This boundary concentrates the ele ctric field and \nflux in nearby regions of lower resistance, amplifying localized cargo transport. These insights \npoint toward a generalizable design principle: patterning nanoporous membranes to strategically \nincrease edge-adjacent areas. Moving forward, we aim to investigate the optimal void fraction and \nfeature size of patterned PCTE substrates to facilitate uniform NanoEP transfection across large \ncontiguous areas (e.g., T25 flask scale); a feat which up till now has not been accomplished in the \nliterature. \n \nAlthough the electric field is the dominant factor shaping cargo delivery profiles, other factors not \ncaptured by our COMSOL or Nernst–Planck model may contribute. For instance, electroosmotic \nflow can impose pressures up to ~1 kPa on the cell monolayer during electroporation37, which may \noppose the migration of negatively charged cargo (e.g., calcein) toward the anode (+), particularly \nin the device center. Additional system-level variability arises from the stochastic distribution of \nnanopores in PCTE membranes and from non-uniform cell coverage or membrane contact, all of \nwhich can introduce noise and heterogeneity in cargo flux. Despite these challenges, we \nsuccessfully demonstrated that lateral electric field distributions, and thus intracellular NanoEP  \ndelivery or depletion outcomes, can be predicted and customized simply by altering membrane \ngeometry. Breaking lateral symmetry enables device designs that promote either more uniform or \nintentionally patterned delivery. This geometric control offers a vi able path toward scalable, \nsubstrate-based transfection platforms for clinically relevant applications, including complex 2D \ntissue models. While further work is required to identify scalability limits, increasing the \nperimeter-to-area ratio remains a promising strategy for expanding effective substrate surface area \nand enhancing delivery performance.  \n \nConclusions \n \nIn this study, we demonstrated that NanoEP membrane geometry plays a critical role in shaping \nthe in-plane (x-y) electric field distribution and, consequently, drives anisotropic molecular flux \nduring cargo delivery or removal. By systematically varying na noporous membrane geometries, \nwe showed that the spatial heterogeneity of cargo transport can be predictably controlled through \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n17 \nlateral electric field manipulation. We identified and characterized a geometry -dependent edge \neffect, wherein enhanced cargo transport occurs near the perimeter of the nanoporous membrane \ndue to lateral gradients of the vertically amplified electric field. By coupling experimental results \nwith finite element voltage simulations and a modified Nernst–Planck flux model, we established \nstrong agreement between predicted and observed lateral heterogeneity in cargo flux, validating \nthe underlying electrokinetic  mechanism. Building on this insight, we introduced device \ngeometries with various internal angles to guide spatial gradients in both cargo delivery and \ndepletion. We further demonstrated that concave geometries with high perimeter -to-area ratios \nsignificantly reduce the average distance between target cells and membrane edges, leading to \nhigher efficiency and more uniform delivery of protein and plasmid cargos across the cell \nmonolayer. Overall, this work establishes the previously overlooked lateral membr ane geometry \nas an important design parameter for controlling localized electric fields and the resulting \nintercellular cargo distribution in substrate-based delivery systems.  \n \n \nAcknowledgements \n \nSchematic figures were generated in BioRender. HT1080 cells were provided to us from the \nThurber lab at the University of Michigan. SEM images were taken at the Michigan Center for \nMaterials Characterization (MC2). We would like to thank the University of Michigan College of \nEngineering START grant (Grant Number: U081613). We would also like to acknowledge support \nfrom the American Heart Association under Award No. 25IPA1455592 \n(https://doi.org/10.58275/AHA.25IPA1455592.pc.gr.235709), E.M. through the NSF GRFP under \nGrant No. DGE 2241144. In addition, A.T.L. would like to acknowledge supports from the \nNational Science Foundation (Grant Number: 2243104, Center for Complex Particle Syst ems, \nCOMPASS), American Chemical Society Petroleum Research Fund (Grant Number: 66979 -\nDNI10), the Michigan Materials Research Institute (MMRI), and the COMPASS -Biointerfaces \nInstitute Challenge Award. We would like to thank Bobby Kent from the Baker Lab at  the \nUniversity of Michigan for assistance with the MATLAB code for creating a mask around the cells \nfor image analysis.  \n  \nMethods \n \nDevice Fabrication  \nMolds of different geometries were designed with Fusion 360 and 3D printed with the Asiga Pro \n4k45 DLP printer. DentaMODEL (Asiga) resin was used for the printing material. Post -printing, \nthe 3D printed molds were cured with UV light for 2 minutes at 36 W (Asiga Flash), followed by \na 30-minute isopropyl alcohol wash, and then baked overnight at 60 °C. The area of the device \ngeometries was kept constant to 28.3 mm2 as well as a height of 2 mm unless specified otherwise.  \nPolydimethylsiloxane (PDMS Sylgard™ 184 DOW) at a 10:1 ratio (base to curing agent) was cast \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n18 \ninto the molds and cured overnight at 60 °C. To attach the polycarbonate track etched membranes \n(PCTE) of 200 nm (calcein depletion, propidium iodide and BSA delivery) or 800 nm (plasmid \ndelivery) pore diameters (Cytiva Whatman) to the PDMS devices, uncure d PDMS was spun coat \non a glass slide to create a 20 µm PDMS layer. Devices were then tapped onto the glass slide to \ncoat the device surface with uncured PDMS, and the PCTE membranes were then placed on the \ndevice and cured overnight at 60 °C 24,44. Indium tin oxide (ITO) glass slides (Nanocs, 5 Ω /sq) \nwere used as both the positive and negative electrodes.  \n \nCell Culture and Seeding in Devices \nHT1080 cells, a fibrosarcoma cell line, were cultured in ATCC Eagle's Minimum Essential \nMedium (EMEM) with 10% fetal bovine serum (Gibco) and 1% penicillin streptomycin (Gibco). \nOn Day 0, the devices were treated with oxygen plasma for 1 minute (Plasma Etc h, Inc.) for \nsterilization and increasing wettability. The devices were then coated with 27.5 µg/mL of \nfibronectin, from human plasma (Sigma -Aldrich), in phosphate buffered saline (Gibco) and \nincubated for 1 hour. Following fibronectin incubation, the devi ces were washed with media and \nHT1080 cells were seeded in the devices at a cell density of 125,000 cells/cm 2. Cells were \nelectroporated the following day.  \n \nElectroporation: Cargo Delivery and Depletion \nAll cells were electroporated one day after cell seeding (Day 1) with Gene Pulser Electroporation \nBuffer (Bio -Rad). Cells were exposed to the buffer for roughly 10 minutes. A VSP -300 \nPotentiostat (BioLogic) was used for applying the electrical pulses. The electroporation buffer or \ncargo solution was pipetted on the bottom electrode at a volume of 10 -100 µL. The device was \nthen placed on top of the droplet and overfilled with electroporation buffer to prevent any air gaps \nwhen placing the top electrode above the device15,24. Copper tape was used to connect the alligator \nclips to the ITO slides.  \n \nFor delivery of Bovine Serum Albumin (BSA) Alexa Fluor ™ 488 and 647 conjugates \n(Invitrogen™), the cells were pre -stained with Hoechst 33342 (Invitrogen) at 15 µg/mL, and \nfluorescent BSA cargo solution was placed at a concentration of 2.5 mg/mL in the electroporation \nbuffer. The cells were electroporated at an applied voltage of 15 -30 V at 20 Hz and 1 ms pulse \nsquare wave pulse widths for 5-20 s. The top electrode was the anode (+) and the bottom electrode \nwas the cathode (-). BSA delivery images were taken approximately 15 min after electroporation \non the ECHO Revolve microscope or the Cytation 5 (Biotek Agilent).  \n \nFor depletion of calcein, cells were pre -stained with calcein AM (Invitrogen) at 3 µM for 30 \nminutes, approximately 1 hour before electroporation. The cells were electroporated at an applied \nvoltage of 15 V at 20 Hz and 0.2 -1 ms pulse widths for 60 -120 s. For electrophoretically driven \ncalcein removal, the top electrode was the cathode (-) and the bottom electrode was the anode (+), \nimaging through the nanoporous membrane to avoid imaging the cathode reduction. For anti -\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n19 \nelectrophoretically driven calcein removal, the top electrode was the anode (+) and the bottom \nelectrode was the cathode ( -), imaging above the nanoporous membrane to avoid imaging the \ncathode reduction. Calcein depletion experiments were recorded in real time on the ECHO \nRevolve fluorescent microscope.  \n \nFor delivery of plasmid, pLenti3.7 -DsRed plasmid (5 MDa) was stained with YOYO -1 dye \n(Biotium) at a ratio of 10 base pairs: 1 YOYO -1 molecule. The solution was left to incubate at \n37°C for 2 hours. A PCR purification kit (GeneJET, Thermo Scientific) was used to separate \nunbound YOYO -1 molecules from the solution of bound YOYO -1 molecules to the plasmid. \nSolutions were diluted with an electroporation buffer at concentrations of 5 to 100 ng/𝜇L. The cells \nwere electroporated at an applied voltage of 25 V, 1 Hz, 10 ms square-wave pulses for 4 s duration. \nCell viability was taken 24 –48 hours after electroporation with Cy5 NucSpot® Nuclear Stain \n(Biotium) and Hoechst 33342 (Invitrogen). \n  \nITO Reaction Experiment  \nFor imaging the reaction of the cathode, 2 mm and 6 mm diameter PDMS well devices (2 mm tall) \nwere used with or without a membrane with an applied voltage of 30 V, 20 Hz, 1 ms square-wave \npulses for 40–60 s duration. No cells were used, and Gene Pulser Electroporation Buffer was used \nas the buffer. Images were analyzed using MATLAB or Python to measure the reaction over time.  \n \nPotentiostat Data Collection \nBiologic’s EC Lab software was used to control the electrical parameters of the NanoEP \nexperiments. Prior to running the electroporation experiment, potentio -electrical impedance \nspectroscopy (PEIS) was conducted over frequencies ranging from 2 MHz to 500 mHz, with a sine \namplitude of 10 mV and base potential of 0 V DC. No reference electrodes were used in this study. \nPEIS was used to elucidate the solution/device resistance near 100-1 kHz, the x-coordinate where \nthe imaginary (y -coordinate) Nyquist impedan ce is ~0 Ω. PEIS was also conducted after the \nNanoEP experiment to see if the device resistance changed. NanoEP was conducted using the \nsoftware’s differential pulse amperometry (DPA) technique. Average currents reported are only \nwhen the pulse is applied, not an average of the on and off state.  \n \nCOMSOL Simulation & Circuit Modeling \nThe COMSOL geometry was created and evaluated using the Primary Current Distribution \npackage. All simulations were run at 37 ℃. The electrolyte was modeled as water, with a fixed \nconductivity of 0.2 S/m. Electrodes for the 3 -D geometry were ITO and 100 nm thick, with a \nconductivity of 3 × 10 6 S/m. The simulation incorporated a “surface resistance” node at the EEI, \nwith an experimentally measured value of 0.0015 Ωm2. This value was similar for all tested device \ngeometries. The surface resistance was experimentally determined by calculating the average \nvoltage drop over the electrolyte –electrode interface (EEI; averaged among several devices of a \ncertain shape), dividing by the current through the system, and multiplying it by the surface area. \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n20 \nIn all simulations, both electrodes were matched to have the same surface resistance and \ncapacitance. The top electrode is separated from the bottom by ~2 mm. Equivalent circuit modeling \nwas performed using the LTspice software. Built -in modules for circuit elements were used, and \na square pulse element was used to apply the voltage. No product specifications were added to the \ncircuit elements. \n \nSEM Imaging \nSEM imaging was performed using the Thermo Fisher Nova 200 Nanolab at the Michigan Center \nfor Materials Characterization (MC2). The ITO coated glass was mounted using conductive carbon \ntape and grounded using colloidal graphite glue (Electron Microscopy Sciences). Images of ITO \nsurfaces were acquired using secondary electrons at 5 kV and 1.6 nA of beam current.  \n \nNernst-Planck Simulation \nTo leverage simulated voltage profiles to easily predict cargo depletion rates, a simplified Nernst–\nPlanck (NP) equation was implemented in Python. The movement of charged molecules in \nsolution is described by the NP equation ( Equation 5)45. An equivalent form of the NP equation \ncan be found according to the divergence theorem (Equation 5)46, so that the number (np) and area \n(Ap) of electropores can be considered in the analysis. The flux term (J) incorporates the effects of \nconcentration (c), fluid velocit y (v), electric field ( E), temperature ( T), and cargo diffusivity in \nwater at 37℃ (DAB). The electric field is related to flux using the molecule charge (z), elemental \ncharge (e), and Boltzmann constant (kb).  \n \n𝜕𝑐\n𝜕𝑡 + 𝛻 ⋅ 𝐽 = 0 ⇔ 𝑉\n𝜕𝑐\n𝜕𝑡 + 𝐽𝐴𝑝𝑛𝑝 = 0 (5) \n \n𝐽 = −𝐷𝛻𝑐+ 𝑐𝑣 +\n−𝐷𝑧𝑒\n𝑘𝑏𝑇 𝑐\n𝑑𝜓\n𝑑𝑧 (6) \n \nThe flux of the molecules ( J) is the vector sum of contributions from diffusion, advection, and \nelectromigration (Equation 6). The equation was simplified by removing the effect of advection \n(there is no fluid velocity) and calcein diffusion. Molecular diffusion was neglected since the \ncalculated electromotive species flux across the nanoporous membrane was ~1350× greater than \nthat of diffusion (Supplemental Information S4) and dominates cargo transport.  The flux is then \nplugged into Equation 5 with no assumed reaction and a transient concentration of cargo inside \nthe cell volume (V). Here, Ap represents the area of one electropore on the cell and np is the number \nof electropores. When the simplified Equation 6 is plugged into Equation 5 and integrated with \nrespect to time, it yields Equation 7.   \n𝐶(𝑡) = 𝐶0𝑒\n(−[\n𝐷𝑧𝑒𝐴𝑝𝑛𝑝\n𝑉𝑘𝑏𝑇\n𝑑𝜑\n𝑑𝑧 ]𝑡)\n≡ 𝐶0𝑒\n−(𝐷𝑒𝑧\n𝑘𝑏𝑇\n𝑑𝜑\n𝑑𝑧\n1\n𝑙𝑒𝑓𝑓(𝜑))𝑡\n≡ 𝐶0𝑒−𝑘𝑡 (7) \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n21 \n \n \n𝑙𝑒𝑓𝑓(𝜑) =\n𝑉\n𝐴𝑝(𝜑)𝑛𝑝(𝜑) [=] 𝑚                                (8) \n \n \nWe further lump the electropore area, number of electropores, and the cell volume into a fitting \nparameter leff, as these values can be difficult to ascertain or are uncertain during the experiment \n(Equation 8 ). As discussed in the main text, this yields an interpretable meaning for the \nexperimental calcein rate constants. We use this parameter to adjust the timescale of our simulation \nequation to match experimental data by fitting leff to minimize the mean absolute error. Specific \nvalues used in the simulation are included in Supplemental Information S4.  \n \nThis lumped model for charged molecule transport is mapped onto our device geometry by \nutilizing the electric field at each point in space retrieved from COMSOL simulations in a 3 -D \nNanoEP device. Our NP simulation is 0-D and treats the hypothetical cell as a point in space, but \nwe use input voltages from different (x, y) points in the COMSOL solution space to effectively \npredict calcein depletion rates over the entire membrane geometric area.  \n        \nEvaluation of Cargo Depletion and Decay in Rate Constant/Intensity Distance from Edge/Corner \nCargo depletion was assessed by tracking the reduction in fluorescent signal intensity of cells pre-\nstained with calcein AM during time -lapse imaging, conducted using the ECHO Revolve \nmicroscope. The fluorescent intensity drop is modeled by exponential dec ay in Equation 1. If is \nthe fluorescence intensity of each pixel (or bin) tracked over time (t), starting at an initial \nfluorescence intensity If,o and reaching a plateau ( b). Depletion rate constants ( k) were extracted \nby fitting the experimental data to  Equation 128. The normalized depletion rate as a function of \ndistance for the angled geometries (60°, 90°, and 120° NanoEP devices) is also modeled by \nexponential decay in Equation 1 for determining the characteristic length and Δ knorm for the rate \nconstant heat maps and the delivery of BSA A647 in the triangle, however rather than a change \nover time, the change would occur over a distance. Time-lapse imaging data were analyzed using \nPython 3.11.5 with the packages cv2, matplotlib, seab orn, scipy, and sklea rn. Exponential \nregression models were optimized for each pixel by minimizing the sum of squared errors. The \ndepletion rate constants were visualized as a heat map, where each pixel directly corresponds to \nthe same location in the sample, and the color int ensity reflects the value of the depletion rate \nconstant. For the binned calcein depletion data, MATLAB was used to measure the fluorescence \nintensity decrease over time in each bin.  \n \n \n \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n22 \n \nReferences \n \n1 Pathak, N. et al. Cellular Delivery of Large Functional Proteins and Protein–Nucleic Acid \nConstructs via Localized Electroporation. Nano Lett. 23, 3653–3660 (2023). \n \n2 Hu, T., Kumar, A. R., Luo, Y. & Tay, A. Automating CAR-T Transfection with Micro and \nNano-Technologies. Small Methods 8, 2301300 (2024). \n \n3 Lowdell, M. W. Considerations for manufacturing of cell and gene medicines for clinical \ndevelopment. Cytotherapy 27, 874–883 (2025). \n \n4 Lapteva, L., Purohit-Sheth, T., Serabian, M. & Puri, R. K. Clinical Development of Gene \nTherapies: The First Three Decades and Counting. Mol Ther Methods Clin Dev 19, 387–397 \n(2020). \n \n5 Lee, G. W. et al. Nanoporous electroporation needle for localized intracellular delivery in \ndeep tissues. Bioengineering & Translational Medicine 8, e10418 (2023). \n \n6 Kim, T. K. & Eberwine, J. H. Mammalian cell transfection: the present and the future. Anal \nBioanal Chem 397, 3173–3178 (2010). \n \n7 Brooks, J. et al. High Throughput and Highly Controllable Methods for In Vitro Intracellular \nDelivery. Small 16, 2004917 (2020). \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n23 \n8 Chang, L. et al. 3D nanochannel electroporation for high-throughput cell transfection with \nhigh uniformity and dosage control. Nanoscale 8, 243–252 (2015). \n \n9 Xie, X. et al. Nanostraw–Electroporation System for Highly Efficient Intracellular Delivery \nand Transfection. ACS Nano 7, 4351–4358 (2013). \n \n10 Chiappini, C. et al. Tutorial: using nanoneedles for intracellular delivery. Nat Protoc 16, \n4539–4563 (2021). \n \n11 Yoh, H. Z. et al. Polymeric Nanoneedle Arrays Mediate Stiffness-Independent Intracellular \nDelivery. Advanced Functional Materials 32, 2104828 (2022). \n \n12 Schmiderer, L. et al. Efficient and nontoxic biomolecule delivery to primary human \nhematopoietic stem cells using nanostraws. Proceedings of the National Academy of Sciences \n117, 21267–21273 (2020). \n \n13 Cao, Y. et al. Universal intracellular biomolecule delivery with precise dosage control. \nScience Advances 4, eaat8131 (2018). \n \n14 Kang, W. et al. Microfluidic device for stem cell differentiation and localized electroporation \nof postmitotic neurons. Lab Chip 14, 4486–4495 (2014). \n \n15 Mukherjee, P., Nathamgari, S. S. P., Kessler, J. A. & Espinosa, H. D. Combined Numerical \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n24 \nand Experimental Investigation of Localized Electroporation-Based Cell Transfection and \nSampling. ACS Nano 12, 12118–12128 (2018). \n \n16 Boukany, P. E. et al. Nanochannel electroporation delivers precise amounts of biomolecules \ninto living cells. Nature Nanotech 6, 747–754 (2011). \n \n17 Ekstrand, F. et al. Achieving efficient clonal beta cells transfection using \nnanostraw/nanopore-assisted electroporation. RSC Adv. 14, 22244–22252 (2024). \n \n18 Patino, C. A. et al. High-Throughput Microfluidics Platform for Intracellular Delivery and \nSampling of Biomolecules from Live Cells. ACS Nano 16, 7937–7946 (2022). \n \n19 Mukherjee, P. et al. Temporal Sampling of Enzymes from Live Cells by Localized \nElectroporation and Quantification of Activity by SAMDI Mass Spectrometry. Small 16, \n2000584 (2020). \n \n20 Neumann, E., Schaefer-Ridder, M., Wang, Y. & Hofschneider, P. H. Gene transfer into \nmouse lyoma cells by electroporation in high electric fields. EMBO J 1, 841–845 (1982). \n \n21 Shi, J. et al. A Review on Electroporation-Based Intracellular Delivery. Molecules 23, 3044 \n(2018). \n \n22 Baek, K., Tu, C., Zoldan, J. & Suggs, L. J. Gene Transfection for Stem Cell Therapy. Curr \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n25 \nStem Cell Rep 2, 52–61 (2016). \n \n23 Mukherjee, P. et al. Single cell transcriptomics reveals reduced stress response in stem cells \nmanipulated using localized electric fields. Materials Today Bio 19, 100601 (2023). \n \n24 Cao, Y. et al. Nontoxic nanopore electroporation for effective intracellular delivery of \nbiological macromolecules. Proceedings of the National Academy of Sciences 116, 7899–7904 \n(2019). \n \n25 Wei, X. F. & Grill, W. M. Current density distributions, field distributions and impedance \nanalysis of segmented deep brain stimulation electrodes. J. Neural Eng. 2, 139 (2005). \n \n26 Kim, Y., Fahy, J. B. & Tupper, B. J. Optimal Electrode Designs for Electrosurgery, \nDefibrillation, and External Cardiac Pacing. IEEE Transactions on Biomedical Engineering \nBME-33, 845–853 (1986). \n \n27 Tan, Y.-J. & Lim, K. Y. Understanding and improving the uniformity of electrodeposition. \nSurface and Coatings Technology 167, 255–262 (2003). \n \n 28 Patino, C. A. et al. Multiplexed high-throughput localized electroporation workflow with \ndeep learning–based analysis for cell engineering. Science Advances 8, eabn7637 (2022). \n \n29 Vindiš, T. et al. Gene Electrotransfer into Mammalian Cells Using Commercial Cell Culture \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n26 \nInserts with Porous Substrate. Pharmaceutics 14, 1959 (2022). \n \n30 Sekar, R. B. et al. IK1 Heterogeneity Affects Genesis and Stability of Spiral Waves in \nCardiac Myocyte Monolayers. Circulation Research 104, 355–364 (2009). \n \n31 Campbell, K. et al. Spatial gradients in action potential duration created by regional \nmagnetofection of hERG are a substrate for wavebreak and turbulent propagation in \ncardiomyocyte monolayers. The Journal of Physiology 590, 6363–6379 (2012). \n \n32 Liu, L., Yellinek, S., Valdinger, I., Donval, A. & Mandler, D. Important Implications of the \nElectrochemical Reduction of ITO. Electrochimica Acta 176, 1374–1381 (2015). \n \n33 Wahab, O. J., Kang, M., Meloni, G. N., Daviddi, E. & Unwin, P. R. Nanoscale Visualization \nof Electrochemical Activity at Indium Tin Oxide Electrodes. Anal. Chem. 94, 4729–4736 \n(2022). \n \n34 Brooks, J. R. et al. An Equivalent Circuit Model for Localized Electroporation on Track \nEtched Membranes. Biosens Bioelectron 199, 113862 (2022). \n \n35 Magar, H. S., Hassan, R. Y. A. & Mulchandani, A. Electrochemical Impedance Spectroscopy \n(EIS): Principles, Construction, and Biosensing Applications. Sensors (Basel) 21, 6578 (2021). \n \n36 Lazanas, A. Ch. & Prodromidis, M. I. Electrochemical Impedance Spectroscopy─A Tutorial. \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n27 \nACS Meas. Sci. Au 3, 162–193 (2023). \n \n37 Brooks, J. R. et al. Transepithelial Electrical Impedance Increase Following Porous Substrate \nElectroporation Enables Label-Free Delivery. Small 20, 2310221 (2024). \n \n38 Chen, Z. et al. Nanopore-mediated protein delivery enabling three-color single-molecule \ntracking in living cells. Proceedings of the National Academy of Sciences 118, e2012229118 \n(2021). \n \n39 Liu, J. et al. Nanochannel Electro-Injection as a Versatile Platform for Efficient RNA/DNA \nProgramming on Dendritic Cells. Small 19, 2303088 (2023). \n \n40 Ekstrand, F. et al. Plasmid-induced cytotoxicity revealed by nanopore and nanostraw \nelectroporation. Nanoscale (2025) doi:10.1039/D5NR02352A. \n \n41 Liu, J. et al. Nanopore Electroporation Device for DNA Transfection into Various Spreading \nand Nonadherent Cell Types. ACS Appl. Mater. Interfaces 15, 50015–50033 (2023). \n \n42 Dong, Z. et al. On-chip multiplexed single-cell patterning and controllable intracellular \ndelivery. Microsyst Nanoeng 6, 2 (2020). \n \n43 Dong, Z. et al. Single Living Cell Analysis Nanoplatform for High-Throughput Interrogation \nof Gene Mutation and Cellular Behavior. Nano Lett. 21, 4878–4886 (2021). \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n28 \n \n44 Chueh, B. et al. Leakage-Free Bonding of Porous Membranes into Layered Microfluidic \nArray Systems. Anal Chem 79, 3504–3508 (2007). \n \n45 Kirby, B. J. Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices. \n(Cambridge University Press, Cambridge, 2010). doi:10.1017/CBO9780511760723. \n \n46 Kreyszig, E., Kreyszig, H. & Norminton, E. J. Advanced Engineering Mathematics. (John \nWiley and Sons, 2011). \n \n47 Anantharaj, S. & Noda, S. Appropriate Use of Electrochemical Impedance Spectroscopy in \nWater Splitting Electrocatalysis. ChemElectroChem 7, 2297–2308 (2020). \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint \n\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted September 30, 2025. ; https://doi.org/10.1101/2025.09.28.679060doi: bioRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}