A Theoretical Study of Single-Cell Electroporation in a Microchannel

Hybrid analytical-numerical approach for investigation of differential effects in normal and cancer cells under electroporation

Electroporation has offered important biomedical applications in electrochemotherapy, tissue ablation and gene editing recently. Time and computation efficient analytical and numerical models should be developed to understand the differential effects of electroporation on normal and cancer cells. In this work, we present a hybrid analytical-numerical approach to investigate the behavior of normal and cancer cells under electroporation. We have compared the human breast cancer cell (MCF-7) and non-tumorigenic human breast cell (MCF-10A) under electroporation in terms of change in transmembrane voltage and pore formation on cell surface. The effects of electric pulse time, amplitude and membrane conductivity variation are analyzed in a systematic manner. To accelerate the calculation of transmembrane voltage, we have introduced a simple Multilayer Electric Potential Model (MEPM) which calculates the potential distribution across the cell analytically. The MEPM calculates electric potential distribution across a biological cell sandwiched between two semi-circular electrodes held at fixed potential, by solving the Laplace's equation over an equivalent planar, multilayer geometry. The MEPM model is then used in a Finite Element Method (FEM) based numerical model of electroporation. Transmembrane voltage and pore density for electroporated MCF-10A are estimated to be 1.31 V and 2.98 × 1013 m-2 respectively, and for MCF-7 the estimated values are 0.53 V and 1.93 × 1014 m-2, respectively. Our results suggest that under electroporation, the cancer cell's membrane get much more permeabilized than its counterpart normal cell even at small values of transmembrane voltage. This work provides a theoretical basis for further experimental exploration of electroporation process in cancer therapy, and serves as a design tool for performance optimization.

Theoretical Study of Molecular Transport Through a Permeabilized Cell Membrane in a Microchannel

A two-dimensional model is developed to study the molecular transport into an immersed cell in a microchannel and to investigate the effects of finite boundary (a cell is suspended in a microchannel), amplitude of electric pulse, and geometrical parameter (microchannel height and size of electrodes) on cell uptake. Embedded electrodes on the walls of the microchannel generate the required electric pulse to permeabilize the cell membrane, pass the ions through the membrane, and transport them into the cell. The shape of electric pulses is square with the time span of 6 ms; their intensities are in the range of 2.2, 2.4, 2.6, 3 V. Numerical simulations have been performed to comprehensively investigate the molecular uptake into the cell. The obtained results of the current study demonstrate that calcium ions enter the cell from the anodic side (the side near positive electrode); after a while, the cell faces depletion of the calcium ions on a positive electrode-facing side within the microchannel; the duration of depletion depends on the amplitude of electric pulse and geometry that lasts from microseconds to milliseconds. By keeping geometrical parameters and time span constant, increment of a pulse intensity enhances molecular uptake and rate of propagation inside the cell. If a ratio of electrode size to cell diameter is larger than 1, the transported amount of Ca ²⁺ into the cell, as well as the rate of propagation, will be significantly increased. By increasing the height of the microchannel, the rate of uptake is decreased. In an infinite domain, the peak concentration becomes constant after reaching the maximum value; this value depends on the intra-extracellular conductivity and diffusion coefficient of interior and exterior domains of the cell. In comparison, the maximum concentration is changed by geometrical parameters in the microchannel. After reaching the maximum value, the peak concentration reduces due to the depletion of Ca ²⁺ ions within the microchannel. Electrophoretic velocity has a significant effect on the cell uptake.

Micro-/nanoscale electroporation

Electroporation has been one of the most popular non-viral technologies for cell transfection. However, conventional bulk electroporation (BEP) shows significant limitations in efficiency, cell viability and transfection uniformity. Recent advances in microscale-electroporation (MEP) resulted in improved cell viability. Further miniaturization of the electroporation system (i.e., nanoscale) has brought up many unique advantages, including negligible cell damage and dosage control capabilities with single-cell resolution, which has enabled more translational applications. In this review, we give an insight into the fundamental and technical aspects of micro- and nanoscale/nanochannel electroporation (NEP) and go over several examples of MEP/NEP-based cutting-edge research, including gene editing, adoptive immunotherapy, and cellular reprogramming. The challenges and opportunities of advanced electroporation technologies are also discussed.

Modelling the Bioelectronic Interface in Engineered Tethered Membranes: From Biosensing to Electroporation

This paper studies the construction and predictive models of three novel measurement platforms: (i) a Pore Formation Measurement Platform (PFMP) for detecting the presence of pore forming proteins and peptides, (ii) the Ion Channel Switch (ICS) biosensor for detecting the presence of analyte molecules in a fluid chamber, and (iii) an Electroporation Measurement Platform (EMP) that provides reliable measurements of the electroporation phenomenon. Common to all three measurement platforms is that they are comprised of an engineered tethered membrane that is formed via a rapid solvent exchange technique allowing the platform to have a lifetime of several months. The membrane is tethered to a gold electrode bioelectronic interface that includes an ionic reservoir separating the membrane and gold surface, allowing the membrane to mimic the physiological response of natural cell membranes. The electrical response of the PFMP, ICS, and EMP are predicted using continuum theories for electrodiffusive flow coupled with boundary conditions for modelling chemical reactions and electrical double layers present at the bioelectronic interface. Experimental measurements are used to validate the predictive accuracy of the dynamic models. These include using the PFMP for measuring the pore formation dynamics of the antimicrobial peptide PGLa and the protein toxin Staphylococcal α-Hemolysin; the ICS biosensor for measuring nano-molar concentrations of streptavidin, ferritin, thyroid stimulating hormone (TSH), and human chorionic gonadotropin (pregnancy hormone hCG); and the EMP for measuring electroporation of membranes with different tethering densities, and membrane compositions.

An engineered membrane to measure electroporation: effect of tethers and bioelectronic interface

This article reports on the construction and predictive models for a platform comprised of an engineered tethered membrane. The platform provides a controllable and physiologically relevant environment for the study of the electroporation process. The mixed self-assembled membrane is formed via a rapid solvent exchange technique. The membrane is tethered to the gold electrode and includes an ionic reservoir separating the membrane and gold surface. Above the membrane, there is an electrolyte solution, and a gold counterelectrode. A voltage is applied between the gold electrodes and the current measured. The current is dependent on the energy required to form aqueous pores and the conductance of each pore. A two-level predictive model, consisting of a macroscopic and a continuum model, is developed to relate the pore dynamics to the measured current. The macroscopic model consists of an equivalent circuit model of the tethered membrane, and asymptotic approximations to the Smoluchowski-Einstein equation of electroporation that is dependent on the pore conductance and the energy required to form aqueous pores. The continuum model is a generalized Poisson-Nernst-Planck (GPNP) system where an activity coefficient to account for steric effects of ions is added to the standard PNP system. The GPNP is used to evaluate the conductance of aqueous pores, and the electrical energy required to form the pores. As an outcome of the setup of the device and the two-level model, biologically important variables can be estimated from experimental measurements. To validate the accuracy of the two-level model, the predicted current is compared with experimentally measured current for different tethering densities.

Scaling relationship and optimization of double-pulse electroporation

The efficacy of electroporation is known to vary significantly across a wide variety of biological research and clinical applications, but as of this writing, a generalized approach to simultaneously improve efficiency and maintain viability has not been available in the literature. To address that discrepancy, we here outline an approach that is based on the mapping of the scaling relationships among electroporation-mediated molecular delivery, cellular viability, and electric pulse parameters. The delivery of Fluorescein-Dextran into 3T3 mouse fibroblast cells was used as a model system. The pulse was rationally split into two sequential phases: a first precursor for permeabilization, followed by a second one for molecular delivery. Extensive data in the parameter space of the second pulse strength and duration were collected and analyzed with flow cytometry. The fluorescence intensity correlated linearly with the second pulse duration, confirming the dominant role of electrophoresis in delivery. The delivery efficiency exhibited a characteristic sigmoidal dependence on the field strength. An examination of short-term cell death using 7-Aminoactinomycin D demonstrated a convincing linear correlation with respect to the electrical energy. Based on these scaling relationships, an optimal field strength becomes identifiable. A model study was also performed, and the results were compared with the experimental data to elucidate underlying mechanisms. The comparison reveals the existence of a critical transmembrane potential above which delivery with the second pulse becomes effective. Together, these efforts establish a general route to enhance the functionality of electroporation.

Numerical modeling of bi-polar (AC) pulse electroporation of single cell in microchannel to create nanopores on its membrane

AC electroporation of a single cell in a microchannel was numerically studied. A 15 μm diameter cell was considered in a microchannel 25 μm in height and the influences of AC electric pulse on its membrane were numerically investigated. The cell was assumed to be suspended between two electroporative electrodes embedded on the walls of a microchannel. An amplitude and a time span of applied electric pulse were chosen to be 80 kV/m and 10 μs, respectively. For different frequency values (50, 100, 200, and 500 kHz), simulations were performed to show how the cell membrane was electroporated and the creation of nanopores. Obtained numerical results show that the most and the largest nanopores are created around poles of cell (nearest points of cell membrane to the electrodes). The numerical simulations also demonstrate that increased frequency will slightly decrease electroporated area of the cell membrane; additionally, growth of the created nanopores will be stabilized. It has also been proven that size and number of the created nanopores will be decreased by moving from the poles to the equator of the cell. There is almost no nanopore created in the vicinity of the equator. Frequency affects the rate of generation of nanopores. In case of AC electroporation, creation of nanopores has two phases that periodically repeat over time. In each period, the pore density sharply increases and then becomes constant. Enhancement of the frequency will result in decrease in time span of the periods. In each period, size of the created nanopores sharply increases and then slightly decreases. However, until the AC electric pulse is present, overall trends of creation and development of nanopores will be ascending. Variation of the size and number of created nanopores can be explained by considering time variation of transmembrane potential (difference of electric potential on two sides of cell membrane) which is clear in the results presented in this study.