Cylindrical cell membranes in uniform applied electric fields: validation of a transport lattice method

Advances in pulsed electric stimuli as a physical method for treating liquid foods

There is a need for alternative technologies that can deliver safe and nutritious foods at lower costs as compared to conventional processes. Pulsed electric field (PEF) technology has been utilised for a plethora of different applications in the life and physical sciences, such as gene/drug delivery in medicine and extraction of bioactive compounds in food science and technology. PEF technology for treating liquid foods involves engineering principles to develop the equipment, and quantitative biochemistry and microbiology techniques to validate the process. There are numerous challenges to address for its application in liquid foods such as the 5-log pathogen reduction target in food safety, maintaining the food quality, and scale up of this physical approach for industrial integration. Here, we present the engineering principles associated with pulsed electric fields, related inactivation models of microorganisms, electroporation and electropermeabilization theory, to increase the quality and safety of liquid foods; including water, milk, beer, wine, fruit juices, cider, and liquid eggs. Ultimately, we discuss the outlook of the field and emphasise research gaps.

Application of the Taguchi method to explore a robust condition of tumor-treating field treatment

Tumor-treating fields have potential as minimally invasive cancer treatment. This study aimed to explore the optimum tumor-treating field conditions that minimize unpredicted variations in therapeutic outcomes resulting from differences in cell size and electrical properties. The electric field concentration that induces a dielectrophoretic force near the division plane of a mitotic cell was calculated by finite element analysis for 144 cases, based on different combinations of six noise factors associated with cells and four controllable factors including frequency, as determined by the Taguchi method. Changing the frequency from 200 to 400 kHz strongly increased robustness in producing a dielectrophoretic force, irrespective of noise factors. However, this frequency change reduced the force magnitude, which can be increased by simply applying a higher voltage. Based on additional simulations that considered this trade-off effect, a frequency of 300 kHz is recommended for a robust TTF treatment with allowable variations. The dielectrophoretic force was almost independent of the angle of applied electric field deviated from the most effective direction by ±20 degrees. Furthermore, increased robustness was observed for extracellular fluid with higher conductivity and permittivity. The Taguchi method was useful for identifying robust tumor-treating field therapy conditions from a considerably small number of replicated simulations.

Flow micropillar array electroporation to enhance size specific transfection to a large population of cells

Despite serving as a popular non-viral delivery approach, electroporation carries several drawbacks in its current configurations. We developed a Flow Micropillar-array Electroporation (FME) system to wisely regulate an important transmembrane-determining factor, namely cell size variations among individual cells, to achieve effective transfection. In FME, cells flow through a slit-type microfluidic channel on which carbon electrodes with well-patterned micropillar array texture are integrated as the top and bottom wall. Gravity helps bring cells to the micropillar array surface so that the permeable area on cells in different size populations is specified by their size regardless their random location fact. Without sacrificing cell viability, we demonstrate this FME concept by delivering DNA plasmids to several mammalian cell lines with obvious transfection enhancement when compared to a commercial system (K562: 3.0 folds; A549: 3.3 folds; HeLa: 1.8 folds, COS7: 1.7 folds; 293T: 2.9 folds; mES: 2.5 folds). Moreover, carbon-based electrodes are less expensive, more durable, and convenient for integration with a microfluidic setup which enables rapid and massive transfection capability that many therapeutic application needs. The success of FME may benefit many emerging biological studies and clinical practice that requires effective transfection to a large population of cells in limited processing time.

Intracellular Delivery and Sensing System Based on Electroplated Conductive Nanostraw Arrays

One-dimensional nanoneedle-like arrays have emerged as an attractive tool for penetrating the cell membrane to achieve intracellular applications including drug delivery, electrical recording, and biochemical detection. Hollow nanoneedles, also called nanostraws (NSs), combined with nanoelectroporation have been demonstrated as a powerful platform for intracellular drug delivery and extraction of intracellular contents. However, the fabrication technique of nanostraws still requires complicated and expensive atomic layer deposition and etching processes and fails to produce conductive nanostraws. Herein, we developed a commonly accessible and versatile electrodeposition approach to controllably fabricate conductive nanostraw arrays based on various types of metal or conductive polymer materials. Representatively, Pt nanostraws (Pt NSs) with 400 nm diameter were further integrated with a low-voltage nanoelectroporation system to achieve cell detection, intracellular drug delivery, and sensing of intracellular enzymes. Both theoretical simulations and experimental results revealed that the conductive nanostraws in direct contact with cells could induce high-efficiency cell electroporation at relatively low voltage (∼5 V). Efficient delivery of reagents into live cells with spatial control and repeated extraction of intracellular enzymes (e.g., caspase-3) for temporal monitoring from the same set of cells were demonstrated. This work not only pioneers a new avenue for universal production of conductive nanostraws on a large scale but also presents great potential for developing nanodevices to achieve a variety of biomedical applications including cell re-engineering, cell-based therapy, and signaling pathway monitoring.

From Cell to Tissue Properties-Modeling Skin Electroporation With Pore and Local Transport Region Formation

Current models of tissue electroporation either describe tissue with its bulk properties or include cell level properties, but model only a few cells of simple shapes in low-volume fractions or are in two dimensions. We constructed a three-dimensional model of realistically shaped cells in realistic volume fractions. By using a 'unit cell' model, the equivalent dielectric properties of whole tissue could be calculated. We calculated the dielectric properties of electroporated skin. We modeled electroporation of single cells by pore formation on keratinocytes and on the papillary dermis which gave dielectric properties of the electroporated epidermis and papillary dermis. During skin electroporation, local transport regions are formed in the stratum corneum. We modeled local transport regions and increase in their radii or density which affected the dielectric properties of the stratum corneum. The final model of skin electroporation accurately describes measured electric current and voltage drop on the skin during electroporation with long low-voltage pulses. The model also accurately describes voltage drop on the skin during electroporation with short high-voltage pulses. However, our results indicate that during application of short high-voltage pulses additional processes may occur which increase the electric current. Our model connects the processes occurring at the level of cell membranes (pore formation), at the level of a skin layer (formation of local transport region in the stratum corneum) with the tissue (skin layers) and even level of organs (skin). Using a similar approach, electroporation of any tissue can be modeled, if the morphology of the tissue is known.

Size Specific Transfection to Mammalian Cells by Micropillar Array Electroporation

Electroporation serves as a promising non-viral gene delivery approach, while its current configuration carries several drawbacks associated with high-voltage electrical pulses and heterogeneous treatment on individual cells. Here we developed a new micropillar array electroporation (MAE) platform to advance the electroporation-based delivery of DNA and RNA probes into mammalian cells. By introducing well-patterned micropillar array texture on the electrode surface, the number of pillars each cell faces varies with its plasma membrane surface area, despite their large population and random locations. In this way, cell size specific electroporation is conveniently carried out, contributing to a 2.5~3 fold increase on plasmid DNA transfection and an additional 10–55% transgene knockdown with siRNA probes, respectively. The delivery efficiency varies with the number and size of micropillars as well as their pattern density. As MAE works like many single cell electroporation are carried out in parallel, the electrophysiology response of individual cells is representative, which has potentials to facilitate the tedious, cell-specific protocol screening process in current bulk electroporation (i.e., electroporation to a large population of cells). Its success might promote the wide adoption of electroporation as a safe and effective non-viral gene delivery approach needed in many biological research and clinical treatments.

An Overview of Sub-Cellular Mechanisms Involved in the Action of TTFields

Long-standing research on electric and electromagnetic field interactions with biological cells and their subcellular structures has mainly focused on the low- and high-frequency regimes. Biological effects at intermediate frequencies between 100 and 300 kHz have been recently discovered and applied to cancer cells as a therapeutic modality called Tumor Treating Fields (TTFields). TTFields are clinically applied to disrupt cell division, primarily for the treatment of glioblastoma multiforme (GBM). In this review, we provide an assessment of possible physical interactions between 100 kHz range alternating electric fields and biological cells in general and their nano-scale subcellular structures in particular. This is intended to mechanistically elucidate the observed strong disruptive effects in cancer cells. Computational models of isolated cells subject to TTFields predict that for intermediate frequencies the intracellular electric field strength significantly increases and that peak dielectrophoretic forces develop in dividing cells. These findings are in agreement with in vitro observations of TTFields' disruptive effects on cellular function. We conclude that the most likely candidates to provide a quantitative explanation of these effects are ionic condensation waves around microtubules as well as dielectrophoretic effects on the dipole moments of microtubules. A less likely possibility is the involvement of actin filaments or ion channels.

Modeling Tumor Treating Fields (TTFields) application in single cells during metaphase and telophase

Effects of electric fields on biological cells have been extensively studied but primarily in the low and high frequency regimes. Low frequency AC fields have been investigated for applications to nerve and muscle stimulation or to examine possible environmental effects of 60 Hz excitation. High frequency fields have been studied to understand tissue heating and tumor ablation. Biological effects at intermediate frequencies (in the 100-500 kHz regime) have only recently been discovered and are now being used clinically to disrupt cell division, primarily for the treatment of recurrent glioblastoma multiforme. In this study, we develop a computational framework to investigate the mechanisms of action of these Tumor Treating Fields (TTFields) and to understand in vitro findings observed in cell culture. Using Finite Element Method models of isolated cells we show that the intermediate frequency range is unique because it constitutes a transition region in which the intracellular electric field, shielded at low frequencies, increases significantly. We also show that the threshold at which this increase occurs depends on the dielectric properties of the cell membrane. Furthermore, our models of different stages of the cell cycle and of the morphological changes associated with cytokinesis show that peak dielectrophoretic forces develop within dividing cells exposed to TTFields. These findings are in agreement with in vitro observations, and enhance our understanding of how TTFields disrupt cellular function.

Fundamental mathematical model shows that applied electrical field enhances chemotherapy delivery to tumors

Biobarriers imposed by the tumor microenvironment create a challenge to deliver chemotherapeutics effectively. Electric fields can be used to overcome these biobarriers in the form of electrochemotherapy, or by applying an electric field to tissue after chemotherapy has been delivered systemically. A fundamental understanding of the underlying physical phenomena governing tumor response to an applied electrical field is lacking. Building upon the work of Pascal et al. [1], a mathematical model that predicts the fraction of tumor killed due to a direct current (DC) applied electrical field and chemotherapy is developed here for tumor tissue surrounding a single, straight, cylindrical blood vessel. Results show the typical values of various parameters related to properties of the electrical field, tumor tissue and chemotherapy drug that have the most significant influence on the fraction of tumor killed. We show that the applied electrical field enhances tumor death due to chemotherapy and that the direction and magnitude of the applied electrical field have a significant impact on the fraction of tumor killed.

Magnetic tweezers-based 3D microchannel electroporation for high-throughput gene transfection in living cells

A novel high-throughput magnetic tweezers-based 3D microchannel electroporation system capable of transfecting 40 000 cells/cm(2) on a single chip for gene therapy, regenerative medicine, and intracellular detection of target mRNA for screening cellular heterogeneity is reported. A single cell or an ordered array of individual cells are remotely guided by programmable magnetic fields to poration sites with high (>90%) cell alignment efficiency to enable various transfection reagents to be delivered simultaneously into the cells. The present technique, in contrast to the conventional vacuum-based approach, is significantly gentler on the cellular membrane yielding >90% cell viability and, moreover, allows transfected cells to be transported for further analysis. Illustrating the versatility of the system, the GATA2 molecular beacon is delivered into leukemia cells to detect the regulation level of the GATA2 gene that is associated with the initiation of leukemia. The uniform delivery and a sharp contrast of fluorescence intensity between GATA2 positive and negative cells demonstrate key aspects of the platform for gene transfer, screening and detection of targeted intracellular markers in living cells.

Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations

Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace's equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite's membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

Calculation of externally applied electric field intensity for disruption of cancer cell proliferation

It is already known that electrostatic, magnetostatic, extremely low-frequency electric fields, and pulsed electric field could be utilized in cancer treatment. The healing effect depends on frequency and amplitude of electric field. In the present work, a simple theoretical model is developed to estimate the intensity of electrostatic field that damages a living cell during division. By this model, it is shown that magnification of electric field in the bottleneck of dividing cell is enough to break chemical bounds between molecules by an avalanche process. Our model shows that the externally applied electric field of 4 V/cm intensity is able to hurt a cancer cell at the dividing stage.

Micronozzle array enhanced sandwich electroporation of embryonic stem cells

Electroporation is one of the most popular nonviral gene transfer methods for embryonic stem cell transfection. Bulk electroporation techniques, however, require a high electrical field and provide a nonuniform electrical field distribution among randomly distributed cells, leading to limited transfection efficiency and cell viability, especially for a low number of cells. We present here a membrane sandwich electroporation system using a well-defined micronozzle array. This device is capable of transfecting hundred to millions of cells with good performance. The ability to treat a small number of cells (i.e., a hundred) offers great potential to work with hard-to-harvest patient cells for pharmaceutical kinetic studies. Numerical simulation of the initial transmembrane potential distribution and propidium iodide (PI) dye diffusion experiments demonstrated the advantage of highly focused and localized electric field strength provided by the micronozzle array over conventional bulk electroporation.

Single-colloidal particle impedance spectroscopy: complete equivalent circuit analysis of polyelectrolyte microcapsules

We present a high-speed microfluidic technique for characterizing the dielectric properties of individual polyelectrolyte microcapsules with different shell thicknesses using single-particle electrical impedance spectroscopy. Complete equivalent circuit analysis is developed to describe the electrical behavior of solid homogeneous microparticles and shelled microcapsules in suspension. The complete circuit model, which includes the resistance of the shell layer and the capacitance of the inner core, has been used to determine the permittivity and conductivity in the shell of single capsules. The PSpice circuit simulations, based on the developed complete circuit models, are used to analyze the experimental data. The relative permittivity of the polyelectrolyte capsule shell is determined to be 50, and the conductivities of the shells of six- and nine-layer microcapsules are estimated to be 28 +/- 6 and 3.3 +/- 1.7 mS m(-1), respectively.

Active mechanisms are needed to describe cell responses to submicrosecond, megavolt-per-meter pulses: cell models for ultrashort pulses

Intracellular effects of submicrosecond, megavolt-per-meter pulses imply changes in a cell's plasma membrane (PM) and organelle membranes. The maximum reported PM transmembrane voltage is only 1.6 V and phosphatidylserine is translocated to the outer membrane leaflet of the PM. Passive membrane models involve only displacement currents and predict excessive PM voltages (approximately 25 V). Here we use a cell system model with nonconcentric circular PM and organelle membranes to demonstrate fundamental differences between active (nonlinear) and passive (linear) models. We assign active or passive interactions to local membrane regions. The resulting cell system model involves a large number of interconnected local models that individually represent the 1), passive conductive and dielectric properties of aqueous electrolytes and membranes; 2), resting potential source; and 3), asymptotic membrane electroporation model. Systems with passive interactions cannot account for key experimental observations. Our active models exhibit supra-electroporation of the PM and organelle membranes, some key features of the transmembrane voltage, high densities of small pores in the PM and organelle membranes, and a global postpulse perturbation in which cell membranes are depolarized on the timescale of pore lifetimes.

Modeling environment for numerical simulation of applied electric fields on biological cells

The application of electric pulses in cells increases membrane permeability. This phenomenon is called electroporation. Current electroporation models do not explain all experimental findings: part of this problem is due to the limitations of numerical methods. The Equivalent Circuit Method (ECM) was developed in an attempt to solve electromagnetic problems in inhomogeneous and anisotropic media. ECM is based on modeling of the electrical transport properties of the medium by lumped circuit elements as capacitance, conductance, and current sources, representing the displacement, drift, and diffusion current, respectively. The purpose of the present study was to implement a 2-D cell Model Development Environment (MDE) of ionic transport process, local anisotropy around cell membranes, biological interfaces, and the dispersive behaviour of tissues. We present simulations of a single cell, skeletal muscle, and polygonal cell arrangement. Simulation of polygonal form indicates that the potential distribution depends on the geometrical form of cell. The results demonstrate the importance of the potential distributions in biological cells to provide strong evidences for the understanding of electroporation.

Hybrid finite element method for describing the electrical response of biological cells to applied fields

A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.

Electrical behavior and pore accumulation in a multicellular model for conventional and supra-electroporation

Extremely large but very short (20 kV/cm, 300 ns) electric field pulses were reported recently to non-thermally destroy melanoma tumors. The stated mechanism for field penetration into cells is pulse characteristic times faster than charge redistribution (displacement currents). Here we use a multicellular model with irregularly shaped, closely spaced cells to show that instead overwhelming pore creation (supra-electroporation) is dominant, with field penetration due to pores (ionic conduction currents) during most of the pulse. Moreover, the model's maximum membrane potential (about 1.2 V) is consistent with recent experimental observations on isolated cells. We also use the model to show that conventional electroporation resulting from 100 microsecond, 1 kV/cm pulses yields a spatially heterogeneous electroporation distribution. In contrast, the melanoma-destroying pulses cause nearly homogeneous electroporation of cells and their nuclear membranes. Electropores can persist for times much longer than the pulses, and are likely to be an important mechanism contributing to cell death.

Three dimensional transport lattice model for describing action potentials in axons stimulated by external electrodes

Conditions that stimulate action potentials in one or more nerves is of widespread interest. Axon and nerve models are usually based on two dimensional pre-specified lumped equivalents that assume where currents will flow. In contrast, here we illustrate creation of three dimensional (3D) system models with a transport lattice of interconnected local models for external and internal electrolyte and axon membrane. The transport lattice solves Laplace's equation in the extracellular medium and is coupled to the Hodgkin-Huxley model at local membrane sites. These space-filling models incorporate the geometric scale, which allows explicit representation of confined axons and external electrodes. The present results demonstrate feasibility of the basic approach. These models are spatially coarse and approximate, but can be straightforwardly improved. The transport lattice system models are modular and multiscale (spatial scales ranging from the membrane thickness of 5 nm to the axon segment length of 2 cm).

Membrane electroporation: The absolute rate equation and nanosecond time scale pore creation

The recent applications of nanosecond, megavolt-per-meter electric field pulses to biological systems show striking cellular and subcellular electric field induced effects and revive the interest in the biophysical mechanism of electroporation. We first show that the absolute rate theory, with experimentally based parameter input, is consistent with membrane pore creation on a nanosecond time scale. Secondly we use a Smoluchowski equation-based model to formulate a self-consistent theoretical approach. The analysis is carried out for a planar cell membrane patch exposed to a 10 ns trapezoidal pulse with 1.5 ns rise and fall times. Results demonstrate reversible supraelectroporation behavior in terms of transmembrane voltage, pore density, membrane conductance, fractional aqueous area, pore distribution, and average pore radius. We further motivate and justify the use of Krassowska's asymptotic electroporation model for analyzing nanosecond pulses, showing that pore creation dominates the electrical response and that pore expansion is a negligible effect on this time scale.

Model of a confined spherical cell in uniform and heterogeneous applied electric fields

Cells exposed to electric fields are often confined to a small volume within a solid tissue or within or near a device. Here we report on an approach to describing the frequency and time domain electrical responses of a spatially confined spherical cell by using a transport lattice system model. Two cases are considered: (1) a uniform applied field created by parallel plane electrodes, and (2) a heterogeneous applied field created by a planar electrode and a sharp microelectrode. Here fixed conductivities and dielectric permittivities of the extra- and intracellular media and of the membrane are used to create local transport models that are interconnected to create the system model. Consistent with traditional analytical solutions for spherical cells in an electrolyte of infinite extent, in the frequency domain the field amplification, G(m) (f) is large at low frequencies, f<1 MHz. G(m) (f) gradually decreases above 1 MHz and reaches a lower plateau at about 300 MHz, with the cell becoming almost "electrically invisible". In the time domain the application of a field pulse can result in altered localized transmembrane voltage changes due to a single microelectrode. The transport lattice approach provides modular, multiscale modeling capability that here ranges from cell membranes (5 nm scale) to the cell confinement volume ( approximately 40 microm scale).

Microdosimetry for conventional and supra-electroporation in cells with organelles

Conventional electroporation (EP) by 0.1 to 1 kV/cm pulses longer than 100 micros, and supra-electroporation by 10 to 300 kV/cm pulses shorter than 1 micros cause different cellular effects. Conventional EP delivers DNA, proteins, small drugs, and fluorescent indicators across the plasma membrane (PM) and causes moderate levels of phosphatidylserine (PS) translocation at the PM. We hypothesize that supra-EP is central to intracellular effects such as apoptosis induction and higher levels of PS translocation. Our cell system model has 20,000 interconnected local models for small areas of the PM and organelle membranes, small regions of aqueous media, appropriate resting potentials, and the asymptotic EP model. Conventional EP primarily affects the PM, but with a hint of endoplasmic reticulum involvement. Supra-EP can involve all of a cell's membrane at the largest fields. Conventional EP fields tend to go around cells, but supra-EP fields go through cells, extensively penetrating organelles.

Field stimulation of cells in suspension: use of a hybrid finite element method

Electric fields are used in a range of applications, including gene transfection, electrochemotherapy of tumors and cardiac defibrillation. Despite the widespread use of electric fields, most of the theoretical and computational studies on discrete cellular tissue have focused on a single cell. In this work, we propose a hybrid finite element method to simulate the effects of external electric fields on clusters of excitable cells. The method can be used to model cells of arbitrary cell geometries and non-linear membrane dynamics. The results show that the response of multiple cell, like a single cell, is a two-stage process consisting of the initial polarization that proceeds with cellular time constant (less than one microsecond) and the actual excitation of the cell membrane that proceeds with the membrane time constant (on the order of milliseconds). The results also show that the stimulation of a given cell depends in part on the arrangement of cells within the field and not simply the location within the field, suggesting that classical approaches that ignores the effect of the cells on the field do not adequately predict the cellular response.