Electrodiffusion of molecules in aqueous media: a robust, discretized description for electroporation and other transport phenomena

Modeling and simulation of current-clamp electroporation

Current-Clamp electroporation refers to the application of a constant current across a membrane which results in voltage fluctuations due to the creation of electropores. This method allows for the measurement of electroporation across a long timescale (minutes) and facilitates the comparison between experimental and theoretical studies. Of particular interest is the claim in the literature that current-clamp electroporation results in the creation of a single pore. We simulated current-clamp electroporation using the Smoluchowski and Langevin equations and identified two possible mechanisms to explain the observed voltage fluctuations. The voltage fluctuations may be due to a single pore or a few pores growing and shrinking via a negative feedback mechanism or the opening and closing of pores in a larger population of pores. Our results suggest that current-clamp conditions do not necessarily result in the creation of a single pore. Additionally, we showed that the Langevin model is more accurate than the Smoluchowski model under conditions where there are only a few pores.

Drying Technology Assisted by Nonthermal Pulsed Filamentary Microplasma Treatment: Theory and Practice

Nonthermal pulsed filamentary microplasma treatment for drying is a nonthermal technology with promising perspectives to dehydrate plant agricultural materials. The modified set of Luikov’s equations for heat, mass and pressure transfer, has been used to analyze nonthermal pulsed filamentary microplasma treatment effects. The finite element method in combination with the step-by-step finite-difference method for a coupled system of differential equations in partial derivatives was used for numerical simulation of heat, humidity and pressure potentials transfer. The drying time of samples treated by nonthermal pulsed filamentary microplasma treatment assisted by thermionic emission was reduced up to 20.6% (5 kV/cm; 1200 discharges) in comparison to intact tissue. The effect of the obtained approach is very useful for studying process mechanisms and for explaining nonthermal pulsed filamentary microplasma treatment effects. Refined transfer kinetic coefficients from a set of equations based on experimental drying curve can be used for the quantitative determination of thermodynamic coefficients. The agreement of the simulation data with the analytical equation and experimental results is satisfactory (discrepancy less than 3%). Obtained results showed that the proposed model with the refined transfer kinetic coefficients adequately describe the experimental data.

Mathematical model for transport of DNA plasmids from the external medium up to the nucleus by electroporation

We propose a mathematical model for the transport of DNA plasmids from the extracellular matrix up to the cell nucleus. The model couples two phenomena: the electroporation process, describing the cell membrane permeabilization to plasmids and the intracellular transport enhanced by the presence of microtubules. Numerical simulations of cells with arbitrary geometry, in 2D and 3D, and a network of microtubules show numerically the importance of the microtubules and the electroporation on the effectiveness of the DNA transfection, as observed by previous biological data. The paper proposes efficient numerical tools for forthcoming optimized procedures of cell transfection.

Basic features of a cell electroporation model: illustrative behavior for two very different pulses

Science increasingly involves complex modeling. Here we describe a model for cell electroporation in which membrane properties are dynamically modified by poration. Spatial scales range from cell membrane thickness (5 nm) to a typical mammalian cell radius (10 μm), and can be used with idealized and experimental pulse waveforms. The model consists of traditional passive components and additional active components representing nonequilibrium processes. Model responses include measurable quantities: transmembrane voltage, membrane electrical conductance, and solute transport rates and amounts for the representative "long" and "short" pulses. The long pulse--1.5 kV/cm, 100 μs--evolves two pore subpopulations with a valley at ~5 nm, which separates the subpopulations that have peaks at ~1.5 and ~12 nm radius. Such pulses are widely used in biological research, biotechnology, and medicine, including cancer therapy by drug delivery and nonthermal physical tumor ablation by causing necrosis. The short pulse--40 kV/cm, 10 ns--creates 80-fold more pores, all small (<3 nm; ~1 nm peak). These nanosecond pulses ablate tumors by apoptosis. We demonstrate the model's responses by illustrative electrical and poration behavior, and transport of calcein and propidium. We then identify extensions for expanding modeling capability. Structure-function results from MD can allow extrapolations that bring response specificity to cell membranes based on their lipid composition. After a pulse, changes in pore energy landscape can be included over seconds to minutes, by mechanisms such as cell swelling and pulse-induced chemical reactions that slowly alter pore behavior.

Dual-porosity model of solute diffusion in biological tissue modified by electroporation

In many electroporation applications mass transport in biological tissue is of primary concern. This paper presents a theoretical advancement in the field and gives some examples of model use in electroporation applications. The study focuses on post-treatment solute diffusion. We use a dual-porosity approach to describe solute diffusion in electroporated biological tissue. The cellular membrane presents a hindrance to solute transport into the extracellular space and is modeled as electroporation-dependent porosity, assigned to the intracellular space (the finite rate of mass transfer within an individual cell is not accounted for, for reasons that we elaborate on). The second porosity is that of the extracellular space, through which solute vacates a block of tissue. The model can be used to study extraction out of or introduction of solutes into tissue, and we give three examples of application, a full account of model construction, validation with experiments, and a parametrical analysis. To facilitate easy implementation and experimentation by the reader, the complete derivation of the analytical solution for a simplified example is presented. Validation is done by comparing model results to experimentally-obtained data; we modeled kinetics of sucrose extraction by diffusion from sugar beet tissue in laboratory-scale experiments. The parametrical analysis demonstrates the importance of selected physicochemical and geometrical properties of the system, illustrating possible outcomes of applying the model to different electroporation applications. The proposed model is a new platform that supports rapid extension by state-of-the-art models of electroporation phenomena, developed as latest achievements in the field of electroporation.

Transmembrane molecular transport during versus after extremely large, nanosecond electric pulses

Recently there has been intense and growing interest in the non-thermal biological effects of nanosecond electric pulses, particularly apoptosis induction. These effects have been hypothesized to result from the widespread creation of small, lipidic pores in the plasma and organelle membranes of cells (supra-electroporation) and, more specifically, ionic and molecular transport through these pores. Here we show that transport occurs overwhelmingly after pulsing. First, we show that the electrical drift distance for typical charged solutes during nanosecond pulses (up to 100 ns), even those with very large magnitudes (up to 10 MV/m), ranges from only a fraction of the membrane thickness (5 nm) to several membrane thicknesses. This is much smaller than the diameter of a typical cell (∼16 μm), which implies that molecular drift transport during nanosecond pulses is necessarily minimal. This implication is not dependent on assumptions about pore density or the molecular flux through pores. Second, we show that molecular transport resulting from post-pulse diffusion through minimum-size pores is orders of magnitude larger than electrical drift-driven transport during nanosecond pulses. While field-assisted charge entry and the magnitude of flux favor transport during nanosecond pulses, these effects are too small to overcome the orders of magnitude more time available for post-pulse transport. Therefore, the basic conclusion that essentially all transmembrane molecular transport occurs post-pulse holds across the plausible range of relevant parameters. Our analysis shows that a primary direct consequence of nanosecond electric pulses is the creation (or maintenance) of large populations of small pores in cell membranes that govern post-pulse transmembrane transport of small ions and molecules.