Axel T. Esser

A brief overview of electroporation pulse strength-duration space: a region where additional intracellular effects are expected.

Electroporation (EP) of outer cell membranes is widely used in research, biotechnology and medicine. Now intracellular effects by organelle EP are of growing interest, mainly due to nanosecond pulsed electric fields (nsPEF). For perspective, here we provide an approximate overview of EP pulse strength-duration space. This overview locates approximately some known effects and applications in strength-duration space, and includes a region where additional intracellular EP effects are expected. A feature of intracellular EP is direct, electrical redistribution of endogenous biochemicals among cellular compartments. For example, intracellular EP may initiate a multistep process for apoptosis. In this hypothesis, initial EP pulses release calcium from the endoplasmic reticulum, followed by calcium redistribution within the cytoplasm. With further EP pulses calcium penetrates mitochondrial membranes and causes changes that trigger release of cytochrome c and other death molecules. Apoptosis may therefore occur even in the presence of apoptotic inhibitors, using pulses that are smaller, but longer, than nsPEF.

Towards solid tumor treatment by irreversible electroporation: intrinsic redistribution of fields and currents in tissue.

Local and drug-free tissue treatment by irreversible electroporation (IRE) involves the creation of aqueous pores in a cells plasma membrane (PM) and leads to non-thermal cell death by necrosis. To investigate explicit pore-based effects we use two-dimensional system models with different spatial scales. The first is a multicellular system model (spatial scale 100 μm) that has irregularly shaped cells, and quantitatively describes dynamic (creation and destruction, evolution in pore size) pore behavior at the PM. The second is a tissue model (spatial scale 200 mm) that is constructed from a unit cell and uses the asymptotic (fixed pore size) electroporation model. Both system models show that significant redistribution of fields and currents occurs through transient PM pores. Pore histograms for the multicellular model demonstrate the simultaneous presence of small and large pores during IRE pulses. The associated significant increase of PM permeability may prove to be essential to understanding how cell death by necrosis occurs. The averaged tissue conductivity in both models increases during IRE pulses because of electroporation. This leads to greater electrical dissipation (heating) and, thus, to larger temperature increases than suggested by tissue models with passive and static electrical properties.

The Spatially Distributed Dynamic Transmembrane Voltage of Cells and Organelles due to 10 ns Pulses: Meshed Transport Networks

The authors describe two versions of a two-dimensional (2-D) cell model that contains three circular membranes representing the plasma membrane (PM) and single bilayer approximations to both the nuclear envelope and the mitochondrial membrane. The first version uses a Cartesian transport network, which respects topology but approximates geometry. The second version uses a meshed transport network, which respects both. The asymptotic electroporation model is assigned to all local membrane sites in order to assess the electrical response of the membranes. The predictions of these two models are presented for 10-ns trapezoidal pulses with 1.5 ns rise and fall times. The applied field magnitudes range from 1 to 100 kV/cm, corresponding to recent experiments. The spatially distributed electroporation models exhibit a supraelectroporation for the larger pulses with a maximum transmembrane voltage of Um~1.5 V for both the PM and organelle membranes. For the larger fields, the PM and organelle membranes electroporate essentially simultaneously. The meshed version of the transport network eliminates numerical artifacts and is more computationally efficient

Mathematical model of morphogen electrophoresis through gap junctions

Gap junctional communication is important for embryonic morphogenesis. However, the factors regulating the spatial properties of small molecule signal flows through gap junctions remain poorly understood. Recent data on gap junctions, ion transporters, and serotonin during left–right patterning suggest a specific model: the net unidirectional transfer of small molecules through long‐range gap junctional paths driven by an electrophoretic mechanism. However, this concept has only been discussed qualitatively, and it is not known whether such a mechanism can actually establish a gradient within physiological constraints. We review the existing functional data and develop a mathematical model of the flow of serotonin through the early Xenopus embryo under an electrophoretic force generated by ion pumps. Through computer simulation of this process using realistic parameters, we explored quantitatively the dynamics of morphogen movement through gap junctions, confirming the plausibility of the proposed electrophoretic mechanism, which generates a considerable gradient in the available time frame. The model made several testable predictions and revealed properties of robustness, cellular gradients of serotonin, and the dependence of the gradient on several developmental constants. This work quantitatively supports the plausibility of electrophoretic control of morphogen movement through gap junctions during early left–right patterning. This conceptual framework for modeling gap junctional signaling—an epigenetic patterning mechanism of wide relevance in biological regulation—suggests numerous experimental approaches in other patterning systems. Developmental Dynamics 235:2144–2159, 2006.

Towards solid tumor treatment by nanosecond pulsed electric fields.

Local and drug-free solid tumor ablation by large nanosecond pulsed electric fields leads to supra-electroporation of all cellular membranes and has been observed to trigger nonthermal cell death by apoptosis. To establish pore-based effects as the underlying mechanism inducing apoptosis, we use a multicellular system model (spatial scale 100 μm) that has irregularly shaped liver cells and a multiscale liver tissue model (spatial scale 200 mm). Pore histograms for the multicellular model demonstrate the presence of only nanometer-sized pores due to nanosecond electric field pulses. The number of pores in the plasma membrane is such that the average tissue conductance during nanosecond electric field pulses is even higher than for longer irreversible electroporation pulses. It is shown, however, that these nanometer-sized pores, although numerous, only significantly change the permeability of the cellular membranes to small ions, but not to larger molecules. Tumor ablation by nanosecond pulsed electric fields causes small to moderate temperature increases. Thus, the underlying mechanism(s) that trigger cell death by apoptosis must be non-thermal electrical interactions, presumably leading to different ionic and molecular transport than for much longer irreversible electroporation pulses.

Intracellular electroporation site distributions: Modeling examples for nsPEF and IRE pulse waveforms

We illustrate expected electroporation (EP) responses to two classes of large electric field pulses by employing systems models, one of a cell in vitro and the other of multiple cells in vivo. The first pulse class involves “nsPEF” (nanosecond pulsed electric fields). The durations are less than a microsecond, but the magnitudes are extremely large, often 10 kV/cm or more, and all of the pores remain small. The second class involves “IRE” (irreversible electroporation). Durations are many microseconds to several milliseconds, but with magnitudes smaller than 10 kV/cm, and a wide range of pore sizes evolves. A key feature of both pulse classes is non-thermal cell killing by multiple pulses without delivering external drugs or genes. For small pulses the models respond passively (no pore creation) providing negative controls. For larger pulses transient aqueous pore populations evolve. These greatly increase local membrane conductance temporarily, causing rapid redistribution of fields near and within cells. This complex electrical behavior is generally not revealed by experiments reporting biological end points resulting from cumulative ionic and molecular transport through cell membranes. The underlying, heterogeneous pore population distributions are also not obtained from typical experiments. Further, traditional EP applications involving molecular delivery are usually assumed to create pores solely in the outer, plasma membrane (PM). In contrast, our examples support the occurrence of intracellular EP by both nsPEF and IRE, but with different intracellular spatial distributions of EP sites.

In Silico Assessment of Nanosecond Pulse Exposures of Cells, Tissues and Organs

We have developed an in silico framework that integrates macro- and microdosimetry models, and incorporates biophysical mechanism models to estimate biochemical change resulting from exposure to nanosecond electrical pulses. This approach provides estimates of conductance changes and biochemical release/uptake within cells, local tissue regions and organs