Modeling normal and altered human erythrocyte shapes by a new parametric equation: application to the calculation of induced transmembrane potentials

We present simple parametric equations in terms of Jacobi elliptic functions that provide a realistic model of abnormal variations in size which maintain the biconcave shape of a normal erythrocyte (anisocytosis) and abnormal variations in shape which maintain the original volume of the erythrocyte (poikilocytosis), as well as continuous deformations from the normal to the altered shapes. We illustrate our results with parameterizations of microcytes, macrocytes, and stomatocytes, and we apply these parameterizations to the numerical calculation of the induced transmembrane voltage in microcytes, macrocytes, and stomatocytes exposed to an external electromagnetic field of 1800 MHz.     

Measuring the Induced Membrane Voltage with Di-8-ANEPPS

Placement of a cell into an external electric field causes a local charge redistribution inside and outside of the cell in the vicinity of the cell membrane, resulting in a voltage across the membrane. This voltage, termed the induced membrane voltage (also induced transmembrane voltage, or induced transmembrane potential difference) and denoted by ΔΦ, exists only as long as the external field is present. If the resting voltage is present on the membrane, the induced voltage superimposes (adds) onto it. By using one of the potentiometric fluorescent dyes, such as di-8-ANEPPS, it is possible to observe the variations of ΔΦ on the cell membrane and to measure its value noninvasively. di-8-ANEPPS becomes strongly fluorescent when bound to the lipid bilayer of the cell membrane, with the change of the fluorescence intensity proportional to the change of ΔΦ. This video shows the protocol for measuring ΔΦ using di-8-ANEPPS and also demonstrates the influence of cell shape on the amplitude and spatial distribution of ΔΦ.     

Non-uniform Distribution of Outer Hair Cell Transmembrane Potential Induced by Extracellular Electric Field

Intracochlear electric fields arising out of sound-induced receptor currents, silent currents, or electrical current injected into the cochlea induce transmembrane potential along the outer hair cell (OHC) but its distribution along the cells is unknown. In this study, we investigated the distribution of OHC transmembrane potential induced along the cell perimeter and its sensitivity to the direction of the extracellular electric field (EEF) on isolated OHCs at a low frequency using the fast voltage-sensitive dye ANNINE-6plus. We calibrated the potentiometric sensitivity of the dye by applying known voltage steps to cells by simultaneous whole-cell voltage clamp. The OHC transmembrane potential induced by the EEF is shown to be highly nonuniform along the cell perimeter and strongly dependent on the direction of the electrical field. Unlike in many other cells, the EEF induces a field-direction-dependent intracellular potential in the cylindrical OHC. We predict that without this induced intracellular potential, EEF would not generate somatic electromotility in OHCs. In conjunction with the known heterogeneity of OHC membrane microdomains, voltage-gated ion channels, charge, and capacitance, the EEF-induced nonuniform transmembrane potential measured in this study suggests that the EEF would impact the cochlear amplification and electropermeability of molecules across the cell.     

Non-uniform Distribution of Outer Hair Cell Transmembrane Potential Induced by Extracellular Electric Field

Intracochlear electric fields arising out of sound-induced receptor currents, silent currents, or electrical current injected into the cochlea induce transmembrane potential along the outer hair cell (OHC) but its distribution along the cells is unknown. In this study, we investigated the distribution of OHC transmembrane potential induced along the cell perimeter and its sensitivity to the direction of the extracellular electric field (EEF) on isolated OHCs at a low frequency using the fast voltage-sensitive dye ANNINE-6plus. We calibrated the potentiometric sensitivity of the dye by applying known voltage steps to cells by simultaneous whole-cell voltage clamp. The OHC transmembrane potential induced by the EEF is shown to be highly nonuniform along the cell perimeter and strongly dependent on the direction of the electrical field. Unlike in many other cells, the EEF induces a field-direction-dependent intracellular potential in the cylindrical OHC. We predict that without this induced intracellular potential, EEF would not generate somatic electromotility in OHCs. In conjunction with the known heterogeneity of OHC membrane microdomains, voltage-gated ion channels, charge, and capacitance, the EEF-induced nonuniform transmembrane potential measured in this study suggests that the EEF would impact the cochlear amplification and electropermeability of molecules across the cell.     

Effect of electric field induced transmembrane potential on spheroidal cells: theory and experiment

The transmembrane potential on a cell exposed to an electric field is a critical parameter for successful cell permeabilization. In this study, the effect of cell shape and orientation on the induced transmembrane potential was analyzed. The transmembrane potential was calculated on prolate and oblate spheroidal cells for various orientations with respect to the electric field direction, both numerically and analytically. Changing the orientation of the cells decreases the induced transmembrane potential from its maximum value when the longest axis of the cell is parallel to the electric field, to its minimum value when the longest axis of the cell is perpendicular to the electric field. The dependency on orientation is more pronounced for elongated cells while it is negligible for spherical cells. The part of the cell membrane where a threshold transmembrane potential is exceeded represents the area of electropermeabilization, i.e. the membrane area through which the transport of molecules is established. Therefore the surface exposed to the transmembrane potential above the threshold value was calculated. The biological relevance of these theoretical results was confirmed with experimental results of the electropermeabilization of plated Chinese hamster ovary cells, which are elongated. Theoretical and experimental results show that permeabilization is not only a function of electric field intensity and cell size but also of cell shape and orientation.     

The antiepileptic drug diphenylhydantoin affects the structure of the human erythrocyte membrane

Phenytoin (diphenylhydantoin) is an antiepileptic agent effective against all types of partial and tonic-clonic seizures. Phenytoin limits the repetitive firing of action potentials evoked by a sustained depolarization of mouse spinal cord neurons maintained in vitro. This effect is mediated by a slowing of the rate of recovery of voltage activated Na+ channels from inactivation. For this reasons it was thought of interest to study the binding affinities of phenytoin with cell membranes and their perturbing effects upon membrane structures. The effects of phenytoin on the human erythrocyte membrane and molecular models have been investigated in the present work. This report presents the following evidence that phenytoin interacts with cell membranes: a) X-ray diffraction and fluorescence spectroscopy of phospholipid bilayers showed that phenytoin perturbed a class of lipids found in the outer moiety of cell membranes; b) in isolated unsealed human erythrocyte membranes (IUM) the drug induced a disordering effect on the polar head groups and acyl chains of the erythrocyte membrane lipid bilayer; c) in scanning electron microscopy (SEM) studies on human erythrocytes the formation of echinocytes was observed, due to the insertion of phenytoin in the outer monolayer of the red cell membrane. This is the first time that an effect of phenytoin on the red cell shape is described. However, the effects of the drug were observed at concentrations higher than those currently found in plasma when phenytoin is therapeutically administered.     

Nonlinear Dispersive Model of Electroporation for Irregular Nucleated Cells

In this work, the electroporation phenomenon induced by pulsed electric field on different nucleated biological cells is studied. A nonlinear, non‐local, dispersive, and space–time multiphysics model based on Maxwell’s and asymptotic Smoluchowski’s equations has been developed to calculate the transmembrane voltage and pore density on both plasma and nuclear membrane perimeters. The irregular cell shape has been modeled by incorporating in the numerical algorithm the analytical functions pertaining to Gielis curves. The dielectric dispersion of the cell media has been modeled considering the multi‐relaxation Debye‐based relationship. Two different irregular nucleated cells have been investigated and their response has been studied applying both the dispersive and non‐dispersive models. By a comparison of the obtained results, differences can be highlighted confirming the need to make use of the dispersive model to effectively investigate the cell response in terms of transmembrane voltages, pore densities, and electroporation opening angle, especially when irregular cell shapes and short electric pulses are considered. Bioelectromagnetics. 2019;40:331–342. © 2019 Wiley Periodicals, Inc.     

Further evidence for a membrane potential-dependent shape transformation of the human erythrocyte membrane

The influence of various factors (pH, temperature, sodium gluconate) on the ionic strength-dependent stomatocyte-discocyte-echinocyte transformation of the human erythrocyte membrane was investigated. The results give further evidence for a correlation between shape of erythrocyte membrane and the transmembrane potential of the cells.     

Influence of band 3 protein absence and skeletal structures on amphiphile- and Ca(2+)-induced shape alterations in erythrocytes: a study with lamprey (Lampetra fluviatilis), trout (Onchorhynchus mykiss) and human erythrocytes

Amphiphiles which induce either spiculated (echinocytic) or invaginated (stomatocytic) shapes in human erythrocytes, and ionophore A23187 plus Ca(2+), were studied for their capacity to induce shape alterations, vesiculation and hemolysis in the morphologically and structurally different lamprey and trout erythrocytes. Both qualitative and quantitative differences were found. Amphiphiles induced no gross morphological changes in the non-axisymmetric stomatocyte-like lamprey erythrocyte or in the flat ellipsoidal trout erythrocyte, besides a rounding up at higher amphiphile concentrations. No shapes with large broad spicula were seen. Nevertheless, some of the 'echinocytogenic' amphiphiles induced plasma membrane protrusions in lamprey and trout erythrocytes, from where exovesicles were shed. In trout erythrocytes, occurrence of corrugations at the cell rim preceded protrusion formation. Other 'echinocytogenic' amphiphiles induced invaginations in lamprey erythrocytes. The 'stomatocytogenic' amphiphiles induced invaginations in both lamprey and trout erythrocytes. Surprisingly, in trout erythrocytes, some protrusions also occurred. Some of the amphiphiles hemolyzed lamprey, trout and human erythrocytes at a significantly different concentration/membrane area. Ionophore A23187 plus Ca(2+) induced membrane protrusions and sphering in human and trout erythrocytes; however, the lamprey erythrocyte remained unperturbed. The shape alterations in lamprey erythrocytes, we suggest, are characterized by weak membrane skeleton-lipid bilayer interactions, due to band 3 protein and ankyrin deficiency. In trout erythrocyte, the marginal band of microtubules appears to strongly influence cell shape. Furthermore, the presence of intermediate filaments and nuclei, additionally affecting the cell membrane shear elasticity, apparently influences cell shape changes in lamprey and trout erythrocytes. The different types of shape alterations induced by certain amphiphiles in the cell types indicates that their plasma membrane phospholipid composition differs.     

Dependence of Electroporation Detection Threshold on Cell Radius: An Explanation to Observations Non Compatible with Schwan’s Equation Model

It is widely accepted that electroporation occurs when the cell transmembrane voltage induced by an external applied electric field reaches a threshold. Under this assumption, in order to trigger electroporation in a spherical cell, Schwan’s equation leads to an inversely proportional relationship between the cell radius and the minimum magnitude of the applied electric field. And, indeed, several publications report experimental evidences of an inverse relationship between the cell size and the field required to achieve electroporation. However, this dependence is not always observed or is not as steep as predicted by Schwan’s equation. The present numerical study attempts to explain these observations that do not fit Schwan’s equation on the basis of the interplay between cell membrane conductivity, permeability, and transmembrane voltage. For that, a single cell in suspension was modeled and the electric field necessary to achieve electroporation with a single pulse was determined according to two effectiveness criteria: a specific permeabilization level, understood as the relative area occupied by the pores during the pulse, and a final intracellular concentration of a molecule due to uptake by diffusion after the pulse, during membrane resealing. The results indicate that plausible model parameters can lead to divergent dependencies of the electric field threshold on the cell radius. These divergent dependencies were obtained through both criteria and using two different permeabilization models. This suggests that the interplay between cell membrane conductivity, permeability, and transmembrane voltage might be the cause of results which are noncompatible with the Schwan’s equation model.     

Shape transformation of erythrocyte ghosts depends on ion concentrations

Resealed human erythrocyte ghosts undergo shape transformations similar to those of intact erythrocytes. The results indicate that the shape of these ghosts depends on the inner as well as on the outer NaCl concentration. A correlation between shape and calculated transmembrane potential was established similar to that for intact human erythrocytes.     

Actin networks regulate the cell membrane permeability during electroporation

Transient physical disruption of cell membranes by electric pulses (or electroporation) has significance in biomedical and biological applications requiring the delivery of exogenous (bio)molecules to living cells. We demonstrate that actin networks regulate the cell membrane permeability during electroporation. Disruption of actin networks increases the uptake of membrane-impermeable molecules such as propidium iodide during electroporation. Our experiments at different temperatures ranging from 11 °C to 37 °C show that molecular uptake during electroporation increases with temperature. Furthermore, by examining the temperature-dependent kinetics of propidium iodide uptake, we infer that the activation energy barrier of electroporation is lowered when the actin networks are disrupted. Our numerical calculations of transmembrane voltage show that the reduced activation energy barrier for the cells with disrupted actin is not a consequence of the changes in transmembrane voltage associated with changes in the cell shape due to the disruption of actin, indicating that this could be due to changes in membrane mechanical properties. Our results suggest that the current theoretical models of electroporation should be advanced further by including the contributions of the cytoskeletal networks on the cell membrane permeability during the delivery of exogenous materials.     

Critical cell volume and shape of bovine erythrocytes.

The relationship between erythrocyte shape and the critical cell volume was investigated. Agents able to increase the critical cell volume induced three main stable shapes of erythrocytes: discocytic, stomatocytic, and echinocytic. The absence of correlation between shape and critical cell volume under isoosmotic conditions suggests that relative differences between the surface areas of the inner and the outer leaflet of the cell membrane do not influence the critical volume of a cell.     

An optical determination of the series resistance in Loligo

The resistance in series with the membrane capacitance in the giant axon of the squid Loligo pealei was measured using potentiometric probes that exhibit absorbance changes proportional to the voltage across the plasma membrane proper. The method relies upon the fact that a voltage drop across the series resistance produces a deviation in the true transmembrane voltage from that imposed by a voltage clamp. Optical measurement of the true transmembrane potential, together with electrical measurement of the ionic current, permits the immediate determination of the series resistance by Ohm's law. An alternative method monitored the amount of electronic series resistance compensation required to force the optical signal to match the shape of the reference potential. The value of the series resistance measured in artificial seawater was 3.78 +/- 0.95 omega X cm2. The estimated value of the contribution of the Schwann cell layer to the series resistance was 2.57 +/- 0.89 omega X cm2.     

Structure and function of human erythrocyte membrane skeletons

On the basis of extensive studies of the literature and of own results the present knowledge about the structure of the membrane skeleton of human erythrocytes is summarized and functional and clinical aspects are described. The spectrins are the centre of interest. Their interconnections, spatial arrangement and association with other components of the membrane are explained in greater detail. With regard to the membrane skeleton questions of erythrocyte shape, membrane integrity, phospholipid asymmetry, distribution of transmembrane proteins and cell deformation are discussed.     

Electric Field-Induced Transmembrane Potential Depends on Cell Density and Organizatio

Electrochemotherapy is a novel technique to enhance the delivery of chemotherapeutic drugs into tumor cells. In this procedure, electric pulses are delivered to cancerous cells, which induce membrane permeabilization, to facilitate the passage of cytotoxic drugs through the cell membrane. This study examines how electric fields interact with and polarize a system of cells. Specifically, we consider how cell density and organization impact on induced cell transmembrane potential due to an external electric field. First, in an infinite volume of spherical cells, we examined how cell packing density impacts on induced transmembrane potential. With high cell density, we found that maximum induced transmembrane potential is suppressed and that the transmembrane potential distribution is altered. Second, we considered how orientation of cell sheets and strands, relative to the applied field, affects induced transmembrane potential. Cells that are parallel to the field direction suppress induced transmembrane potential, and those that lie perpendicular to the applied field potentiate its effect. Generally, we found that both cell density and cell organization are very important in determining the induced transmembrane potential resulting from an applied electric field.     

Effective bilayer expansion and erythrocyte shape change induced by monopalmitoyl phosphatidylcholine. Quantitative light microscopy and nuclear magnetic resonance spectroscopy measurements.

When human erythrocytes are treated with exogenous monopalmitoyl phosphatidylcholine (MPPC), the normal biconcave disk shape red blood cells (RBC) become spiculate echinocytes. The present study examines the quantitative aspect of the relationship between effective bilayer expansion and erythrocyte shape change by a newly developed method. This method is based on the combination of direct surface area measurement of micropipette and relative bilayer expansion measurement of 13C crosspolarization/magic angle spinning nuclear magnetic resonance (NMR). Assuming that 13C NMR chemical shift of fatty acyl chain can be used as an indicator of lateral packing of membrane bilayers, it is possible for us to estimate the surface area expansion of red cell membrane induced by MPPC from that induced by ethanol. Partitions of lipid molecules into cell membrane were determined by studies of shape change potency as a function of MPPC and red cell concentration. It is found that 8(+/- 0.5) x 10(6) molecules of MPPC per cell will effectively induce stage three echinocytes and yield 3.2(+/- 0.2)% expansion of outer monolayer surface area. Surface area of normal cells determined by direct measurements from fixed geometry of red cells aspirated by micropipette was 118.7 +/- 8.5 microns2. The effective cross-sectional area of MPPC molecules in the cell membrane therefore was determined to be 48(+/- 4) A2, which is in agreement with those determined by x-ray from model membranes and crystals of lysophospholipids. We concluded that surface area expansion of RBC can be explained by a simple consideration of cross-sectional area of added molecules and that erythrocyte shape changes correspond quantitatively to the incorporated lipid molecules.