The effect of ion channels on cell membrane motion

Cell membranes possess ion channels and pumps which allow them to pass electrical currents. In this paper it is shown that the ion channels and pumps should induce electric fields in the area surrounding the membrane. The magnitude of this field is computed. It is shown that when the channels and pumps are separated by a sufficient distance, then the electric fields which they induce will cause the solution which surrounds the membrane to move. This movement of the fluid should cause motion of the membrane. Thus it is demonstrated that under certain conditions the conductance of ions across cell membranes will give rise to cell membrane motion. It is suggested that this phenomenon may play a role in processes such as chemotaxis, cell division, and pinocytosis.     

Determination of the induced ELF electric field distribution in a two layer in vitro system simulating biological cells in nutrient solution

In-vitro studies of biological effects of electromagnetic fields are often conducted with cultured cells either in suspension or grown in a monolayer. In the former case, the exposed medium can be assumed to be homogeneous; however, eventually the cells settle to the bottom of the container forming a two layer system with different dielectric and conductive properties. In the present work the effect of this separation on the electric field distribution is calculated and experimentally measured at selected positions for a commonly used exposure configuration. The settled cell suspension is modeled by a well-defined two layer system placed in a rectangular container with the base of the container parallel to the direction of the magnetic field. Theoretical calculations based on numerical techniques are done for various two layer systems with different conductivities in each layer. The agreement between the theoretical calculations and the experimental measurements is within ± 1.5 mV/m, or 10% of the maximum induced field when the conductivity of the lower layer is ten times that of the upper layer. This result is well within experimental error. When the thickness of one of the layers is small compared to the thickness of the other layer, it is found that the electric field distribution is essentially that of the homogeneous case. The latter situation corresponds to a typical cell exposure condition. © 1993 Wiley-Liss, Inc.     

Effect of cell electroporation on the conductivity of a cell suspension

An increased permeability of a cell membrane during the application of high-voltage pulses results in increased transmembrane transport of molecules that otherwise cannot enter the cell. Increased permeability of a cell membrane is accompanied by increased membrane conductivity; thus, by measuring electric conductivity the extent of permeabilized tissue could be monitored in real time. In this article the effect of cell electroporation caused by high-voltage pulses on the conductivity of a cell suspension was studied by current-voltage measurements during and impedance measurement before and after the pulse application. At the same time the percentage of permeabilized and survived cells was determined and the extent of osmotic swelling measured. For a train of eight pulses a transient increase in conductivity of a cell suspension was obtained above permeabilization threshold in low- and high-conductive medium with complete relaxation in <1 s. Total conductivity changes and impedance measurements showed substantial changes in conductivity due to the ion efflux in low-conductive medium and colloid-osmotic swelling in both media. Our results show that by measuring electric conductivity during the pulses we can detect limit permeabilization threshold but not directly permeabilization level, whereas impedance measurements in seconds after the pulse application are not suitable.     

The representation of membrane admittance.

An integral representation for the membrane admittance in terms of its known current response to a voltage step function is presented. It is demonstrated that the frequency-dependent terms in the contribution to the membrane admittance by the ion-selective conductance of the nerve membrane are proportional to the static conductances. The additional information contained in the real and imaginary parts of the membrane admittance should allow the parameters of the ion conductance to be determined. Eventually, these measurements should also give information about the electric dipole displacement currents of the conductance systems themselves, and about the metabolically supported active ion transport currents that maintain the ion concentration gradients.     

Structural model of the CopA copper ATPase of Enterococcus hirae based on chemical cross-linking

The CopA copper ATPase of Enterococcus hirae belongs to the family of heavy metal pumping CPx-type ATPases and shares 43% sequence similarity with the human Menkes and Wilson copper ATPases. Due to a lack of suitable protein crystals, only partial three-dimensional structures have so far been obtained for this family of ion pumps. We present a structural model of CopA derived by combining topological information obtained by intramolecular cross-linking with molecular modeling. Purified CopA was cross-linked with different bivalent reagents, followed by tryptic digestion and identification of cross-linked peptides by mass spectrometry. The structural proximity of tryptic fragments provided information about the structural arrangement of the hydrophilic protein domains, which was integrated into a three-dimensional model of CopA. Comparative modeling of CopA was guided by the sequence similarity to the calcium ATPase of the sarcoplasmic reticulum, Serca1, for which detailed structures are available. In addition, known partial structures of CPx-ATPase homologous to CopA were used as modeling templates. A docking approach was used to predict the orientation of the heavy metal binding domain of CopA relative to the core structure, which was verified by distance constraints derived from cross-links. The overall structural model of CopA resembles the Serca1 structure, but reveals distinctive features of CPx-type ATPases. A prominent feature is the positioning of the heavy metal binding domain. It features an orientation of the Cu binding ligands which is appropriate for the interaction with Cu-loaded metallochaperones in solution. Moreover, a novel model of the architecture of the intramembranous Cu binding sites could be derived.     

Transport mechanisms of seawater teleost chloride cells: an inclusive model of a multifunctional cell

This review assembles recent information on seawater-type chloride cells of marine teleost fish and evaluates the secretion of Na+, Cl-, K+, H+ and NH4+ and the absorption of Ca2+. The evidence for the distribution (apical vs basolateral) and the abundance of the various ion pumps, cotransporters, channels and exchangers is assessed and an inclusive model is constructed. Relationships among the transport systems are presented to suggest that many, if not all, of these systems may be operating simultaneously in individual, multifunctional chloride cells.     

Nonequilibrium voltage fluctuations in biological membranes. II. Voltage and current noise generated by ion carriers, channels and electrogenic pumps

As applications of the general theoretical framework of charge transport in biological membranes and related voltage and current noise, a number of model calculations are presented for ion carriers, rigid channels, channels with conformational substates and electrogenic pumps. The results are discussed with special reference to the problem of threshold values for sensory transduction processes and their limitations by voltage fluctuations. Furthermore, starting from the special results of model calculations, an attempt is made to determine more general aspects of electric fluctuations generated by charge-transport processes in biological membranes: different frequency dependences of voltage and current noise, and dependence of noise intensities with increasing distance from the equilibrium state.     

Brassinosteroids regulate plasma membrane anion channels in addition to proton pumps during expansion of Arabidopsis thaliana cells

Brassinosteroids (BRs) are involved in numerous physiological processes associated with plant development and especially with cell expansion. Here we report that two BRs, 28-homobrassinolide (HBL) and its direct precursor 28-homocastasterone (HCS), promote cell expansion of Arabidopsis thaliana suspension cells. We also show that cell expansions induced by HBL and HCS are correlated with the amplitude of the plasma membrane hyperpolarization they elicited. HBL, which promoted the larger cell expansion, also provoked the larger hyperpolarization. We observed that membrane hyperpolarization and cell expansion were partially inhibited by the proton pump inhibitor erythrosin B, suggesting that proton pumps were not the only ion transport system modulated by the two BRs. We used a voltage clamp approach in order to find the other ion transport systems involved in the PM hyperpolarization elicited by HBL and HCS. Interestingly, while anion currents were inhibited by both HBL and HCS, outward rectifying K+ currents were increased by HBL but inhibited by HCS. The different electrophysiological behavior shown by HBL and HCS indicates that small changes in the BR skeleton might be responsible for changes in bioactivity.     

Influence of the red blood cell Ca2+-ion concentration on the erythrocyte aggregation in stasis

Ca2+ ions were transported into the cell by incubation of the erythrocyte suspension with ionophore A23187, a lipophil electric neutral ion complexing substance. Erythrocyte aggregation could be increased twice, when doubling the intracellular Ca2+-ion concentration. Our measurements lead to the suggestion that an increase of the cytoplasmatic Ca2+ ion changes the physical and/or biochemical properties of the aggregation receptors on the membrane surface, i.e., cell-protein interactions are regulated by alteration of the intracellular Ca2+-ion concentration.     

23Na-nuclear magnetic resonance study of ionophore-mediated cation exchange between two populations of liposomes.

A model system to observe and investigate the transfer of Na+ ions between different internal compartments in suspension of liposomes was developed, and the exchange was followed by nuclear magnetic resonance spectroscopy. The experiments were performed under conditions of a Donnan equilibrium. Quantitative analysis of this three-site transmembrane exchange system allowed us to distinguish between direct and indirect exchange between liposomes. It also disclosed a "confining" effect on the exchange between the two populations of liposomes. This confining effect may have been due to an electrostatic field in the presence of a membrane potential. Donnan potentials and ionic compositions at equilibrium for the three-compartment system were calculated numerically. The model system may be used to explore further the effects of membrane potentials, surface potentials, and ionic mobilities on ion transport in biological (model) systems in general.     

Toward the Experimental Understanding of the Energy Storage Mechanism and Ion Dynamics in Ionic Liquid Based Supercapacitors

A series of salt‐templated carbons with gradually changed pore structure and their corresponding nitrogen‐doped analogues are synthesized and applied as model systems to thoroughly study the ion migration dynamics and energy storage mechanism in hierarchical pore structures with different surface functionalization in electric double‐layer capacitors with a model ionic liquid electrolyte (1‐ethyl‐3‐methylimidazolium tetrafluoroborate). Ion conformation and phase variation during the charging/discharging process and their contribution to the energy storage mechanism are investigated. A significant contribution of structural changes in the bulk of the ionic liquid electrolyte strengthening charge storage in the electric double‐layer beyond the usual expectations is uncovered. Furthermore, a quantitative model of the structure–dynamics relationship is proposed, in which the optimal ratio of mesopores to micropores is determined to be 3:1 in pore volume. Below this ratio, the ion dynamics can be promoted by increasing mesopore content and/or doping with nitrogen, while those parameters show only minor influence when the ratio is surpassing 3:1. Nitrogen doping in this system improves the rate capability (due to the enhanced ion transport dynamics) rather than the amount of energy stored.     

Capturing Intracellular pH Dynamics by Coupling Its Molecular Mechanisms within a Fully Tractable Mathematical Model

We describe the construction of a fully tractable mathematical model for intracellular pH. This work is based on coupling the kinetic equations depicting the molecular mechanisms for pumps, transporters and chemical reactions, which determine this parameter in eukaryotic cells. Thus, our system also calculates the membrane potential and the cytosolic ionic composition. Such a model required the development of a novel algebraic method that couples differential equations for slow relaxation processes to steady-state equations for fast chemical reactions. Compared to classical heuristic approaches based on fitted curves and ad hoc constants, this yields significant improvements. This model is mathematically self-consistent and allows for the first time to establish analytical solutions for steady-state pH and a reduced differential equation for pH regulation. Because of its modular structure, it can integrate any additional mechanism that will directly or indirectly affect pH. In addition, it provides mathematical clarifications for widely observed biological phenomena such as overshooting in regulatory loops. Finally, instead of including a limited set of experimental results to fit our model, we show examples of numerical calculations that are extremely consistent with the wide body of intracellular pH experimental measurements gathered by different groups in many different cellular systems.     

Electrical Counting and Sizing of Mammalian Cells in Suspension

A recently developed method of determining the number and size of particles suspended in a conducting solution is to pump the suspension through a small orifice having an immersed electrode on each side to supply electrical current. The current changes due to the passage of particles of resistivity different from that of the solution. Theoretical expressions are developed which relate the current change caused by such particles to their volume and shape. It is found that most biological cells may be treated as dielectric particles whose capacitive effects are negligible. Electrolytic tank measurements on models confirm the theoretical development, and electric field plots of model orifices are used to predict the observed pulse shapes. An equivalent circuit of the orifice-electrode system is analyzed and shows that the current pulse may be made conductivity-independent when observed with a zero input impedance amplifier.     

Speculations on the evolution of ion transport mechanisms.

Primate cells evolved a plasma membrane to restrict the loss of important molecules. The osmotic problems that then arose were solved in one of several ways. Of major importance was the evolution of specific ion pumps, to actively extrude those salts whose inward diffusion would have led to swelling and lysis. In addition, these pumps allowed the cell to store energy in the form of ion gradients across the membrane. Thus, even in the earliest stages, the evolution of ion transport systems coincided with the development of mechanisms which catalyzes the energy transformations. It is postulated that an "ATP"-driven proton pump was one of the first ion transport systems. Such a proton pump would extrude hydrogen ions from the cell, establishing both a transmembrane pH gradient (alkaline inside) and a membrane potential (negative inside). This difference in electrochemical potential for protons (the proton-motive force) could then drive a variety of essential membrane functions, such as the active transport of ions and nutrients. A second major advance was the evolution of an ion transport system that converted light energy into a form which could be used by the cell. The modern model for this is the "purple membrane" of Halobacterium halobium, which catalyzes the extrusion of protons after the capture of light. The protonmotive force generated by such a light-driven proton pump could then power net synthesis of ATP by a reversal of the ATP-driven proton pump. A third important evolutionary step associated with ion transport was the development of a system to harness energy released by biological oxidations. Again, the solution of this problem was to conserve energy as a protonmotive force by coupling the activity of a respiratory chain to the extrusion of protons. Finally, with the development of animal cells a more careful regulation of internal and external pH was required. Thus, an ATP-driven Na+-K+ pump replaced the proton-translocating ATPase as the major ion pump found in plasma membranes.     

A Bidomain Model for Lens Microcirculation

There exists a large body of research on the lens of the mammalian eye over the past several decades. The objective of this work is to provide a link between the most recent computational models and some of the pioneering work in the 1970s and 80s. We introduce a general nonelectroneutral model to study the microcirculation in the lens of the eye. It describes the steady-state relationships among ion fluxes, between water flow and electric field inside cells, and in the narrow extracellular spaces between cells in the lens. Using asymptotic analysis, we derive a simplified model based on physiological data and compare our results with those in the literature. We show that our simplified model can be reduced further to the first-generation models, whereas our full model is consistent with the most recent computational models. In addition, our simplified model captures in its equations the main features of the full computational models. Our results serve as a useful link intermediate between the computational models and the first-generation analytical models. Simplified models of this sort may be particularly helpful as the roles of similar osmotic pumps of microcirculation are examined in other tissues with narrow extracellular spaces, such as cardiac and skeletal muscle, liver, kidney, epithelia in general, and the narrow extracellular spaces of the central nervous system, the “brain.” Simplified models may reveal the general functional plan of these systems before full computational models become feasible and specific.     

Measurement of Extracellular Ion Fluxes Using the Ion-selective Self-referencing Microelectrode Technique

Cells from animals, plants and single cells are enclosed by a barrier called the cell membrane that separates the cytoplasm from the outside. Cell layers such as epithelia also form a barrier that separates the inside from the outside or different compartments of multicellular organisms. A key feature of these barriers is the differential distribution of ions across cell membranes or cell layers. Two properties allow this distribution: 1) membranes and epithelia display selective permeability to specific ions; 2) ions are transported through pumps across cell membranes and cell layers. These properties play crucial roles in maintaining tissue physiology and act as signaling cues after damage, during repair, or under pathological condition. The ion-selective self-referencing microelectrode allows measurements of specific fluxes of ions such as calcium, potassium or sodium at single cell and tissue levels. The microelectrode contains an ionophore cocktail which is selectively permeable to a specific ion. The internal filling solution contains a set concentration of the ion of interest. The electric potential of the microelectrode is determined by the outside concentration of the ion. As the ion concentration varies, the potential of the microelectrode changes as a function of the log of the ion activity. When moved back and forth near a source or sink of the ion (i.e. in a concentration gradient due to ion flux) the microelectrode potential fluctuates at an amplitude proportional to the ion flux/gradient. The amplifier amplifies the microelectrode signal and the output is recorded on computer. The ion flux can then be calculated by Fick’s law of diffusion using the electrode potential fluctuation, the excursion of microelectrode, and other parameters such as the specific ion mobility. In this paper, we describe in detail the methodology to measure extracellular ion fluxes using the ion-selective self-referencing microelectrode and present some representative results.     

Reduction of electrode polarization capacitance in low-frequency impedance spectroscopy by using mesh electrodes

Dielectric measurements of biological samples are obscured by electrode polarization, which at low frequencies dominates over the actual sample response. Reduction of this artifact is especially necessary in studying interactions of electric field with biological systems in the α-dispersion range. We developed a method to reduce the influence of electrode polarization by employing mesh instead of solid electrodes as sensing probes, thereby reducing the area of the double layer. The design decreases the electrode-electrolyte contact area by almost 40% while keeping the bulk sample capacitance the same. Interrogation electric fields away from the electrode surface and sensitivity are unaffected. Electrodes were microfabricated (600μm×50μm, spacing of 100μm) with and without mesh holes 7.5μm×7.5μm in size. Simulations of electric field performed using Comsol Multiphysics showed non-uniformity of the electric field within less than 1.5μm from the electrode surface, which encompasses the double layer region, but at greater distance the solid and mesh electrodes gave the same results. Mesh electrodes reduced capacitance measurements for water and KCl solutions of different concentrations at low frequencies (<10kHz), while higher frequency capacitance remained the same for both electrode types, confirming our hypothesis that this design leaves the electric field mainly unaffected. Impedance measurements at low frequencies for water and mice heart mitochondrial suspension were lower for mesh than for solid electrodes. Comsol simulations confirmed these results by showing that mesh electrodes have a greater charge density than solid electrodes, which affects conductance. These electrodes are being used for mitochondrial membrane potential studies.     

Families of stationary patterns producing illusory movement: insights into the visual system.

A computational explanation of the illusory movement experienced upon extended viewing of Enigma, a static figure painted by Leviant, is presented. The explanation relies on a model for the interpretation of three-dimensional motion information contained in retinal motion measurements. This model shows that the Enigma figure is a special case of a larger class of figures exhibiting the same illusory movement and these figures are introduced here. Our explanation suggests that eye movements and/or accommodation changes cause weak retinal motion signals, which are interpreted by higher-level processes in a way that gives rise to these illusions, and proposes a number of new experiments to unravel the functional structure of the motion pathway.     

A model for photoreceptor-based magnetoreception in birds

A large variety of animals has the ability to sense the geomagnetic field and utilize it as a source of directional (compass) information. It is not known by which biophysical mechanism this magnetoreception is achieved. We investigate the possibility that magnetoreception involves radical-pair processes that are governed by anisotropic hyperfine coupling between (unpaired) electron and nuclear spins. We will show theoretically that fields of geomagnetic field strength and weaker can produce significantly different reaction yields for different alignments of the radical pairs with the magnetic field. As a model for a magnetic sensory organ we propose a system of radical pairs being 1) orientationally ordered in a molecular substrate and 2) exhibiting changes in the reaction yields that affect the visual transduction pathway. We evaluate three-dimensional visual modulation patterns that can arise from the influence of the geomagnetic field on radical-pair systems. The variations of these patterns with orientation and field strength can furnish the magnetic compass ability of birds with the same characteristics as observed in behavioral experiments. We propose that the recently discovered photoreceptor cryptochrome is part of the magnetoreception system and suggest further studies to prove or disprove this hypothesis.