Effect of ion concentration,solution and membrane permittivity on electric energy storage and capacitance

Bio-membranes as capacitors store electric energy, but their permittivity is low whereas the permittivity of surrounding solution is high. To evaluate the effective capacitance of the membrane/solution system and determine the electric energy stored within the membrane and in the solution, we estimated their electric variables using Poisson-Nernst-Planck simulations. We calculated membrane and solution capacitances from stored electric energy. The effective capacitance was calculated by fitting a six-capacitance model to charges (fixed and ion) and associated potentials, because it cannot be considered as a result of membrane and solution capacitance in series. The electric energy stored within the membrane (typically much smaller than that in the solution), depends on the membrane permittivity, but also on the external electric field, surface charge density, water permittivity and ion concentration. The effect on capacitances is more specific. Solution capacitance rises with greater solution permittivity or ion concentration, but the membrane capacitance (much smaller than solution capacitance) is only influenced by its permittivity. Interestingly, the effective capacitance is independent of membrane or solution permittivity, but rises as the ion concentration increases and surface charge becomes positive. Experimental estimates of membrane capacitance are thus not necessarily a reliable index of its surface area.     

Electrical capacitances of thin lipid films

Based on the considerations of surface charge and surface recombination (or ion binding), the capacitances of the diffused double layer and the polar region are calculated as functions of ionic strength, pH value and external bias. Electrical capacitances of thin lipid films were measured under various conditions. In all cases, the change in capacitance is not more than 5%. Agreement between theory and experiment is fairly good except for the capacitance-voltage relation. It is concluded that though the magnitude of the observed membrane capacitance is determined by the center hydrocarbon region, its constancy and stability are attributed to the largeness and guarding action of the interface capacitances.     

Anatomical distribution of voltage-dependent membrane capacitance in frog skeletal muscle fibers

Components of nonlinear capacitance, or charge movement, were localized in the membranes of frog skeletal muscle fibers by studying the effect of 'detubulation' resulting from sudden withdrawal of glycerol from a glycerol-hypertonic solution in which the muscles had been immersed. Linear capacitance was evaluated from the integral of the transient current elicited by imposed voltage clamp steps near the holding potential using bathing solutions that minimized tubular voltage attenuation. The dependence of linear membrane capacitance on fiber diameter in intact fibers was consistent with surface and tubular capacitances and a term attributable to the capacitance of the fiber end. A reduction in this dependence in detubulated fibers suggested that sudden glycerol withdrawal isolated between 75 and 100% of the transverse tubules from the fiber surface. Glycerol withdrawal in two stages did not cause appreciable detubulation. Such glycerol-treated but not detubulated fibers were used as controls. Detubulation reduced delayed (q gamma) charging currents to an extent not explicable simply in terms of tubular conduction delays. Nonlinear membrane capacitance measured at different voltages was expressed normalized to accessible linear fiber membrane capacitance. In control fibers it was strongly voltage dependent. Both the magnitude and steepness of the function were markedly reduced by adding tetracaine, which removed a component in agreement with earlier reports for q gamma charge. In contrast, detubulated fibers had nonlinear capacitances resembling those of q beta charge, and were not affected by adding tetracaine. These findings are discussed in terms of a preferential localization of tetracaine-sensitive (q gamma) charge in transverse tubule membrane, in contrast to a more even distribution of the tetracaine-resistant (q beta) charge in both transverse tubule and surface membranes. These results suggest that q beta and q gamma are due to different molecules and that the movement of q gamma in the transverse tubule membrane is the voltage-sensing step in excitation-contraction coupling.     

Kinetic analysis of displacement photocurrents elicited in two types of bacteriorhodopsin model membranes.

Fast displacement photocurrents have been reported in bacteriorhodopsin model membranes by several groups of investigators since 1977. A fast component (B1) is associated with positive charge displacement in the direction opposite to that of a physiological proton translocation. A slower component (B2) of opposite polarity is associated with positive charge displacement in the same direction as the proton translocation. Using two slightly different methods for model membrane formation, we observed photosignals with or without a significant B2 component under appropriate conditions. By means of the tunable voltage clamp method of measurement (Hong, F.T., and D. Mauzerall, 1974, Proc. Natl. Acad. Sci. USA, 71:1564-1568) we demonstrated that the time course of the B1 signal is completely predictable by an equivalent circuit containing a chemical capacitance. From the equivalent circuit analysis, we obtained a first-order relaxation time constant of 12.3 +/- 0.7 microseconds at room temperature. We also found a slight temperature dependence of the B1 relaxation with an activation energy of 2.54 +/- 0.24 kcal/mol. We found no pH dependence of the B1 component in the range of 0 to 11, whereas the B2 component is diminishing in a graded manner when the pH is varied from 0 to 10. These results are diametrically different from what reported previously (Drachev, L.A., A.D. Kaulen, L.V. Khitrina, and V.P. Skulachev, 1981, Eur. J. Biochem., 117:461-470). Our results support the interpretation that the B1 component is generated by an intramolecular charge displacement accompanying the light-induced reactions of bacteriorhodopsin and that the B2 component is generated by a process of proton uptake from the intracellular aqueous phase and subsequent release into the same aqueous phase. The impact of the present results on the conventional practice of identifying photointermediates of bacteriorhodopsin by spectroscopic means is discussed.     

A new system for bilayer lipid membrane capacitance measurements: method, apparatus and applications.

A new method and a new apparatus for capacitance measurements on bilayer lipid membranes are described. The membrane is charged and discharged with a constant current during the measurement. The charge-discharge cycle duration, which is proportional to the membrane capacitance, is measured. The measured time period is converted into a binary number by digital systems and then this number is either further converted into a constant capacity-proportional voltage or read out by the computer. The apparatus makes it possible to measure the capacitances of voltage-polarized membranes. Application of the apparatus to capacitance measurements of bilayer lipid membranes during their potential on the capacitance is presented. The capacitances of membranes stimulated by rectangular voltage pulses and of those stimulated by a linearly varying potential were reported.     

cAmp activation of apical membrane Cl(-) channels: theoretical considerations for impedance analysis.

Transepithelial electrical impedance analysis provides a sensitive method to evaluate the conductances and capacitances of apical and basolateral plasma membranes of epithelial cells. Impedance analysis is complicated, due not only to the anatomical arrangement of the cells and their paracellular shunt pathways, but also in particular to the existence of audio frequency-dependent capacitances or dispersions. In this paper we explore implications and consequences of anatomically related Maxwell-Wagner and Cole-Cole dielectric dispersions that impose limitations, approximations, and pitfalls of impedance analysis when tissues are studied under widely ranging spontaneous rates of transport, and in particular when apical membrane sodium and chloride channels are activated by adenosine 3',5'-cyclic monophosphate (cAMP) in A6 epithelia. We develop the thesis that capacitive relaxation processes of any origin lead not only to dependence on frequency of the impedance locus, but also to the appearance of depressed semicircles in Nyquist transepithelial impedance plots, regardless of the tightness or leakiness of the paracellular shunt pathways. Frequency dependence of capacitance precludes analysis of data in traditional ways, where capacitance is assumed constant, and is especially important when apical and/or basolateral membranes exhibit one or more dielectric dispersions.     

The molecular organisation of bimolecular lipid membranes. The effect of benzyl alcohol on the structure

The separate effects of benzyl alcohol on the hydrocarbon and polar-head region capacitances and conductances of phosphatidylcholine bimolecular lipid membranes were obtained from measurements of the very low frequency impedance dispersion. It was found that the conductance of the hydrocarbon region (and, to a lesser extent, the polar-head region) increased progressively with increasing concentrations of benzyl alcohol in the external solution. The polar-head capacitance did not show a systematic dependence on the concentration of benzyl alcohol.At low concentrations of benzyl alcohol (7.5 μM) the capacitance of the hydrocarbon region was not significantly affected by the alcohol. At high concentrations (? 7.5 mM) of benzyl alcohol, however, the capacitance of this region was reduced by ≈25%. This is interpreted in terms of an increase in the thickness of this region caused by a straightening of the otherwise kinked, folded (across neighbouring molecules) and perhaps even partially interdigitated hydrocarbon tails of the phosphatidylcholine molecules. This effect of benzyl alcohol is probably closely related also to the apparent increase in the fluidity of the membrane. The effect of benzyl alcohol on the thickness of the hydrocarbon region of the membrane provides a ready insight into its mode of action as a local anaesthetic.     

On the mechanism of electrical coupling between cells of earlyXenopus embryos

Summary The mechanism of electrical coupling between cells of earlyXenopus embryos has been studied by examination of the nonjunctional membrane resistances and capacitances as a function of cleavage stage, the junctional and nonjunctional membrane resistances as functions of time during the first cleavage, and the electrical properties of the primitive blastocoel. The changes in membrane resitances and capacitances during the first two cleavages may be completely explained by the addition of new membrane, identical in specific resistance and capacitance to the original membrane, at a constant rate to furrows which are electrically connected to the perivitelline space. Microelectrode recording from the primitive blastocoel indicates that there is no electrical difference detectable between it and the perivitelline space. These results are discussed in the context of current theories of the mechanism of intercellular electrotonic coupling.     

Frequency domain analysis of membrane capacitance of cultured cells (HeLa and myeloma) using the micropipette technique.

The membrane capacitance and conductance of cultured cells (HeLa and mouse myeloma) are investigated using the micropipette method. Mean values of the membrane capacities were found to be 1.9 microF/cm2 for HeLa cells and 1.0 microF/cm2 for myeloma cells. These values are in agreement with those obtained using the suspension method. Whereas the suspension method is unable to provide the information on membrane conductance, the micropipette method is able to measure even an extremely small membrane conductance if leakage current is negligibly small. The membrane conductances were found, using this technique, to be approximately 90-100 microS/cm2 for both HeLa and myeloma cells. One of the purposes of this study is to establish the frequency profile of membrane capacitance. It was found, however, that membrane capacitances of these cells are independent of frequency between 1 Hz and 1 KHz within the resolution of this technique.     

Electrical properties of squid axon membrane. II. Effect of partial degradation by phospholipase A and pronase on electrical characteristics.

Passive electrical characteristics of perfused squid axon membrane are investigated. In a previous publication, we reported that the capacitance of intact squid axon membrane is partly frequency dependent. We extended the same measurement to perfused axons. We found that the electrical characteristics of perfused axon membrane are essentially the same as those of intact axons. In this work, we investigated the effects of phospholipase A and pronase on the membrane capacitance. Phospholipase A is known to block the sodium activation and pronase to eliminate the sodium inactivation. Phospholipase A is found to increase the frequency dependent as well as the frequency independent capacitances. Our tentative conclusion is that this enzyme perturbs the lipid structure and decreases its thickness. Pronase is found to increase the frequency dependent capacitance slightly while the capacitance of the lipid layer remains unaltered. Although voltage clamp data indicate that the pronase disrupts the excitatory mechanism extensively, this enzyme has relatively little effect on the overall membrane capacitance.     

Electrical properties of squid axon membrane. II. Effect of partial degradation by phospholipase A and pronase on electrical characteristics

Passive electrical characteristics of perfused squid axon membrane are investigated. In a previous publication, we reported that the capacitance of intact squid axon membrane is partly frequency dependent. We extended the same measurement to perfused axons. We found that the electrical characteristics of perfused axon membrane are essentially the same as those of intact axons. In this work, we investigated the effects of phospholipase A and pronase on the membrane capacitance. Phospholipase A is known to block the sodium activation and pronase to eliminate the sodium inactivation. Phospholipase A is found to increase the frequency dependent as well as the frequency independent capacitances. Our tentative conclusion is that this enzyme perturbs the lipid structure and decreases its thickness. Pronase is found to increase the frequency dependent capacitance slightly while the capacitance of the lipid layer remains unaltered. Although voltage clamp data indicate that the pronase disrupts the excitatory mechanism extensively, this enzyme has relatively little effect on the overall membrane capacitance.     

Inner field compensation as a tool for the characterization of asymmetric membranes and Peptide-membrane interactions

Symmetric and asymmetric planar lipid bilayers prepared according to the Montal-Mueller method are a powerful tool to characterize peptide-membrane interactions. Several electrical properties of lipid bilayers such as membrane current, membrane capacitance, and the inner membrane potential differences and their changes can be deduced. The time-resolved determination of peptide-induced changes in membrane capacitance and inner membrane potential difference are of high importance for the characterization of peptide-membrane interactions. Intercalation and accumulation of peptides lead to changes in membrane capacitance, and membrane interaction of charged peptides induces changes in the charge distribution within the membrane and with that to changes in the membrane potential profile. In this study, we establish time-resolved measurements of the capacitance minimization potential DeltaPsi on various asymmetric planar lipid bilayers using the inner field compensation method. The results are compared to the respective ones of inner membrane potential differences DeltaPhi determined from ion carrier transport measurements. Finally, the time courses of membrane capacitances and of DeltaPsi have been used to characterize the interaction of cathelicidins with reconstituted lipid matrices of various Gram-negative bacteria.     

Influence of sodium concentration on changes of membrane capacitance associated with the electrogenic ion transport by the Na,K-ATPase

Electrogenic ion transport by the Na,K-ATPase was investigated in a model system of protein-containing membrane fragments adsorbed to a lipid bilayer. Transient Na⁺ currents were induced by photorelease of ATP from inactive caged ATP. This process was accompanied by a capacitance change of the membrane system. Two methods were applied to measure capacitances in the frequency range 1 to 6000 Hz. The frequency dependent capacitance increment, ΔC, was of sigmoidal shape and decreased at high frequencies. The midpoint frequency, f ₀, depended on the ionic strength of the buffer. At 150 mm NaCl f ₀ was about 200 Hz and decreased to 12 Hz at high ionic strength (1 M). At low frequencies (f≪f ₀) the capacitance increment became frequency independent. It was, however, dependent on Na⁺ concentration and on the membrane potential which was generated by the charge transferred. A simple model is presented to analyze the experimental data quantitatively as a function of two parameters, the capacitance of the adsorbed membrane fragments, C _P, and the potential of maximum capacitance increment, ψ ₀. Below 5 mm Na⁺ a negative capacitance change was detected which may be assigned to electrogenic Na⁺ binding to cytoplasmic sites. It could be shown that the results obtained by experiments with the presented alternating current method contain the information which is determined by current-relaxation experiments with cell membranes. Received: 3 November 1997 / Revised version: 19 February 1998 / Accepted: 21 February 1998     

Can root electrical capacitance be used to predict root mass in soil?

Background

Electrical capacitance, measured between an electrode inserted at the base of a plant and an electrode in the rooting substrate, is often linearly correlated with root mass. Electrical capacitance has often been used as an assay for root mass, and is conventionally interpreted using an electrical model in which roots behave as cylindrical capacitors wired in parallel. Recent experiments in hydroponics show that this interpretation is incorrect and a new model has been proposed. Here, the new model is tested in solid substrates.

Methods

The capacitances of compost and soil were determined as a function of water content, and the capacitances of cereal plants growing in sand or potting compost in the glasshouse, or in the field, were measured under contrasting irrigation regimes.

Key Results

Capacitances of compost and soil increased with increasing water content. At water contents approaching field capacity, compost and soil had capacitances at least an order of magnitude greater than those of plant tissues. For plants growing in solid substrates, wetting the substrate locally around the stem base was both necessary and sufficient to record maximum capacitance, which was correlated with stem cross-sectional area: capacitance of excised stem tissue equalled that of the plant in wet soil. Capacitance measured between two electrodes could be modelled as an electrical circuit in which component capacitors (plant tissue or rooting substrate) are wired in series.

Conclusions

The results were consistent with the new physical interpretation of plant capacitance. Substrate capacitance and plant capacitance combine according to standard physical laws. For plants growing in wet substrate, the capacitance measured is largely determined by the tissue between the surface of the substrate and the electrode attached to the plant. Whilst the measured capacitance can, in some circumstances, be correlated with root mass, it is not a direct assay of root mass.     

Robust, high-resolution, whole cell patch-clamp capacitance measurements using square wave stimulation.

High-resolution, whole cell capacitance measurements are usually performed using sine wave stimulation using a single frequency or a sum of two frequencies. We present here a high-resolution technique for whole-cell capacitance measurements based on square-wave stimulation. The square wave represents a sum of sinusoidal frequencies at odd harmonics of the base frequency, the amplitude of which is highest for the base frequency and decreases as the frequency increases. The resulting currents can be analyzed by fitting the current relaxations with exponentials, or by a phase-sensitive detector technique. This method provides a resolution undistinguishable from that of single-frequency sine wave stimulation, and allows for clear separation of changes in capacitance, membrane conductance, and access resistance. In addition, it allows for the analysis of more complex equivalent circuits as associated with the presence of narrow fusion pores during degranulation, tracking many equivalent circuit parameters simultaneously. The method is insensitive to changes in the reversal potential, pipette capacitance, or widely varying cell circuit parameters. It thus provides important advantages in terms of robustness for measuring cell capacitances, and allows analysis of complicated changes of the equivalent circuits.     

The molecular organization of bimolecular lipid membranes. A study of the low frequency Maxwell-Wagner impedance dispersion

Theoretical considerations show that the presence of the polar group regions in bimolecular lipid membranes will produce a small (2–3%) dispersion of the bimolecular lipid membrane capacitance at low frequencies (0.1–100 Hz).A dispersion in conductance will also result. Calculations are given of the resolution of phase angle and impendance amplitude required to detect this dispersion and a new measuring technique is described which can achieve this. From the experimental result presented for lecithin bimolecular lipid membranes a determination was made of the individual capacitances and conductances of both the hydrocarbon and polar groups regions. The polar group conductance was found to vary from 700 μΩ^?1 · cm^?2 (in 1 mM KCl) to 2000 μΩ^?1 · cm^?2 (in 1 M KCl).The polar group capacitances were found to be approx.30 μF · cm^?2 and not systematically dependent on the concentration of the external electrolyte.     

Properties of the demarcation membrane system in living rat megakaryocytes

The demarcation membrane system (DMS) is the precursor of platelet cell membranes yet little is known of its properties in living megakaryocytes. Using confocal microscopy, we now demonstrate that demarcation membranes in freshly isolated rat marrow megakaryocytes are rapidly stained by styryl membrane indicators such as di-8-ANEPPS and FM 2-10, confirming that they are invaginations of the plasma membrane and readily accessible from the extracellular space. Two-photon excitation of an extracellular indicator displayed the extensive nature of the channels formed by the DMS throughout the extranuclear volume. Under whole-cell patch clamp, the DMS is electrophysiologically contiguous with the peripheral plasma membrane such that a single capacitative component can account for the biophysical properties of all surface-connected membranes in the majority of recordings. Megakaryocyte capacitances were in the range of 64-694 pF, equivalent to 500-5500 platelets (mean value 1850). Based upon calculations for a spherical geometry, the DMS results in a 4- to 14-fold (average 8.1-fold) increase in specific membrane capacitance expressed per unit spherical surface area. This indicates a level of plasma membrane invagination comparable with mammalian skeletal muscle. Whole-cell capacitance measurements and confocal imaging of membrane-impermeant fluorescent indicators therefore represent novel approaches to monitor the DMS during megakaryocytopoiesis and thrombopoiesis.     

铁/紫膜/胶/铜光电池在光触发瞬时的界面电势研究

在分析菌紫质光驱质子泵过程的基础上 ,应用Hong的化学电容的概念 ,提出在菌紫质人工膜系统中等效存在C -电容和N -电容 ,并由此研究了铁/紫膜/胶/铜光电池在光触发瞬时的界面电势。结果可提供于以菌紫质为基础的分子电子器件 ,和菌紫质光驱质子泵机理的研究。     

Current-voltage relations of the apical and basolateral membranes of the frog skin

We determined the current-voltage (I-V) relations of the apical and basolateral barriers of frog skins by impaling the cells with an intracellular microelectrode and assuming that the current across the cellular pathway was equal to the amiloride-inhibitable current. We found that: (a) The responses in transepithelial current and intracellular potential to square pulses of transepithelial potential (VT) varied markedly with time. (b) As a consequence of these transient responses, the basolateral I-V relation was markedly dependent on the time of sampling after the beginning of each pulse. The apical I-V plot was much less sensitive to the time of sampling within the pulse. (c) The I-V data for the apical barrier approximated the I-V relations calculated from the Goldman constant field equation over a relatively wide range of membrane potentials (+/- 100 mV). (d) A sudden reduction in apical bath [Na+] resulted in an increase in apical permeability and a shift in the apical barrier zero-current potential (Ea) toward less positive values. The shift in Ea was equivalent to a change of 45 mV for a 10-fold change in apical [Na+]. (e) The transient responses of the skin to square VT pulses were described by the sum of two exponentials with time constants of 114 and 1,563 ms, which are compatible with the time constants that would be produced by an RC circuit with capacitances of 65 and 1,718 microF. The larger capacitance is too large to identify it comfortably with a true dielectric membrane capacitance.     

Astrocyte swelling leads to membrane unfolding, not membrane insertion

The mechanisms mediating the release of chemical transmitters from astrocytes are the subject of intense research. Recent experiments have shown that hypotonic conditions stimulate the release of glutamate and ATP from astrocytes, but a mechanistic understanding of this process is not available. To determine whether hypotonicity activates the process of regulated exocytosis, we monitored membrane capacitance by the whole-cell patch-clamp technique whilst a hypotonic medium was applied to cultured astrocytes. If exocytosis is triggered under hypotonic conditions, as it is following increases in cytosolic calcium, a net increase in membrane surface area, monitored by measuring the whole-cell membrane capacitance, is expected. Simultaneous measurements of cell size and whole-cell membrane conductance and surface area demonstrated that hypotonic medium (210 mOsm for 200 s) resulted in an increase in membrane conductance and in the swelling of cultured astrocytes by an average of 40%, as monitored by cell cross-sectional area, but without any corresponding change in membrane surface area. As we have demonstrated that capacitance measurements have the sensitivity to detect increases in cell surface area as small as 0.5%, we conclude that cell swelling occurs via an exocytosis-independent mechanism, probably involving the unfolding of the plasma membrane.