An improved method for real-time monitoring of membrane capacitance in Xenopus laevis oocytes

Measurements of membrane capacitance (C(m)) in Xenopus laevis oocytes offer unique experimental possibilities but are difficult to perform with current methods. To improve C(m) measurements in the two-electrode voltage clamp (TEVC) mode, we developed a paired-ramp protocol and tested its performance in a model circuit (with tunable C(m), membrane resistance R(m), and series resistance R(s)) and in Xenopus oocytes. In the cell model and with R(s) = 0 Omega, inaccuracy of C(m) estimates was <1% under widely varying conditions (R(m) ranging from 100 to 2000 kOmega, and C(m) from 50 to 1000 nF). With R(s) > 0 Omega, C(m) was underestimated by a relative error epsilon closely approximated as epsilon approximate 2 x R(s)/(R(s) + R(m)), in keeping with the theoretical prediction. Thus, epsilon may be neglected under standard conditions or, under extreme conditions, corrected for if R(s) is known. Relative imprecision of C(m) estimates was small, independent of R(s), and inversely related to C(m) (<1.5% at 50 nF, <0.4% at 200 nF). Averaging allowed reliable detection of C(m) deviations from 200 nF of 0.1 nF, i.e., 0.05%. In Xenopus oocytes, we could resolve C(m) changes that were small (e.g., DeltaC(m) approximate 2 nF upon 100 muM 8-Br-cAMP), fast (e.g., DeltaC(m)/Deltat approximate 20nF/30s upon 1 muM phorbol myristate acetate (PMA)) or extended and complex (e.g., fast increase, followed by prolonged C(m) decrease upon 1 muM PMA). Rapidly alternating between paired ramps and a second, step protocol allowed quasi-simultaneous monitoring of additional electrical parameters such as R(m), slope conductance g(m), and reversal potential E(rev). Taken together, our method is suited to monitor C(m) in Xenopus oocytes conveniently, with high temporal resolution, accuracy and precision, and in parallel with other electrical parameters. Thus, it may be useful for the study of endo- and exocytosis and of membrane protein regulation and for electrophysiological high-throughput screening.     

Frequency domain studies of impedance characteristics of biological cells using micropipet technique. I. Erythrocyte.

This study aims at precise measurement of the membrane capacity and its frequency dependence of small biological cells using the micropipet technique. The use of AC fields as an input signal enables the magnitude and phase angle of membrane impedance to be measured at various frequencies. The micropipet technique was applied to human erythrocyte, and passive membrane capacity and conductivity were determined between 4 Hz and 10 KHz. Membrane capacity thus determined changed from 1.05 to 0.73 microF/cm2 between 4 Hz and 10 KHz. In addition to the micropipet technique, we used suspension method between 50 KHz and 10 MHz for the purpose of supplementing the new method with the one which has been in use for many years. We obtained a membrane capacity of 0.65-0.8 microF/cm2 using this technique. These values agree with the capacitance obtained with the micropipet method. Although this paper discusses only human erythrocytes, the study has been performed with lymphocytes and various forms of cancer cells. This paper is the first of the series of reports on frequency domain studies of the impedance characteristics of various biological cells.     

Ripening of Nectarine Fruit (Changes in the Cell Wall,Vacuole, and Membranes Detected Using Electrical Impedance Measurements)

Electrical impedance measurements were used to characterize changes in intracellular and extracellular resistance as well as changes in the condition of membranes during ripening of nectarines (Prunus persica [L.] Batsch cv Fantasia). These measurements were related to changes in fruit texture assessed by flesh firmness and apparent juice content. An electrical model indicated that, during ripening (d 1-5) of freshly harvested fruit, the resistance of the cell wall and vacuole declined by 60 and 26%, respectively, and the capacitance of the membranes decreased by 9%. Accurate modeling of the impedance data required an additional resistance component. This resistance, which declined by 63% during ripening, was thought to be associated with either the cytoplasmic or membrane resistance. Changes in tissue resistance measured using low frequencies of alternating current were closely related to flesh firmness. After storage at 0[deg]C for 8 weeks, the nectarines developed a woolly (dry) texture during ripening at 20[deg]C. The main difference between these chilling-injured nectarines and fruit ripened immediately after harvest was the resistance of the cell wall, which was higher in woolly tissue (4435 [omega] after 5 d at 20[deg]C) than in nonwoolly tissue (2911 [omega] after 5 d at 20[deg]C). The results are discussed in relation to physiological changes that occur during the ripening and development of chilling injury in nectarine fruit.     

Electrical Impedance Analysis in Plant Tissues11

Electrical impedance was measured at a range of AC frequenciesof 100 Hz to 1 MHz in potato tubers and carrot roots. Detailsof a method for analysing the data in relation to electricalmodels, using complex non-linear least squares (CNLS), are described.The measured data were analysed in relation to four previously-describedelectrical models for plant tissues. The results showed thatplant tissue conforms well to a double-shell model which includescomponents (resistors and capacitors) representing the vacuole,as well as cytoplasm, plasma membrane, and extracellular space.The method permitted the calculation of specific membrane capacitance,which was found to approximate l0µF cm^–2. Key words: Electrical impedance, complex non-linear least squares (CNLS), electrical modelling, membrane capacitance     

Evaluation of process-induced dimensional changes in the membrane structure of biological cells using impedance measurement

The impact of high intensity electric field pulses, high hydrostatic pressure, and freezing-thawing on local structural changes of the membrane was determined for potato, sugar beet tissue, and yeast suspensions. On the basis of the electrophysical model of cell systems in biological tissues and suspensions, a method was derived for determining the extent of local damage of cell membranes. The method was characterized by an accurate and rapid on-line determination of frequency-dependent electrical conductivity properties from which information on microscopic events on cellular level may be deduced. Evaluation was based on the measurement of the relative change in the sample's impedance at characteristically low (f(l)) and high (f(h)) frequencies within the beta-dispersion range. For plant and animal cells the characteristic frequencies were f(l) approximately 5 kHz and f(h) > 5 MHz and for yeast cells in the range f(l) approximately 50 kHz and f(h) > 25 MHz. The observed phenomena were complex. The identification of the underlying mechanisms required consideration of the time-dependent nature of the processing effects and stress reactions of the biological systems, which ranged from seconds to several hours. A very low but significantly detectable membrane damage (0.004% of the total area) was found after high hydrostatic pressure treatment of potato tissue at 200 MPa. The membrane rupture in plant tissue cells was higher after freezing and subsequent thawing (0.9% of total area for potato cells and 0.05-0.07% for sugar beet cells determined immediately after thawing), which increased substantially during the next 2 h.     

Impedance profiles of peripheral and central neurons

The electrical impedance of trigeminal ganglion cells (in vivo) and hippocampal CA1 neurons (in vitro) of guinea pigs was measured in the frequency range of 5-1250 Hz using intracellular recording techniques with single microelectrodes and computerized methodology. The transfer functions of the electrode and the electrode-neuron system were computed from the ratio of fast Fourier transforms of the output voltage response from the neuron and input current composed of sine waves with rapidly increasing frequency which displaced membrane potential by 2-5 mV. We believe these to be the first measurements of complex impedance and transfer functions in peripheral and central neurons of vertebrates and the first use of such input current functions. The majority of trigeminal ganglion cells did not exhibit electrical behaviour ascribable to a simple resistance-capacitance (RC) circuit but showed a hump at low frequencies (5-250 Hz) in the computed transfer function, probably attributable to resonance. The transfer function in less than 20% of the trigeminal neurons could be fitted approximately to a theoretical transfer function (resistance in series with a parallel RC circuit model) providing values for electrode resistance, effective input resistance, and effective input capacitance. The transfer functions measured in hippocampal CA1 neurons were characterized by a rapid fall-off in the low frequency range (less than 200 Hz). Impedance locus plots approximate the locus corresponding to a series RC circuit in parallel with a parallel RC circuit.     

Different ratios of sucrose/raffinose-induced membrane depolarizations in the mesophyll of species with symplasmic (Catharanthus roseus, Ocimum basilicum) or apoplasmic (Impatiens walleriana, Vicia faba) minor-vein configurations

In mesophyll cells of species with a symplasmic (Ocimum basilicum, Catharanthus roseus, Magnolia denudata) or an apoplasmic (Vicia faba, Impatiens walleriana, Bellis perennis) minor-vein configuration, membrane depolarizations in response to 20 or 200 mol·m^–3 raffinose and sucrose were measured. Ageing period and resting potential marginally affected the degree of depolarization. The symplasmic species showed similar depolarization responses to 20 and 200 mol·m^–3 sucrose or raffinose. In the apoplasmic species, depolarization increased statistically significantly from 20 to 200 mol·m^–3 sucrose, whereas the depolarization response to raffinose was equal at both concentrations. In the apoplasmic species, moreover, the depolarization response to raffinose was significantly weaker than to sucrose at all concentrations. A major difference between symplasmic and apoplasmic species seems to lie in the scantiness of raffinose carriers in the mesophyll plasma membrane of species with the apoplasmic mode of phloem loading.Abbreviations 20R(200R) 20(200) mol·m^–3 raffinose - 20S(200S) 20(200) mol·m^–3 sucrose     

Transverse Impedance of Single Frog Skeletal Muscle Fibers

The transverse electrical impedance of single frog skeletal muscle fibers was measured at 31 frequencies that ranged from 1 to 100,000 Hz. Each fiber was bathed entirely in Ringer's solution, but it was positioned so that a central length of 5 mm was in a hollow plastic disk and was electrically isolated from the ends of the fiber. The diameter of the segment of the fiber in the disk was measured and then the segment was pressed from opposite sides by two insulating wedges. Electrical current was passed transversely through the segment between two platinum-platinum black electrodes that were located in the pools of Ringer's solution within the disk. The results were corrected for stray parallel capacitance, series resistance of the Ringer's solution between the fiber and the electrodes, parallel shunt resistance around the fiber, and the phase shift of the measuring apparatus. A nonlinear least-squares routine was used to fit a lumped equivalent circuit to the data from six fibers. The equivalent circuit that was chosen for the fibers contained three parallel branches; each branch was composed of a resistor and a capacitor in series. The model also included a seventh adjustable parameter that was designed to account for the degree of compression of the fibers by the insulating wedges. The branches of the equivalent circuit were assumed to represent the electrical properties of: (a) the myoplasm in series with the membrane capacitance that was exposed directly to the pools of Ringer's solution; (b) the capacitance and series resistance of the transverse tubules that were exposed directly to the pools of Ringer's solution; (c) the membrane capacitance in series with the shunt resistance between the fibers and the insulating wedges. The results gave no indication that current entered the sarcoplasmic reticulum.     

In vivo plant impedance measurements and characterization of membrane electrical properties: The influence of cold acclimation

A procedure to measure both the real (resistance) and complex (reactance) part of plant tissue impedance is described. Bare metal electrodes were used and the impedance of electrodes was determined by obtaining measurements at four interelectrode distances. The frequency (f) dependence of the impedance of birdsfoot trefoil (Lotus corniculatus L.) stems could be modeled, approximately, by a resistor representing an extracellular resistance, a resistor representing an intracellular resistance, and a resistor and capacitor representing cell membranes. However, the membrane parameters appeared to be frequency dependent. Therefore, they were characterized by calculating a time constant at each frequency. For example, for one plant stem the time constant (τ) decreased from 1.19 × 10⁻³ sec at 101 hz to 1.36 × 10⁻⁶ sec at 100 KHz. This decrease with frequency could be described by an equation of the form: ln(τ) = a + bln(f) + c(ln[f])². Cold acclimation increased (P ⩽ 0.05) the intracellular resistance. But cold acclimation did not have a significant effect on estimates of the extracellular resistance, the membrane resistance, or the membrane time constant. Depending on the cultivar, cold acclimation either decreased or increased the estimate of membrane capacitance.     

Capacitance of bilayers in the presence of lipophilic ions

The capacitance of glycerolmonooleate and egg phosphatidylcholine bilayer membranes in the presence of NaCl solutions containing tetraphenylborate, tetraphenylarsonium or dipicrylamine ions has been measured using alternating current techniques over a wide range of frequencies (1–200 kHz). The concentrations of ions corresponded to the lower limits of conductance saturation. Similar determinations were also made with solutions containing no lipophilic ions. The experimental method used in this work requires correction of admittance measurements for the solution resistance in series with the membrane, as well as careful area determinations. In all cases membrane capacitance levels off at sufficiently high frequencies to values which are independent of frequency. The high-frequency capacitance, which is regarded as the ‘geometrical capacitance’ due to dielectric polarization, is practically unaffected by the presence of lipophilic ions. The results support the assumption made in other studies, such as in charge pulse investigations, that the adsorption of lipophilic ions at concentrations up to the saturation range does not have an important effect on the dielectric properties of bilayers.     

Theoretical and experimental study towards a nanogap dielectric biosensor

Theoretical and experimental studies of nanogap capacitors as potential label free biosensors are presented. The nanogap device is capable of detecting the existence of single stranded DNA (ssDNA) oligonucleotides (20-mer) in 100 nM aqueous solutions using a 20 nm gap of 1.2 pl in volume. While the dielectric properties of DNA solution have been widely investigated, early approaches are limited at low frequency by the parasitic noise due to the electrical double layer (EDL) impedance. Nanogap electrodes have the potential to serve as biomolecular junctions because their size (5-100 nm) minimizes electrode polarization effects regardless of frequency. In this paper, we modeled the effects of the EDL interaction between two parallel nanogap electrodes by solving the Poisson-Boltzmann (PB) equation for equilibrium state. When the gap size is smaller than the EDL thickness, the dependence of the nanogap capacitance on the ionic strength is insignificant. This is critical in using the capacitance change as an indicator of the existence of target molecules. The predicted capacitance of nanogaps filled with various ionic strength electrolytes was in quantitative agreement with the experimental measurements. The various concentrations of the target molecules in nanogap sensor were characterized. A capacitance change of a 20 nm x (10)1.5 microm x 4mm gap from 3.5 to 4.1 nF at 200 Hz was recorded between deionized water (DI) and 100 nM ssDNA solution (about 70,000 molecules inside the gap for equilibrium state).     

Electrical Characteristics of Tunicate Heart Cell Membranes and Nexuses

The tubular ascidian heart is composed of a single layer of cells joined together by apical (zonulae occludentes) and spot (maculae occludentes) nexuses. Intercalated discs or desmosomes were not observed in this tissue. Rectangular pulses of current were applied across the opened and flattened myocardium. Assuming that all the transepithelial current flowed through a uniform gap between cells, the resistivity in the gap must be very high compared to that in bulk solution. It is likely, therefore, that the gap width is of the order of an ionic radius or smaller. Assuming that all the transepithelial current flowed through the cells and that the inner and outer membranes had the same resistivity, the membrane resistivity was about 210 ohms cm² and the membrane capacitance was about 1.6 µF per cm². The myocardial cells were found to be in electrical continuity with each other through the nexuses since current could be passed through a strip of myocardium in a sucrose gap. Assuming that the longitudinal resistance of the cytoplasm was negligible, the cell-to-cell resistivity of the nexuses was 0.2 ohm cm². It is concluded that the nexuses provide a low resistance pathway between cells and a transepithelial barrier.     

Chronopotentiometric studies of phosphatidylcholine bilayers modified by ergosterol

We have monitored the effect of ergosterol on electrical capacitance and electrical resistance of the phosphatidylcholine bilayer membranes using chronopotentiometry method. The chronopotentiometric characteristic of the bilayers depends on constant-current flow through the membranes. For low current values, no electroporation takes place and the membrane voltage rises exponentially to a constant value described by the Ohm's law. Based on these kinds of chronopotentiometric curves, a method of the membrane capacitance and the membrane resistance calculations is presented.     

Estimation of the junctional resistance between electrically coupled receptor cells in Necturus taste buds

Junctional resistance between coupled receptor cells in Necturus taste buds was estimated by modeling the results from single patch pipette voltage clamp studies on lingual slices. The membrane capacitance and input resistance of coupled taste receptor cells were measured to monitor electrical coupling and the results compared with those calculated by a simple model of electrically coupled taste cells. Coupled receptor cells were modeled by two identical receptor cells connected via a junctional resistance. On average, the junctional resistance was approximately 200-300 M omega. This was consistent with the electrophysiological recordings. A junctional resistance of 200-300 M omega is close to the threshold for Lucifer yellow dye-coupling detection (approximately 500 M omega). Therefore, the true extent of coupling in taste buds might be somewhat greater than that predicted from Lucifer yellow dye coupling. Due to the high input resistance of single taste receptor cells (> 1 G omega), a junctional resistance of 200-300 M omega assures a substantial electrical communication between coupled taste cells, suggesting that the electrical activity of coupled cells might be synchronized.     

PGE(2) activation of apical membrane Cl(-) channels in A6 epithelia: impedance analysis.

Measurements of transepithelial electrical impedance of continuously short-circuited A6 epithelia were made at audio frequencies (0.244 Hz to 10.45 kHz) to investigate the time course and extent to which prostaglandin E(2) (PGE(2)) modulates Cl(-) transport and apical membrane capacitance in this cell-cultured model epithelium. Apical and basolateral membrane resistances were determined by nonlinear curve-fitting of the impedance vectors at relatively low frequencies (<50 Hz) to equations (P?unescu, T. G., and S. I. Helman. 2001. Biophys. J. 81:838--851) where depressed Nyquist impedance semicircles were characteristic of the membrane impedances under control Na(+)-transporting and amiloride-inhibited conditions. In all tissues (control, amiloride-blocked, and amiloride-blocked and furosemide-pretreated), PGE(2) caused relatively small (< approximately 3 microA/cm(2)) and rapid (<60 s) maximal increase of chloride current due to activation of a rather large increase of apical membrane conductance that preceded significant activation of Na(+) transport through amiloride-sensitive epithelial Na(+) channels (ENaCs). Apical membrane capacitance was frequency-dependent with a Cole-Cole dielectric dispersion whose relaxation frequency was near 150 Hz. Analysis of the time-dependent changes of the complex frequency-dependent equivalent capacitance of the cells at frequencies >1.5 kHz revealed that the mean 9.8% increase of capacitance caused by PGE(2) was not correlated in time with activation of chloride conductance, but rather correlated with activation of apical membrane Na(+) transport.     

Pore formation in lipid bilayer membranes made of phosphatidylinositol and oxidized cholesterol followed by means of alternating current.

The kinetics of porin incorporation into black lipid membranes (BLM) made of phosphatidylinositol (PI) or oxidized cholesterol (Ox Ch) were studied by means of alternating current; the set-up was able to acquire resistance and capacitance simultaneously by means of a mixed double-frequency approach at 1 Hz and 1 KHz, respectively. Conductance was dependent on the interaction between protein-forming pores and lipids. For PI membranes below a porin concentration of 12.54 ng/ml, there was no membrane conductivity, whereas at 200 ng/ml a steady-state value was reached. Different behavior was displayed by Ox Ch membranes, in which a concentration of 12.54 ng/ml was sufficient to reach a steady state. The incorporation kinetics when porin was added after membrane formation were sigmoidal. When porin was present in the medium before membrane formation, the kinetics were sigmoidal for PI membranes but became exponential for Ox Ch membranes. Furthermore, for BLM made of PI, the conductance-versus-porin concentration relationship is sigmoidal, with a Hill coefficient of 5.6 +/- 0.07, which is functional evidence corroborating the six-channel repeating units seen previously. For BLM made of Ox Ch, this relationship followed a binding isotherm curve with a Hill coefficient of 0.934 +/- 0.129.     

Mechanisms of conduction slowing during myocardial stretch by ventricular volume loading in the rabbit

Acute ventricular loading by volume inflation reversibly slows epicardial electrical conduction, but the underlying mechanism remains unclear. This study investigated the potential contributions of stretch-activated currents, alterations in resting membrane potential, or changes in intercellular resistance and membrane capacitance. Conduction velocity was assessed using optical mapping of isolated rabbit hearts at end-diastolic pressures of 0 and 30 mmHg. The addition of 50 microM Gd3+ (a stretch-activated channel blocker) to the perfusate had no effect on slowing. The effect of volume loading on conduction velocity was independent of changes in resting membrane potential created by altering the perfusate potassium concentration between 1.5 and 8 mM. Bidomain model analysis of optically recorded membrane potential responses to a unipolar stimulus suggested that the cross-fiber space constant and membrane capacitance both increased with loading (21%, P = 0.006, and 56%, P = 0.004, respectively), and these changes, when implemented in a resistively coupled one-dimensional network model, were consistent with the observed slowing (14%, P = 0.005). In conclusion, conduction slowing during ventricular volume loading is not attributable to stretch-activated currents or altered resting membrane potential, but a reduction of intercellular resistance with a concurrent increase of effective membrane capacitance results in a net slowing of conduction.     

A synthetic strand of cardiac muscle: its passive electrical properties

The passive electrical properties of synthetic strands of cardiac muscle, grown in tissue culture, were studied using two intracellular microelectrodes: one to inject a rectangular pulse of current and the other to record the resultant displacement of membrane potential at various distances from the current source. In all preparations, the potential displacement, instead of approaching a steady value as would be expected for a cell with constant electrical properties, increased slowly with time throughout the current step. In such circumstances, the specific electrical constants for the membrane and cytoplasm must not be obtained by applying the usual methods, which are based on the analytical solution of the partial differential equation describing a one-dimensional cell with constant electrical properties. A satisfactory fit of the potential waveforms was, however, obtained with numerical solutions of a modified form of this equation in which the membrane resistance increased linearly with time. Best fits of the waveforms from 12 preparations gave the following values for the membrane resistance times unit length, membrane capacitance per unit length, and for the myoplasmic resistance: 1.22 plus or minus 0.13 x 10-5 omegacm, 0.224 plus or minus 0.023 uF with cm-minus 1, and 1.37 plus or minus 0.13 x 10-7 omegacm-minus 1, respectively. The value of membrane capacitance per unit length was close to that obtained from the time constant of the foot of the action potential and was in keeping with the generally satisfactory fit of the recorded waveforms with solutions of the cable equation in which the membrane impedance is that of a single capacitor and resistor in parallel. The area of membrane per unit length and the cross-sectional area of myoplasm at any given length of the preparation were determined from light and composite electron micrographs, and these were used to calculate the following values for the specific electrical membrane resistance, membrane capacitance, and the resistivity of the cytoplasm: 20.5 plus or minus 3.0 x 10-3 omegacm-2, l.54 plus or minus 0.24 uFWITHcm-minus 2, and 180 plus or minus 34 omegacm, respectively.     

Caged probes: a novel tool in studying symplasmic transport in plant tissues

Summary. Caged probes offer a novel approach to study plant cell-to-cell communication. Instead of introducing fluorescent molecules into cells by microinjection, their caged counterparts can be preloaded into the tissue by diffusion. Following spatially controlled photoactivation, movement of the uncaged fluorochrome can be followed in time and direction by confocal laser scanning microscopy. In the onion bulb scale epidermis used as a model system, symplasmic transport of the tracer out of a target cell was followed. Transport via the symplasmic pathway was challenged by plasmolysing the tissue. The experiments confirmed the symplasmic nature of tracer transport.Correspondence and reprints: Department of Plant Biology, Royal Veterinary and Agricultural University, Thorvaldsensvej 40, 1871 Frederiksberg C. Denmark. E-mail: hjm@kvl.dk     

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.