Membrane capacity of squid giant axon during hyper- and depolarizations

Summary The change in membrane capacitance and conductance of squid giant axons during hyper- and depolarizations was investigated. The measurements of capacitance and conductance were performed using an admittance bridge with resting, hyperpolarized and depolarized membranes. The duration of DC pulses is 20–40 msec and is long enough to permit the admittance measurements between 1 and 50 kHz. The amplitudes of DC pulses were varied between 0 and 40mV for both depolarization and hyperpolarization. Within these limited experimental conditions, we found a substantial increase in membrane capacitance with depolarization and a decrease with hyperpolarization. Our results indicate that the change in membrane capacitance will increase further if low frequencies are used with larger depolarizing pulses. The change in membrane capacitance is frequency dependent and it increases with decreasing frequencies. The analyses based on an equivalent circuit (vide infra) gives rise to a time constant of active membrane capacitance close to that of sodium currents. This result indicates that the observed capacitance changes may arise from sodium channels. A brief discussion is given on the nature of frequency-dependent membrane capacitance of nerve axons.     

An Electrophysiological Approach to Measure Changes in the Membrane Surface Potential in Real Time

Biological membranes carry fixed charges at their surfaces. These arise primarily from phospholipid headgroups. In addition, membrane proteins contribute to the surface potential with their charged residues. Membrane lipids are asymmetrically distributed. Because of this asymmetry, the net-negative charge at the inner leaflet exceeds that at the outer leaflet. Changes in surface potential are predicted to give rise to apparent changes in membrane capacitance. Here, we show that it is possible to detect changes in surface potential by an electrophysiological approach; the analysis of cellular currents relies on assuming that the electrical properties of a cell are faithfully described by a three-element circuit (i.e., the minimal equivalent circuit) comprised of two resistors and one capacitor. However, to account for changes in surface potential, it is necessary to add a battery to this circuit connected in series with the capacitor. This extended circuit model predicts that the current response to a square-wave voltage pulse harbors information, which allows for separating the changes in surface potential from a true capacitance change. We interrogated our model by investigating changes in the capacitance induced by ligand binding to the serotonin transporter and to the glycine transporters (GlyT1 and GlyT2). The experimental observations were consistent with the predictions of the extended circuit. We conclude that ligand-induced changes in surface potential (reflecting the binding event) and in true membrane capacitance (reflecting the concomitant conformational change) can be detected in real time even in instances in which they occur simultaneously.     

Integral correction of end-plate potentials: A useful alternative to peak amplitude correction

Validity of correction of peak amplitudes of end-plate potentials for non-linear summation of unit potentials may be affected by membrane capacitance and asynchrony of action of unit potentials. Compensatory adjustment for the opposing and interacting effects of these factors on the correction is difficult to calculate but may be circumvented by use of an integral correction procedure described here. This procedure involves correction of the voltage of the potential over its entire time course rather than at the peak only.     

Frequency domain impedance measurements of erythrocytes. Constant phase angle impedance characteristics and a phase transition.

We report measurements of the electrical impedance of human erythrocytes in the frequency range from 1 Hz to 10 MHz, and for temperatures from 4 to 40 degrees C. In order to achieve high sensitivity in this frequency range, we embedded the cells in the pores of a filter, which constrains the current to pass through the cells in the pores. Based on the geometry of the cells embedded in the filter a circuit model is proposed for the cell-filter saline system. A constant phase angle (CPA) element, i.e., an impedance of the form Z = A/(j omega)alpha, where A is a constant, j = square root of -1, omega is angular frequency, and 0 less than alpha less than 1 has been used to describe the ac response of the interface between the cell surface and the electrolyte solution, i.e., the electrical double layer. The CPA and other elements of the circuit model are determined by a complex nonlinear least squares (CNLS) fit, which simultaneously fits the real and imaginary parts of the experimental data to the circuit model. The specific membrane capacitance is determined to be 0.901 +/- 0.036 microF/cm2, and the specific cytoplasm conductivity to be 0.413 +/- 0.031 S/m at 26 degrees C. The temperature dependence of the cytoplasm conductivity, membrane capacitance, and CPA element has been obtained. The membrane capacitance increases markedly at approximately 37 degrees C, which suggests a phase transition in the cell membrane.     

The influence of sterols on pentachlorophenol-induced charge transfer across lipid bilayers studied by alternating current methods

The frequency dependence of membrane admittance has been determined for a series of phosphatidylcholine/sterol/n-decane bilayers in the presence of an aqueous environment containing pentachlorophenol. Variations in the results among membranes can be related to differences in the kinetic parameters of a kinetic model of pentachlorophenol-induced charge transport by characterizing both measurements and model behavior in terms of a common equivalent circuit. The kinetic model assumes a three-layer structure for the membrane and immediate environment. Data from membranes formed with beta-hydroxysterols having a flat ring structure and an intact side-chain (cholestanol, cholesterol, 7-dehydrocholesterol), after correction for sterol-induced membrane thinning, suggest that these sterols affect charge translocation by altering both interior fluidity and surface dipolar fields. The effects almost cancel for the case of cholesterol. These sterols also affect interfacial processes, either by inhibiting proton exchange between the aqueous and lipid environments, or by suppressing the adsorption of pentachlorophenol anions. Stigmasterol, coprostanol and epicholesterol cause only minor alterations in both translocation and interfacial processes. None of the sterols investigated has a significant influence on the capacitance of the interfacial region.     

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.     

Linear electrical properties of isolated cardiac cells

Summary A frequency domain equivalent circuit analysis of isolated ventricular cells indicated the presence of an internal membrane structure which has a total capacitance four- to sixfold larger than the surface membrane. The internal membrane was mainly attributed to the sarcoplasmic reticulum since other morphological studies have shown that its area is many-fold larger than that of the surface membrane. Corresponding estimates from the transverse tubular system indicate an area less than that of the surface; thus this structure is not a likely candidate for the observed internal capacitance. Measurements in hypertonic solutions showed that the access resistance to the internal membrane reversibly increased as the tonicity was elevated. Freeze-fractured electron microscopic studies confirmed that hypertonic solutions increased the volume of transverse tubular system, which thus appears to have little relation to the access resistance. The most probable source of the access resistance is the diadic junction to the sarcoplasmic reticulum, which therefore would electrically couple it to the surface membrane.     

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.     

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.     

The equivalent circuit of single crab muscle fibers as determined by impedance measurements with intracellular electrodes

The input impedance of muscle fibers of the crab was determined with microelectrodes over the frequency range 1 cps to 10 kc/sec. Care was taken to analyze, reduce, and correct for capacitive artifact. One dimensional cable theory was used to determine the properties of the equivalent circuit of the membrane admittance, and the errors introduced by the neglect of the three dimensional spread of current are discussed. In seven fibers the equivalent circuit of an element of the membrane admittance must contain a DC path and two capacitances, each in series with a resistance. In two fibers, the element of membrane admittance could be described by one capacitance in parallel with a resistance. In several fibers there was evidence for a third very large capacitance. The values of the elements of the equivalent circuit depend on which of several equivalent circuits is chosen. The circuit (with a minimum number of elements) that was considered most reasonably consistent with the anatomy of the fiber has two branches in parallel: one branch having a resistance R_e in series with a capacitance C_e; the other branch having a resistance R_b in series with a parallel combination of a resistance R_m and a capacitance C_m. The average circuit values (seven fibers) for this model, treating the fiber as a cylinder of sarcolemma without infoldings or tubular invaginations, are R_e = 21 ohm cm²; C_e = 47 µf/cm²; R_b = 10.2 ohm cm²; R_m = 173 ohm cm²; C_m = 9.0 µf/cm². The relation of this equivalent circuit and another with a nonminimum number of circuit elements to the fine structure of crab muscle is discussed. In the above equivalent circuit R_m and C_m are attributed to the sarcolemma; R_e and C_e, to the sarcotubular system; and R_b, to the amorphous material found around crab fibers. Estimates of actual surface area of the sarcolemma and sarcotubular system permit the average circuit values to be expressed in terms of unit membrane area. The values so expressed are consistent with the dielectric properties of predominantly lipid membranes.     

电压钳控制电流钳的设计

研究证明,传统膜片钳放大器在电流钳模式下记录到的快速电压信号会存在失真,且造成失真的根本原因是由于膜片钳的探头电路设计.为了克服这些缺陷重新设计了一种探头,新探头电路不仅能像传统的电压跟随器一样测量瞬态电压,而且适用于传统的电压钳工作模式.此外,一种命名为电压钳控制的电流钳技术被应用来改进传统的膜片钳放大器.用可变的低通滤波器来调整电压钳模块的响应速度,从而在实现膜电位钳位的同时准确记录快速电压信号.桥平衡电路用来消除命令电流流过串联电阻时带来的电压误差.而传统膜片钳中的快电容补偿环节则被改进用来补偿电极分布电容和探头放大器输入电容并提高电流钳模式下系统的响应速度.细胞模型实验结果表明,改进后的膜片钳放大器能够满足电生理研究中快速电位变化测量的需要.     

System for dynamic measurements of membrane capacitance in intact epithelial monolayers.

Dynamic measurements of exocytosis have been difficult to perform in intact epithelial monolayers. We have designed a system that estimates with +/-1% accuracy (99% confidence) the total membrane capacitance of monolayers represented by a lumped model. This impedance measurement and analysis system operates through a conventional transepithelial electrophysiology clamp, performing all signal measurements as frequently as every 5 s. Total membrane capacitance (the series combination of apical and basolateral membranes) is the inverse of one of three unique coefficients that describe the monolayer impedance. These coefficients are estimated using a weighted, nonlinear, least-squares algorithm. Using the estimated coefficients, solution ranges for individual membrane parameters are calculated, frequently providing results within +/-20% of true values without additional electrophysiological measurements. We determined the measurement system specifications and statistical significance of estimated parameters using 1) analytical testing with circuit simulation software and equation-generated data; 2) a system noise analysis combined with Monte Carlo simulations; and 3) analog model circuits for calibration of the electronic system and to check equation-generated results. Finally, the time course of capacitance changes associated with purinergically stimulated mucin exocytosis are quantified in monolayers of the colonic goblet cell-like cell line HT29-CI.16E.     

Distribution and kinetics of membrane dielectric polarization. II. Frequency domain studies of gating currents

We have studied the admittance of the membrane of squid giant axon under voltage clamp in the absence of ionic conductances in the range of 0-12 kHz for membrane potentials (V) between --130 and 70 mV. The admittance was measured at various holding potentials (HP) or 155 ms after pulsing from a given holding potential. Standard P/4 procedure was used to study gating currents in the same axons. We found that the membrane capacity Cm (omega) is voltage as well as frequency dependent. For any given V, the voltage-dependent part of the membrane capacitance has a maximum as the frequency approaches zero and requires at least a two-time constant equivalent circuit to be described. When the holding potential is varied, the voltage-dependent capacitance follows a bell- shaped curve with a maximum change of 0.15 muF/cm2 at about --60 mV. With the pulse method, the maximum is at --40 mV for HP = --70 and it shifts to --70 mV for HP = 0. The shift in the maximum of the voltage- dependent capacitance is consistent with the shift in the charge (Q) vs. V curve observed in our experiments with regular P/4 procedure when the HP is varied. Our data can be explained qualitatively by a four- state model for the sodium channel gating, where a charged particle can move within the field and interact with another particle not affected by the field.     

Capacitance measurements. An analysis of the phase detector technique used to study exocytosis and endocytosis.

We have studied the admittance of patch-clamped mast cells during exocytosis and found that they are adequately described by a four parameter equivalent circuit. On the basis of these measurements, we show that, contrary to current belief, when using a phase sensitive detector, small capacitance changes due to exocytosis or endocytosis should be studied by measuring current 90 degrees out of phase, relative to the component that corresponds to changes in series resistance. We have extended the theory on phase-detectors to include the errors in the estimation of step changes of membrane capacitance. We show that the measured capacitance of a secretory granule can be up to 80% smaller than its true value, during the course of a typical mast cell degranulation. We also describe a software-based phase-detector that simplifies capacitance measurements.     

Effect of stress on the membrane capacitance of the auditory outer hair cell.

The membrane capacitance of the outer hair cell, which has unique membrane potential-dependent motility, was monitored during application of membrane tension. It was found that the membrane capacitance of the cell decreased when stress was applied to the membrane. This result is the opposite of stretching the lipid bilayer in the plasma membrane. It thus indicates the importance of some other capacitance component that decreases on stretching. It has been known that charge movement across the membrane can appear to be a nonlinear capacitance. If membrane stress at the resting potential restricts the movement of the charge associated with force generation, the nonlinear capacitance will decrease. Furthermore, less capacitance reduction by membrane stretching is expected when the membrane is already extended by the (hyperpolarizing) membrane potential. Indeed, it was found that at hyperpolarized potentials, the reduction of the membrane capacitance due to stretching is less. The capacitance change can be described by a two state model of a force-producing unit in which the free energy difference between the contracted and stretched states has both electrical and mechanical components. From the measured change in capacitance, the estimated difference in the membrane area of the unit between the two states is about 2 nm2.     

Intracellular microelectrode measurements in small cells evaluated with the patch clamp technique.

Microelectrode penetration of small cells leads to a sustained depolarization of the resting membrane potential due to a transmembrane shunt resistance (Rs) introduced by the microelectrode. This has led to underestimation of the resting membrane potential of various cell types. However, measurement of the fast potential transient occurring within the first few milliseconds after microelectrode penetration can provide information about pre-impalement membrane electrophysiological properties. We have analyzed an equivalent circuit of a microelectrode measurement to establish the conditions under which the peak of the impalement transients (Ep) approaches the pre-impalement resting membrane potential (Em) of small cells most closely. The simulation studies showed that this is the case when the capacitance of the microelectrode is low and the membrane capacitance of the cell high. In experiments performed to assess the reliability of Ep as a measure of Em, whole-cell patch clamp measurements were performed in the current clamp mode to monitor, free from the effects of Rs, Em in cultured human monocytes. Microelectrode impalement of such patch clamped cells and measurement of Ep made it possible to detect correlation between Ep and Em and showed that for small cells such as human monocytes Ep is on average 6 mV less negative than the resting membrane potential.     

Photocurrents generated by bacteriorhodopsin on planar bilayer membranes

When purple-membrane fragments from Halobacterium halobium are added to one aqueous phase of a positively-charged black lipid membrane, the membrane becomes photoelectrically active. Under normal conditions the steady-state photo-current is extremely low, but increases considerably when the lipid bilayer is doped with proton-permeable gramicidin channels or with a lipophilic acid-base system. These findings indicate that the purple-membrane sheets are bound to the surface of the bilayer, forming a sandwich-like structure. The time-behaviour of the photocurrent may be interpreted on the basis of a simple equivalent circuit which contains the conductance and capacitance of the purple membrane in series with the conductance and capacitance of the lipid bilayer. From the dependence of the photocurrent on the polarization of the exciting light the average angle between the transition moment of the retinal chromophore and the plane of the bilayer was calculated to be about 28 degrees. Furthermore, it was shown that chromophore-free apomembrane binds to the lipid bilayer and that its photoelectrical activity can be restored in situ by adding all-trans-retinal to the aqueous phase.     

Electrical Impedance Analysis in Plant Tissues3

Based on the electrical model for plant tissue proposed by Hayden,Moyse, Calder, Crawford, and Fensom (1969), a method is describedfor calculating symplasmic resistance and cell membrane capacitancefrom impedances measured over a range of alternating current(AC) frequencies. The method of calculation has been appliedto ten different plant organs using frequencies from 20 Hz to300 KHz. In contrast with previous assumptions, it was foundthat both the symplasmic resistance and the membrane capacitancewere not constant but decreased with increasing frequency, giventhe constraints of the Hayden model. In cucumber fruit tissue,the symplasmic resistance was 20 000 ohms at 3 KHz but only1200 ohms at 200 KHz; the capacitance was 2.4 nF at 3 KHz butonly 0.8 nF at 200 KHz. The changes were similar in other materials,such as carrot root and cabbage leaf. It is concluded that theHayden model does not represent plant tissues accurately. Itis suggested that a better representation would be obtainedby including a capacitor in the component of the circuit whichrepresents the symplasm, in order to make allowance for membranesof organelles, particularly the vacuole. Key words: Electrical impedance, electrical modelling, membrane capacitance     

Impedance analysis of a tight epithelium using a distributed resistance model.

This paper develops techniques for equivalent circuit analysis of tight epithelia by alternating-current impedance measurements, and tests these techniques on rabbit urinary bladder. Our approach consists of measuring transepithelial impedance, also measuring the DC voltage-divider ratio with a microelectrode, and extracting values of circuit parameters by computer fit of the data to an equivalent circuit model. We show that the commonly used equivalent circuit models of epithelia give significant misfits to the impedance data, because these models (so-called "lumped models") improperly represent the distributed resistors associated with long and narrow spaces such as lateral intercellular spaces (LIS). We develop a new "distributed model" of an epithelium to take account of these structures and thereby obtain much better fits to the data. The extracted parameters include the resistance and capacitance of the apical and basolateral cell membranes, the series resistance, and the ratio of the cross-sectional area to the length of the LIS. The capacitance values yield estimates of real area of the apical and basolateral membranes. Thus, impedance analysis can yield morphological information (configuration of the LIS, and real membrane areas) about a living tissue, independently of electron microscopy. The effects of transport-modifying agents such as amiloride and nystatin can be related to their effects on particular circuit elements by extracting parameter values from impedance runs before and during application of the agent. Calculated parameter values have been validated by independent electrophysiological and morphological measurements.