Voltage-clamp of cut-end skeletal muscle fibre: a diffusion experiment

Membrane potential and current were studied in cut end fibres of frog skeletal muscle under current and voltage clamp conditions, by the double sucrose gap technique. Similar action potentials were recorded under current clamp conditions with either the microelectrode or the double sucrose gap techniques. Under voltage clamp conditions, the control of the membrane potential was maintained adequately. The early current was sensitive to both TTX and external Na concentration suggesting that the current was carried by Na ions. Sodium current (INa) was subsequently analysed using the Hodgkin-Huxley formulae. INa half-activation and inactivation occurred at -34 mV and -60 mV, respectively. Na-rich solution applied internally by diffusion through cut ends produced a reduction of INa associated with a shift of the sodium current reversal potential (VNa) towards more negative membrane potentials. This suggested that the sodium electromotive force was reduced by the increase in internal Na content of the fibre. Iodate applied externally changed neither the activation nor the inactivation time courses of INa, but reduced the peak current. Conversely, internally applied by diffusion from the cut end of skeletal muscle fibre, iodate slowed down the time course of INa inactivation and decreased the current peak. In conclusion, the double sucrose gap technique adapted to cut end frog skeletal muscle fibre allows a satisfactory analysis of INa.     

An Assessment of the Double Sucrose-Gap Voltage Clamp Technique as Applied to Frog Atrial Muscle

The homogeneity of voltage clamp control in small bundles of frog atrial tissue under double sucrose-gap voltage clamp conditions was assessed by intracellular microelectrode potential measurements from cells in the test node region. The microelectrode potential measurements demonstrated that (1) good voltage control of the impaled cell existed in the absence of the excitatory inward currents (e.g., during small depolarizing clamp pulses of 10-15 mV), (2) voltage control of the impaled cell was lost during either the fast or slow excitatory inward currents, and (3) voltage control of the impaled cell was regained following the inward excitatory currents. Under nonvoltage clamp conditions the transgap recorded action potential had a magnitude and waveform similar to the intracellular microelectrode recorded action potentials from cells in the test node. Transgap impedance measured with a sine-wave voltage of 1,000 Hz was about 63% of that measured either by a sine-wave voltage of 10 Hz or by an action potential method used to determine the longitudinal resistance through the sucrose-gap region. The action potential data in conjunction with the impedance data indicate that the extracellular resistance (R_s) through the sucrose gap is very large with respect to the longitudinal intracellular resistance (R_i); the frequency dependence of the transgap impedance suggests that at least part of the intracellular resistance is paralleled by a capacitance. The severe loss of spatial voltage control during the excitatory inward current raises serious doubts concerning the use of the double sucrose-gap technique to voltage clamp frog atrial muscle.     

Axon voltage-clamp simulations. II. Double sucrose-gap method.

This is the second in a series of four papers on the simulation of the voltage clamp of cylindrical excitable cells. In this paper we evaluate the double sucrose-gap voltage-clamp technique for the squid and lobster giant axons. Using the Crank-Nicolson method of solution of the cable equations and differential equations representing the voltage clamp circuit we studied the effect of length of the sucrose gap "node" on the voltage profile along an excitable cell during a simulated voltage clamp. The voltage gradients along the region of the cell within the node produce "notches" in the current recording as well as changes in the magnitude of the sodium and potassium current for a given voltage step. Our results show that good voltage clamp control requires node lengths less than one-half the axon diameter.     

Computed Membrane Currents in Cardiac Purkinje Fibers during Voltage Clamps

Recent measurements have indicated that some of the cardiac cell electrical capacitance is in series with a resistance. The computations of currents in a voltage clamp presented below show that, in this case, there is a danger that capacitive transient currents recorded during voltage clamp experiments may be confused with currents arising through rapid active membrane conductance changes. Secondly, a voltage clamp technique aimed at avoiding capacitive transients, namely the linear or ramp clamp, has recently been introduced. An attempt has been made here to evaluate the usefulness of ramp clamps in studying membrane electrical properties, by computing ramp clamp results and considering the difficulties in reconstructing the original model from these results. It is concluded that such a reconstruction is not feasible.     

Influence of intercellular clefts on potential and current distribution in a multifiber preparation.

A theoretical model is presented for current and voltage clamp of multifiber bundles in a double sucrose gap. Attention is focused on methodological errors introduced by the intercellular cleft resistance. The bundle is approximated by a continuous geometry. Voltage distribution, as a function of radial distance and time, is defined by a parabolic partial differential equation which is specified for different membrane characteristics. Assuming a linear membrane, analytical solutions are given for current step and voltage step conditions. The theoretical relations (based on Bessel functions) may be used to calculate membrane conductance and capacity from experimental clamp data. The case of a nonlinear membrane with standard Hodgkin-Huxley kinetics for excitatory Na current is treated assuming maximum Na conductances (gNa) of 120, 10, and 1 mmho/cm2. Numerical simulations are presented for potential and current distribution in a bundle of 60 microns diameter during depolarizing voltage steps. Adequate voltage control is restricted to the peripheral fibers of the bundle whereas the membrane potential of the inner fibers deviates from the command level during early inward current, tending to the Na equilibrium potential. In the peak current-voltage diagram the loss of voltage control is reflected by an increased steepness of the negative region and a decreased slope conductance of the positive region. With gNa = 120 mmho/cm2, the positive slope conductance is approximately 25% of the slope expected from ideal space clamping. With the lower values of gNa, the slope conductance ratio is in the order of 50%. Implications of the results for an experimental voltage clamp analysis of early inward current on multifiber preparations are discussed.     

Voltage clamp simulations for multifiber bundles in a double sucrose gap: cable complications

A theoretical model is presented for voltage clamp of a bundle of cylindrical excitable cells in a double sucrose gap. The preparation in the test node is represented by a single one-dimensional cable (length/diameter ratio approximately) with standard Hodgkin-Huxley kinetics for transmembrane Na current. Imperfections of voltage control due to internal (longitudinal) resistivity and external (radial) resistance in series to the membrane are analysed. The electrical behavior of a fiber is described by the cable equation with appropriate boundary conditions and subsidiary equations reflecting the membrane characteristics. Membrane voltage and current distribution in response to a step command was obtained by numerical integration. The results are described in two papers. The present paper deals with the effect of internal resistivity with the external resistance being neglected. The closed loop response of a fiber displays a strong tendency to oscillate. To stabilize the system a phase lead was inserted and the gain of the control amplifier was reduced. Conditions for stability were examined by Nyquist analysis. When the Na system was activated by a command pulse below ENa, a voltage gradient developed between a depolarization (relative to the command signal) at the end where voltage was monitored and a hyperpolarization at the site of current injection. In spite of a poor voltage control the total measured current appeared to have a smooth transient. With large voltage gradients a small, second inward current was seen. At a low (high) Na conductance maximum peak inward current was larger (smaller) that the current expected from ideal space clamping.     

Electrical characteristics of frog atrial trabeculae in the double sucrose gap.

The electrical behavior of small single frog atrial trabeculae in the double sucrose gap has been investigated. The currents injected during voltage clamp experiments did not behave as predicted from the assumption of spatial uniformity of the voltage across a Hodgkin-Huxley membrane. Much of the difference is due to the geometrical complexities of this tissue. Nonetheless, two transient inward currents have been identified, the faster of which is blocked by tetrodotoxin (TTX). The magnitude of the slower transient varies markedly between preparations but always increases in a given preparation with increase of external calcium. The fast transient current traces, at small to intermediate depolarizations, are often marred by the presence of notches and secondary peaks due most probably to the loss of space clamp conditions. In many preparations these could be removed by reducing the current magnitude through application of a partially-blocking dose of TTX. Conversely, in the preparations whose fast transient was fully blocked by TTX, notches and secondary peaks in the slow transient could by induced through increasing calcium concentration and thereby the slow current magnitude. Previously used techniques for the measurement of the reversal potential of the fast inward transient have been shown to be invalid. In so far as they can be measured, the reversal potentials of the fast and slow inward transient are in the same neighborhood, i.e. around 120 mV from rest. The true values may be quite a bit apart. The total charge flow in the capacitive transient was measured for different sized nodes and preparations. From these data and estimates of plasma membrane area per unit trabecular volume, specific membrane capacitances of around 3 muF/cm2 were calculated for small bundles. The apparent ion current densities on this basis are approximately 1/10 of those measured in axons. The capacitive current occurring in small bundles decayed as the sum of at least three exponential functions of time. On the basis of these data and the anomalously large stable node widths, we suggest a coaxial core model of the preparation with the inner elements in series with an additional large extracellular resistance.     

Voltage Clamp of Cardiac Muscle: A Theoretical Analysis of Early Currents in the Single Sucrose Gap

A theoretical model is presented for the early currents in the voltage clamp of cardiac muscle using the single sucrose gap technique. The preparation is represented by a single one-dimensional active cable with modified Hodgkin-Huxley membrane and the interent imperfections in the technique are also included, e.g., leakage through the sucrose gap and resistance in series with the membrane in the test compartment. The stability of the control system was found to depend on the position of the control point with respect to the sucrose gap border. Computed currents for a stable system closely resembled those in the literature and those from a near-ideal system (e.g., squid axon.) The potential immediately across the membrane, however (not including potential drops across the series resistance external to the membrane), was found to be essentially uncontrolled and the “current-voltage” relationship was shown to be almost independent of membrane properties.     

Membrane Currents in Mammalian Ventricular Heart Muscle Fibers Using a Voltage-Clamp Technique

Bundles of sheep ventricular fibers were voltage-clamped utilizing a modified sucrose gap technique and intracellular voltage control. An action potential was fired off in the usual way, and the clamp circuit was switched on at preselected times during activity. Clamping the membrane back to its resting potential during the early part of an action potential resulted in a surge of inward current. The initial amplitude of this current surge decreased as the clamp was switched on progressively later during the action potential. Inward current decreasing as a function of time was also recorded if the membrane potential was clamped beyond the presumed K equilibrium potential (to -130 mv). Clamping the membrane to the inside positive range (+40 mv to +60 mv) at different times of an action potential resulted in a step of outward current which was not time-dependent. The results suggest that normal repolarization of sheep ventricle depends on a time-dependent decrease of inward current (Na, Ca) rather than on a time-dependent increase of outward current (K).     

Fusion of membranes during fertilization. Increases of the sea urchin egg''s membrane capacitance and membrane conductance at the site of contact with the sperm

The early events of fertilization that precede and cause activation of an egg have not been fully elucidated. The earliest electrophysiological change in the sea urchin egg is a sperm-evoked increase of the egg's membrane conductance. The resulting depolarization facilitates entry of the fertilizing sperm and precludes the entry of supernumerary sperm. The sequence of the increase in the egg's membrane conductance, gamete membrane fusion, egg activation, and sperm entry, including causal relationships between these events, are not known. This study reports the use of whole egg voltage clamp and loose patch clamp to monitor simultaneously changes of membrane conductance and capacitance at the site of sperm-egg contact. Measurements were made during sperm-egg interactions where sperm entry readily proceeded or was precluded by maintaining the egg's membrane potential either at large, negative values or at positive values. Whenever the sperm evoked an increase of the egg's membrane conductance, that increase initiated abruptly, was localized to the site of sperm attachment, and was accompanied by a simultaneous abrupt increase of the membrane capacitance. This increase of capacitance indicated the establishment of electrical continuity between gametes (possibly fusion of the gametes' plasma membranes). If sperm entry was blocked by large negative membrane potentials, the capacitance cut off rapidly and simultaneously with a decrease of the membrane conductance, indicating that electrical continuity between gametes was disrupted. When sperm entry was precluded by positive membrane potentials, neither conductance nor capacitance increased, indicating that sperm entry was halted before the fusion of membranes. A second, smooth increase of capacitance was associated with the exocytosis of cortical granules near the sperm in eggs that were activated. Electrical continuity between the gametes always preceded activation of the egg, but transient electrical continuity between the gametes alone was not always sufficient to induce activation.     

Two-microelectrode voltage clamp of Xenopus oocytes: voltage errors and compensation for local current flow.

Oocytes from Xenopus laevis are commonly used as an expression system for ion channel proteins. The most common method for their electrophysiological investigation is the two-microelectrode voltage clamp technique. The quality of voltage clamp recordings obtained with this technique is poor when membrane currents are large and when rapid charging of the membrane is desired. Detailed mathematical modeling of the experimental setup shows that the reasons for this weak performance are the electrical properties of the oocytes and the geometry of the setup. We measured the cytosolic conductivity to be approximately 5 times lower than that of the typical bath solution, and the specific membrane capacitance to be approximately 6 times higher than that of a simple lipid bilayer. The diameter of oocytes is typically approximately 1 mm, whereas the penetration depth of the microelectrodes is limited to approximately 100 microm. This eccentric current injection, in combination with the large time constants caused by the low conductivity and the high capacitance, yields large deviations from isopotentiality that decay slowly with time constants of up to 150 micros. The inhomogeneity of the membrane potential can be greatly reduced by introducing an additional, extracellular current-passing electrode. The geometrical and electrical parameters of the setup are optimized and initial experiments show that this method should allow for faster and more uniform control of membrane potential.     

Electrical Response to Vibration of a Lipid Bilayer Membrane

The discovery and characterization of a vibration response in a black lipid bilayer membrane is the topic of this paper. An electrical vibration response is obtained when the membrane is under voltage clamp and a weaker, but significant, response is obtained under current clamp. The effect arises from an induced variation in the membrane capacitance. It is further shown that the capacitance variation arises from a change in the membrane area as the membrane undergoes drumhead vibration. Possible physiological significance in mechanoreception is discussed.     

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.     

Patch voltage clamp of squid axon membrane.

A small area (patch) of the external surface of a squid axon can be "isolated" electrically from the surrounding bath by means of a pair of concentric glass pipettes. The seawater-filled inner pipette makes contact with the axon and constitutes the external access to the patch. The outer pipette is used to direct flowing sucrose solution over the area surrounding the patch of membrane underlying the inner pipette. Typically, sucrose isolated patches remain in good condition (spike amplitude greater than 90 mV) for periods of approximately one half hour. Patches of axon membrane which had previously been exposed to sucrose solution were often excitable. Membrane survival of sucrose treatment apparently arises from an outflow of ions from the axon and perhaps satellite cells into the interstitial cell space surrounding the exolemma. Estimate of the total access resistance (electrode plus series resistance) to the patch is about 100 komega (7 omega cm2). Patch capacitance ranges from 10-100 pF, which suggests areas of 10(-4) to 10(-5) cm2 and resting patch resistances of 10-100 Momega. Shunt resistance through the interstitial space exposed to sucrose solution, which isolates the patch, is typically 1-2 Momega. These parameters indicate that good potential control and response times can be achieved on a patch. Furthermore, spatial uniformity is demonstrated by measurement of an exoplasmic isopotential during voltage clamp of an axon patch. The method may be useful for other preparations in which limited membrane area is available or in special instances such as in the measurement of membrane conduction noise.     

Influence of conductance changes on patch clamp capacitance measurements using a lock-in amplifier and limitations of the phase tracking technique.

We characterized the influence of conductance changes on whole-cell patch clamp capacitance measurements with a lock-in amplifier and the limitations of the phase-tracking method by numerical computer simulations, error formulas, and experimental tests. At correct phase setting, the artifacts in the capacitance measurement due to activation of linear conductances are small. The cross talk into the capacitance trace is well approximately by the second-order term in the Taylor expansion of the admittance. In the case of nonlinear current-voltage relationships, the measured conductance corresponds to the slope conductance in the range of the sine wave amplitude, and the cross talk into the capacitance trace corresponds to the second-order effect of the slope conductance. The finite gating kinetics of voltage-dependent channels generate phase-shifted currents. These lead to major artifacts in the capacitance measurements when the angular frequency of the sine wave is close to the kinetic rate constant of the channel. However, when the channel kinetics are sufficiently slow, or sufficiently fast, the cross talk is still close to the second-order effect of the measured conductance. The effects of activation of voltage-dependent currents on the capacitance measurements may be estimated, provided a detailed characterization of the kinetics and voltage dependence is available. A phase error of the lock-in amplifier of a few degrees leads to significant projections. The phase-tracking method can be used to keep the phase aligned only during periods of low membrane conductance. However, nonideal properties of the equivalent circuit, in particular the fast capacitance between the pipette and the bath solutions, may lead to large phase errors when the phase-tracking method is used, depending on the electrical properties of the cell. In this article we provide practical values, setting the range where possible artifacts are below defined limits. For proper evaluation of capacitance measurements, the capacitance and conductance traces should always be displayed together.     

Membrane tension directly shifts voltage dependence of outer hair cell motility and associated gating charge.

The unique electromotility of the outer hair cell (OHC) is believed to promote sharpening of the passive mechanical vibration of the mammalian basilar membrane. The cell also presents a voltage-dependent capacitance, or equivalently, a nonlinear gating current, which correlates well with its mechanical activity, suggesting that membrane-bound voltage sensor-motor elements control OHC length. We report that the voltage dependence of the gating charge and motility are directly related to membrane stress induced by intracellular pressure. A tracking procedure was devised to continuously monitor the voltage at peak capacitance (VpkCm) after obtaining whole cell voltage clamp configuration. In addition, nonlinear capacitance was more fully evaluated with a stair step voltage protocol. Upon whole cell configuration, VpkCm was typically near -20 mV. Negative patch pipette pressure caused a negative shift in VpkCm, which obtained a limiting value near the normal resting potential of the OHC (approximately -70 mV) at the point of cell collapse. Positive pressure in the pipette caused a positive shift that could reach values greater than 0 mV. Measures of the mechanical activity of the OHC mirrored those of charge movement. Similar membrane-tension dependent peak shifts were observed after the cortical cytoskeletal network was disrupted by intracellular dialysis of trypsin from the patch pipette. We conclude that unlike stretch receptors, which may sense tension through elastic cytoskeletal elements, the OHC motor senses tension directly. Furthermore, since the voltage dependence of the OHC nonlinear capacitance and motility is directly regulated by intracellular turgor pressure, we speculate that modification of intracellular pressure in vivo provides a mechanism for controlling the gain of the mammalian "cochlear amplifier".     

The Xenopus Oocyte Cut-open Vaseline Gap Voltage-clamp Technique With Fluorometry

The cut-open oocyte Vaseline gap (COVG) voltage clamp technique allows for analysis of electrophysiological and kinetic properties of heterologous ion channels in oocytes. Recordings from the cut-open setup are particularly useful for resolving low magnitude gating currents, rapid ionic current activation, and deactivation. The main benefits over the two-electrode voltage clamp (TEVC) technique include increased clamp speed, improved signal-to-noise ratio, and the ability to modulate the intracellular and extracellular milieu.Here, we employ the human cardiac sodium channel (hNa_V1.5), expressed in Xenopus oocytes, to demonstrate the cut-open setup and protocol as well as modifications that are required to add voltage clamp fluorometry capability.The properties of fast activating ion channels, such as hNa_V1.5, cannot be fully resolved near room temperature using TEVC, in which the entirety of the oocyte membrane is clamped, making voltage control difficult. However, in the cut-open technique, isolation of only a small portion of the cell membrane allows for the rapid clamping required to accurately record fast kinetics while preventing channel run-down associated with patch clamp techniques.In conjunction with the COVG technique, ion channel kinetics and electrophysiological properties can be further assayed by using voltage clamp fluorometry, where protein motion is tracked via cysteine conjugation of extracellularly applied fluorophores, insertion of genetically encoded fluorescent proteins, or the incorporation of unnatural amino acids into the region of interest¹. This additional data yields kinetic information about voltage-dependent conformational rearrangements of the protein via changes in the microenvironment surrounding the fluorescent molecule.     

Developmental Expression of the Outer Hair Cell Motor Prestin in the Mouse

The development of motor protein activity in the lateral membrane of the mouse outer hair cell (OHC) from postnatal day 5 (P5) to P18 was investigated under whole-cell voltage clamp. Voltage-dependent, nonlinear capacitance (C _v), which represents the conformational fluctuations of the motor molecule, progressively increased during development. At P12, the onset of hearing in the mouse, C _v was about 70% of the mature level. C _v saturated at P18 when hearing shows full maturation. On the other hand, C _lin, which represents the membrane area of the OHC, showed a relatively small increase with development, reaching steady state at P10. This early maturation of linear capacitance is further supported by morphological estimates of surface area during development. These results, in light of recent prestin knockout experiments and our results with quantitative polymerase chain reaction, suggest that, rather than the incorporation of new motors into the lateral membrane after P10, molecular motors mature to augment nonlinear capacitance. Thus, current estimates of motor protein density based on charge movement may be exaggerated. A corresponding indicator of motor maturation, the motor’s operating voltage midpoint, V _pkcm, tended to shift to depolarized potentials during postnatal development, although it was unstable prior to P10. However, after P14, V _pkcm reached a steady-state level near −67 mV, suggesting that intrinsic membrane tension or intracellular chloride, each of which can modulate V _pkcm, may mature at P14. These developmental data significantly alter our understanding of the cellular mechanisms that control cochlear amplification and provide a foundation for future analysis of genetic modifications of mouse auditory development.     

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.