Core-coat conductor of lipid bilayer and micromachined silicon

We have etched a groove into a (110) plane of silicon and have covered it with a bilayer of glycerol monooleate. We have varied the depth of the groove, the concentration of salt in the electrolyte and the density of gramicidin in the membrane. We have clamped one end of the groove at a constant voltage with respect to the bath keeping the other end sealed or electrically open with respect to the bath. We have measured (i) the voltage at the center of the groove and at the sealed distal end and (ii) the current through the system in sealed and open configuration. We have found that the spread of voltage is in quantitative agreement with the stationary solutions of Kelvin's equation for a homogeneous cable.     

The electrical response to light of bacteriorhodopsin in planar membranes.

We have measured the light-induced short-circuit current generated by a planar membrane containing bacteriorhodopsin incorporated by vesicle fusion. The experimental results are consistent with an equivalent electrical circuit analogue that assumes that the vesicles remain intact after fusion and that the current generator equivalent of the light-driven proton pump is linearly dependent on bias voltage. The transient response to light of the planar membrane has also been examined. Slow response times are seen to be associated with the capacitive charging and discharging of the fused vesicles. A study of the leading edge of the light response curve of the planar membrane yields information about the transient response of the light-driven proton pump. We propose that the translocation of protons across the membrane is associated with a first-order process characterized by a rate constant lambda.     

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.     

Cellular and paracellular resistances of theNecturus proximal tubule

Summary Individual resistances of the apical cell membrane,R _a , the basolateral cell membrane,R _bl , and the paracellular shunt,R _s , were determined in theNecturus proximal tubule using a set of three electrical parameters. Four electrical parameters were measured: the transepithelial resistance, (R _te ), the apical and basolateral cell membrane resistance in parallel, (R _Z free-flow tubules), the basolateral cell membrane resistance in oil-filled tubules, (R _Z oil-filled), and the ratio of apical and basolateral cell membrane resistance (R _a /R _bl ).R _te was determined from an analysis of the spatial decay of luminal voltage following luminal current injection.R _Z free-flow andR _Z oil-filled were measured by the analysis of the spatial decay of intracellular voltage deflections following cellular current injection in free flow and oil-filled tubules, respectively.R _a /R _bl was estimated from the ratio of voltage deflections across the apical and basolateral cell membranes following transepithelial current injection. In addition, the magnitude of cellular and luminal cable interactions was evaluated, by comparing the spatial decay of voltage deflections in the cell and in the lumen following intracellular current injection. The combined cell membrane resistance (R _a +R _bl ) is between one to two orders of magnitude greater than the paracellular resistance. This result supports the view that theNecturus proximal tubule is a leaky epithelium.     

Modelling the electrotonic structure of starburst amacrine cells in the rabbit retina: A functional interpretation of dendritic morphology

A detailed morphometric analysis of a Lucifer yellow-filled Cb amacrine cell was undertaken to provide raw data for the construction of a neuronal cable model. The cable model was employed to determine whether distal input-output regions of dendrites were electrically isolated from the soma and each other. Calculations of steady state electrotonic current spread suggested reasonable electrical communication between cell body and dendrites. In particular, the centripetal voltage attenuation revealed that a synaptic signal introduced at the distal end of the equivalent dendrite could spread passively along the dendrite and reach the soma with little loss in amplitude. A functional interpretation of this results could favour a postsynaptic rather than a presynaptic scheme for the operation of directional selectivity in the rabbit retina. On the other hand, dendrites of starburst amacrine cells process information electrotonically with a bias towards the centrifugal direction and for a restricted range of membrane resistance values the voltage attenuation in the centripetal direction suggests that the action of these dendrites can be confined locally. A functional interpretation of this result favours a presynaptic version of Vaney's cotransmission model which attempts to explain how the neural network of starburst amacrine cells might account for directionally selective responses observed in the rabbit retina.     

Measurement of GABA-evoked conductance changes of lobster muscle fibres by a three-microelectrode voltage clamp technique

The effective membrane conductance and capacity of lobster muscle fibres was measured by a three-intracellular-microelectrode voltage clamp technique. Conductance values agreed well with those determined under current clamp, by means of the 'short' cable equations. Reversible increases in conductance evoked by gamma-aminobutyric acid (GABA) were reflected by differences (delta V) in electrotonic potential amplitude recorded at the centre, and midway between the centre and fibre end respectively. GABA dose--conductance curves derived from cable theory or from delta V measurements were virtually identical. The effective capacity (ceff), determined from the area beneath the 'on' delta V capacity transient, yielded values of the membrane time constant consistently lower than those obtained by the graphical method of E. Stefani & A.B. Steinbach (J. Physiol., London. 203, 383-401 (1969)); one possible explanation for this discrepancy is discussed. In the presence of GABA, the effective capacity was reduced in a dose-related manner. The results were interpreted in terms of an equivalent circuit in which surface membrane was arranged in parallel with cleft-tubular membrane of finite conductance, charged through an access resistance. GABA was though to be decreasing ceff by selectively increasing the conductance of the cleft-tubular membranes.     

The resealing process of lipid bilayers after reversible electrical breakdown

The resealing process of lipid bilayer membranes after reversible electrical breakdown was investigated using two voltage pulses switched on together. Electrical breakdown of the membranes was induced with a voltage pulse of high intensity and short duration. The time course of the change in membrane conductance after the application of the high (short) voltage pulse was measured with a longer voltage pulse of low amplitude. The decrease in membrane conductance during the resealing process could be fitted to a single exponential curve with a time constant of 10-2 μs in the temperature range between 2 and 20°C. The activation energy for this exponential decay process was found to be about 50 kJ/mol, which might indicate a diffusion process. Above 25°C the resealing process is controlled by two exponential processes.The data obtained for the time course of the resealing process can be explained in terms of pore formation in the membranes in response to the high electrical field strength. A radius of about 4 nm is calculated for the initial pore size. From the assumed exponential change of the pore area with progressive resealing time a diffusion constant of 10^?8 cm²/s for lateral lipid diffusion can be estimated.     

Distributions of Potential in Cylindrical Coordinates and Time Constants for a Membrane Cylinder

A mathematical problem relating to membrane cylinders is stated and solved; its implications are illustrated and discussed. The problem concerns the volume distribution, in cylindrical coordinates, of the electric potential inside and outside a membrane cylinder of finite length (with sealed ends), during passive decay of an initially nonuniform membrane potential. The time constants for equalization with respect to the angle, theta, are shown to be typically about ten thousand times smaller than the time constant, tau(m) = R(m)C(m), for uniform passive membrane potential decay. The time constants for equalization with respect to length are shown to agree with those from one-dimensional cable theory; typically, they are smaller than tau(m) by a factor between 2 and 10. The relation of the membrane current density, I(m)(theta, x, t), to the values (at the outer membrane surface) of the extracellular potential phi(e)(r, theta, x, t) and of partial differential(2)phi(e)/ partial differentialx(2), is examined and it is shown that these quantities are not proportional to each other, in general; however, under certain specified conditions, all three of these quantities are proportional with each other and with phi(i)(r, theta, x, t) and partial differential(2)phi(i)/ partial differentialx(2) (at the inner membrane surface). The relation of these results to those of one-dimensional cable theory is discussed.     

Voltage and Ca(2+) dependence of pre-steady-state currents of the Na-Ca exchanger generated by Ca(2+) concentration jumps

The Ca(2+) concentration and voltage dependence of the relaxation kinetics of the Na-Ca exchanger after a Ca(2+) concentration jump was measured in excised giant membrane patches from guinea pig heart. Ca(2+) concentration jumps on the cytoplasmic side were achieved by laser flash-induced photolysis of DM-nitrophen. In the Ca-Ca exchange mode a transient inward current is generated. The amplitude and the decay rate of the current saturate at concentrations >10 microM. The integrated current signal, i.e., the charge moved is fairly independent of the amount of Ca(2+) released. The amount of charge translocated increases at negative membrane potentials, whereas the decay rate constant shows no voltage dependence. It is suggested that Ca(2+) translocation occurs in at least four steps: intra- and extracellular Ca(2+) binding and two intramolecular transport steps. Saturation of the amplitude and of the relaxation of the current can be explained if the charge translocating reaction step is preceded by two nonelectrogenic steps: Ca(2+) binding and one conformational transition. Charge translocation in this mode is assigned to one additional conformational change which determines the equilibrium distribution of states. In the Na-Ca exchange mode, the stationary inward current depends on the cytoplasmic Ca(2+) concentration and voltage. The K(m) for Ca(2+) is 4 microM for guinea pig and 10 microM for rat myocytes. The amplitude of the pre-steady-state current and its relaxation saturate with increasing Ca(2+) concentrations. In this mode the relaxation is voltage dependent.     

Mapping the distribution of outer hair cell voltage-dependent conductances by electrical amputation.

The mammalian outer hair cell (OHC) functions not only as sensory receptor, but also as mechanical effector; this unique union is believed to enhance our ability to discriminate among acoustic frequencies, especially in the kilohertz range. An electrical technique designed to isolate restricted portions of the plasma membrane was used to map the distribution of voltage-dependent conductances along the cylindrical extent of the cell. We show that three voltage-dependent currents, outward K, I(K,n), and I(Ca) are localized to the basal, synaptic pole of the OHC. Previously we showed that the lateral membrane of the OHC harbors a dense population of voltage sensor-motor elements responsible for OHC motility. This segregation of membrane molecules may have important implications for auditory function. The distribution of OHC conductances will influence the cable properties of the cell, thereby potentially controlling the voltage magnitudes experienced by the motility voltage sensors in the lateral membrane, and thus the output of the "cochlear amplifier."     

An Electrical Inspection of the Subsurface Cisternae of the Outer Hair Cell

The cylindrical outer hair cell (OHC) of Corti’s organ drives cochlear amplification by a voltage-dependent activation of the molecular motor, prestin (SLC26a5), in the cell’s lateral membrane. The voltage-dependent nature of this process leads to the troublesome observation that the membrane resistor-capacitor filter could limit high-frequency acoustic activation of the motor. Based on cable theory, the unique 30 nm width compartment (the extracisternal space, ECS) formed between the cell’s lateral membrane and adjacent subsurface cisternae (SSC) could further limit the influence of receptor currents on lateral membrane voltage. Here, we use dual perforated/whole-cell and loose patch clamp on isolated OHCs to sequentially record currents resulting from excitation at apical, middle, and basal loose patch sites before and after perforated patch rupture. We find that timing of currents is fast and uniform before whole-cell pipette washout, suggesting little voltage attenuation along the length of the lateral membrane. Prior treatment with salicylate, a disrupter of the SSC, confirms the influence of the SSC on current spread. Finally, a cable model of the OHC, which can match our data, indicates that the SSC poses a minimal barrier to current flow across it, thereby facilitating rapid delivery of voltage excitation to the prestin-embedded lateral membrane.     

Ladder network prediction of transients in linear spatially inhomogeneous cables

A numerical method is described for finding steady state and transient responses in electrically linear, spatially inhomogeneous cables. Spatial inhomogeneities are incorporated by representing the cable by a number of finite length uniform cylindrical segments, each having the radius and electrical characteristics of a small region along the cable. Input waveforms are approximated by truncated Fourier series of sinusoidal components. Output waveforms are produced by multiplying the input Fourier series sinusoids by their respective transfer functions between input and output points on the cable and summing the resultant output point sinusoids. The transfer functions, representing attenuation and phase shift for each input sinusoid, are obtained by numerical analysis of an electrical ladder network derived from the cylindrical segment model of the cable. Results are shown for application of this method to both cylindrical and expanding radius cable geometries.     

Electrical properties of sheep Purkinje strands. Electrical and chemical potentials in the clefts

The impedence of sheep Purkinje strands, measured to 3-5 kHz, is interpreted with circuit models based on morphology. The strand is described as a one-dimensional electrical cable. Clefts between myocytes of the strand allow radial current to flow in parallel with current across the outer membrane. A lumped model of the clefts, in which all the cleft membrane is in series with 100 omega-cm2, fits only below 20 Hz. Two distributed models, pie and disk, fit at all frequencies with somewhat different (31%) luminal resistivities, but with similar membrane parameters. Series resistance representing the endothelial sheath is small. Simulations of voltage clamp experiments include measured linear parameters and nonlinear membrane channels, as well as radial variation of cleft concentration, membrane flux, voltage, and current. Cleft potential is drastically nonuniform when sodium current flows. Cleft potential is reasonably uniform when calcium and potassium currents flow, but the calcium and potassium concentrations change markedly, enough to turn off the calcium current, even if the calcium channel did not inactivate. We conclude that physiological current flows produce significant nonuniformities in electrochemical potentials in the clefts of this cardiac preparation.     

The steady-state finite cable: Numerical method for non-linear membrane

An iterative numerical method is described for finding steady-state solutions to the one-dimensional cable equations for finite cable lengths and open-circuit termination. The method is suitable for any non-linear membrane with a single positive-slope crossing of the zero current axis, including those with regions of negative slope conductance. The method generates the current necessary to cause any desired voltage displacement at the input end of the cable as well as solutions for the transmembrane potential and axial current along the cable.     

A generalized tapering equivalent cable model for dendritic neurons

A mathematical model has been developed which collapses a dendritic neuron of complex geometry into a single electrotonically tapering equivalent cable. The modified cable equation governing the transient distribution of subthreshold membrane potential in a branching tree is transformed, becoming amenable to analytic solution. This transformation results in a Riccati differential equation whose six solutions (expressed in terms of elementary functions) control the amount and degree of taper found in the equivalent cable model. To illustrate the theory, an analytic solution (in series form) of the modified cable equation is obtained for a voltage-clamp present at the soma of a quadratically tapering equivalent cable whose distal end is sealed.     

Charge-pulse relaxation studies with lipid bilayer membranes modified by alamethicin

Charge-pulse relaxation studies with the alamethicin-lipid membrane system reveal a triphasic decay of membrane voltage. At short times (resolution time 2 microseconds), where a voltage decay due to the orientation of alamethicin dipoles from the interface into the membranes interior ("gating current") could possibly be expected, only a slow decrease with a time constant determined by the bare membrane conductance occurs. After approximately 1 ms (depending on the experimental conditions) the formation of alamethicin pores starts, leading to an increase in the voltage decay rate. When the characteristic voltage Vcpc is approached, pores close and after passing Vcpc the voltage decreases slowly again according to the bare membrane conductance. Vcpc is determined as a function of the initially applied voltage Vo, alamethicin and KCl concentration. Since the membrane voltage decreases continuously, the system does not reach the equilibrium states obtained at constant voltages. Taking the presented experimental results into account the estimate of the electrical potential at the functional membrane of photosynthesis induced by a saturating single turnover flash of deltaphio approximately 105-135 mV (Zickler, Witt and Boheim (1976) FEBS Lett. 66, 142-148) is changed to deltaphio approximately 200 mV.     

Membrane potential and input resistance are ambiguous measures of sealing of transected cable-like structures.

For many years, membrane potential (Vm) and input resistance have been used to characterize the electrophysiological nature of a seal (barrier) that forms at the cut end of a transected axon or other extended cytoplasmic structure. Data from a mathematical and an analog model of a transected axon and other theoretical considerations show that steady-state values of Vm and input resistance measured from any cable-like structure provide a very equivocal assessment of the electrical barrier (seal) at the cut end. Extracellular assessments of injury currents almost certainly provide a better electrophysiological measure of the status of plasma membrane sealing because measurements of these currents do not depend on the cable properties of extended cytoplasmic processes after transection.     

Evaluation of surface tension and ion occupancy effects on gramicidin A channel lifetime.

The surface tension of glycerylmonooleate-hexadecane lipid bilayer membranes and the lifetime of gramicidin A channels were measured at various concentrations of the surrounding solutions. For HCl the surface tension is essentially constant at approximately 5 mN/m up to approximately 1 M, whereas the average lifetime increases approximately 40-fold. At higher concentrations the surface tension decreases markedly. For CsCl the surface tension is constant up to about 1 M then increases with salt level. The average lifetime in this case increases about sixfold. In both cases the lifetime levels off and even decreases at higher salt levels. The increase in lifetime observed with ion activity is therefore qualitatively different from, and not explained by, the established dependence of lifetime on membrane properties (Elliot, J.R., D. Needham, J.P. Dilger, and D.A. Haydon. 1983. Biochim. Biophys. Acta. 735:95-103). We have previously proposed that ion occupancy is a determinant of channel stability, and to test this hypothesis the voltage dependence of channel lifetime was measured in asymmetrical solutions. For the case of a potassium chloride solution on one side of the membrane and a hydrogen chloride solution, on the other, the voltage dependence of the lifetime is asymmetrical. The asymmetry is such that when the electrical field is applied in the direction of the chemical gradient for each of the ions, the channel lifetime approaches, at increasing field strengths, that of a symmetrical solution of the respective ion. The voltage dependence of the surface tension, on the other hand, is negligible for the range of voltages used.(ABSTRACT TRUNCATED AT 250 WORDS)     

Membrane nanotubes in the electric field as a model for measurement of mechanical parameters of the lipid bilayer

Pulling a membrane cylindrical tubule from a planar bilayer lipid membrane held under a high lateral tension produces a nanotube (NT) with an internal radius of several nanometers. When NT is pulled in an electrolyte solution, its interior is conductive and the internal radius is calculated from the hyperbolic fitting of the NT conductance-length relationship. Depending on the membrane lipid composition, the internal radius of NT varies from 2 to 20 nm, the higher the cholesterol and lysolipid content, the wider the tubes. The application of an electrical field across the NT membrane allows variation of effective lateral tension according to the Lippman effect. The NT radii were measured at different values of voltage applied along NT, and the membrane bending modulus was recalculated upon the supposition that the shape of NT deviates from cylindrical only slightly. The calculated values of the phospholipid membrane stiffness obtained in this work correspond to previously published data.