Theory of initial current density in membrane voltage-clamp experiments

Herein we show that the voltage-clamp current density at zero time calculated from electrodiffusion equations is linear in the clamping voltage for a simple membrane (no charge structure) and for a membrae with fixed charges. Such membranes are nonexcitable. Excitable membranes can be represented by a homogeneous membrane with dipole layers at the surface. In this case the initial current density will be linear in the clamping voltage if a critical field for a dipole layer reorientation is not passed through in changing from holding to clamping potential. Otherwise, deviation from nonlinearity may occur. This is in agreement with experimental data for the squid giant axon.     

Reversible electrical breakdown of squid giant axon membrane

Charge pulse relaxation experiments were performed on squid giant axon. In the low voltage range, the initial voltage across squid axon membrane was a linear function of the injected charge. For voltages of the order of 1 V this relationship between injected charge and voltage across the membrane changes abruptly. Because of a high conductance state caused by these large electric fields the voltage across the membrane cannot be made large enough to exceed a critical value, Vc, defined as the breakdown voltage, Vc has for squid axon membrane a value of 1.1 V at 12 degrees C. During breakdown the specific membrane conductance exceeds 1 S. cm-2. Electrical breakdown produced by charge pulses of few microseconds duration have no influence on the excitability of the squid axon membrane. The resealing process of the membrane is so fast that a depolarizing breakdown is followed by the falling phase of a normal action potential. Thus, membrane voltages close to Vc open the sodium channels in few microseconds, but do not produce a decrease of the time constant of potassium activation large enough to cause the opening of a significant percentage of channels in a time of about 10 mus. It is probable that the reversible electrical breakdown is mainly caused by mechanical instability produced by electrostriction of the membrane (electrochemical model), but the decrease in the Born energy for ion injection into the membrane, accompanying the decrease in membrane thickness, may play also an important role. Because of the high conductance of the membrane during breakdown it seems very likely that this results in pore formation.     

Charge-shift probes of membrane potential. Characterization of aminostyrylpyridinium dyes on the squid giant axon.

The characteristics of transmittance and fluorescence changes of 4-(p-aminostyryl)-1-pyridinium dyes in response to voltage-clamp pulses on the squid giant axon were examined. A zwitterionic styryl dye displays transmittance and excitation spectra on the voltage-clamped squid axon with shapes similar to those previously measured on a model membrane system and consistent with a postulated electrochromic mechanism. The speed of the transmittance response is faster than 1.2 microseconds. The size of the fluorescence change is a factor of 40 lower than on the model membrane; this diminution can be rationalized in terms of the background fluorescence from Schwann cells and the nonoptimal geometric arrangement of the axon membrane. When the emission spectrum is dissected from the excitation response, a nonelectrochromic component is found. This component might result from molecular motion during the excited state lifetime. A positively charged dye permeates the axon membrane and displays complex response waveforms dependent on the method of application and the axon holding potential. This contrasts markedly with model membrane results where the behavior of the cationic and zwitterionic dyes were indistinguishable.     

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

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

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

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

Light scattering spectroscopy of the squid axon membrane

Light scattering studies on the giant squid axon were done using the technique of optical mixing spectroscopy. This experimental approach is based on the use of laser light to detect the fluctuations of membrane macromolecules which are associated with conductance fluctuations. The light scattering spectra were similar to the Lorentzian-like behavior of conductance fluctuations, possibly reflecting an underlying conformational change in the specific membrane sites responsible for the potassium ion conductance. The amplitude of the spectra measured, increased when the membrane was depolarized and decreased on hyperpolarization. The spectra were fit to the sum of two terms, a (1/fcomponent and a simple Lorentzian term. Spectra from deteriorating axons did not show sensitivity to membrane potential changes. It is shown theoretically that fluctuations due to the voltage-dependent variable, n, of the Hodgkin-Huxley formalism are identical to the voltage fluctuations. The derived power spectrum is that of a second order system, capable of showing resonance peaking only if the voltage dependence of the potassium rate constants is included in the analysis. The lack of resonance peaking in the observed light scattering spectra, indicates that the data are best described by a damped second order system.     

Effects of external ions on membrane potentials of a lobster giant axon

The effects of varying external concentrations of normally occurring cations on membrane potentials in the lobster giant axon have been studied and compared with data presently available from the squid giant axon. A decrease in the external concentration of sodium ions causes a reversible reduction in the amplitude of the action potential and its rate of rise. No effect on the resting potential was detected. The changes are of the same order of magnitude, but greater than would be predicted for an ideal sodium electrode. Increase in external potassium causes a decrease in resting potential, and a decrease in potassium causes an increase in potential. The data so obtained are similar to those which have been reported for the squid giant axon, and cannot be exactly fitted to the Goldman constant field equation. Lowering external calcium below 25 mM causes a reduction in resting and action potentials, and the occasional occurrence of repetitive activity. The decrease in action potential is not solely attributable to a decrease in resting potential. Increase of external calcium from 25 to 50 mM causes no change in transmembrane potentials. Variations of external magnesium concentration between zero and 50 mM had no measurable effect on membrane potentials. These studies on membrane potentials do not indicate a clear choice between the use of sea water and Cole's perfusion solution as the better external medium for studies on lobster nerve.     

Electrical characteristics of the ionic psn-junction as a model of the resting axon membrane

Summary As a model for the resting axon membrane, we propose the ionic psn-junction. Its electrical characteristics can be determined in close analogy to the corresponding electronic semiconductor junction. Using the semianalytic approximation, we calculated the electrical capacity and the ionic currents. In contrast to the abrupt pn-junction, the electrical capacity of the psn-junction turns out to be practically voltage-independent, as it is observed for the squid axon membrane. The passive ionic fluxes for K⁺, Na⁺ and Cl^–, as the main contributions to the total charge flux, are calculated and compared with literature data on the ion fluxes through the resting squid axon membrane as measured by use of radioactive tracers. From this comparison, the ionic permeabilities can be evaluated and used to compute the resting membrane conductivity, which is found to be close to the experimental value. Further evidence in favor of the proposed asymmetrical membrane structure and possible ways of its test by the methods of protein chemistry are discussed.Part of this work was carried out at the Institut für Physiologische Chemie, Universität München, during the tenure of a Habilitandenstipendium of the Deutsche Forschungsgemeinschaft.     

A physical model of sodium channel gating

Most current models of membrane ion channel gating are abstract compartmental models consisting of many undefined states connected by rate constants arbitrarily assigned to fit the known kinetics. In this paper is described a model with states that are defined in terms of physically plausible real systems which is capable of describing accurately most of the static and dynamic properties measured for the sodium channel of the squid axon. The model has two components. The Q-system consists of charges and dipoles that can move in response to an electric field applied across the membrane. It would contain and may compose the gating charge that is known to transfer prior to channel opening. The N-system consists of a charged group or dipole that is constrained to move only in the plane of the membrane and thus does not interact directly with the trans-membrane electric field but can interact electrostatically with the Q-system. The N-system has only two states, its resting state (channel closed) and its excited state (channel open) and its response time is very short in comparison with that of the Q-system. On depolarizing the membrane the the N-system will not make a transition to its open state until a critical amount of Q-charge transfer has occurred. Using only four adjustable parameters that are fully determined by fitting the equilibrium properties of the model to those of the sodium channel in the squid axon, the model is then able to describe with some accuracy the kinetics of channel opening and closing and includes the Cole and Moore delay. In addition to these predictions of the behaviour of assemblies of channels the model predicts some of the individual channel properties measured by patch clamp techniques.     

Possibility of electron tunneling through a nerve membrane

From a quantum mechanical standpoint, electron tunneling may occur in a nerve axon because the nerve membrane (60 to 100 angstroms) is thin enough for the tunnel effect and because the external solution and the axoplasma are redox systems which can provide electrons. Calculations and diagrams of the density-of-states are given to predict theN-shaped current-voltage characteristics which have been observed in the studies of squid giant axons, of the reconstituted liquid membranes and of the marine algae.     

Nonlinear cable equations for axons. II. Computations and experiments with external current electrodes

We have investigated the steady-state potential and current distributions resulting from current injection into a close-fitting channel into which a squid axon is placed. Hybrid computer solutions of the cable equations, using the Hodgkin-Huxley equations to give the membrane current density, were in good agreement with experimental observations. A much better fit was obtained when the Hodgkin-Huxley leakage conductance was reduced fivefold.     

Alignment of anilinonaphthalene-sulfonate and related fluorescent probe molecules in squid axon membrane and in synthetic polymers

As a fluorescent probe for the squid axon membrane, the behavior of 1-anilinonaphthalene-8-sulfonate (1,8-ANS) was found to be very different from that of its positional isomer, 2,6-ANS, or of the methylated derivative, 2,6-TNS. The degree of polarization of the fluorescent light contributing to a transient intensity reduction during nerve excitation was larger than about 0.7 for both 2,6-ANS and 2,6-TNS, while the corresponding value for 1,8-ANS in a squid axon was about 0.35.The physicochemical basis of this difference was investigated by measuring the fluorescence polarization of these probe molecules incorporated into poly(vinyl alcohol) sheets. In a stretched sheet of this synthetic polymer, 1,8-ANS showed poor alignment, while the 2,6-derivatives were highly oriented with their transition moments aligned approximately in the direction of stretching. Based on these findings, the experimental results obtained from squid axons were interpreted as an indication of the existence, at or near the membrane, of a longitudinally oriented macromolecular structure, bringing about a high degree of alignment of 2,6-ANS or 2,6-TNS molecules.It is clear that, as a probe for fluorescence polarization studies of macromolecular structures, 2,6-TNS is far superior to 1,8-ANS.     

Estimation of surface charges in some biological membranes.

The resting membrane potential data existing in the literature for the giant axon of the squid, frog muscle and barnacle muscle have been analyzed from the standpoint of the theory of membrane potential due to Kobatake and co-workers. The average values derived for the effective charge density phi chi (where phi is a constant, 0 less than phi less than 1, and represents the fraction of counterions that are free, and chi is the stoichiometric charge density in the membrane) present on the different biomembranes existing in their normal ionic environment are 0.3, 0.325 and 0.17 M for the squid axon, frog and barnacle muscles, respectively. On the assumption that the values of phi are 0.4 and 0.2 for nerve and muscle membranes, respectively, values of 0.75, 1.62 and 0.85 M have been derived for the stoichiometric charge density (chi) present in the respective biological membranes. These correspond to 1 negative charge per 222, 103 and 195 A2 of the membrane area of the squid axon, frog and barnacle muscles, respectively.     

Fluorescence of squid axon membrane labelled with hydrophobic probes

Summary Extrinsic fluorescence changes in squid giant axons were examined under a variety of experimental conditions using 2-p-toluidinylnaphthalene-6-sulfonate (TNS) and other fluorescent probes. Measurements of the degree of polarization of the fluorescent light (with the axis of the polarizer parallel to the longitudinal axis of the axon) indicated that the class of the TNS molecules in the axon membrane which participate in production of fluorescence signals have a definite orientation with their absorption and emission oscillators directed parallel to the long axis of the axon. Rectangular depolarizing voltage pulses produced a transient decrease in the fluorescent intensity, of which the early component is correlated tentatively with the rise in the membrane conductance. In response to hyperpolarizing pulses, there was an increase in fluorescence intensity which may be explained in terms of increased incorporation of TNS into the ordered structure in the membrane. Hyperpolarizing responses in KCl depolarized axons were accompanied by a change in fluorescent intensity. Tetrodotoxin appeared to suppress the initial component of the fluorescence signal produced by depolarizing clamping pulses. The technique for detecting these fluorescence changes and the physico-chemical properties of TNS are described in some detail.     

Effects of batrachotoxin on membrane potential and conductance of squid giant axons

The effects of batrachotoxin (BTX) on the membrane potential and conductances of squid giant axons have been studied by means of intracellular microelectrode recording, internal perfusion, and voltage clamp techniques. BTX (550–1100 nM) caused a marked and irreversible depolarization of the nerve membrane, the membrane potential being eventually reversed in polarity by as much as 15 mv. The depolarization progressed more rapidly with internal application than with external application of BTX to the axon. External application of tetrodotoxin (1000 nM) completely restored the BTX depolarization. Removal or drastic reduction of external sodium caused a hyperpolarization of the BTX-poisoned membrane. However, no change in the resting membrane potential occurred when BTX was applied in the absence of sodium ions in both external and internal phases. These observations demonstrate that BTX specifically increases the resting sodium permeability of the squid axon membrane. Despite such an increase in resting sodium permeability, the BTX-poisoned membrane was still capable of undergoing a large sodium permeability increase of normal magnitude upon depolarizing stimulation provided that the membrane potential was brought back to the original or higher level. The possibility that a single sodium channel is operative for both the resting sodium, permeability and the sodium permeability increase upon stimulation is discussed.     

Effects of the dipolar form of phloretin on potassium conductance in squid giant axons.

The effects of phloretin on membrane ionic conductances have been studied in the giant axon of the squid, Loligo pealei. Phloretin reversibly suppresses the potassium and sodium conductances and modifies their dependence on membrane potential (Em). Its effects on the potassium conductance (GK) are much greater than on the sodium conductance; no effects on sodium inactivation are observed. Internal perfusion of phloretin produces both greater shifts in GK(Em) and greater reductions maximum GK than does external perfusion; the effect of simultaneous internal and external perfusion is little greater than that of internal perfusion alone. Lowering the internal pH, which favors the presence of the neutral species of weakly acidic phloretin (pKa 7.4), potentiates the actions of internally perfused phloretin. Other organic cations with dipole moments similar to phloretin's have little effect on either potassium or sodium conductances in squid axons. These results can be explained by either of two mechanisms; on postulates a phloretin "receptor" near the voltage sensor component of the potassium channel which is accessible to drug molecules applied at either the outer or inner membrane surface and is much more sensitive to the neutral than the negatively charged form of the drug. The other mechanism proposes that neutral phloretin molecules are dispersed in an ordered array in the membrane interior, producing a diffuse dipole field which modifies potassium channel gating. Different experimental results support these two mechanisms, and neither hypothesis can be disproven.     

Collective Equilibrium Behaviour of Ion Channel Gating in Cell Membranes: An Ising Model Formulation

A statistical mechanical model for voltage-gated ion channels in cell membranes is proposed using the transfer matrix method. Equilibrium behavior of the system is studied. Representing the distribution of channels over the cellular membrane on a one-dimensional array with each channel having two states (open and closed) and incorporating channel–channel cooperative interactions, we calculate the fraction of channels in the open state at equilibrium. Experimental data obtained from batrachotoxin-modified sodium channels in the squid giant axon, using the cut-open axon technique, is best fit by the model when there is no interaction between the channels.     

Are axoplasmic microtubules necessary for membrane excitation?

Summary The excitability of the squid giant axon was studied as a function of transmembrane hydrostatic pressure differences, the latter being altered by the technique of intracellular perfusion. When a KF solution was used as the internal medium, a pressure difference of about 15 cm water had very little effect on either the membrane potential or excitability. However, within a few minutes after introducing either a KCl-containing, a KBr-containing, or a colchicine-containing solution as the internal medium, with the same pressure difference across the membrane, the axon excitability was suppressed. In these cases, removal of the pressure difference restored the excitability, indicating that the structure of membrane was not irreversibly damaged. Electron-microscopic observations of these axons revealed that the perfusion with a KF solution or colchicine-containing solution preserves the submembranous cytoskeletal layer, whereas perfusion with a KCl or KBr solution dissolves it. These results suggest that the submembranous cytoskeletons including microtubules provide an important mechanical support to the excitable membrane but are not essential elements in channel activities.     

A study of the effects of externally applied sodium-ions and detection of spatial non-uniformity of the squid axon membrane under internal perfusion

Electrical properties of the axon membrane were examined under internal perfusion of squid giant axons with a dilute solution of NaF or CsF. The rate of propagation of the action potential was markedly enhanced when NaCl was added to the external CaCl₂ solution. The membrane conductance both at rest and during the action potential was increased with increasing Na-concentration in the external medium. In the perfusion zone of these axons, the action potentials in different parts of the membrane were found to terminate in a more-or-less spatially random and temporally irregular fashion. When the electric field outside the axon membrane was examined with hyperfine glass-pipette electrodes, small rectangular potential changes of uniform amplitude were observed. The small potential changes, which resemble those obtained by Bean in EIM-treated lipid bilayer, were interpreted as indicating spatial non-uniformity of the axon membrane during excitation. The importance of long-range electric interaction between different parts of the axon membrane is emphasized.     

Currents recorded through small areas of squid axon membrane with an internal virtual ground voltage clamp.

A new voltage-clamp apparatus for the squid axon has been implemented to enable recording of currents through small areas of axon membrane. The performance of this clamp was tested by recording total sodium currents from perfused axons (I total) and sodium currents from small membrane patches (I patch), which were recorded from inside the axon with an L-shaped pipette. The I patch records, although four orders of magnitude smaller than I total, were stable and showed normal kinetics and voltage dependence, and appeared to reflect the activation of a small population of normal sodium channels. The size of the current recorded from the patch was mainly a function of the tip diameter of the L-shaped pipette and of the shunt resistance between inside the pipette and the axoplasm.