Sodium currents in the giant axon of the crab Carcinus maenas

Measurements were made of the kinetics and steady-state properties of the sodium conductance changes in the giant axon of the crab Carcinus maenas. The conductance measurements were made in the presence of small concentrations of tetrodotoxin and as much electrical compensation as possible in order to minimize errors caused by the series resistance. After an initial delay of 10-150 microsec, the conductance increase during depolarizing voltage clamp pulses followed the Hodgkin-Huxley kinetics. Values of the time constant for the activation of the sodium conductance lay on a bell-shaped curve with a maximum under 180 microsec at -40 mV (at 18 degrees C). Values of the time constant for the inactivation of the sodium conductance were also fitted using a bell-shaped curve with a maximum under 7 msec at -70 mV. The effects of membrane potential on the fraction of Na channels available for activation studied using double pulse protocols suggest that hyperpolarizing potentials more negative than -100 mV lock a fraction of the Na channels in a closed conformation.     

Modelling action potentials and membrane currents of mammalian skeletal muscle fibres in coherence with potassium concentration changes in the T-tubular system

During prolonged activity the action potentials of skeletal muscle fibres change their shape. A model study was made as to whether potassium accumulation and removal in the tubular space is important with respect to those variations. Classical Hodgkin-Huxley type sodium and (potassium) delayed rectifier currents were used to determine the sarcolemmal and tubular action potentials. The resting membrane potential was described with a chloride conductance, a potassium conductance (inward rather than outward rectifier) and a sodium conductance (minor influence) in both sarcolemmal and tubular membranes. The two potassium conductances, the Na-K pump and the potassium diffusion between tubular compartments and to the external medium contributed to the settlement of the potassium concentration in the tubular space. This space was divided into 20 coupled concentric compartments. In the longitudinal direction the fibre was a cable series of 56 short segments. All the results are concerned with one of the middle segments. During action potentials, potassium accumulates in the tubular space by outward current through both the delayed and inward rectifier potassium conductances. In between the action potentials the potassium concentration decreases in all compartments owing to potassium removal processes. In the outer tubular compartment the diffusion-driven potassium export to the bathing solution is the main process. In the inner tubular compartment, potassium removal is mainly effected by re-uptake into the sarcoplasm by means of the inward rectifier and the Na-K pump. This inward transport of potassium strongly reduces the positive shift of the tubular resting membrane potential and the consequent decrease of the action potential amplitude caused by inactivation of the sodium channels. Therefore, both potassium removal processes maintain excitability of the tubular membrane in the centre of the fibre, promote excitation-contraction coupling and contribute to the prevention of fatigue. Received: 5 May 1998 / Revised version: 27 October 1998 / Accepted: 19 January 1999     

The localization of transport properties in the frog lens.

The selectivity of fiber-cell membranes and surface-cell membranes in the frog lens is examined using a combination of ion substitutions and impedance studies. We replace bath sodium and chloride, one at a time, with less permeant substitute ions and we increase bath potassium at the expense of sodium. We then record the time course and steady-state value of the intracellular potential. Once a new steady state has been reached, we perform a small signal-frequency-domain impedance study. The impedance study allows us to separately determine the values of inner fiber-cell membrane conductance and surface-cell membrane conductance. If a membrane is permeable to a particular ion, we presume that the conductance of that membrane will change with the concentration of the permeant ion. Thus, the impedance studies allow us to localize the site of permeability to inner or surface membranes. Similarly, the time course of the change in intracellular potential will be rapid if surface membranes are the site of permeation whereas it will be slow if the new solution has to diffuse into the intercellular space to cause voltage changes. Lastly, the value of steady-state voltage change provides an estimate of the lens' permeability, at least for chloride and potassium. The results for sodium are complex and not well understood. From the above studies we conclude: (a) surface membranes are dominated by potassium permeability; (b) inner fiber-cell membranes are permeable to sodium and chloride, in approximately equal amounts; and (c) inner fiber-cell membranes have a rather small permeability to potassium.     

Sodium currents in the giant axon of the crabCarcinus maenas

Summary Measurements were made of the kinetics and steady-state properties of the sodium conductance changes in the giant axon of the crabCarcinus maenas. The conductance measurements were made in the presence of small concentrations of tetrodotoxin and as much electrical compensation as possible in order to minimize errors caused by the series resistance. After an initial delay of 10–150 sec, the conductance increase during depolarizing voltage clamp pulses followed the Hodgkin-Huxley kinetics. Values of the time constant for the activation of the sodium conductance lay on a bell-shaped curve with a maximum under 180 sec at –40 mV (at 18°C). Values of the time constant for the inactivation of the sodium conductance were also fitted using a bell-shaped curve with a maximum under 7 msec at –70 mV. The effects of membrane potential on the fraction of Na channels available for activation studied using double pulse protocols suggest that hyperpolarizing potentials more negative than –100 mV lock a fraction of the Na channels in a closed conformation.     

Inactivation of the Sodium Current in Myxicola Giant Axons : Evidence for coupling to the activation process

Experiments were conducted on Myxicola giant axons to determine if the sodium activation and inactivation processes are coupled or independent. The main experimental approach was to examine the effects of changing test pulses on steady-state inactivation curves. Arguments were presented to show that in the presence of a residual uncompensated series resistance the interpretation of the results depends critically on the manner of conducting the experiment. Analytical and numerical calculations were presented to show that as long as test pulses are confined to an approximately linear negative conductance region of the sodium current-voltage characteristic, unambiguous interpretations can be made. When examined in the manner of Hodgkin and Huxley, inactivation in Myxicola is quantitatively similar to that described by the h variable in squid axons. However, when test pulses were increased along the linear negative region of the sodium current-voltage characteristic, steady-state inactivation curves translate to the right along the voltage axis. The shift in the inactivation curve is a linear function of the ratio of the sodium, conductance of the test pulses, showing a 5.8 mv shift for a twofold increase in conductance. An independent line of evidence indicated that the early rate of development of inactivation is a function of the rise of the sodium conductance.     

Inhibition of potassium conductance with external tetraethylammonium ion in Myxicola giant axons.

In voltage clamp experiments, externally applied tetraethylammonium ion (TEA) was found to have minimal effects on transient sodium currents and to suppress steady-state potassium currents of Myxicola giant axons by causing a specific decrease in the maximum potassium conductance gK. The dose-response curve suggests a one-to-one stoichiometry for TEA-receptor binding with an apparent dissociation constant on 24 mM. The suppression of IK is essentially reversible. Experiments performed on high external potassium ion concentrations indicate that both outward and inward IK were blocked by external TEA. The results thus suggest the presence of TEA receptors on the outer surface of Myxicola axonal membrane similar to those reported in the frog node.     

Two levels of resting potential in cardiac purkinje fibers

In an appropriate ionic environment, the resting potential of canine cardiac purkinje fibers may have either of two value. By changing the external K concentration, [K](0), in small steps, it was shown that, in the low (1 mM) Cl, Na-containing solutions used in this study, the two levels of resting potential could be obtained only within a narrow range of [K](0) values; that range was usually found between 1 and 4 mM. Within the critical [K](0) range the resting potential could be shifted from either level to the other by the application of small current pulses. It was shown that under these conditions the steady-state current- voltage relationship was “N-shaped,” and that a region of both negative slope, and negative chord conductance lay between the two stable zero-current potentials. The negative chord conductance was largely due to inward sodium current, only part of which was sensitive to tetrodotoxin (TTX). Under appropriate conditions, the negative chord conductance could be abolished by several experimental interventions and the membrane potential thereby shifted from the lower to the higher resting level: those interventions which were effective by presumably diminishing the steady-state inward current included reducing the external sodium concentration, adding TTX, or adding lidocaine; those which presumably increased the steady-state outward current included small increases in [K](0), brief depolarizations to around -20 mV, or the addition of acetylcholine chloride.     

On The Mechanism of Spontaneous Impulse Generation in the Pacemaker of the Heart

Rhythmic activity in Purkinje fibers of sheep and in fibers of the rabbit sinus can be produced or enhanced when a constant depolarizing current is applied. When extracellular calcium is reduced successively, the required current strength is less, and eventually spontaneous beating occurs. These effects are believed due to an increase in steady-state sodium conductance. A significant hyperpolarization occurs in fibers of the rabbit sinus bathed in a sodium-free medium, suggesting an appreciable sodium conductance of the "resting" membrane. During diastole, there occurs a voltage-dependent and, to a smaller extent, time-dependent reduction in potassium conductance, and a pacemaker potential occurs as a result of a large resting sodium conductance. It is postulated that the mechanism underlying the spontaneous heart beat is a high resting sodium current in pacemaker tissue which acts as the generator of the heart beat when, after a regenerative repolarization, the decrease in potassium conductance during diastole reestablishes the condition of threshold.     

Gating currents in the node of Ranvier: voltage and time dependence.

Like the axolemma of the giant nerve fibre of the squid, the nodal membrane of frog myelinated nerve fibres after blocking transmembrane ionic currents exhibits asymmetrical displacement currents during and after hyperpolarizing and depolarizing voltage clamp pulses of equal size. The steady-state distribution of charges as a function of membrane potential is consistent with Boltzmanns law (midpoint potential minus 33.7 mV; saturation value 17200 charges/mum-2). The time course of the asymmetry current and the voltage dependence of its time constant are consistent with the notion that due to a sudden change in membrane potential the charges undergo a first order transition between two configurations. Size and voltage dependence of the time constant are similar to those of the activation of the sodium conductance assuming m-2h kinetics. The results suggest that the presence of ten times more sodium channels (5000/mum-2) in the node of Ranvier than in the squid giant axon with similar sodium conductance per channel (2-3 pS).     

Glial and neuronal forms of the voltage-dependent sodium channel: characteristics and cell-type distribution

Two functionally different forms of the voltage-dependent sodium channel were observed in glia and in neurons of the mammalian nervous system. Both forms had identical conductance and tetrodotoxin sensitivity and displayed steady-state inactivation, a strongly voltage-dependent rate of activation, and a faster but weakly voltage-sensitive rate of inactivation. However, the glial form had significantly slower kinetics and a more negative voltage dependence, suggesting that it was functionally specialized for glia. This form was found in most glial types studied, while the neuronal form was observed in retinal ganglion cells, cortical motor neurons, and O2A glial progenitor cells. Both forms occurred in type-2 astrocytes. The presence of the glial form correlated with the RAN-2 surface antigen.     

Alamethicin channels incorporated into frog node of ranvier: calcium-induced inactivation and membrane surface charges

Alamethicin, a peptide antibiotic, partitions into artificial lipid bilayer membranes and into frog myelinated nerve membranes, inducing a voltage-dependent conductance. Discrete changes in conductance representing single-channel events with multiple open states can be detected in either frog node or lipid bilayer membranes. In 120 mM salt solution, the average conductance of a single channel is approximately 600 pS. The channel lifetimes are roughly two times longer in the node membrane than in a phosphatidylethanolamine bilayer at the same membrane potential. With 2 or 20 mM external Ca and internal CsCl, the alamethicin-induced conductance of frog nodal membrane inactivates. Inactivation is abolished by internal EGTA, suggesting that internal accumulation of calcium ions is responsible for the inactivation, through binding of Ca to negative internal surface charges. As a probe for both external and internal surface charges, alamethicin indicates a surface potential difference of approximately -20 to -30 mV, with the inner surface more negative. This surface charge asymmetry is opposite to the surface potential distribution near sodium channels.     

Kinetic properties of a voltage-dependent junctional conductance

We have proposed that the gap junctions between amphibian blastomeres are comprised of voltage-sensitive channels. The kinetic properties of the junctional conductance are here studied under voltage clamp. When the transjunctional voltage is stepped to a new voltage of the same polarity, the junctional conductance changes as a single exponential to a steady-state level. The time constant of the conductance change is determined by the existing transjunctional voltage and is independent of the previous voltage. For each voltage polarity, the relations between voltage, time constant, and steady-state conductance are well modeled by a reversible two-state reaction scheme in which the calculated rate constants for the transitions between the states are exponential functions of voltage. The calculated rate constant for the transition to the low-conductance state is approximately twice as voltage dependent as that for the transition to the high-conductance state. When the transjunctional voltage polarity is reversed, the junctional conductance undergoes a transient recovery. The polarity reversal data are well modeled by a reaction scheme in which the junctional channel has two gates, each with opposite voltage sensitivity, and in which an open gate may close only if the gate in series with it is open. A simple explanation for this contingent gating is a mechanism in which each gate senses only the local voltage drop within the channel.     

Potassium ion currents in the crayfish giant axon. Dynamic characteristics.

The kinetics of the voltage-sensitive potassium channel in crayfish axon have been examined. The conductance increase after a step depolarization from rest can be described by a first-order kinetic process raised to the third power. When conditioning voltage levels preceded the test pulse, the steady-state conductance was found to be independent of initial conditions. Depolarizing conditioning voltages in general allowed superposition of test voltage potassium currents by a shift along the time axis. Hyperpolarizing conditioning voltages produced a delay in onset of conductance during the test pulse and changed the kinetics so that superposition was not possible. The delay increased during the hyperpolarization with a first-order lag having a time constant in the range of 1.5-3 ms. Return to the resting level caused recovery from the delayed state to follow a single exponential decay with a time constant of 1.9-2.2 ms. The steady state delay vs. voltage curves were not saturated at potentials as negative as -180 mV.     

A model for conductance changes in the squid giant axon. II. Channel kinetics

The kinetics of the sodium and potassium channels in voltage clamped squid giant axon following a relaxation of the membrane subunits are examined and compared with the Hodgkin-Huxley equations. Mechanisms are suggested for the turn-off of the sodium conductance and a set of kinetic states are proposed for the potassium channel which are consistent with the experimental observations. Determination of the rate constants for relaxation of the surface subunits which triggers the subsequent changes within the independent channels provide information on the equilibrium constant and free energy for this process. The free energy is observed to approach zero as the depolarizing voltage of the clamp approaches $\text{E}{}_{\mathrm{<mtext>Na</mtext>}}$, the voltage for zero sodium current in voltage clamped axons. Analysis of the final rate constants in the kinetic sequence for potassium indicates a symmetry of the channel when it is in its steady-state configuration during clamp in the absence of external gradients.     

Kinetic analysis of pancuronium interaction with sodium channels in squid axon membranes

The interaction of pancuronium with sodium channels was investigated in squid axons. Sodium current turns on normally but turns off more quickly than the control with pancuronium 0.1-1mM present internally; The sodium tail current associated with repolarization exhibits an initial hook and then decays more slowly than the control. Pancuronium induces inactivation after the sodium inactivation has been removed by internal perfusion of pronase. Such pancuronium-induced sodium inactivation follows a single exponential time course, suggesting first order kinetics which represents the interaction of the pancuronium molecule with the open sodium channel. The rate constant of association k with the binding site is independent of the membrane potential ranging from 0 to 80 mV, but increases with increasing internal concentration of pancuronium. However, the rate constant of dissociation l is independent of internal concentration of pancuronium but decreases with increasing the membrane potential. The voltage dependence of l is not affected by changine external sodium concentration, suggesting a current-independent conductance block, The steady-state block depends on the membrane potential, being more pronounced with increasing depolarization, and is accounted for in terms of the voltage dependence of l. A kinetic model, based on the experimental observations and the assumption on binding kinetics of pancuronium with the open sodium channel, successfully simulates many features of sodium current in the presence of pancuronium.     

Determinants of time-dependent membrane conductance. The nonrole of classical ion-membrane molecule interactions

We have examined the steady-state and time-dependent electrical properties of a model membrane system. The model assumes that the directed velocity and energy of ions moving through the membrane are determined by the applied electric field, ionic diffusion forces, and central elastic collisions between ions and membrane molecules. A simple analysis of the steady-state electrical properties of the model yields results identical with ones obtained previously using a more complex analysis procedure. The time-dependent conductance changes of the model in response to a step change in electric field strength when there is solution symmetry display three qualitative patterns dependent on the nature of the ion-membrane molecule interaction. One of the patterns of conductance change is quite similar to that observed in the sodium conductance system of a number of excitable tissues: an initial conductance rise to a maximum (activation) followed by a decay to a final steady-state value (inactivation). However, the correspondence between the time-dependent model behavior and known experimental behavior of excitable systems is only qualitative. We conclude that the classical ion-membrane molecule interactions we consider are not involved in determining time-dependent conductance processes in the excitable systems for which comparison is possible.     

Effects of proteolytic enzymes on ionic conductances of squid axon membranes.

The effects of proteolytic enzymes on ionic conductances of squid axon membranes have been studied by means of the voltage clamp technique. When perfused internally alpha-chymotrypsin (1 mg/ml) increased and prolonged the depolarizing after-potential. Sodium inactivation was partially inhibited causing a prolonged sodium current, and peak sodium and steady-state potassium currents were suppressed. The time for sodium current to reach its peak was not affected. Leakage conductance increased later. On the other hand, carboxypeptidases A and B, both at 1mg/ml, suppressed the sodium and potassium conductance increases with little or no change in sodium inactivation. The mechanism that controls sodium inactivation appears to be associated with the structure of membrane proteins which is modified by alpha-chymotrypsin but not by carboxypeptidases and is located in a position accessible to alpha-chymotrypsin only from inside the membrane.     

Insulation of the conduction pathway of muscle transverse tubule calcium channels from the surface charge of bilayer phospholipid

Functional calcium channels present in purified skeletal muscle transverse tubules were inserted into planar phospholipid bilayers composed of the neutral lipid phosphatidylethanolamine (PE), the negatively charged lipid phosphatidylserine (PS), and mixtures of both. The lengthening of the mean open time and stabilization of single channel fluctuations under constant holding potentials was accomplished by the use of the agonist Bay K8644. It was found that the barium current carried through the channel saturates as a function of the BaCl2 concentration at a maximum current of 0.6 pA (at a holding potential of 0 mV) and a half-saturation value of 40 mM. Under saturation, the slope conductance of the channel is 20 pS at voltages more negative than -50 mV and 13 pS at a holding potential of 0 mV. At barium concentrations above and below the half-saturation point, the open channel currents were independent of the bilayer mole fraction of PS from XPS = 0 (pure PE) to XPS = 1.0 (pure PS). It is shown that in the absence of barium, the calcium channel transports sodium or potassium ions (P Na/PK = 1.4) at saturating rates higher than those for barium alone. The sodium conductance in pure PE bilayers saturates as a function of NaCl concentration, following a curve that can be described as a rectangular hyperbola with a half-saturation value of 200 mM and a maximum conductance of 68 pS (slope conductance at a holding potential of 0 mV). In pure PS bilayers, the sodium conductance is about twice that measured in PE at concentrations below 100 mM NaCl. The maximum channel conductance at high ionic strength is unaffected by the lipid charge. This effect at low ionic strength was analyzed according to J. Bell and C. Miller (1984. Biophysical Journal. 45:279-287) and interpreted as if the conduction pathway of the calcium channel were separated from the bilayer lipid by approximately 20 A. This distance thereby effectively insulates the ion entry to the channel from the bulk of the bilayer lipid surface charge. Current vs. voltage curves measured in NaCl in pure PE and pure PS show that similarly small surface charge effects are present in both inward and outward currents. This suggests that the same conduction insulation is present at both ends of the calcium channel.     

Theoretical reconstruction of myotonia and paralysis caused by incomplete inactivation of sodium channels.

Muscle fibers from individuals with hyperkalemic periodic paralysis generate repetitive trains of action potentials (myotonia) or large depolarizations and block of spike production (paralysis) when the extracellular K+ is elevated. These pathologic features are thought to arise from mutations of the sodium channel alpha subunit which cause a partial loss of inactivation (steady-state Popen approximately 0.02, compared to < 0.001 in normal channels). We present a model that provides a possible mechanism for how this small persistent sodium current leads to repetitive firing, why the integrity of the T-tubule system is required to produce myotonia, and why paralysis will occur when a slightly larger proportion of channels fails to inactivate. The model consists of a two-compartment system to simulate the surface and T-tubule membranes. When the steady-state sodium channel open probability exceeds 0.0075, trains of repetitive discharges occur in response to constant current injection. At the end of the current injection, the membrane potential may either return to the normal resting value, continue to discharge repetitive spikes, or settle to a new depolarized equilibrium potential. This after-response depends on both the proportion of noninactivating sodium channels and the magnitude of the activity-driven K+ accumulation in the T-tubular space. A reduced form of model is presented in which a two-dimensional phase-plane analysis shows graphically how this diversity of after-responses arises as extracellular [K+] and the proportion of noninactivating sodium channels are varied.     

Isomorphism on a physical system of the Hodgkin-Huxley equations for sodium conductance: toxin allosteric effects and gating currents

An isomorphism on a physical system of the Hodgkin-Huxley equations for sodium ion conductance in the nerve membrane is derived. The physical system consists of 8 states. It shows that the voltage dependence of the sodium conductance arises from a change in ionization of the molecule that provides the ion-selective conductance channels. It associates reversibly with singly charged (H+?) and doubly charged (Ca++?) ions. The inactivation process is the result of the associating of an ionized particle by half of the states. The effect of toxins and narcotics in blocking or inactivating sodium conductance can be understood as an enzyme or allosteric change of the standard free energy difference of the molecule that provides the sodium channels. The effect of changing pH and Ca++ substrate concentration on the sodium conductance is predicted. The gating charge current is predicted. The time constant predicted is in agreement with experiment.