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.     

Gating current harmonics. II. Model simulations of axonal gating currents

A kinetic model of sodium activation gating is presented. The kinetics are based on harmonic analysis of gating current data obtained during large-amplitude sinusoidal voltage clamp in dynamic steady state. The technique classifies gating kinetic schemes into groups based on patterns of the harmonic content in the periodic gating current records. The kinetics that simulate the experimental data contain two independently constrained processes. The model predicts (a) sizable gating currents in response to hyperpolarizing voltage steps from rest; (b) a substantial increase in the initial peak of the gating current following voltage steps from prehyperpolarized potentials; (c) a small delay in the onset of sodium ion current following voltage steps from prehyperpolarized potentials; and (d) flickering during the open state in single channel current records. Although fundamentally different in kinetic structure from the Hodgkin-Huxley model, the present model reproduces the phenomenological development of Na conductance during the initiation and development of action potentials. The implications for possible gating mechanisms are discussed. A model gate is presented.     

A fully coupled transient excited state model for the sodium channel

Summary The axon membrane is simulated by standard Hodgkin-Huxley leakage and potassium channels plus a coupled transient excited state kinetic scheme for the sodium channel. This scheme for the sodium channel is as proposed previously by the author. Simultations are presented showing the form of the action potential, threshold behavior, accommodation, and repetitive firing. It is seen that the form of the individual action potential, its all-or-none nature, and its refractory period are well simulated by this model, as they are by the standard Hodgkin-Huxley model. However, the model differs markedly from the Hodgkin-Huxley model with respect to repetitive firing and accommodation to stimulating currents of slowly rising intensity, in ways that are anomn to be related to those features of the sodium inactivation which are anomalous to the H-H model. The tendency for repetitive firing is highly dependent on that parameter which primarily determintes the existence of the inactivation shift in voltage clamp experiments, in such a way that the more pronounced the inactivation shift, the less the tendency for repetitive firing,. The tendency for accommodation is highly dependent on that parameter which primarily determines the “τ_c − τ_h” separation, in such a way that the greater the separation the greater the tendency for the membrane to accommodate without firing action potentials to a slowly rising current.     

Rate of opening of a population of Na channels in frog skeletal muscle fibers

Linear Systems convolution analysis of muscle sodium currents was used to predict the opening rate of sodium channels as a function of time during voltage clamp pulses. If open sodium channel lifetimes are exponentially distributed, the channel opening rate corresponding to a sodium current obtained at any particular voltage, can be analytically obtained using a simple equation, given single channel information about the mean open-channel lifetime and current.Predictions of channel opening rate during voltage clamp pulses show that sodium channel inactivation arises coincident with a decline in channel opening rate.Sodium currents pharmacologically modified with Chloramine-T treatment so that they do not inactivate, show a predicted sustained channel opening rate.Large depolarizing voltage clamp pulses produce channel opening rate functions that resemble gating currents.The predicted channel opening rate functions are best described by kinetic models for Na channels which confer most of the charge movement to transitions between closed states.Comparisons of channel opening rate functions with gating currents suggests that there may be subtypes of Na channel with some contributing more charge movement per channel opening than others.Na channels open on average, only once during the transient period of Na activation and inactivation.After transiently opening during the activation period and then closing by entering the inactivated state, Na channels reopen if the voltage pulse is long enough and contribute to steady-state currents.The convolution model overestimates the opening rate of channels contributing to the steady-state currents that remain after the transient early Na current has subsided.     

A transient excited state model for sodium permeability changes in excitable membranes.

In this paper we explore the properties of a mathematical model for the passive sodium permeability system of excitable membranes. This model is distinguished by the explicit inclusion of a rate constant which depends not on instantaneous voltage, but on rate of voltage change. Actually, the model is a rather modest modification of the Hodgkin-Huxley model, but displays some behaviors which the H-H model does not. Among these behaviors are a pronounced inactivation shift (for certain parameter values), a difference between inactivation time constant as measured by turning off a sodium current under sustained depolarization and as measured by double pulse experiments, skip runs under sustained current stimulation, and accommodation to slowing rising currents.     

Multiple-state model of ionic channel in reproducing the time course of electrophysiological events.

BACKGROUND: The predictions of the Hodgkin-Huxley model do not accurately fit all the measurements of voltage-clamp currents, gating charge and single-channel currents. There are many quantitative differences between the predicted and measured characteristics of the sodium and potassium channels. For example, the two-state gate model has exponential onset kinetics, whereas the sodium and potassium conductances show S-shaped activation and the sodium conductance shows an exponential inactivation. In this paper we shall examine a more general channel model that can more faithfully represent the measured properties of ionic channels in the membrane of the excitable cell. METHODS: The model is based on the generalisation of the notion of a channel with a discrete set of states. Each state has state attributes such as the state conductance, state ionic current and state gating charge. These variables can have quite different waveforms in time, in contrast with a two-state gate channel model, in which all have the same waveforms. RESULTS: The kinetics of all variables are equivalent: gating and ionic currents give equivalent information about channel kinetics; both the equilibrium values of the current and the time constants are functions of membrane potential. The results are in almost perfect concordance with the experimental data regarding the characteristics of nerve impulse. CONCLUSIONS: The expected values of the gating charge and the ionic conductance are weighted sums of the state occupancy probabilities, but the weights differ: for the expected value of the gating charge the weights are the state gating charges and for the expected value of the ionic conductance the weights are the state conductances. Since these weights are different, the expected values of the gating charge and the ionic conductance will differ.     

Effect of N-bromoacetamide on single sodium channel currents in excised membrane patches

We have studied the effect of N-bromoacetamide (NBA) on the behavior of single sodium channel currents in excised patches of rat myotube membrane at 10 degree C. Inward sodium currents were activated by voltage steps from holding potentials of about -100 mV to test potentials of -40 mV. The cytoplasmic-face solution was isotonic CsF. Application of NBA or pronase to the cytoplasmic face of the membrane irreversibly removed sodium channel inactivation, as determined by averaged single-channel records. Teh lifetime of the open channel at - 40 mV was increased about 10-fold by NBA treatment without affecting the amplitude of single-channel currents. A binomial analysis was used both before and after treatment to determine the number of channels within the excised patch. NBA was shown to have little effect on activation kinetics, as determined by an examination of both the rising phase of averaged currents and measurements f the delay between the start of the pulse and the first channel opening. Our data support a kinetic model of sodium channel activation in which the rate constant leading back from the open state to the last closed state is slower than expected from a strict Hodgkin-Huxley model. The data also suggest that the normal open-channel lifetime is primarily determined by the inactivation process in the voltage range we have examined.     

An assessment of a coupled three-state kinetic model for sodium conductance changes.

The behavior of a coupled three-state kinetic scheme is examined to see if it might be a viable model for the conductance changes of sodium channels. It is found that for simulations of experiments which determine the properties of the Hodgkin-Huxley m and h gates, the three-state scheme performs approximately equivalently to the Hodgkin-Huxley model. In particular, the three-state scheme successfully simulates those experiments which the Hodgkin-Huxley model successfully simulates, but fails to simulate those newer voltage clamp experiments which give results anomalous to the H-H model. It is concluded that the three-state scheme is probably as good as the H-H model, but is not a viable successor to it.     

Inactivation of the sodium channel. I. Sodium current experiments

Inactivation of sodium conductance has been studied in squid axons with voltage clamp techniques and with the enzyme pronase which selectively destroys inactivation. Comparison of the sodium current before and after pronase treatment shows a lag of several hundred microseconds in the onset of inactivation after depolarization. This lag can of several hundred microseconds in the onset of inactivation after polarization. This lag can also be demonstrated with double-pulse experiments. When the membrane potential is hyperpolarized to -140 mV before depolarization, both activation and inactivation are delayed. These findings suggest that inactivation occurs only after activation are delayed. These findings suggest that inactivation occurs only after activation; i.e. that the channels must open before they can inactivate. The time constant of inactivation measured with two pulses (τ(c)) is the same as the one measured from the decay of the sodium current during a single pulse (τ(h)). For large depolarizations, steady-state inactivation becomes more incomplete as voltage increases; but it is relatively complete and appears independent of voltage when determined with a two- pulse method. This result confirms the existence of a second open state for Na channels, as proposed by Chandler and Meves (1970. J. Physiol. [Lond.]. 211:653-678). The time constant of recovery from inactivation is voltage dependent and decreases as the membrane potential is made more negative. A model for Na channels is presented which has voltage-dependent transitions between the closed and open states, and a voltage-independent transition between the open and the inactivated state. In this model the voltage dependence of inactivation is a consequence of coupling to the activation process.     

Early development of voltage-dependent sodium currents in cultured mouse spinal cord neurons

Spinal cord neurons were dissociated from 13-day embryonic mice and grown in culture for 1-28 days. Sodium currents of neurons in culture for 1-2 days were compared with those in culture for 2-4 weeks, using the whole-cell voltage clamp method. Rapid neurite outgrowth created space clamp limitations so that unclamped neuritic sodium action potentials prevented accurate analysis of sodium current properties. Therefore neurons were bathed in sodium-free solution and brief puffs of sodium were delivered to the cell soma so that only somatic sodium currents were recorded. Sodium currents of neurons at 1-2 days in culture had voltage-dependent activation and inactivation characteristic of these channels, both in mature cultured spinal neurons and in other preparations. However, the estimated channel density on the soma of neurons 1-2 days in culture was less than two channels per micron2. Since the available sodium conductance (as measured by action potential rise rates) increases during development of spinal cord neurons in culture (Westbrook and Brenneman, 1984), we suggest that changes in channel density and/or distribution, rather than in channel kinetics, may underlie the increase in sodium conductance.     

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.     

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.     

Characterization of Na(+) currents in isolated dorsal unpaired median neurons of Locusta migratoria and effect of the alpha-like scorpion toxin BmK M1

A primary cell culture was developed for efferent dorsal unpaired median (DUM) neurons of the locust. The isolated somata were able to generate Tetrodotoxin (TTX)-sensitive action potentials in vitro. The alpha-like scorpion toxin BmK M1, from the Asian scorpion Buthus martensi Karsch, prolonged the duration of the action potential up to 50 times. To investigate the mechanism of action of BmK M1, the TTX-sensitive voltage gated Na(+) currents were studied in detail using the whole cell patch clamp technique. BmK M1 slowed down and partially inhibited the inactivation of the TTX-sensitive Na(+) current in a dose dependent manner (EC50=326.8+/-34.5 nM). Voltage and time dependence of the Na(+) current were described in terms of the Hodgkin-Huxley model and compared in control conditions and in the presence of 500 nM BmK M1. The BmK M1 shifted steady state inactivation by 10.8 mV to less negative potentials. The steady state activation was shifted by 5.5 mV to more negative potentials, making the activation window larger. Moreover, BmK M1 increased the fast time constant of inactivation, leaving the activation time constant unchanged. In summary, BmK M1 primarily affected the inactivation parameters of the voltage gated Na(+) current in isolated locust DUM neurons.     

Simulations of voltage clamping poorly space-clamped voltage-dependent conductances in a uniform cylindrical neurite

Significant error is made by using a point voltage clamp to measure active ionic current properties in poorly space-clamped cells. This can even occur when there are no obvious signs of poor spatial control. We evaluated this error for experiments that employ an isochronal I(V) approach to analyzing clamp currents. Simulated voltage clamp experiments were run on a model neuron having a uniform distribution of a single voltage-gated inactivating ionic current channel along an elongate, but electrotonically compact, process. Isochronal Boltzmann I(V) and kinetic parameter values obtained by fitting the Hodgkin-Huxley equations to the clamp currents were compared with the values originally set in the model. Good fits were obtained for both inward and outward currents for moderate channel densities. Most parameter errors increased with conductance density. The activation rate parameters were more sensitive to poor space clamp than the I(V) parameters. Large errors can occur despite normal-looking clamp curves.     

Analysis of Depolarizing and Hyperpolarizing Inactivation Responses in Gymnotid Electroplaques

In electroplaques of several gymnotid fishes hyperpolarizing or depolarizing currents can evoke all-or-none responses that are due to increase in membrane resistance as much as 10- to 12-fold. During a response the emf of the membrane shifts little, if at all, when the cell either is at its normal resting potential, or is depolarized by increasing external K, and in the case of depolarizing responses when either Cl or an impermeant anion is present. Thus, the increase in resistance is due mainly, or perhaps entirely, to decrease in K permeability, termed depolarizing or hyperpolarizing K inactivation, respectively. In voltage clamp measurements the current-voltage relation shows a negative resistance region. This characteristic accounts for the all-or-none initiation and termination of the responses demonstrable in current clamp experiments. Depolarizing inactivation is initiated and reversed too rapidly to measure with present techniques in cells in high K. Both time courses are slowed in cells studied in normal Ringer's. Once established, the high resistance state is maintained as long as an outward current is applied. Hyperpolarizing inactivation occurs in normal Ringer's or with moderate excess K. Its onset is more rapid with stronger stimuli. During prolonged currents it is not maintained; i.e., there is a secondary increase in conductance. Hyperpolarizing inactivation responses exhibit a long refractory period, presumably because of persistence of this secondary increase in conductance.     

Neural repetitive firing: modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons.

The Hodgkin-Huxley equations for space-clamped squid axon (18 degrees C) have been modified to approximate voltage clamp data from repetitive-firing crustacean walking leg axons and activity in response to constant current stimulation has been computed. The m infinity and h infinity parameters of the sodium conductance system were shifted along the voltage axis in opposite directions so that their relative overlap was increased approximately 7 mV. Time constants tau m and tau h, were moved in a similar manner. Voltage-dependent parameters of delayed potassium conductance, n infinity and tau n, were shifted 4.3 mV in the positive direction and tau n was uniformly increased by a factor of 2. Leakage conductance and capacitance were unchanged. Repetitive activity of this modified circuit was qualitatively similar to that of the standard model. A fifth branch was added to the circuit representing a transient potassium conductance system present in the repetitive walking leg axons and in other repetitive neurons. This model, with various parameter choices, fired repetitively down to approximately 2 spikes/s and up to 350/s. The frequency vs. stimulus current plot could be fit well by a straight line over a decade of the low frequency range and the general appearance of the spike trains was similar to that of other repetitive neurons. Stimulus intensities were of the same order as those which produce repetitive activity in the standard Hodgkin-Huxley axon. The repetitive firing rate and first spike latency (utilization time) were found to be most strongly influenced by the inactivation time constant of the transient potassium conductance (tau b), the delayed potassium conductance (tau n), and the value of leakage conductance (gL). The model presents a mechanism by which stable low frequency discharge can be generated by millisecond-order membrane conductance changes.     

Gating of Na channels. Inactivation modifiers discriminate among models

Macroscopic Na currents were recorded from N18 neuroblastoma cells by the whole-cell voltage-clamp technique. Inactivation of the Na currents was removed by intracellular application of proteolytic enzymes, trypsin, alpha-chymotrypsin, papain, or ficin, or bath application of N-bromoacetamide. Unlike what has been reported in squid giant axons and frog skeletal muscle fibers, these treatments often increased Na currents at all test pulse potentials. In addition, removal of inactivation gating shifted the midpoint of the peak Na conductance-voltage curve in the negative direction by 26 mV on average and greatly prolonged the rising phase of Na currents for small depolarizations. Polypeptide toxins from Leiurus quinquestriatus scorpion and Goniopora coral, which slow inactivation in adult nerve and muscle cells, also increase the peak Na conductance and shift the peak conductance curve in the negative direction by 7-10 mV in neuroblastoma cells. Control experiments argue against ascribing the shifts to series resistance artifacts or to spontaneous changes of the voltage dependence of Na channel kinetics. The negative shift of the peak conductance curve, the increase of peak Na currents, and the prolongation of the rise at small depolarization after removal of inactivation are consistent with gating kinetic models for neuroblastoma cell Na channels, where inactivation follows nearly irreversible activation with a relatively high, voltage-independent rate constant and Na channels open only once in a depolarization. As the same kind of experiment does not give apparent shifting of activation and prolongation of the rising phase of Na currents in adult axon and muscle membranes, the Na channels of these other membranes probably open more than once in a depolarization.     

Corrections for space-clamp errors in measured parameters of voltage-dependent conductances in a cylindrical neurite

The ability to correct parameters of voltage-gated conductances measured under poor spatial control by point voltage clamp could rescue much flawed experimental data. We explore a strategy for correcting errors in experiments that employs a full-trace approach to parameter determination. Simulated soma voltage-clamp runs are made on a model neuron with a single voltage-gated, Hodgkin-Huxley channel type distributed uniformly along an elongate process. Estimates for both kinetic and I(V) parameters are obtained by fitting a form of the Hodgkin-Huxley equations to the complete time course of leak-subtracted current curves. The fitted parameters are used to determine how much correction in each parameter is needed to regenerate the set actually belonging to the channel. Corrections are generated for a range of neurite lengths, conductance densities, and channel characteristics.