The influence of an unmyelinated terminal on repetitive firing of a mammalian receptor afferent fiber

The distal end of a myelinated receptor afferent fiber consists of an unmyelinated terminal membrane which is assumed to be the site of sensory transduction, whereas the action potential encoding appears at a distal node of Ranvier. In the present paper a model of a mammalian myelinated nerve fiber was augmented by an unmyelinated terminal segment into which stimulating current was injected thus modelling the situation at a myelinated receptor afferent fiber. It was found that the introduction of the unmyelinated terminal reduces the repetitive firing rate shown by the model. However, also the amplitude of the spikes at the site of action potential generation diminishes through the large electrical load which the unmyelinated terminal imposes onto the active parts of the nerve fiber model. This "loss" of spike amplitude can abolish the ability of the model to show repetitive activity, if the unmyelinated terminal increases in size. On the other hand, the incorporation of sodium channels into the terminal membrane compensates the spike amplitude reduction introduced by the electrical load of that membrane. This allows repetitive firing at a lower frequency than would be possible for a model with an equivalent sodium-channel-free terminal. The results show that the unmyelinated terminal present at the distal end of myelinated receptor afferent fibers has not only the ability to provide sensory transduction but evokes also a reduction in the discharge rate of the encoding membrane.     

Mechanism of conduction block in amphibian myelinated axon induced by biphasic electrical current at ultra-high frequency

The mechanism of axonal conduction block induced by ultra-high frequency (≥20 kHz) biphasic electrical current was investigated using a lumped circuit model of the amphibian myelinated axon based on Frankenhaeuser-Huxley (FH) equations. The ultra-high frequency stimulation produces constant activation of both sodium and potassium channels at the axonal node under the block electrode causing the axonal conduction block. This blocking mechanism is different from the mechanism when the stimulation frequency is between 4 kHz and 10 kHz, where only the potassium channel is constantly activated. The minimal stimulation intensity required to induce a conduction block increases as the stimulation frequency increases. The results from this simulation study are useful to guide future animal experiments to reveal the different mechanisms underlying nerve conduction block induced by high-frequency biphasic electrical current.     

Differentiation of channel models by noise analysis.

Differentiation of membrane channel models based on fluctuation (or noise) analysis is discussed. The theory is particularly useful in distinguishing a single-conductance model (Hodgkin-Huxley formalism) from a multiconductance model. When applied to the frog node of Ranvier, it seems likely that the potassium channels of the membrane may have multiconductance states.     

Modelled temperature-dependent excitability behaviour of a single ranvier node for a human peripheral sensory nerve fibre

The objective of this study was to determine whether the Hodgkin–Huxley model for unmyelinated nerve fibres could be modified to predict excitability behaviour at Ranvier nodes. Only the model parameters were modified to those of human, with the equations left unaltered. A model of a single Ranvier node has been developed as part of a larger model to describe excitation behaviour in a generalised human peripheral sensory nerve fibre. Parameter values describing the ionic and leakage conductances, corresponding equilibrium potentials, resting membrane potential and membrane capacitance of the original Hodgkin–Huxley model were modified to reflect the corresponding parameter values for human. Parameter temperature dependence was included. The fast activating potassium current kinetics were slowed down to represent those of a slow activating and deactivating potassium current, which do not inactivate. All calculations were performed in MATLAB^TM. Action potential shape and amplitude were satisfactorily predicted at 20, 25 and 37°C, and were not influenced by activation or deactivation of the slow potassium current. The calculated chronaxie time constant was 65.5 μs at 37°C. However, chronaxie times were overestimated at temperatures lower than body temperature.     

Effects of KC 3791 on sodium and potassium channels in frog node of Ranvier

Effects of a new antiarrhytmic compound KC 3791 on sodium (INa) and potassium (IK) currents were studied in frog myelinated nerve fibres under voltage clamp conditions. When applied externally to the node of Ranvier, KC 3791 (KC) at concentrations of 10(-5)-10(-4) mol.l-1 produced both tonic and cumulative (use-dependent) inhibition of INa. An analysis of the frequency-, voltage- and time dependence of cumulative block by KC suggested that this block resulted from a voltage-dependent interaction of the drug with open Na channels. The progressive decrease in INa during repetitive pulsing was due to accumulation of Na channels in the resting-blocked state: closing of the activation gate after the end of each depolarizing pulse stabilized the KC-"receptor" complex. To unblock these channels a prolonged washing of the node had to be combined with a subsequent repetitive stimulation of the membrane; this suggested that channel could not become cleared of the blocker unless the activation gate has opened. KC also proved to be capable of blocking open K channels at outwardly directed potassium currents (IK). This block increased during membrane depolarization. Unblocking of K channels after the end of a depolarizing pulse proceeded much faster than unblocking of Na channels under identical conditions. Cumulative inhibition of outward IK during high-frequency membrane stimulation was therefore readily reversible upon a decrease in pulsing frequency.     

The role of a transient potassium current in a bursting neuron model

Presented here is a biophysical cell model which can exhibit low-frequency repetitive activity and bursting behavior. The model is developed from previous models (Av-Ron et al. 1991, 1993) for excitability, oscillations and bursting. A stepwise development of the present model shows the contribution of a transient potassium current (I _A ) to the overall dynamics. By changing a limited set of model parameters one can describe different firing patterns; oscillations with frequencies ranging from 2–200 Hz and a wide range of bursting behaviors in terms of the durations of bursting and quiescence, peak firing frequency and rate of change of the firing frequency.     

Organic calcium channel blockers generate the coexistence of two different types of action potentials in the same muscle membrane following chemical induction of excitability.

1. Following exposure to the sulfhydryl reagents known as alpha,beta-unsaturated carbonyl compounds, the ventroabdominal flexor muscles of the crustacean Atya lanipes, which are normally completely inexcitable, generate trains of overshooting calcium action potentials; the effects of organic calcium channel antagonists and potassium channel blockers on the chemically-induced trains of action potentials have been studied. 2. Verapamil and D600, at micromolar concentrations, elicit the appearance of slow, cardiac-like action potentials which coexist with the much faster chemically-induced calcium spikes, transforming the regular repetitive firing into a cyclic bursting pattern. 3. Bepridil (1 microM) decreases the frequency of firing of the action potentials, probably by increasing the threshold for the activation of a population of the chemically-induced calcium channels. 4. The potassium channel blockers, TEA (30-40 mM) and quinidine (100-200 microM), delayed the rate of repolarization of the chemically-induced action potentials; none of the potassium channel blockers, however, induced the appearance of repetitive spike activity.     

Quinidine blocking of sodium and potassium channels in myelinated nerve fibers

Experiments by the voltage clamp method showed that external application of quinidine (5 × 10^–5 M) to the Ranvier node membrane of the frog nerve fiber inhibitis both sodium and potassium currents. Blocking of the sodium current is considerably intensified by repetitive depolarization of the membrane (1–10 Hz); the rate of development of the block increases with an increase in stimulation frequency. After the end of stimulation the sodium current gradually returns to its initial level (with a time constant of the order of 30 sec at 12°C). Unlike repetitive depolarization with short (5 msec) stimuli, a prolonged shift (1 sec) of potential toward depolarization has no significant effect on quinidine blocking of the sodium current. Analysis of the current-voltage characteristic curves showed that quinidine blocks outward sodium current more strongly than inward. Batrachotoxin protects sodium channels against the blocking action of quinidine in a concentration of 10^–5 M. Inhibition of the outward potassium currents by quinidine is distinctly time-dependent in character: Initially the potassium current rises to a maximum, then falls steadily to a new stationary level. The results agree with the view that quinidine, applied externally, penetrates through the membrane in the basic form and blocks open sodium and potassium channels from within in the charged (protonated) form. The similarity in principle between the action of quinidine and local anesthetics on the sodium suggests that these compounds bind with the same receptor, located in the inner mouth of the sodium channel.A. V. Vishnevskii Institute of Surgery, Academy of Medical Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 14, No. 3, pp. 324–330, May–June, 1982.     

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.     

A study of properties of batrachotoxin modified sodium channels

A further analysis of the effects of the steroidal alkaloid batrachotoxin (BTX) on sodium channels in frog node of Ranvier has been carried out under voltage-clamp conditions. The main properties of modified channels as compared with those of normal ones are as follows: The rate of channel closing is drastically decreased, whereas that of opening is changed slightly if at all; The steady-state voltage dependence of channel activation is shifted towards more negative potentials by 60-70 mV; Currents through modified channels do not show a decay during maintained depolarization as it is typical for normal channels. However modified channels retain the ability to partial inactivation as shown by experiments with depolarizing prepulses; Sodium against potassium selectivity beyond--20 mV suggesting either nonhomogeneity of the modified channels as for their kinetic and selectivity properties or potential-dependence of ionic selectivity for each channel; The selectivity sequence determined from peak current reversal potential measurements is as follows: H: Na :NH4:K = 528:1:0.47: :0.19; The effective pK value of proton block is decreased by about 0.4; 7) The sensitivity of the channels to tetrodotoxin (TTX) block is practically unchanged.     

Simulated tetanic hyperpolarization by sodium loading of a neuronal system in which active transport is linked to the Frankenhaeuser-Huxley equations

Tetanic hyperpolarization for theXenopus node is simulated by means of iterative solutions of the Frankenhaeuser-Huxley excitation equations together with an active transport current density term which is dependent on sodium and potassium levels as well as the ADP/ATP ratio. All time-dependent variables at the end of one interspike interval are introduced as initial conditions for the next response, whereupon all time-dependent changes in voltage and permeability factors appear identical for the third and fourth responses of a sequence. Net change in internal sodium concentration is zero throughout the third and fourth intervals if sodium loading of the system is initially adjusted to a critical level. Extent of tetanic hyperpolarization is a function of the pump conductance. Supported by NIH Grant No. NS08802.     

Pharmacological characterization of ionic currents that regulate the pacemaker rhythm in a weakly electric fish

Electric organ discharge (EOD) frequency in the brown ghost knifefish (Apteronotus leptorhynchus) is sexually dimorphic, steroid-regulated, and determined by the discharge rates of neurons in the medullary pacemaker nucleus (Pn). We pharmacologically characterized ionic currents that regulate the firing frequency of Pn neurons to determine which currents contribute to spontaneous oscillations of these neurons and to identify putative targets of steroid action in regulating sexually dimorphic EOD frequency. Tetrodotoxin (TTX) initially reduced spike frequency, and then reduced spike amplitude and stopped pacemaker activity. The sodium channel blocker muO-conotoxin MrVIA also reduced spike frequency, but did not affect spike amplitude or production. Two potassium channel blockers, 4-aminopyridine (4AP) and kappaA-conotoxin SIVA, increased pacemaker firing rates by approximately 20% and then stopped pacemaker firing. Other potassium channel blockers (tetraethylammonium, cesium, alpha-dendrotoxin, and agitoxin-2) did not affect the pacemaker rhythm. The nonspecific calcium channel blockers nickel and cadmium reduced pacemaker firing rates by approximately 15-20%. Specific blockers of L-, N-, P-, and Q-type calcium currents, however, were ineffective. These results indicate that at least three ionic currents-a TTX- and muO-conotoxin MrVIA-sensitive sodium current; a 4AP- and kappaA-conotoxin SIVA-sensitive potassium current; and a T- or R-type calcium current-contribute to the pacemaker rhythm. The pharmacological profiles of these currents are similar to those of currents that are known to regulate firing rates in other spontaneously oscillating neural circuits.     

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.     

Computation of Impulse Initiation and Saltatory Conduction in a Myelinated Nerve Fiber

A mathematical model of the electrical properties of a myelinated nerve fiber is given, consisting of the Hodgkin-Huxley ordinary differential equations to represent the membrane at the nodes of Ranvier, and a partial differential cable equation to represent the internodes. Digital computer solutions of these equations show an impulse arising at a stimulating electrode and being propagated away, approaching a constant velocity. Action potential curves plotted against distance show discontinuities in slope, proportional to the nodal action currents, at the nodes. Action potential curves plotted against time, at the nodes and in the internodes, show a marked difference in steepness of the rising phase, but little difference in peak height. These results and computed action current curves agree fairly accurately with published experimental data from frog and toad fibers.     

TEA-insensitive K-channels in the crab giant axon

TTX and TEA-insensitive permeabilities were studied in the crab giant axon under voltage-clamp. Membrane currents in the presence of internal TEA (40 mmol/l) and external TTX (300 nmol/l) may be analyzed as the sum of two components: a linear component, identified as the so-called leakage current, and a non-linear component, identified as a TEA-insensitive potassium channel. Ion permeability ratio of the TTX and TEA insensitive cation channel calculated from reversal potential shows the following sequence pK+:pNa+:pCs+:pRb+:pNH+4 = 1.00:0.16:0.16:0.09:0.06. TEA-insensitive outward currents, carried mainly by Cs+, may be recorded in the presence of different external solutions. Voltage-dependence and equilibrium potential of this channel in physiological conditions allows to postulate its contribution to maintain the cell depolarized during repetitive firing.     

Use-dependent potentiation of the Nav1.6 sodium channel

Nav1.2 and Nav1.6 are two voltage-gated sodium channel isoforms that are abundant in the adult central nervous system. These channels are expressed in different cells and localized in different neuronal regions, which may reflect functional specialization. To examine this possibility, we compared the properties of Nav1.2 and Nav1.6 in response to a rapid series of repetitive depolarizations. Currents through Nav1.6 coexpressed with beta1 demonstrated use-dependent potentiation during a rapid train of depolarizations. This potentiation was in contrast to the use-dependent decrease in current for Nav1.2 with beta1. The voltage dependence of potentiation correlated with the voltage dependence of activation, and it still occurred when fast inactivation was removed by mutation. Rapid stimulation accelerated a slow phase of activation in the Nav1.6 channel that had fast inactivation removed, resulting in faster channel activation. Although the Nav1.2 channel with fast inactivation removed also demonstrated slightly faster activation, that channel showed very pronounced slow inactivation compared to Nav1.6. These results indicate that potentiation of Nav1.6 sodium currents results from faster channel activation, and that this effect is masked by slow inactivation in Nav1.2. The data suggest that Nav1.6 might be more resistant to inactivation, which might be helpful for high-frequency firing at nodes of Ranvier compared to Nav1.2.     

Effects of strychnine on the sodium conductance of the frog node of Ranvier

Strychnine blocks sodium conductance in the frog node of Ranvier. This block was studied by reducing and slowing sodium inactivation with scorpion venom. The block is voltage and time dependent. The more positive the axoplasm the greater the block and the faster the approach to equilibrium. Some evidence is presented suggesting that only open channels can be blocked. The block is reduced by raising external sodium or lithium but not impermeant cations. A quaternary derivative of strychnine was synthesized and found to have the same action only when applied intracellularly. We conclude that strychnine blocks sodium channels by a mechanism analogous to that by which it blocks potassium channels. The potassium channel block had previously been found to be identical to that by tetraethylammonium ion derivatives. In addition, strychnine resembles procaine and its derivatives in both its structure and the mechanism of sodium channel block.     

Repetitive firing deficits and reduced sodium current density in retinal ganglion cells developing in the absence of BDNF.

Previous work by Cellerino et al. has shown that chronic absence of brain-derived neurotrophic factor (BDNF) resulted in hypomyelination of the optic nerve. Since myelination is influenced by neuronal activity, it is possible that a deficiency in BDNF during early development could alter the firing properties of retinal neurons. To test this hypothesis, patch-clamp recordings were performed in retinal whole mounts from BDNF-deficient (bdnf-/-), heterozygote (bdnf+/-) or wild-type control mice (bdnf+/+). Ganglion cell layer neurons (RGNs) were tested at different age [postnatal day (P)1-11] for their ability to encode graded depolarization with variable action potential frequency. At all developmental ages examined, RGNs exhibiting frequency coding were less frequently encountered in bdnf-/- than in bdnf+/+ mice. At P1, none of the RGNs from bdnf-/- mice displayed repetitive firing compared to 50% in bdnf+/+ mice, and by P7-11, only 50% of bdnf-/- RGNs exhibited repetitive firing compared to 100% in bdnf+/+ mice. Moreover, in bdnf-/- RGNs repetitive discharge was characterized by a reduced frequency increment per current change. Acquisition of repetitive firing was paralleled by a decrease in input resistance and a steep increase of sodium current density. In bdnf-/- mice, the onset of this increase occurred at later stages of development than in wild-type controls (bdnf-/-: P6-11; bdnf+/+: P2-6). The discharge pattern of P7-11 bdnf-/- RGNs resembled that of RGNs in neonatal wild-type mice and was mimicked by acute application of a Ca(2+) channel blocker. We conclude that BDNF plays an important role in the ontogeny of repetitive firing of RGNs.     

Ionic selectivity of the sodium channel of frog skeletal muscle

The ionic selectivity of the Na channel to a variety of metal and organic cations is studied in frog semitendinosus muscle. Na channel currents are measured under voltage clamp conditions in fibers bathed in solutions with all Na+ replaced by a test ion. Permeability ratios are calculated from measured reversal potentials using the Goldman-Hodgkin-Katz equation. The permeability sequence was Na+ approximately Li+ approximately hydroxylammonium greater than hydrazinium greater than ammonium greater than guanidinium greater than K+ greater than aminoguanidinium in the ratios 1:0.96:0.94:0.31:0.11:0.093:0.048:0.031. No inward currents were observed for Ca++, methylammonium, methylguanidinium, tetraethylammonium, and tetramethylammonium. The results are consistent with the Hille model of the Na channel selectivity filter of the node of Ranvier and suggest that the selectivity filter of the two channels is the same.