Model of adaptation of the nerve fiber ranvier node membrane to the action of a steady current as the result of sodium channel inactivation

The effect of the second-order kinetics of the sodium channel inactivation system on spike activity was studied on a modified Hodgkin-Huxley model of the amphibian Ranvier node (Dodge model). The results of calculations based on the experimental data of Chiu, Kniffki, et al. suggest that the cause of adaptation of the amphibian nerve fiber membrane may be the second-order kinetics of the sodium channel inactivation system. Unlike the potassium mechanism of adaptation, the sodium mechanism is associated with constancy or a progressive decline of response amplitudes.     

Effects of laser-induced hyperthermia treatment on ionic permeability of myelinated nerve

Summary The effect of laser-induced hyperthermia on the ionic permeability of nerve membranes was studied using the nodes of Ranvier in amphibian myelinated nerve as a model. To effect a photothermal modification of nerve membrane functions, con trolled laser irradiation consisting of a 5-sec thermal pulse was applied to the nodal membrane, increasing the temperature to a maximum of 48–58°C at the node. Major electrophysiological changes observed in the nodal membrane following laser-induced hyperthermia were a differential reduction of the sodium and potassium permeability, an increase in the leakage current, and a negative shift on the potential axis of the steady-state Na inactivation. There was no significant change in the kinetics of ion channel activation and inactivation for treatments below 56°C. The results suggest that a primary photothermal damage mecha nism at temperatures below 56°C could be a reduction in the number of active Na channels in the node, rather than a change in individual channel kinetics, or in the properties of the lipid bilayer of intervening nerve membrane. A differential heat sensi tivity between the noninactivated and the inactivated Na channels is also suggested. For the treatments of 56°C and above, a signifi cant increase of membrane leakage current suggests an irrevers ible thermal damage to the lipid bilayer. This work was supported by the ONR/SDIO N00014-86-K-0188 Medical Free-Electron-Laser Program and the Columbus-Cabrini Foundation.     

Subtle Paranodal Injury Slows Impulse Conduction in a Mathematical Model of Myelinated Axons

This study explores in detail the functional consequences of subtle retraction and detachment of myelin around the nodes of Ranvier following mild-to-moderate crush or stretch mediated injury. An equivalent electrical circuit model for a series of equally spaced nodes of Ranvier was created incorporating extracellular and axonal resistances, paranodal resistances, nodal capacitances, time varying sodium and potassium currents, and realistic resting and threshold membrane potentials in a myelinated axon segment of 21 successive nodes. Differential equations describing membrane potentials at each nodal region were solved numerically. Subtle injury was simulated by increasing the width of exposed nodal membrane in nodes 8 through 20 of the model. Such injury diminishes action potential amplitude and slows conduction velocity from 19.1 m/sec in the normal region to 7.8 m/sec in the crushed region. Detachment of paranodal myelin, exposing juxtaparanodal potassium channels, decreases conduction velocity further to 6.6 m/sec, an effect that is partially reversible with potassium ion channel blockade. Conduction velocity decreases as node width increases or as paranodal resistance falls. The calculated changes in conduction velocity with subtle paranodal injury agree with experimental observations. Nodes of Ranvier are highly effective but somewhat fragile devices for increasing nerve conduction velocity and decreasing reaction time in vertebrate animals. Their fundamental design limitation is that even small mechanical retractions of myelin from very narrow nodes or slight loosening of paranodal myelin, which are difficult to notice at the light microscopic level of observation, can cause large changes in myelinated nerve conduction velocity.     

Immuno-ultrastructural localization of sodium channels at nodes of Ranvier and perinodal astrocytes in rat optic nerve

Immuno-electron microscopic localization of sodium channels at nodes of Ranvier within adult optic nerve was demonstrated with polyclonal antibody 7493. The 7493 antisera, which is directed against purified sodium channels from rat brain, recognizes a 260 kDa protein in immunoblots of the crude glycoprotein fraction from adult rat optic nerve. Intense immunoreactivity with 7493 antisera was observed at nodes of Ranvier. Axon membrane at the node was densely stained, whereas paranodal and internodal axon membrane did not exhibit immunoreactivity. The axoplasm beneath the nodal membrane displayed variable immunostaining. Neither terminal paranodal oligodendroglial loops nor oligodendrocyte plasmalemma were immunoreactive with 7493 antisera. However, perinodal astrocyte processes exhibited intense immunoreactivity with the anti-sodium channel antisera. Optic nerves incubated with pre-immune sera, or with 7493 antisera that had been pre-adsorbed with purified sodium channel protein, displayed no immunoreactivity. These results demonstrate localization of sodium channels at high density at mammalian nodes of Ranvier and in some perinodal astrocyte processes. The latter observation offers support for an active role for perinodal astrocyte processes in the aggregation of sodium channels within the axon membrane at the node of Ranvier.     

A numerical approach to ion channel modelling using whole-cell voltage-clamp recordings and a genetic algorithm

The activity of trans-membrane proteins such as ion channels is the essence of neuronal transmission. The currently most accurate method for determining ion channel kinetic mechanisms is single-channel recording and analysis. Yet, the limitations and complexities in interpreting single-channel recordings discourage many physiologists from using them. Here we show that a genetic search algorithm in combination with a gradient descent algorithm can be used to fit whole-cell voltage-clamp data to kinetic models with a high degree of accuracy. Previously, ion channel stimulation traces were analyzed one at a time, the results of these analyses being combined to produce a picture of channel kinetics. Here the entire set of traces from all stimulation protocols are analysed simultaneously. The algorithm was initially tested on simulated current traces produced by several Hodgkin-Huxley–like and Markov chain models of voltage-gated potassium and sodium channels. Currents were also produced by simulating levels of noise expected from actual patch recordings. Finally, the algorithm was used for finding the kinetic parameters of several voltage-gated sodium and potassium channels models by matching its results to data recorded from layer 5 pyramidal neurons of the rat cortex in the nucleated outside-out patch configuration. The minimization scheme gives electrophysiologists a tool for reproducing and simulating voltage-gated ion channel kinetics at the cellular level.     

Effects of a slow potassium permeability on repetitive activity of the frog node of ranvier

Adding a potassium permeability with slow kinetics to the Frankenhaeuser-Huxley equations describing action potential generation at a frog node of Ranvier has a twofold effect on the maintained repetitive firing the model can show. If the contribution of the slow to the total potassium permeability is increased, the maintained discharge frequency for a given stimulating current experiences a decrease. On the other hand, addition of the slow channel narrows the range of currents for which the model can generate repetitive activity. If as little as 6.2% of the total potassium permeability are provided by the slow channels, the Frankenhaeuser-Huxley equations completely lose the ability to show maintained firing. The introduction of the slow potassium current abolishes especially repetitive activity at low values of stimulating current. This effect is so marked that the minimal discharge frequency the model can maintain increases with increasing contribution of the slow channel. Therefore, an important purpose of the slow potassium channel present at the frog nodal membrane could consist of preventing the node of Ranvier from generating consistent firing on its own.     

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.     

Voltage dependence of intramembrane charge movement and conductance activation of batrachotoxin-modified sodium channels in frog node of Ranvier

Sodium current and sodium channel intramembrane gating charge movement (Q) were monitored in voltage-clamped frog node of Ranvier after modification of all sodium channels by batrachotoxin (BTX). BTX caused an approximately threefold increase in steepness of the Q vs. voltage relationship and a 50-mV negative shift in its midpoint. The maximum amount of intramembrane charge was virtually identical before and after BTX treatment. BTX treatment eliminated the charge immobilization observed in untreated nodes after relatively long depolarizing pulses and slowed the rate of OFF charge movement after a pulse. After BTX treatment, the voltage dependence of charge movement was the same as the steady-state voltage dependence of sodium conductance activation. The observations are consistent with the hypothesis that BTX induces an aggregation of the charged gating particles associated with each channel and causes them to move as a unit having approximately three times the average valence of the individual particles. Movement of this single aggregated unit would open the BTX-modified sodium channel.     

Can electromagnetic radiations induce changes in the kinetics of voltage-dependent ion channels?

Ion channels are protein molecules, which can assume distinct open and closed conformational states, a phenomenon termed ion channel kinetics. The transitions from one state to another depend on the potential energy barrier that separates those two states. Therefore, it is rational to suppose that electromagnetic waves could interact with this barrier and induce changes in the rate transitions of this kinetic process. Our aim is to answer the question: can electromagnetic radiations induce changes in the kinetics of voltage-dependent ion channels? We simulated the effects of the low and high frequency electromagnetic waves on the sodium and potassium channels of the giant axon of Loligo. The key parameter measured was the fractional open time (fv), because it reflects the voltage dependence of the kinetics of channels. The electromagnetic radiations induced the following changes in the kinetics of the potassium and sodium channels: i/ low frequency waves kept the potassium channel 50% of the time open independent on the mean voltage applied through the membrane; ii/ a gradual inhibition of the inactivation on the sodium channel, when the amplitudes of the low frequency waves were increased; iii/ high frequency waves on the potassium channel, decreased both Vo (voltage in which the channel stays 50% open) and the steepness of fv (d fv/dV) as the amplitudes of the waves increased, and iv/ high frequency and low amplitude radiations on the sodium channel decreased the maximum value of fv (in relation to control), while high amplitudes increased this value. In conclusion, high and low frequency electromagnetic radiations were able to change the kinetics of the potassium and sodium channels in a squid giant axon model.     

Noise analysis of the glutamate-activated current in photoreceptors.

The glutamate-activated current in photoreceptors has been attributed both to a sodium/glutamate transporter and to a glutamate-activated chloride channel. We have further studied the glutamate-activated current in single, isolated photoreceptors from the tiger salamander using noise analysis on whole-cell patch-clamp recordings. In cones, the current is generated by chloride channels with a single-channel conductance of 0.7 pS and an open lifetime of 2.4 ms. The number of channels per cell is in the range of 10,000-20,000. Activation of the channels requires the presence of both glutamate and sodium. The single-channel conductance and the open lifetime of the channel are independent of the external concentration of glutamate and sodium. External glutamate and sodium affect only the opening rate of the channels. D,L-Threo-3-hydroxyaspartate (THA), a glutamate-transport blocker, is shown to be a partial agonist for the channel. The single-channel conductance is the same regardless of whether glutamate or THA is the ligand, but the open lifetime of the channel is only 0.8 ms with THA as ligand. The glutamate-activated current in rods has a similar single-channel conductance (0.74 pS) and open lifetime (3 ms). We propose a kinetic model, consistent with these results, to explain how a transporter can simultaneously act both as a sodium/glutamate-gated chloride channel and a glutamate/sodium cotransporter.     

Kinetic analysis of phasic inhibition of neuronal sodium currents by lidocaine and bupivacaine.

Phasic ("use-dependent") inhibition of sodium currents by the tertiary amine local anesthetics, lidocaine and bupivacaine, was observed in voltage-clamped node of Ranvier of the toad, Bufo marinus. Local anesthetics were assumed to inhibit sodium channels through occupation of a binding site with 1:1 stoichiometry. A three-parameter empirical model for state-dependent anesthetic binding to the Na channel is presented: this model includes two discrete parameters that represent the time integrals of binding and unbinding reactions during a depolarizing pulse, and one continuous parameter that represents the rate of unbinding of drug between pulses. The change in magnitude of peak sodium current during a train of depolarizing pulses to 0 mV was used as an assay of the extent of anesthetic binding at discrete intervals; estimates of model parameters were made by applying a nonlinear least-squares algorithm to the inhibition of currents obtained at two or more depolarizing pulse rates. Increasing the concentration of drug increased the rate of binding but had little or no effect on unbinding, as expected for a simple bimolecular reaction. The dependence of the model parameters on pulse duration was assessed for both drugs: as the duration of depolarizing pulses was increased, the fraction of channels binding drug during each pulse became significantly larger, whereas the fraction of occupied channels unbinding drug remained relatively constant. The rate of recovery from block between pulses was unaffected by pulse duration or magnitude. The separate contributions of open (O) and inactivated (I) channel binding of drug to the net increase in block per pulse were assessed at 0 mV: for lidocaine, the forward binding rate ko was 1.3 x 10(5) M-1 s-1, kl was 2.4 x 10(4) M-1 s-1; for bupivacaine, ko was 2.5 x 10(5) M-1 s-1, kl was 4.4 x 10(4) M-1 s-1. These binding rates were similar to those derived from time-dependent block of maintained Na currents in nodes where inactivation was incomplete due to treatment with chloramine-T. The dependence of model parameters on the potential between pulses (holding potential) was examined. All three parameters were found to be nearly independent of holding potential from -70 to -100 mV. These results are discussed with respect to established models of dynamic local anesthetic-Na channel interactions.     

Voltage-dependent inactivation of T-tubular skeletal calcium channels in planar lipid bilayers

Single-channel properties of dihydropyridine (DHP)-sensitive calcium channels isolated from transverse tubular (T-tube) membrane of skeletal muscle were explored. Single-channel activity was recorded in planar lipid bilayers after fusion of highly purified rabbit T-tube microsomes. Two populations of DHP-sensitive calcium channels were identified. One type of channel (noninactivating) was active (2 microM +/- Bay K 8644) at steady-state membrane potentials and has been studied in other laboratories. The second type of channel (inactivating) was transiently activated during voltage pulses and had a very low open probability (Po) at steady-state membrane potentials. Inactivating channel activity was observed in 47.3% of the experiments (n = 84 bilayers). The nonstationary kinetics of this channel was determined using a standard voltage pulse (HP = -50 mV, pulse to 0 mV). The time constant (tau) of channel activation was 23 ms. During the mV). The time constant (tau) of channel activation was 23 ms. During the pulse, channel activity decayed (inactivated) with a tau of 3.7 s. Noninactivating single-channel activity was well described by a model with two open and two closed states. Inactivating channel activity was described by the same model with the addition of an inactivated state as proposed for cardiac muscle. The single-channel properties were compared with the kinetics of DHP-sensitive inward calcium currents (ICa) measured at the cellular level. Our results support the hypothesis that voltage-dependent inactivation of single DHP-sensitive channels contributes to the decay of ICa.     

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.     

First node of Ranvier facilitates high-frequency burst encoding

In central neurons the first node of Ranvier is located at the first axonal branchpoint, ～ 100 μm from the axon initial segment where synaptic inputs are integrated and converted into action potentials (APs). Whether the first node contributes to this signal transformation is not well understood. Here it was found that in neocortical layer 5 axons, the first branchpoint is required for intrinsic high-frequency (≥ 100 Hz) AP bursts. Furthermore, block of nodal Na(+) channels or axotomy of the first node in intrinsically bursting neurons depolarized the somatic AP voltage threshold (～ 5 mV) and eliminated APs selectively within a high-frequency cluster in response to steady currents or simulated synaptic inputs. These results indicate that nodal persistent Na(+) current exerts an anterograde influence on AP initiation in the axon initial segment, revealing a computational role of the first node of Ranvier beyond conduction of the propagating AP.     

Ion Channel Clustering at the Axon Initial Segment and Node of Ranvier Evolved Sequentially in Early Chordates

In many mammalian neurons, dense clusters of ion channels at the axonal initial segment and nodes of Ranvier underlie action potential generation and rapid conduction. Axonal clustering of mammalian voltage-gated sodium and KCNQ (Kv7) potassium channels is based on linkage to the actin–spectrin cytoskeleton, which is mediated by the adaptor protein ankyrin-G. We identified key steps in the evolution of this axonal channel clustering. The anchor motif for sodium channel clustering evolved early in the chordate lineage before the divergence of the wormlike cephalochordate, amphioxus. Axons of the lamprey, a very primitive vertebrate, exhibited some invertebrate features (lack of myelin, use of giant diameter to hasten conduction), but possessed narrow initial segments bearing sodium channel clusters like in more recently evolved vertebrates. The KCNQ potassium channel anchor motif evolved after the divergence of lampreys from other vertebrates, in a common ancestor of shark and humans. Thus, clustering of voltage-gated sodium channels was a pivotal early innovation of the chordates. Sodium channel clusters at the axon initial segment serving the generation of action potentials evolved long before the node of Ranvier. KCNQ channels acquired anchors allowing their integration into pre-existing sodium channel complexes at about the same time that ancient vertebrates acquired myelin, saltatory conduction, and hinged jaws. The early chordate refinements in action potential mechanisms we have elucidated appear essential to the complex neural signaling, active behavior, and evolutionary success of vertebrates.     

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).     

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.     

Kinetic and steady-state characteristics of sodium channels modified by aconitine

Kinetic and steady-state characteristics of sodium channels of the Ranvier node membrane, modified by aconitine, were investigated by the voltage clamp method. Channels modified by aconitine were shown to be only partially inactivated. Dependence of the fraction of uninactivated channels on voltage can be described by a model of a channel with three states: closed, open, and inactivated. It is suggested that aconitine does not significantly change the parameters of the inactivated state. Repolarization of the membrane to between –70 and –110 mV after a long (10 msec) test shift of potential induces initially a rapid decline of the current ("tail"), followed by a slow rise to the steady-state value. To explain the kinetics of this current it is necessary to postulate two or more open states of the channel.Institute of Cytology, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 12, No. 6, pp. 612–618, November–December, 1980.     

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.     

Effects of deglycosylation of sodium channels on their structure and function

Voltage-gated sodium channels are important membrane proteins underlying electrical signaling in the nervous and muscular systems. They undergo rapid conformational changes between closed resting, activated, and inactivated states. Approximately 30% of the mass of the sodium channel is carbohydrate, present as glycoconjugate chains, mostly composed of N-acetylhexosamines and sialic acid. In this study, the effects of removing the carbohydrate on the functional and structural properties of highly purified sodium channels from Electrophorus electricus were investigated. After enzymatic deglycosylation, channels were reconstituted into planar lipid bilayers. In the presence of batrachotoxin, substates became evident and the single-channel conductance of the deglycosylated channels was slightly reduced relative to that of native channels, consistent with electrostatic effects due to the reduction in negative charge at the extracellular vestibule of the channel. The previously reported state-dependent changes in the circular dichroism spectra that are associated with the binding of the anticonvulsant drug Lamotrigine and batrachotoxin are also seen in the modified channels. Synchrotron radiation circular dichroism (SRCD) spectroscopy on the type of sugars found in the sodium channel showed that unlike most carbohydrates, these sugars produce a significant dichroic signal in the far-ultraviolet region. This can account for all of the measured SRCD-detected spectral differences between the native and deglycosylated channels, thereby indicating that no net change in protein secondary structure results from the deglycosylation procedure. Furthermore, thermal denaturation studies detected no significant differences in stability between native and deglycosylated channels. In summary, while the sugars of the voltage-gated sodium channels from electroplax are not essential for functional or structural integrity, they do appear to have a modulating effect on the conductance properties of these channels.