Rate of excitation propagation in a reduced Hodgkins-Huxley model. II. Slow relaxation of the sodium current]

The influence of sodium current activation on the value of nerve excitation conduction velocity is investigated on the basis of Hodgkin-Huxley model. The potassium activation and sodium inactivation are considered as slow processes which do not develop to an appreciable extent in the region of conduction velocity formation. The system of equations was derived and solved analytically after neglecting the dependency of sodium relaxation time on potential; the approximation of steady-state sodium activation was also used with the help of Hevyside function. The algebraic equation for conduction velocity was obtained; its solution has a simple analytical form in two limits of rapid and slow sodium current relaxation. The comparison with the experimental data has shown that at not very high temperatures the slow (compared to the potential dynamics) sodium current relaxation approximation is more appropriate. The dependency of impulse velocity on capacitance and conductance of the fiber was analyzed.     

Kinetics of the slow variation of peak sodium current in the membrane of myelinated nerve following changes of holding potential or extracellular pH.

(1) Changes of the holding potential applied to the membrane of myelinated nerve fibres induced slow variations of the peak sodium current, which are super-imposed on the effect of sodium inactivation. (2) These slow variations are transitions between various steady levels of available sodium conductance. Their time course can be described by the function erfc (square root t/tau) where tau is the time and erfc the error function complement. The characteristic time tau lies in the range 2-4 min and depends on the membrane potential. (3) Changes of extracellular pH cause a rapid change of the peak sodium current followed by a slow variation as observed after changes of the holding potential. This slow variation can be prevented by applying simultaneously an appropriate change of the holding potential, e.g. the effect of changing pH from 7.3 to 5.3 is balanced by changing the potential from --70 to --55 mV. (4) The results are interpreted by postulating charged components diffusion slowly within the nodal membrane. Their transverse distribution controls the number of sodium channels available at a given membrane potential. The equivalence between change of pH and voltage is explained by assuming negative fixed charges at the outer surface of the membrane, which are protonated at low pH and thus affect the intrinsic membrane potential. (5) It is concluded that effects which are ascribed to the action of agents on individual sodium channels have to be corrected for variations in the number of available channels if these agents influence the intrinsic membrane potential, e.g. changes of extracellular pH.     

Slow actions of hyperpolarization on sodium channels in the membrane of myelinated nerve.

The mean sodium current, I, and the variance of sodium current fluctuations, var, were measured in myelinated nerve during a depolarization to V = 40 mV applied from the resting potential (VH = 0) or from a hyperpolarizing holding potential VH = -28 mV. From I and var the relative variations in the number N and the conductance gamma of sodium channels following changes of the holding potential were calculated. Hyperpolarizing the membrane from VH = 0 to -28 mV increased N by a factor of 3.7, whereas gamma decreased by a factor of 0.53. These actions of holding potential on sodium channels develop slowly since 500 ms prepulses to 0 or -28 mV do not alter the values of N and gamma.     

Sulfur dioxide derivative modulation of potassium channels in rat ventricular myocytes

The effects of sulfur dioxide (SO2) derivatives (bisulfite and sulfite, 1:3 M/M) on voltage-dependent potassium current in isolated adult rat ventricular myocyte were investigated using the whole cell patch-clamp technique. SO2 derivatives (10 microM) increased transient outward potassium current (I(to)) and inward rectifier potassium current (I(K1)), but did not affect the steady-state outward potassium current (I(ss)). SO2 derivatives significantly shifted the steady-state activation curve of I(to) toward the more negative potential at the V(h) point, but shifted the inactivation curve to more positive potential. SO2 derivatives markedly shifted the curve of time-dependent recovery of I(to) from the steady-state inactivation to the left, and accelerated the recovery of I(to) from inactivation. In addition, SO2 derivatives also significantly change the inactivation time constants of I(to) with increasing fast time constant and decreasing slow time constant. These results indicated a possible correlation between the change of properties of potassium channel and SO2 inhalation toxicity, which might cause cardiac myocyte injury through increasing extracellular potassium via voltage-gated potassium channels.     

Voltage-dependent regulation of modal gating in the rat SkM1 sodium channel expressed in Xenopus oocytes

The TTX-sensitive rat skeletal muscle sodium channel (rSkM1) exhibits two modes of inactivation (fast vs slow) when the alpha subunit is expressed alone in Xenopus oocytes. In this study, two components are found in the voltage dependence of normalized current inactivation, one having a V1/2 in the expected voltage range (approximately -50 mV, I(N)) and the other with a more hyperpolarized V1/2 (approximately -130 mV, IH) at a holding potential of -90 mV. The I(N) component is associated with the gating mode having rapid inactivation and recovery from inactivation of the macroscopic current (N-mode), while IH corresponds to the slow inactivation and recovery mode (H-mode). These two components are interconvertible and their relative contribution to the total current varies with the holding potential: I(N) is favored by hyperpolarization. The interconversion between the two modes is voltage dependent and is well fit to a first-order two-state model with a voltage dependence of e-fold/8.6 mV and a V1/2 of -62 mV. When the rat sodium channel beta 1-subunit is coinjected with rSkM1, IH is essentially eliminated and the inactivation kinetics of macroscopic current becomes rapid. These two current components and their associated gating modes may represent two conformations of the alpha subunit, one of which can be stabilized either by hyperpolarization or by binding of the beta 1 subunit.     

Reconstruction of ionic currents in a molluscan photoreceptor.

Two-microelectrode voltage-clamp measurements were made to determine the kinetics and voltage dependence of ionic currents across the soma membrane of the Hermissenda type B photoreceptor. The voltage-dependent outward potassium currents, IA and ICa(2+)-K+, the inward voltage-dependent calcium current, ICa2+ and the light-induced current, IIgt, were then described with Hodgkin-Huxley-type equations. The fast-activating and inactivating potassium current, IA, was described by the equation; IA(t) = gA(max)(ma infinity[1-exp(-t/tau ma)])3 x (ha infinity [1-exp(-t/tau ha)] + exp(-t/tau ha)) (Vm-EK), where the parameters ma infinity, ha infinity, tau ma, and tau ha are functions of membrane potential, Vm, and ma infinity and ha infinity are steady-state activation and inactivation parameters. Similarly, the calcium-dependent outward potassium current, ICa(2+)-K+, was described by the equation, ICa(2+)-K+ (t) = gc(max)(mc infinity(VC)(1-exp[-t/tau mc (VC)]))pc (hc infinity(VC) [1-exp(-t/tau hc)] + exp(-t/tau hc(VC)])pc(VC-EK). In high external potassium, ICa(2+)-K+ could be measured in approximate isolation from other currents as a voltage-dependent inward tail current following a depolarizing command pulse from a holding potential of -60 mV. A voltage-dependent inward calcium current across the type B soma membrane, ICa2+, activated rapidly, showed little inactivation, and was described by the equation: ICa2+ = gCa(max) [1 + exp](-Vm-5)/7]-1 (Vm-ECa), where gCa(max) was 0.5 microS. The light-induced current with both fast and slow phases was described by: IIgt(t) = IIgt1 + IIgt2 + IIgt3, IIgti = gIgti [1-exp(- ton/tau mi)] exp(-ton/tau hi)(Vm-EIgti) (i = 1, 2).(ABSTRACT TRUNCATED AT 250 WORDS)     

Implication of the C-terminal region of the alpha-subunit of voltage-gated sodium channels in fast inactivation

The α-subunit of both the human heart (hH1) and human skeletal muscle (hSkM1) sodium channels were expressed in a mammalian expression system. The channels displayed slow (hH1) and fast (hSkM1) current decay kinetics similar to those seen in native tissues. Hence, the aim of this study was to identify the region on the α-subunit involved in the differences of these current-decay kinetics. A series of hH1/hSkM1 chimeric sodium channels were constructed with the focus on the C-terminal region. Sodium currents of chimeric channels were recorded using the patch-clamp technique in whole-cell configuration. Chimeras where the C-terminal region had been exchanged between hH1 and hSkM1 revealed that this region contains the elements that cause differences in current decay kinetics between these sodium channel isoforms. Other biophysical characteristics (steady-state activation and inactivation and recovery from inactivation) were similar to the phenotype of the parent channel. This indicates that the C-terminus is exclusively implicated in the differences of current decay kinetics. Several other chimeras were constructed to identify a specific region of the C-terminus causing this difference. Our results showed that the first 100-amino-acid stretch of the C-terminal region contains constituents that could cause the differences in current decay between the heart and skeletal muscle sodium channels. This study has uncovered a direct relationship between the C-terminal region and the current-decay of sodium channels. These findings support the premise that a novel regulatory component exists for fast inactivation of voltage-gated sodium channels. Received: 1 March 2001/Revised: 18 May 2001     

Kinetics of the sodium current through EDTA-modified calcium channels of the molluscan neuron somatic membrane

The kinetics of the slow current carried by sodium ions through potential-dependent calcium channels after addition of EDTA to calcium-free external solution was investigated in experiments by the intracellular dialysis method on isolatedHelix pomatia neurons. The activation kinetics of this current was similar to that of the calcium current and could be described by the use of the square of the activation variable m in Hodgkin-Huxley equations. The decay (inactivation) kinetics of the induced sodium current during prolonged depolarization is biexponential in character. It is suggested that decay of the sodium currents takes place as a result of two independent processes: potential-dependent inactivation with a time constant τ_h～1 sec, taking place as far as a certain steady-state level h_∞, and a decrease in current connected with Na⁺ accumulation inside the cell during passage of the current and a consequent change in the sodium electrochemical potential (τ_c～10 sec). It is concluded that modification of the calcium channels, so that they acquire the ability to conduct sodium, has no significant effect on the gating mechanisms responsible for opening and closing of the channels.     

Slow sodium inactivation in nerve after exposure to sulhydryl blocking reagents

Exposure to N-ethylmaleimide (NEM), a reagent that binds covalently to protein sulfhydryl groups, results in a specific reduction in sodium conductance in crayfish axons. Resting potential, the delayed rise in potassium conductance, and the selectivity of the sodium channel are unaffected. Sodium currents are only slightly increased by hyperpolarizing prepulses of up to 50 ms duration, but can be restored to about 70% of their value before treatment if this duration is increased to 300-800 ms. The time to peak sodium current and the time constant of decay of sodium tail currents are unaffected by NEM, suggesting that the sodium activation system remains unaltered. Kinetic studies suggest that NEM reacts with a "slow" sodium inactivation system that is present in normal axons and that may be seen after depolarization produced by lowered the holding potential or increasing the external potassium concentration. NEM also perturbs the fast h inactivation system, and in a potential-dependent manner. At small depolarizations tauh is decreased, while at strong depolarizations it is increased over control values. Experiments with structural analogs of NEM suggest that sulfhydryl block is involved, but do not rule out an action similar to that of local anesthetics, p- Chloromercuriphenylsulfonic acid (PCMBS), another reagent with high specificity for SH groups, also blocks sodium currents, but restoration with prolonged hyperpolarizations is not possible.     

Mechanisms of sodium channel inactivation

Rapid inactivation of sodium channels is crucial for the normal electrical activity of excitable cells. There are many different types of inactivation, including fast, slow and ultra-slow, and each of these can be modulated by cellular factors or accessory subunits. Fast inactivation occurs by a 'hinged lid' mechanism in which an inactivating particle occludes the pore, whereas slow inactivation is most likely to involve a rearrangement of the channel pore. Subtle defects in either inactivation process can lead to debilitating human diseases, including periodic paralyses in muscle, ventricular fibrillation and long QT syndrome (delayed cardiac repolarization) in the heart, and epilepsy in the CNS.     

Ultra-slow inactivation in mu1 Na+ channels is produced by a structural rearrangement of the outer vestibule

While studying the adult rat skeletal muscle Na+ channel outer vestibule, we found that certain mutations of the lysine residue in the domain III P region at amino acid position 1237 of the alpha subunit, which is essential for the Na+ selectivity of the channel, produced substantial changes in the inactivation process. When skeletal muscle alpha subunits (micro1) with K1237 mutated to either serine (K1237S) or glutamic acid (K1237E) were expressed in Xenopus oocytes and depolarized for several minutes, the channels entered a state of inactivation from which recovery was very slow, i.e., the time constants of entry into and exit from this state were in the order of approximately 100 s. We refer to this process as "ultra-slow inactivation". By contrast, wild-type channels and channels with the charge-preserving mutation K1237R largely recovered within approximately 60 s, with only 20-30% of the current showing ultra-slow recovery. Coexpression of the rat brain beta1 subunit along with the K1237E alpha subunit tended to accelerate the faster components of recovery from inactivation, as has been reported previously of native channels, but had no effect on the mutation-induced ultra-slow inactivation. This implied that ultra-slow inactivation was a distinct process different from normal inactivation. Binding to the pore of a partially blocking peptide reduced the number of channels entering the ultra-slow inactivation state, possibly by interference with a structural rearrangement of the outer vestibule. Thus, ultra-slow inactivation, favored by charge-altering mutations at site 1237 in micro1 Na+ channels, may be analogous to C-type inactivation in Shaker K+ channels.     

Tetrahydrobiopterin and nitric oxide: mechanistic and pharmacological aspects

In previous minireviews in this journal, we discussed work on induction of tetrahydrobiopterin biosynthesis by cytokines and its significance for nitric oxide (NO) production of intact cells as well as functions of H4-biopterin identified at this time for NO synthases (Proc Soc Exp Biol Med 203: 1-12, 1993; Proc Soc Exp Biol Med 219: 171-182, 1998). Meanwhile, the recognition of the importance of tetrahydrobiopterin for NO formation has led to new insights into complex biological processes and revealed possible novel pharmacological strategies to intervene in certain pathological conditions. Recent work could also establish that tetrahydrobiopterin, in addition to its allosteric effects, is redox-active in the NO synthase reaction. In this review, we summarize the current view of how tetrahydrobiopterin functions in the generation of NO and focus on pharmacological aspects of tetrahydrobiopterin availability with emphasis on endothelial function.     

Dynamic and static chromatin

It was found that the dependence of the viscosity of calf thymus chromatin dispersions and human leukocytes on ethidium bromide concentration had two peaks indicative of domains with circular supercoiled DNA and varying resistance to ultrasound in the cells and isolated chromatin. The hypothesis of V. D. Paponov and P. S. Gromov (Bull. Exp. Biol. Med., N5, 590, 1985) on the transformation of static relations of nucleosome DNA-containing nuclei into dynamic, after chromatin exposure to ultrasound due to DNA linearization in chromatin domains possessing circular supercoiled DNA, has been confirmed.     

Na and Ca channels in a transformed line of anterior pituitary cells

The ionic conductances of GH3 cells, a transformed line from rat anterior pituitary, have been studied using the whole-cell variant of the patch-clamp technique (Hamill et al., 1981). Pipettes of very low resistance were used, which improved time resolution and made it possible to control the ion content of the cell interior, which equilibrated very rapidly with the pipette contents. Time resolution was further improved by using series resistance compensation and "ballistic charging" of the cell capacitance. We have identified and partially characterized at least three conductances, one carrying only outward current, and the other two normally inward. The outward current is absent when the pipette is filled with Cs+ instead of K+, and has the characteristics of a voltage-dependent potassium conductance. One of the two inward conductances (studied with Cs+ inside) has fast activation, inactivation and deactivation kinetics, is blocked by tetrodotoxin (TTX), and has a reversal potential at the sodium equilibrium potential. The other inward current activates more slowly and deactivates with a quick phase and a very slow phase after a short pulse. Either Ca++ or Ba++ serves as current carrier. During a prolonged pulse, current inactivates fairly completely if there is at least 5 mM Ca++ outside, and the amplitude of the current tails following the pulse diminishes with the time course of inactivation. When Ba++ entirely replaces Ca++ in the external medium, there is no inactivation, but deactivation kinetics of Ca channels vary as pulse duration increases: the slow phase disappears, the fast phase grows in amplitude. Inactivation (Ca++ outside) is unaltered by 50 mM EGTA in the pipette: inactivation cannot be the result of internal accumulation of Ca++.     

Idiosyncratic Gating of HERG-like K+ Channels in Microglia

A simple kinetic model is presented to explain the gating of a HERG-like voltage-gated K⁺ conductance described in the accompanying paper (Zhou, W., F.S. Cayabyab, P.S. Pennefather, L.C. Schlichter, and T.E. DeCoursey. 1998. J. Gen. Physiol. 111:781–794). The model proposes two kinetically distinct closing pathways, a rapid one favored by depolarization (deactivation) and a slow one favored by hyperpolarization (inactivation). The overlap of these two processes leads to a window current between −50 and +20 mV with a peak at −36 mV of ∼12% maximal conductance. The near absence of depolarization-activated outward current in microglia, compared with HERG channels expressed in oocytes or cardiac myocytes, can be explained if activation is shifted negatively in microglia. As seen with experimental data, availability predicted by the model was more steeply voltage dependent, and the midpoint more positive when determined by making the holding potential progressively more positive at intervals of 20 s (starting at −120 mV), rather than progressively more negative (starting at 40 mV). In the model, this hysteresis was generated by postulating slow and ultra-slow components of inactivation. The ultra-slow component takes minutes to equilibrate at −40 mV but is steeply voltage dependent, leading to protocol-dependent modulation of the HERG-like current. The data suggest that “deactivation” and “inactivation” are coupled through the open state. This is particularly evident in isotonic Cs⁺, where a delayed and transient outward current develops on depolarization with a decay time constant more voltage dependent and slower than the deactivation process observed at the same potential after a brief hyperpolarization.     

A slow component of gating current in crayfish giant axons resembles inactivation charge movement.

Recent experimental evidence from a number of preparations indicates that sodium channel inactivation may be intrinsically voltage sensitive. Intrinsically voltage sensitive inactivation should produce a charge movement. Crayfish giant axons provide a unique opportunity to reexamine the slower components of gating currents (Ig) for a contribution from inactivation (Igh). In reference to other axon preparations, this preparation has relatively rapid inactivation, and steady-state inactivation has a comparatively steep voltage dependence. As predicted by a two-state scheme for voltage-sensitive sodium channel inactivation, Ig in crayfish axons includes a slow component with time constant comparable to the time constant of decay of the sodium current. Allowing for some delay in its onset (60 microseconds), inactivation as described by this slow component of Ig carries roughly the amount of charge predicted by the voltage dependence of inactivation.     

Gating current harmonics. III. Dynamic transients and steady states with intact sodium inactivation gating.

Internally perfused squid giant axons with intact sodium inactivation gating were prepared for gating current experiments. Gating current records were obtained in sinusoidally driven dynamic steady states and as dynamic transients as functions of the mean membrane potential and the frequency of the command sinusoid. Controls were obtained after internal protease treatment of the axons that fully removed inactivation. The nonlinear analysis consisted of determining and interpreting the harmonic content in the current records. The results indicate the presence of three kinetic processes, two of which are associated with activation gating (the so-called primary and secondary processes), and the third with inactivation gating. The dynamic steady state data show that inactivation gating does not contribute a component to the gating current, and has no direct voltage-dependence of its own. Rather, the inactivation kinetics appear to be coupled to the primary activation kinetics, and the coupling mechanism appears to be one of reciprocal steric hindrance between two molecular components. The mechanism allows the channel to become inactivated without first entering the conducting state, and will do so in about 40 percent of depolarizing voltage-clamp steps to 0 mV. The derived model kinetics further indicate that the conducting state may flicker between open and closed with the lifetime of either state being 10 microseconds. Dynamic transients generated by the model kinetics (i.e., the behavior of the harmonic components as a function of time after an instantaneous change in the mean membrane potential from a holding potential of -80 mV) match the experimental dynamic transients in all details. These transients have a duration of 7-10 ms (depending on the level of depolarization), and are the result of the developing inactivation following the discontinuous voltage change. A detailed hypothetical molecular model of the channel and gating machinery is presented.     

Electrophysiological Study of Chimeric Sodium Channels from Heart and Skeletal Muscle

The α-subunit cDNAs encoding voltage-sensitive sodium channels of human heart (hH1) and rat skeletal muscle (rSkM1) have been expressed in the tsA201 mammalian cell line, in which inactivation properties appear to be normal in contrast to Xenopus oocytes. A series of rSkM1/hH1 chimeric sodium channels has been evaluated to identify the domains of the α-subunits that are responsible for a set of electrophysiological differences between hH1 and rSkM1, namely, midpoints and slope factors of steady-state activation and inactivation, inactivation kinetics and recovery from inactivation kinetics and their voltage-dependence. The phenotype of chimeric channels in which each hH1 domain was successively introduced into a rSkM1 α-subunit framework confirmed the following conclusions. (i) The D4 and or/C-ter. are responsible for the slow inactivation of hH1 sodium channels. (ii) Concerning the other differences between rSkM1 and hH1: steady-state activation and inactivation, kinetics of recovery from inactivation, the phenotypes are determined probably by more than one domain of the α-subunit. Received: 20 January 1998/Revised: 19 March 1998     

Effects of Taurine–Magnesium Coordination Compound on Ionic Channels in Rat Ventricular Myocytes of Arrhythmia Induced by Ouabain

Taurine-magnesium coordination compound (TMCC) has anti-arrhythmic effects. The aim of the present study was to explore the targets of the anti-arrhythmic effect of TMCC and the electrophysiological effects of TMCC on ouabain-induced arrhythmias in rat ventricular myocytes. Sodium current (I(Na)), L-type calcium current (I(ca, L)), and transient outward potassium current (I(to)) were measured and analyzed using whole-cell patch-clamp recording technique in normal rat cardiac myocytes and rat ventricular myocytes of arrhythmia induced by ouabain. In isolated ventricular myocytes, I(Na) and I(to) were blocked by TMCC (100, 200, 400 μM) in a concentration-dependent manner, and the effects of TMCC (400 μM) were equal to that of amiodarone. However, I (ca, L) was moderately increased by TMCC (400 μM) while significantly decreased by amiodarone. Ouabain (5 μM) significantly decreased sodium, L-type calcium, and transient outward potassium currents. TMCC (100 μM) relieved abnormal sodium currents induced by ouabain through facilitation of steady-state inactivation. TMCC (200 and 400 μM) relieved abnormal L-type calcium currents induced by ouabain through facilitation of steady-state activation and retardation of steady-state inactivation. TMCC failed to further inhibit abnormal transient outward potassium currents induced by ouabain. However, amiodarone inhibited the decreasing sodium, L-type calcium, and transient outward potassium currents further. These data suggest that I(Na), I(ca, L), and I(to) may be the targets of the antiarrhythmic effect of TMCC, which can antagonize ouabain-induced changes of ionic currents in rat ventricular myocytes.