A physical model of sodium channel gating

Most current models of membrane ion channel gating are abstract compartmental models consisting of many undefined states connected by rate constants arbitrarily assigned to fit the known kinetics. In this paper is described a model with states that are defined in terms of physically plausible real systems which is capable of describing accurately most of the static and dynamic properties measured for the sodium channel of the squid axon. The model has two components. The Q-system consists of charges and dipoles that can move in response to an electric field applied across the membrane. It would contain and may compose the gating charge that is known to transfer prior to channel opening. The N-system consists of a charged group or dipole that is constrained to move only in the plane of the membrane and thus does not interact directly with the trans-membrane electric field but can interact electrostatically with the Q-system. The N-system has only two states, its resting state (channel closed) and its excited state (channel open) and its response time is very short in comparison with that of the Q-system. On depolarizing the membrane the the N-system will not make a transition to its open state until a critical amount of Q-charge transfer has occurred. Using only four adjustable parameters that are fully determined by fitting the equilibrium properties of the model to those of the sodium channel in the squid axon, the model is then able to describe with some accuracy the kinetics of channel opening and closing and includes the Cole and Moore delay. In addition to these predictions of the behaviour of assemblies of channels the model predicts some of the individual channel properties measured by patch clamp techniques.     

Modification of sodium and potassium channel gating kinetics by ether and halothane

The effect of ether and halothane on the kinetics of sodium and potassium currents were investigated in the crayfish giant axon. Both general anesthetics produced a reversible, dose-dependent speeding up of sodium current inactivation at all membrane potentials, with no change in the phase of the currents. Double-pulse inactivation experiments with ether also showed faster inactivation, but the rate of recovery from inactivation at negative potentials was not affected. Ether shifted the midpoint of the steady-state fast inactivation curve in the hyperpolarizing direction and made the curve steeper. The activation of potassium currents was faster with ether present, with no change in the voltage dependence of steady-state potassium currents. Ether and halothane are known to perturb the structure of lipid bilayer membranes; the alterations in sodium and potassium channel gating kinetics are consistent with the hypothesis that the rates of the gating processes of the channels can be affected by the state of the lipids surrounding the channels, but a direct effect of ether and halothane on the protein part of the channels cannot be ruled out. Ether did not affect the capacitance of the axon membrane.     

Kinetic model of the gating system of the sodium channel in a Ranvier node membrane

A kinetic model of the sodium channel gating system consisting of four subunits with three states--closed (X), open (Y) and inactivated (Z)--is proposed. For the channel to conduct, all the four subunits must be in the open state. The transitions between states X and Y are independent, while those between states X and Z are coupled, so that for the particle considered transition of one of two neighbouring particles into state Z increases the activation energy of the step by kT. The model fits rather well to the experimental data.     

Charge immobilization linked to inactivation in the aggregation model of channel gating

Expected gating currents are derived analytically from a continuous, time-homogenous Markov process formulation of the random behavior of a single aggregation gating site. The concept of aggregation gating involves a voltage-dependent reversible conformational change and a voltage-independent reversible aggregation process. A site is assumed to consist of four hypothetical protein subunits. Based on these assumptions the model is defined by the scheme of transitions between 12 possible site configurations. The model can account for the phenomenon of charge immobilization in asymmetry current data of the voltage-clamped sodium conductance system. It predicts gating currents without a rising phase. A rising phase is obtained, however, if the model is subjected to conventional symmetrical pulse protocols for measuring asymmetry currents in the axon. Novel pulse protocols are given that do not result in a rising phase if applied to the aggregation model. Simplified transition schemes that describe the basic kinetic behavior of the potassium and the sodium conductance system are derived by eliminating transitions of negligible probability from the original scheme.     

Redox reagents and divalent cations alter the kinetics of cystic fibrosis transmembrane conductance regulator channel gating.

Gating of the cystic fibrosis Cl(-) channel requires hydrolysis of ATP by its nucleotide binding folds, but how this process controls the kinetics of channel gating is poorly understood. In the present work we show that the kinetics of channel gating and presumably the rate of ATP hydrolysis depends on the species of divalent cation present and the oxidation state of the protein. With Ca(2+) as the dominant divalent cation instead of Mg(2+), the open burst duration of the channel is increased approximately 20-fold, and this change is reversible upon washout of Ca(2+). In contrast, "soft" divalent cations such as Cd(2+) interact covalently with cystic fibrosis transmembrane conductance regulator (CFTR). These metals decrease both opening and closing rates of the channel, and the effects are not reversed by washout. Oxidation of CFTR channels with a variety of oxidants resulted in a similar slowing of channel gating. In contrast, reducing agents had the opposite effect, increasing both opening and closing rates of the channel. In cell-attached patches, CFTR channels exhibit both oxidized and reduced types of gating, raising the possibility that regulation of the redox state of the channel may be a physiological mode of control of CFTR channel activity.     

Gating current harmonics. IV. Dynamic properties of secondary activation kinetics in sodium channel gating.

The kinetics for sodium channel gating appear to involve three coupled processes: (a) "primary" activation, (b) "secondary" activation, and (c) inactivation. Gating current data obtained in dynamic steady states with sinusoidal voltage-clamp were analyzed to give further details about the secondary activation process in sodium channel gating. Unlike primary activation and inactivation, the secondary activation kinetics involve physical processes that become defined when the data are analyzed as a function of the sinusoid frequency in addition to mean membrane potential. The effects of these processes are described, and a physical interpretation is presented.     

A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon.

Sodium channel gating behavior was modeled with Markovian models fitted to currents from the cut-open squid giant axon in the absence of divalent cations. Optimum models were selected with maximum likelihood criteria using single-channel data, then models were refined and extended by simultaneous fitting of macroscopic ionic currents, ON and OFF gating currents, and single-channel first latency densities over a wide voltage range. Best models have five closed states before channel opening, with inactivation from at least one closed state as well as the open state. Forward activation rate constants increase with depolarization, and deactivation rate constants increase with hyperpolarization. Rates of inactivation from the open or closed states are generally slower than activation or deactivation rates and show little or no voltage dependence. Channels tend to reopen several times before inactivating. Macroscopic rates of activation and inactivation result from a combination of closed, open and inactivated state transitions. At negative potentials the time to first opening dominates the macroscopic current due to slow activation rates compared with deactivation rates: channels tend to reopen rarely, and often inactivate from closed states before they reopen. At more positive potentials, the time to first opening and burst duration together produce the macroscopic current.     

Novel regulation of cystic fibrosis transmembrane conductance regulator (CFTR) channel gating by external chloride

The cystic fibrosis transmembrane conductance regulator (CFTR) is vital for Cl(-) and HCO(3)(-) transport in many epithelia. As the HCO(3)(-) concentration in epithelial secretions varies and can reach as high as 140 mm, the lumen-facing domains of CFTR are exposed to large reciprocal variations in Cl(-) and HCO(3)(-) levels. We have investigated whether changes in the extracellular anionic environment affects the activity of CFTR using the patch clamp technique. In fast whole cell current recordings, the replacement of 100 mm external Cl(-) ((Cl(o)(-))) with HCO(3)(-), Br(-), NO(3)(-), or aspartate(-) inhibited inward CFTR current (Cl(-) efflux) by approximately 50% in a reversible manner. Lowering Cl(o)(-) alone by iso-osmotic replacement with mannitol also reduced Cl(-) efflux to a similar extent. The maximal inhibition of CFTR current was approximately 70%. Raising cytosolic calcium shifted the Cl(-) dose-inhibition curve to the left but did not alter the maximal current inhibition observed. In contrast, a reduction in the internal [Cl(-)] neither inhibited CFTR nor altered the block caused by reduced Cl(o)(-). Single channel recordings from outside-out patches showed that lowering Cl(o)(-) markedly reduced channel open probability with little effect on unitary conductance. Together, these results indicate that alterations in Cl(o)(-) alone and not the Cl(-)/HCO(3)(-) ratio regulate the gating of CFTR. Physiologically, our data have implications for current models of epithelial HCO(3)(-) secretion and for the control of pH at epithelial cell surfaces.     

Stationarity of sodium channel gating kinetics in excised patches from neuroblastoma N1E 115.

Na channel gating parameters in a number of preparations are translated along the voltage axis in excised patches compared to cell attached or whole cell recording. The aim of this study is to determine whether these changes in gating behavior continue over an extended period or, rather, develop rapidly on excision with stationary kinetics thereafter. Average currents were constructed from single-channel records from neuroblastoma N1E 115 at various times after excision, excluding the first 5 min, in eight inside-out excised patches. Single exponentials were fitted to the current decay of the average records, and the mean time constant for each patch was determined. Values were plotted as the percentage difference from these means for each patch against time from excision. Collected results show no obvious trend in values from 5 min to 2 h. Kinetics are stationary, and shifts in Na channel gating parameters along the voltage axis seen in excised as compared to whole cell configuration in neuroblastoma must be complete by the first few minutes after excision. Raising the internal Na concentration reduced the single channel current amplitude, confirming that these are Na channels.     

A negatively charged residue in the outer mouth of rat sodium channel determines the gating kinetics of the channel

Previous studies using combined techniques of site-directed mutagenesis and electrophysiology of voltage-gated Na(+) channels have demonstrated that there are significant overlaps in the regions that are important for the two fundamental properties of the channels, namely gating and permeation. We have previously shown that a pore-lining residue, W402 in S5-S6 region (P loop) in domain I of the micro1 skeletal muscle Na(+) channel, was important in the gating of the channel. Here, we determined the role of an adjacent pore-lining negatively charged residue (E403) in channel gating. Charge neutralization or substitution with positively charged side chain at this position resulted in a marked delay in the rate of recovery from slow inactivation. Indeed, the fast inactivation process appeared intact. Restoration of the negatively charged side chain with a sulfhydryl modifier, MTS-ethylsulfonate, resulted in a reactivation profile from a slow-inactivated state, which was indistinguishable from that of the wild-type channels. We propose an additional functional role for the negatively charged residue. Assuming no major changes in the pore structure induced by the mutations, the negatively charged residue E403 may work in concert with other pore regions during recovery from slow inactivation of the channel. Our data represent the first report indicating the role of negative charge in the slow inactivation of the voltage-gated Na(+) channel.     

Simultaneous modifications of sodium channel gating by two scorpion toxins.

The effects of purified scorpion toxins from two different species on the kinetics of sodium currents were evaluated in amphibian myelinated nerves under voltage clamp. A toxin from Leiurus quinquestriatus slowed and prevented sodium channel inactivation, exclusively, and a toxin from Centruroides sculpturatus Ewing reduced transient sodium currents during a maintained depolarization, and induced a novel inward current that appeared following repolarization, as previously reported by Cahalan (1975, J. Physiol. [Lond.]. 244:511-534) for the crude scorpion venom. Both of these effects were observed in fibers treated with both of these toxins, and the kinetics of the induced current were modified in a way that showed that the same sodium channels were modified simultaneously by both toxins. Although the toxins can act on different sites, the time course of the action of C. sculpturatus toxin was accelerated in the presence of the L. quinquestriatus toxin, indicating some form of interaction between the two toxin binding sites.     

Comparison of ion current noise predicted from different models of the sodium channel gating mechanism in nerve membrane

Summary The theoretical power density spectrumS(f) of ion current noise is calculated from several models of the sodium channel gating mechanism in nerve membrane. Sodium ion noise experimental data from the frog node of Ranvier [Conti, F.,et al. (1976),J. Physiol. (London) 262:699] is used as a test of the theoretical results. The motivation for recent modeling has been evidence for a coupling between sodium activation and inactivation from voltage clamp data. The two processes are independent of one another in the Hodgkin and Huxley (HH) model [Hodgkin, A.L., Huxley, A.F. (1952),J. Physiol. (London) 117:500] The noise data is consistent with HH, as noted by Contiet al. (1976). The theoretical results given here appear to indicate that only one case of coupling models is also consistent with the noise data.     

Stochastic description of sodium channel gating

A stochastic model of the sodium channel is proposed. Transitions from the resting to the open state of the channel is described by the gamma distribution. The open state is temporary with an average open time T, and the channel proceeds to the inactivated state. The channel can be represented by two identical control molecules which undergo conformation transitions under changes of the electrical field. The gating of the channel is analyzed and its relation to the gating current is proposed. The movements of the control molecules are not identical with the charge movements. Charged parts of control molecules move in the electrical field of the membrane and make their conformation energetically possible. The model is represented by a set of differential equations, and explicit solutions for long depolarizing voltage steps are found. Parameters are determined to fit literary experimental data.     

A mutation in the pore of the sodium channel alters gating.

Ion permeation and channel gating are classically considered independent processes, but site-specific mutagenesis studies in K channels suggest that residues in or near the ion-selective pore of the channel can influence activation and inactivation. We describe a mutation in the pore of the skeletal muscle Na channel that alters gating. This mutation, I-W53C (residue 402 in the mu 1 sequence), decreases the sensitivity to block by tetrodotoxin and increases the sensitivity to block by externally applied Cd2+ relative to the wild-type channel, placing this residue within the pore near the external mouth. Based on contemporary models of the structure of the channel, this residue is remote from the regions of the channel known to be involved in gating, yet this mutation abbreviates the time to peak and accelerates the decay of the macroscopic Na current. At the single-channel level we observe a shortening of the latency to first opening and a reduction in the mean open time compared with the wild-type channel. The acceleration of macroscopic current kinetics in the mutant channels can be simulated by changing only the activation and deactivation rate constants while constraining the microscopic inactivation rate constants to the values used to fit the wild-type currents. We conclude that the tryptophan at position 53 in the domain IP-loop may act as a linchpin in the pore that limits the opening transition rate. This effect could reflect an interaction of I-W53 with the activation voltage sensors or a more global gating-induced change in pore structure.     

The conductance of the muscle nicotinic receptor channel changes rapidly upon gating.

We have recorded single-channel currents through fetal-type muscle nicotinic receptor channels at recording bandwidths of approximately 50 and 75 kHz. The time course of the rising phase of aligned and averaged openings can be entirely accounted for if it is assumed that the conductance of the single channel changes instantaneously, and that alignment and averaging introduce a dispersion of 2-3 microseconds. We conclude that we find no evidence for a gradual change in conductance as a channel opens or closes. The shapes of averaged power spectra are consistent with this conclusion, insofar as they exclude an exponential relaxation in the transition with a time constant of 10 microseconds or more.     

Modifications of human cardiac sodium channel gating by UVA light

Voltage-gated Na(+) channels are membrane proteins responsible for the generation of action potentials. In this report we demonstrate that UVA light elicits gating changes of human cardiac Na+ channels. First, UVA irradiation hampers the fast inactivation of cardiac Nav1.5 Na(+) channels expressed in HEK293t cells. A maintained current becomes conspicuous during depolarization and reaches its maximal quasi steady-state level within 5-7 min. Second, the activation time course is slowed by UVA light; modification of the activation gating by UVA irradiation continues for 20 min without reaching steady state. Third, along with the slowed activation time course, the peak current is reduced progressively. Most Na(+) currents are eliminated during 20 min of UVA irradiation. Fourth, UVA light increases the holding current nonlinearly; this phenomenon is slow at first but abruptly fast after 20 min. Other skeletal muscle Nav1.4 isoforms and native neuronal Na(+) channels in rat GH(3) cells are likewise sensitive to UVA irradiation. Interestingly, a reactive oxygen metabolite (hydrogen peroxide at 1.5%) and an oxidant (chloramine-T at 0.5 mM) affect Na(+) channel gating similarly, but not identically, to UVA. These results together suggest that UVA modification of Na(+) channel gating is likely mediated via multiple reactive oxygen metabolites. The potential link between oxidative stress and the impaired Na(+) channel gating may provide valuable clues for ischemia/reperfusion injury in heart and in CNS.     

Statistical methods for model discrimination. Applications to gating kinetics and permeation of the acetylcholine receptor channel.

Methods are described for discrimination of models of the gating kinetics and permeation of single ionic channels. Both maximum likelihood and regression procedures are discussed. In simple situations, where models are nested, standard hypothesis tests can be used. More commonly, however, non-nested models are of interest, and several procedures are described for model discrimination in these cases, including Monte Carlo methods, which allow the comparison of models at significance levels of choice. As an illustration, the methods are applied to single-channel data from acetylcholine receptor channels.     

Voltage-dependent gating of the cystic fibrosis transmembrane conductance regulator Cl- channel

When excised inside-out membrane patches are bathed in symmetrical Cl--rich solutions, the current-voltage (I-V) relationship of macroscopic cystic fibrosis transmembrane conductance regulator (CFTR) Cl- currents inwardly rectifies at large positive voltages. To investigate the mechanism of inward rectification, we studied CFTR Cl- channels in excised inside-out membrane patches from cells expressing wild-type human and murine CFTR using voltage-ramp and -step protocols. Using a voltage-ramp protocol, the magnitude of human CFTR Cl- current at +100 mV was 74 +/- 2% (n = 10) of that at -100 mV. This rectification of macroscopic CFTR Cl- current was reproduced in full by ensemble currents generated by averaging single-channel currents elicited by an identical voltage-ramp protocol. However, using a voltage-step protocol the single-channel current amplitude (i) of human CFTR at +100 mV was 88 +/- 2% (n = 10) of that at -100 mV. Based on these data, we hypothesized that voltage might alter the gating behavior of human CFTR. Using linear three-state kinetic schemes, we demonstrated that voltage has marked effects on channel gating. Membrane depolarization decreased both the duration of bursts and the interburst interval, but increased the duration of gaps within bursts. However, because the voltage dependencies of the different rate constants were in opposite directions, voltage was without large effect on the open probability (Po) of human CFTR. In contrast, the Po of murine CFTR was decreased markedly at positive voltages, suggesting that the rectification of murine CFTR is stronger than that of human CFTR. We conclude that inward rectification of CFTR is caused by a reduction in i and changes in gating kinetics. We suggest that inward rectification is an intrinsic property of the CFTR Cl- channel and not the result of pore block.     

Initial conditions and the kinetics of the sodium conductance in Myxicola giant axons. I. effects on the time-course of the sodium conductance

The effects of conditioning polarizations, ranging from--150 to 0 mV and of durations from 50 mus to 30 ms, on the time-course of GNa during test steps in potential were studied in Myxicola giant axons. Beyond the effects of conditioning polarizations on the amplitude of GNa, the only effect was to produce a translation of GNa(t) along the time axis without a change in shape. For depolarizing conditioning potentials, Hodgkin-Huxley kinetics predict time shifts about threefold greater than found experimentally, whereas the predictions of the coupled model of Goldman (1975. Biophys. J. 15:119--136) were in approximate agreement with our experiments. The time shifts developed over an exponential time-course as the conditioning pulse duration was increased. The time constant of development of the time shift was considerably faster than, and showed the opposite dependency on potential from, the values predicted by both models. It had a mean Q10 of 1/2.50. This fast activation process cannot account for the observed rise time behavior of GNa, suggesting that there is an additional activation process. All results are consistent with the idea that the gating structure displays more than three states, with state intermediate between rest and conducting.     

Continuum model of voltage-dependent gating. Macroscopic conductance, gating current, and single-channel behavior.

It is assumed that the conformational change of the voltage-gated channel is continuous, characterized by movement along a generalized one-dimensional reaction coordinate, x, varying from 0 to 1. This large conformational change is coupled to the movement of most of the gating charge. Superimposed on this large movement is a smaller, very fast conformational change that opens or closes the channel. The large conformational change perturbs the channel so that opening is favored near x = 1 and closing is favored near x = 0. The movement along the x axis is described by a generalized Nernst-Planck equation, whereas the open-close transition is modeled as a discrete reaction-rate process. The macroscopic conductance, gating current, and single-channel behavior of a simple, linearized version of the model is described. Although the model has only seven adjustable constants (about the same as would be required for a conventional three-state model), it can mimic the behavior of the delayed rectified K+ channel with 12 or more closed states. The single-channel behavior of the model can have bursts of rapid openings and closings, separated by long closed times. If the conformational change is assumed to correspond to the rotation and translation of charged helices, then this model can be used to estimate the effective rotational diffusion coefficient of the helix. Such calculations for the delayed rectifier K+ channel indicate that the motion must be very restricted.