Estimation of ionic channel surface density from relaxation ionic and gating currents

It is shown that excitable membrane surface density of channels can be estimated from ionic and gating current relaxations. The gating currents are determined thermodynamically from a multistate kinetic model. The parameters of the kinetic model are derived from ionic current relaxations. The assumptions regarding the gating process made here are the same as those made in fluctuation analysis previously regarded as the only method that may yield channel density from membrane currents.     

On the relation between displacement currents and activation of the sodium conductance in the squid giant axon.

The early time course of the current passing across the membrane in squid giant axons in which the ionic currents have been blocked reveals substantial asymmetries during and after the application of hyperpolarizing and depolarizing voltage-clamp pulses of identical size. Since the integral of the 'on' and 'off' current transients is zero, these currents must result from charge movements confined to the membrane and, therefore, they are nonlinear displacement currents. The steady state rearrangement of the charges as a consequence of sudden displacements of the membrane potential is consistent with a Boltzmann distribution of charges between two states characterized by different energy levels. Following changes in membrane potential the charges undergo a first order transition between these states. The relaxation time constant for the transition at a given temperature is a function of membrane potential. We propose that these displacement currents arise from a redistribution of the charges involved in the sodium gating system.     

A physical model of potassium channel activation: from energy landscape to gating kinetics

We have developed a method for rapidly computing gating currents from a multiparticle ion channel model. Our approach is appropriate for energy landscapes that can be characterized by a network of well-defined activation pathways with barriers. To illustrate, we represented the gating apparatus of a channel subunit by an interacting pair of charged gating particles. Each particle underwent spatial diffusion along a bistable potential of mean force, with electrostatic forces coupling the two trajectories. After a step in membrane potential, relaxation of the smaller barrier charge led to a time-dependent reduction in the activation barrier of the principal gate charge. The resulting gating current exhibited a rising phase similar to that measured in voltage-dependent ion channels. Reduction of the two-dimensional diffusion landscape to a circular Markov model with four states accurately preserved the time course of gating currents on the slow timescale. A composite system containing four subunits leading to a concerted opening transition was used to fit a series of gating currents from the Shaker potassium channel. We end with a critique of the model with regard to current views on potassium channel structure.     

Computation of axon gating currents from dipole moment changes in channel subunits.

The gating polarizational currents were computed on the basis of the dipole moment changes occurring in nerve membrane ionic channel subunits. Membrane thickness and surface density of channels were the only parameters used in addition to the Hodgkin-Huxley model. The gating currents computed for membrane potentials where the Hodgkin-Huxley empirical formulae are reliable were found to be in good agreement with the available experimental data. It is demonstrated that the gating currents of the n and h subunits are responsible for the late slowly decaying gating currents.     

The sodium currents of nerve under voltage clamp as heterogeneous kinetics: A model that is consistent with possible kinetic behavior

Voltage clamp; Na⁺ current; Dielectric relaxation: Charge mobility: Intramemhrune diffusion A model is presented which explains the Na⁺ currents of voltage-clamped nerve as resulting from a heterogeneous initiation of a sequential kinetic process. This is in analogy with the heterogeneity of the kinetics of other dielectric relaxations. The results suggest that: (1) The kinetic processes responsible for the voltage response occur within the membrane rather than at the surface; (2) The heterogeneity is due to simultaneous thermal diffusion and electric field-induced charge migration; (3) The slow turnoff upon prolonged depolarization is a voltage-independent, thermally controlled process: (4) The fast turnoff upon instantaneous repolarizalion is the reverse of the turning-on process. All the kinetic parameters depend on the transmembrane potential in accord with the possible behavior expected from activated-stale theory. The diffusion coefficient of the charged species in the membrane as found from the data agrees with that found by photobleaching experiments on general proteins in membranes. The charge on the molecule responsible for the heterogeneous ‘gating’ can be calculated unambiguously from the data.     

Voltage-dependent membrane capacitance in rat pituitary nerve terminals due to gating currents

We investigated the voltage dependence of membrane capacitance of pituitary nerve terminals in the whole-terminal patch-clamp configuration using a lock-in amplifier. Under conditions where secretion was abolished and voltage-gated channels were blocked or completely inactivated, changes in membrane potential still produced capacitance changes. In terminals with significant sodium currents, the membrane capacitance showed a bell-shaped dependence on membrane potential with a peak at approximately -40 mV as expected for sodium channel gating currents. The voltage-dependent part of the capacitance showed a strong correlation with the amplitude of voltage-gated Na+ currents and was markedly reduced by dibucaine, which blocks sodium channel current and gating charge movement. The frequency dependence of the voltage-dependent capacitance was consistent with sodium channel kinetics. This is the first demonstration of sodium channel gating currents in single pituitary nerve terminals. The gating currents lead to a voltage- and frequency-dependent capacitance, which can be well resolved by measurements with a lock-in amplifier. The properties of the gating currents are in excellent agreement with the properties of ionic Na+ currents of pituitary nerve terminals.     

Tracking S4 movement by gating pore currents in the bacterial sodium channel NaChBac

Voltage-gated sodium channels mediate the initiation and propagation of action potentials in excitable cells. Transmembrane segment S4 of voltage-gated sodium channels resides in a gating pore where it senses the membrane potential and controls channel gating. Substitution of individual S4 arginine gating charges (R1–R3) with smaller amino acids allows ionic currents to flow through the mutant gating pore, and these gating pore currents are pathogenic in some skeletal muscle periodic paralysis syndromes. The voltage dependence of gating pore currents provides information about the transmembrane position of the gating charges as S4 moves in response to membrane potential. Here we studied gating pore current in mutants of the homotetrameric bacterial sodium channel NaChBac in which individual arginine gating charges were replaced by cysteine. Gating pore current was observed for each mutant channel, but with different voltage-dependent properties. Mutating the first (R1C) or second (R2C) arginine to cysteine resulted in gating pore current at hyperpolarized membrane potentials, where the channels are in resting states, but not at depolarized potentials, where the channels are activated. Conversely, the R3C gating pore is closed at hyperpolarized membrane potentials and opens with channel activation. Negative conditioning pulses revealed time-dependent deactivation of the R3C gating pore at the most hyperpolarized potentials. Our results show sequential voltage dependence of activation of gating pore current from R1 to R3 and support stepwise outward movement of the substituted cysteines through the narrow portion of the gating pore that is sealed by the arginine side chains in the wild-type channel. This pattern of voltage dependence of gating pore current is consistent with a sliding movement of the S4 helix through the gating pore. Through comparison with high-resolution models of the voltage sensor of bacterial sodium channels, these results shed light on the structural basis for pathogenic gating pore currents in periodic paralysis syndromes.     

On the physico-chemical basis of voltage-dependent molecular gating mechanisms in biological membranes

Summary The possible nature and theoretical treatment of electric field-induced molecular processes in a membrane are examined. Special attention is given to fairly fast switching phenomena as reflected by asymmetry currents as well as ionic gating in squid axon and similar systems. The apparent charge displacement associated with the underlying mechanisms is argued to be brought about by conformational transitions of integral macromolecular structures. Under these circumstances, voltage changes can actually control the functional state of membranes by direct interference with conformational equilibria. A basic model is quantitatively discussed and shown to account for certain observed asymmetry currents. Effects due to temperature, pressure, or chemical interactions can be readily described. It is indicated how more complicated voltage-dependent membrane processes may be approached along these lines.     

Voltage noise influences action potential duration in cardiac myocytes

Stochastic gating of ion channels introduces noise to membrane currents in cardiac muscle cells (myocytes). Since membrane currents drive membrane potential, noise thereby influences action potential duration (APD) in myocytes. To assess the influence of noise on APD, membrane potential is in this study formulated as a stochastic process known as a diffusion process, which describes both the current-voltage relationship and voltage noise. In this framework, the response of APD voltage noise and the dependence of response on the shape of the current-voltage relationship can be characterized analytically. We find that in response to an increase in noise level, action potential in a canine ventricular myocytes is typically prolonged and that distribution of APDs becomes more skewed towards long APDs, which may lead to an increased frequency of early after-depolarization formation. This is a novel mechanism by which voltage noise may influence APD. The results are in good agreement with those obtained from more biophysically-detailed mathematical models, and increased voltage noise (due to gating noise) may partially underlie an increased incidence of early after-depolarizations in heart failure.     

Gating currents: the role of nonlinear capacitative currents of electrostrictive origin.

The nonlinear capacitative currents deriving from electrostrictive changes of membrane capacitance have been calculated under conditions similar to those employed by Armstrong and Bezanilla (1974) and Keynes and Rojas (1974) in their experiments on gating currents. For values of the parameter characterizing membrane electrostriction in the range suggested by optical retardation studies of Cohen et al. (1971), the nonlinear current of electrostrictive origin is comparable in magnitude and time-course, but is opposite in direction to the observed gating currents. Hence, the a priori neglect of electrostrictive currents is probably not justified. Conversely, if this current is, in fact, negligibly small in real situations, it follows that membrane compressibility must be significantly smaller than has been estimated.     

Observations on intramembrane charge movements in skeletal muscle.

Using signal-averaging techniques, one can record small membrane currents which remain even after blockage of the ionic currents which accompany electrical excitation in muscle. These residual currents probably represent the reorientation of charged molecules inside the membrane in response to a change in membrane potential. Two operationally separable types of intramembrane charge movement in muscle are described, one of which may play a role in excitation-contraction coupling. Studies of tetrodotoxin binding to muscle indicate that "sodium gating current" is unlikely to contribute significantly to either type of charge movement.     

Molecular mechanism for depolarization-induced modulation of Kv channel closure

Voltage-dependent potassium (Kv) channels provide the repolarizing power that shapes the action potential duration and helps control the firing frequency of neurons. The K⁺ permeation through the channel pore is controlled by an intracellularly located bundle-crossing (BC) gate that communicates with the voltage-sensing domains (VSDs). During prolonged membrane depolarizations, most Kv channels display C-type inactivation that halts K⁺ conduction through constriction of the K⁺ selectivity filter. Besides triggering C-type inactivation, we show that in Shaker and Kv1.2 channels (expressed in Xenopus laevis oocytes), prolonged membrane depolarizations also slow down the kinetics of VSD deactivation and BC gate closure during the subsequent membrane repolarization. Measurements of deactivating gating currents (reporting VSD movement) and ionic currents (BC gate status) showed that the kinetics of both slowed down in two distinct phases with increasing duration of the depolarizing prepulse. The biphasic slowing in VSD deactivation and BC gate closure was strongly correlated in time and magnitude. Simultaneous recordings of ionic currents and fluorescence from a probe tracking VSD movement in Shaker directly demonstrated that both processes were synchronized. Whereas the first slowing originates from a stabilization imposed by BC gate opening, the subsequent slowing reflects the rearrangement of the VSD toward its relaxed state (relaxation). The VSD relaxation was observed in the Ciona intestinalis voltage-sensitive phosphatase and in its isolated VSD. Collectively, our results show that the VSD relaxation is not kinetically related to C-type inactivation and is an intrinsic property of the VSD. We propose VSD relaxation as a general mechanism for depolarization-induced slowing of BC gate closure that may enable Kv1.2 channels to modulate the firing frequency of neurons based on the depolarization history.     

S3-S4 Linker Length Modulates the Relaxed State of a Voltage-Gated Potassium Channel

Voltage-sensing domains (VSDs) are membrane protein modules found in ion channels and enzymes that are responsible for a large number of fundamental biological tasks, such as neuronal electrical activity. The VSDs switch from a resting to an active conformation upon membrane depolarization, altering the activity of the protein in response to voltage changes. Interestingly, numerous studies describe the existence of a third distinct state, called the relaxed state, also populated at positive potentials. Although some physiological roles for the relaxed state have been suggested, little is known about the molecular determinants responsible for the development and modulation of VSD relaxation. Several lines of evidence have suggested that the linker (S3-S4 linker) between the third (S3) and fourth (S4) transmembrane segments of the VSD alters the equilibrium between resting and active conformations. By measuring gating currents from the Shaker potassium channel, we demonstrate here that shortening the S3-S4 linker stabilizes the relaxed state, whereas lengthening the linker or splitting it and coinjecting two fragments of the channel have little effect. We propose that natural variations of the length of the S3-S4 linker in various VSD-containing proteins may produce differential VSD relaxation in vivo.     

IRK1 inward rectifier K(+) channels exhibit no intrinsic rectification

In intact cells the depolarization-induced outward IRK1 currents undergo profound relaxation so that the steady-state macroscopic I-V curve exhibits strong inward rectification. A modest degree of rectification persists after the membrane patches were perfused with artificial solutions devoid of Mg(2+) and polyamines, which has been interpreted as a reflection of intrinsic channel gating and led to the view that inward rectification results from enhancement of the intrinsic gating by intracellular cations rather than simple pore block. Furthermore, IRK1 exhibits significant extracellular K(+)-sensitive relaxation of its inward current, a feature that has been likened to the C-type inactivation observed in the voltage-activated Shaker K(+) channels. We found that both these current relaxations can be accounted for by impurities in some common constituents of recording solutions, such as residual hydroxyethylpiperazine in HEPES and ethylenediamine in EDTA. Therefore, inherently, IRK1 channels are essentially ohmic at the macroscopic level, and the voltage jump-induced current relaxations do not reflect IRK1 gating but the unusually high affinity of its pore for cations. Furthermore, our study helps define the optimal experimental conditions for studying IRK1.     

Charge displacements in a single potassium ion channel macromolecule during gating.

Single ion channel currents can only provide indirect information on channel molecular events (except for timing). In contrast, the electric displacement currents associated with channel gating, termed gating currents, can provide direct information regarding the channel molecule's conformational changes. However, thus far gating currents have been measured only from ensembles of numerous stochastically activated channels and therefore the information they provide is limited. This work presents, for the first time, measurements of gating currents from a single channel molecule. Averaging close to 8000 pre-open currents, aligned to the single channel opening time, enabled the detection of single channel gating currents with a resolution of 2 electron charges. The measured charge displacements show: 1) a slow component, approximately 2 fA above baseline level, assumed to represent stochastic conformational changes, and 2) transients, the most significant of which occur 1.1 and 0.3 ms before channel opening. The transients most likely represent apparent deterministic stages in the gating process. The largest transient current peak was 5.1 +/- 1.6 fA and the total equivalent charge transported across the membrane was 4.7 +/- 2.5 electron charges. This data is unique also in that it presents monitoring of the behavior of a single, well-defined macromolecule.     

S3-S4 Linker Length Modulates the Relaxed State of a Voltage-Gated Potassium Channel

Voltage-sensing domains (VSDs) are membrane protein modules found in ion channels and enzymes that are responsible for a large number of fundamental biological tasks, such as neuronal electrical activity. The VSDs switch from a resting to an active conformation upon membrane depolarization, altering the activity of the protein in response to voltage changes. Interestingly, numerous studies describe the existence of a third distinct state, called the relaxed state, also populated at positive potentials. Although some physiological roles for the relaxed state have been suggested, little is known about the molecular determinants responsible for the development and modulation of VSD relaxation. Several lines of evidence have suggested that the linker (S3-S4 linker) between the third (S3) and fourth (S4) transmembrane segments of the VSD alters the equilibrium between resting and active conformations. By measuring gating currents from the Shaker potassium channel, we demonstrate here that shortening the S3-S4 linker stabilizes the relaxed state, whereas lengthening the linker or splitting it and coinjecting two fragments of the channel have little effect. We propose that natural variations of the length of the S3-S4 linker in various VSD-containing proteins may produce differential VSD relaxation in vivo.     

Frequency domain analysis of asymmetry current in squid axon membrane.

The change in capacity of squid axon membrane during hyper- and depolarizations was investigated in the absence of ionic currents after the membrane was treated with pronase. In the presence of the inactivation process (h parameter), failure to observe the gating current in the frequency domain was attributed to the rapid attenuation of the possible capacity change during depolarizations, which is likely to be due to the sodium activation process. Elimination of the h process would therefore enable us to observe the gating current in the frequency domain as the change in the capacitance component of membrane admittance. However, even after the inactivation process was abolished by pronase, the capacity of the axon membrane remained constant when ionic currents were blocked by external tetrodotoxin and internal Cs+ ion. Actually capacity was observed to decrease slightly with depolarization, contrary to the prediction based on the magnitude of gating currents.     

Simple shifts in the voltage dependence of sodium channel gating caused by divalent cations

The effect of elevated divalent cation concentration on the kinetics of sodium ionic and gating currents was studied in voltage-clamped frog skeletal muscle fibers. Raising the Ca concentration from 2 to 40 mM resulted in nearly identical 30-mV shifts in the time courses of activation, inactivation, tail current decay, and ON and OFF gating currents, and in the steady state levels of inactivation, charge immobilization, and charge vs. voltage. Adding 38 mM Mg to the 2 mM Ca bathing a fiber produced a smaller shift of approximately 20 mV in gating current kinetics and the charge vs. voltage relationship. The results with both Ca and Mg are consistent with the hypothesis that elevated concentrations of these alkali earth cations alter Na channel gating by changing the membrane surface potential. The different shifts produced by Ca and Mg are consistent with the hypothesis that the two ions bind to fixed membrane surface charges with different affinities, in addition to possible screening.     

Modification of sodium and gating currents by amino group specific cross-linking and monofunctional reagents.

To test the possible role of lysine residues in Na channel function the effects of several imidoesters on Na and gating currents were studied in voltage-clamped single frog nerve fibers. Mono- and bisimidoesters were used. These reagents modify amino groups exclusively and do not change the net charge. The three bisimidoesters used easily introduce cross-links between neighboring amino groups. Their structure is almost identical; only the length of the spacers between the two amino-reactive groups is different. An irreversible reduction of Na currents and gating currents was observed with the longest (dimethyl suberimidate [DMS]) and the shortest (dimethyl adipimidate [DMA]) of the cross-linkers used. Of the three cross-linking reagents only the shortest made Na current inactivation slow and incomplete. The steady-state inactivation curve, h infinity (E), was shifted by greater than 25 mV in the hyperpolarizing direction by each of the reagents. The voltage dependence of activation, however, remained unchanged. Furthermore, the effects of two different monoimidoesters (ethyl acetimidate [EAI] and isethionyl acetimidate [IAI]) on gating currents were tested. EAI can penetrate a membrane, whereas IAI is membrane impermeant. IAI was almost without effect, whereas EAI caused a considerable reduction of the gating currents. EAI and DMS reduced the Qoff/Qon ratio without affecting the decay of the Na currents. The results show that lysine residues are critically involved in Na channel gating.     

Procedure using voltage-sensitive spin-labels to monitor dipole potential changes in phospholipid vesicles: The estimation of phloretin-induced conductance changes in vesicles

Summary Voltage-sensitive membrane potential probes were used to monitor currents resulting from positive or negative charge movement across small and large unilamellar phosphatidylcholine (PC) vesicles. Positive currents were measured for the paramagnetic phosphonium ion or for K⁺-valinomycin. Negative currents were indirectly measured for the anionic proton carriers CCCP and DNP by monitoring transmembrane proton currents. Phloretin, a compound that is believed to decrease dipole fields in planar bilayers, increases positive currents and decreases negative currents when added to egg PC vesicles. In these vesicles, positive currents are increased by phloretin addition to a much larger degree than CCCP currents are reduced. This asymmetry, with respect to the sign of the charge carrier, is apparently not the result of changes in the membrane dielectric constant. It is most easily explained by deeper binding minima at the membrane-solution interface for the CCCP anion, when compared to the phosphonium. The measured asymmetry and the magnitudes of the current changes are consistent with the predictions of a point dipole model. The use of potential-sensitive probes to estimate positive and negative currents, provides a methodology to monitor changes in the membrane dipole potential in vesicle systems.