On the thermodynamic characterization of membrane gating particles by their Boltzmann distribution

The characterizations of gating particles of ionic channels in nerve membranes by their equivalent valencies and their electric dipole moment changes are compared. The gating particle is represented as a system of electric charges in fixed positions in an external electric field and the potential energy of such a system is calculated in the approximation of a constant electric field. The proper expression of the Boltzmann distribution of the gating particles is presented. It is shown that the dipole moment of transition of the gating particle is the only proper thermodynamic (macroscopic) characteristics of the gating particles based on the available experimental information and does not depend on any microscopic assumption as the equivalent valency does.     

Isolation of myocardial L-type calcium channel gating currents with the spider toxin omega-Aga-IIIA

The peptide omega-agatoxin-IIIA (omega-Aga-IIIA) blocks ionic current through L-type Ca channels in guinea pig atrial cells without affecting the associated gating currents. omega-Aga-IIIA permits the study of L- type Ca channel ionic and gating currents under nearly identical ionic conditions. Under conditions that isolate L-type Ca channel currents, omega-Aga-IIIA blocks all ionic current during a test pulse and after repolarization. This block reveals intramembrane charge movements of equal magnitude and opposite sign at the beginning of the pulse (Q(on)) and after repolarization (Q(off)). Q(on) and Q(off) are suppressed by 1 microM felodipine, saturate with increasing test potential, and are insensitive to Cd. The decay of the transient current associated with Q(on) is composed of fast and slow exponential components. The slow component has a time constant similar to that for activation of L-type Ca channel ionic current, over a broad voltage range. The current associated with Q(off) decays monoexponentially and more slowly than ionic current. Similar charge movements are found in guinea pig tracheal myocytes, which lack Na channels and T-type Ca channels. The kinetic and pharmacological properties of Q(on) and Q(off) indicate that they reflect gating currents associated with L-type Ca channels. omega-Aga-IIIA has no effect on gating currents when ionic current is eliminated by stepping to the reversal potential for Ca or by Cd block. Gating currents constitute a significant component of total current when physiological concentrations of Ca are present and they obscure the activation and deactivation of L-type Ca channels. By using omega- Aga-IIIA, we resolve the entire time course of L-type Ca channel ionic and gating currents. We also show that L- and T-type Ca channel ionic currents can be accurately quantified by tail current analysis once gating currents are taken into account.     

Mechanism of inactivation gating of human T-type (low-voltage activated) calcium channels

Recovery from inactivation of T-type Ca channels is slow and saturates at moderate hyperpolarizing voltage steps compared with Na channels. To explore this unique kinetic pattern we measured gating and ionic currents in two closely related isoforms of T-type Ca channels. Gating current recovers from inactivation much faster than ionic current, and recovery from inactivation is much more voltage dependent for gating current than for ionic current. There is a lag in the onset of gating current recovery at -80 mV, but no lag is discernible at -120 mV. The delay in recovery from inactivation of ionic current is much more evident at all voltages. The time constant for the decay of off gating current is very similar to the time constant of deactivation of open channels (ionic tail current), and both are strongly voltage dependent over a wide voltage range. Apparently, the development of inactivation has little influence on the initial deactivation step. These results suggest that movement of gating charge occurs for inactivated states very quickly. In contrast, the transitions from inactivated to available states are orders of magnitude slower, not voltage dependent, and are rate limiting for ionic recovery. These findings support a deactivation-first path for T-type Ca channel recovery from inactivation. We have integrated these concepts into an eight-state kinetic model, which can account for the major characteristics of T-type Ca channel inactivation.     

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.     

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.     

Microscopic origin of gating current fluctuations in a potassium channel voltage sensor

Voltage-dependent ion channels open and close in response to changes in membrane electrical potential due to the motion of their voltage-sensing domains (VSDs). VSD charge displacements within the membrane electric field are observed in electrophysiology experiments as gating currents preceding ionic conduction. The elementary charge motions that give rise to the gating current cannot be observed directly, but appear as discrete current pulses that generate fluctuations in gating current measurements. Here we report direct observation of gating-charge displacements in an atomistic molecular dynamics simulation of the isolated VSD from the KvAP channel in a hydrated lipid bilayer on the timescale (10-μs) expected for elementary gating charge transitions. The results reveal that gating-charge displacements are associated with the water-catalyzed rearrangement of salt bridges between the S4 arginines and a set of conserved acidic side chains on the S1-S3 transmembrane segments in the hydrated interior of the VSD.     

Pharmacological and kinetic analysis of K channel gating currents

We have measured gating currents from the squid giant axon using solutions that preserve functional K channels and with experimental conditions that minimize Na channel contributions to these currents. Two pharmacological agents were used to identify a component of gating current that is associated with K channels. Low concentrations of internal Zn2+ that considerably slow K channel ionic currents with no effect on Na channel currents altered the component of gating current associated with K channels. At low concentrations (10-50 microM) the small, organic, dipolar molecule phloretin has several reported specific effects on K channels: it reduces K channel conductance, shifts the relationship between channel conductance and membrane voltage (Vm) to more positive potentials, and reduces the voltage dependence of the conductance-Vm relation. The K channel gating charge movements were altered in an analogous manner by 10 microM phloretin. We also measured the dominant time constants of the K channel ionic and gating currents. These time constants were similar over part of the accessible voltage range, but at potentials between -40 and 0 mV the gating current time constants were two to three times faster than the corresponding ionic current values. These features of K channel function can be reproduced by a simple kinetic model in which the channel is considered to consist of two, two-state, nonidentical subunits.     

FPL 64176 modification of Ca(V)1.2 L-type calcium channels: dissociation of effects on ionic current and gating current

FPL 64176 (FPL) is a nondihydropyridine compound that dramatically increases macroscopic inward current through L-type calcium channels and slows activation and deactivation. To understand the mechanism by which channel behavior is altered, we compared the effects of the drug on the kinetics and voltage dependence of ionic currents and gating currents. Currents from a homogeneous population of channels were obtained using cloned rabbit Ca(V)1.2 (alpha1C, cardiac L-type) channels stably expressed in baby hamster kidney cells together with beta1a and alpha2delta1 subunits. We found a striking dissociation between effects of FPL on ionic currents, which were modified strongly, and on gating currents, which were not detectably altered. Inward ionic currents were enhanced approximately 5-fold for a voltage step from -90 mV to +10 mV. Kinetics of activation and deactivation were slowed dramatically at most voltages. Curiously, however, at very hyperpolarized voltages (< -250 mV), deactivation was actually faster in FPL than in control. Gating currents were measured using a variety of inorganic ions to block ionic current and also without blockers, by recording gating current at the reversal potential for ionic current (+50 mV). Despite the slowed kinetics of ionic currents, FPL had no discernible effect on the fundamental movements of gating charge that drive channel gating. Instead, FPL somehow affects the coupling of charge movement to opening and closing of the pore. An intriguing possibility is that the drug causes an inactivated state to become conducting without otherwise affecting gating transitions.     

Trimethyloxonium modification of batrachotoxin-activated Na channels alters functionally important protein residues.

The extracellular side of single batrachotoxin-activated voltage-dependent Na channels isolated from rat skeletal muscle membranes incorporated into neutral planar lipid bilayers were treated in situ with the carboxyl methylating reagent, trimethyloxonium (TMO). These experiments were designed to determine whether TMO alters Na channel function by a general through-space electrostatic mechanism or by methylating specific carboxyl groups essential to channel function. TMO modification reduced single-channel conductance by decreasing the maximal turnover rate. Modification increased channel selectivity for sodium ions relative to potassium ions as measured under biionic conditions. TMO modification increased the mu-conotoxin (muCTX) off-rate by three orders of magnitude. Modification did not alter the muCTX on-rate at low ionic strength or Na channel voltage-dependent gating characteristics. These data demonstrate that TMO does not act via a general electrostatic mechanism. Instead, TMO targets protein residues specifically involved in ion conduction, ion selectivity, and muCTX binding. These data support the hypothesis that muCTX blocks open-channel current by physically obstructing the ion channel pore.     

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.     

Modification of potassium channel kinetics by amino group reagents.

We have examined the actions of several amino group reagents on delayed rectifier potassium channels in squid giant axons. Three general classes of reagents were used: (1) those that preserved the positive charge of amino groups; (2) those that neutralize the charge; and (3) those that replace the positive with a negative charge. All three types of reagents produced qualitatively similar effects on K channel properties. Trinitrobenzene sulfonic acid (TNBS) neutralizes the peptide terminal amino groups and the epsilon-amino group of lysine groups. TNBS (a) slowed the kinetics of macroscopic ionic currents; (b) increased the size of ionic currents at large positive voltages; (c) shifted the voltage-dependent probability of channel opening to more positive potentials but had no effect on the voltage sensitivity; and (d) altered several properties of K channel gating currents. The actions of TNBS on gating currents suggest the presence of multiple gating current components. These effects are not all coupled, suggesting that several amino groups on the external surface of K channels are important for channel gating. A simple kinetic model that considers the channel to be composed of independent heterologous subunits is consistent with most of the modifications produced by amino group reagents.     

Rate-limiting Reactions Determining Different Activation Kinetics of Kv1.2and Kv2.1 Channels

To identify the mechanisms underlying the faster activation kinetics in Kv1.2 channels compared to Kv2.1 channels, ionic and gating currents were studied in rat Kv1.2 and human Kv2.1 channels heterologously expressed in mammalian cells. At all voltages the time course of the ionic currents could be described by an initial sigmoidal and a subsequent exponential component and both components were faster in Kv1.2 than in Kv2.1 channels. In Kv1.2 channels, the activation time course was more sigmoid at more depolarized potentials, whereas in Kv2.1 channels it was somewhat less sigmoid at more depolarized potentials. In contrast to the ionic currents, the ON gating currents were similarly fast for both channels. The main portion of the measured ON gating charge moved before the ionic currents were activated. The equivalent gating charge of Kv1.2 ionic currents was twice that of Kv2.1 ionic currents, whereas that of Kv1.2 ON gating currents was smaller than that of Kv2.1 ON gating currents. In conclusion, the different activation kinetics of Kv1.2 and Kv2.1 channels are caused by rate-limiting reactions that follow the charge movement recorded from the gating currents. In Kv1.2 channels, the reaction coupling the voltage-sensor movement to the pore opening contributes to rate limitation in a voltage-dependent fashion, whereas in Kv2.1 channels, activation is additionally rate-limited by a slow reaction in the subunit gating.     

Gating pore currents in DIIS4 mutations of NaV1.4 associated with periodic paralysis: saturation of ion flux and implications for disease pathogenesis

S4 voltage–sensor mutations in CaV1.1 and NaV1.4 channels cause the human muscle disorder hypokalemic periodic paralysis (HypoPP). The mechanism whereby these mutations predispose affected sarcolemma to attacks of sustained depolarization and loss of excitability is poorly understood. Recently, three HypoPP mutations in the domain II S4 segment of NaV1.4 were shown to create accessory ionic permeation pathways, presumably extending through the aqueous gating pore in which the S4 segment resides. However, there are several disparities between reported gating pore currents from different investigators, including differences in ionic selectivity and estimates of current amplitude, which in turn have important implications for the pathological relevance of these aberrant currents. To clarify the features of gating pore currents arising from different DIIS4 mutants, we recorded gating pore currents created by HypoPP missense mutations at position R666 in the rat isoform of Nav1.4 (the second arginine from the outside, at R672 in human NaV1.4). Extensive measurements were made for the index mutation, R666G, which created a gating pore that was permeable to K⁺ and Na⁺. This current had a markedly shallow slope conductance at hyperpolarized voltages and robust inward rectification, even when the ionic gradient strongly favored outward ionic flow. These characteristics were accounted for by a barrier model incorporating a voltage-gated permeation pathway with a single cation binding site oriented near the external surface of the electrical field. The amplitude of the R666G gating pore current was similar to the amplitude of a previously described proton-selective current flowing through the gating pore in rNaV1.4-R663H mutant channels. Currents with similar amplitude and cation selectivity were also observed in R666S and R666C mutant channels, while a proton-selective current was observed in R666H mutant channels. These results add support to the notion that HypoPP mutations share a common biophysical profile comprised of a low-amplitude inward current at the resting potential that may contribute to the pathological depolarization during attacks of weakness.     

N-type calcium channel inactivation probed by gating-current analysis

N-type calcium channels inactivate most rapidly in response to moderate, not extreme depolarization. This behavior reflects an inactivation rate that bears a U-shaped dependence on voltage. Despite this apparent similarity to calcium-dependent inactivation, N-type channel inactivation is insensitive to the identity of divalent charge carrier and, in some reports, to the level of internal buffering of divalent cations. Hence, the inactivation of N-type channels fits poorly with the "classic" profile for either voltage-dependent or calcium-dependent inactivation. To investigate this unusual inactivation behavior, we expressed recombinant N-type calcium channels in mammalian HEK 293 cells, permitting in-depth correlation of ionic current inactivation with potential alterations of gating current properties. Such correlative measurements have been particularly useful in distinguishing among various inactivation mechanisms in other voltage-gated channels. Our main results are the following: 1) The degree of gating charge immobilization was unchanged by the block of ionic current and precisely matched by the extent of ionic current inactivation. These results argue for a purely voltage-dependent mechanism of inactivation. 2) The inactivation rate was fastest at a voltage where only approximately (1)/(3) of the total gating charge had moved. This unusual experimental finding implies that inactivation occurs most rapidly from intermediate closed conformations along the activation pathway, as we demonstrate with novel analytic arguments applied to coupled-inactivation schemes. These results provide strong, complementary support for a "preferential closed-state" inactivation mechanism, recently proposed on the basis of ionic current measurements of recombinant N-type channels (Patil et al., . Neuron. 20:1027-1038).     

Intramembrane Charge Movement Associated with Endogenous K+ Channel Activity in HEK-293 Cells

1. The use of molecular biology in combination with electrophysiology in the HEK-293 cell line has given fascinating insights into neuronal ion channel function. Nevertheless, to fully understand the properties of channels exogenously expressed in these cells, a detailed evaluation of endogenous channels is indispensable. 2. Previous studies have shown the expression of endogenous voltage-gated K+, Ca2+, and Cl- channels and this predicts that changes in membrane potential will cause intramembrane charge movement, though this gating charge translocation remain undefined. Here, we confirm this prediction by performing patch-clamp experiments to record ionic and gating currents. Our data show that HEK-293 cells express at least two types of K+-selective endogenous channels which sustain the majority of the ionic current, and exclude a significant contribution from Ca2+ and Cl- channels to the whole-cell current. 3. Gating currents were unambiguously resolved after ionic current blockade enabling this first report of intramembrane charge movement in HEK-293 cells arising entirely from endogenous K+ channel activity, and providing valuable information concerning the activation mechanism of voltage-gated K+ channels in these cells.     

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.     

Asymmetric electrostatic effects on the gating of rat brain sodium channels in planar lipid membranes.

The effects of ionic strength (10-1,000 mM) on the gating of batrachotoxin-activated rat brain sodium channels were studied in neutral and in negatively charged lipid bilayers. In neutral bilayers, increasing the ionic strength of the extracellular solution, shifted the voltage dependence of the open probability (gating curve) of the sodium channel to more positive membrane potentials. On the other hand, increasing the intracellular ionic strength shifted the gating curve to more negative membrane potentials. Ionic strength shifted the voltage dependence of both opening and closing rate constants of the channel in analogous ways to its effects on gating curves. The voltage sensitivities of the rate constants were not affected by ionic strength. The effects of ionic strength on the gating of sodium channels reconstituted in negatively charged bilayers were qualitatively the same as in neutral bilayers. However, important quantitative differences were noticed: in low ionic strength conditions (10-150 mM), the presence of negative charges on the membrane surface induced an extra voltage shift on the gating curve of sodium channels in relation to neutral bilayers. It is concluded that: (a) asymmetric negative surface charge densities in the extracellular (1e-/533A2) and intracellular (1e-/1,231A2) sides of the sodium channel could explain the voltage shifts caused by ionic strength on the gating curve of the channel in neutral bilayers. These surface charges create negative electric fields in both the extracellular and intracellular sides of the channel. Said electric fields interfere with gating charge movements that occur during the opening and closing of sodium channels; (b) the voltage shifts caused by ionic strength on the gating curve of sodium channels can be accounted by voltage shifts in both the opening and closing rate constants; (c) net negative surface charges on the channel's molecule do not affect the intrinsic gating properties of sodium channels but are essential in determining the relative position of the channel's gating curve; (d) provided the ionic strength is below 150 mM, the gating machinery of the sodium channel molecule is able to sense the electric field created by surface changes on the lipid membrane. I propose that during the opening and closing of sodium channels, the gating charges involved in this process are asymmetrically displaced in relation to the plane of the bilayer. Simple electrostatic calculations suggest that gating charge movements are influenced by membrane electrostatic potentials at distances of 48 and 28 A away from the plane of the membrane in the extracellular sides of the channel, respectively.     

Interference between two modulators of N-type (CaV2.2) calcium channel gating demonstrates that ω-conotoxin GVIA disrupts open state gating

N-type calcium channels play an important role in synaptic transmission and a drug that blocks these channels has become an important tool in controlling chronic pain. The development of new N-channel-targeted drugs is dependent on a better understanding of the gating of these channels and how that gating can be modulated. We have previously concluded that ω-conotoxin GVIA (GVIA) is a gating modifier that acts by destabilizing the N-channel open state. However, this conclusion was largely based on our modeling results and requires experimental support. Roscovitine, a tri-substituted purine, has been shown to stabilize the N-channel open state to slow gating charge relaxation, which provides a direct test of our hypothesis for GVIA-induced gating modification. We found that roscovitine could modulate gating current in the presence of GVIA, which shows that roscovitine can still affect the gating of the GVIA-bound N-channel. However, the magnitude of the roscovitine-induced slowing of Off-gating current was significantly reduced. In addition to confirming our hypothesis, our evidence supports an additional effect of GVIA to alter gating transitions between N-channel closed states. By strongly limiting access to the N-channel open state, GVIA analogs that selectively induce this modulation could provide the basis for the next generation drugs that treat chronic pain.     

Hysteresis in the voltage dependence of HCN channels: conversion between two modes affects pacemaker properties

Hyperpolarization-activated, cyclic nucleotide-gated (HCN) ion channels are important for rhythmic activity in the brain and in the heart. In this study, using ionic and gating current measurements, we show that cloned spHCN channels undergo a hysteresis in their voltage dependence during normal gating. For example, both the gating charge versus voltage curve, Q(V), and the conductance versus voltage curve, G(V), are shifted by about +60 mV when measured from a hyperpolarized holding potential compared with a depolarized holding potential. In addition, the kinetics of the tail current and the activation current change in parallel to the voltage shifts of the Q(V) and G(V) curves. Mammalian HCN1 channels display similar effects in their ionic currents, suggesting that the mammalian HCN channels also undergo voltage hysteresis. We propose a model in which HCN channels transit between two modes. The voltage dependence in the two modes is shifted relative to each other, and the occupancy of the two modes depends on the previous activation of the channel. The shifts in the voltage dependence are fast (tau approximately 100 ms) and are not accompanied by any apparent inactivation. In HCN1 channels, the shift in voltage dependence is slower in a 100 mM K extracellular solution compared with a 1 mM K solution. Based on these findings, we suggest that molecular conformations similar to slow (C-type) inactivation of K channels underlie voltage hysteresis in HCN channels. The voltage hysteresis results in HCN channels displaying different voltage dependences during different phases in the pacemaker cycle. Computer simulations suggest that voltage hysteresis in HCN channels decreases the risk of arrhythmia in pacemaker cells.     

Simulating complex ion channel kinetics with IonChannelLab

In silico simulation based on Markov chains is a powerful way to describe and predict the activity of many transport proteins including ion channels. However, modeling and simulation using realistic models of voltage- or ligand-gated ion channels exposed to a wide range of experimental conditions require building complex kinetic schemes and solving complicated differential equations. To circumvent these problems, we developed IonChannelLab a software tool that includes a user-friendly Graphical User Interface and a simulation library. This program supports channels with Ohmic or Goldman-Hodgkin-Katz behavior and can simulate the time-course of ionic and gating currents, single channel behavior and steady-state conditions. The program allows the simulation of experiments where voltage, ligand and ionic concentration are varied independently or simultaneously.