Computing transient gating charge movement of voltage-dependent ion channels

The opening of voltage-gated sodium, potassium, and calcium ion channels has a steep relationship with voltage. In response to changes in the transmembrane voltage, structural movements of an ion channel that precede channel opening generate a capacitative gating current. The net gating charge displacement due to membrane depolarization is an index of the voltage sensitivity of the ion channel activation process. Understanding the molecular basis of voltage-dependent gating of ion channels requires the measurement and computation of the gating charge, Q. We derive a simple and accurate semianalytic approach to computing the voltage dependence of transient gating charge movement (Q–V relationship) of discrete Markov state models of ion channels using matrix methods. This approach allows rapid computation of Q–V curves for finite and infinite length step depolarizations and is consistent with experimentally measured transient gating charge. This computational approach was applied to Shaker potassium channel gating, including the impact of inactivating particles on potassium channel gating currents.     

A calculation of the current voltage characteristic of a voltage-controlled model membrane ion channel

A simple calculation is made of the current-voltage characteristic of a model ion channel in which the ion transfer rate is controlled by an electrical potential gradient rather than by mechanical gating particles. Although the model deals with sodium and potassium channels similarly, very different characteristics are obtained that approximate to those measured in the squid giant axon. The difference is due essentially to the very different Nernst potentials for these two ions. The ability of the model to predict channel activation due to both depolarization and hyperpolarizing voltage transients is described.     

Biochemical investigations of ionic channels in excitable membranes

Summary Ion channels of excitable membranes are composed of a gating device and a selectivity filter. Two strategies are discussed in this review for the biochemical isolation and characterization of these two functional subunits of channels: Membrane molecules involved in ion translocation can be identified in vitro by their pharmacological properties, i.e. by binding assays with radioactive drugs known to selectively affect a special channel in vivo. More desirable is an assay of their true biological function, i.e. translocation of ions through a membrane. Ion flux measurements with natural and reconstituted membrane systems in vitro are recently available.This article summarizes our present knowledge of electrically excitable sodium and potassium channels of nerve membranes and of the chemically excitable sodium/potassium channel of cholinergic synapses, the acetylcholine receptor complex (AChR). Because of the availability of a great variety of drugs binding with high affinity to axonal sodium channels its investigation is more advanced than that of the axonal potassium channel. The lack of high affinity labels for the latter can be possibly overcome by photoaffinity labels which label components of the channel in situ. Initial success is reported with a photoafinity label derived from the potassium channel blocker TEA.Most advanced is the biochemical investigation of the acetylcholine receptor (AChR) which has been purified in milligram quantities. It represents a protein complex composed of different polypeptide chains with different functions regulating the sodium/potassium permeability of cholinergic postsynaptic membranes. Experiments are described to elucidate the quaternary structure, the site of binding of cholinergic ligands and neurotoxins and to prove dynamic conformation changes of the protein which may be the cause for permeability changes of the membrane. The gating device and the ion translocation system (selectivity filter, ionophor) appear to be present in the receptor complex though located possible in different subunits. This is evidenced by reconstitution of excitable membranes from purified AChR and exogenous lipids by a novel and reproducible method.An invited review article.     

Batrachotoxin-modified sodium channels from squid optic nerve in planar bilayers. Ion conduction and gating properties

Squid optic nerve sodium channels were characterized in planar bilayers in the presence of batrachotoxin (BTX). The channel exhibits a conductance of 20 pS in symmetrical 200 mM NaCl and behaves as a sodium electrode. The single-channel conductance saturates with increasing the concentration of sodium and the channel conductance vs. sodium concentration relation is well described by a simple rectangular hyperbola. The apparent dissociation constant of the channel for sodium is 11 mM and the maximal conductance is 23 pS. The selectivity determined from reversal potentials obtained in mixed ionic conditions is Na+ approximately Li+ greater than K+ greater than Rb+ greater than Cs+. Calcium blocks the channel in a voltage-dependent manner. Analysis of single-channel membranes showed that the probability of being open (Po) vs. voltage relation is sigmoidal with a value of 0.5 between -90 and -100 mV. The fitting of Po requires at least two closed and one open state. The apparent gating charge required to move through the whole transmembrane voltage during the closed-open transition is four to five electronic charges per channel. Distribution of open and closed times are well described by single exponentials in most of the voltage range tested and mean open and mean closed times are voltage dependent. The number of charges associated with channel closing is 1.6 electronic charges per channel. Tetrodotoxin blocked the BTX-modified channel being the blockade favored by negative voltages. The apparent dissociation constant at zero potential is 16 nM. We concluded that sodium channels from the squid optic nerve are similar to other BTX-modified channels reconstituted in bilayers and to the BTX-modified sodium channel detected in the squid giant axon.     

Single sodium channels from the squid giant axon

Since the work of A. L. Hodgkin and A. F. Huxley (1952. J. Physiol. [Lond.].117:500-544) the squid giant axon has been considered the classical preparation for the study of voltage-dependent sodium and potassium channels. In this preparation much data have been gathered on macroscopic and gating currents but no single sodium channel data have been available. This paper reports patch clamp recording of single sodium channel events from the cut-open squid axon. It is shown that the single channel conductance in the absence of external divalent ions is approximately 14 pS, similar to sodium channels recorded from other preparations, and that their kinetic properties are consistent with previous results on gating and macroscopic currents obtained from the perfused squid axon preparation.     

Removal of Na+ channels in squid giant axons by perfusion with trypsin

The irreversible effects of the proteolytic enzyme trypsin on ionic and gating currents of voltage-clamped squid axon membranes have been studied. At physiological pH, internal perfusion of the fibre with trypsin was found to be very effective in removing Na+ channels leaving the potassium system almost unaltered. At T = 13 degrees C the rates of channel-cleavage averaged 1/10 min-1 for the Na+ and 1/128 min-1 for the K+ channel, respectively. As estimated by the decrement of peak sodium conductance, the rate of loss of Na+ channels correlates well with the rate of decrease of the total charge associated with the ON component of gating currents, indicating that trypsin probably interacts with an essential proteic portion of the channel whose removal might prevent both the displacement of gating charges and the subsequent opening of the channel. Intracellular pH remarkably influences the action of the enzyme. A plot of the pH-dependence of the rate of cleavage of Na+ channels suggests the involvement of a positively charged group (either lysine or arginine) in the substrate region of the trypsin catalytic reaction.     

Reversible electrical breakdown of squid giant axon membrane

Charge pulse relaxation experiments were performed on squid giant axon. In the low voltage range, the initial voltage across squid axon membrane was a linear function of the injected charge. For voltages of the order of 1 V this relationship between injected charge and voltage across the membrane changes abruptly. Because of a high conductance state caused by these large electric fields the voltage across the membrane cannot be made large enough to exceed a critical value, Vc, defined as the breakdown voltage, Vc has for squid axon membrane a value of 1.1 V at 12 degrees C. During breakdown the specific membrane conductance exceeds 1 S. cm-2. Electrical breakdown produced by charge pulses of few microseconds duration have no influence on the excitability of the squid axon membrane. The resealing process of the membrane is so fast that a depolarizing breakdown is followed by the falling phase of a normal action potential. Thus, membrane voltages close to Vc open the sodium channels in few microseconds, but do not produce a decrease of the time constant of potassium activation large enough to cause the opening of a significant percentage of channels in a time of about 10 mus. It is probable that the reversible electrical breakdown is mainly caused by mechanical instability produced by electrostriction of the membrane (electrochemical model), but the decrease in the Born energy for ion injection into the membrane, accompanying the decrease in membrane thickness, may play also an important role. Because of the high conductance of the membrane during breakdown it seems very likely that this results in pore formation.     

Interactions of aminopyridines with potassium channels of squid axon membranes.

The effects of aminopyridines on ionic conductances of the squid giant axon membrane were examined using voltage clamp and internal perfusion techniques. 4-Aminopyridine (4-AP) reduced potassium currents, but had no effect upon transient sodium currents. The block of potassium channels by 4-AP was substantially less with (a) strong depolarization to positive membrane potentials, (b) increasing the duration of a given depolarizing step, and (c) increasing the frequency of step depolarizations. Experiments with high external potassium concentrations revealed that the effect of 4-AP was independent of the direction of potassium ion movement. Both 3- and 2-aminopyridine were indistinguishable from 4-AP except in potency. It is concluded that aminopyrimidines may be used as tools to block the potassium conductance in excitable membranes, but only within certain specific voltage and frequency limits.     

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.     

A new look at the mechanism of activation and inactivation of voltage-gated ion channels.

Studies on the kinetics of activation and inactivation of the sodium channels of the squid giant axon, on the sodium gating current, and on the properties of the non-inactivating steady-state current, are briefly reviewed. Taken in conjunction with recent evidence on the structure of voltage-gated ion channels, they have led to the development of a series-parallel model of the sodium channel that can be regarded as a modernized version of the Hodgkin-Huxley model, with some novel features. It is suggested that activation results from conformational changes brought about by the four S4 voltage sensors operating in parallel, each of which makes two discrete steps to reach the fully activated state of the channel. There follows a voltage-independent hydration step, and the channel is ready to open. Inactivation is a potential-dependent process involving a third transition of voltage sensor S4d alone, which, rather than bringing a ball and chain blocking group into position to close the channels, serves to switch the system so that it passes from an initial activated mode, in which there is a high probability of arriving at an open state with a brief latency, to a second steady-state mode, in which the probability of opening is very much lower.     

Modeling squid axon K+ channel by a nucleation and growth kinetic mechanism

A kinetic model accounting for all salient features of the K⁺ channel of the squid giant axon, including the rising phase of the ON gating charge and the Cole-Moore effect, is provided. Upon accounting for a significant feature distinguishing K⁺, Na⁺ and Ca^2 + channels from channel-forming peptides modeled in our previous 2016 BBA paper, the nucleation-and-growth kinetic model developed therein is extended to simulate ON ionic and gating currents of the K⁺ channel of the squid giant axon at different depolarization potentials by the use of only two free parameters. K⁺ channel opening is considered to proceed by progressive aggregation of single subunits, while they are moving their gating charge outward under depolarizing conditions within their tetrameric structure; K⁺ channel closing proceeds in the opposite direction, by repolarization-induced disaggregation of subunits, accompanied by inward movement of their gating charge.     

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.     

Specificity of charge-carrying residues in the voltage sensor of potassium channels

Positively charged voltage sensors of sodium and potassium channels are driven outward through the membrane's electric field upon depolarization. This movement is coupled to channel opening. A recent model based on studies of the KvAP channel proposes that the positively charged voltage sensor, christened the "voltage-sensor paddle", is a peripheral domain that shuttles its charged cargo through membrane lipid like a hydrophobic cation. We tested this idea by attaching charged adducts to cysteines introduced into the putative voltage-sensor paddle of Shaker potassium channels and measuring fractional changes in the total gating charge from gating currents. The only residues capable of translocating attached charges through the membrane-electric field are those that serve this function in the native channel. This remarkable specificity indicates that charge movement involves highly specialized interactions between the voltage sensor and other regions of the protein, a mechanism inconsistent with the paddle model.     

Modulation of aminopyridine block of potassium currents in squid axon.

Aminopyridines are known to block potassium (K) currents in excitable membranes in a manner dependent upon membrane potential, such that the block is relieved by depolarization and restored upon repolarization. In the present study, the effects of aminopyridines on voltage-dependent potassium (K) channels were examined in internally perfused, voltage-clamped squid giant axons. The time course of block restoration after conditioning depolarization was found to be modulated by membrane electric field, K-channel gating, and external cations. Depolarized holding potentials accelerated block restoration without altering steady-state block levels, suggesting that the voltage dependence of block restoration may be related to K channel gating rather than drug binding per se. In support of this notion, low external calcium concentration, which shifts the voltage dependence of K-channel gating to more negative potentials, also accelerated block restoration. Conversely, the relationship between the rate of block restoration and membrane holding potential was shifted in the depolarizing direction by phloretin, an agent that shifts the dependence of K-channel opening on membrane potential in a similar manner. Modification of K-channel gating also was found to alter the rate of block restoration. Addition of internal zinc or internal treatment with glutaraldehyde slowed the time course of both K-channel activation and aminopyridine block restoration. Aminopyridines also were found to interact in the K channel with external Cs+, NH4+, and Rb+, each of which slowed aminopyridine block restoration. Our results suggest that aminopyridines enter and occlude K channels, and that the availability of the binding site may be modulated by channel gating such that access is limited by the probability of the channel reaching an intermediate closed state at the resting potential.     

A new double-chamber model of ion channels. Beyond the Hodgkin and Huxley model

This paper proposes a new double-chamber model (DCM) of ion channels. The model ion channel consists of a series of three pores alternating with two chambers. The chambers are net negatively charged. The chamber's electric charge originates from dissociated amino acid side chains and is pH dependent. The chamber's net negative charge is compensated by cations present inside the chamber and in a diffuse electric layer outside the chamber. The pore's permeability is constant independent of time. One pore of the sodium channel and one of the potassium channel is a voltage-sensing pore. Due to the channel's structure, ions flow through the pores and chambers in a time-dependent manner. The model reproduces experimental voltage clamp and action potential data. The current flowing through a single sodium channel is less then one femtoampere. The DCM is considerably simpler then the Hodgkin and Huxley model (HHM) used to describe the electrophysiological properties of an axon. Unlike the HHM, the DCM can explain refractoriness, anode break excitation, accommodation and the effect of pH and temperature on the channels without additional parameters. In the DCM, the axon membrane shows repetitive activity depending on the channel density, sodium to potassium channel ratio and external potassium concentration. In the DCM, the action potential starts from 'hot spot areas' of higher channel densities and a higher sodium to potassium channel ratio, and then propagates through the whole axon.     

The influence of lipids on voltage-gated ion channels

Voltage-gated ion channels are responsible for transmitting electrochemical signals in both excitable and non-excitable cells. Structural studies of voltage-gated potassium and sodium channels by X-ray crystallography have revealed atomic details on their voltage-sensor domains (VSDs) and pore domains, and were put in context of disparate mechanistic views on the voltage-driven conformational changes in these proteins. Functional investigation of voltage-gated channels in membranes, however, showcased a mechanism of lipid-dependent gating for voltage-gated channels, suggesting that the lipids play an indispensible and critical role in the proper gating of many of these channels. Structure determination of membrane-embedded voltage-gated ion channels appears to be the next frontier in fully addressing the mechanism by which the VSDs control channel opening. Currently electron crystallography is the only structural biology method in which a membrane protein of interest is crystallized within a complete lipid-bilayer mimicking the native environment of a biological membrane. At a sufficiently high resolution, an electron crystallographic structure could reveal lipids, the channel and their mutual interactions at the atomic level. Electron crystallography is therefore a promising avenue toward understanding how lipids modulate channel activation through close association with the VSDs.     

The compensation of potential changes produced by trivalent erbium ion in squid giant axon with applied potentials.

The transmembrane potential of voltage-clamped squid giant axon is increased to compensate for a reduction in the rate of potassium channel kinetics when artificial seawater with trivalent erbium ion is substituted for artificial seawater. The additional potential required to produce an equivalent rise time is a measure of the potential shift produced by the erbium ions. When the kinetics of K+ channels are matched in this manner, the maximal K+ currents are larger for the larger transmembrane potential. This observation requires a functional separation of the open K+ channel and the voltage sensor for the gating mechanism of this channel.     

Rate of opening of a population of Na channels in frog skeletal muscle fibers

Linear Systems convolution analysis of muscle sodium currents was used to predict the opening rate of sodium channels as a function of time during voltage clamp pulses. If open sodium channel lifetimes are exponentially distributed, the channel opening rate corresponding to a sodium current obtained at any particular voltage, can be analytically obtained using a simple equation, given single channel information about the mean open-channel lifetime and current.Predictions of channel opening rate during voltage clamp pulses show that sodium channel inactivation arises coincident with a decline in channel opening rate.Sodium currents pharmacologically modified with Chloramine-T treatment so that they do not inactivate, show a predicted sustained channel opening rate.Large depolarizing voltage clamp pulses produce channel opening rate functions that resemble gating currents.The predicted channel opening rate functions are best described by kinetic models for Na channels which confer most of the charge movement to transitions between closed states.Comparisons of channel opening rate functions with gating currents suggests that there may be subtypes of Na channel with some contributing more charge movement per channel opening than others.Na channels open on average, only once during the transient period of Na activation and inactivation.After transiently opening during the activation period and then closing by entering the inactivated state, Na channels reopen if the voltage pulse is long enough and contribute to steady-state currents.The convolution model overestimates the opening rate of channels contributing to the steady-state currents that remain after the transient early Na current has subsided.     

A comparison of sodium channel kinetics in the squid axon,the frog node and the frog node with BTX using the “silent gate” model

In this paper it is shown that the very different kinetics measured for the rise of the sodium current which follows a depolarization of the membrane in the squid giant axon, the frog node and the frog node treated with Batrachotoxin may be accurately predicted using only the measured equilibrium and static characteristics for the three preparations and the kinetics measured for the gating charge transfer.The kinetic predictions follow the use of the silent gate model for ion channel gating. The model is electrostatic and its chief assumptions are that the channel gate, called here the N-system, has fast kinetics and responds to the gating charge that transfers but not directly to the trans-membrane voltage applied. Because channel gating, corresponding here to the motion of the N-system, does not change its energy in the trans-membrane applied electric field the gating is electrically silent as far as gating charge transfer measurement is concerned. However the probability of gating rises with the quantity of gating charge that transfers due to the electrostatic interaction between the N-system and the gating charge, redistributed under the influence of the applied trans-membrane electric field. With these assumptions the kinetics of sodium channel gating are predictable using only the static and equilibrium characteristics of gating charge and channel activation measured as a function of membrane voltage, and the kinetics of the gating charge transfer. Because of the fast kinetics assumed for the N-system the predicted kinetics are the same for channels with any number of equivalent and independent N-systems or gates acting in parallel.The model predictions for sodium permeability kinetics are compared in detail with those recently measured for the frog node treated with Batrachotoxin and excellent agreement is obtained.     

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.