Statistical properties of ion channel records. Part II: estimation from the macroscopic current

Macroscopic ion channel current is the summation of the stochastic records of individual channel currents and therefore relates to their statistical properties. As a consequence of this relationship, it may be possible to derive certain statistical properties of single channel records or even generate some estimates of the records themselves from the macroscopic current when the direct measurement of single channel currents is not applicable. We present a procedure for generating the single channel records of an ion channel from its macroscopic current when the stochastic process of channel gating has the following two properties: (I) the open duration is independent of the time of opening event and has a single exponential probability density function (pdf), (II) all the channels have the same probability to open at time t. The application of this procedure is considered for cases where direct measurement of single channel records is difficult or impossible. First, the probability density function (pdf) of opening events, a statistical property of single channel records, is derived from the normalized macroscopic current and mean channel open duration. Second, it is shown that under the conditions (I) and (II), a non-stationary Markov model can represent the stochastic process of channel gating. Third, the non-stationary Markov model is calibrated using the results of the first step. The non-stationary formulation increases the model ability to generate a variety of different single channel records compared to common stationary Markov models. The model is then used to generate single channel records and to obtain other statistical properties of the records. Experimental single channel records of inactivating BK potassium channels are used to evaluate how accurately this procedure reconstructs measured single channel sweeps.     

Separation of Gating Properties from Permeation and Block in mslo Large Conductance Ca-activated K+ Channels

In this and the following paper we have examined the kinetic and steady-state properties of macroscopic mslo Ca-activated K⁺ currents in order to interpret these currents in terms of the gating behavior of the mslo channel. To do so, however, it was necessary to first find conditions by which we could separate the effects that changes in Ca²⁺ concentration or membrane voltage have on channel permeation from the effects these stimuli have on channel gating. In this study we investigate three phenomena which are unrelated to gating but are manifest in macroscopic current records: a saturation of single channel current at high voltage, a rapid voltage-dependent Ca²⁺ block, and a slow voltage-dependent Ba²⁺ block. Where possible methods are described by which these phenomena can be separated from the effects that changes in Ca²⁺ concentration and membrane voltage have on channel gating. Where this is not possible, some assessment of the impact these effects have on gating parameters determined from macroscopic current measurements is provided. We have also found that without considering the effects of Ca²⁺ and voltage on channel permeation and block, macroscopic current measurements suggest that mslo channels do not reach the same maximum open probability at all Ca²⁺ concentrations. Taking into account permeation and blocking effects, however, we find that this is not the case. The maximum open probability of the mslo channel is the same or very similar over a Ca²⁺ concentration range spanning three orders of magnitude indicating that over this range the internal Ca²⁺ concentration does not limit the ability of the channel to be activated by voltage.     

Gating characteristics of a steeply voltage-dependent gap junction channel in rat Schwann cells

The gating properties of macroscopic and microscopic gap junctional currents were compared by applying the dual whole cell patch clamp technique to pairs of neonatal rat Schwann cells. In response to transjunctional voltage pulses (Vj), macroscopic gap junctional currents decayed exponentially with time constants ranging from < 1 to < 10 s before reaching steady-state levels. The relationship between normalized steady-state junctional conductance (Gss) and (Vj) was well described by a Boltzmann relationship with e-fold decay per 10.4 mV, representing an equivalent gating charge of 2.4. At Vj > 60 mV, Gss was virtually zero, a property that is unique among the gap junctions characterized to date. Determination of opening and closing rate constants for this process indicated that the voltage dependence of macroscopic conductance was governed predominantly by the closing rate constant. In 78% of the experiments, a single population of unitary junctional currents was detected corresponding to an unitary channel conductance of approximately 40 pS. The presence of only a limited number of junctional channels with identical unitary conductances made it possible to analyze their kinetics at the single channel level. Gating at the single channel level was further studied using a stochastic model to determine the open probability (Po) of individual channels in a multiple channel preparation. Po decreased with increasing Vj following a Boltzmann relationship similar to that describing the macroscopic Gss voltage dependence. These results indicate that, for Vj of a single polarity, the gating of the 40 pS gap junction channels expressed by Schwann cells can be described by a first order kinetic model of channel transitions between open and closed states.     

Effects of stochastic channel gating and distribution on the cardiac action potential

Ion channels exhibit stochastic conformational changes determining their gating behavior. In addition, the process of protein turnover leads to a natural variability of the number of membrane and gap junctional channels. Nevertheless, in computational models, these two aspects are scarcely considered and their impacts are largely unknown. We investigated the effects of stochastic current fluctuations and channel distributions on action potential duration (APD), intercellular conduction delays (ICDs) and conduction blocks using a modified ventricular cell model (Rudy et al.) with Markovian formulations of the principal ion currents (to simulate their stochastic open-close gating behavior) and with channel counts drawn from Poisson distributions (to simulate their natural variability). In single cells, APD variability (coefficient of variation: 1.6% at BCL=1000 ms) was essentially caused by stochastic channel gating of I_Ks, persistent I_Na and I_Ca,L. In cell strands, ICD variability induced by stochastic channel gating and Poissonian channel distributions was low under normal conditions. Nonetheless, at low intercellular coupling levels, Poissonian gap junctional channel distribution resulted in a large ICD variability (coefficient of variation >20%), highly heterogeneous conduction patterns and conduction blocks. Therefore, the stochastic behavior of current fluctuations and channel distributions can contribute to the heterogeneity of conduction patterns and to conduction block, as observed previously in experiments in cardiac tissue with altered intercellular coupling.     

Inactivation viewed through single sodium channels

Recordings of the sodium current in tissue-cultured GH3 cells show that the rate of inactivation in whole cell and averaged single channel records is voltage dependent: tau h varied e-fold/approximately 26 mV. The source of this voltage dependence was investigated by examining the voltage dependence of individual rate constants, estimated by maximum likelihood analysis of single channel records, in a five-state kinetic model. The rate constant for inactivating from the open state, rather than closing, increased with depolarization, as did the probability that an open channel inactivates. The rate constant for closing from the open state had the opposite voltage dependence. Both rate constants contributed to the mean open time, which was not very voltage dependent. Both open time and burst duration were less than tau h for voltages up to -20 mV. The slowest time constant of activation, tau m, was measured from whole cell records, by fitting a single exponential either to tail currents or to activating currents in trypsin-treated cells, in which the inactivation was abolished. tau m was a bell-shaped function of voltage and had a voltage dependence similar to tau h at voltages more positive than -35 mV, but was smaller than tau h. At potentials more negative than about -10 mV, individual channels may open and close several times before inactivating. Therefore, averaged single channel records, which correspond with macroscopic current elicited by a depolarization, are best described by a convolution of the first latency density with the autocorrelation function rather than with 1 - (channel open time distribution). The voltage dependence of inactivation from the open state, in addition to that of the activation process, is a significant factor in determining the voltage dependence of macroscopic inactivation. Although the rates of activation and inactivation overlapped greatly, independent and coupled inactivation could not be statistically distinguished for two models examined. Although rates of activation affect the observed rate of inactivation at intermediate voltages, extrapolation of our estimates of rate constants suggests that at very depolarized voltages the activation process is so fast that it is an insignificant factor in the time course of inactivation. Prediction of gating currents shows that an inherently voltage-dependent inactivation process need not produce a conspicuous component in the gating current.     

Properties of single voltage-gated proton channels in human eosinophils estimated by noise analysis and by direct measurement

Voltage-gated proton channels were studied under voltage clamp in excised, inside-out patches of human eosinophils, at various pHi with pHo 7.5 or 6.5 pipette solutions. H+ current fluctuations were observed consistently when the membrane was depolarized to voltages that activated H+ current. At pHi < or = 5.5 the variance increased nonmonotonically with depolarization to a maximum near the midpoint of the H+ conductance-voltage relationship, gH-V, and then decreased, supporting the idea that the noise is generated by H+ channel gating. Power spectral analysis indicated Lorentzian and 1/f components, both related to H+ currents. Unitary H+ current amplitude was estimated from stationary or quasi-stationary variance, sigmaH2. We analyze sigmaH2 data obtained at various voltages on a linearized plot that provides estimates of both unitary conductance and the number of channels in the patch, without requiring knowledge of open probability. The unitary conductance averaged 38 fS at pHi 6.5, and increased nearly fourfold to 140 fS at pHi 5.5, but was independent of pHo. In contrast, the macroscopic gH was only 1.8-fold larger at pHi 5.5 than at pHi 6.5. The maximum H+ channel open probability during large depolarizations was 0.75 at pHi 6.5 and 0.95 at pHi 5.5. Because the unitary conductance increases at lower pHi more than the macroscopic gH, the number of functional channels must decrease. Single H+ channel currents were too small to record directly at physiological pH, but at pHi < or = 5.5 near Vthreshold (the voltage at which gH turns on), single channel-like current events were observed with amplitudes 7-16 fA.     

Voltage-dependent Gating of Single Wild-Type and S4 Mutant KAT1 Inward Rectifier Potassium Channels

The voltage-dependent gating mechanism of KAT1 inward rectifier potassium channels was studied using single channel current recordings from Xenopus oocytes injected with KAT1 mRNA. The inward rectification properties of KAT1 result from an intrinsic gating mechanism in the KAT1 channel protein, not from pore block by an extrinsic cation species. KAT1 channels activate with hyperpolarizing potentials from −110 through −190 mV with a slow voltage-dependent time course. Transitions before first opening are voltage dependent and account for much of the voltage dependence of activation, while transitions after first opening are only slightly voltage dependent. Using burst analysis, transitions near the open state were analyzed in detail. A kinetic model with multiple closed states before first opening, a single open state, a single closed state after first opening, and a closed-state inactivation pathway accurately describes the single channel and macroscopic data. Two mutations neutralizing charged residues in the S4 region (R177Q and R176L) were introduced, and their effects on single channel gating properties were examined. Both mutations resulted in depolarizing shifts in the steady state conductance–voltage relationship, shortened first latencies to opening, decreased probability of terminating bursts, and increased burst durations. These effects on gating were well described by changes in the rate constants in the kinetic model describing KAT1 channel gating. All transitions before the open state were affected by the mutations, while the transitions after the open state were unaffected, implying that the S4 region contributes to the early steps in gating for KAT1 channels.     

Alterations in the cytoplasmic domain of CLCN2 result in altered gating kinetics.

Mutations in the human ClC-2 Cl(-) channel have been described to influence its function dramatically. To test for naturally occurring gene variants in a human population and their functionality, all 24 CLCN2 exons from a Central African population were sequenced. Six single amino acid exchanges in the intracellular N-terminus (P48R, R68H), in the pore domain (G199A), or in the intracellular C-terminus (R646Q, R725W, R747H) were identified at low frequency. Heterologous expression of these polymorphisms in Xenopus laevis oocytes demonstrated their functional significance as determined by two-electrode voltage-clamp. The polymorphisms R68H, R725W, and R747H exhibited faster voltage-stimulated gating as compared to the wild type channel, resulting in higher steady state currents of R725W. Probably due to decreased surface expression P48R, R68H, and R646Q mutants generated lower currents than the wild type channels. The inward currents of the mutated channels R725W, R747H, and G199A failed to increase during hypotonic swelling, a defect paralleled by impaired swelling-accelerated voltage-gating in one mutant (G199A). In conclusion, the Africans' gene pool comprises CLCN2 gene variants in the N-terminus, the C-terminus or the pore domain that affect surface expression and voltage- or cell-swelling-stimulated channel gating.     

Coupling between voltage sensor activation,Ca2+ binding and channel opening in large conductance (BK) potassium channels

To determine how intracellular Ca(2+) and membrane voltage regulate the gating of large conductance Ca(2+)-activated K(+) (BK) channels, we examined the steady-state and kinetic properties of mSlo1 ionic and gating currents in the presence and absence of Ca(2+) over a wide range of voltage. The activation of unliganded mSlo1 channels can be accounted for by allosteric coupling between voltage sensor activation and the closed (C) to open (O) conformational change (Horrigan, F.T., and R.W. Aldrich. 1999. J. Gen. Physiol. 114:305-336; Horrigan, F.T., J. Cui, and R.W. Aldrich. 1999. J. Gen. Physiol. 114:277-304). In 0 Ca(2+), the steady-state gating charge-voltage (Q(SS)-V) relationship is shallower and shifted to more negative voltages than the conductance-voltage (G(K)-V) relationship. Calcium alters the relationship between Q-V and G-V, shifting both to more negative voltages such that they almost superimpose in 70 microM Ca(2+). This change reflects a differential effect of Ca(2+) on voltage sensor activation and channel opening. Ca(2+) has only a small effect on the fast component of ON gating current, indicating that Ca(2+) binding has little effect on voltage sensor activation when channels are closed. In contrast, open probability measured at very negative voltages (less than -80 mV) increases more than 1,000-fold in 70 microM Ca(2+), demonstrating that Ca(2+) increases the C-O equilibrium constant under conditions where voltage sensors are not activated. Thus, Ca(2+) binding and voltage sensor activation act almost independently, to enhance channel opening. This dual-allosteric mechanism can reproduce the steady-state behavior of mSlo1 over a wide range of conditions, with the assumption that activation of individual Ca(2+) sensors or voltage sensors additively affect the energy of the C-O transition and that a weak interaction between Ca(2+) sensors and voltage sensors occurs independent of channel opening. By contrast, macroscopic I(K) kinetics indicate that Ca(2+) and voltage dependencies of C-O transition rates are complex, leading us to propose that the C-O conformational change may be described by a complex energy landscape.     

pH modification of human T-type calcium channel gating

External pH (pH(o)) modifies T-type calcium channel gating and permeation properties. The mechanisms of T-type channel modulation by pH remain unclear because native currents are small and are contaminated with L-type calcium currents. Heterologous expression of the human cloned T-type channel, alpha1H, enables us to determine the effect of changing pH on isolated T-type calcium currents. External acidification from pH(o) 8.2 to pH(o) 5.5 shifts the midpoint potential (V(1/2)) for steady-state inactivation by 11 mV, shifts the V(1/2) for maximal activation by 40 mV, and reduces the voltage dependence of channel activation. The alpha1H reversal potential (E(rev)) shifts from +49 mV at pH(o) 8.2 to +36 mV at pH(o) 5.5. The maximal macroscopic conductance (G(max)) of alpha1H increases at pH(o) 5.5 compared to pH(o) 8.2. The E(rev) and G(max) data taken together suggest that external protons decrease calcium/monovalent ion relative permeability. In response to a sustained depolarization alpha1H currents inactivate with a single exponential function. The macroscopic inactivation time constant is a steep function of voltage for potentials < -30 mV at pH(o) 8.2. At pH(o) 5.5 the voltage dependence of tau(inact) shifts more depolarized, and is also a more gradual function of voltage. The macroscopic deactivation time constant (tau(deact)) is a function of voltage at the potentials tested. At pH(o) 5.5 the voltage dependence of tau(deact) is simply transposed by approximately 40 mV, without a concomitant change in the voltage dependence. Similarly, the delay in recovery from inactivation at V(rec) of -80 mV in pH(o) 5.5 is similar to that with a V(rec) of -120 mV at pH(o) 8.2. We conclude that alpha1H is uniquely modified by pH(o) compared to other calcium channels. Protons do not block alpha1H current. Rather, a proton-induced change in activation gating accounts for most of the change in current magnitude with acidification.     

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.     

Effects of ultraviolet modification on the gating energetics of cyclic nucleotide-gated channels

Middendorf et al. (Middendorf, T.R., R.W. Aldrich, and D.A. Baylor. 2000. J. Gen. Physiol. 116:227-252) showed that ultraviolet light decreases the current through cloned cyclic nucleotide-gated channels from bovine retina activated by high concentrations of cGMP. Here we probe the mechanism of the current reduction. The channels' open probability before irradiation, P(o)(0), determined the sign of the change in current amplitude that occurred upon irradiation. UV always decreased the current through channels with high initial open probabilities [P(o)(0) > 0.3]. Manipulations that promoted channel opening antagonized the current reduction by UV. In contrast, UV always increased the current through channels with low initial open probabilities [P(o)(0) < or = 0.02], and the magnitude of the current increase varied inversely with P(o)(0). The dual effects of UV on channel currents and the correlation of both effects with P(o)(0) suggest that the channels contain two distinct classes of UV target residues whose photochemical modification exerts opposing effects on channel gating. We present a simple model based on this idea that accounts quantitatively for the UV effects on the currents and provides estimates for the photochemical quantum yields and free energy costs of modifying the UV targets. Simulations indicate that UV modification may be used to produce and quantify large changes in channel gating energetics in regimes where the associated changes in open probability are not measurable by existing techniques.     

Involvement of helices at the dimer interface in ClC-1 common gating

ClC-1 is a dimeric, double-pored chloride channel that is present in skeletal muscle. Mutations of this channel can result in the condition myotonia, a muscle disorder involving increased muscle stiffness. It has been shown that the dominant form of myotonia often results from mutations that affect the so-called slow, or common, gating process of the ClC-1 channel. Mutations causing dominant myotonia are seen to cluster at the interface of the ClC-1 channel monomers. This study has investigated the role of the H, I, P, and Q helices, which lie on this interface, as well as the G helix, which is situated immediately behind the H and I helices, on ClC-1 gating. 11 mutant ClC-1 channels (T268M, C277S, C278S, S289A, T310M, S312A, V321S, T539A, S541A, M559T, and S572V) were produced using site-directed mutagenesis, and gating properties of these channels were investigated using electrophysiological techniques. Six of the seven mutations in G, H, and I, and two of the four mutations in P and Q, caused shifts of the ClC-1 open probability. In the majority of cases this was due to alterations in the common gating process, with only three of the mutants displaying any change in fast gating. Many of the mutant channels also showed alterations in the kinetics of the common gating process, particularly at positive potentials. The changes observed in common gating were caused by changes in the opening rate (e.g. T310M), the closing rate (e.g. C277S), or both rates. These results indicate that mutations in the helices forming the dimer interface are able to alter the ClC-1 common gating process by changing the energy of the open and/or closed channel states, and hence altering transition rates between these states.     

Counting channels: a tutorial guide on ion channel fluctuation analysis

Ion channels open and close in a stochastic fashion, following the laws of probability. However, distinct from tossing a coin or a die, the probability of finding the channel closed or open is not a fixed number but can be modified (i.e., we can cheat) by some external stimulus, such as the voltage. Single-channel records can be obtained using the appropriate electrophysiological technique (e.g., patch clamp), and from these records the open probability and the channel conductance can be calculated. Gathering these parameters from a membrane containing many channels is not straightforward, as the macroscopic current I = iNP(o), where i is the single-channel current, N the number of channels, and P(o) the probability of finding the channel open, cannot be split into its individual components. In this tutorial, using the probabilistic nature of ion channels, we discuss in detail how i, N, and P(o max) (the maximum open probability) can be obtained using fluctuation (nonstationary noise) analysis (Sigworth FJ. G Gen Physiol 307: 97-129, 1980). We also analyze the sources of possible artifacts in the determination of i and N, such as channel rundown, inadequate filtering, and limited resolution of digital data acquisition by use of a simulation computer program (available at www.cecs.cl).     

Shaker potassium channel gating. III: Evaluation of kinetic models for activation

Predictions of different classes of gating models involving identical conformational changes in each of four subunits were compared to the gating behavior of Shaker potassium channels without N-type inactivation. Each model was tested to see if it could simulate the voltage dependence of the steady state open probability, and the kinetics of the single-channel currents, macroscopic ionic currents and macroscopic gating currents using a single set of parameters. Activation schemes based upon four identical single-step activation processes were found to be incompatible with the experimental results, as were those involving a concerted, opening transition. A model where the opening of the channel requires two conformational changes in each of the four subunits can adequately account for the steady state and kinetic behavior of the channel. In this model, the gating in each subunit is independent except for a stabilization of the open state when all four subunits are activated, and an unstable closed conformation that the channel enters after opening. A small amount of negative cooperativity between the subunits must be added to account quantitatively for the dependence of the activation time course on holding voltage.     

Allosteric voltage gating of potassium channels II. Mslo channel gating charge movement in the absence of Ca(2+).

Large-conductance Ca(2+)-activated K(+) channels can be activated by membrane voltage in the absence of Ca(2+) binding, indicating that these channels contain an intrinsic voltage sensor. The properties of this voltage sensor and its relationship to channel activation were examined by studying gating charge movement from mSlo Ca(2+)-activated K(+) channels in the virtual absence of Ca(2+) (<1 nM). Charge movement was measured in response to voltage steps or sinusoidal voltage commands. The charge-voltage relationship (Q-V) is shallower and shifted to more negative voltages than the voltage-dependent open probability (G-V). Both ON and OFF gating currents evoked by brief (0.5-ms) voltage pulses appear to decay rapidly (tau(ON) = 60 microseconds at +200 mV, tau(OFF) = 16 microseconds at -80 mV). However, Q(OFF) increases slowly with pulse duration, indicating that a large fraction of ON charge develops with a time course comparable to that of I(K) activation. The slow onset of this gating charge prevents its detection as a component of I(gON), although it represents approximately 40% of the total charge moved at +140 mV. The decay of I(gOFF) is slowed after depolarizations that open mSlo channels. Yet, the majority of open channel charge relaxation is too rapid to be limited by channel closing. These results can be understood in terms of the allosteric voltage-gating scheme developed in the preceding paper (Horrigan, F.T., J. Cui, and R.W. Aldrich. 1999. J. Gen. Physiol. 114:277-304). The model contains five open (O) and five closed (C) states arranged in parallel, and the kinetic and steady-state properties of mSlo gating currents exhibit multiple components associated with C-C, O-O, and C-O transitions.     

A mutation causing pseudohypoaldosteronism type 1 identifies a conserved glycine that is involved in the gating of the epithelial sodium channel.

Pseudohypoaldosteronism type 1 (PHA-1) is an inherited disease characterized by severe neonatal salt-wasting and caused by mutations in subunits of the amiloride-sensitive epithelial sodium channel (ENaC). A missense mutation (G37S) of the human ENaC beta subunit that causes loss of ENaC function and PHA-1 replaces a glycine that is conserved in the N-terminus of all members of the ENaC gene family. We now report an investigation of the mechanism of channel inactivation by this mutation. Homologous mutations, introduced into alpha, beta or gamma subunits, all significantly reduce macroscopic sodium channel currents recorded in Xenopus laevis oocytes. Quantitative determination of the number of channel molecules present at the cell surface showed no significant differences in surface expression of mutant compared with wild-type channels. Single channel conductances and ion selectivities of the mutant channels were identical to that of wild-type. These results suggest that the decrease in macroscopic Na currents is due to a decrease in channel open probability (P(o)), suggesting that mutations of a conserved glycine in the N-terminus of ENaC subunits change ENaC channel gating, which would explain the disease pathophysiology. Single channel recordings of channels containing the mutant alpha subunit (alphaG95S) directly demonstrate a striking reduction in P(o). We propose that this mutation favors a gating mode characterized by short-open and long-closed times. We suggest that determination of the gating mode of ENaC is a key regulator of channel activity.     

Gating of Shaker K+ channels: I. Ionic and gating currents.

Ionic and gating currents from noninactivating Shaker B K+ channels were studied with the cut-open oocyte voltage clamp technique and compared with the macropatch clamp technique. The performance of the cut-open oocyte voltage clamp technique was evaluated from the electrical properties of the clamped upper domus membrane, K+ tail current measurements, and the time course of K+ currents after partial blockade. It was concluded that membrane currents less than 20 microA were spatially clamped with a time resolution of at least 50 microseconds. Subtracted, unsubtracted gating currents with the cut-open oocyte voltage clamp technique and gating currents recorded in cell attached macropatches had similar properties and time course, and the charge movement properties directly obtained from capacity measurements agreed with measurements of charge movement from subtracted records. An accurate estimate of the normalized open probability Po(V) was obtained from tail current measurements as a function of the prepulse V in high external K+. The Po(V) was zero at potentials more negative than -40 mV and increased sharply at this potential, then increased continuously until -20 mV, and finally slowly increased with voltages more positive than 0 mV. Deactivation tail currents decayed with two time constants and external potassium slowed down the faster component without affecting the slower component that is probably associated with the return between two of the closed states near the open state. In correlating gating currents and channel opening, Cole-Moore type experiments showed that charge moving in the negative region of voltage (-100 to -40 mV) is involved in the delay of the conductance activation but not in channel opening. The charge moving in the more positive voltage range (-40 to -10 mV) has a similar voltage dependence to the open probability of the channel, but it does not show the gradual increase with voltage seen in the Po(V).     

Single-channel, macroscopic, and gating currents from sodium channels in the squid giant axon.

Single-channel, macroscopic ionic, and macroscopic gating currents were recorded from the voltage-dependent sodium channel using patch-clamp techniques on the cut-open squid giant axon. To obtain a complete set of physiological measurements of sodium channel gating under identical conditions, and to facilitate comparison with previous work, comparison was made between currents recorded in the absence of extracellular divalent cations and in the presence of physiological concentrations of extracellular Ca2+ (10 mM) and Mg2+ (50 mM). The single-channel currents were well resolved when divalent cations were not included in the extracellular solution, but were decreased in amplitude in the presence of Ca2+ and Mg2+ ions. The instantaneous current-voltage relationship obtained from macroscopic tail current measurements similarly was depressed by divalents, and showed a negative slope-conductance region for inward current at negative potentials. Voltage dependent parameters of channel gating were shifted 9-13 mV towards depolarized potentials by external divalent cations, including the peak fraction of channels open versus voltage, the time constant of tail current decline, the prepulse inactivation versus voltage relationship, and the charge-voltage relationship for gating currents. The effects of divalent cations are consistent with open channel block by Ca2+ and Mg2+ together with divalent screening of membrane charges.