CFTR displays voltage dependence and two gating modes during stimulation

The patch-clamp technique in conjunction with current noise analysis was employed to clarify the events underlying the regulation of the CFTR (cystic fibrosis transmembrane conductance regulator) during cAMP- dependent stimulation. 3T3 fibroblast cells expressing the CFTR were stimulated in cell-attached mode with forskolin. The number (N) of activated channels per patch ranged from 1 to approximately 100. In true single-channel recordings, CFTR's gating was best described by two open states (approximately 5 and approximately 100 ms) and three closed states (< or = 5, approximately 100, and approximately 1,000 ms). Current noise analysis resulted in spectra containing two distinct Lorentzian noise components with corner frequencies of 1.3 Hz and approximately 50 Hz, respectively. Single-channel time constants were dependent on voltage. The fastest closed state increased its contribution from 48% at +100 mV to 87% at -100 mV, and the medium open state reduced its length to one half, resulting in gating dominated by fast events. Similarly, the fast Lorentzian increased its amplitude, and its corner frequency increased from 44 Hz at +100 mV to 91 Hz at - 100 mV, while the slow Lorentzian was voltage independent. In multi- channel recordings N.Po (i.e., N times open probability) increased significantly, on average by 52% between -90 and +90 mV. Stimulation with forskolin increased Po of CFTR to approximately 0.5, which resulted from a decrease of the longest closed state while the faster open and closed states were unaffected. Neither corner frequency was affected during stimulation. Recordings from multichannel patches revealed in addition, unique, very long channel openings (high Po mode, average 13 s). Channels exhibiting high Po (i.e., Po approximately 1.0) or low Po (i.e., Po approximately 0.5) gating modes were both present in multichannel recordings, and CFTRs switched modes during stimulation. In addition, the switch to the high Po mode appeared to be a cooperative event for channel pairs. High forskolin concentration (i.e., 10 microM) favored transition into the high Po mode, suggesting a cellularly mediated regulation of model switching due to a fundamental change in configuration of the CFTR. Thus, during stimulation the CFTR increased its activity through two distinct effects: the reduction of the long closed state and modal switching to the high Po mode.     

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).     

Kinetics of 9-aminoacridine block of single Na channels

The kinetics of 9-aminoacridine (9-AA) block of single Na channels in neuroblastoma N1E-115 cells were studied using the gigohm seal, patch clamp technique, under the condition in which the Na current inactivation had been eliminated by treatment with N-bromoacetamide (NBA). Following NBA treatment, the current flowing through individual Na channels was manifested by square-wave open events lasting from several to tens of milliseconds. When 9-AA was applied to the cytoplasmic face of Na channels at concentrations ranging from 30 to 100 microM, it caused repetitive rapid transitions (flickering) between open and blocked states within single openings of Na channels, without affecting the amplitude of the single channel current. The histograms for the duration of blocked states and the histograms for the duration of open states could be fitted with a single-exponential function. The mean open time (tau o) became shorter as the drug concentration was increased, while the mean blocked time (tau b) was concentration independent. The association (blocking) rate constant, kappa, calculated from the slope of the curve relating the reciprocal mean open time to 9-AA concentration, showed little voltage dependence, the rate constant being on the order of 1 X 10(7) M-1s-1. The dissociation (unblocking) rate constant, l, calculated from the mean blocked time, was strongly voltage dependent, the mean rate constant being 214 s-1 at 0 mV and becoming larger as the membrane being hyperpolarized. The voltage dependence suggests that a first-order blocking site is located at least 63% of the way through the membrane field from the cytoplasmic surface. The equilibrium dissociation constant for 9-AA to block the Na channel, defined by the relation of l/kappa, was calculated to be 21 microM at 0 mV. Both tau -1o and tau -1b had a Q10 of 1.3, which suggests that binding reaction was diffusion controlled. The burst time in the presence of 9-AA, which is the sum of open times and blocked times, was longer than the lifetime of open channels in the absence of drug. All of the features of 9-AA block of single Na channels are compatible with the sequential model in which 9-AA molecules block open Na channels, and the blocked channels could not close until 9-AA molecules had left the blocking site in the channels.     

Single channel properties of P2X2 purinoceptors

The single channel properties of cloned P2X2 purinoceptors expressed in human embryonic kidney (HEK) 293 cells and Xenopus oocytes were studied in outside-out patches. The mean single channel current-voltage relationship exhibited inward rectification in symmetric solutions with a chord conductance of approximately 30 pS at -100 mV in 145 mM NaCl. The channel open state exhibited fast flickering with significant power beyond 10 kHz. Conformational changes, not ionic blockade, appeared responsible for the flickering. The equilibrium constant of Na+ binding in the pore was approximately 150 mM at 0 mV and voltage dependent. The binding site appeared to be approximately 0.2 of the electrical distance from the extracellular surface. The mean channel current and the excess noise had the selectivity: K+ > Rb+ > Cs+ > Na+ > Li+. ATP increased the probability of being open (Po) to a maximum of 0.6 with an EC50 of 11.2 microM and a Hill coefficient of 2.3. Lowering extracellular pH enhanced the apparent affinity of the channel for ATP with a pKa of approximately 7.9, but did not cause a proton block of the open channel. High pH slowed the rise time to steps of ATP without affecting the fall time. The mean single channel amplitude was independent of pH, but the excess noise increased with decreasing pH. Kinetic analysis showed that ATP shortened the mean closed time but did not affect the mean open time. Maximum likelihood kinetic fitting of idealized single channel currents at different ATP concentrations produced a model with four sequential closed states (three binding steps) branching to two open states that converged on a final closed state. The ATP association rates increased with the sequential binding of ATP showing that the binding sites are not independent, but positively cooperative. Partially liganded channels do not appear to open. The predicted Po vs. ATP concentration closely matches the single channel current dose-response curve.     

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.     

The Estimation of Rapid Rate Constants from Current-Amplitude Frequency Distributions of Single-Channel Recordings

A method is described for estimating rapid rate constants from the distributions of current amplitude observed in single-channel electrical recordings. It has the advantages over previous, similar approaches that it can accommodate both multistate kinetic models and adjustable filtering of the data using an 8-pole Bessel filter. The method is conceptually straightforward: the observed distributions of current amplitude are compared with theoretical distributions derived by combining several simplifying assumptions about the underlying stochastic process with a model of the filter and electrical noise. Parameters are estimated by approximate maximum likelihood. The method was used successfully to estimate rate constants for both a simple two-state kinetic model (the transitions between open and closed states during the rapid gating of an outward-rectifying K⁺-selective channel in the plasma membrane of Acetabularia) and a complex multistate kinetic model (the blockade of the maxi cation channel in the plasma membrane of rye roots by verapamil). For the two-state model, parameters were estimated well, provided that they were not too fast or too slow in relation to the sampling rate. In the three-state model the precision of estimates depended in a complex way on the values of all rate parameters in the model. Received: 4 October 1996/Revised: 2 September 1997     

Voltage-dependent inactivation of T-tubular skeletal calcium channels in planar lipid bilayers

Single-channel properties of dihydropyridine (DHP)-sensitive calcium channels isolated from transverse tubular (T-tube) membrane of skeletal muscle were explored. Single-channel activity was recorded in planar lipid bilayers after fusion of highly purified rabbit T-tube microsomes. Two populations of DHP-sensitive calcium channels were identified. One type of channel (noninactivating) was active (2 microM +/- Bay K 8644) at steady-state membrane potentials and has been studied in other laboratories. The second type of channel (inactivating) was transiently activated during voltage pulses and had a very low open probability (Po) at steady-state membrane potentials. Inactivating channel activity was observed in 47.3% of the experiments (n = 84 bilayers). The nonstationary kinetics of this channel was determined using a standard voltage pulse (HP = -50 mV, pulse to 0 mV). The time constant (tau) of channel activation was 23 ms. During the mV). The time constant (tau) of channel activation was 23 ms. During the pulse, channel activity decayed (inactivated) with a tau of 3.7 s. Noninactivating single-channel activity was well described by a model with two open and two closed states. Inactivating channel activity was described by the same model with the addition of an inactivated state as proposed for cardiac muscle. The single-channel properties were compared with the kinetics of DHP-sensitive inward calcium currents (ICa) measured at the cellular level. Our results support the hypothesis that voltage-dependent inactivation of single DHP-sensitive channels contributes to the decay of ICa.     

Serine protease activation of near-silent epithelial Na+ channels

The regulation of epithelial Na+ channel (ENaC) function is critical for normal salt and water balance. This regulation is achieved through cell surface insertion/retrieval of channels, by changes in channel open probability (Po), or through a combination of these processes. Epithelium-derived serine proteases, including channel activating protease (CAP) and prostasin, regulate epithelial Na+ transport, but the molecular mechanism is unknown. We tested the hypothesis that extracellular serine proteases activate a near-silent ENaC population resident in the plasma membrane. Single-channel events were recorded in outside-out patches from fibroblasts (NIH/3T3) stably expressing rat alpha-, beta-, and gamma-subunits (rENaC), before and during exposure to trypsin, a serine protease homologous to CAP and prostasin. Under baseline conditions, near-silent patches were defined as having rENaC activity (NPo) < 0.03, where N is the number of channels. Within 1-5 min of 3 microg/ml bath trypsin superfusion, NPo increased approximately 66-fold (n = 7). In patches observed to contain a single functional channel, trypsin increased Po from 0.02 +/- 0.01 to 0.57 +/- 0.03 (n = 3, mean +/- SE), resulting from the combination of an increased channel open time and decreased channel closed time. Catalytic activity was required for activation of near-silent ENaC. Channel conductance and the Na+/Li+ current ratio with trypsin were similar to control values. Modulation of ENaC Po by endogenous epithelial serine proteases is a potentially important regulator of epithelial Na+ transport, distinct from the regulation achieved by hormone-induced plasma membrane insertion of channels.     

Na channel kinetics: developing models from non-stationary current fluctuations by analytic methods

In a previous study, we analyzed Na current fluctuations in myelinated axons from Xenopus laevis under voltage clamp conditions. The statistical properties were analyzed in terms of covariance functions for consecutive time intervals of varying duration during the pulse step. The underlying channel kinetics was analyzed by performing stochastic simulations of published Na channel models and calculating corresponding covariance functions. None of the models explained the fluctuation results. We therefore developed a novel minimal Na channel model that satisfactorily described the results. In the present paper, we extend the analysis and specify the possible models explaining the experimental data by using analytical methods. We derive general relations between the experimental data, including the covariance functions, and the rate constants of specific one-open-state models. A general feature of these models is that they comprise an inactivation step from the first closed state and a relatively low backward rate from the open state. This is in accordance the minimal model inferred from numerical stochastic calculations in the previous study.     

Basic properties and potential regulators of the apical K+ channel in macula densa cells

These studies examine the properties of an apical potassium (K+) channel in macula densa cells, a specialized group of cells involved in tubuloglomerular feedback signal transmission. To this end, individual glomeruli with thick ascending limbs (TAL) and macula densa cells were dissected from rabbit kidney and the TAL covering macula densa cells was removed. Using patch clamp techniques, we found a high density (up to 54 channels per patch) of K+ channels in the apical membrane of macula densa cells. An inward conductance of 41.1 +/- 4.8 pS was obtained in cell-attached patches (patch pipette, 140 mM K+). In inside- out patches (patch pipette, 140 mM; bath, 5 mM K+), inward currents of 1.1 +/- 0.1 pA (n = 11) were observed at 0 mV and single channel current reversed at a pipette potential of -84 mV giving a permeability ratio (PK/PNa) of over 100. In cell-attached patches, mean channel open probability (N,Po, where N is number of channels in the patch and Po is single channel open probability) was unaffected by bumetanide, but was reduced from 11.3 +/- 2.7 to 1.6 +/- 1.3 (n = 5, p < 0.02) by removal of bath sodium (Na+). Simultaneous removal of bath Na+ and calcium (Ca2+) prevented the Na(+)-induced decrease in N.Po indicating that the effect of Na+ removal on N.Po was probably mediated by stimulation of Ca2+ entry. This interpretation was supported by studies where ionomycin, which directly increases intracellular Ca2+, produced a fall in N.Po from 17.8 +/- 4.0 to 5.9 +/- 4.1 (n = 7, p < 0.02). In inside- out patches, the apical K+ channel was not sensitive to ATP but was directly blocked by 2 mM Ca2+ and by lowering bath pH from 7.4 to 6.8. These studies constitute the first single channel observations on macula densa cells and establish some of the characteristics and regulators of this apical K+ channel. This channel is likely to be involved in macula densa transepithelial Cl- transport and perhaps in the tubuloglomerular feedback signaling process.     

Voltage-dependent block of anthrax toxin channels in planar phospholipid bilayer membranes by symmetric tetraalkylammonium ions. Single-channel analysis

Previous studies have shown that symmetric tetraalkylammonium ions affect, in a voltage-dependent manner, the conductance of membranes containing many channels formed by the PA65 fragment of anthrax toxin. In this paper we analyze this phenomenon at the single-channel level for tetrabutylammonium ion (Bu4N+). We find that Bu4N+ induces a flickery block of the PA65 channel when present on either side of the membrane, and this block is relieved by large positive voltages on the blocking-ion side. At high frequencies (greater than 2 kHz) we have resolved individual blocking events and measured the dwell times in the blocked and unblocked states. These dwell times have single-exponential distributions, with time constants tau b and tau u that are voltage dependent, consistent with the two-barrier, single-well potential energy diagram that we postulated in our previous paper. The fraction of time the channel spends unblocked [tau u/(tau u + tau b)] as a function of voltage is identical to the normalized conductance-voltage relation determined from macroscopic measurements of blocking, thus demonstrating that these single channels mirror the behavior seen with many (greater than 10,000) channels in the membrane. In going from large negative to large positive voltages (-100 to +160 mV) on the cis (PA65-containing) side of the membrane, one sees the mean blocked time (tau b) increase to a maximum at +60 mV and then steadily decline for voltages greater than +60 mV, thereby clearly demonstrating that Bu4N+ is driven through the channel by positive voltages on the blocking-ion side. In other words, the channel is permeable to Bu4N+. An interesting finding that emerges from analysis of the voltage dependence of mean blocked and unblocked times is that the blocking rate, with Bu4N+ present on the cis side of the membrane, plateaus at large positive cis voltages to a voltage-independent value consistent with the rate of Bu4N+ entry into the blocking site being diffusion limited.     

Voltage and Ca2+ activation of single large-conductance Ca2+-activated K+ channels described by a two-tiered allosteric gating mechanism

The voltage- and Ca2+-dependent gating mechanism of large-conductance Ca2+-activated K+ (BK) channels from cultured rat skeletal muscle was studied using single-channel analysis. Channel open probability (Po) increased with depolarization, as determined by limiting slope measurements (11 mV per e-fold change in Po; effective gating charge, q(eff), of 2.3 +/- 0.6 e(o)). Estimates of q(eff) were little changed for intracellular Ca2+ (Ca2+(i)) ranging from 0.0003 to 1,024 microM. Increasing Ca2+(i) from 0.03 to 1,024 microM shifted the voltage for half maximal activation (V(1/2)) 175 mV in the hyperpolarizing direction. V(1/2) was independent of Ca2+(i) for Ca2+(i) < or = 0.03 microM, indicating that the channel can be activated in the absence of Ca2+(i). Open and closed dwell-time distributions for data obtained at different Ca2+(i) and voltage, but at the same Po, were different, indicating that the major action of voltage is not through concentrating Ca2+ at the binding sites. The voltage dependence of Po arose from a decrease in the mean closing rate with depolarization (q(eff) = -0.5 e(o)) and an increase in the mean opening rate (q(eff) = 1.8 e(o)), consistent with voltage-dependent steps in both the activation and deactivation pathways. A 50-state two-tiered model with separate voltage- and Ca2+-dependent steps was consistent with the major features of the voltage and Ca2+ dependence of the single-channel kinetics over wide ranges of Ca2+(i) (approximately 0 through 1,024 microM), voltage (+80 to -80 mV), and Po (10(-4) to 0.96). In the model, the voltage dependence of the gating arises mainly from voltage-dependent transitions between closed (C-C) and open (O-O) states, with less voltage dependence for transitions between open and closed states (C-O), and with no voltage dependence for Ca2+-binding and unbinding. The two-tiered model can serve as a working hypothesis for the Ca2+- and voltage-dependent gating of the BK channel.     

Light-dependent K(+) channels in the mollusc Onchidium simple photoreceptors are opened by cGMP

Light-dependent K(+) channels underlying a hyperpolarizing response of one extraocular (simple) photoreceptor, Ip-2 cell, in the marine mollusc Onchidium ganglion were examined using cell-attached and inside-out patch-clamp techniques. A previous report (Gotow, T., T. Nishi, and H. Kijima. 1994. Brain Res. 662:268-272) showed that a depolarizing response of the other simple photoreceptor, A-P-1 cell, results from closing of the light-dependent K(+) channels that are activated by cGMP. In the cell-attached patch recordings of Ip-2 cells, external artificial seawater (ASW) was replaced with a modified ASW containing 150 mM K(+) and 200 mM Mg(2+) to suppress any synaptic input and to maintain the membrane potential constant. When Ip-2 cells were equilibrated with this modified ASW, the internal K(+) concentration was estimated to be 260 mM. Light-dependent single-channels in the cell-attached patch on these cells were opened by light but scarcely by voltage. After confirming the light-dependent channel activity in the cell-attached patches, an application of cGMP to the excised inside-out patches newly activated a channel that disappeared on removal of cGMP. Open and closed time distributions of this cGMP-activated channel could be described by the sum of two exponents with time constants tau(o1), tau(o2) and tau(c1), tau(c2), respectively, similar to those of the light-dependent channel. In both the channels, tau(o1) and tau(o2) in ms ranges were similar to each other, although tau(c2) over tens of millisecond ranges was different. tau(o1), tau(o2), and the mean open time tau(o) were both independent of light intensity, cGMP concentration, and voltage. In both channels, the open probability increased as the membrane was depolarized, without changing any of tau(o2) or tau(o). In both, the reversal potentials using 200- and 450-mM K(+)-filled pipettes were close to the K(+) equilibrium potentials, suggesting that both the channels are primarily K(+) selective. Both the mean values of the channel conductance were estimated to be the same at 62 and 91 pS in 200- and 450-mM K(+) pipettes at nearly 0 mV, respectively. Combining these findings with those in the above former report, it is concluded that cGMP is a second messenger which opens the light-dependent K(+) channel of Ip-2 to cause hyperpolarization, and that the channel is the same as that of A-P-1 closed by light.     

Gating of Na channels in the rat cortical collecting tubule: effects of voltage and membrane stretch

The gating kinetics of apical membrane Na channels in the rat cortical collecting tubule were assessed in cell-attached and inside-out excised patches from split-open tubules using the patch-clamp technique. In patches containing a single channel the open probability (Po) was variable, ranging from 0.05 to 0.9. The average Po was 0.5. However, the individual values were not distributed normally, but were mainly < or = 0.25 or > or = 0.75. Mean open times and mean closed times were correlated directly and inversely, respectively, with Po. In patches where a sufficient number of events could be recorded, two time constants were required to describe the open-time and closed-time distributions. In most patches in which basal Po was < 0.3 the channels could be activated by hyperpolarization of the apical membrane. In five such patches containing a single channel hyperpolarization by 40 mV increased Po by 10-fold, from 0.055 +/- 0.023 to 0.58 +/- 0.07. This change reflected an increase in the mean open time of the channels from 52 +/- 17 to 494 +/- 175 ms and a decrease in the mean closed time from 1,940 +/- 350 to 336 +/- 100 ms. These responses, however, could not be described by a simple voltage dependence of the opening and closing rates. In many cases significant delays in both the activation by hyperpolarization and deactivation by depolarization were observed. These delays ranged from several seconds to several tens of seconds. Similar effects of voltage were seen in cell-attached and excised patches, arguing against a voltage-dependent chemical modification of the channel, such as a phosphorylation. Rather, the channels appeared to switch between gating modes. These switches could be spontaneous but were strongly influenced by changes in membrane voltage. Voltage dependence of channel gating was also observed under whole-cell clamp conditions. To see if mechanical perturbations could also influence channel kinetics or gating mode, negative pressures of 10-60 mm Hg were applied to the patch pipette. In most cases (15 out of 22), this maneuver had no significant effect on channel behavior. In 6 out of 22 patches, however, there was a rapid and reversible increase in Po when the pressure was applied. In one patch, there was a reversible decrease. While no consistent effects of pressure could be documented, membrane deformation could contribute to the variation in Po under some conditions.     

Cytochrome c folds through a smooth funnel

A dominant feature of folding of cytochrome c is the presence of nonnative His-heme kinetic traps, which either pre-exist in the unfolded protein or are formed soon after initiation of folding. The kinetically trapped species can constitute the majority of folding species, and their breakdown limits the rate of folding to the native state. A temperature jump (T-jump) relaxation technique has been used to compare the unfolding/folding kinetics of yeast iso-2 cytochrome c and a genetically engineered double mutant that lacks His-heme kinetic traps, H33N,H39K iso-2. The results show that the thermodynamic properties of the transition states are very similar. A single relaxation time tau(obs) is observed for both proteins by absorbance changes at 287 nm, a measure of solvent exclusion from aromatic residues. At temperatures near Tm, the midpoint of the thermal unfolding transitions, tau(obs) is four to eight times faster for H33N,H39K iso-2 (tau(obs) approximately 4-10 ms) than for iso-2 (tau(obs) approximately 20-30 ms). T-jumps show that there are no kinetically unresolved (tau < 1-3 micros T-jump dead time) "burst" phases for either protein. Using a two-state model, the folding (k(f)) and unfolding (k(u)) rate constants and the thermodynamic activation parameters standard deltaGf, standard deltaGu, standard deltaHf, standard deltaHu, standard deltaSf, standard deltaSu are evaluated by fitting the data to a function describing the temperature dependence of the apparent rate constant k(obs) (= tau(obs)(-1)) = k(f) + k(u). The results show that there is a small activation enthalpy for folding, suggesting that the barrier to folding is largely entropic. In the "new view," a purely entropic kinetic barrier to folding is consistent with a smooth funnel folding landscape.     

Gating kinetics of batrachotoxin-modified Na+ channels in the squid giant axon. Voltage and temperature effects.

The gating kinetics of batrachotoxin-modified Na+ channels were studied in outside-out patches of axolemma from the squid giant axon by means of the cut-open axon technique. Single channel kinetics were characterized at different membrane voltages and temperatures. The probability of channel opening (Po) as a function of voltage was well described by a Boltzmann distribution with an equivalent number of gating particles of 3.58. The voltage at which the channel was open 50% of the time was a function of [Na+] and temperature. A decrease in the internal [Na+] induced a shift to the right of the Po vs. V curve, suggesting the presence of an integral negative fixed charge near the activation gate. An increase in temperature decreased Po, indicating a stabilization of the closed configuration of the channel and also a decrease in entropy upon channel opening. Probability density analysis of dwell times in the closed and open states of the channel at 0 degrees C revealed the presence of three closed and three open states. The slowest open kinetic component constituted only a small fraction of the total number of transitions and became negligible at voltages greater than -65 mV. Adjacent interval analysis showed that there is no correlation in the duration of successive open and closed events. Consistent with this analysis, maximum likelihood estimation of the rate constants for nine different single-channel models produced a preferred model (model 1) having a linear sequence of closed states and two open states emerging from the last closed state. The effect of temperature on the rate constants of model 1 was studied. An increase in temperature increased all rate constants; the shift in Po would be the result of an increase in the closing rates predominant over the change in the opening rates. The temperature study also provided the basis for building an energy diagram for the transitions between channel states.     

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 channel gating events in tracer flux experiments I. Theory

Tracer ion flux measurements are a commonly used method for studying ion transport through membranes of cellular systems, where the rate of ion flow is determined by gating processes which control the opening and closing of transmembrane channels. Due to recent advances in the theoretical analysis of tracer flux from or into closed membrane structures (CMS), the mechanism of gating reactions can, in principle, be derived from flux data. A physically well founded analysis is presented for the dependence of the total tracer ion content of a collection of CMS on the gating processes. For functionally uncoupled gating units a mean single channel flux contribution [equation, see text] can be defined, where k is the intrinsic single channel flux coefficient, t the time over which flux is measured, and p(tau,t) is the probability that a given channel was open for a total period tau during t. This quantity reflects the mean time course of the tracer content due to flux through a single channel. Expressions for are derived that explicitly take into account a distribution in the lifetime of open channels. On the basis of the results, kinetic and thermodynamic parameters of multiphasic gating reactions can be determined from the time course of the overall tracer content in a colleciion of CMS.