Evidence for cooperativity between nicotinic acetylcholine receptors in patch clamp records

It is often assumed that ion channels in cell membrane patches gate independently. However, in the present study nicotinic receptor patch clamp data obtained in cell-attached mode from embryonic chick myotubes suggest that the distribution of steady-state probabilities for conductance multiples arising from concurrent channel openings may not be binomial. In patches where up to four active channels were observed, the probabilities of two or more concurrent openings were greater than expected, suggesting positive cooperativity. For the case of two active channels, we extended the analysis by assuming that 1) individual receptors (not necessarily identical) could be modeled by a five-state (three closed and two open) continuous-time Markov process with equal agonist binding affinity at two recognition sites, and 2) cooperativity between channels could occur through instantaneous changes in specific transition rates in one channel following a change in conductance state of the neighboring channel. This allowed calculation of open and closed sojourn time density functions for either channel conditional on the neighboring channel being open or closed. Simulation studies of two channel systems, with channels being either independent or cooperative, nonidentical or identical, supported the discriminatory power of the optimization algorithm. The experimental results suggested that individual acetylcholine receptors were kinetically identical and that the open state of one channel increased the probability of opening of its neighbor.     

Effects of insulin and phosphatase on a Ca2(+)-dependent Cl- channel in a distal nephron cell line (A6)

A Cl- channel with a small single-channel conductance (3 pS) was observed in cell-attached patches formed on the apical membrane of cells from the distal nephron cell line (A6) cultured on permeable supports. The current-voltage (I-V) relationship from cell-attached patches or inside-out patches with 1 microM cytosolic Ca2+ strongly rectified with no inward current at potentials more negative than ECl. However, the rectification decreased (i.e., inward current increased) when the cytosolic Ca2+ concentration ([Ca2+]i) was increased above 1 microM. If [Ca2+]i is increased to 800 microM, the I-V relationship became linear. Besides the change in the I-V relationship, an increase in [Ca2+]i also increases the open probability of the channel. Regardless of the recording condition, the channel has one open and one closed state. Both closing and opening rates were dependent on [Ca2+]i; an increase of [Ca2+]i decreased the closing rate and increased the opening rate. The Ca2+ dependence of transition rates at positive membrane potentials (cell interior with respect to external surface) were much larger than the dependence at negative intracellular potentials. The I-V relationship of chloride channels in inside-out patches from cells pretreated with insulin was linear even with 1 microM [Ca2+]i, while channel currents from cells under similar conditions but without insulin still strongly rectified. Alkaline phosphatase applied to the intracellular surface of inside-out patches altered the outward rectification of single channels in a manner qualitatively similar to that of insulin pretreatment. These observations suggest that phosphorylation/dephosphorylation of the channel modulates the sensitivity of the Cl- channel to cytosolic Ca2+ and that insulin produces its effect by promoting dephosphorylation of the channel.     

Estimating kinetic constants from single channel data.

The process underlying the opening and closing of ionic channels in biological or artificial lipid membranes can be modeled kinetically as a time-homogeneous Markov chain. The elements of the chain are kinetic states that can be either open or closed. A maximum likelihood procedure is described for estimating the transition rates between these states from single channel data. The method has been implemented for linear kinetic schemes of fewer than six states, and is suitable for nonstationary data in which one or more independent channels are functioning simultaneously. It also provides standard errors for all estimates of rate constants and permits testing of smoothly parameterized subhypotheses of a general model. We have illustrated our approach by analysis of single channel data simulated on a computer and have described a procedure for analysis of experimental data.     

Mechanism of asymmetric block of K channels by tetraalkylammonium ions in mouse neuroblastoma cells

Experiments were performed to compare the mechanism of block of voltage-dependent K channels by various short and long alkyl chain tetraalkylammonium (TAA) ions at internal and external sites. Current through single channels was recorded from excised membrane patches of cultured neuroblastoma cells using the patch-clamp technique. All of the TAA derivatives tested blocked the open channel when applied to either side of the membrane. Tetraethylammonium (TEA) reduced the amplitude of current through the open channel. Tetrabutylammonium (TBA) and tetrapentylammonium (TPeA) reduced the open time as a function of the concentration. An additional nonconducting state was observed when TBA or TPeA was applied internally or externally, due to the presence of a drug-bound and blocked state of the channel. The closing rate under control conditions was similar to that in the presence of external tetramethylammonium (TMA), suggesting that channel closing is independent of external drug binding. The concentration for half maximal block of the channel by external TEA was 80 microM. The channel was less sensitive to internal TEA, which half blocked the channel at 27 mM. The dissociation rate of long alkyl chain TAA ions from the channel was slower when applied to the inside, compared to external application, suggesting the presence of distinct internal and external receptors. Long alkyl chain TAA derivatives, such as TBA had a faster association rate with the open channel when applied to the inside of the membrane than when applied to the outside.     

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.     

Statistical analysis of single sodium channels. Effects of N-bromoacetamide

Currents were obtained from single sodium channels in outside-out excised patches of membrane from the cell line GH3. The currents were examined in control patches and in patches treated with N- bromoacetamide ( NBA ) to remove inactivation. The single-channel current-voltage relationship was linear over the range -60 to + 10 mV, and was unaffected by NBA . The slope conductance at 9.3 degrees C was 12 pS, and the Q10 for single channel currents was about 1.35. The currents in both control and NBA -treated patches showed evidence of a slow process similar to desensitization in acetylcholine-receptor channels. This process was especially apparent at rapid rates of stimulation (5 Hz), where openings occurred in clusters of records. The clustering of records with and without openings was analyzed by runs analysis, which showed a statistically significant trend toward nonrandom ordering in the responses of channels to voltage pulses. NBA made this nonrandom pattern more apparent. The probability that an individual channel was "hibernating" during an activating depolarization was estimated by a maximum likelihood method. The lifetime of the open state was also estimated by a maximum likelihood method, and was examined as a function of voltage. In control patches the open time was mildly voltage-dependent, showing a maximum at about -50 mV. In NBA -treated patches the open time was greater than in the control case and increased monotonically with depolarization; it asymptotically approached that of the control patches at hyperpolarized potentials. By comparing channel open times in control and NBA -treated patches, we determined beta A and beta I, the rate constants for closing activation gates and fast inactivation gates. Beta I was an exponential function of voltage, increasing e-fold for 34 mV. beta A had the opposite voltage dependence. The probability of an open channel closing its fast inactivation gate, rather than its activation gate, increased linearly with depolarization from -60 to -10 mV. These results indicate that inactivation is inherently voltage dependent.     

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.     

Superposition properties of interacting ion channels.

Quantitative analysis of patch clamp data is widely based on stochastic models of single-channel kinetics. Membrane patches often contain more than one active channel of a given type, and it is usually assumed that these behave independently in order to interpret the record and infer individual channel properties. However, recent studies suggest there are significant channel interactions in some systems. We examine a model of dependence in a system of two identical channels, each modeled by a continuous-time Markov chain in which specified transition rates are dependent on the conductance state of the other channel, changing instantaneously when the other channel opens or closes. Each channel then has, e.g., a closed time density that is conditional on the other channel being open or closed, these being identical under independence. We relate the two densities by a convolution function that embodies information about, and serves to quantify, dependence in the closed class. Distributions of observable (superposition) sojourn times are given in terms of these conditional densities. The behavior of two channel systems based on two- and three-state Markov models is examined by simulation. Optimized fitting of simulated data using reasonable parameters values and sample size indicates that both positive and negative cooperativity can be distinguished from independence.     

Kinetic diversity of Na+ channel bursts in frog skeletal muscle

Individual Na+ channels of dissociated frog skeletal muscle cells at 10 degrees C fail to inactivate in 0.02% of depolarizing pulses, thus producing bursts of openings lasting hundreds of milliseconds. We present here a kinetic analysis of 87 such bursts that were recorded in multi-channel patches at four pulse potentials. We used standard dwell-time histograms as well as fluctuation analysis to analyze the gating kinetics of the bursting channels. Since each burst contained only 75-150 openings, detailed characterization of the kinetics from single bursts was not possible. Nevertheless, at this low kinetic resolution, the open and closed times could be well fitted by single exponentials (or Lorentzians for the power spectra). The best estimates of both the open and closed time constants produced by either technique were much more broadly dispersed then expected from experimental or analytical variability, with values varying by as much as an order of magnitude. Furthermore, the values of the open and closed time constants were not significantly correlated with one another from burst to burst. The bursts thus expressed diverse kinetic behaviors, all of which appear to be manifestations of a single type of Na+ channel. Although the opening and closing rates were dispersed, their average values were close to those of alpha m and 2 beta m derived from fits to the early transient Na+ currents over the same voltage range. We propose a model in which the channel has both primary states (e.g., open, closed, and inactivated), as well as "modes" that are associated with independent alterations in the rate constants for transition between each of these primary states.     

Kinetics of light-sensitive channels in vertebrate photoreceptors

We have studied the ion channels mediating the light response of vertebrate rod photoreceptors by analysing fluctuations in the current across the rod membrane, using the whole cell patch-clamp technique on rods isolated from the axolotl retina. Light decreases the membrane current fluctuations. Noise analysis reveals two components to this decrease: a low frequency component due to biochemical noise in the transduction mechanism, and a high frequency component we attribute to the random opening and closing of the ion channels in the dark. The probability of any one channel being open in the dark is low. The spectrum of the high frequency component of the current fluctuations indicates that the current through an open channel is 4 X 10(-15)A, that the mean channel open time is 2 ms, and that about 10000 channels are open in each rod in the dark. The effect of light is to reduce the opening rate constant of these channels, with no effect on the closing rate constant.     

Nonselective cation channels in intact human T lymphocytes.

Nonselective cation channels were found in single channel recordings from cell-attached patches on human T lymphocytes. These channels were active under conditions that should lead to cell swelling (hypotonic bath solutions with NaCl or KCl); however, a definite dependence of activity on cell swelling has not been proven. Under these conditions similar channels were found in 20 of 23 patches from 11 different blood donors. The current-voltage relation was approximately linear for outward current (11-14 pS) and inwardly rectifying (to 23 pS) when the intact cells were depolarized with high KCl in the bath. The voltage dependence of channel activity is consistent with closing at hyperpolarized membrane potentials (Vm less than or equal to -50 mV) and block of open channels at strongly depolarized membrane potentials (Vm greater than 0 mV). Reversal potentials under all ionic gradients tested are consistent with a channel that is poorly selective between Na+ and K+ ions. Active channels in cell-attached patches were rapidly blocked by bath addition of the membrane-permeant inhibitor quinine. Channels that were active in cell-attached became quiescent after patch excision; however, two patches remained active long enough to obtain current-voltage relations. These were linear with a slope conductance for outward current of 8-11 pS. Because of the clustering of single-channel openings, detailed voltage dependence of kinetics and probability of opening were not studied.     

Estimation of kinetic rate constants from multi-channel recordings by a direct fit of the time series.

The maximum-likelihood technique for the direct estimation of rate constants from the measured patch clamp current is extended to the analysis of multi-channel recordings, including channels with subconductance levels. The algorithm utilizes a simplified approach for the calculation of the matrix exponentials of the probability matrix from the rate constants of the Markov model of the involved channel(s) by making use of the Kronecker sum and product. The extension to multi-channel analysis is tested by the application to simulated data. For these tests, three different channel models were selected: a two-state model, a three-state model with two open states of different conductance, and a three-state model with two closed states. For the simulations, time series of these models were calculated from the related first-order, finite-state, continuous-time Markov processes. Blue background noise was added, and the signals were filtered by a digital filter similar to the anti-aliasing low-pass. The tests showed that the fit algorithm revealed good estimates of the original rate constants from time series of simulated records with up to four independent and identical channels even in the case of signal-to-noise ratios being as low as 2. The number of channels in a record can be determined from the dependence of the likelihood on channel number. For large enough data sets, it takes on a maximum when the assumed channel number is equal to the "true" channel number.     

Effect of ATP concentration on CFTR Cl- channels: a kinetic analysis of channel regulation.

Phosphorylated cystic fibrosis transmembrane conductance regulator (CFTR) Cl- channels require nucleoside triphosphates, such as ATP, to open. As the concentration of intracellular ATP increases, the probability of the channel being open (Po) increases. To better understand how ATP regulates the channel, we studied excised inside-out membrane patches that contained single, phosphorylated CFTR Cl- channels and examined the kinetics of gating at different concentrations of ATP. As the ATP concentration increased from 0.1 to 3 mM the mean closed time decreased, but mean open time did not change. Analysis of the data using histograms of open- and closed-state durations, the maximum likelihood method, and the log-likelihood ratio test suggested that channel behavior could be described by a model containing one open and two closed states (C1<==>C2<==>O). ATP regulated phosphorylated channels at the transition between the closed states C1 and C2: as the concentration of ATP increased, the rate of transition from C1 to C2 (C1-->C2) increased. In contrast, transitions from C2 to C1 and between C2 and the open state (O) were not significantly altered by ATP. Addition of ADP in the presence of ATP decreased the transition rate from C1 to C2 without affecting other transition rates. These data suggest that ATP regulates CFTR Cl- channels through an interaction that increases the rate of transition from the closed state to a bursting state in which the channel flickers back and forth between an open and a closed state (C2). This transition may reflect ATP binding or perhaps a step subsequent to binding.     

Gating of the squid sodium channel at positive potentials: II. Single channels reveal two open states.

Single-channel recordings from squid axon Na+ channels were made under conditions of reverse sodium gradient. In the range of potentials studied, +40-(+)120 mV, channels opened promptly after depolarization, closed and reopened several times during the pulse. In patches containing only one channel, the distributions of open dwell times showed two components showing the existence of a second open state. The ensemble average of single-channel records showed incomplete inactivation that became more pronounced at more positive potentials, showing that the maintained phase of the current is the result of only one type of sodium channel with two open states. Analysis of bursts indicated that the dwell times of the events at the onset of the depolarization are longer than those later in the pulse. The dwell open times of the first events could be fitted with a single exponential. This indicated that the channels open preferentially through the first open state, the access to the second open state happening subsequently. Maximum likelihood analysis was used to evaluate several possible kinetic schemes incorporating a second open state. The best model to fit the data from single channels, and consistent with the data from macroscopic and gating currents, has a second open state evolving from the inactivated state. A kinetic model is proposed that incorporates information obtained from dialyzed axons.     

Stochastic description of the three-state model of the Na channel

The three-state model of the Na channel is formulated stochastically and various observable quantities calculated from this model. This model assumes that the Na channel can occupy one of three states--resting, open and inactivated--and that each channel is independent. This is a simplified representation of the model proposed by Aldrich et al. (1983) mainly with respect to the neuroblastoma. When the system contains many channels, the probability distribution of the numbers of the channels that occupy each of these states is a time-dependent multinomial distribution and the distribution of the first passage time from resting state to open state becomes an exponential decay function with higher components. The average and variance of the channel current calculated by the distribution show the time course with a single peak and its ratio converges to the current of a single channel. Stochastic treatment of the transient process developed here gives a method of estimating all of the transition rates and the number of channels in the system.     

Single-channel acetylcholine receptor kinetics.

The temporal relationships among junctional acetylcholine receptor single-channel currents have been examined to probe the mechanism of channel activation. We have presented an analytical approach, termed single-channel ensemble analysis, that allows one to estimate the kinetic transition rate constants for channel-opening and closing as well as the rate of leaving the specific doubly-liganded, closed state from which opening occurs. This approach may be applied to data produced by any number of independent channels as long as the probability of channel opening is low, a condition that is experimentally verifiable. The method has been independently validated using simulated single-channel data generated by computer from one or 100 hypothetical channels. Typical experimental values for the transition rate constants estimated from acetylcholine-activated single channels at the garter snake neuromuscular junction were: opening = 1,200 s-1, closing = 455 s-1, back rate for leaving the doubly-liganded, closed state = 3,200 s-1 at a transmembrane potential of -92 mV at room temperature. Each of these three rate constants was voltage dependent, with the closing rate decreasing e-fold for 173 mV of hyperpolarization, the opening rate increasing e-fold for 78 mV, and the unbinding rate increasing e-fold for 105 mV. The channel-closing rate was agonist dependent, being greater at all potentials for channels activated with carbamylcholine than for channels activated with acetylcholine. However, the single-channel conductance and reversal potential were the same for these two agonists.     

A functional model for G protein activation of the muscarinic K+ channel in guinea pig atrial myocytes. Spectral analysis of the effect of GTP on single-channel kinetics

To elucidate the functional interaction between the active G protein subunit (GK*) and the cardiac muscarinic K+ (KACh) channel, the effect of intracellular GTP on the channel current fluctuation in the presence of 0.5 microM extracellular acetylcholine was examined in inside-out patches from guinea pig atrial myocytes using spectral analysis technique. The power density spectra of current fluctuations induced at various concentrations of GTP ([GTP]) were well fitted by the sum of two Lorentzian functions. Because the channel has one open state, the open-close transitions of the channel gate represented by the spectra could be described as C2<-->C1<-->O. As [GTP] was raised, the channel activity increased in a positive cooperative manner. The powers of the two Lorentzian components concomitantly increased, while the corner frequencies and the ratio of the powers at 0 Hz remained almost constant. This indicates that G protein activation did not affect the gating of each channel but mainly increased the number of functionally active channels in the patch to enhance the channel activity. Regulation of the number of functionally active channels could be described by a slow transition of the channel states, U (unavailable)<-- >A (available), which is independent of the gating. The equilibrium of this slow transition was shifted by GTP from U to A. Monod-Wyman- Changeux's allosteric model for the channel state transition(U<-->A) could well describe the positive cooperative increase in the channel availability by GTP, assuming that, in the presence of saturating concentrations of ACh, [GK*] linearly increased as [GTP] was raised in our experimental range. The model indicates that the cardiac KACh channel could be described as a multimer composed of four or more functionally identical subunits, to each of which one GK* binds.     

Effects of GsMTx4 on bacterial mechanosensitive channels in inside-out patches from giant spheroplasts

GsMTx4 is a 34-residue peptide isolated from the tarantula Grammostola spatulata folded into an inhibitory cysteine knot and it selectively affects gating of some mechanosensitive channels. Here we report the effects of cytoplasmic GsMTx4 on the two bacterial channels, MscS and MscL, in giant Escherichia coli spheroplasts. In excised inside-out patches, GsMTx4 sensitized both channels to tension by increasing the opening rate and decreasing the closing rate. With ascending and descending pressure ramps, GsMTx4 increased the gating hysteresis for MscS, a consequence of slower gating kinetics. Quantitative kinetic analysis of the primary C↔O transition showed that the hysteresis is a result of the decreased closing rate. The gating barrier location relative to the open state energy well was unaffected by GsMTx4. A reconstructed energy profile suggests that the peptide prestresses the resting state of MscS, lowering the net barrier to opening and stabilizes the open conformation by ∼8 kT. In excised patches, both MscL and MscS exhibit reversible adaptation, a process separable from inactivation for MscS. GsMTx4 decreased the rate of reversible adaptation for both channels and the MscS recovery rate from the inactivation. These measurements support a mechanism where GsMTx4 binds to the lipid interface of the channel, increasing the local stress that is sensed by the channels and stabilizing the expanded conformations.     

Kinetic characteristics of the excitability-inducing material channel in oxidized cholesterol and brain lipid bilayer membranes

The kinetic characteristics of the opening and closing of the excitability-inducing material (EIM) channel in oxidized cholesterol and in brain lipid bilayers are compared. The kinetics of the opening and closing of individual ion-conducting channels in bilayers doped with small amounts of EIM are determined from discrete fluctuations in ionic current. The kinetics for approach to steady-state conductance are determined for lipid bilayers containing many channels. Steady-state and kinetic characteristics for the EIM channel incorporated in brain lipid bilayers can be accounted for by the model developed for the EIM channel incorporated in oxidized cholesterol membranes. Relaxation time, calculated from rate constants of single-channel membranes or directly measured in many-channel membranes is strongly temperature dependent, and is always shorter in brain lipid membranes. Changes in temperature do not affect the interaction of the electric field and the open channel, but the open configuration of the EIM channel in brain lipid bilayers is stablized with increasing temperature. The configurational energy difference between the open and closed channel, calculated from temperature studies, is larger in brain lipid bilayers. The energy barrier which separates the two configurations of the channel is larger in oxidized cholesterol bilayers.