Fractal properies of gating in potential-dependent K+-channels in Lymnaea stagnalis neurons

Sets of the channel open times, [tau(o)], and closed times, [tau(c)], and the full set of the channel open and closed times, [tau(o), tau(c)], in the activity of single voltage-dependent K+-channels in mollusc L. stagnalis neurons were analyzed using the rescaled range analysis (Hurst method), fast Fourier and wavelet transforms. It was found that the Hurst dependence for each time series could be approximated by a polygonal line with at least two slopes: H1 and H2 (Hurst exponents). The averaged values of H1 and H2 for the sets [tau(o), tau(c)] were equal to 0.61 +/- 0.03 and 0.83 +/- 0.11, respectively; for the [tau(o)] sets H1 = 0.66 +/- 0.03 and H2 = 0.95 +/- 0.10; for the [tau(c)] sets, H1 = 0.62 +/- 0.05 and H2 = 0.85 +/- 0.10. In some cases, a third slope appeared on the Hurst dependences. It was very variable and ranged between 0.5 and 1. The Hurst exponents H1, H2, and H3 characterized short, intermediate, and long time ranges, respectively. The ranges greatly varied from experiment to experiment. The data obtained show that the channel openings and closings (gating process) represent a persistent process correlated in time. The randomization of the time sets resulted in a single slope, H, of 0.52 +/- 0.02 characteristic of random processes. The results were confirmed by the fast Fourier and wavelet transforms. In addition, possible voltage dependences of Hurst exponents and their correlation with tau(o) and tau(c) were investigated. As a whole, single channel activity may be characterized as a multifractal process with a slight voltage dependence of the Hurst exponents.     

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.     

Preventing errors when estimating single channel properties from the analysis of current fluctuations.

The conductance, number, and mean open time of ion channels can be estimated from fluctuations in membrane current. To examine potential errors associated with fluctuation analysis, we simulated ensemble currents and estimated single channel properties. The number (N) and amplitude (i) of the underlying single channels were estimated using nonstationary fluctuation analysis, while mean open time was estimated using covariance and spectral analysis. Both excessive filtering and the analysis of segments of current that were too brief led to underestimates of i and overestimates of N. Setting the low-pass cut-off frequency of the filter to greater than five times the inverse of the effective mean channel open time (burst duration) and analyzing segments of current that were at least 80 times the effective mean channel open time reduced the errors to < 2%. With excessive filtering, Butterworth filtering gave up to 10% less error in estimating i and N than Bessel filtering. Estimates of mean open time obtained from the time constant of decay of the covariance, tau obs, at low open probabilities (Po) were much less sensitive to filtering than estimates of i and N. Extrapolating plots of tau obs versus mean current to the ordinate provided a method to estimate mean open time from data obtained at higher Po, where tau obs no longer represents mean open time. Bessel filtering gave the least error when estimating tau obs from the decay of the covariance function, and Butterworth filtering gave the least error when estimating tau obs from spectral density functions.     

Mutations within the P-loop of Kir6.2 modulate the intraburst kinetics of the ATP-sensitive potassium channel

The ATP-sensitive potassium (K(ATP)) channel exhibits spontaneous bursts of rapid openings, which are separated by long closed intervals. Previous studies have shown that mutations at the internal mouth of the pore-forming (Kir6.2) subunit of this channel affect the burst duration and the long interburst closings, but do not alter the fast intraburst kinetics. In this study, we have investigated the nature of the intraburst kinetics by using recombinant Kir6.2/SUR1 K(ATP) channels heterologously expressed in Xenopus oocytes. Single-channel currents were studied in inside-out membrane patches. Mutations within the pore loop of Kir6.2 (V127T, G135F, and M137C) dramatically affected the mean open time (tau(o)) and the short closed time (tauC1) within a burst, and the number of openings per burst, but did not alter the burst duration, the interburst closed time, or the channel open probability. Thus, the V127T and M137C mutations produced longer tau(o), shorter tauC1, and fewer openings per burst, whereas the G135F mutation had the opposite effect. All three mutations also reduced the single-channel conductance: from 70 pS for the wild-type channel to 62 pS (G135F), 50 pS (M137C), and 38 pS (V127T). These results are consistent with the idea that the K(ATP) channel possesses a gate that governs the intraburst kinetics, which lies close to the selectivity filter. This gate appears to be able to operate independently of that which regulates the long interburst closings.     

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).     

Acetylcholine receptor in planar lipid bilayers. Characterization of the channel properties of the purified nicotinic acetylcholine receptor from Torpedo californica reconstituted in planar lipid bilayers

The properties of the channel of the purified acetylcholine receptor (AChR) were investigated after reconstitution in planar lipid bilayers. The time course of the agonist-induced conductance exhibits a transient peak that relaxes to a steady state value. The macroscopic steady state membrane conductance increases with agonist concentration, reaching saturation at 10(-5) M for carbamylcholine (CCh). The agonist-induced membrane conductance was inhibited by d-tubocurarine (50% inhibition, IC50, at approximately 10(-6) M) and hexamethonium (IC50 approximately 10(-5) M). The single channel conductance, gamma, is ohmic and independent of the agonist. At 0.3 M monovalent salt concentrations, gamma = 28 pS for Na+, 30 pS for Rb+, 38 pS for Cs+, and 50 pS for NH+4. The distribution of channel open times was fit by a sum of two exponentials, reflecting the existence of two distinct open states. tau o1 and tau o2, the fast and slow components of the distribution of open times, are independent of the agonist concentration: for CCh this was verified in the range of 10(-6) M less than C less than 10(-3)M. tau 01 and tau o2 are approximately three times longer for suberyldicholine ( SubCh ) than for CCh. tau o1 and tau o2 are moderately voltage dependent, increasing as the applied voltage in the compartment containing agonist is made more positive with respect to the other. At desensitizing concentrations of agonist, the AChR channel openings occurred in a characteristic pattern of sudden paroxysms of channel activity followed by quiescent periods. A local anesthetic derivative of lidocaine ( QX -222) reduced both tau o1 and tau o2. This effect was dependent on both the concentration of QX -222 and the applied voltage. Thus, the AChR purified from Torpedo electric organ and reconstituted in planar lipid bilayers exhibits ion conduction and kinetic and pharmacological properties similar to AChR in intact muscle postsynaptic membranes.     

A TEA-insensitive flickering potassium channel active around the resting potential in myelinated nerve

A novel potassium-selective channel which is active at membrane potentials between -100 mV and +40 mV has been identified in peripheral myelinated axons of Xenopus laevis using the patch-clamp technique. At negative potentials with 105 mM-K on both sides of the membrane, the channel at 1 kHz resolution showed a series of brief openings and closings interrupted by longer closings, resulting in a flickery bursting activity. Measurements with resolution up to 10 kHz revealed a single-channel conductance of 49 pS with 105 mM-K and 17 pS with 2.5 mM-K on the outer side of the membrane. The channel was selective for K ions over Na ions (PNa/PK = 0.033). The probability of being within a burst in outside-out patches varied from patch to patch (> 0.2, but often > 0.9), and was independent of membrane potential. Open-time histograms were satisfactorily described with a single exponential (tau o = 0.09 msec), closed times with the sum of three exponentials (tau c = 0.13, 5.9, and 36.6 msec). Sensitivity to external tetraethylammonium was comparatively low (IC50 = 19.0 mM). External Cs ions reduced the apparent unitary conductance for inward currents at Em = -90 mV (IC50 = 1.1 mM). Ba and, more potently, Zn ions lowered not only the apparent single-channel conductance but also open probability. The local anesthetic bupivacaine with high potency reduced probability of being within a burst (IC50 = 165 nM). The flickering K channel is clearly different from the other five types of K channels identified so far in the same preparation. We suggest that this channel may form the molecular basis of the resting potential in vertebrate myelinated axons.     

A molecular scheme for the reaction between acetylcholine and nicotinic channels.

In outside-out patches of mouse-muscle membrane, embryonic-like channels were activated by pulses of acetylcholine (ACh). On increasing the ACh concentration, the rate of desensitization, 1/tau d, increased linearly with the peak open probability, indicating desensitization from the open state. Desensitization had only one time constant tau d at each ACh concentration. Recovery from desensitization was only approximately 10 times slower than desensitization, whereas the probability of steady-state channel opening, declined to < 0.01 with > 10(-6) M ACh. The peak probability of opening in > 10(-4) M ACh pulse was close to 1. A linear reaction scheme was not compatible with these results. The scheme had to be expanded resulting in a circular scheme with two additional ACh binding steps to desensitized channel states. The approximate rate constants of all reaction steps in the circular scheme could be determined using computer simulations. The model predicted that clusters of channel opening had the average duration tau d at the respective ACh concentration. In cell-attached patches on intact muscle fibers, similar average cluster durations were observed at the respective ACh concentration. This indicates that tau d in the intact muscle fibers has similar values as in outside-out patches.     

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.     

Hofmeister effect in ion transport: reversible binding of halide anions to the roflamycoin channel.

We have studied the anion-dependent gating of roflamycoin ion channels using spectral analysis of noise in currents through multichannel planar lipid bilayers. We have found that in addition to low frequency current fluctuations that may be attributed to channel switching between open and closed conformations, roflamycoin channels exhibit a pronounced higher frequency noise indicating that the open channel conductance has substates with short lifetimes. This noise is well described by a Lorentzian spectrum component with a characteristic cutoff frequency that depends on the type of halide anions according to their position in the Hofmeister series. It is suggested that transitions between the substates correspond to a reversible ionization of the channel by a penetrating anion that binds to the channel structure, more chaotropic anions being bound for longer times. Within a framework of a two-substate model, the duration of the substate with reduced electrostatic barrier for cation current varies exponentially with anion electron polarizability. This explains two features of the roflamycoin channel reported earlier: the increase in apparent single-channel conductance along the series F- < Cl- < Br- < I- and the reverse of channel selectivity from anionic for KF to cationic for KI.     

Spontaneous and GABA-induced single channel currents in cultured murine spinal cord neurons

Intracellular and patch clamp recordings were made from embryonic mouse spinal cord neurons growing in primary cell culture. Outside-out membrane patches obtained from these cells usually showed spontaneous single channel currents when studied at the resting potential (-56 +/- 1.5 mV). In 18 out of 30 patches tested, spontaneous single channel activity was abolished by making Tris+ the major cation on both sides of the membrane. The remaining patches continued to display spontaneous single channel currents under these conditions. These events reversed polarity at a patch potential of 0 mV and displayed a mean single channel conductance of 24 +/- 1.2 pS. Application of the putative inhibitory transmitter gamma-aminobutyric acid (0.5-10 microM) to outside-out patches of spinal cord cell membrane induced single channel currents in 10 out of 15 patches tested. These channels had a primary conductance of 29 +/- 2.8 pS in symmetrical 145 mM Cl- solutions. Frequency distributions for the open times of these channels were well fit by the sum of a fast exponential term ("of") with a time constant tau of = 4 +/- 1.3 ms and a slow exponential term ("os") with a time constant tau os = 24 +/- 8.1 ms. Frequency distributions for channel closed times were also well fit by a double exponential equation, with time constants tau cf = 2 +/- 0.2 ms and tau cs = 62 +/- 20.9 ms.     

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.     

Monotonic and non-monotonic single channel open time distributions with two sequential open states

Some conditions under which kinetic schemes including two sequential open states of identical conductance will display a non-monotonic (i.e. with a deficit of short open times and a maximum at t>0) distribution of single channel open times are described theoretically. Neither a closed cyclic scheme nor exclusively irreversible transitions between states are required for non-monotonic distributions. A required condition for the schemes considered here is that all openings are to a state from which closing is not possible. It is the presence of a precursor process to channel closing that produces the non-monotonic distribution. Following each channel opening some time is required for a transition into the second open state from which all closings proceed. Simple schemes of this sort cannot provide the basis of any experimental reports of non-monotonic distributions.     

Voltage- and cold-dependent gating of single TRPM8 ion channels

Transient receptor potential (TRP) channels play critical roles in cell signaling by coupling various environmental factors to changes in membrane potential that modulate calcium influx. TRP channels are typically activated in a polymodal manner, thus integrating multiple stimuli. Although much progress has been made, the underlying mechanisms of TRP channel activation are largely unknown. The TRPM8 cation channel has been extensively investigated as a major neuronal cold sensor but is also activated by voltage, calcium store depletion, and some lipids as well as by compounds that produce cooling sensations, such as menthol or icilin. Several models of TRPM8 activation have been proposed to explain the interaction between these diverse stimuli. However, a kinetic scheme is not yet available that can describe the detailed single-channel kinetics to gain further insight into the underlying gating mechanism. To work toward this goal, we investigated voltage-dependent single-channel gating in cell-attached patches at two different temperatures (20 and 30 °C) using HEK293 cells stably expressing TRPM8. Both membrane depolarization and cooling increased channel open probability (P(o)) mainly by decreasing the duration of closed intervals, with a smaller increase in the duration of open intervals. Maximum likelihood analysis of dwell times at both temperatures indicated gating in a minimum of five closed and two open states, and global fitting over a wide range of voltages identified a seven-state model that described the voltage dependence of P(o), the single-channel kinetics, and the response of whole-cell currents to voltage ramps and steps. The major action of depolarization and cooling was to accelerate forward transitions between the same two sets of adjacent closed states. The seven-state model provides a general mechanism to account for TRPM8 activation by membrane depolarization at two temperatures and can serve as a starting point for further investigations of multimodal TRP activation.     

Ca2+-activated K+ channels from cultured renal medullary thick ascending limb cells: Effects of pH

Summary Ca²⁺-activated K⁺ channels were studied in cultured medullary thick ascending limb cells (MTAL) using the patch-clamp technique. The purpose was to determine the effect of acidic pH on channel properties in excised patches of apical cell membrane. At pH 7.4, increasing Ca²⁺ on the intracellular side or applying positive voltages increases channel open probability. Reducing pH to 5.8 on the intracellular face of the channel decreases channel open probability at each voltage and Ca²⁺ concentration. Channel mean open times display two distributions and mean closed times display three distributions. Increasing Ca²⁺ or applying depolarizing voltages lengthens each of the mean open times and shortens each of the closed times. Lowering pH to 5.8 decreases the mean open times and increases mean closed times at each Ca²⁺ and voltage with the greatest effect on the mean closed times. In contrast, both single-channel conductance and channel kinetics are unaffected when pH is reduced to 5.8 on the extracellular face of the membrane. We conclude that protons interfere with Ca²⁺ binding to the gate of Ca²⁺-activated K⁺ channels reducing the probability of channel opening.     

Activation of cardiac ryanodine receptors by the calcium channel agonist FPL-64176

We investigated the possibility that the Ca(2+) channel agonist FPL-64176 (FPL) might also activate the cardiac sarcoplasmic reticulum (SR) Ca(2+) release channel ryanodine receptor (RyR). The effects of FPL were tested on single channel activity of purified and crude vesicular RyR (RyR2) isolated from human and dog hearts using the planar lipid bilayer technique. FPL (100-200 microM) increased single channel open probability (P(o)) when added to the cytoplasmic side of the channel (P(o) = 0.070 +/- 0.021 in control RyR2; 0.378 +/- 0.086 in 150 microM FPL, n = 9, P < 0.01) by prolonging open times and decreasing closed times without changing current magnitude. FPL had no effect on P(o) when added to the trans (luminal) side of the bilayer (P(o) = 0.079 +/- 0.036 in control and 0.103 +/- 0.066 in FPL, n = 4, no significant difference). The bell-shaped [Ca(2+)] dependence of [(3)H]ryanodine binding and of P(o) was altered by FPL, suggesting that the mechanism by which FPL increases channel activity is by an increase in Ca(2+)-induced activation at low [Ca(2+)] (without a change in threshold) and suppression of Ca(2+)-induced inactivation at high [Ca(2+)]. However, the fact that inactivation was restored at elevated [Ca(2+)] suggests a competitive interaction between Ca(2+) and FPL on inactivation. FPL had no effect on RyR skeletal channels (RyR1), where P(o) was 0.039 +/- 0.005 in control versus 0.030 +/- 0.006 in 150 microM FPL (no significant difference). These results suggest that, in addition to its ability to activate the L-type Ca(2+) channels, FPL activates cardiac RyR2 primarily by reducing the Ca(2+) sensitivity of inactivation.     

The inhibitory chloride channel of the lobster Panulirus penicillatus neuromuscular junction.

1. Single channel activity was recorded from muscle membranes of the lobster Panulirus penicillatus using the patch-clamp technique. 2. Cell-attached, outside-out and inside-out patches were prepared from the deep abdominal extensor muscle. 3. Low amplitude single channel currents were observed in most patches, and were identified as being chloride-currents. 4. The chloride channel was active spontaneously, and tended to desensitize when outside-out patches were exposed to a small jet of glutamate. 5. Amplitude histograms of single channel currents presented a well defined peak of 8 pA at a membrane potential of -160 mV, while open and closed time histograms were fit to single exponential functions with tau open of 3.27 msec and tau closed of 31.58 msec.     

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.     

Measuring kinetics of complex single ion channel data using mean-variance histograms.

The measurement of single ion channel kinetics is difficult when those channels exhibit subconductance events. When the kinetics are fast, and when the current magnitudes are small, as is the case for Na+, Ca2+, and some K+ channels, these difficulties can lead to serious errors in the estimation of channel kinetics. I present here a method, based on the construction and analysis of mean-variance histograms, that can overcome these problems. A mean-variance histogram is constructed by calculating the mean current and the current variance within a brief "window" (a set of N consecutive data samples) superimposed on the digitized raw channel data. Systematic movement of this window over the data produces large numbers of mean-variance pairs which can be assembled into a two-dimensional histogram. Defined current levels (open, closed, or sublevel) appear in such plots as low variance regions. The total number of events in such low variance regions is estimated by curve fitting and plotted as a function of window width. This function decreases with the same time constants as the original dwell time probability distribution for each of the regions. The method can therefore be used: 1) to present a qualitative summary of the single channel data from which the signal-to-noise ratio, open channel noise, steadiness of the baseline, and number of conductance levels can be quickly determined; 2) to quantify the dwell time distribution in each of the levels exhibited. In this paper I present the analysis of a Na+ channel recording that had a number of complexities. The signal-to-noise ratio was only about 8 for the main open state, open channel noise, and fast flickers to other states were present, as were a substantial number of subconductance states. "Standard" half-amplitude threshold analysis of these data produce open and closed time histograms that were well fitted by the sum of two exponentials, but with apparently erroneous time constants, whereas the mean-variance histogram technique provided a more credible analysis of the open, closed, and subconductance times for the patch. I also show that the method produces accurate results on simulated data in a wide variety of conditions, whereas the half-amplitude method, when applied to complex simulated data shows the same errors as were apparent in the real data. The utility and the limitations of this new method are discussed.     

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.