Open channel noise. VI. Analysis of amplitude histograms to determine rapid kinetic parameters.

Recently we reported that rapid fluctuations of ion currents flowing through open gramicidin A channels exceed the expected level of pure transport noise at low ion concentrations (Heinemann, S. H. and F. J. Sigworth. 1990. Biophys. J. 57:499-514). Based on comparisons with kinetic ion transport models we concluded that this excess noise is likely caused by current interruptions lasting approximately 1 microsecond. Here we introduce a method using the higher-order cumulants of the amplitude distribution to estimate the kinetics of channel closing events far below the actual time resolution of the recording system. Using this method on data recorded with 10 kHz bandwidth, estimates for gap time constants on the order of 1 microsecond were obtained, similar to the earlier predictions.     

Ba2+ release from soda glass modifies single maxi K+ channel activity in patch clamp experiments.

Glasses used to fabricate patch pipettes may release components which affect ion channels (Cota, G., and C.M. Armstrong. 1988. Biophys. J. 53:107-109; Furman, R.E., and J.C. Tanaka. 1988. Biophys. J. 53:287-292; Rojas, L., and C. Zuazaga. 1988. Neurosci. Lett. 88:39-44). The gating properties of maxi K+ channels from Necturus gallbladder epithelium depend on whether borosilicate glass (BG) or blue tip hematocrit glass (SG) is used to construct the patch pipettes. The data are consistent with solubilization from SG of a component which exerts voltage-dependent, cytosolic-side specific block, closely resembling "slow block" by Ba2+ ions. Ringer's solution preincubated with SG, but not with BG, blocked inside-out maxi K+ channels when used as bathing solution. Mass spectrometry revealed that Ba2+ is released by the glass from fast and slow-release compartments (SG contains 3% wt/wt BaO), and is the only ion found in the solution at concentrations consistent with the observed channel block. Additionally, SG released O2-, Na+, Ca2+, and Mg2+, all to micromolar concentrations. These elements do not interfere with maxi K+ channels but they could in principle alter the properties of other ion channels. Thus, screening for channel-modifying substances released by the glass may be necessary for the adequate interpretation of patch-clamp results.     

A channel model with fluctuating barrier structures.

Following the theory 'Fluctuations of barrier structure in ionic channels' (L?uger, P., Stephan, W. and Frehland, E. (1980) Biochim. Biophys. Acta 602, 167-180), we constructed a model of a channels with several conformational states. The origin of these conformational states and the source for the transitions from one to the other are given explicitly for the presented model. In this work the effect of multiple conformational states on the ion transport process is analyzed. We considered a channel protein with two main barriers and one binding site. The site is surrounded by dipolar groups. The dipole moment of these groups can be reoriented by thermal activity and also by electrical interaction with the transported ions. Differently polarized states generate different activation energy barriers for the ions. The set of conformational states of the channel is constituted by all the possible polarized states of the binding site. Using the rate-theory analysis of ion transport (Gl?sstone, S., Laider, K.J. and Eyring, H. (1941) The theory of rate processes, McGraw-Hill, New York), the possible coupling between ion flux and the channel conformational transitions has been incorporated into the model by considering the dependence of the rate constants on the heights of the energy barriers. The resulting multistate kinetic equations have been solved numerically. It was shown that the simple saturation characteristic of the flux-concentration curve was obtained. For certain values of the model parameters, the channel shows a strongly different conductance for anions compared to cations. In fact, the model contains an interesting mechanism that exhibits selectivity with respect to the charge of the ions.     

The transport of hydrophobic ions across lipid bilayers

The three-capacitor model for hydrophobic ion adsorption in lipid membranes (Andersen, O.S., Feldberg, S., Nakadomari, H., Levy, S. and McLaughlin, S. (1978) Biophys. J. 21, 35-70) is extended to ion transport whereby electrostatic effects from the interfacially adsorbed hydrophobic space charge have been encountered. The phenomena of current saturation with increasing concentrations of hydrophobic ions in the bulk electrolyte and the associated increase of the time constant of current relaxation can be quantitatively understood on the basis of space charge-limited currents as well as the nonexponential current decay.     

Unitary cardiac Na+, Ca2+ exchange current magnitudes determined from channel-like noise and charge movements of ion transport.

The cardiac Na+, Ca2+ exchanger (NCX1) is thought to achieve a high turnover rate, but all estimates to date are indirect. Two new strategies demonstrate that maximum unitary exchange currents are about 1 fA (6000 unitary charges per s) and that they fluctuate between on and off levels similar to ion channel currents. First, exchange current noise has been identified in small cardiac patches with properties expected for a gated transport process. Noise power density spectra correlate well with exchanger inactivation kinetics, and the noise has a predicted bell-shaped dependence on the activation states of the exchanger. From the magnitudes of exchange current noise, maximum unitary exchange currents are estimated to be 0.6-1.3 fA. Second, charge movements with rates of approximately 5000 s-1 have been isolated for the transport of both Na+ and Ca2+ in giant membrane patches using nonsaturating ion concentrations. The Na+ transport reactions are disabled or "immobilized" by exchanger inactivation reactions, thus confirming that inactivation generates fully inactive exchanger states.     

Theory of the effect of extracellular potassium on oscillations in the pancreatic beta-cell.

Based on the observation that potassium ions are compartmentalized near the surface of pancreatic beta-cells in mouse islets (Perez-Armendariz, E.M., I. Atwater, and E. Rojas 1985, Biophys. J. 48:741-749), we present a theoretical treatment of the effect of external potassium on oscillations in the pancreatic beta-cell. Our model includes the effects of ionic diffusion, the Ca2+-activated K+ channel, voltage-gated K+ and Ca2+ channels, and some of the effects of glucose. It is described by four ordinary differential equations. Numerical integration of these equations allows us to examine the effect of glucose, external K+, quinine, and tetraethylammonium ion (TEA) on the oscillations in membrane potential, intracellular Ca2+, and compartmentalized K+. The results are in good agreement with experiment.     

Ionic permeation and blockade in Ca2+-activated K+ channels of bovine chromaffin cells

Single channel currents through Ca2+-activated K+ channels of bovine chromaffin cells were measured to determine the effects of small ions on permeation through the channel. The channel selects strongly for K+ over Na+ and Cs+, and Rb+ carries a smaller current through the channel than K+. Tetraethylammonium ion (TEA+) blocks channel currents when applied to either side of the membrane; it is effective at lower concentrations when applied externally. Millimolar concentrations of internal Na+ reduce the average current through the channel and produce large fluctuations (flicker) in the open channel currents. This flickery block is analyzed by a new method, amplitude distribution analysis, which can measure block and unblock rates in the microsecond time range even though individual blocking events are not time-resolved by the recording system. The analysis shows that the rate of block by Na+ is very voltage dependent, but the unblock rate is voltage independent. These results can be explained easily by supposing that current flow through the channel is diffusion limited, a hypothesis consistent with the large magnitude of the single channel current.     

On the mechanism by which bupivacaine conducts protons across the membranes of mitochondria and liposomes.

Bupivacaine and etidocaine possess the remarkable property of stimulating mitochondrial respiration to levels comparable with those observed with classical anionic protonophores (Dabadie, P., Bendriss, P., Erny, P., and Mazat, J.P. (1987) FEBS Lett. 226, 77-82). We show that these amphiphilic amines conduct protons across the membranes of mitochondria and liposomes and stimulate respiration by a true protonophoretic mechanism. The kinetics of drug-induced H+ flux exhibited integer Hill coefficients that were greater than two under all conditions, suggesting that multimers are required for H+ transport. When the energy barrier for ion transport was lowered in mitochondria, by increasing the membrane potential, or in liposomes, by adding phloretin, the Hill coefficients decreased to lower integer numbers. Protonophoretic activity depended exclusively on medium concentration of free base, leading us to conclude that bupivacaine and etidocaine conduct protons as associated, intramembrane multimers of the free base. Bupivacaine-induced H+ leak was ohmic rather than nonohmic, as would be expected of a mobile charged carrier. This kinetic behavior seems improbable for a multimeric mobile carrier mechanism and suggests a channel mechanism, in which ohmicity results from splitting of the energy barrier by energy wells along the transport pathway (Garlid, K. D., Beavis, A. D., and Ratkje, S. K. (1989) Biochim. Biophys. Acta 976, 109-120). We hypothesize that bupivacaine and etidocaine act by a novel "flickering channel" mechanism, in which transient linear complexes of free base molecules provide weak binding sites (energy wells) for protons within lipid bilayer membranes.     

Attenuation of proton currents by methanol in a dioxolane-linked gramicidin A channel in different lipid bilayers.

The mobility of protons in a dioxolane-linked gramicidin A channel (D1) is comparable to the mobility of protons in aqueous solutions (Cukierman, S., E. P. Quigley, and D. S. Crumrine. 1997. Biophys. J. 73:2489-2502). Aliphatic alcohols decrease the mobility of H+ in aqueous solutions. In this study, the effects of methanol on proton conduction through D1 channels were investigated in different lipid bilayers and at different HCl concentrations. Methanol attenuated H+ currents in a voltage-independent manner. Attenuation of proton currents was also independent of H+ concentrations in solution. In phospholipid bilayers, methanol decreased the single channel conductance to protons without affecting the binding affinity of protons to bilayers. In glycerylmonooleate membranes, the attenuation of single channel proton conductances qualitatively resembled the decrease of conductivities of HCl solutions by methanol. However, in both types of lipid bilayers, single channel proton conductances through D1 channels were considerably more attenuated than the conductivities of different HCl solutions. This suggests that methanol modulates single proton currents through D1 channels. It is proposed that, on average, one methanol molecule binds to a D1 channel, and attenuates H+ conductance. The Gibbs free energy of this process (DeltaG0) is approximately 1.2 kcal/mol, which is comparable to the free energy of decrease of HCl conductivity in methanol solutions (1.6 kcal/mol). Apolar substances like urea and glucose that do not transport protons in HCl solutions and do not permeate D1 channels decreased solution conductivity and single channel conductance by a considerably larger proportion than methanol. Cs+ currents through D1 channels were considerably less (fivefold) attenuated by methanol than proton currents. It is proposed that methanol partitions inside the pore of gramicidin channels and delays the transfer of protons between water and methanol molecules, causing a significant attenuation of the single channel proton conductance. Gramicidin channels offer an interesting experimental model to study proton hopping along a single chain of water molecules interrupted by a single methanol molecule.     

Characterization of a chloroplast inner envelope K+ channel.

A K(+)-conducting protein of the chloroplast inner envelope was characterized as a K+ channel. Studies of this transport protein in the native membrane documented its sensitivity to K+ channel blockers. Further studies of native membranes demonstrated a sensitivity of K+ conductance to divalent cations such as Mg2+, which modulate ion conduction through interaction with negative surface charges on the inner-envelope membrane. Purified chloroplast inner-envelope vesicles were fused into an artificial planar lipid bilayer to facilitate recording of single-channel K+ currents. These single-channel K+ currents had a slope conductance of 160 picosiemens. Antibodies generated against the conserved amino acid sequence that serves as a selectivity filter in the pore of K+ channels immunoreacted with a 62-kD polypeptide derived from the chloroplast inner envelope. This polypeptide was fractionated using density gradient centrifugation. Comigration of this immunoreactive polypeptide and K+ channel activity in sucrose density gradients further suggested that this polypeptide is the protein facilitating K+ conductance across the chloroplast inner envelope.     

Modification of ion transport in lipid bilayer membranes in the presence of 2,4-dichlorophenoxyacetic acid. I. Enhancement of cationic conductance and changes of the kinetics of nonactin-mediated transport of potassium.

We have found that herbicide 2,4-dichlorophenoxyacetic acid (2,4-D) has the ability to increase the rate of transport of positive ions of several kinds, and to inhibit transport of negatively charged tetraphenylborate ions in lipid bilayer membranes. It has been found that only the neutral form of 2,4-D is transport active, whereas the ionized from of 2,4-D does not modify transport of ions, and does not by itself permeate through lipid membranes. The results suggest that the enhancement of transport of positively charged ions such as tetraphenylarsonium + and nonactin-K+ is dominated by the increase of the ion translocation rate constant. It has been shown that the enhancement of nonactin-mediated transport of K+ by 2,4-D can be accounted for by a simple carrier model. We have observed that a 2,4-D concentration above 3 X 10(-4) M the potassium ion transport in phosphatidylcholine-cholesterol as well as in cholesterol-free glycerolmonooleate membranes is enhanced to such a degree that, depending upon the concentration of potassium ions, it becomes limited by the rate of recombination of K+ with nonactin, and/or by backdiffusion of unloaded nonactin molecules. Furthermore, the effect of 2,4-D is enhanced by ionic strength of aqueous solution. From the changes of kinetic parameters of nonactin-K+ transport, as well as from the changes of membranes conductance due to tetraphenylarsonium + ions, we have estimated the changes of the electrical potential of the membrane interior. We have found that the potential of the interior of the membrane becomes more negative in the presence of 2,4-D, and that its change is proportional to the aqueous concentration of 2,4-D. The effect of 2,4-D on ion transport has been attributed to a layer of 2,4-D molecules absorbed within the interfacial region, and having a dipole moment directed toward the aqueous medium. The results of kinetic studied of nonactin-K+ transport suggest that this layer is located on the hydrocarbon side of the interface.     

Ca channel kinetics during the spontaneous heart beat in embryonic chick ventricle cells.

The ability of Ca ions to inhibit Ca channels presents one of the most intriguing problems in membrane biophysics. Because of this negative feedback, Ca channels can regulate the current that flows through them. The kinetics of the channels depend on voltage, and, because the voltage controls the current, a strong interaction exists between voltage dependence and Ca dependence. In addition to this interaction, the proximity of pores and the local concentration of ions also determine how effectively the Ca ions influence channel kinetics. The present article proposes a model that incorporates voltage-dependent kinetics, current-dependent kinetics, and channel clustering. We have based the model on previous voltage-clamp data and on Ca and Ba action currents measured during the action potential in beating heart cells. In general we observe that great variability exists in channel kinetics from patch to patch: Ba or Ca currents have low or high amplitudes and slow or fast kinetics during essentially the same voltage regime, either applied step-protocols or spontaneous cell action potentials. To explain this variability, we have postulated that Ca channels interact through shared ions. The model we propose expands on our previous model for Ba currents. We use the same voltage-dependent rate constants for the Ca currents that we did for the Ba currents. However, we vary the current-dependent rate constants according to the species of the conducting ion. The model reproduces the main features of our data, and we use it to predict Ca channel kinetics under physiological conditions. Preliminary reports of this work have appeared (DeFelice et al., 1991, Biophys. J. 59:551a; Risso et al., 1992, Biophys. J. 61:248a).     

Stochastic theory of singly occupied ion channels. II. Effects of access resistance and potential gradients extending into the bath.

In a previous paper (Jakobsson, E., and S. W. Chiu. 1987. Biophys. J. 52:33-46), we presented the stochastic theory of the singly occupied ion channel as applied to sodium permeation of gramicidin channels, with the assumption of perfect equilibration between the bathing solutions and the ends of the ion channel. In the present paper we couple the previous theory to electrodiffusion of ions from the bulk of the bathing solution to the channel mouth. Our electrodiffusion calculations incorporate estimates of the potential gradients near the channel mouth due to image forces and due to the fraction of the applied potential that falls beyond the ends of the channel. To keep the diffusion calculation one-dimensional, we make the assumption that the electrical potentials in the bath exhibit hemispherical symmetry. As in the previous paper, the flux equations are fit to data on sodium permeation of normal gramicidin A, and gramicidins modified by the fluorination of the valine at the No. 1 position (Barrett Russell, E. W., L. B. Weiss, F. I. Navetta, R. E. Koeppe II, and O. S. Anderson. 1986. Biophys. J. 49:673-686). The conclusions of our previous paper with respect to the effect of fluorination on the mobility, surface potential well depth, and central barrier, are confirmed. However the absolute values of these quantities are somewhat changed when diffusive resistance to the mouth is taken into account, as in the present paper. Future possibilities for more accurate calculations by other methods are outlined.     

Open channel noise. IV. Estimation of rapid kinetics of formamide block in gramicidin A channels.

Blocking events in currents through biological ion channels occur over a wide range of characteristic times. The interruptions in single-channel currents from blocking events may be characterized by the direct measurement of gap durations or by analyzing open-channel current histograms, provided that the events are not much shorter than the time resolution of single-channel recordings (approximately 10 microseconds). Here we present a method for the characterization of channel block on a much faster time scale by combining open-channel noise measurements with subsequent model fits according to a theoretical approach (Frehland, E. 1978. Biophysical Chemistry. 8:255-265). Although the bandwidth limitations in open-channel noise experiments are the same as in conventional single-channel experiments, from the dependence of the mean current and the spectral density of the noise on the concentration of the blocking agent, kinetics of very brief blocking events can be estimated. As an example we have analyzed the open-channel noise of K+ currents through the gramicidin A channel in the presence of various concentrations of formamide, a weak blocker, at neutral pH. We estimate the blocking and unblocking rates to be approximately 10(7)s-1 at 1 M formamide and discuss possible mechanisms for the blocking process.     

Open channel noise. I. Noise in acetylcholine receptor currents suggests conformational fluctuations.

The random passage of ions through an open channel is expected to result in shot noise fluctuations in the channel current. The patch-clamp technique now allows fluctuations of this size to be observed in single-channel currents. In the experiments reported here the acetylcholine-induced currents in cultured rat muscle cells were analyzed; fluctuations were found that were considerably larger than expected for shot noise. A low-frequency component, which was fitted with a Lorentzian, was examined in detail; it appears to arise from fluctuations in channel conductance of approximately 3% on a time scale of 1 ms. The characteristic relaxation time is voltage dependent and temperature dependent (Q10 approximately equal to 3) suggesting that the fluctuations arise from conformational fluctuations in the channel protein.     

Ionic currents of channels that are permeable to monovalent and divalent cations.

The cation-selective channel from Tetrahymena cilia is permeable to both monovalent and divalent cations. The single channel conductance in mixed solutions of K+ and Ca2+ was determined by the Gibbs-Donnan ratio of K+ and Ca2+, and the binding sites of this channel were considered to be always occupied by two potassium ions or by one calcium ion under the experimental conditions: 5-90 mM K+ and 0.5-35 mM Ca2+ (Oosawa and Kasai, 1988). A two-barrier model for the channel was introduced and the values of Michaelis-Menten constants and maximum currents carried by K+ and Ca2+ were calculated using this model. Single channel current amplitudes and reversal potentials were calculated from these values. The calculated single-channel currents were compared with those obtained experimentally. The calculated reversal potentials were compared with the resting potentials of Tetrahymena measured in various concentrations of extracellular K+ and Ca2+. The method of calculation of ionic currents and reversal potentials presented here is helpful for understanding the properties of the channels permeable to both monovalent and divalent cations.     

ATP transport through a single mitochondrial channel, VDAC, studied by current fluctuation analysis.

The "molecular Coulter counter" concept has been used to study transport of ATP molecules through the nanometer-scale aqueous pore of the voltage-dependent mitochondrial ion channel, VDAC. We examine the ATP-induced current fluctuations and the change in average current through a single fully open channel reconstituted into a planar lipid bilayer. At high salt concentration (1 M NaCl), the addition of ATP reduces both solution conductivity and channel conductance, but the effect on the channel is several times stronger and shows saturation behavior even at 50 mM ATP concentration. These results and simple steric considerations indicate pronounced attraction of ATP molecules to VDAC's aqueous pore and permit us to evaluate the effect of a single ATP molecule on channel conductance. ATP addition also generates an excess noise in the ionic current through the channel. Analysis of this excess noise shows that its spectrum is flat in the accessible frequency interval up to several kilohertz. ATP exchange between the pore and the bulk is fast enough not to display any dispersion at these frequencies. By relating the low-frequency spectral density of the noise to the equilibrium diffusion of ATP molecules in the aqueous pore, we calculate a diffusion coefficient D = (1.6-3.3)10(-11) m2/s. This is one order of magnitude smaller than the ATP diffusion coefficient in the bulk, but it agrees with recent results on ATP flux measurements in multichannel membranes using the luciferin/luciferase method.     

Tuning ion coordination architectures to enable selective partitioning

K+ ions seemingly permeate K-channels rapidly because channel binding sites mimic coordination of K+ ions in water. Highly selective ion discrimination should occur when binding sites form rigid cavities that match K+, but not the smaller Na+, ion size or when binding sites are composed of specific chemical groups. Although conceptually attractive, these views cannot account for critical observations: 1), K+ hydration structures differ markedly from channel binding sites; 2), channel thermal fluctuations can obscure sub-Angstr?m differences in ion sizes; and 3), chemically identical binding sites can exhibit diverse ion selectivities. Our quantum mechanical studies lead to a novel paradigm that reconciles these observations. We find that K-channels utilize a "phase-activated" mechanism where the local environment around the binding sites is tuned to sustain high coordination numbers (>6) around K+ ions, which otherwise are rarely observed in liquid water. When combined with the field strength of carbonyl ligands, such high coordinations create the electrical scenario necessary for rapid and selective K+ partitioning. Specific perturbations to the local binding site environment with respect to strongly selective K-channels result in altered K+/Na+ selectivities.     

Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems

Voltage-dependent ion channels determine the electric properties of axonal cell membranes. They not only allow the passage of ions through the cell membrane, but also contribute to an additional charging of the cell membrane resulting in the so-called capacitance loading. The switching of the channel gates between an open and a closed configuration is intrinsically related to the movement of gating charge within the cell membrane. At the beginning of an action potential, the transient gating current is opposite to the direction of the current of sodium ions through the membrane. Therefore, the excitability is expected to become reduced due to the influence of a gating current. Our stochastic Hodgkin-Huxley-like modeling takes into account both the channel noise-i.e. the fluctuations of the number of open ion channels-and the capacitance fluctuations that result from the dynamics of the gating charge. We investigate the spiking dynamics of membrane patches of a variable size and analyze the statistics of the spontaneous spiking. As a main result, we find that the gating currents yield a drastic reduction of the spontaneous spiking rate for sufficiently large ion channel clusters. Consequently, this demonstrates a prominent mechanism for channel noise reduction.