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current to the ordinate provided a method to estimate mean open time from data obtained at higher Po, where tau obs no longer represents mean open time.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.     

Deterministic chaos in the dynamics of biomembrane ion channel current

Within the framework of the theory of deterministic chaos, a nonlinear first-order differential equation with delay and relaxation with periodic influence on channel current for the parameter of order (deviation of channel current from the equilibrium value) was obtained. The numerical solutions of the equation indicate a chaotic dynamics of the order parameter and conformation potential of the channel protein with positive Lyapunov indices. By integration in the time interval between the "jumps" of ions through energy barriers of the channel protein, a mapping was obtained that also results in chaotic solutions realized in experiments. Basic kinetic characteristics of ionic channels for the mapping were obtained: the probability for the channel to be in the open state, P0, and the mean duration of a pack of current pulses depending on controlling parameters. Algorithms for constructing bifurcation diagrams with the transition to chaos and for determining Lyapunov indices and Kholmogorov entropy, pulsation spectra, and other parameters of chaotic dymanics were developed.     

Estimation of ion channel kinetics from fluctuations of macroscopic currents

For single channel recordings, the maximum likelihood estimation (MLE) of kinetic rates and conductance is well established. A direct extrapolation of this method to macroscopic currents is computationally prohibitive: it scales as a power of the number of channels. An approximated MLE that ignored the local time correlation of the data has been shown to provide estimates of the kinetic parameters. In this article, an improved approximated MLE that takes into account the local time correlation is proposed. This method estimates the channel kinetics using both the time course and the random fluctuations of the macroscopic current generated by a homogeneous population of ion channels under white noise. It allows arbitrary kinetic models and stimulation protocols. The application of the proposed algorithm to simulated data from a simple three-state model on nonstationary conditions showed reliable estimates of all the kinetic constants, the conductance and the number of channels, and reliable values for the standard error of those estimates. Compared to the previous approximated MLE, it reduces by a factor of 10 the amount of data needed to secure a given accuracy and it can even determine the kinetic rates in macroscopic stationary conditions.     

Alteration of the pH-dependent ion selectivity of the colicin E1 channel by site-directed mutagenesis.

Colicin E1 is a soluble, bacteriocidal protein that forms voltage-gated channels in planar lipid bilayers. The channel-forming region of the 522-amino acid protein is near the COOH terminus, and contains a 35-amino acid hydrophobic segment which is presumed to be important in interacting with the membrane. We have used site-directed mutagenesis in the region immediately upstream from the hydrophobic segment to construct several functional colicin mutants in which a wild-type residue was replaced with a cysteine. We also replaced the only naturally occurring cysteine in the molecule, Cys-505, with alanine, so that synthetically introduced cysteines could unambiguously serve as targets for chemical modification. All of the replacements reported here (at positions 449, 459, 473, 505, and some combinations) resulted in a channel that had an ion selectivity (K+ versus Cl-) identical to wild type at low pH. At higher pH, however, one of these mutations, which replaced the negatively charged aspartate at position 473 (the upstream boundary of the hydrophobic segment), resulted in a channel that was less cation-selective than was wild type. When the introduced Cys-473 was reacted with iodoacetic acid, which inserted a COOH group close to the position of the missing aspartate COOH, wild-type ion selectivity was restored, suggesting that the greater cation selectivity of the wild-type channel was directly produced by the negative charge at Asp-473. By comparing the ion selectivity of the Cys-473 mutant channel to that of the wild type as a function of the pH on the cis and trans sides of the membrane, it was possible to locate residue 473 close to the cis side. Locating in this manner the positions in the channel of particular residues places important constraints on channel model building.     

Molecular dynamics simulation of a synthetic ion channel.

A molecular dynamics simulation has been performed on a synthetic membrane-spanning ion channel, consisting of four alpha-helical peptides, each of which is composed of the amino acids leucine (L) and serine (S), with the sequence Ac-(LSLLLSL)3-CONH2. This four-helix bundle has been shown experimentally to act as a proton-conducting channel in a membrane environment. In the present simulation, the channel was initially assembled as a parallel bundle in the octane portion of a phase-separated water/octane system, which provided a membrane-mimetic environment. An explicit reversible multiple-time-step integrator was used to generate a dynamical trajectory, a few nanoseconds in duration for this composite system on a parallel computer, under ambient conditions. After more than 1 ns, the four helices were found to adopt an associated dimer state with twofold symmetry, which evolved into a coiled-coil tetrameric structure with a left-handed twist. In the coiled-coil state, the polar serine side chains interact to form a layered structure with the core of the bundle filled with H2O. The dipoles of these H2O molecules tended to align opposite the net dipole of the peptide bundle. The calculated dipole relaxation function of the pore H2O molecules exhibits two reorientation times. One is approximately 3.2 ps, and the other is approximately 100 times longer. The diffusion coefficient of the pore H2O is about one-third of the bulk H2O value. The total dipole moment and the inertia tensor of the peptide bundle have been calculated and reveal slow (300 ps) collective oscillatory motions. Our results, which are based on a simple united atom force-field model, suggest that the function of this synthetic ion channel is likely inextricably coupled to its dynamical behavior.     

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.     

Protonation of histidine and histidine-tryptophan interaction in the activation of the M2 ion channel from influenza a virus

The M2 protein of influenza A virus forms a homotetramer ion channel in the lipid membrane. The channel is specific for proton conductance and is activated by low pH with a transition midpoint at pH 5.7. We have studied the structure of the transmembrane domain of the M2 ion channel by using UV resonance Raman spectroscopy, with special attention to the side chains of histidine (His37) and tryptophan (Trp41) residues. The Raman spectra provide direct evidence that the imidazole ring of His37 is protonated upon channel activation at low pH. Concomitantly, the UV resonance Raman scattering from Trp41 shows an unusual intensity change, which is ascribed to a cation-pi interaction between the protonated (cationic) imidazole ring of His37 and the indole ring of Trp41. The protonation of His37 and the Raman intensity change of Trp41 do not occur in the presence of amantadine that blocks the M2 ion channel. These observations clearly show that the protonation of His37 and concomitant cation-pi interaction with Trp41 is a key step in the activation of the M2 ion channel. The His37-Trp41 interaction associated with the channel activation is explained by assuming a conformational transition of His37 induced by electrostatic repulsion among the protonated imidazole rings of four His37 residues in the tetramer channel. Trp41 may play a role in stabilizing the channel open state through cation-pi interaction with His37. A molecular model for the activation of M2 ion channel is proposed on the basis of the gating mechanism.     

Structure and dynamics of hydronium in the ion channel gramicidin A.

The effects of the hydronium ion, H(3)0+, on the structure of the ion channel gramicidin A and the hydrogen-bonded network of waters within the channel were studied to help elucidate a possible mechanism for proton transport through the channel. Several classical molecular dynamics studies were carried out with the hydronium in either the center of a gramicidin monomer or in the dimer junction. Structural reorganization of the channel backbone was observed for different hydronium positions, which were most apparent when the hydronium was within the monomer. In both cases the average O-O distance between the hydronium ion and its nearest neighbor water molecule was found to be approximately 2.55 A, indicating a rather strong hydrogen bond. Importantly, a subsequent break in the hydrogen-bonded network between the nearest neighbor and the next-nearest neighbor(approximately 2.7 -3.0 A) was repeatedly observed. Moreover, the carbonyl groups of gramicidin A were found to interact with the charge on the hydronium ion, helping in its stabilization. These facts may have significant implications for the proton hopping mechanism. The presence of the hydronium ion in the channel also inhibits to some degree the reorientational motions of the channel water molecules.     

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

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

Modulation of proton-induced current fluctuations in the human nicotinic acetylcholine receptor channel

The nicotinic acetylcholine receptor (nAChR) is a ligand-gated ion channel that switches upon activation from a closed state to a full conducting state. We found that the mutation delta S268K, located at 12' position of the second transmembrane domain of the delta subunit of the human nAChR generates a long-lived intermediate conducting state, from which openings to a wild-type like conductance level occur on a submillisecond time scale. Aiming to understand the interplay between structural changes near the 12' position and channel gating, we investigated the influence of various parameters: different ligands (acetylcholine, choline and epibatidine), ligand concentrations, transmembrane voltages and both fetal and adult nAChRs. Since sojourns in the high conductance state are not fully resolved in time, spectral noise analysis was used as a complement to dwell time analysis to determine the gating rate constants. Open channel current fluctuations are described by a two-state Markov model. The characteristic time of the process is markedly influenced by the ligand and the receptor type, whereas the frequency of openings to the high conductance state increases with membrane hyperpolarization. Conductance changes are discussed with regard to reversible transfer reaction of single protons at the lysine 12' side chain.     

Modulation of proton-induced current fluctuations in the human nicotinic acetylcholine receptor channel

The nicotinic acetylcholine receptor (nAChR) is a ligand-gated ion channel that switches upon activation from a closed state to a full conducting state. We found that the mutation δ S268K, located at 12′ position of the second transmembrane domain of the δ subunit of the human nAChR generates a long-lived intermediate conducting state, from which openings to a wild-type like conductance level occur on a submillisecond time scale. Aiming to understand the interplay between structural changes near the 12′ position and channel gating, we investigated the influence of various parameters: different ligands (acetylcholine, choline and epibatidine), ligand concentrations, transmembrane voltages and both fetal and adult nAChRs. Since sojourns in the high conductance state are not fully resolved in time, spectral noise analysis was used as a complement to dwell time analysis to determine the gating rate constants. Open channel current fluctuations are described by a two-state Markov model. The characteristic time of the process is markedly influenced by the ligand and the receptor type, whereas the frequency of openings to the high conductance state increases with membrane hyperpolarization. Conductance changes are discussed with regard to reversible transfer reaction of single protons at the lysine 12′ side chain.     

Mass spectral analysis and fragment ion structure of fusarochromanone.

Fusarochromanone is a mycotoxin produced by Fusarium equiseti that is implicated in the poultry disease tibial dyschrondroplasia. Electron impact ionization tandem mass spectrometry was used to elucidate probable structures of fragment ions found at m/z 274, 275, 261, 233, 218 and 191 and for devising an analytical rationale for the metabolites of the parent compound. In addition, a sensitive, qualitative liquid chromatographic technique using direct injection continuous-flow fast atom bombardment for the detection of fusarochromanone in corn was devised. Analysis was carried out on a hybrid tandem instrument (VG-7070EQ) using open tubular columns (75 microns i.d.) with direct-flow open-loop injection. The limit of detection of the pure compound was 500 pg in the selected ion monitoring mode. A 50 p.p.b. (500 pg injected) of the pure compound added to ground corn samples was the lowest detectable amount in a biological matrix.     

Patch clamp analysis of a partially purified ion channel from rat liver mitochondria.

A protein fraction isolated from detergent-solubilized mitochondrial membranes by affinity chromatography on immobilized quinine was reconstituted into phospholipid vesicles by detergent dialysis. Vesicles were fused to a diameter of 10 microns or larger by dehydration and rehydration. Patch clamp recordings carried out in detached mode with a symmetrical solution of 150 mM KCl, 5 mM HEPES, and 0.1 mM CaCl2 revealed conductance increments of 140 pS. Transitions of 40 pS were less frequently observed. Control vesicles which lacked protein showed no channel activity. The probability for the 140 pS channel to be open increased with increasing voltage in the range from 20 to 80 mV (positive potentials relative to what was the vesicle interior prior to excision), while the single channel conductance remained essentially constant. The 140 pS channel did not open at negative voltages. The voltage dependence suggests asymmetric incorporation of the 140 pS channel into vesicle membranes during reconstitution.     

Parametric spectral analysis of nonstationary fluctuations of excitatory synaptic currents

We assessed on Monte-Carlo simulated excitatory post-synaptic currents the ability of autoregressive (AR)-model fitting to evaluate their fluctuations. AR-model fitting consists of a linear filter describing the process that generates the fluctuations when driven with a white noise. Its fluctuations provide a filtered version of the signal and have a spectral density depending on the properties of the linear filter. When the spectra of the non-stationary fluctuations of excitatory post-synaptic currents were estimated by fitting AR-models to the segments of current fluctuations, assumed to be stationary and independent, the parameter and spectral estimates were scattered. The scatter was much reduced if the time-variant AR-models were fitted using stochastic adaptive estimators (Kalman, recursive least squares and least mean squares). The ability of time-variant AR-models to accurately fit the current fluctuations was monitored by comparing the fluctuations with predicted fluctuations, and by evaluating the model-learning rate. The median frequency of current fluctuations, which could be rapidly tracked and estimated from the individual quantal events (either Monte-Carlo simulated or recorded from pyramidal neurons of rat hippocampus), rose during the rise phase, before declining to a lower steady-state level during the decay phase of quantal event, whereas the variance showed a broad peak. The closing rate of AMPA channels directly affects the steady-state median frequency, whereas the transient peak can be modulated by a variety of factors—number of molecules released, ability of glutamate molecules to re-enter the synaptic cleft, diffusion constant of glutamate in the cleft and opening rate of AMPA channels. In each case, the effect on the amplitude and decay time of mEPSCs and on the current fluctuations differs. Each factor thus leaves its own kinetic fingerprint arguing that the contribution of such factors can be inferred from the combined kinetic properties of individual mEPSCs.     

Statistical properties of ion channel records. Part I: relationship to the macroscopic current

Macroscopic ion channel current can be derived by summation of the stochastic records of individual channel currents. In this paper, we present two probability density functions of single channel records that can uniquely determine the macroscopic current regardless of other statistical properties of records or the stochastic model of channel gating (presented often with stationary Markov models). We show that H(t), probability density function of channel opening events (introduced explicitly in this paper), and D(t), probability density function of the open duration (sometimes has named dwell time distribution as well), determine the normalized macroscopic current, G(t), through G(t) = P(t) - H(t) * Q(t) where P(t) is the cumulative density function of H(t), Q(t) is the cumulative density function of D(t), * is the symbol of convolution integral and G(t) is the macroscopic current divided by the amplitude of single channel current and the number of single channel sweeps. Compared to other equations for the macroscopic current, here the macroscopic current is expressed only in terms of the statistical properties of single channel current and not the stochastic model of ion channel gating or a conditioned form of macroscopic current. Single channel currents of an inactivating BK channel were used to validate this relationship experimentally too. In this paper, we used median filters as they can remove the unwanted noise without smoothing the transitions between open and closed states (compare to low pass filters). This filtering leads to more accurate measurement of transition times and less amount of missed events.     

Cardiac ion channel current modulation by the CFTR inhibitor GlyH-101

The role in the heart of the cardiac isoform of the cystic fibrosis transmembrane conductance regulator (CFTR), which underlies a protein kinase A-dependent Cl⁻ current (I_Cl.PKA) in cardiomyocytes, remains unclear. The identification of a CFTR-selective inhibitor would provide an important tool for the investigation of the contribution of CFTR to cardiac electrophysiology. GlyH-101 is a glycine hydrazide that has recently been shown to block CFTR channels but its effects on cardiomyocytes are unknown. Here the action of GlyH-101 on cardiac I_Cl.PKA and on other ion currents has been established. Whole-cell patch-clamp recordings were made from rabbit isolated ventricular myocytes. GlyH-101 blocked I_Cl.PKA in a concentration- and voltage-dependent fashion (IC₅₀ at +100 mV = 0.3 ± 1.5 μM and at −100 mV = 5.1 ± 1.3 μM). Woodhull analysis suggested that GlyH-101 blocks the open pore of cardiac CFTR channels at an electrical distance of 0.15 ± 0.03 from the external membrane surface. A concentration of GlyH-101 maximally effective against I_Cl.PKA (30 μM) was tested on other cardiac ion currents. Inward current at −120 mV, comprised predominantly of the inward-rectifier background K⁺ current, I_K1, was reduced by ∼43% (n = 5). Under selective recording conditions, the Na⁺ current (I_Na) was markedly inhibited by GlyH-101 over the entire voltage range (with a fractional block at −40 mV of ∼82%; n = 8). GlyH-101 also produced a voltage-dependent inhibition of L-type Ca²⁺ channel current (I_Ca,L); fractional block at +10 mV of ∼49% and of ∼28% at −10 mV; n = 11, with a ∼−3 mV shift in the voltage-dependence of I_Ca,L activation. Thus, this study demonstrates for the first time that GlyH-101 blocks cardiac I_Cl.PKA channels in a similar fashion to that reported for recombinant CFTR. However, inhibition of other cardiac conductances may limit its use as a CFTR-selective blocker in the heart.     

Open channel block by gadolinium ion of the stretch-inactivated ion channel in mdx myotubes.

Currents flowing through single stretch-inactivated ion channels were recorded from cell-attached patches on myotubes from mdx mice. Adding micromolar concentrations of gadolinium to patch electrodes containing normal saline produced rapid transitions in the single-channel current between the fully open and closed states. The kinetics of the current fluctuations followed the predictions of a simple model of open channel block in which the transitions in the current arise from the entry and exit of Gd from the channel pore: histograms of the open and closed times were well fit with single exponentials, the blocking rate depended linearly on the concentration of gadolinium in the patch electrode, and the unblocking rate was independent of the concentration of gadolinium. Hyperpolarizing the patch increased the rate of unblocking (approximately e-fold per 85 mV), suggesting the charged blocking particle can exit the channel into the cell under the influence of the applied membrane field. The rate of blocking was rapid and was independent of the patch potential, consistent with the rate of ion entry into the pore being determined by its rate of diffusion in solution. When channel open probability was reduced by applying suction to the electrode, the blocking kinetics were independent of the extent of inactivation, suggesting that mechanosensitive gating does not modify the structure of the channel pore.     

Staphylococcal alpha-toxin increases the permeability of lipid vesicles by cholesterol- and pH-dependent assembly of oligomeric channels

alpha-Toxin, a lethal hemolytic toxin secreted by Staphylococcus aureus, forms ionic channels of large size in lipid membranes. To investigate the mechanism of channel assembly we have studied the kinetics of pore formation on small unilamellar vesicles. We have used two assays of vesicle permeabilization: one is the release of a fluorescent molecule trapped in their inner compartment; the other is the dissipation of an imposed potential. Both methods indicate that the kinetics are complex consisting of an initial delay followed by a non-linear relaxation. The dependence of the pore formation rate and the extent of permeabilization on the toxin/vesicle ratio indicates that aggregation of 4-10 preinserted toxin monomers underlies channel assembly. The pH dependence of permeabilization suggests that protonation of an acidic group of the toxin is a prerequisite to channel formation. Inclusion of cholesterol in the target vesicles potentiates alpha-toxin effects, in a dose-dependent way, possibly by facilitating its protonation. The location of the proton-binding site on the two adjacent aspartic acid residues in positions 127 and 128 of the toxin monomer is proposed.