A Subsequent Fit of Time Series and Amplitude Histogram of Patch-Clamp Records Reveals Rate Constants up to 1 per Microsecond

Fast gating in time series of patch-clamp current demands powerful tools to reveal the rate constants of the adequate Hidden Markov model. Here, two approaches are presented to improve the temporal resolution of the direct fit of the time series. First, the prediction algorithm is extended to include intermediate currents between the nominal levels as caused by the anti-aliasing filter. This approach can reveal rate constants that are about 4 times higher than the corner frequency of the anti-aliasing filter. However, this approach is restricted to time series with very low noise. Second, the direct fit of the time series is combined with a beta fit, i.e., a fit of the deviations of the amplitude histogram from the Gaussian distribution. Since the “theoretical” amplitude histograms for higher-order Bessel filters cannot be calculated by analytical tools, they are generated from simulated time series. In a first approach, a simultaneous fit of the time series and of the Beta fit is tested. This simultaneous fit, however, inherits the drawbacks of both approaches, not the benefits. More successful is a subsequent fit: The fit of the time series yields a set of rate constants. The subsequent Beta fit uses the slow rate constants of the fit of the time series as fixed parameters and the optimization algorithm is restricted to the fast ones. The efficiency of this approach is illustrated by means of time series obtained from simulation and from the dominant K⁺ channel in Chara. This shows that temporal resolution can reach the microsecond range.     

Computing transient gating charge movement of voltage-dependent ion channels

The opening of voltage-gated sodium, potassium, and calcium ion channels has a steep relationship with voltage. In response to changes in the transmembrane voltage, structural movements of an ion channel that precede channel opening generate a capacitative gating current. The net gating charge displacement due to membrane depolarization is an index of the voltage sensitivity of the ion channel activation process. Understanding the molecular basis of voltage-dependent gating of ion channels requires the measurement and computation of the gating charge, Q. We derive a simple and accurate semianalytic approach to computing the voltage dependence of transient gating charge movement (Q–V relationship) of discrete Markov state models of ion channels using matrix methods. This approach allows rapid computation of Q–V curves for finite and infinite length step depolarizations and is consistent with experimentally measured transient gating charge. This computational approach was applied to Shaker potassium channel gating, including the impact of inactivating particles on potassium channel gating currents.     

A comparison of sodium channel kinetics in the squid axon,the frog node and the frog node with BTX using the “silent gate” model

In this paper it is shown that the very different kinetics measured for the rise of the sodium current which follows a depolarization of the membrane in the squid giant axon, the frog node and the frog node treated with Batrachotoxin may be accurately predicted using only the measured equilibrium and static characteristics for the three preparations and the kinetics measured for the gating charge transfer.The kinetic predictions follow the use of the silent gate model for ion channel gating. The model is electrostatic and its chief assumptions are that the channel gate, called here the N-system, has fast kinetics and responds to the gating charge that transfers but not directly to the trans-membrane voltage applied. Because channel gating, corresponding here to the motion of the N-system, does not change its energy in the trans-membrane applied electric field the gating is electrically silent as far as gating charge transfer measurement is concerned. However the probability of gating rises with the quantity of gating charge that transfers due to the electrostatic interaction between the N-system and the gating charge, redistributed under the influence of the applied trans-membrane electric field. With these assumptions the kinetics of sodium channel gating are predictable using only the static and equilibrium characteristics of gating charge and channel activation measured as a function of membrane voltage, and the kinetics of the gating charge transfer. Because of the fast kinetics assumed for the N-system the predicted kinetics are the same for channels with any number of equivalent and independent N-systems or gates acting in parallel.The model predictions for sodium permeability kinetics are compared in detail with those recently measured for the frog node treated with Batrachotoxin and excellent agreement is obtained.     

Distributions-per-Level: A Means of Testing Level Detectors and Models of Patch-Clamp Data

Level or jump detectors generate the reconstructed time series from a noisy record of patch-clamp current. The reconstructed time series is used to create dwell-time histograms for the kinetic analysis of the Markov model of the investigated ion channel. It is shown here that some additional lines in the software of such a detector can provide a powerful new means of patch-clamp analysis. For each current level that can be recognized by the detector, an array is declared. The new software assigns every data point of the original time series to the array that belongs to the actual state of the detector. From the data sets in these arrays distributions-per-level are generated. Simulated and experimental time series analyzed by Hinkley detectors are used to demonstrate the benefits of these distributions-per-level. First, they can serve as a test of the reliability of jump and level detectors. Second, they can reveal beta distributions as resulting from fast gating that would usually be hidden in the overall amplitude histogram. Probably the most valuable feature is that the malfunctions of the Hinkley detectors turn out to depend on the Markov model of the ion channel. Thus, the errors revealed by the distributions-per-level can be used to distinguish between different putative Markov models of the measured time series. Abbreviations: AMFE = anomalous mole fraction effect; C, Z = closed state; DHD = sublevel Hinkley detector; HMM = Hidden Markov model; O, F = openstate; S = subconductance level     

Hydrogen ion modulation of Ca channel current in cardiac ventricular cells. Evidence for multiple mechanisms

We have investigated the effects of H ions on (L-type) Ca channel current in isolated ventricular cells. We find that the current amplitude is enhanced in solutions that are alkaline relative to pH 7.4 and reduced in solutions acidic to this pH. We measured pH0-induced shifts in channel gating and analyzed our results in terms of surface potential theory. The shifts are well described by changes in surface potential caused by the binding of H ions to negative charges on the cell surface. The theory predicts a pK of 5.8 for this binding. Gating shifts alone cannot explain all of our observations on modulation of current amplitude. Our results suggest that an additional mechanism contributes to modification of the current amplitude.     

A physical model of potassium channel activation: from energy landscape to gating kinetics

We have developed a method for rapidly computing gating currents from a multiparticle ion channel model. Our approach is appropriate for energy landscapes that can be characterized by a network of well-defined activation pathways with barriers. To illustrate, we represented the gating apparatus of a channel subunit by an interacting pair of charged gating particles. Each particle underwent spatial diffusion along a bistable potential of mean force, with electrostatic forces coupling the two trajectories. After a step in membrane potential, relaxation of the smaller barrier charge led to a time-dependent reduction in the activation barrier of the principal gate charge. The resulting gating current exhibited a rising phase similar to that measured in voltage-dependent ion channels. Reduction of the two-dimensional diffusion landscape to a circular Markov model with four states accurately preserved the time course of gating currents on the slow timescale. A composite system containing four subunits leading to a concerted opening transition was used to fit a series of gating currents from the Shaker potassium channel. We end with a critique of the model with regard to current views on potassium channel structure.     

QX-314 restores gating charge immobilization abolished by chloramine-T treatment in squid giant axons.

The gating status of the QX-314 bound Na channels before and after suppressing the fast inactivation by chloramine-T (CT) was investigated by studying the gating charge immobilization using the OFF gating current (Ig,OFF). CT treatment, which abolishes the charge immobilization induced by a prolonged depolarization, altered the kinetics of Ig,OFF: the fast phase became insensitive to the pulse duration and the slow phase became three times faster than the control one. However, internally applied QX-314 (in the presence of external TTX) caused an immediate charge immobilization similar to that observed in the absence of CT treatment. The Ig,OFF exhibited kinetics similar to the inactivated channels, decaying with a very fast time course. We conclude that the charge immobilization is restored by QX-314 in the chloramine-T-treated axon and that the gating state of the QX-314-bound channel is similar to the inactivated one. The role of the gating charge immobilization in the use-dependent block mechanism is discussed.     

Superstatistics analysis of the ion current distribution function: Met3PbCl influence study

A novel analysis of ion current time series is proposed. It is shown that higher (second, third and fourth) statistical moments of the ion current probability distribution function (PDF) can yield new information about ion channel properties. The method is illustrated on a two-state model where the PDF of the compound states are given by normal distributions. The proposed method was applied to the analysis of the SV cation channels of vacuolar membrane of Beta vulgaris and the influence of trimethyllead chloride (Met₃PbCl) on the ion current probability distribution. Ion currents were measured by patch-clamp technique. It was shown that Met₃PbCl influences the variance of the open-state ion current but does not alter the PDF of the closed-state ion current. Incorporation of higher statistical moments into the standard investigation of ion channel properties is proposed.     

The power of two-dimensional dwell-time analysis for model discrimination, temporal resolution, multichannel analysis and level detection

Two-dimensional (2D) dwell-time analysis of time series of single-channel patch-clamp current was improved by employing a Hinkley detector for jump detection, introducing a genetic fit algorithm, replacing maximum likelihood by a least square criterion, averaging over a field of 9 or 25 bins in the 2D plane and normalizing per measuring time, not per events. Using simulated time series for the generation of the "theoretical" 2D histograms from assumed Markov models enabled the incorporation of the measured filter response and noise. The effects of these improvements were tested with respect to the temporal resolution, accuracy of the determination of the rate constants of the Markov model, sensitivity to noise and requirement of open time and length of the time series. The 2D fit was better than the classical hidden Markov model (HMM) fit in all tested fields. The temporal resolution of the two most efficient algorithms, the 2D fit and the subsequent HMM/beta fit, enabled the determination of rate constants 10 times faster than the corner frequency of the low-pass filter. The 2D fit was much less sensitive to noise. The requirement of computing time is a problem of the 2D fit (100 times that of the HMM fit) but can now be handled by personal computers. The studies revealed a fringe benefit of 2D analysis: it can reveal the "true" single-channel current when the filter has reduced the apparent current level by averaging over undetected fast gating.     

Tl+-induced micros gating of current indicates instability of the MaxiK selectivity filter as caused by ion/pore interaction

Patch clamp experiments on single MaxiK channels expressed in HEK293 cells were performed at high temporal resolution (50-kHz filter) in asymmetrical solutions containing 0, 25, 50, or 150 mM Tl+ on the luminal or cytosolic side with [K+] + [Tl+] = 150 mM and 150 mM K+ on the other side. Outward current in the presence of cytosolic Tl+ did not show fast gating behavior that was significantly different from that in the absence of Tl+. With luminal Tl+ and at membrane potentials more negative than -40 mV, the single-channel current showed a negative slope resistance concomitantly with a flickery block, resulting in an artificially reduced apparent single-channel current I(app). The analysis of the amplitude histograms by beta distributions enabled the estimation of the true single-channel current and the determination of the rate constants of a simple two-state O-C Markov model for the gating in the bursts. The voltage dependence of the gating ratio R = I(true)/I(app) = (k(CO) + k(OC))/k(CO) could be described by exponential functions with different characteristic voltages above or below 50 mM Tl(+). The true single-channel current I(true) decreased with Tl+ concentrations up to 50 mM and stayed constant thereafter. Different models were considered. The most likely ones related the exponential increase of the gating ratio to ion depletion at the luminal side of the selectivity filter, whereas the influence of [Tl+] on the characteristic voltage of these exponential functions and of the value of I(true) were determined by [Tl+] at the inner side of the selectivity filter or in the cavity.     

The anomalous mole fraction effect in Chara: gating at the edge of temporal resolution

The anomalous mole fraction effect (AMFE) of the K(+) channel in excised patches of the tonoplast of Chara showed a minimum of apparent open-channel current at 20 mM Tl(+) and 230 mM K(+). Time series obtained at a sampling rate of 100 kHz (filter 25 kHz) were analyzed by three methods to find out whether the AMFE results from an effect on gating or on the conductivity of the open state. Fitting the amplitude histograms by a superposition of gaussians showed a broadening in the presence of Tl(+). Dwell-time analysis based on an O-O-C-C-C model failed to evaluate rate constants above the filter frequency. Thus, the absence of any reduction of apparent open-channel current in time series simulated with the evaluated rate constants could not be taken as evidence against the hypothesis of gating. Finally, a direct fit of the measured time series using five different 5-state Hidden Markov models revealed that the presence of Tl(+) changed the rate constants in such a way that the number of transitions into the short-lived open state (30 micros) increased strongly compared to those in the absence of Tl(+). These models explain 25% reduction of apparent single-channel current amplitude through a rapid gating mechanism.     

Open channel noise. II. A test for coupling between current fluctuations and conformational transitions in the acetylcholine receptor.

The first paper of this series demonstrated that the open-channel currents in the acetylcholine receptors in cultured rat muscle show fluctuations on a time scale of approximately 1 ms. In this paper the hypothesis is tested that these fluctuations are coupled to the gating mechanism that opens and closes the channel. Such a coupling could arise if the channel current and the energy barrier for gating transitions both showed fluctuations having a common origin such as a motion of part of the receptor molecule. A test for coupled fluctuations is made by averaging approximately 1,000 channel opening or closing transitions to search for the small relaxation in the current that is predicted. At a resolution of approximately 1% of the single-channel current amplitude, no such relaxation is observed. It is concluded that any coupled fluctuations are small; fluctuations in the energy barrier for the open-closed conformational transition must be smaller than about 0.3 kT.     

Structural determinants for the differences in voltage gating of chicken Cx56 and Cx45.6 gap-junctional hemichannels

The voltage- and calcium-dependent gating properties of two lens gap-junctional hemichannels were compared at the macroscopic and single channel level. In solutions containing zero added calcium and 1 mM Mg, chicken Cx56 hemichannels were mostly closed at negative potentials and application of depolarizing voltage clamp steps elicited a slowly activating outward current. In contrast, chicken Cx45.6 hemichannels were predominantly open at negative potentials and rapidly closed in response to application of large depolarizing potentials. Another difference was that macroscopic Cx45.6 currents were much smaller in size than the hemichannel currents induced by oocytes with similar amounts of cRNA for Cx56. The aim of this study was to identify which regions of the connexins were responsible for the differences in voltage-dependent gating and macroscopic current amplitude by constructing a series of chimeric Cx45.6-Cx56 channels. Our results show that two charged amino acids that are specific for the alpha3-group connexins (R9 in the N-terminus and E43 in the first extracellular loop) are important determinants for the difference in voltage-dependent gating between Cx45.6 and Cx56 hemichannels; the first transmembrane-spanning domain, M1, is an important determinant of macroscopic current magnitude; R9 and E43 are also determinants of single channel conductance and rectification.     

细胞外氯离子浓度对大鼠ClC-1通道去激活动力学特性的影响

为探讨C1C－1通道的门控机制,实验应用爪蟾母细胞异源性表达大鼠野生型C1C－1（WT RC1C-1)通道基因,并使用双电极电压钳法记录通道电流。通过改变细胞外氯离子浓度,采用双指数拟合的方法分析通道去激活电流,对其去激活门控动力学特性进行了研究。结果表明,降低细胞外氯离子浓度可增加快速去激活电流成分,减少慢速去激活成分;同时,慢速去激活和快速去激活电流的时间常数都显著减小,说明细胞外氯离子浓度的改变可影响通道去激活动力学参数,从而改变通道的门控过程。     

Phosphorylation of K+ channels in the squid giant axon. A mechanistic analysis

Protein phosphorylation is an important mechanism in the modulation of voltage-dependent ionic channels. In squid giant axons, the potassium delayed rectifier channel is modulated by an ATP-mediated phosphorylation mechanism, producing important changes in amplitude and kinetics of the outward current. The characteristics and biophysical basis for the phosphorylation effects have been extensively studied in this preparation using macroscopic, single-channel and gating current experiments. Phosphorylation produces a shift in the voltage dependence of all voltage-dependent parameters including open probability, slow inactivation, first latency, and gating charge transferred. The locus of the effect seems to be located in a fast 20 pS channel, with characteristics of delayed rectifier, but at least another channel is phosphorylated under our experimental conditions. These results are interpreted quantitatively with a mechanistic model that explains all the data. In this model the shift in voltage dependence is produced by electrostatic interactions between the transferred phosphate and the voltage sensor of the channel.     

Gating properties of gap junction channels assembled from connexin43 and connexin43 fused with green fluorescent protein.

We used cell lines expressing wild-type connexin43 (Cx43) and Cx43 fused with enhanced green fluorescent protein (Cx43-EGFP) to examine mechanisms of gap junction channel gating. Previously it was suggested that each hemichannel in a cell-cell channel possesses two gates, a fast gate that closes channels to a nonzero conductance or residual state via fast (< approximately 2 ms) transitions and a slow gate that fully closes channels via slow transitions (> approximately 10 ms). Here we demonstrate that transjunctional voltage (V(j)) regulates both gates and that they are operating in series and in a contingent manner in which the state of one gate affects gating of the other. Cx43-EGFP channels lack fast V(j) gating to a residual state but show slow V(j) gating. Both Cx43 and Cx43-EGFP channels exhibit slow gating by chemical uncouplers such as CO(2) and alkanols. Chemical uncouplers do not induce obvious changes in Cx43-EGFP junctional plaques, indicating that uncoupling is not caused by dispersion or internalization of junctional plaques. Similarity of gating transitions during chemical gating and slow V(j) gating suggests that both gating mechanisms share common structural elements. Cx43/Cx43-EGFP heterotypic channels showed asymmetrical V(j) gating with fast transitions between open and residual states only when the Cx43 side was relatively negative. This result indicates that the fast V(j) gate of Cx43 hemichannels closes for relative negativity at its cytoplasmic end.     

The early phase of sodium channel gating current in the squid giant axon

A fast component of displacement current which accompanies the sodium channel gating current has been recorded from the membrane of the giant axon of the squid Loligo forbesii. This component is characterized by relaxation time constants typically shorter than 25 µs. The charge displaced accounts for about 10% (or 2 nC/cm²) of the total displacement charge attributed to voltage-dependent sodium channels. Using a low noise, wide-band voltage clamp system and specially designed voltage step protocols we could demonstrate that this component: (i) is not a recording artifact; (ii) is kinetically independent from the sodium channel activation and inactivation processes; (iii) can account for a significant fraction of the initial amplitude of recorded displacement current and (iv) has a steady state charge transfer which saturates for membrane potentials above + 20 mV and below – 100 mV This component can be modelled as a single step transition using the Eyring-Boltzmann formalism with a quantal charge of 1 e^– and an asymmetrical energy barrier. Furthermore, if it were associated with the squid sodium channel, our data would suggest one fast transition per channel. A possible role as a sodium channel activation trigger, which would still be consistent with kinetic independence, is discussed. Despite uncertainties about its origin, the property of kinetic independence allows subtraction of this component from the total displacement current to reveal a rising phase in the early time course of the remaining current. This will have to be taken into account when modelling the voltage-dependent sodium channel.     

Gating current and potassium channels in the giant axon of the squid.

Gating current (Ig) underlying Na-channel activation is large enough to enable resolution of components both preceding and paralleling Na conductance (gNa) turn-on. For large depolarizations (beyond +20 mV), an additional "slow phase" of Ig is observed during a time when Na activation is already complete, but when K-channel opening is just becoming detectable. If Na- and K-channel gating are similar, the slow kinetics and long delay for K activation predict that K channel Ig must be relatively small and slow. Externally applied dibucaine almost totally blocks gNa and greatly reduces the fast (Na channel) Ig without altering gK or the Ig slow phase. The slow phase of Ig depends in part of the presence of functional K channels. Selective diminution in amplitude of the slow phase is consistently observed after a 30-min perfusion with both external and internal K-free media, a procedure which destroys nearly all K channels. This decrease of Ig amounts to approximately 10% of the total charge movements at +40 to +80 mV, with gating charge and K channels disappearing in a ratio of less than 1 e- per picosiemens of gK. These findings are consistent with the idea that part of the Ig slow phase represents gating current generated by the early steps in K-channel activation.     

Gap junction channel gating

Over the last two decades, the view of gap junction (GJ) channel gating has changed from one with GJs having a single transjunctional voltage-sensitive (V(j)-sensitive) gating mechanism to one with each hemichannel of a formed GJ channel, as well as unapposed hemichannels, containing two, molecularly distinct gating mechanisms. These mechanisms are termed fast gating and slow or 'loop' gating. It appears that the fast gating mechanism is solely sensitive to V(j) and induces fast gating transitions between the open state and a particular substate, termed the residual conductance state. The slow gating mechanism is also sensitive to V(j), but there is evidence that this gate may mediate gating by transmembrane voltage (V(m)), intracellular Ca(2+) and pH, chemical uncouplers and GJ channel opening during de novo channel formation. A distinguishing feature of the slow gate is that the gating transitions appear to be slow, consisting of a series of transient substates en route to opening and closing. Published reports suggest that both sensorial and gating elements of the fast gating mechanism are formed by transmembrane and cytoplamic components of connexins among which the N terminus is most essential and which determines gating polarity. We propose that the gating element of the slow gating mechanism is located closer to the central region of the channel pore and serves as a 'common' gate linked to several sensing elements that are responsive to different factors and located in different regions of the channel.