Hidden Markov model analysis of intermediate gating steps associated with the pore gate of shaker potassium channels

Evaluating sequential and allosteric activation models in IKs channels with mutated voltage sensors

The ion-conducting IKs channel complex, important in cardiac repolarization and arrhythmias, comprises tetramers of KCNQ1 α-subunits along with 1-4 KCNE1 accessory subunits and calmodulin regulatory molecules. The E160R mutation in individual KCNQ1 subunits was used to prevent activation of voltage sensors and allow direct determination of transition rate data from complexes opening with a fixed number of 1, 2, or 4 activatable voltage sensors. Markov models were used to test the suitability of sequential versus allosteric models of IKs activation by comparing simulations with experimental steady-state and transient activation kinetics, voltage-sensor fluorescence from channels with two or four activatable domains, and limiting slope currents at negative potentials. Sequential Hodgkin-Huxley-type models approximately describe IKs currents but cannot explain an activation delay in channels with only one activatable subunit or the hyperpolarizing shift in the conductance-voltage relationship with more activatable voltage sensors. Incorporating two voltage sensor activation steps in sequential models and a concerted step in opening via rates derived from fluorescence measurements improves models but does not resolve fundamental differences with experimental data. Limiting slope current data that show the opening of channels at negative potentials and very low open probability are better simulated using allosteric models of activation with one transition per voltage sensor, which implies that movement of all four sensors is not required for IKs conductance. Tiered allosteric models with two activating transitions per voltage sensor can fully account for IKs current and fluorescence activation kinetics in constructs with different numbers of activatable voltage sensors.

Opening of capsaicin receptor TRPV1 is stabilized equally by its four subunits

Capsaicin receptor TRPV1 is a nociceptor for vanilloid molecules, such as capsaicin and resiniferatoxin (RTX). Even though cryo-EM structures of TRPV1 in complex with these molecules are available, how their binding energetically favors the open conformation is not known. Here, we report an approach to control the number of bound RTX molecules (0-4) in functional rat TRPV1. The approach allowed direct measurements of each of the intermediate open states under equilibrium conditions at both macroscopic and single-molecule levels. We found that RTX binding to each of the four subunits contributes virtually the same activation energy, which we estimated to be 1.70 to 1.86 kcal/mol and found to arise predominately from destabilizing the closed conformation. We further showed that sequential bindings of RTX increase open probability without altering single-channel conductance, confirming that there is likely a single open-pore conformation for TRPV1 activated by RTX.

TRPV1 Opening is Stabilized Equally by Its Four Subunits

Capsaicin receptor TRPV1 is a nociceptor for vanilloid molecules such as capsaicin and resiniferatoxin (RTX). Even though cryo-EM structures of TRPV1 in complex with these molecules are available, how their binding energetically favors the open conformation is not known. Here we report an approach to control the number of bound RTX molecules (0-to-4) in functional mouse TRPV1. The approach allowed direct measurements of each of the intermediate open states under equilibrium conditions at both macroscopic and single-molecule levels. We found that RTX binding to each of the four subunits contributes virtually the same activation energy, which we estimated to be 1.86 kcal/mol and found to arise predominately from destabilizing the closed conformation. We further showed that sequential bindings of RTX increase open probability without altering single-channel conductance, confirming that there is likely a single open-pore conformation for TRPV1 activated by RTX.

The conformational wave in capsaicin activation of transient receptor potential vanilloid 1 ion channel

The capsaicin receptor TRPV1 has been intensively studied by cryo-electron microscopy and functional tests. However, though the apo and capsaicin-bound structural models are available, the dynamic process of capsaicin activation remains intangible, largely due to the lack of a capsaicin-induced open structural model and the low occupancy of the transition states. Here we report that reducing temperature toward the freezing point substantially increased channel closure events even in the presence of saturating capsaicin. We further used a combination of fluorescent unnatural amino acid (fUAA) incorporation, computational modeling, and rate-equilibrium linear free-energy relationships analysis (Φ-analysis) to derive the fully open capsaicin-bound state model, and reveal how the channel transits from the apo to the open state. We observed that capsaicin initiates a conformational wave that propagates through the S4–S5 linker towards the S6 bundle and finally reaching the selectivity filter. Our study provides a temporal mechanism for capsaicin activation of TRPV1.

The capsaicin receptor TRPV1 has been structurally characterized, but the capsaicin activation dynamics remain elusive. Here authors use fluorescent unnatural amino acid incorporation, computational modeling and Φ-analysis to derive the capsaicin-bound open state model and reveal the capsaicin induced conformational changes.

How to resolve microsecond current fluctuations in single ion channels: the power of beta distributions

A main ingredient for the understanding of structure/function correlates of ion channels is the quantitative description of single-channel gating and conductance. However, a wealth of information provided from fast current fluctuations beyond the temporal resolution of the recording system is often ignored, even though it is close to the time window accessible to molecular dynamics simulations. This kind of current fluctuations provide a special technical challenge, because individual opening/closing or blocking/unblocking events cannot be resolved, and the resulting averaging over undetected events decreases the single-channel current. Here, I briefly summarize the history of fast-current fluctuation analysis and focus on the so-called "beta distributions." This tool exploits characteristics of current fluctuation-induced excess noise on the current amplitude histograms to reconstruct the true single-channel current and kinetic parameters. A guideline for the analysis and recent applications demonstrate that a construction of theoretical beta distributions by Markov Model simulations offers maximum flexibility as compared to analytical solutions.

Mechanosensitive gating of Kv channels

K-selective voltage-gated channels (Kv) are multi-conformation bilayer-embedded proteins whose mechanosensitive (MS) Popen(V) implies that at least one conformational transition requires the restructuring of the channel-bilayer interface. Unlike Morris and colleagues, who attributed MS-Kv responses to a cooperative V-dependent closed-closed expansion↔compaction transition near the open state, Mackinnon and colleagues invoke expansion during a V-independent closed↔open transition. With increasing membrane tension, they suggest, the closed↔open equilibrium constant, L, can increase >100-fold, thereby taking steady-state Popen from 0→1; "exquisite sensitivity to small…mechanical perturbations", they state, makes a Kv "as much a mechanosensitive…as…a voltage-dependent channel". Devised to explain successive gK(V) curves in excised patches where tension spontaneously increased until lysis, their L-based model falters in part because of an overlooked IK feature; with recovery from slow inactivation factored in, their g(V) datasets are fully explained by the earlier model (a MS V-dependent closed-closed transition, invariant L≥4). An L-based MS-Kv predicts neither known Kv time courses nor the distinctive MS responses of Kv-ILT. It predicts Kv densities (hence gating charge per V-sensor) several-fold different from established values. If opening depended on elevated tension (L-based model), standard gK(V) operation would be compromised by animal cells' membrane flaccidity. A MS V-dependent transition is, by contrast, unproblematic on all counts. Since these issues bear directly on recent findings that mechanically-modulated Kv channels subtly tune pain-related excitability in peripheral mechanoreceptor neurons we undertook excitability modeling (evoked action potentials). Kvs with MS V-dependent closed-closed transitions produce nuanced mechanically-modulated excitability whereas an L-based MS-Kv yields extreme, possibly excessive (physiologically-speaking) inhibition.

Multiple pore conformations driven by asynchronous movements of voltage sensors in a eukaryotic sodium channel

Voltage-dependent Na(+) channels are crucial for electrical signalling in excitable cells. Membrane depolarization initiates asynchronous movements in four non-identical voltage-sensing domains of the Na(+) channel. It remains unclear to what extent this structural asymmetry influences pore gating as compared with outwardly rectifying K(+) channels, where channel opening results from a final concerted transition of symmetric pore gates. Here we combine single channel recordings, cysteine accessibility and voltage clamp fluorimetry to probe the relationships between voltage sensors and pore conformations in an inactivation deficient Nav1.4 channel. We observe three distinct conductance levels such that DI-III voltage sensor activation is kinetically correlated with formation of a fully open pore, whereas DIV voltage sensor movement underlies formation of a distinct subconducting pore conformation preceding inactivation in wild-type channels. Our experiments reveal that pore gating in sodium channels involves multiple transitions driven by asynchronous movements of voltage sensors. These findings shed new light on the mechanism of coupling between activation and fast inactivation in voltage-gated sodium channels.

Being flexible: the voltage-controllable activation gate of kv channels

Kv channels form voltage-dependent potassium selective pores in the outer cell membrane and are composed out of four α-subunits, each having six membrane-spanning α-helices (S1–S6). The α-subunits tetramerize such that the S5–S6 pore domains co-assemble into a centrally located K⁺ pore which is surrounded by four operational voltage-sensing domains (VSD) that are each formed by the S1–S4 segments. Consequently, each subunit is capable of responding to changes in membrane potential and dictates whether the pore should be conductive or not. K⁺ permeation through the pore can be sealed off by two separate gates in series: (a) at the inner S6 bundle crossing (BC gate) and (b) at the level of the selectivity filter (SF gate) located at the extracellular entrance of the pore. Within the last years a general consensus emerged that a direct communication between the S4S5-linker and the bottom part of S6 (S6_c) constitutes the coupling with the VSD thus making the BC gate the main voltage-controllable activation gate. While the BC gate listens to the VSD, the SF changes its conformation depending on the status of the BC gate. Through the eyes of an entering K⁺ ion, the operation of the BC gate apparatus can be compared with the iris-like motion of the diaphragm from a camera whereby its diameter widens. Two main gating motions have been proposed to create this BC gate widening: (1) tilting of the helix whereby the S6 converts from a straight α-helix to a tilted one or (2) swiveling of the S6_c whereby the S6 remains bent. Such motions require a flexible hinge that decouples the pre- and post-hinge segment. Roughly at the middle of the S6 there exists a highly conserved glycine residue and a tandem proline motif that seem to fulfill the role of a gating hinge which allows for tilting/swiveling/rotations of the post-hinge S6 segment. In this review we delineate our current view on the operation of the BC gate for controlling K⁺ permeation in Kv channels.

Using a five-state model for fitting amplitude histograms from MaxiK channels: beta-distributions reveal more than expected

Fast gating of ion channels with rate constants higher than the corner frequency of the recording set-up can be evaluated by fitting so-called beta distributions to measured amplitude histograms. Up to now, this was preferentially done for O-C Markov sub-models with one open and one closed state. Here, a fit of the amplitude histograms from MaxiK (BK) single-channel records was achieved with a five-state model with two open and three closed states including three open-close transitions with rate constants higher than the corner frequency (20 kHz) of the inevitable low-pass filter of the recording system. The numerical values of the rate constants of these transitions enabled a nearly one-to-one relationship between typical regions of the histograms and the reactions in the Markov model. These characteristic features are the width of the peak at the apparent single-channel current, the side slopes at the open and at the closed peak, and the depth of the valley between the two peaks. However, the simplex routine alone was incapable of finding the solution but could do so if guided by hand along a suggested strategy.

Molecular template for a voltage sensor in a novel K+ channel. III. Functional reconstitution of a sensorless pore module from a prokaryotic Kv channel

KvLm is a prokaryotic voltage-gated K⁺ (Kv) channel from Listeria monocytogenes. The sequence of the voltage-sensing module (transmembrane segments S1-S4) of KvLm is atypical in that it contains only three of the eight conserved charged residues known to be deterministic for voltage sensing in eukaryotic Kv's. In contrast, the pore module (PM), including the S4-S5 linker and cytoplasmic tail (linker-S5-P-S6-C-terminus) of KvLm, is highly conserved. Here, the full-length (FL)-KvLm and the KvLm-PM only proteins were expressed, purified, and reconstituted into giant liposomes. The properties of the reconstituted FL-KvLm mirror well the characteristics of the heterologously expressed channel in Escherichia coli spheroplasts: a right-shifted voltage of activation, micromolar tetrabutylammonium-blocking affinity, and a single-channel conductance comparable to that of eukaryotic Kv's. Conversely, ionic currents through the PM recapitulate both the conductance and blocking properties of the FL-KvLm, yet the KvLm-PM exhibits only rudimentary voltage dependence. Given that the KvLm-PM displays many of the conduction properties of FL-KvLm and of other eukaryotic Kv's, including strict ion selectivity, we conclude that self-assembly of the PM subunits in lipid bilayers, in the absence of the voltage-sensing module, generates a conductive oligomer akin to that of the native KvLm, and that the structural independence of voltage sensing and PMs observed in eukaryotic Kv channels was initially implemented by nature in the design of prokaryotic Kv channels. Collectively, the results indicate that this robust functional module will prove valuable as a molecular template for coupling new sensors and to elucidate PM residue–specific contributions to Kv conduction properties.

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 β 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.

Direct analysis of cooperativity in multisubunit allosteric proteins

Allosteric regulation of protein function is a fundamental phenomenon of major importance in many cellular processes. Such regulation is often achieved by ligand-induced conformational changes in multimeric proteins that may give rise to cooperativity in protein function. At the heart of allosteric mechanisms offered to account for such phenomenon, involving either concerted or sequential conformational transitions, lie changes in intersubunit interactions along the ligation pathway of the protein. However, structure-function analysis of such homooligomeric proteins by means of mutagenesis, although it provides valuable indirect information regarding (allosteric) mechanisms of action, it does not define the contribution of individual subunits nor interactions thereof to cooperativity in protein function, because any point mutation introduced into homooligomeric proteins will be present in all subunits. Here, we present a general strategy for the direct analysis of cooperativity in multisubunit proteins that combines measurement of the effects on protein function of all possible combinations of mutated subunits with analysis of the hierarchy of intersubunit interactions, assessed by using high-order double-mutant cycle-coupling analysis. We show that the pattern of high-order intersubunit coupling can serve as a discriminative criterion for defining concerted versus sequential conformational transitions underlying protein function. This strategy was applied to the particular case of the voltage-activated potassium channel protein (Kv) to provide compelling evidence for a concerted all-or-none activation gate opening of the Kv channel pore domain. An direct and detailed analysis of the contribution of high-order intersubunit interactions to cooperativity in the function of an allosteric protein has not previously been presented.

Ion binding in the open HCN pacemaker channel pore: fast mechanisms to shape "slow" channels

I_H pacemaker channels carry a mixed monovalent cation current that, under physiological ion gradients, reverses at ∼−34 mV, reflecting a 4:1 selectivity for K over Na. However, I_H channels display anomalous behavior with respect to permeant ions such that (a) open channels do not exhibit the outward rectification anticipated assuming independence; (b) gating and selectivity are sensitive to the identity and concentrations of externally presented permeant ions; (c) the channels' ability to carry an inward Na current requires the presence of external K even though K is a minor charge carrier at negative voltages. Here we show that open HCN channels (the hyperpolarization-activated, cyclic nucleotide sensitive pore forming subunits of I_H) undergo a fast, voltage-dependent block by intracellular Mg in a manner that suggests the ion binds close to, or within, the selectivity filter. Eliminating internal divalent ion block reveals that (a) the K dependence of conduction is mediated via K occupancy of site(s) within the pore and that asymmetrical occupancy and/or coupling of these sites to flux further shapes ion flow, and (b) the kinetics of equilibration between K-vacant and K-occupied states of the pore (10–20 μs or faster) is close to the ion transit time when the pore is occupied by K alone (∼0.5–3 μs), a finding that indicates that either ion:ion repulsion involving Na is adequate to support flux (albeit at a rate below our detection threshold) and/or the pore undergoes rapid, permeant ion-sensitive equilibration between nonconducting and conducting configurations. Biophysically, further exploration of the Mg site and of interactions of Na and K within the pore will tell us much about the architecture and operation of this unusual pore. Physiologically, these results suggest ways in which “slow” pacemaker channels may contribute dynamically to the shaping of fast processes such as Na-K or Ca action potentials.

Time-dependent molecular memory in single voltage-gated sodium channel

Excitability in neurons is associated with firing of action potentials and requires the opening of voltage-gated sodium channels with membrane depolarization. Sustained membrane depolarization, as seen in pathophysiological conditions like epilepsy, can have profound implications on the biophysical properties of voltage-gated ion channels. Therefore, we sought to characterize the effect of sustained membrane depolarization on single voltage-gated Na+ channels. Single-channel activity was recorded in the cell-attached patch-clamp mode from the rNa(v)1.2 alpha channels expressed in CHO cells. Classical statistical analysis revealed complex nonlinear changes in channel dwell times and unitary conductance of single Na+ channels as a function of conditioning membrane depolarization. Signal processing tools like weighted wavelet Z (WWZ) and discrete Fourier transform analyses attributed a "pseudo-oscillatory" nature to the observed nonlinear variation in the kinetic parameters. Modeling studies using the hidden Markov model (HMM) illustrated significant changes in kinetic states and underlying state transition rate constants upon conditioning depolarization. Our results suggest that sustained membrane depolarization induces novel nonlinear properties in voltage-gated Na+ channels. Prolonged membrane depolarization also induced a "molecular memory" phenomenon, characterized by clusters of dwell time events and strong autocorrelation in the dwell time series similar to that reported recently for single enzyme molecules. The persistence of such molecular memory was found to be dependent on the duration of depolarization. Voltage-gated Na+ channel with the observed time-dependent nonlinear properties and the molecular memory phenomenon may determine the functional state of the channel and, in turn, the excitability of a neuron.

Saturation and microsecond gating of current indicate depletion-induced instability of the MaxiK selectivity filter

Patch clamp experiments on single MaxiK channels expressed in HEK293 cells were performed with a high temporal resolution (50-kHz filter) in symmetrical solutions with 50, 150, or 400 mM KCl and 2.5 mM CaCl(2) and 2.5 mM MgCl(2). At membrane potentials >+100 mV, the single-channel current showed a negative slope resistance, concomitantly with a flickery block, which was not influenced by Ca(2+) or Mg(2+). The analysis of the amplitude histograms by beta distributions revealed that current in this voltage range was reduced by two effects: rate limitation at the cytosolic side of the pore and gating with rate constants 10-20-fold higher than the cutoff frequency of the filter (i.e., dwell times in the microsecond range). The data were analyzed in terms of a model that postulates a coupling between both effects; if the voltage over the selectivity filter withdraws ions from the cavity at a higher rate than that of refilling from the cytosol, the selectivity filter becomes instable because of ion depletion, and current is interrupted by the resulting flickering. The fit of the IV curves revealed a characteristic voltage of 35 mV. In contrast, the voltage dependence of the gating factor R, i.e., the ratio between true and apparent single-channel current, could be fitted by exponentials with a characteristic voltage of 60 mV, suggesting that only part of the transmembrane potential is felt by the flux through the selectivity filter.

Thermosensitive TRPV channel subunits coassemble into heteromeric channels with intermediate conductance and gating properties

Heat-sensitive transient receptor potential (TRP) channels (TRPV1–4) form the major cellular sensors for detecting temperature increases. Homomeric channels formed by thermosensitive TRPV subunits exhibit distinct temperature thresholds. While these subunits do share significant sequence similarity, whether they can coassemble into heteromeric channels has been controversial. In the present study we investigated the coassembly of TRPV subunits using both spectroscopy-based fluorescence resonance energy transfer (FRET) and single-channel recordings. Fluorescent protein–tagged TRPV subunits were coexpressed in HEK 293 cells; FRET between different subunits was measured as an indication of the formation of heteromeric channels. We observed strong FRET when fluorescence signals were collected selectively from the plasma membrane using a “spectra FRET” approach but much weaker or no FRET from intracellular fluorescence. In addition, no FRET was detected when TRPV subunits were coexpressed with members of the TRPM subfamily or CLC-0 chloride channel subunits. These results indicate that a substantial fraction of TRP channels in the plasma membrane of cotransfected cells were heteromeric. Single-channel recordings confirmed the existence of multiple heteromeric channel forms. Interestingly, heteromeric TRPV channels exhibit intermediate conductance levels and gating kinetic properties. As these subunits coexpress both in sensory neurons and in other tissues, including heart and brain, coassembly between TRPV subunits may contribute to greater functional diversity.

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.

The patch clamp technique: principles and technical considerations

The development of techniques that allow the high fidelity measurement of small scale ionic currents ushered in a new era of investigation into the role of ion channels in the physiologic and pathophysiologic function of excitable tissue. Based upon the formation of a high resistance (gigaohm) seal with the membrane of the cell being studied, these "patch clamp" techniques have improved our understanding of a wide variety of cardiac disease states with respect to diagnosis, treatment and prognosis. This review outlines the basic principles underlying the patch clamp technique, including the properties of biological membranes and ion channels, and provides an elementary summary of its application to the recording of cardiac ionic currents, with a particular focus on issues related to myocyte isolation, electrode manufacturing and the voltage clamp configuration.

Strengths and limits of Beta distributions as a means of reconstructing the true single-channel current in patch clamp time series with fast gating

Single-channel current seems to be one of the most obvious characteristics of ion transport. But in some cases, its determination is more complex than anticipated at first glance. Problems arise from fast gating in time series of patch-clamp current, which can lead to a reduced apparent (measured) single-channel current. Reduction is caused by undetected averaging over closed and open intervals in the anti-aliasing filter. Here it is shown that fitting the measured amplitude histograms by Beta distributions is an efficient tool of reconstructing the true current level from measured data. This approach becomes even more powerful when it is applied to amplitude distributions-per-level. Simulated time series are employed to show that the error sum is a good guideline for finding the correct current level. Furthermore, they show that a Markov model smaller than the one used for gating analysis can be used for current determination (mostly O-C, i.e., open-closed). This increases the reliability of the Beta fit. The knowledge of the true current level is not only important for the understanding of the biophysical properties of the channel. It is also a prerequisite for the correct determination of the rate constants of gating. The approach is applied to measured data. The examples reveal the limits of the analysis imposed by the signal-to-noise ratio and the shape of the amplitude distribution. One application shows that the negative slope of the I-V curve of the human MaxiK channel expressed in HEK293 cells is caused by fast gating.

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.

Y3+ block demonstrates an intracellular activation gate for the alpha1G T-type Ca2+ channel

Classical electrophysiology and contemporary crystallography suggest that the activation gate of voltage-dependent channels is on the intracellular side, but a more extracellular “pore gate” has also been proposed. We have used the voltage dependence of block by extracellular Y³⁺ as a tool to locate the activation gate of the α1G (Ca_V3.1) T-type calcium channel. Y³⁺ block exhibited no clear voltage dependence from −40 to +40 mV (50% block at 25 nM), but block was relieved rapidly by stronger depolarization. Reblock of the open channel, reflected in accelerated tail currents, was fast and concentration dependent. Closed channels were also blocked by Y³⁺ at a concentration-dependent rate, only eightfold slower than open-channel block. When extracellular Ca²⁺ was replaced with Ba²⁺, the rate of open block by Y³⁺ was unaffected, but closed block was threefold faster than in Ca²⁺, suggesting the slower closed-block rate reflects ion–ion interactions in the pore rather than an extracellularly located gate. Since an extracellular blocker can rapidly enter the closed pore, the primary activation gate must be on the intracellular side of the selectivity filter.

The cooperative voltage sensor motion that gates a potassium channel

The four arginine-rich S4 helices of a voltage-gated channel move outward through the membrane in response to depolarization, opening and closing gates to generate a transient ionic current. Coupling of voltage sensing to gating was originally thought to operate with the S4s moving independently from an inward/resting to an outward/activated conformation, so that when all four S4s are activated, the gates are driven to open or closed. However, S4 has also been found to influence the cooperative opening step (Smith-Maxwell et al., 1998a), suggesting a more complex mechanism of coupling. Using fluorescence to monitor structural rearrangements in a Shaker channel mutant, the ILT channel (Ledwell and Aldrich, 1999), that energetically isolates the steps of activation from the cooperative opening step, we find that opening is accompanied by a previously unknown and cooperative movement of S4. This gating motion of S4 appears to be coupled to the internal S6 gate and to two forms of slow inactivation. Our results suggest that S4 plays a direct role in gating. While large transmembrane rearrangements of S4 may be required to unlock the gating machinery, as proposed before, it appears to be the gating motion of S4 that drives the gates to open and close.

A gastropod toxin selectively slows early transitions in the Shaker K channel's activation pathway

A toxin from a marine gastropod's defensive mucus, a disulfide-linked dimer of 6-bromo-2-mercaptotryptamine (BrMT), was found to inhibit voltage-gated potassium channels by a novel mechanism. Voltage-clamp experiments with Shaker K channels reveal that externally applied BrMT slows channel opening but not closing. BrMT slows K channel activation in a graded fashion: channels activate progressively slower as the concentration of BrMT is increased. Analysis of single-channel activity indicates that once a channel opens, the unitary conductance and bursting behavior are essentially normal in BrMT. Paralleling its effects against channel opening, BrMT greatly slows the kinetics of ON, but not OFF, gating currents. BrMT was found to slow early activation transitions but not the final opening transition of the Shaker ILT mutant, and can be used to pharmacologically distinguish early from late gating steps. This novel toxin thus inhibits activation of Shaker K channels by specifically slowing early movement of their voltage sensors, thereby hindering channel opening. A model of BrMT action is developed that suggests BrMT rapidly binds to and stabilizes resting channel conformations.

Differential modulation of cardiac Ca2+ channel gating by beta-subunits

To investigate the mechanisms that increase ionic currents when Ca(2+) channels' alpha(1) subunits are co-expressed with the beta-subunits, we compared channel activity of Ca(V)1.2 (alpha(1C)) co-expressed with beta(1a) and beta(2a) in Xenopus oocytes. Normalized by charge movement, ionic currents were near threefold larger with beta(2a) than with beta(1a). At the single-channel level, the open probability (P(o)) was over threefold larger with beta(2a), and traces with high P(o) were more frequent. Among traces with P(o) > 0.1, the mean duration of burst of openings (MBD) were nearly twice as long for alpha(1C)beta(2a) (15.1 +/- 0.7 ms) than for alpha(1C)beta(1a) (8.4 +/- 0.5 ms). Contribution of endogenous beta(3xo) was ruled out by comparing MBDs with alpha(1C)-cRNA alone (4.7 +/- 0.1 ms) with beta(3xo) (14.3 +/- 1.1 ms), and with beta(1b) (8.2 +/- 0.5 ms). Open-channel current amplitude distributions were indistinguishable for alpha(1C)beta(1a) and alpha(1C)beta(2a), indicating that opening and closing kinetics are similar with both subunits. Simulations with constant opening and closing rates reproduced the microscopic kinetics accurately, and therefore we conclude that the conformational change-limiting MBD is differentially regulated by the beta-subunits and contributes to the larger ionic currents associated with beta(2a), whereas closing and opening rates do not change, which should reflect the activity of a separate gate.

The link between ion permeation and inactivation gating of Kv4 potassium channels

Kv4 potassium channels undergo rapid inactivation but do not seem to exhibit the classical N-type and C-type mechanisms present in other Kv channels. We have previously hypothesized that Kv4 channels preferentially inactivate from the preopen closed state, which involves regions of the channel that contribute to the internal vestibule of the pore. To further test this hypothesis, we have examined the effects of permeant ions on gating of three Kv4 channels (Kv4.1, Kv4.2, and Kv4.3) expressed in Xenopus oocytes. Rb(+) is an excellent tool for this purpose because its prolonged residency time in the pore delays K(+) channel closing. The data showed that, only when Rb(+) carried the current, both channel closing and the development of macroscopic inactivation are slowed (1.5- to 4-fold, relative to the K(+) current). Furthermore, macroscopic Rb(+) currents were larger than K(+) currents (1.2- to 3-fold) as the result of a more stable open state, which increases the maximum open probability. These results demonstrate that pore occupancy can influence inactivation gating in a manner that depends on how channel closing impacts inactivation from the preopen closed state. By examining possible changes in ionic selectivity and the influence of elevating the external K(+) concentration, additional experiments did not support the presence of C-type inactivation in Kv4 channels.

Coupling between voltage sensor activation, Ca2+ binding and channel opening in large conductance (BK) potassium channels

To determine how intracellular Ca(2+) and membrane voltage regulate the gating of large conductance Ca(2+)-activated K(+) (BK) channels, we examined the steady-state and kinetic properties of mSlo1 ionic and gating currents in the presence and absence of Ca(2+) over a wide range of voltage. The activation of unliganded mSlo1 channels can be accounted for by allosteric coupling between voltage sensor activation and the closed (C) to open (O) conformational change (Horrigan, F.T., and R.W. Aldrich. 1999. J. Gen. Physiol. 114:305-336; Horrigan, F.T., J. Cui, and R.W. Aldrich. 1999. J. Gen. Physiol. 114:277-304). In 0 Ca(2+), the steady-state gating charge-voltage (Q(SS)-V) relationship is shallower and shifted to more negative voltages than the conductance-voltage (G(K)-V) relationship. Calcium alters the relationship between Q-V and G-V, shifting both to more negative voltages such that they almost superimpose in 70 microM Ca(2+). This change reflects a differential effect of Ca(2+) on voltage sensor activation and channel opening. Ca(2+) has only a small effect on the fast component of ON gating current, indicating that Ca(2+) binding has little effect on voltage sensor activation when channels are closed. In contrast, open probability measured at very negative voltages (less than -80 mV) increases more than 1,000-fold in 70 microM Ca(2+), demonstrating that Ca(2+) increases the C-O equilibrium constant under conditions where voltage sensors are not activated. Thus, Ca(2+) binding and voltage sensor activation act almost independently, to enhance channel opening. This dual-allosteric mechanism can reproduce the steady-state behavior of mSlo1 over a wide range of conditions, with the assumption that activation of individual Ca(2+) sensors or voltage sensors additively affect the energy of the C-O transition and that a weak interaction between Ca(2+) sensors and voltage sensors occurs independent of channel opening. By contrast, macroscopic I(K) kinetics indicate that Ca(2+) and voltage dependencies of C-O transition rates are complex, leading us to propose that the C-O conformational change may be described by a complex energy landscape.

Stepwise contribution of each subunit to the cooperative activation of BK channels by Ca2+

BK channels (Slo1) are widely distributed K+ channels that control Ca2+-dependent processes and cellular excitability. Their activation by intracellular Ca2+ (Ca(i)2+) is highly cooperative, with Hill coefficients of typically 2-5. To investigate the cooperativity contributed by each of the four alpha subunits that form the BK channel, we studied single channels comprised of mixtures of functional subunits and subunits with a mutation to disrupt a key site (Ca-bowl) required for activation by low concentrations of Ca(i)2+. As the number of functional subunits increased, we found a stepwise increase in the Hill coefficient of 0.3-0.8 per functional subunit and a stepwise decrease in the Ca(i)2+ required for half activation (K(d)). These results show directly that BK channels can open with 0, 1, 2, 3, or 4 functional Ca-bowls, and that each subunit with a functional Ca-bowl contributes a stepwise increase to both the cooperativity of activation and the apparent Ca2+ affinity. A model with 0-4 high-affinity allosteric activators and four low-affinity allosteric activators was examined. In this model, Ca2+ bindings were independent of one another and the cooperativity arose from the joint action of the allosteric activators on the open-closed equilibrium. Although this model described well the major features of the experimental data, some differences between the observed and predicted results indicated that additional factors not included in the model also contribute to the cooperativity.

Ion channels: does each subunit do something on its own?

The advent of the patch-clamp technique 25 years ago revolutionized the study of ion channels. This method also made it possible to measure the kinetic behavior of single protein molecules. The low-noise recordings of ionic currents through single channels, coupled with other cutting-edge technologies, have revealed a rich complexity of functional states that are not readily explained by simple allosteric protein models such as the popular concerted model and the sequential model. Although these models can each account for elements of ion channel function, we propose that variations or extensions of the lesser-known general allosteric model provide a more promising framework for explaining the intricate behaviors of ion channels.

Applying hidden Markov models to the analysis of single ion channel activity

Hidden Markov models have recently been used to model single ion channel currents as recorded with the patch clamp technique from cell membranes. The estimation of hidden Markov models parameters using the forward-backward and Baum-Welch algorithms can be performed at signal to noise ratios that are too low for conventional single channel kinetic analysis; however, the application of these algorithms relies on the assumptions that the background noise be white and that the underlying state transitions occur at discrete times. To address these issues, we present an "H-noise" algorithm that accounts for correlated background noise and the randomness of sampling relative to transitions. We also discuss three issues that arise in the practical application of the algorithm in analyzing single channel data. First, we describe a digital inverse filter that removes the effects of the analog antialiasing filter and yields a sharp frequency roll-off. This enhances the performance while reducing the computational intensity of the algorithm. Second, the data may be contaminated with baseline drifts or deterministic interferences such as 60-Hz pickup. We propose an extension of previous results to consider baseline drift. Finally, we describe the extension of the algorithm to multiple data sets.