Application of the ensemble nonequilibrium response spectroscopy to shaker potassium channel gating

Standard electrophysiology techniques study relaxation transients in voltage-gated ion channels generated by discrete voltage steps. The nonequilibrium response spectroscopy involves analyzing responses to fluctuating potentials. We apply the ensemble NRS method to gating kinetics of Shaker potassium ion channels. We evaluate various proposed Markov models of channel gating from the nonequilibrium response viewpoint. These new NRS protocols can be used to test otherwise indistinguishable models or improve estimates for parameters of channel kinetics models.     

Wavelet analysis of nonequilibrium ionic currents in human heart sodium channel (hH1a)

Nonequilibrium response spectroscopy (NRS), the technique of using rapidly fluctuating voltage pulses in the study of ion channels, is applied here. NRS is known to drive an ensemble of ion channels far from equilibrium where, it has been argued, new details of ion channel kinetics can be studied under nonequilibrium conditions. In this paper, a single-pulse NRS technique with custom-designed waveforms built from wavelets is used. The pulses are designed to produce different responses from two competing models of a human heart isoform of the sodium channel (hH1a). Experimental data using this new type of pulses are obtained through whole-cell recordings from mammalian cells (HEK 293). Wavelet analysis of the model response and the experimental data is introduced to show how these NRS pulses can aid in distinguishing the better of the two models and thus introduces another important application of this new technique.     

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

Cooperativity among the four subunits helps give rise to the remarkable voltage sensitivity of Shaker potassium channels, whose open probability changes tenfold for a 5-mV change in membrane potential. The cooperativity in these channels is thought to arise from a concerted structural transition as the final step in opening the channel. Recordings of single-channel ionic currents from certain other channel types, as well as our previous recordings from T442S mutant Shaker channels, however, display intermediate conductance levels in addition to the fully open and closed states. These sublevels might represent stepwise, rather than concerted, transitions in the final steps of channel activation. Here, we report a similar fine structure in the closing transitions of Shaker channels lacking the mutation. Describing the deactivation time course with hidden Markov models, we find that two subconductance levels are rapidly traversed during most closing transitions of chimeric, high conductance Shaker channels. The lifetimes of these levels are voltage-dependent, with maximal values of 52 and 22 micros at -100 mV, and the voltage dependences of transitions among these states suggest that they arise from equivalent conformational changes occurring in individual subunits. At least one subconductance level is found to be traversed in normal conductance Shaker channels. We speculate that voltage-dependent conformational changes in the subunits give rise to changes in a "pore gate" associated with the selectivity filter region of the channel, producing the subconductance states. As a control for the hidden Markov analysis, we applied the same procedures to recordings of the recovery from N-type inactivation in Shaker channels. These transitions are found to be instantaneous in comparison.     

Three-dimensional structure of a voltage-gated potassium channel at 2.5 nm resolution

BACKGROUND: The voltage-gated potassium channel Shaker from Drosophila consists of a tetramer of identical subunits, each containing six transmembrane segments. The atomic structure of a bacterial homolog, the potassium channel KcsA, is much smaller than Shaker. It does not have a voltage sensor and other important domains like the N-terminal tetramerization (T1) domain. The structure of these additional elements has to be studied in the more complex voltage-gated channels. RESULTS: We determined the three-dimensional structure of the entire Shaker channel at 2.5 nm resolution using electron microscopy. The four-fold symmetric structure shows a large and a small domain linked by thin 2 nm long connectors. To interpret the structure, we used the crystal structures of the isolated T1 domain and the KcsA channel. A unique density assignment was made based on the symmetry and dimensions of the crystal structures and domains, identifying the smaller domain as the cytoplasmic mass of Shaker containing T1 and the larger domain as embedded in the membrane. CONCLUSIONS: The two-domain architecture of the Shaker channel is consistent with the recently proposed "hanging gondola" model for the T1 domain, putting the T1 domain at a distance from the membrane domain but attached to it by thin connectors. The space between the two domains is sufficient to permit cytoplasmic access of ions and the N-terminal inactivation domain to the pore region. A hanging gondola architecture has also been observed in the nicotinic acetylcholine receptor and the KcsA structure, suggesting that it is a common element of ion channels.     

Voltage-dependent potassium channels: minK and Shaker families

In the last 4 years, the molecular identity of several types of voltage-dependent potassium channels has been discovered. These include channels that terminate action potentials and control repetitive neuronal firing, as well as channels whose biological role is not yet understood. The majority of these are encoded by genes related to the Drosophila Shaker gene. The large number of genes comprising the Shaker gene family, coupled with the existence of different channels that result from alternatively spliced messages from the same gene, provide both vertebrates and invertebrates with a wide selection of channels whose voltage-dependence and kinetics can be tailored to the needs of a specific cell. Mutagenesis experiments on such channels are providing new information on those regions of the protein that govern essential aspects of channel activity, such as gating by voltage and ion permeation. Another gene, unrelated to the Shaker family, encodes a voltage-dependent potassium channel that activates much more slowly than the Shaker channels. This has been termed the MinK channel.     

Shaker K(+)-channels are predicted to reduce the metabolic cost of neural information in Drosophila photoreceptors

Shaker K(+)-channels are one of several voltage-activated K(+)-channels expressed in Drosophila photoreceptors. We have shown recently that Shaker channels act as selective amplifiers, attenuating some signals while boosting others. Loss of these channels reduces the photoreceptor information capacity (bits s(-1)) and induces compensatory changes in photoreceptors enabling them to minimize the impact of this loss upon coding natural-like stimuli. Energy as well as coding is also an important consideration in understanding the role of ion channels in neural processing. Here, we use a simple circuit model that incorporates the major ion channels, pumps and exchangers of the photoreceptors to derive experimentally based estimates of the metabolic cost of neural information in wild-type (WT) and Shaker mutant photoreceptors. We show that in WT photoreceptors, which contain Shaker K(+)-channels, each bit of information costs approximately half the number of ATP molecules than each bit in Shaker photoreceptors, in which lack of the Shaker K(+)-channels is compensated by increased leak conductance. Additionally, using a Hodgkin-Huxley-type model coupled to the circuit model we show that the amount of leak present in both WT and Shaker photoreceptors is optimized to both maximize the available voltage range and minimize the metabolic cost.     

Invariant manifold reductions for Markovian ion channel dynamics

We show that many Markov models of ion channel kinetics have globally attracting stable invariant manifolds, even when the Markov process is time dependent. The primary implication of this is that, since the dimension of the invariant manifold is often substantially smaller than the full master equation system, simulations of ion channel kinetics can be substantially simplified, with no approximation. We show that this applies to certain models of potassium channels, sodium channels, ryanodine receptors and IP₃ receptors. We also use this to show that the original Hodgkin–Huxley formulations of potassium channel conductance and sodium channel conductance are the exact solutions of full Markov models for these channels.      

A novel conus peptide ligand for K+ channels

Voltage-gated ion channels determine the membrane excitability of cells. Although many Conus peptides that interact with voltage-gated Na(+) and Ca(2+) channels have been characterized, relatively few have been identified that interact with K(+) channels. We describe a novel Conus peptide that interacts with the Shaker K(+) channel, kappaM-conotoxin RIIIK from Conus radiatus. The peptide was chemically synthesized. Although kappaM-conotoxin RIIIK is structurally similar to the mu-conotoxins that are sodium channel blockers, it does not affect any of the sodium channels tested, but blocks Shaker K(+) channels. Studies using Shaker K(+) channel mutants with single residue substitutions reveal that the peptide interacts with the pore region of the channel. Introduction of a negative charge at residue 427 (K427D) greatly increases the affinity of the toxin, whereas the substitutions at two other residues, Phe(425) and Thr(449), drastically reduced toxin affinity. Based on the Shaker results, a teleost homolog of the Shaker K(+) channel, TSha1 was identified as a kappaM-conotoxin RIIIK target. Binding of kappaM-conotoxin RIIIK is state-dependent, with an IC(50) of 20 nm for the closed state and 60 nm at 0 mV for the open state of TSha1 channels.     

A self-consistent approach for determining pairwise interactions that underlie channel activation

Signaling proteins such as ion channels largely exist in two functional forms, corresponding to the active and resting states, connected by multiple intermediates. Multiparametric kinetic models based on sophisticated electrophysiological experiments have been devised to identify molecular interactions of these conformational transitions. However, this approach is arduous and is not suitable for large-scale perturbation analysis of interaction pathways. Recently, we described a model-free method to obtain the net free energy of activation in voltage- and ligand-activated ion channels. Here we extend this approach to estimate pairwise interaction energies of side chains that contribute to gating transitions. Our approach, which we call generalized interaction-energy analysis (GIA), combines median voltage estimates obtained from charge-voltage curves with mutant cycle analysis to ascertain the strengths of pairwise interactions. We show that, for a system with an arbitrary gating scheme, the nonadditive contributions of amino acid pairs to the net free energy of activation can be computed in a self-consistent manner. Numerical analyses of sequential and allosteric models of channel activation also show that this approach can measure energetic nonadditivities even when perturbations affect multiple transitions. To demonstrate the experimental application of this method, we reevaluated the interaction energies of six previously described long-range interactors in the Shaker potassium channel. Our approach offers the ability to generate detailed interaction energy maps in voltage- and ligand-activated ion channels and can be extended to any force-driven system as long as associated “displacement” can be measured.     

Finite Sample Properties of the Maximum Likelihood Estimator and of Likelihood Ratio Tests in Hidden Markov Models

Hidden Markov models were successfully applied in various fields of time series analysis, especially for analyzing ion channel recordings. The maximum likelihood estimator (MLE) has recently been proven to be asymptotically normally distributed. Here, we investigate finite sample properties of the MLE and of different types of likelihood ratio tests (LRTs) by means of simulation studies. The MLE is shown to reach the asymptotic behavior within sample sizes that are common for various applications. Thus, reliable estimates and confidence intervals can be obtained. We give an approximative scaling function for the estimation error for finite samples, and investigate the power of different LRTs suitable for applications to ion channels, including tests for superimposed hidden Markov processes. Our results are applied to physiological sodium channel data.     

On identification of Na+ channel gating schemes using moving-average filtered hidden Markov models

 Transitions between distinct kinetic states of an ion channel are described by a Markov process. Hidden Markov models (HMM) have been successfully applied in the analysis of single ion channel recordings with a small signal-to-noise ratio. However, we have recently shown that the anti-aliasing low-pass filter misleads parameter estimation. Here, we show for the case of a Na⁺ channel recording that the standard HMM do neither allow parameter estimation nor a correct identification of the gating scheme. In particular, the number of closed and open states is determined incorrectly, whereas a modified HMM considering the anti-aliasing filter (moving-average filtered HMM) is able to reproduce the characteristic properties of the time series and to perform gating scheme identification. Received: 11 February 1999 / Revised version: 18 June 1999 / Accepted: 21 June 1999     

Involvement of the S4-S5 linker and the C-linker domain regions to voltage-gating in plant Shaker channels: Comparison with animal HCN and Kv channels

Among the different transport systems present in plant cells, Shaker channels constitute the major pathway for K⁺ in the plasma membrane. Plant Shaker channels are members of the 6 transmembrane-1 pore (6TM-1P) cation channel superfamily as the animal Shaker (Kv) and HCN channels. All these channels are voltage-gated K⁺ channels: Kv channels are outward-rectifiers, opened at depolarized voltages and HCN channels are inward-rectifiers, opened by membrane hyperpolarization. Among plant Shaker channels, we can find outward-rectifiers, inward-rectifiers and also weak-rectifiers, with weak voltage dependence. Despite the absence of crystal structures of plant Shaker channels, functional analyses coupled to homology modeling, mostly based on Kv and HCN crystals, have permitted the identification of several regions contributing to plant Shaker channel gating. In the present mini-review, we make an update on the voltage-gating mechanism of plant Shaker channels which seem to be comparable to that proposed for HCN channels.     

Models of the structure and voltage-gating mechanism of the shaker K+ channel

In the preceding, accompanying article, we present models of the structure and voltage-dependent gating mechanism of the KvAP bacterial K+ channel that are based on three types of evidence: crystal structures of portions of the KvAP protein, theoretical modeling criteria for membrane proteins, and biophysical studies of the properties of native and mutated voltage-gated channels. Most of the latter experiments were performed on the Shaker K+ channel. Some of these data are difficult to relate directly to models of the KvAP channel's structure due to differences in the Shaker and KvAP sequences. We have dealt with this problem by developing new models of the structure and gating mechanism of the transmembrane and extracellular portions of the Shaker channel. These models are consistent with almost all of the biophysical data. In contrast, much of the experimental data are incompatible with the "paddle" model of gating that was proposed when the KvAP crystal structures were first published. The general folding pattern and gating mechanisms of our current models are similar to some of our earlier models of the Shaker channel.     

Comparative study of the energetics of ion permeation in Kv1.2 and KcsA potassium channels

Biological ion channels rely on a multi-ion transport mechanism for fast yet selective permeation of ions. The crystal structure of the KcsA potassium channel provided the first microscopic picture of this process. A similar mechanism is assumed to operate in all potassium channels, but the validity of this assumption has not been well investigated. Here, we examine the energetics of ion permeation in Shaker Kv1.2 and KcsA channels, which exemplify the six-transmembrane voltage-gated and two-transmembrane inward-rectifier channels. We study the feasibility of binding a third ion to the filter and the concerted motion of ions in the channel by constructing the potential of mean force for K⁺ ions in various configurations. For both channels, we find that a pair of K⁺ ions can move almost freely within the filter, but a relatively large free-energy barrier hinders the K⁺ ion from stepping outside the filter. We discuss the effect of the CMAP dihedral energy correction that was recently incorporated into the CHARMM force field on ion permeation dynamics.     

Mapping the receptor site for charybdotoxin, a pore-blocking potassium channel inhibitor.

The Shaker K+ channel belongs to a family of structurally related voltage-activated cation channels that play a central role in cellular electrical signaling. By studying multiple site-directed mutants of the Shaker K+ channel, a region that forms the binding site for a pore-blocking scorpion toxin has been identified. The region contains a sequence that is highly conserved among cloned K+ channels and may contribute to the formation of the ion conduction pore.     

Dual Effect of Phosphatidyl (4,5)-Bisphosphate PIP2 on Shaker K+ Channels

Phosphatidylinositol (4,5)-bisphosphate (PIP₂) is a phospholipid of the plasma membrane that has been shown to be a key regulator of several ion channels. Functional studies and more recently structural studies of Kir channels have revealed the major impact of PIP₂ on the open state stabilization. A similar effect of PIP₂ on the delayed rectifiers Kv7.1 and Kv11.1, two voltage-gated K⁺ channels, has been suggested, but the molecular mechanism remains elusive and nothing is known on PIP₂ effect on other Kv such as those of the Shaker family. By combining giant-patch ionic and gating current recordings in COS-7 cells, and voltage-clamp fluorimetry in Xenopus oocytes, both heterologously expressing the voltage-dependent Shaker channel, we show that PIP₂ exerts 1) a gain-of-function effect on the maximal current amplitude, consistent with a stabilization of the open state and 2) a loss-of-function effect by positive-shifting the activation voltage dependence, most likely through a direct effect on the voltage sensor movement, as illustrated by molecular dynamics simulations.     

Constitutive activation of the Shaker Kv channel

In different types of K+ channels the primary activation gate is thought to reside near the intracellular entrance to the ion conduction pore. In the Shaker Kv channel the gate is closed at negative membrane voltages, but can be opened with membrane depolarization. In a previous study of the S6 activation gate in Shaker (Hackos, D.H., T.H. Chang, and K.J. Swartz. 2002. J. Gen. Physiol. 119:521-532.), we found that mutation of Pro 475 to Asp results in a channel that displays a large macroscopic conductance at negative membrane voltages, with only small increases in conductance with membrane depolarization. In the present study we explore the mechanism underlying this constitutively conducting phenotype using both macroscopic and single-channel recordings, and probes that interact with the voltage sensors or the intracellular entrance to the ion conduction pore. Our results suggest that constitutive conduction results from a dramatic perturbation of the closed-open equilibrium, enabling opening of the activation gate without voltage-sensor activation. This mechanism is discussed in the context of allosteric models for activation of Kv channels and what is known about the structure of this critical region in K+ channels.     

KvAP-based model of the pore region of shaker potassium channel is consistent with cadmium- and ligand-binding experiments

Potassium channels play fundamental roles in excitable cells. X-ray structures of bacterial potassium channels show that the pore-lining inner helices obstruct the cytoplasmic entrance to the closed channel KcsA, but diverge in widely open channels MthK and KvAP, suggesting a gating-hinge role for a conserved Gly in the inner helix. A different location of the gating hinge and a narrower open pore were proposed for voltage-gated Shaker potassium channels that have the Pro-473-Val-Pro motif. Two major observations back the proposal: cadmium ions lock mutant Val-476-Cys in the open state by bridging Cys-476 and His-486 in adjacent helices, and cadmium blocks the locked-open double mutant Val-474-Cys/Val-476-Cys by binding to Cys-474 residues. Here we used molecular modeling to show that the open Shaker should be as wide as KvAP to accommodate an open-channel blocker, correolide. We further built KvAP-, MthK-, and KcsA-based models of the Shaker mutants and Monte-Carlo-minimized them with constraints Cys-476-Cd(2+)-His-486. The latter were consistent with the KvAP-based model, causing a small-bend N-terminal to the Pro-473-Val-Pro motif. The constraints significantly distorted the MthK-based structure, making it similar to KvAP. The KcsA structure resisted the constraints. Two Cd(2+) ions easily block the locked-open KvAP-based model at Cys-474 residues, whereas constraining a single cadmium ion to four Cys-474 caused large conformational changes and electrostatic imbalance. Although mutual disposition of the voltage-sensor and pore domains in the KvAP x-ray structure is currently disputed, our results suggest that the pore-region domain retains a nativelike conformation in the crystal.