Kinetic structure of large-conductance Ca2+-activated K+ channels suggests that the gating includes transitions through intermediate or secondary states. A mechanism for flickers

HS-AFM single-molecule structural biology uncovers basis of transporter wanderlust kinetics

The Pyrococcus horikoshii amino acid transporter GltPh revealed, like other channels and transporters, activity mode switching, previously termed wanderlust kinetics. Unfortunately, to date, the basis of these activity fluctuations is not understood, probably due to a lack of experimental tools that directly access the structural features of transporters related to their instantaneous activity. Here, we take advantage of high-speed atomic force microscopy, unique in providing simultaneous structural and temporal resolution, to uncover the basis of kinetic mode switching in proteins. We developed membrane extension membrane protein reconstitution that allows the analysis of isolated molecules. Together with localization atomic force microscopy, principal component analysis and hidden Markov modeling, we could associate structural states to a functional timeline, allowing six structures to be solved from a single molecule, and an inward-facing state, IFSopen-1, to be determined as a kinetic dead-end in the conformational landscape. The approaches presented on GltPh are generally applicable and open possibilities for time-resolved dynamic single-molecule structural biology.

How much does TRPV1 deviate from an ideal MWC-type protein?

Many ion channels are known to behave as an allosteric protein, coupling environmental stimuli captured by specialized sensing domains to the opening of a central pore. The classic Monod-Wyman-Changeux (MWC) model, originally proposed to describe binding of gas molecules to hemoglobin, has been widely used as a framework for analyzing ion channel gating. Here, we address the issue of how accurately the MWC model predicts activation of the capsaicin receptor TRPV1 by vanilloids. Taking advantage of a concatemeric design that makes it possible to lock TRPV1 in states with zero to four bound vanilloid molecules, we showed quantitatively that the overall gating behavior is satisfactorily predicted by the MWC model. There is, however, a small yet detectable subunit position effect: ligand binding to two kitty-corner subunits is 0.3-0.4 kcal/mol more effective in inducing opening than binding to two neighbor subunits. This difference-less than 10% of the overall energetic contribution from ligand binding-might be due to the restriction on subunit arrangement imposed by the planar membrane; if this is the case, then the position effect is not expected in hemoglobin, in which each subunit is related equivalently to all the other subunits.

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.

How Much Does TRPV1 Deviate from An Ideal MWC-Type Protein

Many ion channels are known to behave as an allosteric protein, coupling environmental stimuli captured by specialized sensing domains to the opening of a central pore. The classic Monod-Wyman-Changeux (MWC) model, originally proposed to describe binding of gas molecules to hemoglobin, has been widely used for analyzing ion channel gating. Here we address the issue of how accurate the MWC model predicts activation of the capsaicin receptor TRPV1 by vanilloids. Taking advantage of a concatemeric design that makes it possible to lock TRPV1 in states with zero-to-four bound vanilloid molecules, we showed quantitatively that the overall gating behavior is satisfactorily predicted by the MWC model. There is however a small yet detectable subunit position effect: ligand binding to two kitty-corner subunits is 0.4-to-0.6 kcal/mol more effective in inducing opening than binding to two neighbor subunits. This difference, less than 10% of the overall energetic contribution from ligand binding, is not expected in hemoglobin, in which each subunit is related equivalently to all the other subunits.

Significance

The MWC model, proposed more than 50 years ago, is elegantly simple yet powerful in predicting the behavior of allosteric proteins like hemoglobin. Its prediction power for ion channel gating has been beautifully demonstrated in the studies of BK channels. Our present work aims to determine how accurate the MWC model predicts TRPV1 activation induced by vanilloids. Our findings support the notion that the evolutionary drive upon allosteric proteins applies generally to multi-subunit proteins.

Microscopic mechanism of PIEZO1 activation by pressure-induced membrane stretch

Mechanosensitive PIEZO1 ion channels open in response to membrane stretch. Yet, the underlying microscopic mechanism of this activation remains unknown. To probe this mechanism, we used cell-attached pressure-clamp recordings to measure single channel currents at different steady-state negative pipette pressures, spanning the full range of the channel's pressure sensitivity. Pressure-dependent activation occurs through a sharp reduction of the mean shut duration and through a moderate increase of the mean open duration. Across all tested pressures, the distribution of open and shut dwell times best follows sums of two and three exponential components, respectively. As the magnitude of the pressure stimulus increases, the time constants of most of these exponential components gradually change, in opposite directions for open and shut dwell times, and to a similar extent. In addition, while the relative amplitudes of fast and slow components remain unchanged for open intervals, they fully reverse for shut intervals, further reducing the mean shut duration. Using two-dimensional dwell time analysis, Markov-chain modeling, and simulations, we identified a minimal five-states model which recapitulates essential characteristics of single channel data, including microscopic reversibility, correlations between adjacent open and shut intervals, and asymmetric modulation of dwell times by pressure. This study identifies a microscopic mechanism for the activation of PIEZO1 channels by pressure-induced membrane stretch and deepens our fundamental understanding of mechanotransduction by a vertebrate member of the PIEZO channel family.

2D-dwell-time analysis with simulations of ion-channel gating using high-performance computing

Single-channel patch-clamp recordings allow observing the action of a single protein complex in real time and hence the deduction of the underlying conformational changes in the ion-channel protein. Commonly, recordings are modeled using hidden Markov chains, connecting open and closed states in the experimental data with protein conformations. The rates between states denote transition probabilities that could be modified by membrane voltage or ligand binding. Modeling algorithms have to deal with limited recording bandwidth and a very noisy background. It was previously shown that the fit of two-dimensional (2D)-dwell-time histograms with simulations is very robust in that regard. Errors introduced by the low-pass filter or noise cancel out to a certain degree when comparing experimental and simulated data. In addition, the topology of models (that is, the chain of open and closed states) could be inferred from 2D-histograms. However, the 2D-fit was never applied to its full potential. A major reason may be the extremely time-consuming and often unreliable fitting process, due to the stochastic variability in the simulations. We have now solved these issues by introducing a message-passing interface (MPI) allowing massive parallel computing on a high-performance computing (HPC) cluster and obtaining ensemble solutions. With ensembles, we have demonstrated how important ranked solutions are for difficult tasks related to a noisy background, fast gating events beyond the corner frequency of the low-pass filter, and topology estimation of the underlying Markov model. Finally, we have shown that, by combining the objective function of the 2D-fit with the deviation of the current amplitude distributions, automatic determination of the current level of the conducting state is possible, even with an apparent current reduction due to low-pass filtering. Making use of an HPC cluster, the power of 2D-dwell-time analysis can be used to its fullest with minor input of the experimenter.

Regulatory mechanisms of mitochondrial BKCa channels

The mitochondrial BKCa channel (mitoBKCa) is a splice variant of plasma membrane BKCa (Maxi-K, BKCa, Slo1, KCa1.1). While a high-resolution structure of mitoBKCa is not available yet, functional and structural studies of the plasma membrane BKCa have provided important clues on the gating of the channel by voltage and Ca2+, as well as the interaction with auxiliary subunits. To date, we know that the control of expression of mitoBKCa, targeting and voltage-sensitivity strongly depends on its association with its regulatory β1-subunit, which overall participate in the control of mitochondrial Ca2+-overload in cardiac myocytes. Moreover, novel regulatory mechanisms of mitoBKCa such as β-subunits and amyloid-β have recently been proposed. However, major basic questions including how the regulatory BKCa-β1-subunit reaches mitochondria and the mechanism through which amyloid-β impairs mitoBKCa channel function remain to be addressed.

Anti-cross-correlation between the adjacent open and closed durations of Markovian channels

We show that a non-Markovian behavior can appear in a type of Markovian multimeric channel. Such a channel consists of N independent subunits, and each subunit has at least one open state and more than one closed state. Suppose the open state of the channel is defined as M out of N subunits in the open state with N>M>0. We show that, although the gating dynamics for each subunit between open and closed states is Markovian, the channel can show a memory behavior of weak anti-cross-correlation between the adjacent open and closed durations. Our study indicates that a non-Markovian binary time series can be obtained from a linear superposition of some independent channel subunits with Markovian gating dynamics.

Permeating disciplines: Overcoming barriers between molecular simulations and classical structure-function approaches in biological ion transport

Ion translocation across biological barriers is a fundamental requirement for life. In many cases, controlling this process-for example with neuroactive drugs-demands an understanding of rapid and reversible structural changes in membrane-embedded proteins, including ion channels and transporters. Classical approaches to electrophysiology and structural biology have provided valuable insights into several such proteins over macroscopic, often discontinuous scales of space and time. Integrating these observations into meaningful mechanistic models now relies increasingly on computational methods, particularly molecular dynamics simulations, while surfacing important challenges in data management and conceptual alignment. Here, we seek to provide contemporary context, concrete examples, and a look to the future for bridging disciplinary gaps in biological ion transport. This article is part of a Special Issue entitled: Beyond the Structure-Function Horizon of Membrane Proteins edited by Ute Hellmich, Rupak Doshi and Benjamin McIlwain.

Understanding the conformational motions of RCK gating rings

A timely review of the structural basis of Ca²⁺-activated K⁺ channel modulation by regulator of conduction of K⁺ (RCK) domains

Regulator of conduction of K⁺ (RCK) domains are ubiquitous regulators of channel and transporter activity in prokaryotes and eukaryotes. In humans, RCK domains form an integral component of large-conductance calcium-activated K channels (BK channels), key modulators of nerve, muscle, and endocrine cell function. In this review, we explore how the study of RCK domains in bacterial and human channels has contributed to our understanding of the structural basis of channel function. This knowledge will be critical in identifying mechanisms that underlie BK channelopathies that lead to epilepsy and other diseases, as well as regions of the channel that might be successfully targeted to treat such diseases.

Deletion of cytosolic gating ring decreases gate and voltage sensor coupling in BK channels

Both cellular depolarization and intracellular Ca²⁺ can gate open large conductance Ca²⁺-activated K⁺ channels. Zhang et al. show that the intracellular gating ring, which forms the Ca²⁺-sensing machinery of the channel, is also required for activated voltage sensors to effectively gate open the pore.

Large conductance Ca²⁺-activated K⁺ channels (BK channels) gate open in response to both membrane voltage and intracellular Ca²⁺. The channel is formed by a central pore-gate domain (PGD), which spans the membrane, plus transmembrane voltage sensors and a cytoplasmic gating ring that acts as a Ca²⁺ sensor. How these voltage and Ca²⁺ sensors influence the common activation gate, and interact with each other, is unclear. A previous study showed that a BK channel core lacking the entire cytoplasmic gating ring (Core-MT) was devoid of Ca²⁺ activation but retained voltage sensitivity (Budelli et al. 2013. Proc. Natl. Acad. Sci. USA. http://dx.doi.org/10.1073/pnas.1313433110). In this study, we measure voltage sensor activation and pore opening in this Core-MT channel over a wide range of voltages. We record gating currents and find that voltage sensor activation in this truncated channel is similar to WT but that the coupling between voltage sensor activation and gating of the pore is reduced. These results suggest that the gating ring, in addition to being the Ca²⁺ sensor, enhances the effective coupling between voltage sensors and the PGD. We also find that removal of the gating ring alters modulation of the channels by the BK channel’s β1 and β2 subunits.

Molecular Determinants of BK Channel Functional Diversity and Functioning

Large-conductance Ca2+- and voltage-activated K+ (BK) channels play many physiological roles ranging from the maintenance of smooth muscle tone to hearing and neurosecretion. BK channels are tetramers in which the pore-forming α subunit is coded by a single gene ( Slowpoke, KCNMA1). In this review, we first highlight the physiological importance of this ubiquitous channel, emphasizing the role that BK channels play in different channelopathies. We next discuss the modular nature of BK channel-forming protein, in which the different modules (the voltage sensor and the Ca2+ binding sites) communicate with the pore gates allosterically. In this regard, we review in detail the allosteric models proposed to explain channel activation and how the models are related to channel structure. Considering their extremely large conductance and unique selectivity to K+, we also offer an account of how these two apparently paradoxical characteristics can be understood consistently in unison, and what we have learned about the conduction system and the activation gates using ions, blockers, and toxins. Attention is paid here to the molecular nature of the voltage sensor and the Ca2+ binding sites that are located in a gating ring of known crystal structure and constituted by four COOH termini. Despite the fact that BK channels are coded by a single gene, diversity is obtained by means of alternative splicing and modulatory β and γ subunits. We finish this review by describing how the association of the α subunit with β or with γ subunits can change the BK channel phenotype and pharmacology.

Structural basis for gating the high-conductance Ca2+-activated K+ channel

The precise control of an ion channel gate by environmental stimuli is crucial for the fulfilment of its biological role. The gate in Slo1 K⁺ channels is regulated by two separate stimuli, intracellular Ca²⁺ concentration and membrane voltage. Slo1 is thus central to understanding the relationship between intracellular Ca²⁺ and membrane excitability. Here we present the Slo1 structure from Aplysia californica in the absence of Ca²⁺ and compare it with the Ca²⁺-bound channel. We show that Ca²⁺ binding at two unique binding sites per subunit stabilizes an expanded conformation of the Ca²⁺ sensor gating ring. These conformational changes are propagated from the gating ring to the pore through covalent linkers and through protein interfaces formed between the gating ring and the voltage sensors. The gating ring and the voltage sensors are directly connected through these interfaces, which allow membrane voltage to regulate gating of the pore by influencing the Ca²⁺ sensors.

Single-channel kinetics of BK (Slo1) channels

Single-channel kinetics has proven a powerful tool to reveal information about the gating mechanisms that control the opening and closing of ion channels. This introductory review focuses on the gating of large conductance Ca²⁺- and voltage-activated K⁺ (BK or Slo1) channels at the single-channel level. It starts with single-channel current records and progresses to presentation and analysis of single-channel data and the development of gating mechanisms in terms of discrete state Markov (DSM) models. The DSM models are formulated in terms of the tetrameric modular structure of BK channels, consisting of a central transmembrane pore-gate domain (PGD) attached to four surrounding transmembrane voltage sensing domains (VSD) and a large intracellular cytosolic domain (CTD), also referred to as the gating ring. The modular structure and data analysis shows that the Ca²⁺ and voltage dependent gating considered separately can each be approximated by 10-state two-tiered models with five closed states on the upper tier and five open states on the lower tier. The modular structure and joint Ca²⁺ and voltage dependent gating are consistent with a 50 state two-tiered model with 25 closed states on the upper tier and 25 open states on the lower tier. Adding an additional tier of brief closed (flicker states) to the 10-state or 50-state models improved the description of the gating. For fixed experimental conditions a channel would gate in only a subset of the potential number of states. The detected number of states and the correlations between adjacent interval durations are consistent with the tiered models. The examined models can account for the single-channel kinetics and the bursting behavior of gating. Ca²⁺ and voltage activate BK channels by predominantly increasing the effective opening rate of the channel with a smaller decrease in the effective closing rate. Ca²⁺ and depolarization thus activate by mainly destabilizing the closed states.

Statistical analysis of modal gating in ion channels

Ion channels regulate the concentrations of ions within cells. By stochastically opening and closing its pore, they enable or prevent ions from crossing the cell membrane. However, rather than opening with a constant probability, many ion channels switch between several different levels of activity even if the experimental conditions are unchanged. This phenomenon is known as modal gating: instead of directly adapting its activity, the channel seems to mix sojourns in active and inactive modes in order to exhibit intermediate open probabilities. Evidence is accumulating that modal gating rather than modulation of opening and closing at a faster time scale is the primary regulatory mechanism of ion channels. However, currently, no method is available for reliably calculating sojourns in different modes. In order to address this challenge, we develop a statistical framework for segmenting single-channel datasets into segments that are characteristic for particular modes. The algorithm finds the number of mode changes, detects their locations and infers the open probabilities of the modes. We apply our approach to data from the inositol-trisphosphate receptor. Based upon these results, we propose that mode changes originate from alternative conformational states of the channel protein that determine a certain level of channel activity.

Free-energy relationships in ion channels activated by voltage and ligand

Many ion channels are modulated by multiple stimuli, which allow them to integrate a variety of cellular signals and precisely respond to physiological needs. Understanding how these different signaling pathways interact has been a challenge in part because of the complexity of underlying models. In this study, we analyzed the energetic relationships in polymodal ion channels using linkage principles. We first show that in proteins dually modulated by voltage and ligand, the net free-energy change can be obtained by measuring the charge-voltage (Q-V) relationship in zero ligand condition and the ligand binding curve at highly depolarizing membrane voltages. Next, we show that the voltage-dependent changes in ligand occupancy of the protein can be directly obtained by measuring the Q-V curves at multiple ligand concentrations. When a single reference ligand binding curve is available, this relationship allows us to reconstruct ligand binding curves at different voltages. More significantly, we establish that the shift of the Q-V curve between zero and saturating ligand concentration is a direct estimate of the interaction energy between the ligand- and voltage-dependent pathway. These free-energy relationships were tested by numerical simulations of a detailed gating model of the BK channel. Furthermore, as a proof of principle, we estimate the interaction energy between the ligand binding and voltage-dependent pathways for HCN2 channels whose ligand binding curves at various voltages are available. These emerging principles will be useful for high-throughput mutagenesis studies aimed at identifying interaction pathways between various regulatory domains in a polymodal ion channel.

The BK channel: a vital link between cellular calcium and electrical signaling

Large-conductance Ca²⁺-activated K⁺ channels (BK channels) constitute an key physiological link between cellular Ca²⁺ signaling and electrical signaling at the plasma membrane. Thus these channels are critical to the control of action potential firing and neurotransmitter release in several types of neurons, as well as the dynamic control of smooth muscle tone in resistance arteries, airway, and bladder. Recent advances in our understanding of K⁺ channel structure and function have led to new insight toward the molecular mechanisms of opening and closing (gating) of these channels. Here we will focus on mechanisms of BK channel gating by Ca²⁺, transmembrane voltage, and auxiliary subunit proteins.

Modulation of BK channel voltage gating by different auxiliary β subunits

Calcium- and voltage-activated potassium channels (BK) are regulated by a multiplicity of signals. The prevailing view is that different BK gating mechanisms converge to determine channel opening and that these gating mechanisms are allosterically coupled. In most instances the pore forming α subunit of BK is associated with one of four alternative β subunits that appear to target specific gating mechanisms to regulate the channel activity. In particular, β1 stabilizes the active configuration of the BK voltage sensor having a large effect on BK Ca(2+) sensitivity. To determine the extent to which β subunits regulate the BK voltage sensor, we measured gating currents induced by the pore-forming BK α subunit alone and with the different β subunits expressed in Xenopus oocytes (β1, β2IR, β3b, and β4). We found that β1, β2, and β4 stabilize the BK voltage sensor in the active conformation. β3 has no effect on voltage sensor equilibrium. In addition, β4 decreases the apparent number of charges per voltage sensor. The decrease in the charge associated with the voltage sensor in α β4 channels explains most of their biophysical properties. For channels composed of the α subunit alone, gating charge increases slowly with pulse duration as expected if a significant fraction of this charge develops with a time course comparable to that of K(+) current activation. In the presence of β1, β2, and β4 this slow component develops in advance of and much more rapidly than ion current activation, suggesting that BK channel opening proceeds in two steps.

Short isoforms of the cold receptor TRPM8 inhibit channel gating by mimicking heat action rather than chemical inhibitors

Transient receptor potential (TRP) channels couple various environmental factors to changes in membrane potential, calcium influx, and cell signaling. They also integrate multiple stimuli through their typically polymodal activation. Thus, although the TRPM8 channel has been extensively investigated as the major neuronal cold sensor, it is also regulated by various chemicals, as well as by several short channel isoforms. Mechanistic understanding of such complex regulation is facilitated by quantitative single-channel analysis. We have recently proposed a single-channel mechanism of TRPM8 regulation by voltage and temperature. Using this gating mechanism, we now investigate TRPM8 inhibition in cell-attached patches using HEK293 cells expressing TRPM8 alone or coexpressed with its short sM8-6 isoform. This is compared with inhibition by the chemicals N-(4-tert-butylphenyl)-4-(3-chloropyridin-2-yl)piperazine-1-carboxamide (BCTC) and clotrimazole or by elevated temperature. We found that within the seven-state single-channel gating mechanism, inhibition of TRPM8 by short sM8-6 isoforms closely resembles inhibition by increased temperature. In contrast, inhibition by BCTC and that by clotrimazole share a different set of common features.

Voltage- and cold-dependent gating of single TRPM8 ion channels

Transient receptor potential (TRP) channels play critical roles in cell signaling by coupling various environmental factors to changes in membrane potential that modulate calcium influx. TRP channels are typically activated in a polymodal manner, thus integrating multiple stimuli. Although much progress has been made, the underlying mechanisms of TRP channel activation are largely unknown. The TRPM8 cation channel has been extensively investigated as a major neuronal cold sensor but is also activated by voltage, calcium store depletion, and some lipids as well as by compounds that produce cooling sensations, such as menthol or icilin. Several models of TRPM8 activation have been proposed to explain the interaction between these diverse stimuli. However, a kinetic scheme is not yet available that can describe the detailed single-channel kinetics to gain further insight into the underlying gating mechanism. To work toward this goal, we investigated voltage-dependent single-channel gating in cell-attached patches at two different temperatures (20 and 30°C) using HEK293 cells stably expressing TRPM8. Both membrane depolarization and cooling increased channel open probability (P_o) mainly by decreasing the duration of closed intervals, with a smaller increase in the duration of open intervals. Maximum likelihood analysis of dwell times at both temperatures indicated gating in a minimum of five closed and two open states, and global fitting over a wide range of voltages identified a seven-state model that described the voltage dependence of P_o, the single-channel kinetics, and the response of whole-cell currents to voltage ramps and steps. The major action of depolarization and cooling was to accelerate forward transitions between the same two sets of adjacent closed states. The seven-state model provides a general mechanism to account for TRPM8 activation by membrane depolarization at two temperatures and can serve as a starting point for further investigations of multimodal TRP activation.

Voltage-dependent inactivation gating at the selectivity filter of the MthK K+ channel

Voltage-dependent K⁺ channels can undergo a gating process known as C-type inactivation, which involves entry into a nonconducting state through conformational changes near the channel’s selectivity filter. C-type inactivation may involve movements of transmembrane voltage sensor domains, although the mechanisms underlying this form of inactivation may be heterogeneous and are often unclear. Here, we report on a form of voltage-dependent inactivation gating observed in MthK, a prokaryotic K⁺ channel that lacks a canonical voltage sensor and may thus provide a reduced system to inform on mechanism. In single-channel recordings, we observe that Po decreases with depolarization, with a half-maximal voltage of 96 ± 3 mV. This gating is kinetically distinct from blockade by internal Ca²⁺ or Ba²⁺, suggesting that it may arise from an intrinsic inactivation mechanism. Inactivation gating was shifted toward more positive voltages by increasing external [K⁺] (47 mV per 10-fold increase in [K⁺]), suggesting that K⁺ binding at the extracellular side of the channel stabilizes the open-conductive state. The open-conductive state was stabilized by other external cations, and selectivity of the stabilizing site followed the sequence: K⁺ ≈ Rb⁺ > Cs⁺ > Na⁺ > Li⁺ ≈ NMG⁺. Selectivity of the stabilizing site is weaker than that of sites that determine permeability of these ions, suggesting that the site may lie toward the external end of the MthK selectivity filter. We could describe MthK gating over a wide range of positive voltages and external [K⁺] using kinetic schemes in which the open-conductive state is stabilized by K⁺ binding to a site that is not deep within the electric field, with the voltage dependence of inactivation arising from both voltage-dependent K⁺ dissociation and transitions between nonconducting (inactivated) states. These results provide a quantitative working hypothesis for voltage-dependent, K⁺-sensitive inactivation gating, a property that may be common to other K⁺ channels.

Coupling and cooperativity in voltage activation of a limited-state BK channel gating in saturating Ca2+

Voltage-dependent gating mechanisms of large conductance Ca²⁺ and voltage-activated (BK) channels were investigated using two-dimensional maximum likelihood analysis of single-channel open and closed intervals. To obtain sufficient data at negative as well as positive voltages, single-channel currents were recorded at saturating Ca²⁺ from BK channels mutated to remove the RCK1 Ca²⁺ and Mg²⁺ sensors. The saturating Ca²⁺ acting on the Ca²⁺ bowl sensors of the resulting BK_B channels increased channel activity while driving the gating into a reduced number of states, simplifying the model. Five highly constrained idealized gating mechanisms based on extensions of the Monod-Wyman-Changeux model for allosteric proteins were examined. A 10-state model without coupling between the voltage sensors and the opening/closing transitions partially described the voltage dependence of Po but not the single-channel kinetics. With allowed coupling, the model gave improved descriptions of Po and approximated the single-channel kinetics; each activated voltage sensor increased the opening rate approximately an additional 23-fold while having little effect on the closing rate. Allowing cooperativity among voltage sensors further improved the description of the data: each activated voltage sensor increased the activation rate of the remaining voltage sensors approximately fourfold, with little effect on the deactivation rate. The coupling factor was decreased in models with cooperativity from ∼23 to ∼18. Whether the apparent cooperativity among voltage sensors arises from imposing highly idealized models or from actual cooperativity will require additional studies to resolve. For both cooperative and noncooperative models, allowing transitions to five additional brief (flicker) closed states further improved the description of the data. These observations show that the voltage-dependent single-channel kinetics of BK_B channels can be approximated by highly idealized allosteric models in which voltage sensor movement increases Po mainly through an increase in channel opening rates, with limited effects on closing rates.

Allosteric control of gating mechanisms revisited: the large conductance Ca2+-activated K+ channel

Large-conductance Ca(2+)-activated K(+) channels (BK) play a fundamental role in modulating membrane potential in many cell types. The gating of BK channels and its modulation by Ca(2+) and voltage has been the subject of intensive research over almost three decades, yielding several of the most complicated kinetic mechanisms ever proposed. A large number of open and closed states disposed, respectively, in two planes, named tiers, characterize these mechanisms. Transitions between states in the same plane are cooperative and modulated by Ca(2+). Transitions across planes are highly concerted and voltage-dependent. Here we reexamine the validity of the two-tiered hypothesis by restricting attention to the modulation by Ca(2+). Large single channel data sets at five Ca(2+) concentrations were simultaneously analyzed from a Bayesian perspective by using hidden Markov models and Markov-chain Monte Carlo stochastic integration techniques. Our results support a dramatic reduction in model complexity, favoring a simple mechanism derived from the Monod-Wyman-Changeux allosteric model for homotetramers, able to explain the Ca(2+) modulation of the gating process. This model differs from the standard Monod-Wyman-Changeux scheme in that one distinguishes when two Ca(2+) ions are bound to adjacent or diagonal subunits of the tetramer.

Intracellular Mg2+ influences both open and closed times of a native Ca2+-activated BK channel in cultured human renal proximal tubule cells

Effects of intracellular Mg2+ on a native Ca(2+)-and voltage-sensitive large-conductance K+ channel in cultured human renal proximal tubule cells were examined with the patch-clamp technique in the inside-out mode. At an intracellular concentration of Ca2+ ([Ca2+](i)) of 10(-5)-10(-4) M, addition of 1-10 mM: Mg2+ increased the open probability (P(o)) of the channel, which shifted the P(o) -membrane potential (V(m)) relationship to the negative voltage direction without causing an appreciable change in the gating charge (Boltzmann constant). However, the Mg(2+)-induced increase in P(o) was suppressed at a relatively low [Ca2+](i) (10(-5.5)-10(-6) M). Dwell-time histograms have revealed that addition of Mg2+ mainly increased P(o) by extending open times at 10(-5) M Ca2+ and extending both open and closed times simultaneously at 10(-5.5) M Ca2+. Since our data showed that raising the [Ca2+](i) from 10(-5) to 10(-4) M increased P(o) mainly by shortening the closed time, extension of the closed time at 10(-5.5) M Ca(2+) would result from the Mg(2+)-inhibited Ca(2+)-dependent activation. At a constant V(m), adding Mg2+ enhanced the sigmoidicity of the P(o)-[Ca2+](i) relationship with an increase in the Hill coefficient. These results suggest that the major action of Mg2+ on this channel is to elevate P(o) by lengthening the open time, while extension of the closed time at a relatively low [Ca2+](i) results from a lowering of the sensitivity to Ca2+ of the channel by Mg2+, which causes the increase in the Hill coefficient.

An extracellular Cu2+ binding site in the voltage sensor of BK and Shaker potassium channels

Copper is an essential trace element that may serve as a signaling molecule in the nervous system. Here we show that extracellular Cu²⁺ is a potent inhibitor of BK and Shaker K⁺ channels. At low micromolar concentrations, Cu²⁺ rapidly and reversibly reduces macrosocopic K⁺ conductance (G_K) evoked from mSlo1 BK channels by membrane depolarization. G_K is reduced in a dose-dependent manner with an IC₅₀ and Hill coefficient of ∼2 μM and 1.0, respectively. Saturating 100 μM Cu²⁺ shifts the G_K-V relation by +74 mV and reduces G_Kmax by 27% without affecting single channel conductance. However, 100 μM Cu²⁺ fails to inhibit G_K when applied during membrane depolarization, suggesting that Cu²⁺ interacts poorly with the activated channel. Of other transition metal ions tested, only Zn²⁺ and Cd²⁺ had significant effects at 100 μM with IC₅₀s > 0.5 mM, suggesting the binding site is Cu²⁺ selective. Mutation of external Cys or His residues did not alter Cu²⁺ sensitivity. However, four putative Cu²⁺-coordinating residues were identified (D133, Q151, D153, and R207) in transmembrane segments S1, S2, and S4 of the mSlo1 voltage sensor, based on the ability of substitutions at these positions to alter Cu²⁺ and/or Cd²⁺ sensitivity. Consistent with the presence of acidic residues in the binding site, Cu²⁺ sensitivity was reduced at low extracellular pH. The three charged positions in S1, S2, and S4 are highly conserved among voltage-gated channels and could play a general role in metal sensitivity. We demonstrate that Shaker, like mSlo1, is much more sensitive to Cu²⁺ than Zn²⁺ and that sensitivity to these metals is altered by mutating the conserved positions in S1 or S4 or reducing pH. Our results suggest that the voltage sensor forms a state- and pH-dependent, metal-selective binding pocket that may be occupied by Cu²⁺ at physiologically relevant concentrations to inhibit activation of BK and other channels.

Linking exponential components to kinetic states in Markov models for single-channel gating

Discrete state Markov models have proven useful for describing the gating of single ion channels. Such models predict that the dwell-time distributions of open and closed interval durations are described by mixtures of exponential components, with the number of exponential components equal to the number of states in the kinetic gating mechanism. Although the exponential components are readily calculated (Colquhoun and Hawkes, 1982, Phil. Trans. R. Soc. Lond. B. 300:1-59), there is little practical understanding of the relationship between components and states, as every rate constant in the gating mechanism contributes to each exponential component. We now resolve this problem for simple models. As a tutorial we first illustrate how the dwell-time distribution of all closed intervals arises from the sum of constituent distributions, each arising from a specific gating sequence. The contribution of constituent distributions to the exponential components is then determined, giving the relationship between components and states. Finally, the relationship between components and states is quantified by defining and calculating the linkage of components to states. The relationship between components and states is found to be both intuitive and paradoxical, depending on the ratios of the state lifetimes. Nevertheless, both the intuitive and paradoxical observations can be described within a consistent framework. The approach used here allows the exponential components to be interpreted in terms of underlying states for all possible values of the rate constants, something not previously possible.

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

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

A role for the S0 transmembrane segment in voltage-dependent gating of BK channels

BK (Maxi-K) channel activity is allosterically regulated by a Ca²⁺ sensor, formed primarily by the channel's large cytoplasmic carboxyl tail segment, and a voltage sensor, formed by its transmembrane helices. As with other voltage-gated K channels, voltage sensing in the BK channel is accomplished through interactions of the S1–S4 transmembrane segments with the electric field. However, the BK channel is unique in that it contains an additional amino-terminal transmembrane segment, S0, which is important in the functional interaction between BK channel α and β subunits. In this study, we used perturbation mutagenesis to analyze the role of S0 in channel gating. Single residues in the S0 region of the BK channel were substituted with tryptophan to give a large change in side chain volume; native tryptophans in S0 were substituted with alanine. The effects of the mutations on voltage- and Ca²⁺-dependent gating were quantified using patch-clamp electrophysiology. Three of the S0 mutants (F25W, L26W, and S29W) showed especially large shifts in their conductance–voltage (G-V) relations along the voltage axis compared to wild type. The G-V shifts for these mutants persisted at nominally 0 Ca²⁺, suggesting that these effects cannot arise simply from altered Ca²⁺ sensitivity. The basal open probabilities for these mutants at hyperpolarized voltages (where voltage sensor activation is minimal) were similar to wild type, suggesting that these mutations may primarily perturb voltage sensor function. Further analysis using the dual allosteric model for BK channel gating showed that the major effects of the F25W, L26W, and S29W mutations could be accounted for primarily by decreasing the equilibrium constant for voltage sensor movement. We conclude that S0 may make functional contact with other transmembrane regions of the BK channel to modulate the equilibrium between resting and active states of the channel's voltage sensor.

High-conductance potassium channels of the SLO family

High-conductance, 'big' potassium (BK) channels encoded by the Slo gene family are among the largest and most complex of the extended family of potassium channels. The family of SLO channels apparently evolved from voltage-dependent potassium channels, but acquired a large conserved carboxyl extension, which allows channel gating to be altered in response to the direct sensing of several different intracellular ions, and by other second-messenger systems, such as those activated following neurotransmitter binding to G-protein-coupled receptors (GPCRs). This versatility has been exploited to serve many cellular roles, both within and outside the nervous system.

Regulation of the gating of BKCa channel by lipid bilayer thickness

Transmembrane segments of ion channels tend to match the hydrophobic thickness of lipid bilayers to minimize mismatch energy and to maintain their proper organization and function. To probe how ion channels respond to mismatch with lipid bilayers of different thicknesses, we examined the single channel activities of BK(Ca) (hSlo alpha-subunit) channels in planar bilayers of binary mixtures of DOPE (1,2-dioleoyl-sn-glycero-3-phosphoethanolamine) with phosphatidylcholines (PCs) of varying chain lengths, including PC 14:1, PC 18:1, PC 22:1, PC 24:1, and with porcine brain sphingomyelin. Bilayer thickness and structure was measured with small angle x-ray diffraction and atomic force microscopy. The open probability (P(o)) of the BK(Ca) channel was finely tuned by bilayer thickness, first decreasing with increases in bilayer thickness from PC 14:1 to PC 22:1 and then increasing from PC 22:1 to PC 24:1 and to porcine brain sphingomyelin. Single channel kinetic analyses revealed that the mean open time of the channel increased monotonically with bilayer thickness and, therefore, could not account for the biphasic changes in P(o). The mean closed time increased with bilayer thickness from PC 14:1 up to PC 22:1 and then decreased with further increases in bilayer thickness to PC 24:1 and sphingomyelin, correlating with changes in P(o). This is consistent with the proposition that bilayer thickness affects channel activity mainly through altering the stability of the closed state. We suggest a simple mechanical model that combines forces of lateral stress within the lipid bilayer with local hydrophobic mismatch between lipids and the protein to account for the biphasic modulation of BK(Ca) gating.

Desensitization contributes to the synaptic response of gain-of-function mutants of the muscle nicotinic receptor

Although the muscle nicotinic receptor (AChR) desensitizes almost completely in the steady presence of high concentrations of acetylcholine (ACh), it is well established that AChRs do not accumulate in desensitized states under normal physiological conditions of neurotransmitter release and clearance. Quantitative considerations in the framework of plausible kinetic schemes, however, lead us to predict that mutations that speed up channel opening, slow down channel closure, and/or slow down the dissociation of neurotransmitter (i.e., gain-of-function mutations) increase the extent to which AChRs desensitize upon ACh removal. In this paper, we confirm this prediction by applying high-frequency trains of brief (∼1 ms) ACh pulses to outside-out membrane patches expressing either lab-engineered or naturally occurring (disease-causing) gain-of-function mutants. Entry into desensitization was evident in our experiments as a frequency-dependent depression in the peak value of succesive macroscopic current responses, in a manner that is remarkably consistent with the theoretical expectation. We conclude that the comparatively small depression of the macroscopic currents observed upon repetitive stimulation of the wild-type AChR is due, not to desensitization being exceedingly slow but, rather, to the particular balance between gating, entry into desensitization, and ACh dissociation rate constants. Disruption of this fine balance by, for example, mutations can lead to enhanced desensitization even if the kinetics of entry into, and recovery from, desensitization themselves are not affected. It follows that accounting for the (usually overlooked) desensitization phenomenon is essential for the correct interpretation of mutagenesis-driven structure–function relationships and for the understanding of pathological synaptic transmission at the vertebrate neuromuscular junction.

Relationship between pore occupancy and gating in BK potassium channels

Permeant ions can have significant effects on ion channel conformational changes. To further understand the relationship between ion occupancy and gating conformational changes, we have studied macroscopic and single-channel gating of BK potassium channels with different permeant monovalent cations. While the slopes of the conductance–voltage curve were reduced with respect to potassium for all permeant ions, BK channels required stronger depolarization to open only when thallium was the permeant ion. Thallium also slowed the activation and deactivation kinetics. Both the change in kinetics and the shift in the GV curve were dependent on the thallium passing through the permeation pathway, as well as on the concentration of thallium. There was a decrease in the mean open time and an increase in the number of short flicker closing events with thallium as the permeating ion. Mean closed durations were unaffected. Application of previously established allosteric gating models indicated that thallium specifically alters the opening and closing transition of the channel and does not alter the calcium activation or voltage activation pathways. Addition of a closed flicker state into the allosteric model can account for the effect of thallium on gating. Consideration of the thallium concentration dependence of the gating effects suggests that the flicker state may correspond to the collapsed selectivity filter seen in crystal structures of the KcsA potassium channel under the condition of low permeant ion concentration.

Estimating binding affinities of the nicotinic receptor for low-efficacy ligands using mixtures of agonists and two-dimensional concentration-response relationships

The phenomenon of ligand-induced ion channel gating hinges upon the ability of a receptor channel to bind ligand molecules with conformation-specific affinities. However, our understanding of this fundamental phenomenon is notably limited, not only because the changes in binding site structure and ligand conformation that occur upon gating are largely unknown but, also, because the strength of these ligand–receptor interactions are experimentally elusive. Both high- and low-efficacy ligands pose a number of analytical and experimental challenges that can render the estimation of their conformation-specific binding affinities impossible. In this paper, we present a novel assay that overcomes some of the hurdles presented by weak agonists of the muscle nicotinic receptor and allows the estimation of their closed-state affinities. The method, which we have termed the “activation-competition” assay, consists of a single-channel concentration–response assay performed in the presence of a binary mixture of ligands of widely different efficacies. By plotting the channel response (i.e., the open probability) as a function of the concentration of each agonist in the mixture, interpreting the observed response in the framework of a plausible kinetic scheme, and fitting the open probability surface with the corresponding function, the affinities of the closed receptor for the two agonists can be simultaneously extracted as free parameters. Here, we applied this methodology to estimate the closed-state affinity of the muscle nicotinic receptor for choline (a very weak agonist) using acetylcholine (ACh) as the partner in the mixture. We estimated the dissociation equilibrium constant of choline (K_D) from the wild type's closed state to be 4.1 ± 0.5 mM (and that of ACh to be 106 ± 6 μM). We also discuss the use of accurate estimates of affinities for low-efficacy agonists as a tool to discriminate between binding and gating effects of mutations, and in the context of the rational design of therapeutic drugs.

Calcium-dependent gating of MthK, a prokaryotic potassium channel

MthK is a calcium-gated, inwardly rectifying, prokaryotic potassium channel. Although little functional information is available for MthK, its high-resolution structure is used as a model for eukaryotic Ca²⁺-dependent potassium channels. Here we characterize in detail the main gating characteristics of MthK at the single-channel level with special focus on the mechanism of Ca²⁺ activation. MthK has two distinct gating modes: slow gating affected mainly by Ca²⁺ and fast gating affected by voltage. Millimolar Ca²⁺ increases MthK open probability over 100-fold by mainly increasing the frequency of channel opening while leaving the opening durations unchanged. The Ca²⁺ dose–response curve displays an unusually high Hill coefficient (n = ∼8), suggesting strong coupling between Ca²⁺ binding and channel opening. Depolarization affects both the fast gate by dramatically reducing the fast flickers, and to a lesser extent, the slow gate, by increasing MthK open probability. We were able to capture the mechanistic features of MthK with a modified MWC model.

Statistical evaluation of ion-channel gating models based on distributions of log-likelihood ratios

The distributions of log-likelihood ratios (DeltaLL) obtained from fitting ion-channel dwell-time distributions with nested pairs of gating models (Xi, full model; Xi(R), submodel) were studied both theoretically and using simulated data. When Xi is true, DeltaLL is asymptotically normally distributed with predictable mean and variance that increase linearly with data length (n). When Xi(R) is true and corresponds to a distinct point in full parameter space, DeltaLL is Gamma-distributed (2DeltaLL is chi-square). However, when data generated by an l-component multiexponential distribution are fitted by l+1 components, Xi(R) corresponds to an infinite set of points in parameter space. The distribution of DeltaLL is a mixture of two components, one identically zero, the other approximated by a Gamma-distribution. This empirical distribution of DeltaLL, assuming Xi(R), allows construction of a valid log-likelihood ratio test. The log-likelihood ratio test, the Akaike information criterion, and the Schwarz criterion all produce asymmetrical Type I and II errors and inefficiently recognize Xi, when true, from short datasets. A new decision strategy, which considers both the parameter estimates and DeltaLL, yields more symmetrical errors and a larger discrimination power for small n. These observations are explained by the distributions of DeltaLL when Xi or Xi(R) is true.

Allosteric modulation of ion channels: the case of maxi-K

Maxi-K channel gating is modulated by both membrane voltage and cytoplasmic Ca2+. Recent work has led to a quantitative understanding of this dual regulatory mechanism, derived from classical allosteric principles, in terms of the energetic coupling among membrane voltage, Ca2+ binding, and opening of the channel's gate. Our new understanding of the gating pathway can be applied to the interpretation of mutagenesis experiments and may serve as an example in the analysis of other dually regulated signaling molecules.

Ca(2+)- and voltage-dependent gating of Ca(2+)- and ATP-sensitive cationic channels in brain capillary endothelium

Biophysical properties of the Ca(2+)-activated nonselective cation channel expressed in brain capillaries were studied in inside-out patches from primary cultures of rat brain microvascular endothelial cells. At -40 mV membrane potential, open probability (P(o)) was activated by cytosolic [Ca(2+)] > 1 micro M and was half-maximal at approximately 20 micro M. Increasing [Ca(2+)] stimulated opening rate with little effect on closing rate. At constant [Ca(2+)], P(o) was voltage-dependent, and effective gating charge corresponded to 0.6 +/- 0.1 unitary charges. Depolarization accelerated opening and slowed closing, thereby increasing apparent affinity for Ca(2+). Within approximately 1 min of excision, P(o) declined to a lower steady state with decreased sensitivity toward activating Ca(2+) when studied at a fixed voltage, and toward activating voltage when studied at a fixed [Ca(2+)]. Deactivated channels opened approximately 5-fold slower and closed approximately 10-fold faster. The sulfhydryl-reducing agent dithiotreitol (1 mM) completely reversed acceleration of closing rate but failed to recover opening rate. Single-channel gating was complex; distributions of open and closed dwell times contained at least four and five exponential components, respectively. The longest component of the closed-time distribution was markedly sensitive to both [Ca(2+)] and voltage. We conclude that the biophysical properties of gating of this channel are remarkably similar to those of large-conductance Ca(2+)-activated K(+) channels.

Capsaicin activation of the pain receptor, VR1: multiple open states from both partial and full binding

Capsaicin, the pungent ingredient of hot peppers, has long been used to identify nociceptors. Its molecular target, the vanilloid receptor VR1, was recently cloned and confirmed functionally as a polymodal detector of multiple pain stimuli: heat, acid, and vanilloids. Previous electrophysiology studies have focused on whole-cell characteristics of the receptor. Here, we provide the first in-depth single-channel kinetic study of VR1 to understand its activation mechanism. At low to medium concentrations, channel activity appeared as bursts. Not only did the durations of the interburst gaps vary with capsaicin, the bursts also appeared ligand-dependent, with high capsaicin prolonging bursts and stabilizing openings. Gating involved at least five closed and three open states, with strong correlations between short closures and long openings, and long closures and short openings. Increasing capsaicin reduced the long closures with little effect on short ones. The open time constants changed little with capsaicin concentration, though their relative proportions varied. These results suggest that 1), the channel contains multiple capsaicin binding sites; 2), both partial and full binding are capable of opening the channel; 3), when activated, multiple open states are accessible irrespective of the level of binding; and 4), capsaicin association occurs preferentially to the closed channel.

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.

Gating and conductance properties of BK channels are modulated by the S9-S10 tail domain of the alpha subunit. A study of mSlo1 and mSlo3 wild-type and chimeric channels

The COOH-terminal S9-S10 tail domain of large conductance Ca(2+)-activated K(+) (BK) channels is a major determinant of Ca(2+) sensitivity (Schreiber, M., A. Wei, A. Yuan, J. Gaut, M. Saito, and L. Salkoff. 1999. Nat. Neurosci. 2:416-421). To investigate whether the tail domain also modulates Ca(2+)-independent properties of BK channels, we explored the functional differences between the BK channel mSlo1 and another member of the Slo family, mSlo3 (Schreiber, M., A. Yuan, and L. Salkoff. 1998. J. Biol. Chem. 273:3509-3516). Compared with mSlo1 channels, mSlo3 channels showed little Ca(2+) sensitivity, and the mean open time, burst duration, gaps between bursts, and single-channel conductance of mSlo3 channels were only 32, 22, 41, and 37% of that for mSlo1 channels, respectively. To examine which channel properties arise from the tail domain, we coexpressed the core of mSlo1 with either the tail domain of mSlo1 or the tail domain of mSlo3 channels, and studied the single-channel currents. Replacing the mSlo1 tail with the mSlo3 tail resulted in the following: increased open probability in the absence of Ca(2+); reduced the Ca(2+) sensitivity greatly by allowing only partial activation by Ca(2+) and by reducing the Hill coefficient for Ca(2+) activation; decreased the voltage dependence approximately 28%; decreased the mean open time two- to threefold; decreased the mean burst duration three- to ninefold; decreased the single-channel conductance approximately 14%; decreased the K(d) for block by TEA(i) approximately 30%; did not change the minimal numbers of three to four open and five to seven closed states entered during gating; and did not change the major features of the dependency between adjacent interval durations. These observations support a modular construction of the BK channel in which the tail domain modulates the gating kinetics and conductance properties of the voltage-dependent core domain, in addition to determining most of the high affinity Ca(2+) sensitivity.

Two-dimensional kinetic analysis suggests nonsequential gating of mechanosensitive channels in Xenopus oocytes

Xenopus oocytes express mechanosensitive (MS(XO)) channels that can be studied in excised patches of membrane with the patch-clamp technique. This study examines the steady-state kinetic gating properties of MS(XO) channels using detailed single-channel analysis. The open and closed one-dimensional dwell-time distributions were described by the sums of 2-3 open and 5-7 closed exponential components, respectively, indicating that the channels enter at least 2-3 open and 5-7 closed kinetic states during gating. Dependency plots revealed that the durations of adjacent open and closed intervals were correlated, indicating two or more gateway states in the gating mechanism for MS channels. Maximum likelihood fitting of two-dimensional dwell-time distributions to both generic and specific models was used to examine gating mechanism and rank models. A kinetic scheme with five closed and five open states, in which each closed state could make a direct transition to an open state (two-tiered model) could account for the major features of the single-channel data. Two-tiered models that allowed direct transitions to subconductance open states in addition to the fully open state were also consistent with multiple gateway states. Thus, the gating mechanism of MS(XO) channels differs from the sequential (linear) gating mechanisms considered for MS channels in bacteria, chick skeletal muscle, and Necturus proximal tubule.

Oxidative regulation of large conductance calcium-activated potassium channels

Reactive oxygen/nitrogen species are readily generated in vivo, playing roles in many physiological and pathological conditions, such as Alzheimer's disease and Parkinson's disease, by oxidatively modifying various proteins. Previous studies indicate that large conductance Ca(2+)-activated K(+) channels (BK(Ca) or Slo) are subject to redox regulation. However, conflicting results exist whether oxidation increases or decreases the channel activity. We used chloramine-T, which preferentially oxidizes methionine, to examine the functional consequences of methionine oxidation in the cloned human Slo (hSlo) channel expressed in mammalian cells. In the virtual absence of Ca(2+), the oxidant shifted the steady-state macroscopic conductance to a more negative direction and slowed deactivation. The results obtained suggest that oxidation enhances specific voltage-dependent opening transitions and slows the rate-limiting closing transition. Enhancement of the hSlo activity was partially reversed by the enzyme peptide methionine sulfoxide reductase, suggesting that the upregulation is mediated by methionine oxidation. In contrast, hydrogen peroxide and cysteine-specific reagents, DTNB, MTSEA, and PCMB, decreased the channel activity. Chloramine-T was much less effective when concurrently applied with the K(+) channel blocker TEA, which is consistent with the possibility that the target methionine lies within the channel pore. Regulation of the Slo channel by methionine oxidation may represent an important link between cellular electrical excitability and metabolism.

Role of the beta1 subunit in large-conductance Ca(2+)-activated K(+) channel gating energetics. Mechanisms of enhanced Ca(2+) sensitivity

Over the past few years, it has become clear that an important mechanism by which large-conductance Ca(2+)-activated K(+) channel (BK(Ca)) activity is regulated is the tissue-specific expression of auxiliary beta subunits. The first of these to be identified, beta1, is expressed predominately in smooth muscle and causes dramatic effects, increasing the apparent affinity of the channel for Ca(2+) 10-fold at 0 mV, and shifting the range of voltages over which the channel activates -80 mV at 9.1 microM Ca(2+). With this study, we address the question: which aspects of BK(Ca) gating are altered by beta1 to bring about these effects: Ca(2+) binding, voltage sensing, or the intrinsic energetics of channel opening? The approach we have taken is to express the beta1 subunit together with the BK(Ca) alpha subunit in Xenopus oocytes, and then to compare beta1's steady state effects over a wide range of Ca(2+) concentrations and membrane voltages to those predicted by allosteric models whose parameters have been altered to mimic changes in the aspects of gating listed above. The results of our analysis suggest that much of beta1's steady state effects can be accounted for by a reduction in the intrinsic energy the channel must overcome to open and a decrease in its voltage sensitivity, with little change in the affinity of the channel for Ca(2+) when it is either open or closed. Interestingly, however, the small changes in Ca(2+) binding affinity suggested by our analysis (K(c) 7.4 microM --> 9.6 microM; K(o) = 0.80 microM --> 0.65 microM) do appear to be functionally important. We also show that beta1 affects the mSlo conductance-voltage relation in the essential absence of Ca(2+), shifting it +20 mV and reducing its apparent gating charge 38%, and we develop methods for distinguishing between alterations in Ca(2+) binding and other aspects of BK(Ca) channel gating that may be of general use.

Voltage and Ca2+ activation of single large-conductance Ca2+-activated K+ channels described by a two-tiered allosteric gating mechanism

The voltage- and Ca2+-dependent gating mechanism of large-conductance Ca2+-activated K+ (BK) channels from cultured rat skeletal muscle was studied using single-channel analysis. Channel open probability (Po) increased with depolarization, as determined by limiting slope measurements (11 mV per e-fold change in Po; effective gating charge, q(eff), of 2.3 +/- 0.6 e(o)). Estimates of q(eff) were little changed for intracellular Ca2+ (Ca2+(i)) ranging from 0.0003 to 1,024 microM. Increasing Ca2+(i) from 0.03 to 1,024 microM shifted the voltage for half maximal activation (V(1/2)) 175 mV in the hyperpolarizing direction. V(1/2) was independent of Ca2+(i) for Ca2+(i) < or = 0.03 microM, indicating that the channel can be activated in the absence of Ca2+(i). Open and closed dwell-time distributions for data obtained at different Ca2+(i) and voltage, but at the same Po, were different, indicating that the major action of voltage is not through concentrating Ca2+ at the binding sites. The voltage dependence of Po arose from a decrease in the mean closing rate with depolarization (q(eff) = -0.5 e(o)) and an increase in the mean opening rate (q(eff) = 1.8 e(o)), consistent with voltage-dependent steps in both the activation and deactivation pathways. A 50-state two-tiered model with separate voltage- and Ca2+-dependent steps was consistent with the major features of the voltage and Ca2+ dependence of the single-channel kinetics over wide ranges of Ca2+(i) (approximately 0 through 1,024 microM), voltage (+80 to -80 mV), and Po (10(-4) to 0.96). In the model, the voltage dependence of the gating arises mainly from voltage-dependent transitions between closed (C-C) and open (O-O) states, with less voltage dependence for transitions between open and closed states (C-O), and with no voltage dependence for Ca2+-binding and unbinding. The two-tiered model can serve as a working hypothesis for the Ca2+- and voltage-dependent gating of the BK channel.

Functional coupling of the beta(1) subunit to the large conductance Ca(2+)-activated K(+) channel in the absence of Ca(2+). Increased Ca(2+) sensitivity from a Ca(2+)-independent mechanism

Coexpression of the beta(1) subunit with the alpha subunit (mSlo) of BK channels increases the apparent Ca(2+) sensitivity of the channel. This study investigates whether the mechanism underlying the increased Ca(2+) sensitivity requires Ca(2+), by comparing the gating in 0 Ca(2+)(i) of BK channels composed of alpha subunits to those composed of alpha+beta(1) subunits. The beta(1) subunit increased burst duration approximately 20-fold and the duration of gaps between bursts approximately 3-fold, giving an approximately 10-fold increase in open probability (P(o)) in 0 Ca(2+)(i). The effect of the beta(1) subunit on increasing burst duration was little changed over a wide range of P(o) achieved by varying either Ca(2+)(i) or depolarization. The effect of the beta(1) subunit on increasing the durations of the gaps between bursts in 0 Ca(2+)(i) was preserved over a range of voltage, but was switched off as Ca(2+)(i) was increased into the activation range. The Ca(2+)-independent, beta(1) subunit-induced increase in burst duration accounted for 80% of the leftward shift in the P(o) vs. Ca(2+)(i) curve that reflects the increased Ca(2+) sensitivity induced by the beta(1) subunit. The Ca(2+)-dependent effect of the beta(1) subunit on the gaps between bursts accounted for the remaining 20% of the leftward shift. Our observation that the major effects of the beta(1) subunit are independent of Ca(2+)(i) suggests that the beta(1) subunit mainly alters the energy barriers of Ca(2+)-independent transitions. The changes in gating induced by the beta(1) subunit differ from those induced by depolarization, as increasing P(o) by depolarization or by the beta(1) subunit gave different gating kinetics. The complex gating kinetics for both alpha and alpha+beta(1) channels in 0 Ca(2+)(i) arise from transitions among two to three open and three to five closed states and are inconsistent with Monod-Wyman-Changeux type models, which predict gating among only one open and one closed state in 0 Ca(2+)(i).

Kinetic, mechanistic, and structural aspects of unliganded gating of acetylcholine receptor channels: a single-channel study of second transmembrane segment 12' mutants

The spontaneous activity of adult mouse muscle acetylcholine receptor channels, transiently expressed in HEK-293 cells, was studied with the patch-clamp technique. To increase the frequency of unliganded openings, mutations at the 12' position of the second transmembrane segment were engineered. Our results indicate that: (a) in both wild type and mutants, a C <--> O kinetic scheme provides a good description of spontaneous gating. In the case of some mutant constructs, however, additional states were needed to improve the fit to the data. Similar additional states were also needed in one of six patches containing wild-type acetylcholine receptor channels; (b) the delta12' residue makes a more pronounced contribution to unliganded gating than the homologous residues of the alpha, beta, and straightepsilon subunits; (c) combinations of second transmembrane segment 12' mutations in the four different subunits appear to have cumulative effects; (d) the volume of the side chain at delta12' is relevant because residues larger than the wild-type Ser increase spontaneous gating; (e) the voltage dependence of the unliganded gating equilibrium constant is the same as that of diliganded gating, but the voltage dependences of the opening and closing rate constants are opposite (this indicates that the reaction pathway connecting the closed and open states of the receptor changes upon ligation); (f) engineering binding-site mutations that decrease diliganded gating (alphaY93F, alphaY190W, and alphaD200N) reduces spontaneous activity as well (this suggests that even in the absence of ligand the opening of the channel is accompanied by a conformational change at the binding sites); and (g) the diliganded gating equilibrium constant is also increased by the 12' mutations. Such increase is independent of the particular ligand used as the agonist, which suggests that these mutations affect mostly the isomerization step, having little, if any, effect on the ligand-affinity ratio.