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

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.

Hypoxia, Ion Channels and Glioblastoma Malignancy

The malignancy of glioblastoma (GBM), the most aggressive type of human brain tumor, strongly correlates with the presence of hypoxic areas within the tumor mass. Oxygen levels have been shown to control several critical aspects of tumor aggressiveness, such as migration/invasion and cell death resistance, but the underlying mechanisms are still unclear. GBM cells express abundant K+ and Cl- channels, whose activity supports cell volume and membrane potential changes, critical for cell proliferation, migration and death. Volume-regulated anion channels (VRAC), which mediate the swelling-activated Cl- current, and the large-conductance Ca2+-activated K+ channels (BK) are both functionally upregulated in GBM cells, where they control different aspects underlying GBM malignancy/aggressiveness. The functional expression/activity of both VRAC and BK channels are under the control of the oxygen levels, and these regulations are involved in the hypoxia-induced GBM cell aggressiveness. The present review will provide a comprehensive overview of the literature supporting the role of these two channels in the hypoxia-mediated GBM malignancy, suggesting them as potential therapeutic targets in the treatment of GBM.

Modeling Synaptic Integration of Bursty and β Oscillatory Inputs in Ventromedial Motor Thalamic Neurons in Normal and Parkinsonian States

The ventromedial motor thalamus (VM) is implicated in multiple motor functions and occupies a central position in the cortico-basal ganglia-thalamocortical loop. It integrates glutamatergic inputs from motor cortex (MC) and motor-related subcortical areas, and it is a major recipient of inhibition from basal ganglia. Previous in vitro experiments performed in mice showed that dopamine depletion enhances the excitability of thalamocortical (TC) neurons in VM due to reduced M-type potassium currents. To understand how these excitability changes impact synaptic integration in vivo, we constructed biophysically detailed mouse VM TC model neurons fit to normal and dopamine-depleted conditions, using the NEURON simulator. These models allowed us to assess the influence of excitability changes with dopamine depletion on the integration of synaptic inputs expected in vivo We found that VM neuron models in the dopamine-depleted state showed increased firing rates with the same synaptic inputs. Synchronous bursting in inhibitory input from the substantia nigra pars reticulata (SNR), as observed in parkinsonian conditions, evoked a postinhibitory firing rate increase with a longer duration in dopamine-depleted than control conditions, due to different M-type potassium channel densities. With β oscillations in the inhibitory inputs from SNR and the excitatory inputs from cortex, we observed spike-phase locking in the activity of the models in normal and dopamine-depleted states, which relayed and amplified the oscillations of the inputs, suggesting that the increased β oscillations observed in VM of parkinsonian animals are predominantly a consequence of changes in the presynaptic activity rather than changes in intrinsic properties.

BK channels of five different subunit combinations underlie the de novo KCNMA1 G375R channelopathy

The molecular basis of a severe developmental and neurological disorder associated with a de novo G375R variant of the tetrameric BK channel is unknown. Here, we address this question by recording from single BK channels expressed to mimic a G375R mutation heterozygous with a WT allele. Five different types of functional BK channels were expressed: 3% were consistent with WT, 12% with homotetrameric mutant, and 85% with three different types of hybrid (heterotetrameric) channels assembled from both mutant and WT subunits. All channel types except WT showed a marked gain-of-function in voltage activation and a smaller decrease-of-function in single-channel conductance, with both changes in function becoming more pronounced as the number of mutant subunits per tetrameric channel increased. The net cellular response from the five different types of channels comprising the molecular phenotype was a shift of -120 mV in the voltage required to activate half of the maximal current through BK channels, giving a net gain-of-function. The WT and homotetrameric mutant channels in the molecular phenotype were consistent with genetic codominance as each displayed properties of a channel arising from only one of the two alleles. The three types of hybrid channels in the molecular phenotype were consistent with partial dominance as their properties were intermediate between those of mutant and WT channels. A model in which BK channels randomly assemble from mutant and WT subunits, with each subunit contributing increments of activation and conductance, approximated the molecular phenotype of the heterozygous G375R mutation.

Ca2+- and Voltage-Activated K+ (BK) Channels in the Nervous System: One Gene, a Myriad of Physiological Functions

BK channels are large conductance potassium channels characterized by four pore-forming α subunits, often co-assembled with auxiliary β and γ subunits to regulate Ca2+ sensitivity, voltage dependence and gating properties. BK channels are abundantly expressed throughout the brain and in different compartments within a single neuron, including axons, synaptic terminals, dendritic arbors, and spines. Their activation produces a massive efflux of K+ ions that hyperpolarizes the cellular membrane. Together with their ability to detect changes in intracellular Ca2+ concentration, BK channels control neuronal excitability and synaptic communication through diverse mechanisms. Moreover, increasing evidence indicates that dysfunction of BK channel-mediated effects on neuronal excitability and synaptic function has been implicated in several neurological disorders, including epilepsy, fragile X syndrome, mental retardation, and autism, as well as in motor and cognitive behavior. Here, we discuss current evidence highlighting the physiological importance of this ubiquitous channel in regulating brain function and its role in the pathophysiology of different neurological disorders.

To what extent naringenin binding and membrane depolarization shape mitoBK channel gating—A machine learning approach

The large conductance voltage- and Ca2+-activated K+ channels from the inner mitochondrial membrane (mitoBK) are modulated by a number of factors. Among them flavanones, including naringenin (Nar), arise as a promising group of mitoBK channel regulators from a pharmacological point of view. It is well known that in the presence of Nar the open state probability (pop) of mitoBK channels significantly increases. Nevertheless, the molecular mechanism of the mitoBK-Nar interactions remains still unrevealed. It is also not known whether the effects of naringenin administration on conformational dynamics can resemble those which are exerted by the other channel-activating stimuli. In aim to answer this question, we examine whether the dwell-time series of mitoBK channels which were obtained at different voltages and Nar concentrations (yet allowing to reach comparable pops) are discernible by means of artificial intelligence methods, including k-NN and shapelet learning. The obtained results suggest that the structural complexity of the gating dynamics is shaped both by the interaction of channel gate with the voltage sensor (VSD) and the Nar-binding site. For a majority of data one can observe stimulus-specific patterns of channel gating. Shapelet algorithm allows to obtain better prediction accuracy in most cases. Probably, because it takes into account the complexity of local features of a given signal. About 30% of the analyzed time series do not sufficiently differ to unambiguously distinguish them from each other, which can be interpreted in terms of the existence of the common features of mitoBK channel gating regardless of the type of activating stimulus. There exist long-range mutual interactions between VSD and the Nar-coordination site that are responsible for higher levels of Nar-activation (Δpop) at deeply depolarized membranes. These intra-sensor interactions are anticipated to have an allosteric nature.

Molecular mechanism of BK channel activation by the smooth muscle relaxant NS11021

Large-conductance Ca²⁺-activated K⁺ channels (BK channels) are activated by cytosolic calcium and depolarized membrane potential under physiological conditions. Thus, these channels control electrical excitability in neurons and smooth muscle by gating K⁺ efflux and hyperpolarizing the membrane in response to Ca²⁺ signaling. Altered BK channel function has been linked to epilepsy, dyskinesia, and other neurological deficits in humans, making these channels a key target for drug therapies. To gain insight into mechanisms underlying pharmacological modulation of BK channel gating, here we studied mechanisms underlying activation of BK channels by the biarylthiourea derivative, NS11021, which acts as a smooth muscle relaxant. We observe that increasing NS11021 shifts the half-maximal activation voltage for BK channels toward more hyperpolarized voltages, in both the presence and nominal absence of Ca²⁺, suggesting that NS11021 facilitates BK channel activation primarily by a mechanism that is distinct from Ca²⁺ activation. 30 µM NS11021 slows the time course of BK channel deactivation at −200 mV by ∼10-fold compared with 0 µM NS11021, while having little effect on the time course of activation. This action is most pronounced at negative voltages, at which the BK channel voltage sensors are at rest. Single-channel kinetic analysis further shows that 30 µM NS11021 increases open probability by 62-fold and increases mean open time from 0.15 to 0.52 ms in the nominal absence of Ca²⁺ at voltages less than −60 mV, conditions in which BK voltage sensors are largely in the resting state. We could therefore account for the major activating effects of NS11021 by a scheme in which the drug primarily shifts the pore-gate equilibrium toward the open state.

State-dependent inhibition of BK channels by the opioid agonist loperamide

Large-conductance Ca²⁺-activated K⁺ (BK) channels control a range of physiological functions, and their dysfunction is linked to human disease. We have found that the widely used drug loperamide (LOP) can inhibit activity of BK channels composed of either α-subunits (BKα channels) or α-subunits plus the auxiliary γ1-subunit (BKα/γ1 channels), and here we analyze the molecular mechanism of LOP action. LOP applied at the cytosolic side of the membrane rapidly and reversibly inhibited BK current, an effect that appeared as a decay in voltage-activated BK currents. The apparent affinity for LOP decreased with hyperpolarization in a manner consistent with LOP behaving as an inhibitor of open, activated channels. Increasing LOP concentration reduced the half-maximal activation voltage, consistent with relative stabilization of the LOP-inhibited open state. Single-channel recordings revealed that LOP did not reduce unitary BK channel current, but instead decreased BK channel open probability and mean open times. LOP elicited use-dependent inhibition, in which trains of brief depolarizing steps lead to accumulated reduction of BK current, whereas single brief depolarizing steps do not. The principal effects of LOP on BK channel gating are described by a mechanism in which LOP acts as a state-dependent pore blocker. Our results suggest that therapeutic doses of LOP may act in part by inhibiting K⁺ efflux through intestinal BK channels.

BKCa Channel Activation Attenuates the Pathophysiological Progression of Monocrotaline-Induced Pulmonary Arterial Hypertension in Wistar Rats

PURPOSE

In the present study, the therapeutic efficacy of a selective BK_Ca channel opener (compound X) in the treatment of monocrotaline (MCT)-induced pulmonary arterial hypertension (PAH) was investigated.

METHODS

PAH was induced in male Wistar rats by a single injection of MCT. After two weeks, the MCT-treated group was divided into two groups that were either treated with compound X or vehicle. Compound X was administered daily at 28 mg/kg. Electrocardiographic, echocardiographic, and haemodynamic analyses were performed; ex vivo evaluations of pulmonary artery reactivity, right ventricle (RV) and lung histology as well as expression levels of α and β myosin heavy chain, brain natriuretic peptide, and cytokines (TNFα and IL10) in heart tissue were performed.

RESULTS

Pulmonary artery rings of the PAH group showed a lower vasodilatation response to acetylcholine, suggesting endothelial dysfunction. Compound X promoted strong vasodilation in pulmonary artery rings of both control and MCT-induced PAH rats. The untreated hypertensive rats presented remodelling of pulmonary arterioles associated with increased resistance to pulmonary flow; increased systolic pressure, hypertrophy and fibrosis of the RV; prolongation of the QT and T_peak-T_end intervals (evaluated during electrocardiogram); increased lung and liver weights; and autonomic imbalance with predominance of sympathetic activity. On the other hand, treatment with compound X reduced pulmonary vascular remodelling, pulmonary flow resistance and RV hypertrophy and afterload.

CONCLUSION

The use of a selective and potent opener to activate the BK_Ca channels promoted improvement of haemodynamic parameters and consequent prevention of RV maladaptive remodelling in rats with MCT-induced PAH.

KCa channel activation normalizes endothelial function in Type 2 Diabetic resistance arteries by improving intracellular Ca2+ mobilization

BACKGROUND

Endothelial dysfunction is an early pathogenic event in the progression of cardiovascular disease in patients with Type 2 Diabetes (T2D). Endothelial KCa2.3 and KCa3.1 K⁺ channels are important regulators of arterial diameter, and we thus hypothesized that SKA-31, a small molecule activator of KCa2.3 and KCa3.1, would positively influence agonist-evoked dilation in myogenically active resistance arteries in T2D.

METHODOLOGY

Arterial pressure myography was utilized to investigate endothelium-dependent vasodilation in isolated cremaster skeletal muscle resistance arteries from 22 to 24 week old T2D Goto-Kakizaki rats, age-matched Wistar controls, and small human intra-thoracic resistance arteries from T2D subjects. Agonist stimulated changes in cytosolic free Ca²⁺ in acutely isolated, single endothelial cells from Wistar and T2D Goto-Kakizaki cremaster and cerebral arteries were examined using Fura-2 fluorescence imaging.

MAIN FINDINGS

Endothelium-dependent vasodilation in response to acetylcholine (ACh) or bradykinin (BK) was significantly impaired in isolated cremaster arteries from T2D Goto-Kakizaki rats compared with Wistar controls, and similar results were observed in human intra-thoracic arteries. In contrast, inhibition of myogenic tone by sodium nitroprusside, a direct smooth muscle relaxant, was unaltered in both rat and human T2D arteries. Treatment with a threshold concentration of SKA-31 (0.3 μM) significantly enhanced vasodilatory responses to ACh and BK in arteries from T2D Goto-Kakizaki rats and human subjects, whereas only modest effects were observed in non-diabetic arteries of both species. Mechanistically, SKA-31 enhancement of evoked dilation was independent of vascular NO synthase and COX activities. Remarkably, SKA-31 treatment improved agonist-stimulated Ca²⁺ elevation in acutely isolated endothelial cells from T2D Goto-Kakizaki cremaster and cerebral arteries, but not from Wistar control vessels. In contrast, SKA-31 treatment did not affect intracellular Ca²⁺ release by the sarco/endoplasmic reticulum Ca²⁺-ATPase (SERCA) inhibitor cyclopiazonic acid.

CONCLUSIONS

Collectively, our data demonstrate that KCa channel modulation can acutely restore endothelium-dependent vasodilatory responses in T2D resistance arteries from rats and humans, which appears to involve improved endothelial Ca²⁺ mobilization.

Coupling of Ca2+ and voltage activation in BK channels through the αB helix/voltage sensor interface

Large-conductance Ca²⁺ and voltage-activated K⁺ (BK) channels control membrane excitability in many cell types. BK channels are tetrameric. Each subunit is composed of a voltage sensor domain (VSD), a central pore-gate domain, and a large cytoplasmic domain (CTD) that contains the Ca²⁺ sensors. While it is known that BK channels are activated by voltage and Ca²⁺, and that voltage and Ca²⁺ activations interact, less is known about the mechanisms involved. We explore here these mechanisms by examining the gating contribution of an interface formed between the VSDs and the αB helices located at the top of the CTDs. Proline mutations in the αB helix greatly decreased voltage activation while having negligible effects on gating currents. Analysis with the Horrigan, Cui, and Aldrich model indicated a decreased coupling between voltage sensors and pore gate. Proline mutations decreased Ca²⁺ activation for both Ca²⁺ bowl and RCK1 Ca²⁺ sites, suggesting that both high-affinity Ca²⁺ sites transduce their effect, at least in part, through the αB helix. Mg²⁺ activation also decreased. The crystal structure of the CTD with proline mutation L390P showed a flattening of the first helical turn in the αB helix compared to wild type, without other notable differences in the CTD, indicating that structural changes from the mutation were confined to the αB helix. These findings indicate that an intact αB helix/VSD interface is required for effective coupling of Ca²⁺ binding and voltage depolarization to pore opening and that shared Ca²⁺ and voltage transduction pathways involving the αB helix may be involved.

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.

Calcium-driven regulation of voltage-sensing domains in BK channels

Allosteric interactions between the voltage-sensing domain (VSD), the Ca²⁺-binding sites, and the pore domain govern the mammalian Ca²⁺- and voltage-activated K⁺ (BK) channel opening. However, the functional relevance of the crosstalk between the Ca²⁺- and voltage-sensing mechanisms on BK channel gating is still debated. We examined the energetic interaction between Ca²⁺ binding and VSD activation by investigating the effects of internal Ca²⁺ on BK channel gating currents. Our results indicate that Ca²⁺ sensor occupancy has a strong impact on VSD activation through a coordinated interaction mechanism in which Ca²⁺ binding to a single α-subunit affects all VSDs equally. Moreover, the two distinct high-affinity Ca²⁺-binding sites contained in the C-terminus domains, RCK1 and RCK2, contribute equally to decrease the free energy necessary to activate the VSD. We conclude that voltage-dependent gating and pore opening in BK channels is modulated to a great extent by the interaction between Ca²⁺ sensors and VSDs.

A computational model of large conductance voltage and calcium activated potassium channels: implications for calcium dynamics and electrophysiology in detrusor smooth muscle cells

The large conductance voltage and calcium activated potassium (BK) channels play a crucial role in regulating the excitability of detrusor smooth muscle, which lines the wall of the urinary bladder. These channels have been widely characterized in terms of their molecular structure, pharmacology and electrophysiology. They control the repolarising and hyperpolarising phases of the action potential, thereby regulating the firing frequency and contraction profiles of the smooth muscle. Several groups have reported varied profiles of BK currents and I-V curves under similar experimental conditions. However, no single computational model has been able to reconcile these apparent discrepancies. In view of the channels' physiological importance, it is imperative to understand their mechanistic underpinnings so that a realistic model can be created. This paper presents a computational model of the BK channel, based on the Hodgkin-Huxley formalism, constructed by utilising three activation processes - membrane potential, calcium inflow from voltage-gated calcium channels on the membrane and calcium released from the ryanodine receptors present on the sarcoplasmic reticulum. In our model, we attribute the discrepant profiles to the underlying cytosolic calcium received by the channel during its activation. The model enables us to make heuristic predictions regarding the nature of the sub-membrane calcium dynamics underlying the BK channel's activation. We have employed the model to reproduce various physiological characteristics of the channel and found the simulated responses to be in accordance with the experimental findings. Additionally, we have used the model to investigate the role of this channel in electrophysiological signals, such as the action potential and spontaneous transient hyperpolarisations. Furthermore, the clinical effects of BK channel openers, mallotoxin and NS19504, were simulated for the detrusor smooth muscle cells. Our findings support the proposed application of these drugs for amelioration of the condition of overactive bladder. We thus propose a physiologically realistic BK channel model which can be integrated with other biophysical mechanisms such as ion channels, pumps and exchangers to further elucidate its micro-domain interaction with the intracellular calcium environment.

Molecular determinants of Ca2+ sensitivity at the intersubunit interface of the BK channel gating ring

The large-conductance calcium-activated K⁺ (BK) channel contains two intracellular tandem Ca²⁺-sensing RCK domains (RCK1 and RCK2), which tetramerize into a Ca²⁺ gating ring that regulates channel opening by conformational expansion in response to Ca²⁺ binding. Interestingly, the gating ring’s intersubunit assembly interface harbors the RCK2 Ca²⁺-binding site, known as the Ca²⁺ bowl. The gating ring’s assembly interface is made in part by intersubunit coordination of a Ca²⁺ ion between the Ca²⁺ bowl and an RCK1 Asn residue, N449, and by apparent intersubunit electrostatic interactions between E955 in RCK2 and R786 and R790 in the RCK2 of the adjacent subunit. To understand the role of the intersubunit assembly interface in Ca²⁺ gating, we performed mutational analyses of these putative interacting residues in human BK channels. We found that N449, despite its role in Ca²⁺ coordination, does not set the channel’s Ca²⁺ sensitivity, whereas E955 is a determinant of Ca²⁺ sensitivity, likely through intersubunit electrostatic interactions. Our findings provide evidence that the intersubunit assembly interface contains molecular determinants of Ca²⁺-sensitivity in BK channels.

Estimating kinetic mechanisms with prior knowledge I: Linear parameter constraints

New mathematical tools are needed to incorporate existing knowledge into kinetic models of ion channels and other proteins. Salari et al. describe an algebraic transformation that can enforce linearly interdependent parameters into kinetic models in order to test new hypotheses.

To understand how ion channels and other proteins function at the molecular and cellular levels, one must decrypt their kinetic mechanisms. Sophisticated algorithms have been developed that can be used to extract kinetic parameters from a variety of experimental data types. However, formulating models that not only explain new data, but are also consistent with existing knowledge, remains a challenge. Here, we present a two-part study describing a mathematical and computational formalism that can be used to enforce prior knowledge into the model using constraints. In this first part, we focus on constraints that enforce explicit linear relationships involving rate constants or other model parameters. We develop a simple, linear algebra–based transformation that can be applied to enforce many types of model properties and assumptions, such as microscopic reversibility, allosteric gating, and equality and inequality parameter relationships. This transformation converts the set of linearly interdependent model parameters into a reduced set of independent parameters, which can be passed to an automated search engine for model optimization. In the companion article, we introduce a complementary method that can be used to enforce arbitrary parameter relationships and any constraints that quantify the behavior of the model under certain conditions. The procedures described in this study can, in principle, be coupled to any of the existing methods for solving molecular kinetics for ion channels or other proteins. These concepts can be used not only to enforce existing knowledge but also to formulate and test new hypotheses.

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.

Threading the biophysics of mammalian Slo1 channels onto structures of an invertebrate Slo1 channel

Zhou et al. consider the biophysics of large-conductance Ca²⁺-activated Slo1 channels in the context of Aplysia Slo1 structures.

For those interested in the machinery of ion channel gating, the Ca²⁺ and voltage-activated BK K⁺ channel provides a compelling topic for investigation, by virtue of its dual allosteric regulation by both voltage and intracellular Ca²⁺ and because its large-single channel conductance facilitates detailed kinetic analysis. Over the years, biophysical analyses have illuminated details of the allosteric regulation of BK channels and revealed insights into the mechanism of BK gating, e.g., inner cavity size and accessibility and voltage sensor-pore coupling. Now the publication of two structures of an Aplysia californica BK channel—one liganded and one metal free—promises to reinvigorate functional studies and interpretation of biophysical results. The new structures confirm some of the previous functional inferences but also suggest new perspectives regarding cooperativity between Ca²⁺-binding sites and the relationship between voltage- and Ca²⁺-dependent gating. Here we consider the extent to which the two structures explain previous functional data on pore-domain properties, voltage-sensor motions, and divalent cation binding and activation of the channel.

JMV5656, A Novel Derivative of TLQP-21, Triggers the Activation of a Calcium-Dependent Potassium Outward Current in Microglial Cells

TLQP-21 (TLQPPASSRRRHFHHALPPAR) is a multifunctional peptide that is involved in the control of physiological functions, including feeding, reproduction, stress responsiveness, and general homeostasis. Despite the huge interest in TLQP-21 biological activity, very little is known about its intracellular mechanisms of action. In microglial cells, TLQP-21 stimulates increases of intracellular Ca²⁺ that may activate functions, including proliferation, migration, phagocytosis and production of inflammatory molecules. Our aim was to investigate whether JMV5656 (RRRHFHHALPPAR), a novel short analogue of TLQP-21, stimulates intracellular Ca²⁺ in the N9 microglia cells, and whether this Ca²⁺ elevation is coupled with the activation Ca²⁺-sensitive K⁺ channels. TLQP-21 and JMV5656 induced a sharp, dose-dependent increment in intracellular calcium. In 77% of cells, JMV5656 also caused an increase in the total outward currents, which was blunted by TEA (tetraethyl ammonium chloride), a non-selective blocker of voltage-dependent and Ca²⁺-activated potassium (K⁺) channels. Moreover, the effects of ion channel blockers charybdotoxin and iberiotoxin, suggested that multiple calcium-activated K⁺ channel types drove the outward current stimulated by JMV5656. Additionally, inhibition of JMV5656-stimulated outward currents by NS6180 (4-[[3-(trifluoromethyl)phenyl]methyl]-2H-1,4 benzothiazin-3(4H)-one) and TRAM-34 (triarylmethane-34), indicated that K_Ca3.1 channels are involved in this JMV5656 mechanisms of action. In summary, we demonstrate that, in N9 microglia cells, the interaction of JMV5656 with the TLQP-21 receptors induced an increase in intracellular Ca²⁺, and, following extracellular Ca²⁺ entry, the opening of K_Ca3.1 channels.

Emergence of ion channel modal gating from independent subunit kinetics

Many ion channels exhibit a slow stochastic switching between distinct modes of gating activity. This feature of channel behavior has pronounced implications for the dynamics of ionic currents and the signaling pathways that they regulate. A canonical example is the inositol 1,4,5-trisphosphate receptor (IP3R) channel, whose regulation of intracellular Ca(2+) concentration is essential for numerous cellular processes. However, the underlying biophysical mechanisms that give rise to modal gating in this and most other channels remain unknown. Although ion channels are composed of protein subunits, previous mathematical models of modal gating are coarse grained at the level of whole-channel states, limiting further dialogue between theory and experiment. Here we propose an origin for modal gating, by modeling the kinetics of ligand binding and conformational change in the IP3R at the subunit level. We find good agreement with experimental data over a wide range of ligand concentrations, accounting for equilibrium channel properties, transient responses to changing ligand conditions, and modal gating statistics. We show how this can be understood within a simple analytical framework and confirm our results with stochastic simulations. The model assumes that channel subunits are independent, demonstrating that cooperative binding or concerted conformational changes are not required for modal gating. Moreover, the model embodies a generally applicable principle: If a timescale separation exists in the kinetics of individual subunits, then modal gating can arise as an emergent property of channel behavior.

Modeling a Ca(2+) channel/BKCa channel complex at the single-complex level

BKCa-channel activity often affects the firing properties of neurons, the shapes of neuronal action potentials (APs), and in some cases the extent of neurotransmitter release. It has become clear that BKCa channels often form complexes with voltage-gated Ca(2+) channels (CaV channels) such that when a CaV channel is activated, the ensuing influx of Ca(2+) activates its closely associated BKCa channel. Thus, in modeling the electrical properties of neurons, it would be useful to have quantitative models of CaV/BKCa complexes. Furthermore, in a population of CaV/BKCa complexes, all BKCa channels are not exposed to the same Ca(2+) concentration at the same time. Thus, stochastic rather than deterministic models are required. To date, however, no such models have been described. Here, however, I present a stochastic model of a CaV2.1/BKCa(α-only) complex, as might be found in a central nerve terminal. The CaV2.1/BKCa model is based on kinetic modeling of its two component channels at physiological temperature. Surprisingly, The CaV2.1/BKCa model predicts that although the CaV channel will open nearly every time during a typical cortical AP, its associated BKCa channel is expected to open in only 30% of trials, and this percentage is very sensitive to the duration of the AP, the distance between the two channels in the complex, and the presence of fast internal Ca(2+) buffers. Also, the model predicts that the kinetics of the BKCa currents of a population of CaV2.1/BKCa complexes will not be limited by the kinetics of the CaV2.1 channel, and during a train of APs, the current response of the complex is expected to faithfully follow even very rapid trains. Aside from providing insight into how these complexes are likely to behave in vivo, the models presented here could also be of use more generally as components of higher-level models of neural function.

Modulation of BK Channels by Small Endogenous Molecules and Pharmaceutical Channel Openers

Voltage- and Ca(2+)-activated K(+) channels of big conductance (BK channels) are abundantly found in various organs and their relevance for smooth muscle tone and neuronal signaling is well documented. Dysfunction of BK channels is implicated in an array of human diseases involving many organs including the nervous, pulmonary, cardiovascular, renal, and urinary systems. In humans a single gene (KCNMA1) encodes the pore-forming α subunit (Slo1) of BK channels, but the channel properties are variable because of alternative splicing, tissue- and subcellular-specific auxiliary subunits (β, γ), posttranslational modifications, and a multitude of endogenous signaling molecules directly affecting the channel function. Initiatives to develop drugs capable of activating BK channels (channel openers) therefore need to consider the tissue-specific variability of BK channel structure and the potential interference with endogenously produced regulatory factors. The atomic structural basis of BK channel function is only beginning to be revealed. However, building on detailed knowledge of BK channel function, including its single-channel characteristics, voltage- and Ca(2+) dependence of channel gating, and modulation by diffusible messengers, a multi-tier allosteric model of BK channel gating (Horrigan and Aldrich (HA) model) has become a valuable tool in studying modulation of the channel. Using the conceptual framework of the HA model, we here review the functional impact of endogenous modulatory factors and select small synthetic compounds that regulate BK channel activity. Furthermore, we devise experimental approaches for studying BK channel-drug interactions with the aim to classify BK-modulating substances according to their molecular mode of action.

Biophysics of BK Channel Gating

BK channels are universal regulators of cell excitability, given their exceptional unitary conductance selective for K(+), joint activation mechanism by membrane depolarization and intracellular [Ca(2+)] elevation, and broad expression pattern. In this chapter, we discuss the structural basis and operational principles of their activation, or gating, by membrane potential and calcium. We also discuss how the two activation mechanisms interact to culminate in channel opening. As members of the voltage-gated potassium channel superfamily, BK channels are discussed in the context of archetypal family members, in terms of similarities that help us understand their function, but also seminal structural and biophysical differences that confer unique functional properties.

Analyzing single-molecule time series via nonparametric Bayesian inference

The ability to measure the properties of proteins at the single-molecule level offers an unparalleled glimpse into biological systems at the molecular scale. The interpretation of single-molecule time series has often been rooted in statistical mechanics and the theory of Markov processes. While existing analysis methods have been useful, they are not without significant limitations including problems of model selection and parameter nonidentifiability. To address these challenges, we introduce the use of nonparametric Bayesian inference for the analysis of single-molecule time series. These methods provide a flexible way to extract structure from data instead of assuming models beforehand. We demonstrate these methods with applications to several diverse settings in single-molecule biophysics. This approach provides a well-constrained and rigorously grounded method for determining the number of biophysical states underlying single-molecule data.

BK channels: multiple sensors, one activation gate

Ion transport across cell membranes is essential to cell communication and signaling. Passive ion transport is mediated by ion channels, membrane proteins that create ion conducting pores across cell membrane to allow ion flux down electrochemical gradient. Under physiological conditions, majority of ion channel pores are not constitutively open. Instead, structural region(s) within these pores breaks the continuity of the aqueous ion pathway, thereby serves as activation gate(s) to control ions flow in and out. To achieve spatially and temporally regulated ion flux in cells, many ion channels have evolved sensors to detect various environmental stimuli or the metabolic states of the cell and trigger global conformational changes, thereby dynamically operate the opening and closing of their activation gate. The sensors of ion channels can be broadly categorized as chemical sensors and physical sensors to respond to chemical (such as neural transmitters, nucleotides and ions) and physical (such as voltage, mechanical force and temperature) signals, respectively. With the rapidly growing structural and functional information of different types of ion channels, it is now critical to understand how ion channel sensors dynamically control their gates at molecular and atomic level. The voltage and Ca²⁺ activated BK channels, a K⁺ channel with an electrical sensor and multiple chemical sensors, provide a unique model system for us to understand how physical and chemical energy synergistically operate its activation gate.

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.

Temperature and voltage coupling to channel opening in transient receptor potential melastatin 8 (TRPM8)

Expressed in somatosensory neurons of the dorsal root and trigeminal ganglion, the transient receptor potential melastatin 8 (TRPM8) channel is a Ca(2+)-permeable cation channel activated by cold, voltage, phosphatidylinositol 4,5-bisphosphate, and menthol. Although TRPM8 channel gating has been characterized at the single channel and macroscopic current levels, there is currently no consensus regarding the extent to which temperature and voltage sensors couple to the conduction gate. In this study, we extended the range of voltages where TRPM8-induced ionic currents were measured and made careful measurements of the maximum open probability the channel can attain at different temperatures by means of fluctuation analysis. The first direct measurements of TRPM8 channel temperature-driven conformational rearrangements provided here suggest that temperature alone is able to open the channel and that the opening reaction is voltage-independent. Voltage is a partial activator of TRPM8 channels, because absolute open probability values measured with fully activated voltage sensors are less than 1, and they decrease as temperature rises. By unveiling the fast temperature-dependent deactivation process, we show that TRPM8 channel deactivation is well described by a double exponential time course. The fast and slow deactivation processes are temperature-dependent with enthalpy changes of 27.2 and 30.8 kcal mol(-1). The overall Q10 for the closing reaction is about 33. A three-tiered allosteric model containing four voltage sensors and four temperature sensors can account for the complex deactivation kinetics and coupling between voltage and temperature sensor activation and channel opening.

Modeling ion channels: past, present, and future

Ion channels are membrane-bound enzymes whose catalytic sites are ion-conducting pores that open and close (gate) in response to specific environmental stimuli. Ion channels are important contributors to cell signaling and homeostasis. Our current understanding of gating is the product of 60 plus years of voltage-clamp recording augmented by intervention in the form of environmental, chemical, and mutational perturbations. The need for good phenomenological models of gating has evolved in parallel with the sophistication of experimental technique. The goal of modeling is to develop realistic schemes that not only describe data, but also accurately reflect mechanisms of action. This review covers three areas that have contributed to the understanding of ion channels: traditional Eyring kinetic theory, molecular dynamics analysis, and statistical thermodynamics. Although the primary emphasis is on voltage-dependent channels, the methods discussed here are easily generalized to other stimuli and could be applied to any ion channel and indeed any macromolecule.

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.

SOLVING ION CHANNEL KINETICS WITH THE QuB SOFTWARE

The ability to record the currents from single ion channels led to the need to extract the underlying kinetic model from such data. This inverse hidden Markov problem is difficult but led to the creation of a software suite called QuB utilizing likelihood optimization. This review presents the software. The software is open source and, in addition to solving kinetic models, has many generic database operations including report generation with publishable graphics, function fitting and scripting for new and repeated processing and AD/DA I/O. The core algorithms allow for constraints such as fixed rates or maintaining detailed balance in the model. All rate constants can be driven by a stimulus and the system can analyze nonstationary data. QuB also can analyze the kinetics of multichannel data where individual events cannot be discriminated, but the fitting algorithms utilize the signal variance as well as the mean to fit models. QuB can be applied to any data appropriately modeled with Markov kinetics and has been utilized to solve ion channels but also the movement of motor proteins, the sleep cycles in mice, and physics processes.

[Formula: see text]Special Issue Comment: This is a review about the software QuB that can extract a model from the trajectory. It is connected with the review about treatments when solving single molecules,60 and the reviews about enzymes.61,62

Exponential sum-fitting of dwell-time distributions without specifying starting parameters

Fitting dwell-time distributions with sums of exponentials is widely used to characterize histograms of open- and closed-interval durations recorded from single ion channels, as well as for other physical phenomena. However, it can be difficult to identify the contributing exponential components. Here we extend previous methods of exponential sum-fitting to present a maximum-likelihood approach that consistently detects all significant exponentials without the need for user-specified starting parameters. Instead of searching for exponentials, the fitting starts with a very large number of initial exponentials with logarithmically spaced time constants, so that none are missed. Maximum-likelihood fitting then determines the areas of all the initial exponentials keeping the time constants fixed. In an iterative manner, with refitting after each step, the analysis then removes exponentials with negligible area and combines closely spaced adjacent exponentials, until only those exponentials that make significant contributions to the dwell-time distribution remain. There is no limit on the number of significant exponentials and no starting parameters need be specified. We demonstrate fully automated detection for both experimental and simulated data, as well as for classical exponential-sum-fitting problems.

K(+) channels: function-structural overview

Potassium channels are particularly important in determining the shape and duration of the action potential, controlling the membrane potential, modulating hormone secretion, epithelial function and, in the case of those K(+) channels activated by Ca(2+), damping excitatory signals. The multiplicity of roles played by K(+) channels is only possible to their mammoth diversity that includes at present 70 K(+) channels encoding genes in mammals. Today, thanks to the use of cloning, mutagenesis, and the more recent structural studies using x-ray crystallography, we are in a unique position to understand the origins of the enormous diversity of this superfamily of ion channels, the roles they play in different cell types, and the relations that exist between structure and function. With the exception of two-pore K(+) channels that are dimers, voltage-dependent K(+) channels are tetrameric assemblies and share an extremely well conserved pore region, in which the ion-selectivity filter resides. In the present overview, we discuss in the function, localization, and the relations between function and structure of the five different subfamilies of K(+) channels: (a) inward rectifiers, Kir; (b) four transmembrane segments-2 pores, K2P; (c) voltage-gated, Kv; (d) the Slo family; and (e) Ca(2+)-activated SK family, SKCa.

Transduction of voltage and Ca2+ signals by Slo1 BK channels

Large-conductance Ca2+ -and voltage-gated K+ channels are activated by an increase in intracellular Ca2+ concentration and/or depolarization. The channel activation mechanism is well described by an allosteric model encompassing the gate, voltage sensors, and Ca2+ sensors, and the model is an excellent framework to understand the influences of auxiliary β and γ subunits and regulatory factors such as Mg2+. Recent advances permit elucidation of structural correlates of the biophysical mechanism.

Down-regulation of CaV1.2 channels during hypertension: how fewer CaV1.2 channels allow more Ca(2+) into hypertensive arterial smooth muscle

Hypertension is a clinical syndrome characterized by increased arterial tone. Although the mechanisms are varied, the generally accepted view is that increased CaV1.2 channel function is a common feature of this pathological condition. Here, we investigated the mechanisms underlying vascular dysfunction in a mouse model of genetic hypertension. Contrary to expectation, we found that whole-cell CaV1.2 currents (ICa) were lower in hypertensive (BPH line) than normotensive (BPN line) myocytes. However, local CaV1.2 sparklet activity was higher in BPH cells, suggesting that the relatively low ICa in these cells was produced by a few hyperactive CaV1.2 channels. Furthermore, our data suggest that while the lower expression of the pore-forming α1c subunit of CaV1.2 currents underlies the lower ICa in BPH myocytes, the increased sparklet activity was due to a different composition in the auxiliary subunits of the CaV1.2 complexes. ICa currents in BPN cells were produced by channels composed of α1c/α2δ/β3 subunits, while in BPH myocytes currents were probably generated by the opening of channels formed by α1c/α2δ/β2 subunits. In addition, Ca(2+) sparks evoked large conductance, Ca(2+)-activated K(+) (BK) currents of lower magnitude in BPH than in BPN myocytes, because BK channels were less sensitive to Ca(2+). Our data are consistent with a model in which a decrease in the global number of CaV1.2 currents coexist with the existence of a subpopulation of highly active channels that dominate the resting Ca(2+) influx. The decrease in BK channel activity makes the hyperpolarizing brake ineffective and leads BPH myocytes to a more contracted resting state.

Ca2+ block and flickering both contribute to the negative slope of the IV curve in BK channels

Single-channel current–voltage (IV) curves of human large-conductance, voltage- and Ca²⁺-activated K⁺ (BK) channels are quite linear in 150 mM KCl. In the presence of Ca²⁺ and/or Mg²⁺, they show a negative slope conductance at high positive potentials. This is generally explained by a Ca²⁺/Mg²⁺ block as by Geng et al. (2013. J. Gen. Physiol. http://dx.doi.org/10.1085/jgp.201210955) in this issue. Here, we basically support this finding but add a refinement: the analysis of the open-channel noise by means of β distributions reveals what would be found if measurements were done with an amplifier of sufficient temporal resolution (10 MHz), namely that the block by 2.5 mM Ca²⁺ and 2.5 mM Mg²⁺ per se would only cause a saturating curve up to +160 mV. Further bending down requires the involvement of a second process related to flickering in the microsecond range. This flickering is hardly affected by the presence or absence of Ca²⁺/Mg²⁺. In contrast to the experiments reported here, previous experiments in BK channels (Schroeder and Hansen. 2007. J. Gen. Physiol. http://dx.doi.org/10.1085/jgp.200709802) showed saturating IV curves already in the absence of Ca²⁺/Mg²⁺. The reason for this discrepancy could not be identified so far. However, the flickering component was very similar in the old and new experiments, regardless of the occurrence of noncanonical IV curves.

Ligand-gating by Ca2+ is rate limiting for physiological operation of BK(Ca) channels

Large conductance Ca(2+)- and voltage-activated potassium channels (BKCa) shape neuronal excitability and signal transduction. This reflects the integrated influences of transmembrane voltage and intracellular calcium concentration ([Ca(2+)]i) that gate the channels. This dual gating has been mainly studied as voltage-triggered gating modulated by defined steady-state [Ca(2+)]i, a paradigm that does not approximate native conditions. Here we use submillisecond changes of [Ca(2+)]i to investigate the time course of the Ca(2+)-triggered gating of BKCa channels expressed in Chinese hamster ovary cells at distinct membrane potentials in the physiological range. The results show that Ca(2+) can effectively gate BKCa channels and that Ca(2+) gating is largely different from voltage-driven gating. Most prominently, Ca(2+) gating displays a pronounced delay in the millisecond range between Ca(2+) application and channel opening (pre-onset delay) and exhibits slower kinetics across the entire [Ca(2+)]i-voltage plane. Both characteristics are selectively altered by co-assembled BKβ4 or an epilepsy-causing mutation that either slows deactivation or speeds activation and reduces the pre-onset delay, respectively. Similarly, co-assembly of the BKCa channels with voltage-activated Ca(2+) (Cav) channels, mirroring the native configuration, decreased the pre-onset delay to submillisecond values. In BKCa-Cav complexes, the time course of the hyperpolarizing K(+)-current response is dictated by the Ca(2+) gating of the BKCa channels. Consistent with Cav-mediated Ca(2+) influx, gating was fastest at hyperpolarized potentials, but decreased with depolarization of the membrane potential. Our results demonstrate that under experimental paradigms meant to approximate the physiological conditions BKCa channels primarily operate as ligand-activated channels gated by intracellular Ca(2+) and that Ca(2+) gating is tuned for fast responses in neuronal BKCa-Cav complexes.

State-dependent FRET reports calcium- and voltage-dependent gating-ring motions in BK channels

Large-conductance voltage- and calcium-dependent potassium channels (BK, "Big K+") are important controllers of cell excitability. In the BK channel, a large C-terminal intracellular region containing a "gating-ring" structure has been proposed to transduce Ca(2+) binding into channel opening. Using patch-clamp fluorometry, we have investigated the calcium and voltage dependence of conformational changes of the gating-ring region of BK channels, while simultaneously monitoring channel conductance. Fluorescence resonance energy transfer (FRET) between fluorescent protein inserts indicates that Ca(2+) binding produces structural changes of the gating ring that are much larger than those predicted by current X-ray crystal structures of isolated gating rings.

Combined single-channel and macroscopic recording techniques to analyze gating mechanisms of the large conductance Ca2+ and voltage activated (BK) potassium channel

Ion channels are integral membrane proteins that regulate membrane potentials and signaling of cells in response to various stimuli. The patch-clamp technique enables the study of single channels or a population of channels. The macroscopic recording approaches are powerful in revealing population-averaged behaviors of channels both under basal conditions and in response to various stimuli, modulators and drugs. On their own, however, these approaches can be insufficient for determinations of channel gating mechanisms as they do not accurately report channel open probabilities below 10(-2) to 10(-3). This obstacle can be overcome with the use of single-channel recording techniques. Single-channel recording techniques can be applied to one or a few channels to estimate P o over a larger range than macroscopic recordings. The combination of heterologous overexpression of ion channels with macroscopic and single-channel recordings can be applied to hundreds of channels to estimate P o between 1 and 10(-8). Here, we describe practical approaches of single-channel recordings that our laboratory utilizes. We also provide examples where the combined macroscopic and single channel approach can be employed to study gating mechanisms of the BK type, large conductance, Ca(2+) and voltage activated potassium channel in a mammalian expression system. The techniques presented should be generally applicable to the studies of ion channels in heterologous expression systems.

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.

A linkage analysis toolkit for studying allosteric networks in ion channels

A thermodynamic approach to studying allosterically regulated ion channels such as the large-conductance voltage- and Ca(2+)-dependent (BK) channel is presented, drawing from principles originally introduced to describe linkage phenomena in hemoglobin. In this paper, linkage between a principal channel component and secondary elements is derived from a four-state thermodynamic cycle. One set of parallel legs in the cycle describes the "work function," or the free energy required to activate the principal component. The second are "lever operations" activating linked elements. The experimental embodiment of this linkage cycle is a plot of work function versus secondary force, whose asymptotes are a function of the parameters (displacements and interaction energies) of an allosteric network. Two essential work functions play a role in evaluating data from voltage-clamp experiments. The first is the conductance Hill energy W(H)([g]), which is a "local" work function for pore activation, and is defined as kT times the Hill transform of the conductance (G-V) curve. The second is the electrical capacitance energy W(C)([q]), representing "global" gating charge displacement, and is equal to the product of total gating charge per channel times the first moment (V(M)) of normalized capacitance (slope of Q-V curve). Plots of W(H)([g]) and W(C)([q]) versus voltage and Ca(2+) potential can be used to measure thermodynamic parameters in a model-independent fashion of the core gating constituents (pore, voltage-sensor, and Ca(2+)-binding domain) of BK channel. The method is easily generalized for use in studying other allosterically regulated ion channels. The feasibility of performing linkage analysis from patch-clamp data were explored by simulating gating and ionic currents of a 17-particle model BK channel in response to a slow voltage ramp, which yielded interaction energies deviating from their given values in the range of 1.3 to 7.2%.

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.

Relative transmembrane segment rearrangements during BK channel activation resolved by structurally assigned fluorophore-quencher pairing

Voltage-activated proteins can sense, and respond to, changes in the electric field pervading the cell membrane by virtue of a transmembrane helix bundle, the voltage-sensing domain (VSD). Canonical VSDs consist of four transmembrane helices (S1-S4) of which S4 is considered a principal component because it possesses charged residues immersed in the electric field. Membrane depolarization compels the charges, and by extension S4, to rearrange with respect to the field. The VSD of large-conductance voltage- and Ca-activated K(+) (BK) channels exhibits two salient inconsistencies from the canonical VSD model: (1) the BK channel VSD possesses an additional nonconserved transmembrane helix (S0); and (2) it exhibits a "decentralized" distribution of voltage-sensing charges, in helices S2 and S3, in addition to S4. Considering these unique features, the voltage-dependent rearrangements of the BK VSD could differ significantly from the standard model of VSD operation. To understand the mode of operation of this unique VSD, we have optically tracked the relative motions of the BK VSD transmembrane helices during activation, by manipulating the quenching environment of site-directed fluorescent labels with native and introduced Trp residues. Having previously reported that S0 and S4 diverge during activation, in this work we demonstrate that S4 also diverges from S1 and S2, whereas S2, compelled by its voltage-sensing charged residues, moves closer to S1. This information contributes spatial constraints for understanding the BK channel voltage-sensing process, revealing the structural rearrangements in a non-canonical VSD.

The contribution of RCK domains to human BK channel allosteric activation

Large conductance voltage- and Ca(2+)-activated K(+) (BK) channels are potent regulators of cellular processes including neuronal firing, synaptic transmission, cochlear hair cell tuning, insulin release, and smooth muscle tone. Their unique activation pathway relies on structurally distinct regulatory domains including one transmembrane voltage-sensing domain (VSD) and two intracellular high affinity Ca(2+)-sensing sites per subunit (located in the RCK1 and RCK2 domains). Four pairs of RCK1 and RCK2 domains form a Ca(2+)-sensing apparatus known as the "gating ring." The allosteric interplay between voltage- and Ca(2+)-sensing apparati is a fundamental mechanism of BK channel function. Using voltage-clamp fluorometry and UV photolysis of intracellular caged Ca(2+), we optically resolved VSD activation prompted by Ca(2+) binding to the gating ring. The sudden increase of intracellular Ca(2+) concentration ([Ca(2+)](i)) induced a hyperpolarizing shift in the voltage dependence of both channel opening and VSD activation, reported by a fluorophore labeling position 202, located in the upper side of the S4 transmembrane segment. The neutralization of the Ca(2+) sensor located in the RCK2 domain abolished the effect of [Ca(2+)](i) increase on the VSD rearrangements. On the other hand, the mutation of RCK1 residues involved in Ca(2+) sensing did not prevent the effect of Ca(2+) release on the VSD, revealing a functionally distinct interaction between RCK1 and RCK2 and the VSD. A statistical-mechanical model quantifies the complex thermodynamics interplay between Ca(2+) association in two distinct sites, voltage sensor activation, and BK channel opening.

Mg(2+) binding to open and closed states can activate BK channels provided that the voltage sensors are elevated

BK channels are activated by intracellular Ca²⁺ and Mg²⁺ as well as by depolarization. Such activation is possible because each of the four subunits has two high-affinity Ca²⁺ sites, one low-affinity Mg²⁺ site, and a voltage sensor. This study further investigates the mechanism of Mg²⁺ activation by using single-channel recording to determine separately the action of Mg²⁺ on the open and closed states of the channel. To limit Mg²⁺ action to the Mg²⁺ sites, the two high-affinity Ca²⁺ sites are disabled by mutation. When the voltage is stepped from negative holding potentials to +100 mV, we find that 10 mM Mg²⁺ decreases the mean closed latency to the first channel opening 2.1-fold, decreases the mean closed interval duration 8.7-fold, increases mean burst duration 10.1-fold, increases the number of openings per burst 4.4-fold, and increases mean open interval duration 2.3-fold. Hence, Mg²⁺ can bind to closed BK channels, increasing their opening rates, and to open BK channels, decreasing their closing rates. To explore the relationship between Mg²⁺ action and voltage sensor activation, we record single-channel activity in macropatches containing hundreds of channels. Open probability (P_o) is dramatically increased by 10 mM Mg²⁺ when voltage sensors are activated with either depolarization or the mutation R210C. The increased P_o arises from large decreases in mean closed interval durations and moderate increases in mean open interval durations. In contrast, 10 mM Mg²⁺ has no detectable effects on P_o or interval durations when voltage sensors are deactivated with very negative potentials or the mutation R167E. These observations are consistent with a model in which Mg²⁺ can bind to and alter the gating of both closed and open states to increase P_o, provided that one or more voltage sensors are activated.

On the simple random-walk models of ion-channel gate dynamics reflecting long-term memory

Several approaches to ion-channel gating modelling have been proposed. Although many models describe the dwell-time distributions correctly, they are incapable of predicting and explaining the long-term correlations between the lengths of adjacent openings and closings of a channel. In this paper we propose two simple random-walk models of the gating dynamics of voltage and Ca(2+)-activated potassium channels which qualitatively reproduce the dwell-time distributions, and describe the experimentally observed long-term memory quite well. Biological interpretation of both models is presented. In particular, the origin of the correlations is associated with fluctuations of channel mass density. The long-term memory effect, as measured by Hurst R/S analysis of experimental single-channel patch-clamp recordings, is close to the behaviour predicted by our models. The flexibility of the models enables their use as templates for other types of ion channel.

An extracellular domain of the accessory β1 subunit is required for modulating BK channel voltage sensor and gate

A family of tissue-specific auxiliary β subunits modulates large conductance voltage- and calcium-activated potassium (BK) channel gating properties to suit their diverse functions. Paradoxically, β subunits both promote BK channel activation through a stabilization of voltage sensor activation and reduce BK channel openings through an increased energetic barrier of the closed-to-open transition. The molecular determinants underlying β subunit function, including the dual gating effects, remain unknown. In this study, we report the first identification of a β1 functional domain consisting of Y74, S104, Y105, and I106 residues located in the extracellular loop of β1. These amino acids reside within two regions of highest conservation among related β1, β2, and β4 subunits. Analysis in the context of the Horrigan-Aldrich gating model revealed that this domain functions to both promote voltage sensor activation and also reduce intrinsic gating. Free energy calculations suggest that the dual effects of the β1 Y74 and S104–I106 domains can be largely accounted for by a relative destabilization of channels in open states that have few voltage sensors activated. These results suggest a unique and novel mechanism for β subunit modulation of voltage-gated potassium channels wherein interactions between extracellular β subunit residues with the external portions of the gate and voltage sensor regulate channel opening.