Ion conduction and conformational flexibility of a bacterial voltage-gated sodium channel

The chemistry of electrical signaling in sodium channels from bacteria and beyond

Electrical signaling is essential for all fast processes in biology, but its molecular mechanisms have been uncertain. This review article focuses on studies of bacterial sodium channels in order to home in on the essential molecular and chemical mechanisms underlying transmembrane ion conductance and voltage-dependent gating without the overlay of complex protein interactions and regulatory mechanisms in mammalian sodium channels. This minimalist approach has yielded a nearly complete picture of sodium channel function at the atomic level that are mostly conserved in mammalian sodium channels, including sodium selectivity and conductance, voltage sensing and activation, electromechanical coupling to pore opening and closing, slow inactivation, and pathogenic dysfunction in a debilitating channelopathy. Future studies of nature's simplest sodium channels may continue to yield key insights into the fundamental molecular and chemical principles of their function and further elucidate the chemical basis of electrical signaling.

A binding site for phosphoinositides described by multiscale simulations explains their modulation of voltage-gated sodium channels

Voltage-gated sodium channels (Naᵥ) are membrane proteins which open to facilitate the inward flux of sodium ions into excitable cells. In response to stimuli, Naᵥ channels transition from the resting, closed state to an open, conductive state, before rapidly inactivating. Dysregulation of this functional cycle due to mutations causes diseases including epilepsy, pain conditions, and cardiac disorders, making Naᵥ channels a significant pharmacological target. Phosphoinositides are important lipid cofactors for ion channel function. The phosphoinositide PI(4,5)P2 decreases Naᵥ1.4 activity by increasing the difficulty of channel opening, accelerating fast inactivation and slowing recovery from fast inactivation. Using multiscale molecular dynamics simulations, we show that PI(4,5)P2 binds stably to inactivated Naᵥ at a conserved site within the DIV S4-S5 linker, which couples the voltage-sensing domain (VSD) to the pore. As the Naᵥ C-terminal domain is proposed to also bind here during recovery from inactivation, we hypothesize that PI(4,5)P2 prolongs inactivation by competitively binding to this site. In atomistic simulations, PI(4,5)P2 reduces the mobility of both the DIV S4-S5 linker and the DIII-IV linker, responsible for fast inactivation, slowing the conformational changes required for the channel to recover to the resting state. We further show that in a resting state Naᵥ model, phosphoinositides bind to VSD gating charges, which may anchor them and impede VSD activation. Our results provide a mechanism by which phosphoinositides alter the voltage dependence of activation and the rate of recovery from inactivation, an important step for the development of novel therapies to treat Naᵥ-related diseases.

Asymmetric contribution of a selectivity filter gate in triggering inactivation of CaV1.3 channels

Voltage-dependent and Ca2+-dependent inactivation (VDI and CDI, respectively) of CaV channels are two biologically consequential feedback mechanisms that fine-tune Ca2+ entry into neurons and cardiomyocytes. Although known to be initiated by distinct molecular events, how these processes obstruct conduction through the channel pore remains poorly defined. Here, focusing on ultrahighly conserved tryptophan residues in the interdomain interfaces near the selectivity filter of CaV1.3, we demonstrate a critical role for asymmetric conformational changes in mediating VDI and CDI. Specifically, mutagenesis of the domain III-IV interface, but not others, enhanced VDI. Molecular dynamics simulations demonstrate that mutations in distinct selectivity filter interfaces differentially impact conformational flexibility. Furthermore, mutations in distinct domains preferentially disrupt CDI mediated by the N- versus C-lobes of CaM, thus uncovering a scheme of structural bifurcation of CaM signaling. These findings highlight the fundamental importance of the asymmetric arrangement of the pseudotetrameric CaV pore domain for feedback inhibition.

Binding of carboxylate and water to monovalent cations

The interactions of carboxylate anions with water and cations are important for a wide variety of systems, both biological and synthetic. To gain insight on properties of the local complexes, we apply density functional theory, to treat the complex electrostatic interactions, and investigate mixtures with varied numbers of carboxylate anions (acetate) and waters binding to monovalent cations, Li+, Na+ and K+. The optimal structure with overall lowest free energy contains two acetates and two waters such that the cation is four-fold coordinated, similar to structures found earlier for pure water or pure carboxylate ligands. More generally, the complexes with two acetates have the lowest free energy. In transitioning from the overall optimal state, exchanging an acetate for water has a lower free energy barrier than exchanging water for an acetate. In most cases, the carboxylates are monodentate and in the first solvation shell. As water is added to the system, hydrogen bonding between waters and carboxylate O atoms further stabilizes monodentate structures. These structures, which have strong electrostatic interactions that involve hydrogen bonds of varying strength, are significantly polarized, with ChelpG partial charges that vary substantially as the bonding geometry varies. Overall, these results emphasize the increasing importance of water as a component of binding sites as the number of ligands increases, thus affecting the preferential solvation of specific metal ions and clarifying Hofmeister effects. Finally, structural analysis correlated with free energy analysis supports the idea that binding to more than the preferred number of carboxylates under architectural constraints are a key to ion transport.

Asymmetric Contribution of a Selectivity Filter Gate in Triggering Inactivation of CaV1.3 Channels

Voltage-dependent and Ca2+-dependent inactivation (VDI and CDI, respectively) of CaV channels are two biologically consequential feedback mechanisms that fine-tune Ca2+ entry into neurons and cardiomyocytes. Although known to be initiated by distinct molecular events, how these processes obstruct conduction through the channel pore remains poorly defined. Here, focusing on ultra-highly conserved tryptophan residues in the inter-domain interfaces near the selectivity filter of CaV1.3, we demonstrate a critical role for asymmetric conformational changes in mediating VDI and CDI. Specifically, mutagenesis of the domain III-IV interface, but not others, enhanced VDI. Molecular dynamics simulations demonstrate that mutations in distinct selectivity filter interfaces differentially impact conformational flexibility. Furthermore, mutations in distinct domains preferentially disrupt CDI mediated by the N- versus C-lobes of CaM, thus uncovering a scheme of structural bifurcation of CaM signaling. These findings highlight the fundamental importance of the asymmetric arrangement of the pseudo-tetrameric CaV pore domain for feedback inhibition.

Ion channel selectivity through ion-modulated changes of selectivity filter pKa values

In bacterial voltage-gated sodium channels, the passage of ions through the pore is controlled by a selectivity filter (SF) composed of four glutamate residues. The mechanism of selectivity has been the subject of intense research, with suggested mechanisms based on steric effects, and ion-triggered conformational change. Here, we propose an alternative mechanism based on ion-triggered shifts in pKa values of SF glutamates. We study the NavMs channel for which the open channel structure is available. Our free-energy calculations based on molecular dynamics simulations suggest that pKa values of the four glutamates are higher in solution of K+ ions than in solution of Na+ ions. Higher pKa in the presence of K+ stems primarily from the higher population of dunked conformations of the protonated Glu sidechain, which exhibit a higher pKa shift. Since pKa values are close to the physiological pH, this results in predominant population of the fully deprotonated state of glutamates in Na+ solution, while protonated states are predominantly populated in K+ solution. Through molecular dynamics simulations we calculate that the deprotonated state is the most conductive, the singly protonated state is less conductive, and the doubly protonated state has significantly reduced conductance. Thus, we propose that a significant component of selectivity is achieved through ion-triggered shifts in the protonation state, which favors more conductive states for Na+ ions and less conductive states for K+ ions. This mechanism also suggests a strong pH dependence of selectivity, which has been experimentally observed in structurally similar NaChBac channels.

Molecular Dynamics Simulations of Ion Permeation in Human Voltage-Gated Sodium Channels

The recent determination of cryo-EM structures of voltage-gated sodium (Na_v) channels has revealed many details of these proteins. However, knowledge of ionic permeation through the Na_v pore remains limited. In this work, we performed atomistic molecular dynamics (MD) simulations to study the structural features of various neuronal Na_v channels based on homology modeling of the cryo-EM structure of the human Na_v1.4 channel and, in addition, on the recently resolved configuration for Na_v1.2. In particular, single Na⁺ permeation events during standard MD runs suggest that the ion resides in the inner part of the Na_v selectivity filter (SF). On-the-fly free energy parametrization (OTFP) temperature-accelerated molecular dynamics (TAMD) was also used to calculate two-dimensional free energy surfaces (FESs) related to single/double Na⁺ translocation through the SF of the homology-based Na_v1.2 model and the cryo-EM Na_v1.2 structure, with different realizations of the DEKA filter domain. These additional simulations revealed distinct mechanisms for single and double Na⁺ permeation through the wild-type SF, which has a charged lysine in the DEKA ring. Moreover, the configurations of the ions in the SF corresponding to the metastable states of the FESs are specific for each SF motif. Overall, the description of these mechanisms gives us new insights into ion conduction in human Na_v cryo-EM-based and cryo-EM configurations that could advance understanding of these systems and how they differ from potassium and bacterial Na_v channels.

Mechanism of Calcium Permeation in a Glutamate Receptor Ion Channel

The α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs) are neurotransmitter-activated cation channels ubiquitously expressed in vertebrate brains. The regulation of calcium flux through the channel pore by RNA-editing is linked to synaptic plasticity while excessive calcium influx poses a risk for neurodegeneration. Unfortunately, the molecular mechanisms underlying this key process are mostly unknown. Here, we investigated calcium conduction in calcium-permeable AMPAR using Molecular Dynamics (MD) simulations with recently introduced multisite force-field parameters for Ca2+. Our calculations are consistent with experiment and explain the distinct calcium permeability in different RNA-edited forms of GluA2. For one of the identified metal binding sites, multiscale Quantum Mechanics/Molecular Mechanics (QM/MM) simulations further validated the results from MD and revealed small but reproducible charge transfer between the metal ion and its first solvation shell. In addition, the ion occupancy derived from MD simulations independently reproduced the Ca2+ binding profile in an X-ray structure of an NaK channel mimicking the AMPAR selectivity filter. This integrated study comprising X-ray crystallography, multisite MD, and multiscale QM/MM simulations provides unprecedented insights into Ca2+ permeation mechanisms in AMPARs, and paves the way for studying other biological processes in which Ca2+ plays a pivotal role.

Structure and Computational Electrophysiology of Ac-LS3, a Synthetic Ion Channel

Computer simulations are reported on Ac-LS3, a synthetic ion channel, containing 21 residues with a Leu-Ser-Ser-Leu-Leu-Ser-Leu heptad repeat, which forms ions channels upon application of voltage. A hexameric, coiled-coil bundle initially positioned perpendicular to the membrane settled into a stable, tilted structure after 1.5 μs, most likely to improve contacts between the non-polar exterior of the channel and the hydrophobic core of the membrane. Once tilted, the bundle remained in this state during subsequent simulations of nearly 10 μs at voltages ranging from 200 to -100 mV. In contrast, attempts to identify a stable pentameric structure failed, thus supporting the hypothesis that the channel is a hexamer. Results at 100 mV were used to reconstruct the free energy profiles for K⁺ and Cl^- in the channel. This was done by way of several methods in which results of molecular dynamics (MD) simulations were combined with the electrodiffusion model. Two of them developed recently do not require knowledge of the diffusivity. Instead, they utilize one-sided density profiles and committor probabilities. The consistency between different methods is very good, supporting the utility of the newly developed methods for reconstructing free energies of ions in channels. The flux of K⁺, which accounts for most of the current through the channel, calculated directly from MD matches well the total measured current. However, the current of Cl^- is somewhat overestimated, possibly due to a slightly unbalanced force field involving chloride. The current-voltage dependence was also reconstructed by way of a recently developed, efficient method that requires simulations only at a single voltage, yielding good agreement with the experiment. Taken together, the results demonstrate that computational electrophysiology has become a reliable tool for studying how channels mediate ion transport through membranes.

Computational study of ion permeation through claudin-4 paracellular channels

Claudins (Cldns) form a large family of protein homologs that are essential for the assembly of paracellular tight junctions (TJs), where they form channels or barriers with tissue-specific selectivity for permeants. In contrast to several family members whose physiological role has been identified, the function of claudin 4 (Cldn4) remains elusive, despite experimental evidence suggesting that it can form anion-selective TJ channels in the renal epithelium. Computational approaches have recently been employed to elucidate the molecular basis of Cldns' function, and hence could help in clarifying the role of Cldn4. In this work, we use structural modeling and all-atom molecular dynamics simulations to transfer two previously introduced structural models of Cldn-based paracellular complexes to Cldn4 to reproduce a paracellular anion channel. Free energy calculations for ionic transport through the pores allow us to establish the thermodynamic properties driving the ion-selectivity of the structures. While one model shows a cavity permeable to chloride and repulsive to cations, the other forms barrier to the passage of all the major physiological ions. Furthermore, our results confirm the charge selectivity role of the residue Lys65 in the first extracellular loop of the protein, rationalizing Cldn4 control of paracellular permeability.

Simulation and Machine Learning Methods for Ion-Channel Structure Determination, Mechanistic Studies and Drug Design

Ion channels are expressed in almost all living cells, controlling the in-and-out communications, making them ideal drug targets, especially for central nervous system diseases. However, owing to their dynamic nature and the presence of a membrane environment, ion channels remain difficult targets for the past decades. Recent advancement in cryo-electron microscopy and computational methods has shed light on this issue. An explosion in high-resolution ion channel structures paved way for structure-based rational drug design and the state-of-the-art simulation and machine learning techniques dramatically improved the efficiency and effectiveness of computer-aided drug design. Here we present an overview of how simulation and machine learning-based methods fundamentally changed the ion channel-related drug design at different levels, as well as the emerging trends in the field.

Characterizing fenestration size in sodium channel subtypes and their accessibility to inhibitors

Voltage-gated sodium channels (Nav) underlie the electrical activity of nerve and muscle cells. Humans have nine different subtypes of these channels, which are the target of small-molecule inhibitors commonly used to treat a range of conditions. Structural studies have identified four lateral fenestrations within the Nav pore module that have been shown to influence Nav pore blocker access during resting-state inhibition. However, the structural differences among the nine subtypes are still unclear. In particular, the dimensions of the four individual fenestrations across the Nav subtypes and their differential accessibility to pore blockers is yet to be characterized. To address this, we applied classical molecular dynamics simulations to study the recently published structures of Nav1.1, Nav1.2, Nav1.4, Nav1.5, and Nav1.7. Although there is significant variability in the bottleneck sizes of the Nav fenestrations, the subtypes follow a common pattern, with wider DI-II and DIII-IV fenestrations, a more restricted DII-III fenestration, and the most restricted DI-IV fenestration. We further identify the key bottleneck residues in each fenestration and show that the motions of aromatic residue sidechains govern the bottleneck radii. Well-tempered metadynamics simulations of Nav1.4 and Nav1.5 in the presence of the pore blocker lidocaine also support the DI-II fenestration being the most likely access route for drugs. Our computational results provide a foundation for future in vitro experiments examining the route of drug access to sodium channels. Understanding the fenestrations and their accessibility to drugs is critical for future analyses of diseases mutations across different sodium channel subtypes, with the potential to inform pharmacological development of resting-state inhibitors and subtype-selective drug design.

Open-state structure and pore gating mechanism of the cardiac sodium channel

The heartbeat is initiated by voltage-gated sodium channel Na_V1.5, which opens rapidly and triggers the cardiac action potential; however, the structural basis for pore opening remains unknown. Here, we blocked fast inactivation with a mutation and captured the elusive open-state structure. The fast inactivation gate moves away from its receptor, allowing asymmetric opening of pore-lining S6 segments, which bend and rotate at their intracellular ends to dilate the activation gate to ∼10 Å diameter. Molecular dynamics analyses predict physiological rates of Na⁺ conductance. The open-state pore blocker propafenone binds in a high-affinity pose, and drug-access pathways are revealed through the open activation gate and fenestrations. Comparison with mutagenesis results provides a structural map of arrhythmia mutations that target the activation and fast inactivation gates. These results give atomic-level insights into molecular events that underlie generation of the action potential, open-state drug block, and fast inactivation of cardiac sodium channels, which initiate the heartbeat.

Nonselective cation permeation in an AMPA-type glutamate receptor

Fast excitatory synaptic transmission in the central nervous system relies on the AMPA-type glutamate receptor (AMPAR). This receptor incorporates a nonselective cation channel, which is opened by the binding of glutamate. Although the open pore structure has recently became available from cryo-electron microscopy (Cryo-EM), the molecular mechanisms governing cation permeability in AMPA receptors are not understood. Here, we combined microsecond molecular dynamic (MD) simulations on a putative open-state structure of GluA2 with electrophysiology on cloned channels to elucidate ion permeation mechanisms. Na⁺, K⁺, and Cs⁺ permeated at physiological rates, consistent with a structure that represents a true open state. A single major ion binding site for Na⁺ and K⁺ in the pore represents the simplest selectivity filter (SF) structure for any tetrameric cation channel of known structure. The minimal SF comprised only Q586 and Q587, and other residues on the cytoplasmic side formed a water-filled cavity with a cone shape that lacked major interactions with ions. We observed that Cl^- readily enters the upper pore, explaining anion permeation in the RNA-edited (Q586R) form of GluA2. A permissive architecture of the SF accommodated different alkali metals in distinct solvation states to allow rapid, nonselective cation permeation and copermeation by water. Simulations suggested Cs⁺ uses two equally populated ion binding sites in the filter, and we confirmed with electrophysiology of GluA2 that Cs⁺ is slightly more permeant than Na⁺, consistent with serial binding sites preferentially driving selectivity.

Determinants of conductance of a bacterial voltage-gated sodium channel

Through molecular dynamics (MD) and free energy simulations in electric fields, we examine the factors influencing conductance of bacterial voltage-gated sodium channel Na_vMs. The channel utilizes four glutamic acid residues in the selectivity filter (SF). Previously, we have shown, through constant pH and free energy calculations of pKa values, that fully deprotonated, singly protonated, and doubly protonated states are all feasible at physiological pH, depending on how many ions are bound in the SF. With 173 MD simulations of 450 or 500 ns and additional free energy simulations, we determine that the conductance is highest for the deprotonated state and decreases with each additional proton bound. We also determine that the pKa value of the four glutamic residues for the transition between deprotonated and singly protonated states is close to the physiological pH and that there is a small voltage dependence. The pKa value and conductance trends are in agreement with experimental work on bacterial Na_v channels, which show a decrease in maximal conductance with lowering of pH, with pKa in the physiological range. We examine binding sites for Na⁺ in the SF, compare with previous work, and note a dependence on starting structures. We find that narrowing of the gate backbone to values lower than the crystal structure's backbone radius reduces the conductance, whereas increasing the gate radius further does not affect the conductance. Simulations with some amount of negatively charged lipids as opposed to purely neutral lipids increases the conductance, as do simulations at higher voltages.

Physics of Selective Conduction and Point Mutation in Biological Ion Channels

We introduce a statistical and linear response theory of selective conduction in biological ion channels with multiple binding sites and possible point mutation. We derive an effective grand-canonical ensemble and generalized Einstein relations for the selectivity filter, assuming strongly coordinated ionic motion, and allowing for ionic Coulomb blockade. The theory agrees well with data from the KcsA K^{+} channel and a mutant. We show that the Eisenman relations for thermodynamic selectivity follow from the condition for fast conduction and find that maximum conduction requires the binding sites to be nearly identical.

Electrophysiological Properties from Computations at a Single Voltage: Testing Theory with Stochastic Simulations

We use stochastic simulations to investigate the performance of two recently developed methods for calculating the free energy profiles of ion channels and their electrophysiological properties, such as current–voltage dependence and reversal potential, from molecular dynamics simulations at a single applied voltage. These methods require neither knowledge of the diffusivity nor simulations at multiple voltages, which greatly reduces the computational effort required to probe the electrophysiological properties of ion channels. They can be used to determine the free energy profiles from either forward or backward one-sided properties of ions in the channel, such as ion fluxes, density profiles, committor probabilities, or from their two-sided combination. By generating large sets of stochastic trajectories, which are individually designed to mimic the molecular dynamics crossing statistics of models of channels of trichotoxin, p7 from hepatitis C and a bacterial homolog of the pentameric ligand-gated ion channel, GLIC, we find that the free energy profiles obtained from stochastic simulations corresponding to molecular dynamics simulations of even a modest length are burdened with statistical errors of only 0.3 kcal/mol. Even with many crossing events, applying two-sided formulas substantially reduces statistical errors compared to one-sided formulas. With a properly chosen reference voltage, the current–voltage curves can be reproduced with good accuracy from simulations at a single voltage in a range extending for over 200 mV. If possible, the reference voltages should be chosen not simply to drive a large current in one direction, but to observe crossing events in both directions.

Non-extensitivity and criticality of atomic hydropathicity around a voltage-gated sodium channel's pore: a modeling study

Voltage-gated sodium channels (NavChs) are pore-forming membrane proteins that regulate the transport of sodium ions through the cell membrane. Understanding the structure and function of NavChs is of major biophysical, as well as clinical, importance given their key role in cellular pathophysiology. In this work, we provide a computational framework for modeling system-size-dependent, i.e., cumulative, atomic properties around a NavCh's pore. We illustrate our methodologies on the bacterial NavAb channel captured in a closed-pore state where we demonstrate that the atomic environment around its pore exhibits a bi-phasic spatial organization dictated by the structural separation of the pore domains (PDs) from the voltage-sensing domains (VSDs). Accordingly, a mathematical model describing packing of atoms around NavAb's pore is constructed that allows-under certain conservation conditions-for a power-law approximation of the cumulative hydropathic dipole field effect acting along NavAb's pore. This verified the non-extensitivity hypothesis for the closed-pore NavAb channel and revealed a long-range hydropathic interactions law regulating atom-packing around the NavAb's selectivity filter. Our model predicts a PDs-VSDs coupling energy of [Formula: see text] kcal/mol corresponding to a global maximum of the atom-packing energy profile. Crucially, we demonstrate for the first time how critical phenomena can emerge in a single-channel structure as a consequence of the non-extensive character of its atomic porous environment.

Application of a Statistical and Linear Response Theory to Multi-Ion Na+ Conduction in NaChBac

Biological ion channels are fundamental to maintaining life. In this manuscript we apply our recently developed statistical and linear response theory to investigate Na+ conduction through the prokaryotic Na+ channel NaChBac. This work is extended theoretically by the derivation of ionic conductivity and current in an electrochemical gradient, thus enabling us to compare to a range of whole-cell data sets performed on this channel. Furthermore, we also compare the magnitudes of the currents and populations at each binding site to previously published single-channel recordings and molecular dynamics simulations respectively. In doing so, we find excellent agreement between theory and data, with predicted energy barriers at each of the four binding sites of ∼4,2.9,3.6, and 4kT.

Tracking Membrane Protein Dynamics in Real Time

Abstract

Membrane proteins govern critical cellular processes and are central to human health and associated disease. Understanding of membrane protein function is obscured by the vast ranges of structural dynamics—both in the spatial and time regime—displayed in the protein and surrounding membrane. The membrane lipids have emerged as allosteric modulators of membrane protein function, which further adds to the complexity. In this review, we discuss several examples of membrane dependency. A particular focus is on how molecular dynamics (MD) simulation have aided to map membrane protein dynamics and how enhanced sampling methods can enable observing the otherwise inaccessible biological time scale. Also, time-resolved X-ray scattering in solution is highlighted as a powerful tool to track membrane protein dynamics, in particular when combined with MD simulation to identify transient intermediate states. Finally, we discuss future directions of how to further develop this promising approach to determine structural dynamics of both the protein and the surrounding lipids.

Graphic Abstract

Effects of amino acid modifications on the permeability of the pentameric sarcolipin channel

Sarcolipin (SLN) is an important transmembrane (TM) protein encoded by long noncoding RNA. SLN is expressed in the sarcoplasmic reticulum and regulates cardiac and skeletal muscle contractions. SLN forms a pentameric hydrophobic ligand-gated ion channel. The protonation of Glu7 (protonated SLN, pSLN) and mutation of Thr18 to Ala18 (T18A) have been reported to exert a significant influence on the permeability of the channel. In this study, the altered permeability of both the pSLN and T18A pentameric channels was simulated. Combined with molecular dynamics simulation, the free-energy landscape for single ions, computational electrophysiology, diffusion coefficient, and pore geometrical characteristic analyses were performed to further understand the properties of amino acid modifications in the SLN pentameric channel. The results suggest that both the pSLN and T18A pentameric channels form stable hydrophobic ligand-gated channels. The TM voltage has a positive effect on the permeability of water molecules and ions. By using pSLN and T18A, our study provides helpful information on the pore-forming mechanism of SLN and furthers our understanding of the regulatory mechanisms underlying the permeation of ions and water molecules in the pentameric SLN channel.

Ca2+ entry through NaV channels generates submillisecond axonal Ca2+ signaling

Calcium ions (Ca²⁺) are essential for many cellular signaling mechanisms and enter the cytosol mostly through voltage-gated calcium channels. Here, using high-speed Ca²⁺ imaging up to 20 kHz in the rat layer five pyramidal neuron axon we found that activity-dependent intracellular calcium concentration ([Ca²⁺]_i) in the axonal initial segment was only partially dependent on voltage-gated calcium channels. Instead, [Ca²⁺]_i changes were sensitive to the specific voltage-gated sodium (Na_V) channel blocker tetrodotoxin. Consistent with the conjecture that Ca²⁺ enters through the Na_V channel pore, the optically resolved I_Ca in the axon initial segment overlapped with the activation kinetics of Na_V channels and heterologous expression of Na_V1.2 in HEK-293 cells revealed a tetrodotoxin-sensitive [Ca²⁺]_i rise. Finally, computational simulations predicted that axonal [Ca²⁺]_i transients reflect a 0.4% Ca²⁺ conductivity of Na_V channels. The findings indicate that Ca²⁺ permeation through Na_V channels provides a submillisecond rapid entry route in Na_V-enriched domains of mammalian axons.

Nerve cells communicate using tiny electrical impulses called action potentials. Special proteins termed ion channels produce these electric signals by allowing specific charged particles, or ions, to pass in or out of cells across its membrane. When a nerve cell ‘fires’ an action potential, specific ion channels briefly open to let in a surge of positively charged ions which electrify the cell. Action potentials begin in the same place in each nerve cell, at an area called the axon initial segment. The large number of sodium channels at this site kick-start the influx of positively charged sodium ions ensuring that every action potential starts from the same place.

Previous research has shown that, when action potentials begin, the concentration of calcium ions at the axon initial segment also increases, but it was not clear which ion channels were responsible for this entry of calcium. Channels that are selective for calcium ions are the prime candidates for this process. However, research in squid nerve cells gave rise to an unexpected idea by suggesting that sodium channels may not exclusively let in sodium but also allow some calcium ions to pass through. Hanemaaijer, Popovic et al. therefore wanted to test the routes that calcium ions take and see whether the sodium channels in mammalian nerve cells are also permeable to calcium.

Experiments using fluorescent dyes to track the concentration of calcium in rat and human nerve cells showed that calcium ions accumulated at the axon initial segment when action potentials fired. Most of this increase in calcium could be stopped by treating the neurons with a toxin that prevents sodium channels from opening. Electrical manipulations of the cells revealed that, in this context, the calcium ions were effectively behaving like sodium ions. Human kidney cells were then engineered to produce the sodium channel protein. This confirmed that calcium and sodium ions were indeed both passing through the same channel.

These results shed new light on the relationship between calcium ions and sodium channels within the mammalian nervous system and that this interplay occurs at the axon initial segment of the cell. Genetic mutations that ‘nudge’ sodium channels towards favoring calcium entry are also found in patients with autism spectrum disorders, and so this new finding may contribute to our understanding of these conditions.

SCN2A channelopathies: Mechanisms and models

Variants in the SCN2A gene, encoding the voltage-gated sodium channel Na_V 1.2, cause a variety of neuropsychiatric syndromes with different severity ranging from self-limiting epilepsies with early onset to developmental and epileptic encephalopathy with early or late onset and intellectual disability (ID), as well as ID or autism without seizures. Functional analysis of channel defects demonstrated a genotype-phenotype correlation and suggested effective treatment options for one group of affected patients carrying gain-of-function variants. Here, we sum up the functional mechanisms underlying different phenotypes of patients with SCN2A channelopathies and present currently available models that can help in understanding SCN2A-related disorders.

Simulating ion channel activation mechanisms using swarms of trajectories

Atomic-level studies of protein activity represent a significant challenge as a result of the complexity of conformational changes occurring on wide-ranging timescales, often greatly exceeding that of even the longest simulations. A prime example is the elucidation of protein allosteric mechanisms, where localized perturbations transmit throughout a large macromolecule to generate a response signal. For example, the conversion of chemical to electrical signals during synaptic neurotransmission in the brain is achieved by specialized membrane proteins called pentameric ligand-gated ion channels. Here, the binding of a neurotransmitter results in a global conformational change to open an ion-conducting pore across the nerve cell membrane. X-ray crystallography has produced static structures of the open and closed states of the proton-gated GLIC pentameric ligand-gated ion channel protein, allowing for atomistic simulations that can uncover changes related to activation. We discuss a range of enhanced sampling approaches that could be used to explore activation mechanisms. In particular, we describe recent application of an atomistic string method, based on Roux's "swarms of trajectories" approach, to elucidate the sequence and interdependence of conformational changes during activation. We illustrate how this can be combined with transition analysis and Brownian dynamics to extract thermodynamic and kinetic information, leading to understanding of what controls ion channel function. © 2019 Wiley Periodicals, Inc.

Structure and Pharmacology of Voltage-Gated Sodium and Calcium Channels

Voltage-gated sodium and calcium channels are evolutionarily related transmembrane signaling proteins that initiate action potentials, neurotransmission, excitation-contraction coupling, and other physiological processes. Genetic or acquired dysfunction of these proteins causes numerous diseases, termed channelopathies, and sodium and calcium channels are the molecular targets for several major classes of drugs. Recent advances in the structural biology of these proteins using X-ray crystallography and cryo-electron microscopy have given new insights into the molecular basis for their function and pharmacology. Here we review this recent literature and integrate findings on sodium and calcium channels to reveal the structural basis for their voltage-dependent activation, fast and slow inactivation, ion conductance and selectivity, and complex pharmacology at the atomic level. We conclude with the theme that new understanding of the diseases and therapeutics of these channels will be derived from application of the emerging structural principles from these recent structural analyses.

Bases of Bacterial Sodium Channel Selectivity Among Organic Cations

Hille's (1971) seminal study of organic cation selectivity of eukaryotic voltage-gated sodium channels showed a sharp size cut-off for ion permeation, such that no ion possessing a methyl group was permeant. Using the prokaryotic channel, NaChBac, we found some similarity and two peculiar differences in the selectivity profiles for small polyatomic cations. First, we identified a diverse group of minimally permeant cations for wildtype NaChBac, ranging in sizes from ammonium to guanidinium and tetramethylammonium; and second, for both ammonium and hydrazinium, the charge-conserving selectivity filter mutation (E191D) yielded substantial increases in relative permeability (PX/PNa). The relative permeabilities varied inversely with relative Kd calculated from 1D Potential of Mean Force profiles (PMFs) for the single cations traversing the channel. Several of the cations bound more strongly than Na+, and hence appear to act as blockers, as well as charge carriers. Consistent with experimental observations, the E191D mutation had little impact on Na+ binding to the selectivity filter, but disrupted the binding of ammonium and hydrazinium, consequently facilitating ion permeation across the NaChBac-like filter. We concluded that for prokaryotic sodium channels, a fine balance among filter size, binding affinity, occupancy, and flexibility seems to contribute to observed functional differences.

Challenges and advances in atomistic simulations of potassium and sodium ion channel gating and permeation

Ion channels are implicated in many essential physiological events such as electrical signal propagation and cellular communication. The advent of K⁺ and Na⁺ ion channel structure determination has facilitated numerous investigations of molecular determinants of their behaviour. At the same time, rapid development of computer hardware and molecular simulation methodologies has made computational studies of large biological molecules in all-atom representation tractable. The concurrent evolution of experimental structural biology with biomolecular computer modelling has yielded mechanistic details of fundamental processes unavailable through experiments alone, such as ion conduction and ion channel gating. This review is a short survey of the atomistic computational investigations of K⁺ and Na⁺ ion channels, focusing on KcsA and several voltage-gated channels from the K_V and Na_V families, which have garnered many successes and engendered several long-standing controversies regarding the nature of their structure-function relationship. We review the latest advancements and challenges facing the field of molecular modelling and simulation regarding the structural and energetic determinants of ion channel function and their agreement with experimental observations.

Molecular Dynamics of Ion Conduction through the Selectivity Filter of the NaVAb Sodium Channel

The determination of the atomic structures of voltage-gated bacterial sodium channels using X-ray crystallography has provided a first view of this family of membrane proteins. Molecular dynamics simulations offer one approach to clarify the underlying mechanism of permeation and selectivity in these channels. However, it appears that the intracellular gate of the pore domain is either closed or only open partially in the available X-ray structures. The lack of structure with a fully open intracellular gate poses a special challenge to computational studies aimed at simulating ion conduction. To circumvent this problem, we simulated a model of the Na_VAb channel in which the transmembrane S5 and S6 helices of the pore domain have been truncated to provide direct open access to the intracellular entryway to the pore. Molecular dynamics simulations were carried out over a range of membrane potential and ion concentration of sodium and potassium. The simulations show that the Na_VAb selectivity filter is essentially a cationic pore supporting the conduction of ions at a rate comparable to aqueous diffusion with no significant selectivity for sodium. Conductance and selectivity vary as a function of ion concentration for both cations. Permeation occurs primarily via a knock-on mechanism for both sodium and potassium, although the ion ordering in single file along the pore is not strictly maintained. The character of the outward current appears quite different from the inward current, with a buildup on ions in the selectivity filter prior to escape toward the extracellular side, indicating the presence of a rectification effect that is overcome by nonphysiological applied voltages.

Role of the Interaction Motif in Maintaining the Open Gate of an Open Sodium Channel

Voltage-gated sodium channels undergo transitions between open, closed, and inactivated states, enabling regulation of the translocation of sodium ions across membranes. A recently published crystal structure of the full-length prokaryotic NavMs crystal structure in the activated open conformation has revealed the presence of a novel motif consisting of an extensive network of salt bridges involving residues in the voltage sensor, S4-S5 linker, pore, and C-terminal domains. This motif has been proposed to be responsible for maintaining an open conformation that enables ion translocation through the channel. In this study, we have used long-time molecular dynamics calculations without artificial restraints to demonstrate that the interaction network of full-length NavMs indeed prevents a rapid collapse and closure of the gate, in marked difference to earlier studies of the pore-only construct in which the gate had to be restrained to remain open. Interestingly, a frequently discussed "hydrophobic gating" mechanism at nanoscopic level is also observed in our simulations, in which the discontinuous water wire close to the gate region leads to an energetic barrier for ion conduction. In addition, we demonstrate the effects of in silico mutations of several of the key residues in the motif on the open channel's stability and functioning, correlating them with existing functional studies on this channel and homologous disease-associated mutations in human sodium channels; we also examine the effects of truncating/removing the voltage sensor and C-terminal domains in maintaining an open gate.

Selective ion permeation involves complexation with carboxylates and lysine in a model human sodium channel

Bacterial and human voltage-gated sodium channels (Navs) exhibit similar cation selectivity, despite their distinct EEEE and DEKA selectivity filter signature sequences. Recent high-resolution structures for bacterial Navs have allowed us to learn about ion conduction mechanisms in these simpler homo-tetrameric channels, but our understanding of the function of their mammalian counterparts remains limited. To probe these conduction mechanisms, a model of the human Nav1.2 channel has been constructed by grafting residues of its selectivity filter and external vestibular region onto the bacterial NavRh channel with atomic-resolution structure. Multi-μs fully atomistic simulations capture long time-scale ion and protein movements associated with the permeation of Na+ and K+ ions, and their differences. We observe a Na+ ion knock-on conduction mechanism facilitated by low energy multi-carboxylate/multi-Na+ complexes, akin to the bacterial channels. These complexes involve both the DEKA and vestibular EEDD rings, acting to draw multiple Na+ into the selectivity filter and promote permeation. When the DEKA ring lysine is protonated, we observe that its ammonium group is actively participating in Na+ permeation, presuming the role of another ion. It participates in the formation of a stable complex involving carboxylates that collectively bind both Na+ and the Lys ammonium group in a high-field strength site, permitting pass-by translocation of Na+. In contrast, multiple K+ ion complexes with the DEKA and EEDD rings are disfavored by up to 8.3 kcal/mol, with the K+-lysine-carboxylate complex non-existent. As a result, lysine acts as an electrostatic plug that partially blocks the flow of K+ ions, which must instead wait for isomerization of lysine downward to clear the path for K+ passage. These distinct mechanisms give us insight into the nature of ion conduction and selectivity in human Nav channels, while uncovering high field strength carboxylate binding complexes that define the more general phenomenon of Na+-selective ion transport in nature.

The voltage-gated sodium channel pore exhibits conformational flexibility during slow inactivation

Voltage-gated sodium channels undergo slow inactivation during prolonged depolarization by means of a mechanism that is poorly understood. Chatterjee et al. study this process spectroscopically and reveal conformational flexibility of the pore region in the slow-inactivated state.

Slow inactivation in voltage-gated sodium channels (Na_Vs) directly regulates the excitability of neurons, cardiac myocytes, and skeletal muscles. Although Na_V slow inactivation appears to be conserved across phylogenies—from bacteria to humans—the structural basis for this mechanism remains unclear. Here, using site-directed labeling and EPR spectroscopic measurements of membrane-reconstituted prokaryotic Na_V homologues, we characterize the conformational dynamics of the selectivity filter region in the conductive and slow-inactivated states to determine the molecular events underlying Na_V gating. Our findings reveal profound conformational flexibility of the pore in the slow-inactivated state. We find that the P1 and P2 pore helices undergo opposing movements with respect to the pore axis. These movements result in changes in volume of both the central and intersubunit cavities, which form pathways for lipophilic drugs that modulate slow inactivation. Our findings therefore provide novel insight into the molecular basis for state-dependent effects of lipophilic drugs on channel function.

Site-specific ion occupation in the selectivity filter causes voltage-dependent gating in a viral K+ channel

Many potassium channels show voltage-dependent gating without a dedicated voltage sensor domain. This is not fully understood yet, but often explained by voltage-induced changes of ion occupation in the five distinct K+ binding sites in the selectivity filter. To better understand this mechanism of filter gating we measured the single-channel current and the rate constant of sub-millisecond channel closure of the viral K+ channel KcvNTS for a wide range of voltages and symmetric and asymmetric K+ concentrations in planar lipid membranes. A model-based analysis employed a global fit of all experimental data, i.e., using a common set of parameters for current and channel closure under all conditions. Three different established models of ion permeation and various relationships between ion occupation and gating were tested. Only one of the models described the data adequately. It revealed that the most extracellular binding site (S0) in the selectivity filter functions as the voltage sensor for the rate constant of channel closure. The ion occupation outside of S0 modulates its dependence on K+ concentration. The analysis uncovers an important role of changes in protein flexibility in mediating the effect from the sensor to the gate.

Molecular Mechanism of Conductance Enhancement in Narrow Cation-Selective Membrane Channels

Membrane proteins known as ryanodine receptors (RyRs) display large conductance of ∼1 nS and nearly ideal charge selectivity. Both properties are inversely correlated in other large-conductance but nonselective biological nanopores (i.e., α-hemolysin) used as industrial biosensors. Although recent cryo-electron microscopy structures of RyR2 show similarities to K⁺- and Na⁺-selective channels, it remains unclear whether similar ion conduction mechanisms occur in RyR2. Here, we combine microseconds of all-atom molecular dynamics (MD) simulations with mutagenesis and electrophysiology experiments to investigate large K⁺ conductance and charge selectivity (cation vs anion) in an open-state structure of RyR2. Our results show that a water-mediated knock-on mechanism enhances the cation permeation. The polar Q4863 ring may function as a confinement zone amplifying charge selectivity, while the cytoplasmic vestibule can contribute to the efficiency of the cation attraction. We also provide direct evidence that the rings of acidic residues at the channel vestibules are critical for both conductance and charge discrimination in RyRs.

Comparison of permeation mechanisms in sodium-selective ion channels

Voltage-gated sodium channels are the molecular components of electrical signaling in the body, yet the molecular origins of Na⁺-selective transport remain obscured by diverse protein chemistries within this family of ion channels. In particular, bacterial and mammalian sodium channels are known to exhibit similar relative ion permeabilities for Na⁺ over K⁺ ions, despite their distinct signature EEEE and DEKA sequences. Atomic-level molecular dynamics simulations using high-resolution bacterial channel structures and mammalian channel models have begun to describe how these sequences lead to analogous high field strength ion binding sites that drive Na⁺ conduction. Similar complexes have also been identified in unrelated acid sensing ion channels involving glutamate and aspartate side chains that control their selectivity. These studies suggest the possibility of a common origin for Na⁺ selective binding and transport.

Ion-triggered selectivity in bacterial sodium channels

Since the availability of the first crystal structure of a bacterial Na⁺ channel in 2011, understanding selectivity across this family of membrane proteins has been the subject of intense research efforts. Initially, free energy calculations based on molecular dynamics simulations revealed that although sodium ions can easily permeate the channel with their first hydration shell almost intact, the selectivity filter is too narrow for efficient conduction of hydrated potassium ions. This steric view of selectivity was subsequently questioned by microsecond atomic trajectories, which proved that the selectivity filter appears to the permeating ions as a highly degenerate, liquid-like environment. Although this liquid-like environment looks optimal for rapid conduction of Na⁺, it seems incompatible with efficient discrimination between similar ion species, such as Na⁺ and K⁺, through steric effects. Here extensive molecular dynamics simulations, combined with Markov state model analyses, reveal that at positive membrane potentials, potassium ions trigger a conformational change of the selectivity toward a nonconductive metastable state. It is this transition of the selectivity filter, and not steric effects, that prevents the outward flux of K⁺ at positive membrane potentials. This description of selectivity, triggered by the nature of the permeating ions, might have implications on the current understanding of how ion channels, and in particular bacterial Na⁺ channels, operate at the atomic scale.

Protonation state of inhibitors determines interaction sites within voltage-gated sodium channels

Voltage-gated sodium channels are essential for carrying electrical signals throughout the body, and mutations in these proteins are responsible for a variety of disorders, including epilepsy and pain syndromes. As such, they are the target of a number of drugs used for reducing pain or combatting arrhythmias and seizures. However, these drugs affect all sodium channel subtypes found in the body. Designing compounds to target select sodium channel subtypes will provide a new therapeutic pathway and would maximize treatment efficacy while minimizing side effects. Here, we examine the binding preferences of nine compounds known to be sodium channel pore blockers in molecular dynamics simulations. We use the approach of replica exchange solute tempering (REST) to gain a more complete understanding of the inhibitors' behavior inside the pore of NavMs, a bacterial sodium channel, and NavPas, a eukaryotic sodium channel. Using these simulations, we are able to show that both charged and neutral compounds partition into the bilayer, but neutral forms more readily cross it. We show that there are two possible binding sites for the compounds: (i) a site on helix 6, which has been previously determined by many experimental and computational studies, and (ii) an additional site, occupied by protonated compounds in which the positively charged part of the drug is attracted into the selectivity filter. Distinguishing distinct binding poses for neutral and charged compounds is essential for understanding the nature of pore block and will aid the design of subtype-selective sodium channel inhibitors.

Physical basis of specificity and delayed binding of a subtype selective sodium channel inhibitor

Nerve and muscle signalling is controlled by voltage-gated sodium (Nav) channels which are the targets of local anesthetics, anti-epileptics and anti-arrythmics. Current medications do not selectively target specific types of Nav found in the body, but compounds that do so have the potential to be breakthrough treatments for chronic pain, epilepsy and other neuronal disorders. We use long computer simulations totaling more than 26 μs to show how a promising lead compound can target one Nav implicated in pain perception and specific channels found in bacteria, and accurately predict the affinity of the compound to different channel types. Most importantly, we provide two explanations for the slow kinetics of this class of compound that limits their therapeutic utility. Firstly, the negative charge on the compound is essential for high affinity binding but is also responsible for energetic barriers that slow binding. Secondly, the compound has to undergo a conformational reorientation during the binding process. This knowledge aids the design of compounds affecting specific eukaryotic and bacterial channels and suggests routes for future drug development.

Identification of Intrahelical Bifurcated H-Bonds as a New Type of Gate in K+ Channels

Gating of ion channels is based on structural transitions between open and closed states. To uncover the chemical basis of individual gates, we performed a comparative experimental and computational analysis between two K⁺ channels, Kcv_S and Kcv_NTS. These small viral encoded K⁺ channel proteins, with a monomer size of only 82 amino acids, resemble the pore module of all complex K⁺ channels in terms of structure and function. Even though both proteins share about 90% amino acid sequence identity, they exhibit different open probabilities with ca. 90% in Kcv_NTS and 40% in Kcv_S. Single channel analysis, mutational studies and molecular dynamics simulations show that the difference in open probability is caused by one long closed state in Kcv_S. This state is structurally created in the tetrameric channel by a transient, Ser mediated, intrahelical hydrogen bond. The resulting kink in the inner transmembrane domain swings the aromatic rings from downstream Phes in the cavity of the channel, which blocks ion flux. The frequent occurrence of Ser or Thr based helical kinks in membrane proteins suggests that a similar mechanism could also occur in the gating of other ion channels.

A selectivity filter at the intracellular end of the acid-sensing ion channel pore

Increased extracellular proton concentrations during neurotransmission are converted to excitatory sodium influx by acid-sensing ion channels (ASICs). 10-fold sodium/potassium selectivity in ASICs has long been attributed to a central constriction in the channel pore, but experimental verification is lacking due to the sensitivity of this structure to conventional manipulations. Here, we explored the basis for ion selectivity by incorporating unnatural amino acids into the channel, engineering channel stoichiometry and performing free energy simulations. We observed no preference for sodium at the “GAS belt” in the central constriction. Instead, we identified a band of glutamate and aspartate side chains at the lower end of the pore that enables preferential sodium conduction.

DOI:http://dx.doi.org/10.7554/eLife.24630.001

The chemical basis for electrical signaling

Electrical signals generated by minute currents of ions moving across cell membranes are central to all rapid processes in biology. Initiation and propagation of electrical signals requires voltage-gated sodium (Na_V) and calcium (Ca_V) channels. These channels contain a tetramer of membrane-bound subunits or domains comprising a voltage sensor and a pore module. Voltage-dependent activation occurs as membrane depolarization drives outward movements of positive gating changes in the voltage sensor via a sliding-helix mechanism, which leads to a conformational change in the pore module that opens its intracellular activation gate. A unique negatively charged site in the selectivity filter conducts hydrated Na⁺ or Ca²⁺ rapidly and selectively. Ion conductance is terminated by voltage-dependent inactivation, which causes asymmetric pore collapse. This Review focuses on recent advances in structure and function of Na_V and Ca_V channels that expand our current understanding of the chemical basis for electrical signaling mechanisms conserved from bacteria to humans.

Structures of closed and open states of a voltage-gated sodium channel

Bacterial voltage-gated sodium channels (BacNavs) serve as models of their vertebrate counterparts. BacNavs contain conserved voltage-sensing and pore-forming domains, but they are homotetramers of four identical subunits, rather than pseudotetramers of four homologous domains. Here, we present structures of two Na_VAb mutants that capture tightly closed and open states at a resolution of 2.8-3.2 Å. Introduction of two humanizing mutations in the S6 segment (Na_VAb/FY: T206F and V213Y) generates a persistently closed form of the activation gate in which the intracellular ends of the four S6 segments are drawn tightly together to block ion permeation completely. This construct also revealed the complete structure of the four-helix bundle that forms the C-terminal domain. In contrast, truncation of the C-terminal 40 residues in Na_vAb/1-226 captures the activation gate in an open conformation, revealing the open state of a BacNav with intact voltage sensors. Comparing these structures illustrates the full range of motion of the activation gate, from closed with its orifice fully occluded to open with an orifice of ∼10 Å. Molecular dynamics and free-energy simulations confirm designation of Na_VAb/1-226 as an open state that allows permeation of hydrated Na⁺, and these results also support a hydrophobic gating mechanism for control of ion permeation. These two structures allow completion of a closed-open-inactivated conformational cycle in a single voltage-gated sodium channel and give insight into the structural basis for state-dependent binding of sodium channel-blocking drugs.

Sodium Binding Sites and Permeation Mechanism in the NaChBac Channel: A Molecular Dynamics Study

NaChBac was the first discovered bacterial sodium voltage-dependent channel, yet computational studies are still limited due to the lack of a crystal structure. In this work, a pore-only construct built using the NavMs template was investigated using unbiased molecular dynamics and metadynamics. The potential of mean force (PMF) from the unbiased run features four minima, three of which correspond to sites IN, CEN, and HFS discovered in NavAb. During the run, the selectivity filter (SF) is spontaneously occupied by two ions, and frequent access of a third one is often observed. In the innermost sites IN and CEN, Na⁺ is fully hydrated by six water molecules and occupies an on-axis position. In site HFS sodium interacts with a glutamate and a serine from the same subunit and is forced to adopt an off-axis placement. Metadynamics simulations biasing one and two ions show an energy barrier in the SF that prevents single-ion permeation. An analysis of the permeation mechanism was performed both computing minimum energy paths in the axial-axial PMF and through a combination of Markov state modeling and transition path theory. Both approaches reveal a knock-on mechanism involving at least two but possibly three ions. The currents predicted from the unbiased simulation using linear response theory are in excellent agreement with single-channel patch-clamp recordings.