Modeling permeation energetics in the KcsA potassium channel

The Optimized Conformation Dynamics of the KcsA Filter as a Probe for Lateral Membrane Effects: A First Principle Based Femto-Sec Resolution MD Study

We provide a high resolution, all-atom, femto-second molecular dynamics (MD) simulation of the passage of K⁺ ions and H₂O molecules through the selectivity filter of the KcsA potassium ion channel, based on first principle physical methods. Our results show that a change in the length of the selectivity filter of as little as 3%, regardless of whether the filter is made longer or shorter, will reduce the K⁺ ion current by around 50%. In addition, further squeezing or stretching by about 9% can effectively stop the current. Our results demonstrate optimized conformational dynamics that associate an increased mobility of parts in the filter linings with a standard configuration, leading to maximized conduction rates that are highly sensitive to geometrical distortions. We discuss this latter aspect in relation to lateral membrane effects on the filter region of ion channels and the 'force from lipids' hypothesis.

Quantum Mechanical Coherence of K+ Ion Wave Packets Increases Conduction in the KcsA Ion Channel

We simulate the transmission of K+ ions through the KcsA potassium ion channel filter region at physiological temperatures, employing classical molecular dynamics (MD) at the atomic scale together with a quantum mechanical version of MD simulation (QMD), treating single ions as quantum wave packets. We provide a direct comparison between both concepts, embedding the simulations into identical force fields and thermal fluctuations. The quantum simulations permit the estimation of coherence times and wave packet dispersions of a K+ ion over a range of 0.5 nm (a range that covers almost 50% of the filter domains longitudinal extension). We find that this observed extension of particle delocalization changes the mean orientation of the coordinating carbonyl oxygen atoms significantly, transiently suppressing their ‘caging action’ responsible for selective ion coordination. Compared to classical MD simulations, this particular quantum effect allows the K+ ions to ‘escape’ more easily from temporary binding sites provided by the surrounding filter atoms. To further elucidate the role of this observation for ion conduction rates, we compare the temporal pattern of single conduction events between classical MD and quantum QMD simulations at a femto-sec time scale. A finding from both approaches is that ion permeation follows a very irregular time pattern, involving flushes of permeation interrupted by non-conductive time intervals. However, as compared with classical behavior, the QMD simulation shortens non-conductive time by more than a half. As a consequence, and given the same force-fields, the QMD-simulated ion current appears to be considerably stronger as compared with the classical current. To bring this result in line with experimentally observed ion currents and the predictions based on Nernst–Planck theories, the conclusion is that a transient short time quantum behavior of permeating ions can successfully compromise high conduction rates with ion selectivity in the filter of channel proteins.

Quantum Dynamics and Non-Local Effects Behind Ion Transition States during Permeation in Membrane Channel Proteins

We present a comparison of a classical and a quantum mechanical calculation of the motion of K⁺ ions in the highly conserved KcsA selectivity filter motive of voltage gated ion channels. We first show that the de Broglie wavelength of thermal ions is not much smaller than the periodic structure of Coulomb potentials in the nano-pore model of the selectivity filter. This implies that an ion may no longer be viewed to be at one exact position at a given time but can better be described by a quantum mechanical wave function. Based on first principle methods, we demonstrate solutions of a non-linear Schrödinger model that provide insight into the role of short-lived (~1 ps) coherent ion transition states and attribute an important role to subsequent decoherence and the associated quantum to classical transition for permeating ions. It is found that short coherences are not just beneficial but also necessary to explain the fast-directed permeation of ions through the potential barriers of the filter. Certain aspects of quantum dynamics and non-local effects appear to be indispensable to resolve the discrepancy between potential barrier height, as reported from classical thermodynamics, and experimentally observed transition rates of ions through channel proteins.

Equilibrium fluctuation relations for voltage coupling in membrane proteins

A general theoretical framework is developed to account for the effects of an external potential on the energetics of membrane proteins. The framework is based on the free energy relation between two (forward/backward) probability densities, which was recently generalized to non-equilibrium processes, culminating in the work-fluctuation theorem. Starting from the probability densities of the conformational states along the "voltage coupling" reaction coordinate, we investigate several interconnected free energy relations between these two conformational states, considering voltage activation of ion channels. The free energy difference between the two conformational states at zero (depolarization) membrane potential (i.e., known as the chemical component of free energy change in ion channels) is shown to be equivalent to the free energy difference between the two "equilibrium" (resting and activated) conformational states along the one-dimensional voltage couplin reaction coordinate. Furthermore, the requirement that the application of linear response approximation to the free energy functionals of voltage coupling should satisfy the general free energy relations, yields a novel closed-form expression for the gating charge in terms of other basic properties of ion channels. This connection is familiar in statistical mechanics, known as the equilibrium fluctuation-response relation. The theory is illustrated by considering the coupling of a unit charge to the external voltage in the two sites near the surface of membrane, representing the activated and resting states. This is done using a coarse-graining (CG) model of membrane proteins, which includes the membrane, the electrolytes and the electrodes. The CG model yields Marcus-type voltage dependent free energy parabolas for the response of the electrostatic environment (electrolytes etc.) to the transition from the initial to the final configuratinal states, leading to equilibrium free energy difference and free energy barrier that follow the trend of the equilibrium fluctuation relation and the Marcus theory of electron transfer. These energetics also allow for a direct estimation of the voltage dependence of channel activation (Q-V curve), offering a quantitative rationale for a correlation between the voltage dependence parabolas and the Q-V curve, upon site-directed mutagenesis or drug binding. Taken together, by introducing the voltage coupling as the energy gap reaction coordinate, our framework brings new perspectives to the thermodynamic models of voltage activation in voltage-sensitive membrane proteins, offering an a framework for a better understating of the structure-function correlations of voltage gating in ion channels as well as electrogenic phenomena in ion pumps and transporters. Significantly, this formulation also provides a powerful bridge between the CG model of voltage coupling and the conventional macroscopic treatments.

Water molecules response to an external GHz electric field in KcsA potassium channel: A molecular modeling approach

KcsA potassium channel is a membrane protein that allows the passage of potassium ions and water molecules across the cellular membrane. Using molecular dynamics (MD) simulation method, the effect of an applied GHz oscillating electric field of strength 0.004 V/nm on the dynamics of K + and water molecules in a KcsA channel was modeled. It was found that the application of GHz range electric field caused a change in the potential energy profile of the water molecules in the filter sites, causing an increase in the delay time of the water molecules in these sites. Therefore, exposing the channel to the GHz fields can perturb the dynamics of the water molecules in the filter, and consequently, the channel operation may be disturbed. Furthermore, the results show that the applied field has no major effects on the dipole orientation of water molecules in the channel.

A quantum-mechanical description of ion motion within the confining potentials of voltage-gated ion channels

Voltage-gated channel proteins cooperate in the transmission of membrane potentials between nerve cells. With the recent progress in atomic-scaled biological chemistry, it has now become established that these channel proteins provide highly correlated atomic environments that may maintain electronic coherences even at warm temperatures. Here we demonstrate solutions of the Schrödinger equation that represent the interaction of a single potassium ion within the surrounding carbonyl dipoles in the Berneche-Roux model of the bacterial KcsA model channel. We show that, depending on the surrounding carbonyl-derived potentials, alkali ions can become highly delocalized in the filter region of proteins at warm temperatures. We provide estimations on the temporal evolution of the kinetic energy of ions depending on their interaction with other ions, their location within the oxygen cage of the proteins filter region, and depending on different oscillation frequencies of the surrounding carbonyl groups. Our results provide the first evidence that quantum mechanical properties are needed to explain a fundamental biological property such as ion selectivity in transmembrane ion currents and the effect on gating kinetics and shaping of classical conductances in electrically excitable cells.

Ion solvation and structural stability in a sodium channel investigated by molecular dynamics calculations

The stability and ion binding properties of the homo-tetrameric pore domain of a prokaryotic, voltage-gated sodium channel are studied by extensive all-atom molecular dynamics simulations, with the channel protein being embedded in a fully hydrated lipid bilayer. It is found that Na(+) ion presents in a mostly hydrated state inside the wide pore of the selectivity filter of the sodium channel, in sharp contrast to the nearly fully dehydrated state for K(+) ions in potassium channels. Our results also indicate that Na(+) ions make contact with only one or two out of the four polypeptide chains forming the selectivity filter, and surprisingly, the selectivity filter exhibits robust stability for various initial ion configurations even in the absence of ions. These findings are quite different from those in potassium channels. Furthermore, an electric field above 0.5V/nm is suggested to be able to induce Na(+) permeation through the selectivity filter.

Conformational changes in the selectivity filter of the open-state KcsA channel: an energy minimization study

Potassium channels switch between closed and open conformations and selectively conduct K(+) ions. There are at least two gates. The TM2 bundle at the intracellular site is the primary gate of KcsA, and rearrangements at the selectivity filter (SF) act as the second gate. The SF blocks ion flow via an inactivation process similar to C-type inactivation of voltage-gated K(+) channels. We recently generated the open-state conformation of the KcsA channel. We found no major, possibly inactivating, structural changes in the SF associated with this massive inner-pore rearrangement, which suggests that the gates might act independently. Here we energy-minimize the open state of wild-type and mutant KcsA, validating in silico structures of energy-minimized SFs by comparison with crystallographic structures, and use these data to gain insight into how mutation, ion depletion, and K(+) to Na(+) substitution influence SF conformation. Both E71 or D80 protonations/mutations and the presence/absence of protein-buried water molecule(s) modify the H-bonding network stabilizing the P-loops, spawning numerous SF conformations. We find that the inactivated state corresponds to conformations with a partially unoccupied or an entirely empty SF. These structures, involving modifications in all four P-loops, are stabilized by H-bonds between amide H and carbonyl O atoms from adjacent P-loops, which block ion passage. The inner portions of the P-loops are more rigid than the outer parts. Changes are localized to the outer binding sites, with innermost site S4 persisting in the inactivated state. Strong binding by Na(+) locally contracts the SF around Na(+), releasing ligands that do not participate in Na(+) coordination, and occluding the permeation pathway. K(+) selectivity primarily appears to arise from the inability of the SF to completely dehydrate Na(+) ions due to basic structural differences between liquid water and the "quasi-liquid" SF matrix.

Structure refinement of the OpcA adhesin using molecular dynamics

OpcA from Neisseria meningitidis, the causative agent of meningococcal meningitis and septicemia, is an integral outer membrane protein that facilitates meningococcal adhesion through binding the proteoglycan receptors of susceptible cells. Two structures of OpcA have been determined by x-ray diffraction to 2 A resolution, revealing dramatically different conformations in the extracellular loops--the protein domain implicated in proteoglycan binding. In the first structure, a positively charged crevice formed by loops 1 and 2 was identified as the site for binding proteoglycans, whereas in the second structure the crevice was not evident as loops 1 and 2 adopted different conformations. To reconcile these results, molecular-dynamics simulations were carried out on both structures embedded in a solvated lipid bilayer membrane. Free of crystal contacts and crystallization agents, the loops were observed to undergo large structural transformations, suggesting that the conformation of the loops in either x-ray structure is affected by crystallization. Subsequent simulations of both structures in their crystal lattices confirmed this conclusion. Based on our molecular-dynamics trajectories, we propose a model for OpcA that combines stable structural features of the available x-ray structures. In this model, all five extracellular loops of OpcA have stable secondary structures. The loops form a funnel that leads to the base of the beta-barrel and that includes Tyr-169 on its exposed surface, which has been implicated in proteoglycan binding.

Cooperative transport in a potassium ion channel

Our current understanding of ion permeation through the selectivity filter of the KcsA potassium channel is based on the concept of a multi-ion transport mechanism. The details of this concerted movement, however, are not well understood. In the present paper we report on molecular dynamics simulations which provides new insights. It is shown that ion translocation is based on the collective hopping of ions and water molecules which is mediated by the flexible charged carbonyl groups lining the backbone of the pore. In particular, there is strong evidence for pairwise translocations where one ion and one water molecule form a bound state. We suggest a physical explanation of the observed phenomena employing a simple lattice model. It is argued that the water molecules can act as rectifiers during the hopping of ion-water pairs.

Quantum mechanical calculations of charge effects on gating the KcsA channel

A series of ab initio (density functional) calculations were carried out on side chains of a set of amino acids, plus water, from the (intracellular) gating region of the KcsA K(+) channel. Their atomic coordinates, except hydrogen, are known from X-ray structures [D.A. Doyle, J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, R. MacKinnon, The structure of the potassium channel: molecular basis of K(+) conduction and selectivity, Science 280 (1998) 69-77; R. MacKinnon, S.L. Cohen, A. Kuo, A. Lee, B.T. Chait, Structural conservation in prokaryotic and eukaryotic potassium channels, Science 280 (1998) 106-109; Y. Jiang, A. Lee, J. Chen, M. Cadene, B.T. Chait, R. MacKinnon, The open pore conformation of potassium channels. Nature 417 (2001) 523-526], as are the coordinates of some water oxygen atoms. The 1k4c structure is used for the starting coordinates. Quantum mechanical optimization, in spite of the starting configuration, places the atoms in positions much closer to the 1j95, more tightly closed, configuration. This state shows four water molecules forming a "basket" under the Q119 side chains, blocking the channel. When a hydrated K(+) approaches this "basket", the optimized system shows a strong set of hydrogen bonds with the K(+) at defined positions, preventing further approach of the K(+) to the basket. This optimized structure with hydrated K(+) added shows an ice-like 12 molecule nanocrystal of water. If the water molecules exchange, unless they do it as a group, the channel will remain blocked. The "basket" itself appears to be very stable, although it is possible that the K(+) with its hydrating water molecules may be more mobile, capable of withdrawing from the gate. It is also not surprising that water essentially freezes, or forms a kind of glue, in a nanometer space; this agrees with experimental results on a rather different, but similarly sized (nm dimensions) system [K.B. Jinesh, J.W.M. Frenken, Capillary condensation in atomic scale friction: how water acts like a glue, Phys. Rev. Lett. 96 (2006) 166103/1-4]. It also agrees qualitatively with simulations on channels [A. Anishkin, S. Sukharev, Water dynamics and dewetting transitions in the small mechanosensitive channel MscS, Biophys. J. 86 (2004) 2883-2895; O. Beckstein, M.S.P. Sansom, Liquid-vapor oscillations of water in hydrophobic nanopores, Proc. Natl Acad. Sci. U. S. A. 100 (2003) 7063-7068] and on featureless channel-like systems [J. Lu, M.E. Green, Simulation of water in a pore with charges: application to a gating mechanism for ion channels, Prog. Colloid Polym. Sci. 103 (1997) 121-129], in that it forms a boundary on water that is not obvious from the liquid state. The idea that a structure is stable, even if individual molecules exchange, is well known, for example from the hydration shell of ions. We show that when charges are added in the form of protons to the domains (one proton per domain), the optimized structure is open. No stable water hydrogen bonds hold it together; an opening of 11.0 A appears, measured diagonally between non-neighboring domains as glutamine 119 carbonyl O-O distance. This is comparable to the opening in the MthK potassium channel structure that is generally agreed to be open. The appearance of the opening is in rather good agreement with that found by Perozo and coworkers. In contrast, in the uncharged structure this diagonal distance is 6.5 A, and the water "basket" constricts the uncharged opening still further, with the ice-like structure that couples the K(+) ion to the gating region freezing the entrance to the channel. Comparison with our earlier model for voltage gated channels suggests that a similar mechanism may apply in those channels.

Ion selectivity in potassium channels

Potassium channels are tetrameric membrane-spanning proteins that provide a selective pore for the conduction of K(+) across the cell membranes. One of the main physiological functions of potassium channels is efficient and very selective transport of K(+) ions through the membrane to the cell. Classical views of ion selectivity are summarized within a historical perspective, and contrasted with the molecular dynamics (MD) simulations free energy perturbation (FEP) performed on the basis of the crystallographic structure of the KcsA phospholipid membrane. The results show that the KcsA channel does not select for K(+) ions by providing a binding site of an appropriate (fixed) cavity size. Rather, selectivity for K(+) arises directly from the intrinsic local physical properties of the ligands coordinating the cation in the binding site, and is a robust feature of a pore symmetrically lined by backbone carbonyl groups. Further analysis reveals that it is the interplay between the attractive ion-ligand (favoring smaller cation) and repulsive ligand-ligand interactions (favoring larger cations) that is the basic element governing Na(+)/K(+) selectivity in flexible protein binding sites. Because the number and the type of ligands coordinating an ion directly modulate such local interactions, this provides a potent molecular mechanism to achieve and maintain a high selectivity in protein binding sites despite a significant conformational flexibility.

Mechanism of Ion Permeation in a Model Channel: Free Energy Surface and Dynamics of K+Ion Transport in an Anion-Doped Carbon Nanotube

The mechanism of the ion permeation is investigated for an anion-doped carbon nanotube, as a model of the K+ channel, by analyzing the free energy surface and the dynamics of the ion permeation through the model channel. It is found that the main rate-determining step is how an ion enters the channel. The entrance of the ion is mostly blocked by a water molecule located at this entrance. Only about 10% of K+ ions which reach the mouth of the channel can really enter the channel. The rejection rate sensitively depends on the location of this water molecule, which is easily controlled by the charge of the carbon nanotube; for example, the maximum permeation is obtained when the anion charge is at a certain value, -5.4e in the present model. At this charge, the facile translocation of the ion inside the channel is also induced due to the number of fluctuations of the ions inside the channel. Therefore, the so-called "Newton's balls", a toy model, combined with a simple ion diffusion model for explaining the fast ion permeation should be modified. The present analysis thus suggests that there exists an optimum combination of the length and the charge of the carbon nanotube for the most efficient ion permeation.

Application of the Poisson-Nernst-Planck theory with space-dependent diffusion coefficients to KcsA

The Poisson-Nernst-Planck electrodiffusion theory serves to compute charge fluxes and is here applied to the ion current through a protein channel. KcsA was selected as an example because of the abundance of experimental and theoretical data. The potassium channels MthK and KvAP were used as templates to define two open channel models for KcsA. Channel boundary surfaces and protein charge distributions were defined according to atomic radii and partial atomic charges. To establish the sensitivity of the results to these parameters, two different sets were used. Assigning the potassium diffusion coefficients equal to the value for free-diffusion in water (1.96 x 10(-9) m(2)/s), the computed currents overestimated the experimental data. Ion distributions inside the channel suggest that the overestimate is not due to an excess of charge shielding. A good agreement with the experimental data was achieved by reducing the potassium diffusion coefficient inside the channel to 1.96 x 10(-10) m(2)/s, a value of substantial motility but nonetheless in accord with the intuitive notion that the channel has a high affinity for the ions and therefore slows them down. These results are independent of the open channel model and the parameterization adopted for atomic radii and partial atomic charges. The method offers a reliable estimate of the channel current with low computational effort.

Three computational methods for studying permeation, selectivity and dynamics in biological ion channels

The cell membrane, confining some ions and molecules on one side and exchanging others with the other side, is the ultimate unit of the physiology of life. The delicate task of regulating the transport of ions across the membrane is carried out by biological nanotubes called 'ion channels'. Recently, there have been enormous strides in our understanding of the structure-function relationships of biological ion channels. The molecular structures of several ion channels have been determined from crystallographic analysis, including potassium channels, mechanosensitive channels, a chloride channel, as well as gramicidin channels and porins. It is expected that the X-ray structures of other ion channels will soon follow these discoveries, ushering in a new era of ion channel studies in which predicting the function of channels from their atomic structures will become the main quest. In parallel to these experimental findings, there have been important advances in computational biophysics. Here we summarize three theoretical approaches that have been utilized to understand the dynamics of ion permeation across bio-nanotubes, highlighting their advantages and shortcomings, and briefly describe some of the salient properties of ion channels uncovered through computational studies.

Ion conduction and selectivity in K(+) channels

Potassium (K(+)) channels are tetrameric membrane-spanning proteins that provide a selective pore for the conductance of K(+) across the cell membranes. These channels are most remarkable in their ability to discriminate K(+) from Na(+) by more than a thousandfold and conduct at a throughput rate near diffusion limit. The recent progress in the structural characterization of K(+) channel provides us with a unique opportunity to understand their function at the atomic level. With their ability to go beyond static structures, molecular dynamics simulations based on atomic models can play an important role in shaping our view of how ion channels carry out their function. The purpose of this review is to summarize the most important findings from experiments and computations and to highlight a number of fundamental mechanistic questions about ion conduction and selectivity that will require further work.

Semimicroscopic modeling of permeation energetics in ion channels

The semimicroscopic (SMC) approach to modeling the energetics of ion permeation through biological channels provides an alternative perspective to standard molecular dynamics methods. It exploits the timescale separation between electronic and structural contributions to dielectric stabilization and accounts for electronic polarization by embedding the channel in a milieu that, on average, describes this polarization. Ions, water, and selected peptide moieties are mobile and comprise the reorganizational contribution to dielectric stabilization. The conceptual advantages and limitations of the technique are described. Methodological details are outlined, stressing three convenient electrical geometries. Practical aspects of the SMC procedure are explained, highlighting the areas ripe for further development. Finally, some specific applications are considered.

Ionic permeation free energy in gramicidin: a semimicroscopic perspective

Ion permeation through the gramicidin channel is studied using a model that circumvents two major difficulties inherent to standard simulational methods. It exploits the timescale separation between electronic and structural contributions to dielectric stabilization, accounting for the influence of electronic polarization by embedding the channel in a dielectric milieu that describes this polarization in a mean sense. The explicit mobile moieties are the ion, multipolar waters, and the carbonyls and amides of the peptide backbone. The model treats the influence of aromatic residues and the membrane dipole potential. A new electrical geometry is introduced that treats long-range electrostatics exactly and avoids problems related to periodic boundary conditions. It permits the translocating ion to make a seamless transition from nearby electrolyte to the channel interior. Other degrees of freedom (more distant bulk electrolyte and nonpolar lipid) are treated as dielectric continua. Reasonable permeation free energy profiles are obtained for potassium, rubidium, and cesium; binding wells are shallow and the central barrier is small. Estimated cationic single-channel conductances are smaller than experiment, but only by factors between 2 (rubidium) and 50 (potassium). When applied to chloride the internal barrier is large, with a corresponding miniscule single-channel conductance. The estimated relative single-channel conductances of gramicidin A, B, and C agree well with experiment.

Computer simulations of membrane proteins

Computer simulations are rapidly becoming a standard tool to study the structure and dynamics of lipids and membrane proteins. Increasing computer capacity allows unbiased simulations of lipid and membrane-active peptides. With the increasing number of high-resolution structures of membrane proteins, which also enables homology modelling of more structures, a wide range of membrane proteins can now be simulated over time spans that capture essential biological processes. Longer time scales are accessible by special computational methods. We review recent progress in simulations of membrane proteins.

Tools for channels: moving towards molecular calculations of gating and permeation in ion channel biophysics

Recent X-ray structures of voltage gated potassium channels provide an exciting opportunity to connect molecular structures with measured biological function. Two of the most important connections for these channels are: first, to the molecular basis behind selectivity and the associated free energy profile underlying ionic current flow and, second, to a true molecular understanding of the large-scale conformational transitions that underlie voltage dependent gating. But, existing computational tools need to be further developed to reach these goals. In this contribution to the symposia on sampling methods we outline our dynamic importance sampling method for sampling large-scale conformational transitions as well as our studies with non-equilibrium work events and equilibrium overlap sampling (OS) methods for sampling events related to the calculation of relative free energies.

Long Distance Interactions within the Potassium Channel Pore Are Revealed by Molecular Diversity of Viral Proteins

Kcv is a 94-amino acid protein encoded by chlorella virus PBCV-1 that corresponds to the pore module of K(+) channels. Therefore, Kcv can be a model for studying the protein design of K(+) channel pores. We analyzed the molecular diversity generated by approximately 1 billion years of evolution on kcv genes isolated from 40 additional chlorella viruses. Because the channel is apparently required for virus replication, the Kcv variants are all functional and contain multiple and dispersed substitutions that represent a repertoire of allowed sets of amino acid substitutions (from 4 to 12 amino acids). Correlations between amino acid substitutions and the new properties displayed by these channels guided site-directed mutations that revealed synergistic amino acid interactions within the protein as well as previously unknown interactions between distant channel domains. The effects of these multiple changes were not predictable from a priori structural knowledge of the channel pore.

Streptomyces lividans potassium channel KcsA is regulated by the potassium electrochemical gradient

It is currently held that the Streptomyces lividans potassium channel, KcsA, requires an intracellular pH<5 to exhibit activity in planar lipid bilayers. Here, we show that KcsA functions well at normal physiological pH in the presence of a potassium electrochemical gradient. Single-channel conductance and open probability increased directly as the extracellular potassium concentration was decreased. Channel activity was sensitive to both the membrane potential and the size of the gradient, thus indicating that gating of the channel depends on both components of the electrochemical potential. When [K(+)(in)]/[K(+)(ex)] was 200 mM/10 mM, chord conductance was 24pS with subconductance 15pS; open probability was 0.9. The permeability series was K(+) > Rb(+) >>> Cs(+); K(+) selectivity over Rb(+) was 1.2-fold and selectivity over Na(+) was 12-fold. The channels were disrupted by intracellular Na(+) and blocked by intracellular Ba(2+). A hypothetical supramolecular model for the channel is presented.