The gramicidin a channel: A review of its permeability characteristics with special reference to the single-file aspect of transport

Summary Gramicidin A forms univalent cation-selective channels of 4 Å diameter in phospholipid bilayer membranes. The transport of ions and water throughout most of the channel length is by a singlefile process; that is, cations and water molecules cannot pass each other within the channel. The implications of this single-file mode of transport for ion movement are considered. In particular, we show that there is no significant electrostatic barrier to ion movement between the energy wells at the two ends of the channel. The rate of ion translocation (e.g., Na⁺ or Cs⁺) through the channel between these wells is limited by the necessity for an ion to move six water molecules in single file along with it; this also limits the maximum possible value for channel conductance. At all attainable concentrations of NaCl, the gramicidin A channel never contains more than one sodium ion, whereas even at 0.1M CsCl, some channels contain two cesium ions. There is no necessity to postulate more than two ion-binding sites in the channel or occupancy of the channel by more than two ions at any time.     

Conducting-state properties of the KcsA potassium channel from molecular and Brownian dynamics simulations.

The mechanisms underlying transport of ions across the potassium channel are examined using electrostatic calculations and three-dimensional Brownian dynamics simulations. We first build open-state configurations of the channel with molecular dynamics simulations, by pulling the transmembrane helices outward until the channel attains the desired interior radius. To gain insights into ion permeation, we construct potential energy profiles experienced by an ion traversing the channel in the presence of other resident ions. These profiles reveal that in the absence of an applied field the channel accommodates three potassium ions in a stable equilibrium, two in the selectivity filter and one in the central cavity. In the presence of a driving potential, this three-ion state becomes unstable, and ion permeation across the channel is observed. These qualitative explanations are confirmed by the results of three-dimensional Brownian dynamics simulations. We find that the channel conducts when the ionizable residues near the extracellular entrance are fully charged and those near the intracellular side are partially charged. The conductance increases steeply as the radius of the intracellular mouth of the channel is increased from 2 A to 5 A. Our simulation results reproduce several experimental observations, including the current-voltage curves, conductance-concentration relationships, and outward rectification of currents.     

Permeation of ions across the potassium channel: brownian dynamics studies

The physical mechanisms underlying the transport of ions across a model potassium channel are described. The shape of the model channel corresponds closely to that deduced from crystallography. From electrostatic calculations, we show that an ion permeating the channel, in the absence of any residual charges, encounters an insurmountable energy barrier arising from induced surface charges. Carbonyl groups along the selectivity filter, helix dipoles near the oval chamber, and mouth dipoles near the channel entrances together transform the energy barrier into a deep energy well. Two ions are attracted to this well, and their presence in the channel permits ions to diffuse across it under the influence of an electric field. Using Brownian dynamics simulations, we determine the magnitude of currents flowing across the channel under various conditions. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength causes a steady decrease in the channel conductance. The current also decreases systematically when the effective dielectric constant of the channel is lowered. The conductance with the optimal choice of dipoles reproduces the experimental value when the dielectric constant of the channel is assumed to be 60. The current-voltage relationship obtained with symmetrical solutions is linear when the applied potential is less than approximately 100 mV but deviates from Ohm's law at a higher applied potential. The reversal potentials obtained with asymmetrical solutions are in agreement with those predicted by the Nernst equation. The conductance exhibits the saturation property observed experimentally. We discuss the implications of these findings for the transport of ions across the potassium channels and membrane channels in general.     

The pore helix dipole has a minor role in inward rectifier channel function

Ion channels lower the energetic barrier for ion passage across cell membranes and enable the generation of bioelectricity. Electrostatic interactions between permeant ions and channel pore helix dipoles have been proposed as a general mechanism for facilitating ion passage. Here, using genetic selections to probe interactions of an exemplar potassium channel blocker, barium, with the inward rectifier Kir2.1, we identify mutants bearing positively charged residues in the potassium channel signature sequence at the pore helix C terminus. We show that these channels are functional, selective, resistant to barium block, and have minimally altered conductance properties. Both the experimental data and model calculations indicate that barium resistance originates from electrostatics. We demonstrate that potassium channel function is remarkably unperturbed when positive charges occur near the permeant ions at a location that should counteract pore helix electrostatic effects. Thus, contrary to accepted models, the pore helix dipole seems to be a minor factor in potassium channel permeation.     

Multiple-state model of ionic channel in reproducing the time course of electrophysiological events.

BACKGROUND: The predictions of the Hodgkin-Huxley model do not accurately fit all the measurements of voltage-clamp currents, gating charge and single-channel currents. There are many quantitative differences between the predicted and measured characteristics of the sodium and potassium channels. For example, the two-state gate model has exponential onset kinetics, whereas the sodium and potassium conductances show S-shaped activation and the sodium conductance shows an exponential inactivation. In this paper we shall examine a more general channel model that can more faithfully represent the measured properties of ionic channels in the membrane of the excitable cell. METHODS: The model is based on the generalisation of the notion of a channel with a discrete set of states. Each state has state attributes such as the state conductance, state ionic current and state gating charge. These variables can have quite different waveforms in time, in contrast with a two-state gate channel model, in which all have the same waveforms. RESULTS: The kinetics of all variables are equivalent: gating and ionic currents give equivalent information about channel kinetics; both the equilibrium values of the current and the time constants are functions of membrane potential. The results are in almost perfect concordance with the experimental data regarding the characteristics of nerve impulse. CONCLUSIONS: The expected values of the gating charge and the ionic conductance are weighted sums of the state occupancy probabilities, but the weights differ: for the expected value of the gating charge the weights are the state gating charges and for the expected value of the ionic conductance the weights are the state conductances. Since these weights are different, the expected values of the gating charge and the ionic conductance will differ.     

Thallous ion movements through gramicidin channels incorporated in lipid monolayers supported by mercury.

The potential independent limiting flux of hydrated Tl(+) ions through gramicidin (GR) channels incorporated in phospholipid monolayers self assembled on a hanging mercury-drop electrode is shown to be controlled both by diffusion and by a dehydration step. Conversely, the potential independent limiting flux of dehydrated Tl(+) ions stemming from Tl amalgam electro-oxidation is exclusively controlled by diffusion of thallium atoms within the amalgam. Modulating the charge on the polar heads of dioleoylphosphatidylserine (DOPS) by changing pH affects the limiting flux of hydrated Tl(+) ions to a notable extent, primarily by electrostatic interactions. The dipole potential of DOPS and dioleoylphosphatidylcholine (DOPC), positive toward the hydrocarbon tails, does not hinder the translocation step of Tl(+) ions to such an extent as to make it rate limiting. Consequently, incorporation in the lipid monolayer of phloretin, which decreases such a positive dipole potential, does not affect the kinetics of Tl(+) flux through GR channels. In contrast, the increase in the positive dipole potential produced by the incorporation of ketocholestanol causes the translocation step to contribute to the rate of the overall process. A model providing a quantitative interpretation of the kinetics of diffusion, dehydration-hydration, translocation, and charge transfer of the Tl(+)/Tl(0)(Hg) couple through GC channels incorporated in mercury-supported phospholipid monolayers is provided. A cut-off disk model yielding the profile of the local electrostatic potential created by an array of oriented dipoles located in the lipid monolayer along the axis of a cylindrical ion channel is developed.     

Transportation behavior of alkali ions through a cell membrane ion channel. A quantum chemical description of a simplified isolated model

Quantum chemical model calculations were carried out for modeling the ion transport through an isolated ion channel of a cell membrane. An isolated part of a natural ion channel was modeled. The model channel was a calixarene derivative, hydrated sodium and potassium ions were the models of the transported ion. The electrostatic potential of the channel and the energy of the channel-ion system were calculated as a function of the alkali ion position. Both attractive and repulsive ion-channel interactions were found. The calculations - namely the dependence of the system energy and the atomic charges of the water molecules with respect to the position of the alkali ion in the channel - revealed the molecular-structural background of the potassium selectivity of this artificial ion channel. It was concluded that the studied ion channel mimics real biological ion channel quite well.     

Electrostatic calculations for an ion channel. I. Energy and potential profiles and interactions between ions

The electrostatic energy profile of one, two, or three ions in an aqueous channel through a lipid membrane is calculated. It is shown that the previous solution to this problem (based on the assumption that the channel is infinitely long) significantly overestimates the electrostatic energy barrier. For example, for a 3-A radius pore, the energy is 16 kT for the infinite channel and 6.7 kT for an ion in the center of a channel 25 A long. The energy as a function of the position of the ion is also determined. With this energy profile, the rate of crossing the membrane (using the Nernst-Planck equation) was estimated and found to be compatible with the maximum conductance observed for the gramicidin A channel. The total electrostatic energy (as a function of position) required to place two or three ions in the channel is also calculated. The electrostatic interaction is small for two ions at opposite ends of the channel and large for any positioning of the three ions. Finally, the gradient through the channel of an applied potential is calculated. The solution to these problems is based on solving an equivalent problem in which an appropriate surface charge is placed on the boundary between the lipid and aqueous regions. The magnitude of the surface charge is obtained from the numerical solution for a system of coupled integral equations.     

Molecular origin of the cation selectivity in OmpF porin: single channel conductances vs. free energy calculation

Ion current through single outer membrane protein F (OmpF) trimers was recorded and compared to molecular dynamics simulation. Unidirectional insertion was revealed from the asymmetry in channel conductance. Single trimer conductance showed particularly high values at low symmetrical salt solution. The conductance values of various alkali metal ion solutions were proportional to the monovalent cation mobility values in the bulk phase, LiCl相似文献   

Study of ionic currents across a model membrane channel using Brownian dynamics.

Brownian dynamics simulations have been carried out to study ionic currents flowing across a model membrane channel under various conditions. The model channel we use has a cylindrical transmembrane segment that is joined to a catenary vestibule at each side. Two cylindrical reservoirs connected to the channel contain a fixed number of sodium and chloride ions. Under a driving force of 100 mV, the channel is virtually impermeable to sodium ions, owing to the repulsive dielectric force presented to ions by the vestibular wall. When two rings of dipoles, with their negative poles facing the pore lumen, are placed just above and below the constricted channel segment, sodium ions cross the channel. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength does not increase the channel conductance further. When only those ions that acquire a kinetic energy large enough to surmount a barrier are allowed to enter the narrow transmembrane segment, the channel conductance decreases monotonically with the barrier height. This barrier represents those interactions between an ion, water molecules, and the protein wall in the transmembrane segment that are not treated explicitly in the simulation. The conductance obtained from simulations closely matches that obtained from ACh channels when a step potential barrier of 2-3 kTr is placed at the channel neck. The current-voltage relationship obtained with symmetrical solutions is ohmic in the absence of a barrier. The current-voltage curve becomes nonlinear when the 3 kTr barrier is in place. With asymmetrical solutions, the relationship approximates the Goldman equation, with the reversal potential close to that predicted by the Nernst equation. The conductance first increases linearly with concentration and then begins to rise at a slower rate with higher ionic concentration. We discuss the implications of these findings for the transport of ions across the membrane and the structure of ion channels.     

Brownian dynamics study of an open-state KcsA potassium channel.

Three-dimensional Brownian dynamics simulations are used to study conductance of the KcsA potassium channel using the known crystallographic structure. Employing an open-state channel created by molecular dynamics simulations, current-voltage and current-concentration curves broadly consistent with experimental measurements are obtained. In the absence of an applied potential, the channel houses three potassium ions at positions that are in close agreement with X-ray diffraction maps.     

Partial purification of a potassium channel with low permeability for sodium from tonoplast membranes of Hordeum vulgare cv. Gerbel

Summary A potassium-specific tonoplast channel was identified by reconstitution of tonoplast polypeptides into planar lipid bilayer membranes. Highly purified tonoplast membranes were solubilized in Triton X-100-containing buffer and fractionated by size-exclusion chromatography. The protein fractions were assayed for ion channel activity in a planar bilayer system, and the potassium channel was routinely recovered in specific fractions corresponding to an apparent molecular mass of 80 kDa. In symmetrical electrolyte solutions of 100 mM potassium chloride, the potassium channel had a single-channel conductance of 72 pS. Substates of the channel with conductances of 17, 33 and 52 pS were frequently observed. After identification of the channel in low or high KCl, addition of sodium acetate or sodium chloride caused only insignificant conductance changes. This result suggested that the channel was not or little permeable for sodium or chloride, whereas it had similar single-channel conductance for rubidium and caesium ions as compared with potassium ions. The channel is presumably responsible for the equilibration of potassium between the vacuole and the cytosol. The role of the channel in the physiology of the barley cell under salt stress is discussed.The authors would like to thank U. Heber for many helpful discussions. This work was supported by grants of the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 176, projects B3 and B7) and by the Fonds der Chemischen Industrie.     

Thallous ion permeation through the cation-selective channel of the sarcoplasmic reticulum. Anomalous mole fraction dependence

The thallous ion was found to permeate the cation-selective channel of rabbit sarcoplasmic reticulum and to block current through this channel when present in mixtures with other permeant ions. Channel conductance in pure thallium acetate saturates with increasing concentration, with a maximum limiting conductance of 60 pS. The conductance ratio GK/GTl at 1 M is 3.7, while the permeability ratio is near 0.4 over the concentration range 0.01 to 1 M. Thallium blockade in mixtures can be described by the equation of Neher (Neher, E. (1975) Biochim. Biophys. Acta 401, 540-544).     

Basolateral potassium channel in turtle colon. Evidence for single-file ion flow

Treatment of the apical surface of the isolated, ouabain-inhibited turtle colon with the polyene antibiotic amphotericin B permitted the properties of a barium-sensitive potassium conductance in the basolateral membrane to be discerned from the measurements of transepithelial fluxes and electrical currents. Simultaneous measurements of potassium currents and 42K fluxes showed that the movement of potassium was not in accord with simple diffusion. Two other cations, thallium and rubidium, were also permeable and, in addition, exhibited strong interactions with the potassium tracer fluxes. The results indicate that permeant cations exhibit positive coupling, which is consistent with a single-file mechanism of ion translocation through a membrane channel.     

Invariant manifold reductions for Markovian ion channel dynamics

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

Ionic dependence of sodium currents in squid axons analyzed in terms of specific ion "channel" interactions.

Inward sodium currents were measured from voltage-clamped giant axons externally perfused with artificial seawater (ASW) solutions containing various concentrations of sodium and potassium ions. The data was analyzed under the assumption that under a constant membrane potential sodium conductance is determined by a specific ion-channel site (SIS) reaction. The sodium current density values were expressed in terms of SIS-reaction rates which were compared, by means of minimization techniques, with those computed for various saturation reaction mechanisms. The following conclusions were drawn: 1) The dependence of peak inward sodium current on external sodium and potassium concentrations can be described in terms of saturation reactions. 2) The experimental data fit well the kinetics of a positive cooperative homotropic reaction, involving at least two allosteric active sites. One of these sites may be catalytic while the other, either catalytic or regulatory. 3) The inhibitory effect of external potassium on inward sodium current, can be described by a reversible competitive or noncompetitive inhibition mechanism. The values of the dissociation constant of the inhibitor-site "complex" (Ki) were found to be close to the external potassium concentration under physiological conditions.     

Membrane surface-charge titration probed by gramicidin A channel conductance.

We manipulate lipid bilayer surface charge and gauge its influence on gramicidin A channel conductance by two strategies: titration of the lipid charge through bulk solution pH and dilution of a charged lipid by neutral. Using diphytanoyl phosphatidylserine (PS) bilayers with CsCl aqueous solutions, we show that the effects of lipid charge titration on channel conductance are masked 1) by conductance saturation with Cs+ ions in the neutral pH range and 2) by increased proton concentration when the bathing solution pH is less than 3. A smeared charge model permits us to separate different contributions to the channel conductance and to introduce a new method for "bilayer pKa" determination. We use the Gouy-Chapman expression for the charged surface potential to obtain equilibria of protons and cations with lipid charges. To calculate cation concentration at the channel mouth, we compare different models for the ion distribution, exact and linearized forms of the planar Poisson-Boltzmann equation, as well as the construction of a "Gibbs dividing surface" between salt bath and charged membrane. All approximations yield the intrinsic pKain of PS lipid in 0.1 M CsCl to be in the range 2.5-3.0. By diluting PS surface charge at a fixed pH with admixed neutral diphytanoyl phosphatidylcholine (PC), we obtain a conductance decrease in magnitude greater than expected from the electrostatic model. This observation is in accord with the different conductance saturation values for PS and PC lipids reported earlier (, Biochim. Biophys. Acta. 552:369-378) and verified in the present work for solvent-free membranes. In addition to electrostatic effects of surface charge, gramicidin A channel conductance is also influenced by lipid-dependent structural factors.     

Molecular dynamics study of the KcsA potassium channel

The structural, dynamical, and thermodynamic properties of a model potassium channel are studied using molecular dynamics simulations. We use the recently unveiled protein structure for the KcsA potassium channel from Streptomyces lividans. Total and free energy profiles of potassium and sodium ions reveal a considerable preference for the larger potassium ions. The selectivity of the channel arises from its ability to completely solvate the potassium ions, but not the smaller sodium ions. Self-diffusion of water within the narrow selectivity filter is found to be reduced by an order of magnitude from bulk levels, whereas the wider hydrophobic section of the pore maintains near-bulk self-diffusion. Simulations examining multiple ion configurations suggest a two-ion channel. Ion diffusion is found to be reduced to approximately (1)/(3) of bulk diffusion within the selectivity filter. The reduced ion mobility does not hinder the passage of ions, as permeation appears to be driven by Coulomb repulsion within this multiple ion channel.     

Experimental and theoretical studies on TI+ interactions with the cation-selective channel of the sarcoplasmic reticulum

Summary This paper presents an experimental study and a theoretical interpretation of the effects of thallous ion on the electrical properties of the cation-selective channel of the sarcoplasmic reticulum (SR channel). The properties of this channel in solutions which do not contain thallous ion are consistent with the predictions of Läuger's theory for singly occupied pores (P. Läuger, 1973,Biochim. Biophys. Acta 311:423–441). However, this theory does not account for SR channel properties in mixtures containing thallous ion. SR channel conductance is less than predicted in mixed salt solutions of thallium with either potassium or ammonium (J. Fox, 1983,Biochim. Biophys. Acta 736:241–245), yet is greater than expected in mixtures of lithium and thallium. In a simple single-ion pore, the ratio of the products of the single-salt binding constants and maximum conductances is equal to the permeability ratio calculated from zero-current potential experiments under near equilibrium conditions. This is not found for the SR channel when thallous ion is present. SR channel properties in the presence of thallous ion can, however, be explained by a model which postulates the existence of two external modulatory sites on the channel, without implying double-occupancy in the permeation pathway. When thallous ion is bound to a modulatory site the maximum conductance of the channel to all permeating ions is altered (thallous included). Two other models (a three-barrier, two-internal-site pore which allows multiple occupancy, and a pore with fluctuating barriers) are discussed, but are found to be unable to fit our conductance data at different concentrations.