Ion movement through gramicidin A channels. Interfacial polarization effects on single-channel current measurements

Transcendent Aspects of Proton Channels

A handful of biological proton-selective ion channels exist. Some open at positive or negative membrane potentials, others open at low or high pH, and some are light activated. This review focuses on common features that result from the unique properties of protons. Proton conduction through water or proteins differs qualitatively from that of all other ions. Extraordinary proton selectivity is needed to ensure that protons permeate and other ions do not. Proton selectivity arises from a proton pathway comprising a hydrogen-bonded chain that typically includes at least one titratable amino acid side chain. The enormously diverse functions of proton channels in disparate regions of the phylogenetic tree can be summarized by considering the chemical and electrical consequences of proton flux across membranes. This review discusses examples of cells in which proton efflux serves to increase pHi, decrease pHo, control the membrane potential, generate action potentials, or compensate transmembrane movement of electrical charge.

Effect of membrane potential on entry of lactoferricin B-derived 6-residue antimicrobial peptide into single Escherichia coli cells and lipid vesicles

The antimicrobial peptide (AMP) derived from lactoferricin B, LfcinB (4-9) (RRWQWR), and lissamine rhodamine B red-labeled peptide (Rh-LfcinB (4-9)) exhibit strong antimicrobial activities, and they can enter Escherichia coli cells without damaging the cell membranes. Thus, these peptides are cell-penetrating peptide (CPP) -type AMPs. In this study, to elucidate the effect of the membrane potential (Δφ) on the action of the CPP-type AMP, Rh-LfcinB (4-9), we investigated the interactions of Rh-LfcinB (4-9) with single E. coli cells and spheroplasts containing calcein in the cytosol using confocal laser scanning microscopy. At low peptide concentrations, Rh-LfcinB (4-9) entered the cytosol of single E. coli cells and spheroplasts without damaging the cell membranes, and the H⁺-ionophore carbonyl cyanide m-chlorophenyl-hydrazone (CCCP) suppressed its entry. The studies using the time-kill method indicate that these low concentrations of peptide exhibit antimicrobial activity but CCCP inhibits this activity. Next, we investigated the effect of Δφ on the interaction of Rh-LfcinB (4-9) with single giant unilamellar vesicles (GUVs) comprising E. coli polar lipid extracts and containing a fluorescent probe, Alexa Fluor 647 hydrazide. At low concentrations (0.2-0.5 μM), Rh-LfcinB (4-9) showed significant entry to the single GUV lumen without pore formation in the presence of Δφ. The fraction of entry of peptide increased with increasing negative membrane potential, indicating that the rate of peptide entry into the GUV lumen increased with increasing negative membrane potential. These results indicate that Δφ enhances the entry of Rh-LfcinB (4-9) into single E. coli cells, spheroplasts, and GUVs and its antimicrobial activity.IMPORTANCE: Bacterial cells have a membrane potential (Δφ), but the effect of Δφ on action of cell-penetrating peptide-type antimicrobial peptides (AMPs) is not clear. Here, we investigated the effect of Δφ on the action of fluorescent probe-labeled AMP derived from lactoferricin B, Rh-LfcinB (4-9). At low peptide concentrations, Rh-LfcinB (4-9) enters the cytosol of Escherichia coli cells and spheroplasts without damaging their cell membrane, but a protonophore suppresses this entry and its antimicrobial activity. The rate of entry of Rh-LfcinB (4-9) into the giant unilamellar vesicles (GUVs) comprising E. coli lipids without pore formation increases with increasing Δφ. These results indicate that Δφ enhances the antimicrobial activity of Rh-LfcinB (4-9) and hence LfcinB (4-9) by increasing the rate of their entry into the cytosol.

Action of antimicrobial peptides and cell-penetrating peptides on membrane potential revealed by the single GUV method

Membrane potential plays various key roles in live bacterial and eukaryotic cells. So far, the effects of membrane potential on action of antimicrobial peptides (AMPs) and cell-penetrating peptides (CPPs) have been examined using cells and small lipid vesicles. However, due to the technical drawbacks of these experiments, the effect of membrane potential on the actions of AMPs and CPPs and the elementary processes of interactions of these peptides with cell membranes and vesicle membranes are not well understood. In this short review, we summarize the results of the effect of membrane potential on the action of an AMP, lactoferricin B (LfcinB), and a CPP, transportan 10 (TP10), in vesicle membranes revealed by the single giant unilamellar vesicle (GUV) method. Parts of the actions and their elementary steps of AMPs and CPPs interacting vesicle membranes under membrane potential are clearly revealed using the single GUV method. The experimental methods and their analysis described here can be used to elucidate the effects of membrane potential on various activities of peptides such as AMPs, CPPs, and proteins. Moreover, GUVs with membrane potential are more suitable as a model of cells or artificial cells, as well as GUVs containing small vesicles.

Membrane potential is vital for rapid permeabilization of plasma membranes and lipid bilayers by the antimicrobial peptide lactoferricin B

Lactoferricin B (LfcinB) is a cationic antimicrobial peptide, and its capacity to damage the bacterial plasma membrane is suggested to be a main factor in LfcinB's antimicrobial activity. However, the specific processes and mechanisms in LfcinB-induced membrane damage are unclear. In this report, using confocal laser-scanning microscopy, we examined the interaction of LfcinB with single Escherichia coli cells and spheroplasts containing the water-soluble fluorescent probe calcein in the cytoplasm. LfcinB induced rapid calcein leakage from single E. coli cells and from single spheroplasts, indicating that LfcinB interacts directly with the plasma membrane and induces its rapid permeabilization. The proton ionophore carbonyl cyanide m-chlorophenylhydrazone suppressed this leakage. Next, we used the single giant unilamellar vesicle (GUV) method to examine LfcinB's interaction with GUVs comprising polar lipid extracts of E. coli containing a water-soluble fluorescent probe, Alexa Fluor 647 hydrazide (AF647). We observed that LfcinB stochastically induces local rupture in single GUVs, causing rapid AF647 leakage; however, higher LfcinB concentrations were required for AF647 leakage from GUVs than from E. coli cells and spheroplasts. To identify the reason for this difference, we examined the effect of membrane potential on LfcinB-induced pore formation, finding that the rate of LfcinB-induced local rupture in GUVs increases greatly with increasing negative membrane potential. These results indicate that membrane potential plays an important role in LfcinB-induced local rupture of lipid bilayers and rapid permeabilization of E. coli plasma membranes. On the basis of these results, we discuss the mode of action of LfcinB's antimicrobial activity.

Scaling Behavior of Ionic Transport in Membrane Nanochannels

Ionic conductance in membrane channels exhibits a power-law dependence on electrolyte concentration ( G ∼ c^α). The many scaling exponents, α, reported in the literature usually require detailed interpretations concerning each particular system under study. Here, we critically evaluate the predictive power of scaling exponents by analyzing conductance measurements in four biological channels with contrasting architectures. We show that scaling behavior depends on several interconnected effects whose contributions change with concentration so that the use of oversimplified models missing critical factors could be misleading. In fact, the presence of interfacial effects could give rise to an apparent universal scaling that hides the channel distinctive features. We complement our study with 3D structure-based Poisson-Nernst-Planck (PNP) calculations, giving results in line with experiments and validating scaling arguments. Our findings not only provide a unified framework for the study of ion transport in confined geometries but also highlight that scaling arguments are powerful and simple tools with which to offer a comprehensive perspective of complex systems, especially those in which the actual structure is unknown.

Nature of the neurotoxic membrane actions of amyloid-β on hippocampal neurons in Alzheimer's disease

The mechanism by which amyloid-β (Aβ) produces brain dysfunction in patients with Alzheimer's disease is largely unknown. According to previous studies, Aβ might share perforating properties with gramicidin, a well-accepted membrane-disrupting peptide. Therefore, we hypothesize that the key steps leading to synaptotoxicity by Aβ and gramicidin involve peptide aggregation, pore formation, and calcium dysregulation. Here, we show that Aβ and gramicidin form aggregates enriched in β-sheet structures using electron microscopy, and Thioflavin and Congo Red staining techniques. Also, we found that Aβ and gramicidin display fairly similar actions in hippocampal cell membranes, i.e. inducing Ca(2+) entry and synaptoxicity characterized by the loss of synaptic proteins and a decrease in neuronal viability. These effects were not observed in a Ca(2+) free solution, indicating that both Aβ and gramicidin induce neurotoxicity by a Ca(2+)-dependent mechanism. Using combined perforated patch clamp and imaging recordings, we found that only Aβ produced a perforation that progressed from a small (Cl(-)-selective pore) to a larger perforation that allowed the entry of fluorescent molecules. Therefore, based on these results, we propose that the perforation at the plasma membrane by Aβ is a dynamic process that is critical in producing neurotoxicity similar to that found in the brains of AD patients.

A permeation theory for single-file ion channels: one- and two-step models

How many steps are required to model permeation through ion channels? This question is investigated by comparing one- and two-step models of permeation with experiment and MD simulation for the first time. In recent MD simulations, the observed permeation mechanism was identified as resembling a Hodgkin and Keynes knock-on mechanism with one voltage-dependent rate-determining step [Jensen et al., PNAS 107, 5833 (2010)]. These previously published simulation data are fitted to a one-step knock-on model that successfully explains the highly non-Ohmic current-voltage curve observed in the simulation. However, these predictions (and the simulations upon which they are based) are not representative of real channel behavior, which is typically Ohmic at low voltages. A two-step association/dissociation (A/D) model is then compared with experiment for the first time. This two-parameter model is shown to be remarkably consistent with previously published permeation experiments through the MaxiK potassium channel over a wide range of concentrations and positive voltages. The A/D model also provides a first-order explanation of permeation through the Shaker potassium channel, but it does not explain the asymmetry observed experimentally. To address this, a new asymmetric variant of the A/D model is developed using the present theoretical framework. It includes a third parameter that represents the value of the "permeation coordinate" (fractional electric potential energy) corresponding to the triply occupied state n of the channel. This asymmetric A/D model is fitted to published permeation data through the Shaker potassium channel at physiological concentrations, and it successfully predicts qualitative changes in the negative current-voltage data (including a transition to super-Ohmic behavior) based solely on a fit to positive-voltage data (that appear linear). The A/D model appears to be qualitatively consistent with a large group of published MD simulations, but no quantitative comparison has yet been made. The A/D model makes a network of predictions for how the elementary steps and the channel occupancy vary with both concentration and voltage. In addition, the proposed theoretical framework suggests a new way of plotting the energetics of the simulated system using a one-dimensional permeation coordinate that uses electric potential energy as a metric for the net fractional progress through the permeation mechanism. This approach has the potential to provide a quantitative connection between atomistic simulations and permeation experiments for the first time.

Electrostatic-gated transport in chemically modified glass nanopore electrodes

Electrostatic-gated transport in chemically modified glass nanopore electrodes with orifice radii as small as 15 nm is reported. A single conical-shaped nanopore in glass, with a approximately 1 microm radius Pt disk located at the pore base, is prepared by etching the exposed surface of a glass-sealed Pt nanodisk. The electrochemical response of the nanopore electrode corresponds to diffusion of redox-active species through the nanopore orifice to the Pt microdisk. Silanization of the exterior glass surface with Cl(Me)(2)Si(CH(2))(3)CN and the interior pore surface with EtO(Me)(2)Si(CH(2))(3)NH(2) introduces pH-dependent ion selectivity at the pore orifice, a consequence of the electrostatic interactions between the redox ions and protonated surface amines. Nanopore electrodes with very small pore orifice radii (< approximately 50 nm) display anion permselectively at pH < 4, as demonstrated by electrochemical measurement of transport through the pore orifice. Ion selective transport vanishes at pH > 6 or when the pore radius is significantly larger than the Debye screening length, consistent with the observed ion selectivity resulting from electrostatic interactions. The ability to introduce different surface functionalities to the interior and exterior surfaces of glass nanopores is demonstrated using fluorescence microscopy to monitor the localized covalent attachment of 5- (and 6)-carboxytetramethylrhodamine succinimidyl ester to interior pore surfaces previously silanized with EtO(Me)(2)Si(CH(2))(3)NH(2).

Chance and design—Proton transfer in water, channels and bioenergetic proteins

Proton transfer and transport in water, gramicidin and some selected channels and bioenergetic proteins are reviewed. An attempt is made to draw some conclusions about how Nature designs long distance, proton transport functionality. The prevalence of water rather than amino acid hydrogen bonded chains is noted, and the possible benefits of waters as the major component are discussed qualitatively.

Tryptophan contributions to the empirical free-energy profile in gramicidin A/M heterodimer channels

Gramicidin A/gramicidin M heterodimer conductances were measured in planar lipid bilayers and found to form two distinguishable populations about halfway between the gramicidin A and gramicidin M homodimer conductances. This implies that the principle difference in the gramicidin A and gramicidin M transport free-energy profiles occurs at the channel center, where it would produce similar effects on the rate-limiting barrier for the two heterodimers. Kinetic analysis based on this and nearly all previously published homodimer conductance data for both gramicidin A and gramicidin M channels confirms this conclusion, indicating that the translocation step is approximately 100-fold slower in gramicidin M homodimers than in gramicidin A homodimers and that first- and second-ion exit-rate constants are higher by factors of 24 and 10, respectively. Assuming that the ratios of rate constants are related to the free-energy difference between gramicidin A and gramicidin M, we construct an effective ion-Trp free-energy interaction profile that has a minimum at the channel center.

Gramicidin channels

Gramicidin channels are mini-proteins composed of two tryptophan-rich subunits. The conducting channels are formed by the transbilayer dimerization of nonconducting subunits, which are tied to the bilayer/solution interface through hydrogen bonds between the indole NH groups and the phospholipid backbone and water. The channel structure is known at atomic resolution and the channel's permeability characteristics are particularly well defined: gramicidin channels are selective for monovalent cations, with no measurable permeability to anions or polyvalent cations; ions and water move through a pore whose wall is formed by the peptide backbone; and the single-channel conductance and cation selectivity vary when the amino acid sequence is varied, even though the permeating ions make no contact with the amino acid side chains. Given the amount of experimental information that is available--for both the wild-type channels and for channels formed by amino acid-substituted gramicidin analogues--gramicidin channels provide important insights into the microphysics of ion permeation through bilayer-spanning channels. For the same reason, gramicidin channels constitute the system of choice for evaluating computational strategies for obtaining mechanistic insights into ion permeation through the complex channels formed by integral membrane proteins.

The effect of interaction between K+ ions and gramicidin D on the lecithin membrane interfacial tension

The effect of the presence of gramicidin D in a lecithin membrane on its interfacial tension has been studied. The studies have been carried out at various forming solution compositions and at various potassium ion concentrations in the electrolyte solution. Potassium chloride was used as the electrolyte. The complex was formed between the gramicidin molecule and K(+) ion. The following parameters describing the complex were determined: the surface area occupied by GK(+) complex (A(GK(+))), the interfacial tension of the GK(+) membrane complex (gamma(GK+)), and the stability constant of the gramicidin-K(+) complex (K). These values are 156 A(2), 1.89 mN m(-1) and 0.033 m(3) mol(-1), respectively.

Voltage-gated proton channels and other proton transfer pathways

Proton channels exist in a wide variety of membrane proteins where they transport protons rapidly and efficiently. Usually the proton pathway is formed mainly by water molecules present in the protein, but its function is regulated by titratable groups on critical amino acid residues in the pathway. All proton channels conduct protons by a hydrogen-bonded chain mechanism in which the proton hops from one water or titratable group to the next. Voltage-gated proton channels represent a specific subset of proton channels that have voltage- and time-dependent gating like other ion channels. However, they differ from most ion channels in their extraordinarily high selectivity, tiny conductance, strong temperature and deuterium isotope effects on conductance and gating kinetics, and insensitivity to block by steric occlusion. Gating of H(+) channels is regulated tightly by pH and voltage, ensuring that they open only when the electrochemical gradient is outward. Thus they function to extrude acid from cells. H(+) channels are expressed in many cells. During the respiratory burst in phagocytes, H(+) current compensates for electron extrusion by NADPH oxidase. Most evidence indicates that the H(+) channel is not part of the NADPH oxidase complex, but rather is a distinct and as yet unidentified molecule.

The role of Trp side chains in tuning single proton conduction through gramicidin channels

We present an extensive set of measurements of proton conduction through gramicidin A (gA), B (gB), and M (gM) homodimer channels which have 4, 3, or 0 Trp residues at each end of the channel, respectively. In gA we find a shoulder separating two domains of conductance increasing with concentration, confirming the results of Eisenman, G., B. Enos, J. Hagglund, and J. Sandblom. 1980. Ann. NY. Acad. Sci. 339:8-20. In gB, the shoulder is shifted by approximately 1/2 pH unit to higher H(+) concentrations and is very sharply defined. No shoulder appears in the gM data, but an associated transition from sublinear to superlinear I-V values occurs at a 100-fold higher [H(+)] in gM than in gA. The data in the low concentration domain are analyzed using a configuration space model of single-proton conduction, assuming that the difference in the proton potential of mean force (PMF) between gA and its analogs is constant, similar to the results of Anderson, D., R. B. Shirts, T. A. Cross, and D. D. Busath. 2001. Biophys. J. 81:1255-1264. Our results suggest that the average amplitudes of the calculated proton PMFs are nearly correct, but that the water reorientation barrier calculated for gA by molecular dynamics using the PM6 water model (Pomès, R., and B. Roux. 1997. Biophys. J. 72:246a) must be reduced in amplitude by 1.5 kcal/mol or more, and is not rate-limiting for gA.

Cellular microtransport processes: intercellular, intracellular, and aggregate behavior

Ionic and molecular transfer among cells occurs by a variety of transport processes operative at different length scales. Cell membrane permeability and electrical conductance derive from channel proteins producing pores at the molecular (ultrastructural) scale. Intracellular mobility involves the dynamics of motion through the complex ultrastructure of the cytoplasm. These phenomena unite in the larger-scale (microscopic) process of gross intercellular transfer. When such movement occurs among sufficiently many cells, it in turn begins to reflect their average collective (macroscopic) behavior as bulk tissue. This article surveys selected aspects of intercellular and intracellular transport, with emphasis on detailed mechanistic theory, experimental probes of cellular permeability, and systematic transcendence from small to large length scales.

Model channel ion currents in NaCl-extended simple point charge water solution with applied-field molecular dynamics

Using periodic boundary conditions and a constant applied field, we have simulated current flow through an 8.125-A internal diameter, rigid, atomistic channel with polar walls in a rigid membrane using explicit ions and extended simple point charge water. Channel and bath currents were computed from 10 10-ns trajectories for each of 10 different conditions of concentration and applied voltage. An electric field was applied uniformly throughout the system to all mobile atoms. On average, the resultant net electric field falls primarily across the membrane channel, as expected for two conductive baths separated by a membrane capacitance. The channel is rarely occupied by more than one ion. Current-voltage relations are concentration dependent and superlinear at high concentrations.

Noncontact dipole effects on channel permeation. IV. Kinetic model of 5F-Trp(13) gramicidin A currents

Nonlinear least squares fitting was used to assign rate constants for the three-barrier, two-site, double-occupancy, single-filing kinetic model for previously reported current-voltage relations of (5F-Indole)Trp(13) gramicidin A and gramicidin A channels (, 75:2830-2844). By judicious coupling of parameters, it was possible to reduce the parameter space from 64 parameters to 24, and a reasonable fit consistent with other experimental data was obtained. The main features of the fit were that fluorination increased the rate constant for translocation by a factor of 2.33, consistent with a free energy change in the translocation barrier of -0.50 kcal/mol, and increased first-ion binding affinity by a factor of 1.13, primarily by decreasing the first-ion exit rate constant. The translocation rate constant was 5.62 times slower in diphytanoyl phosphatidylcholine (DPhPC) bilayers than in monoolein (GMO) bilayers (coupled for the four combinations of peptide and salt), suggesting a 44.2-mV difference in the projection of the interfacial dipole into the channel. Thus fluorination caused increased currents in DPhPC bilayers, where a high interfacial dipole potential makes translocation more rate limiting because the translocation barrier was reduced, and decreased currents in GMO bilayers, where ion exit or entry is rate limiting because these barriers were increased.

Framework model for single proton conduction through gramicidin

This paper describes a framework model for proton conduction through gramicidin; a model designed to incorporate information from molecular dynamics and use this to predict conductance properties. The state diagram describes both motion of an excess proton within the pore as well as the reorientation of waters within the pore in the absence of an excess proton. The model is constructed as the diffusion limit of a random walk, allowing control over the boundary behavior of trajectories. Simple assumptions about the boundary behavior are made, which allow an analytical solution for the proton current and conductance. This is compared with corresponding expressions from statistical mechanics. The random walk construction allows diffusing trajectories underlying the model to be simulated in a simple way. Details of the numerical algorithm are described.

A combined molecular dynamics and diffusion model of single proton conduction through gramicidin

We develop a model for proton conduction through gramicidin based on the molecular dynamics simulations of Pomès and Roux (Biophys. J. 72:A246, 1997). The transport of a single proton through the gramicidin pore is described by a potential of mean force and diffusion coefficient obtained from the molecular dynamics. In addition, the model incorporates the dynamics of a defect in the hydrogen bonding structure of pore waters without an excess proton. Proton entrance and exit were not simulated by the molecular dynamics. The single proton conduction model includes a simple representation of these processes that involves three free parameters. A reasonable value can be chosen for one of these, and the other two can be optimized to yield a good fit to the proton conductance data of, Ann. N.Y. Acad. Sci. 339:8-20) for pH > or = 1.7. A sensitivity analysis shows the significance of this fit.

A lattice relaxation algorithm for three-dimensional Poisson-Nernst-Planck theory with application to ion transport through the gramicidin A channel

A lattice relaxation algorithm is developed to solve the Poisson-Nernst-Planck (PNP) equations for ion transport through arbitrary three-dimensional volumes. Calculations of systems characterized by simple parallel plate and cylindrical pore geometries are presented in order to calibrate the accuracy of the method. A study of ion transport through gramicidin A dimer is carried out within this PNP framework. Good agreement with experimental measurements is obtained. Strengths and weaknesses of the PNP approach are discussed.

Noncontact dipole effects on channel permeation. I. Experiments with (5F-indole)Trp13 gramicidin A channels

Gramicidin A (gA), with four Trp residues per monomer, has an increased conductance compared to its Phe replacement analogs. When the dipole moment of the Trp13 side chain is increased by fluorination at indole position 5 (FgA), the conductance is expected to increase further. gA and FgA conductances to Na+, K+, and H+ were measured in planar diphytanoylphosphatidylcholine (DPhPC) or glycerylmonoolein (GMO) bilayers. In DPhPC bilayers, Na+ and K+ conductances increased upon fluorination, whereas in GMO they decreased. The low ratio in the monoglyceride bilayer was not reversed in GMO-ether bilayers, solvent-inflated or -deflated bilayers, or variable fatty acid chain monoglyceride bilayers. In both GMO and DPhPC bilayers, fluorination decreased conductance to H+ but increased conductance in the mixed solution, 1 M KCl at pH 2.0, where K+ dominates conduction. Eadie-Hofstee plot slopes suggest similar destabilization of K+ binding in both lipids. Channel lifetimes were not affected by fluorination in either lipid. These observations indicate that fluorination does not change the rotameric conformation of the side chain. The expected difference in the rate-limiting step for transport through channels in the two bilayers qualitatively explains all of the above trends.

Proton conduction in gramicidin A and in its dioxolane-linked dimer in different lipid bilayers

Gramicidin A (gA) molecules were covalently linked with a dioxolane ring. Dioxolane-linked gA dimers formed ion channels, selective for monovalent cations, in planar lipid bilayers. The main goal of this study was to compare the functional single ion channel properties of natural gA and its covalently linked dimer in two different lipid bilayers and HCl concentrations (10-8000 mM). Two ion channels with different gating and conductance properties were identified in bilayers from the product of dimerization reaction. The most commonly observed and most stable gramicidin A dimer is the main object of this study. This gramicidin dimer remained in the open state most of the time, with brief closing flickers (tau(closed) approximately 30 micros). The frequency of closing flickers increased with transmembrane potential, making the mean open time moderately voltage dependent (tau(open) changed approximately 1.43-fold/100 mV). Such gating behavior is markedly different from what is seen in natural gA channels. In PEPC (phosphatidylethanolamine-phosphatidylcholine) bilayers, single-channel current-voltage relationships had an ohmic behavior at low voltages, and a marked sublinearity at relatively higher voltages. This behavior contrasts with what was previously described in GMO (glycerylmonooleate) bilayers. In PEPC bilayers, the linear conductance of single-channel proton currents at different proton concentrations was essentially the same for both natural and gA dimers. g(max) and K(D), obtained from fitting experimental points to a Langmuir adsorption isotherm, were approximately 1500 pS and 300 mM, respectively, for both the natural gA and its dimer. In GMO bilayers, however, proton affinities of gA and the dioxolane-dimer were significantly lower (K(D) of approximately 1 and 1.5 M, respectively), and the g(max) higher (approximately 1750 and 2150 pS, respectively) than in PEPC bilayers. Furthermore, the relationship between single-channel conductance and proton concentration was linear at low bulk concentrations of H+ (0.01-2 M) and saturated at concentrations of more than 3 M. It is concluded that 1) The mobility of protons in gramicidin A channels in different lipid bilayers is remarkably similar to proton mobilities in aqueous solutions. In particular, at high concentrations of HCl, proton mobilities in gramicidin A channel and in solution differ by only 25%. 2) Differences between proton conductances in gramicidin A channels in GMO and PEPC cannot be explained by surface charge effects on PEPC membranes. It is proposed that protonated phospholipids adjacent to the mouth of the pore act as an additional source of protons for conduction through gA channels in relation to GMO bilayers. 3) Some experimental results cannot be reconciled with simple alterations in access resistance to proton flow in gA channels. Said differences could be explained if the structure and/or dynamics of water molecules inside gramicidin A channels is modulated by the lipid environment and by modifications in the structure of gA channels. 4) The dioxolane ring is probably responsible for the closing flickers seen in the dimer channel. However, other factors can also influence closing flickers.

Separation of gating properties from permeation and block in mslo large conductance Ca-activated K+ channels

In this and the following paper we have examined the kinetic and steady-state properties of macroscopic mslo Ca-activated K+ currents in order to interpret these currents in terms of the gating behavior of the mslo channel. To do so, however, it was necessary to first find conditions by which we could separate the effects that changes in Ca2+ concentration or membrane voltage have on channel permeation from the effects these stimuli have on channel gating. In this study we investigate three phenomena which are unrelated to gating but are manifest in macroscopic current records: a saturation of single channel current at high voltage, a rapid voltage-dependent Ca2+ block, and a slow voltage-dependent Ba2+ block. Where possible methods are described by which these phenomena can be separated from the effects that changes in Ca2+ concentration and membrane voltage have on channel gating. Where this is not possible, some assessment of the impact these effects have on gating parameters determined from macroscopic current measurements is provided. We have also found that without considering the effects of Ca2+ and voltage on channel permeation and block, macroscopic current measurements suggest that mslo channels do not reach the same maximum open probability at all Ca2+ concentrations. Taking into account permeation and blocking effects, however, we find that this is not the case. The maximum open probability of the mslo channel is the same or very similar over a Ca2+ concentration range spanning three orders of magnitude indicating that over this range the internal Ca2+ concentration does not limit the ability of the channel to be activated by voltage.

Boundary conditions for- single-ion diffusion

We have constructed a theory for diffusion through the pore of a single-ion channel by taking a limit of a random walk around a cycle of states. Similar to Levitt's theory of single-ion diffusion, one obtains boundary conditions for the Nernst-Planck equation that guarantee that the pore is occupied by at most one ion. Two of the terms in the boundary conditions are identical to those given by Levitt. However, the construction gives rise to a third term not found in Levitt's theory. With this term, the channel spends exponentially distributed intervals in the empty state. Ion sample paths have been simulated to help visualize trajectories near the channel entrances, with and without the new term. We use the modified Levitt theory to fit several potential profiles to the conductance data of Russell et al. In particular, we have analyzed the profile for Na+ in gramicidin calculated by Roux and Karplus. The peak-to-peak amplitude of their result must be reduced to at most 35% of its original value to fit the data. But with this reduction, excellent fits are obtained.

Electrostatic interactions in gramicidin channels. Three-dielectric model

A model based on the solution of the electrostatic potential for a geometry of three dielectric regions associated with a gramicidin A channel (GA) is presented. The model includes a cylindrical dielectric layer to represent the peptide backbone and dipole rings to account for dipolar side chains. Image potential and dipolar contributions for different orientations and positions along the channel are analyzed. The conductance of GA and two analogues obtained by substituting the amino acid at position 1 are studied. The numerical simulation reproduces experimental results (Barrett et al. 1986, Biophys J 49, 673-686) and supports the idea that electrostatic dipole-ion interactions are of primary importance in gramicidin channel function.

Zero-current potentials in a large membrane channel: a simple theory accounts for complex behavior

Flow of ions through large channels is complex because both cations and anions can penetrate and multiple ions can be in the channel at the same time. A modification of the fixed-charge membrane theory of Teorell was reported (Peng, S., E. Blachly-Dyson, M. Forte, and M. Colombini. 1992. Biophys. J. 62:123-135) in which the channel is divided into two compartments: a relatively charged cylindrical shell of solution adjacent to the wall of the pore and a relatively neutral central cylinder of solution. The zero-current (reversal) potential results in current flow in opposite directions in these two compartments. This description accounted rather well for the observed reversal potential changes following site-directed mutations. Here we report the results of systematic tests of this simple theory with the mitochondrial channel, VDAC (isolated from Neurospora crassa), reconstituted into planar phospholipid membranes. The variation of the observed reversal potential with transmembrane activity ratio, ionic strength, ion mobility ratio, and net charge on the wall of the pore are accounted for reasonably well. The Goldman-Hodgkin-Katz theory fails to account for the observations.

Flux, coupling, and selectivity in ionic channels of one conformation

Ions crossing biological membranes are described as a concentration of charge flowing through a selective open channel of one conformation and analyzed by a combination of Poisson and Nernst-Planck equations and boundary conditions, called the PNP theory for short. The ion fluxes in this theory interact much as ion fluxes interact in biological channels and mediated transporters, provided the theoretical channel contains permanent charge and has selectivity created by (electro-chemical) resistance at its ends. Interaction occurs because the flux of different ionic species depends on the same electric field. That electric field is a variable, changing with experimental conditions because the screening (i.e., shielding) of the permanent charge within the channel changes with experimental conditions. For example, the screening of charge and the shape of the electric field depend on the concentration of all ionic species on both sides of the channel. As experimental interventions vary the screening, the electric field varies, and thus the flux of each ionic species varies conjointly, and is, in that sense, coupled. Interdependence and interaction are the rule, independence is the exception, in this channel.

The permeation properties of small organic cations in gramicidin A channels

The conductance properties of organic cations in single gramicidin A channels were studied using planar lipid bilayers. From measurements at 10 mM and at 27 mV the overall selectivity sequence was found to be NH4+ > K+ > hydrazinium > formamidinium > Na+ > methylammonium, which corresponds to Eisenman polyatomic cation sequence X'. Methylammonium and formamidinium exhibit self block, suggesting multiple occupancy and single filing. Formamidinium has an apparent dissociation constant (which is similar to those of alkali metal cations) for the first ion being 22 mM from the Eadie-Hofstee plot (G0 vs. G0/C), 12 mM from the rate constants of a three-step kinetic model. The rate-limiting step for formamidinium is translocation judging from supralinear I-V relations at low concentrations. 1 M formamidinium solutions yields exceptionally long single channel lifetimes, 20-fold longer than methylammonium, which yields lifetimes similar to those found with alkali metal cations. The average lifetime in formamidinium solution significantly decreases with increasing voltage up to 100 mV but is relatively voltage independent between 100 and 200 mV. At lower voltages (< or = 100 mV), the temperature and concentration dependences of the average lifetime of formamidinium were steep. At very low salt concentrations (0.01 M, 100 mV), there was no significant difference in average lifetime from that formed with 0.01 M methylammonium or hydrazinium. We conclude that formamidinium very effectively stabilizes the dimeric channel while inside the channel and speculate that it does so by affecting tryptophan-reorientation or tryptophan-lipid interactions at binding sites.

A functional view of the entrances of L-type Ca2+ channels: estimates of the size and surface potential at the pore mouths

At extreme membrane potentials, the unitary inward and outward currents through L-type Ca2+ channels become diffusion controlled and saturate. The magnitudes of these currents indicate that the pore entrances are asymmetric, with the external mouth being much larger than the internal one. On the other hand, negative surface potentials at the two ends of the pore are rather similar. Both would be significant only when the ambient ionic strength is 110 mM or less. We conclude that the surface charges will not help much in concentrating the channel's favorite divalent cations in the physiological condition. However, the pore does possess an external mouth large enough to make the important inward Ca2+ flow not limited by diffusion, even with only 1 mM external Ca2+.

Small iminium ions block gramicidin channels in lipid bilayers

Guanidinium and acetamidinium, when added to the bathing solution in concentrations of approximately 0.1M, cause brief blocks in the single channel potassium currents from channels formed in planar lipid bilayers by gramicidin A. Single channel lifetimes are not affected indicating that the channel structure is not modified by the blockers. Guanidinium block durations and interblock times are approximately exponential in distribution. Block frequencies increase with guanidinium concentration whereas block durations are unaffected. Increases in membrane potential cause an increase in block frequency as expected for a positively charged blocker but a decrease in block duration suggesting that the block is relieved when the blocker passes through the channel. At low pH, urea, formamide, and acetamide cause similar blocks suggesting that the protonated species of these molecules also block. Arginine and several amines do not block. This indicates that only iminium ions which are small enough to enter the channel can cause blocks in gramicidin channels.

Diffusion around a cardiac calcium channel and the role of surface bound calcium

The diffusion of Ca as it converges to the external mouth of a Ca channel is examined. Diffusional limitation on Ca ions entering Ca channels during current flow, cause local extracellular Ca depletions. Such extracellular Ca depletions have been reported in cardiac muscle. The cardiac sarcolemma has a large number of low-affinity Ca binding sites that can buffer these local Ca depletions. For a hemisphere of extracellular space (of radius less than 0.33 microns) centered on the external mouth of a Ca channel the amount of Ca bound at the membrane surface exceeds that which is free within the associated hemisphere. The ratio of bound Ca/free Ca increases as r decreases, such that the [Ca] nearest the Ca channel is the most strongly buffered by sarcolemmal bound Ca. It is demonstrated that Ca ions coming from these sarcolemmal Ca binding sites contribute quantitatively to the integrated Ca current. The electric field generated by the local depletion of Ca near the channel mouth has little impact on the extent of Ca depletion, but if an additional electric field exists at the mouth of the channel, Ca depletion can be significantly altered. Other low-affinity Ca binding sites in the interstitium may also contribute to the buffering of extracellular Ca. The complex geometry of the extracellular space in cardiac muscle (e.g., transverse tubules and restrictions of extracellular space between cells) increases both the predicted Ca depletions (in the absence of binding) and the bound/free ratio. Thus, the impact of this surface Ca binding is greatly increased. By considering arrays of Ca channels in transverse tubules or in parallel planes (e.g., membranes of neighboring cells), extracellular Ca depletions are predicted which agree with those measured experimentally. Membrane Ca binding may also be expected to buffer increases in [Ca] around the inner mouth of Ca channels. It is demonstrated that in the absence of other intracellular systems most of the Ca entering the cell via Ca channels might be expected to be bound to the inner sarcolemmal surface. It is concluded that surface Ca binding may have a substantial impact on the processes of extracellular Ca depletion (and intracellular Ca accumulation).

Calculation of deformation energies and conformations in lipid membranes containing gramicidin channels

In this paper we calculate surface conformation and deformation free energy associated with the incorporation of gramicidin channels into phospholipid bilayer membranes. Two types of membranes are considered. One is a relatively thin solvent-free membrane. The other is a thicker solvent-containing membrane. We follow the approach used for the thin membrane case by Huang (1986) in that we use smectic liquid crystal theory to evaluate the free energy associated with distorting the membrane to other than a flat configuration. Our approach is different from Huang, however, in two ways. One is that we include a term for surface tension, which Huang did not. The second is that one of our four boundary conditions for solving the fourth-order differential equation describing the free energy of the surface is different from Huang's. The details of the difference are described in the text. Our results confirm that for thin membranes Huang's neglect of surface tension is appropriate. However, the precise geometrical form that we calculate for the surface of the thin membrane in the region of the gramicidin channel is somewhat different from his. For thicker membranes that have to deform to a greater extent to accommodate the channel, we find that the contribution of surface tension to the total energy in the deformed surface is significant. Computed results for the shape of the deformed surface, the total energy in the deformed surface, and the contributions of different components to the total energy, are presented for the two types of membranes considered. These results may be significant for understanding the mechanisms of dimer formation and breakup, and the access resistance for ions entering gramicidin channels.

A novel method for measuring membrane conductance changes by a voltage-sensitive optical probe

This study presents a method whose principles enable using a voltage-sensitive optical probe, to quantitatively measure conductivity changes elicited in membrane vesicles and cells. The procedure is based on the fact that the amplitude of the transmembrane potential difference, established across a membrane by an external electric field, is decreased when membrane conductivity is increased upon incorporation of ionophores into the membrane. The method was applied to osmotically swollen thylakoid membranes whose membrane conductivity was changed by the addition of gramicidin or ionomycin. The electric field induced stimulated luminescence from photosystem I (electrophotoluminescence-EPL) was used as a voltage-sensitive optical probe. We calculated the induced conductance changes by using a calibrated EPL vs external electric field response curve and measuring the ionophore-mediated attenuation of the EPL signal. The calculated ionophore-unmodified conductance of the thylakoid membrane yields a value of 171 +/- 56 nS/cm. The value of the membrane conductance, modified by 10 nM gramicidin was found to be 190 +/- 56 nS/cm. The modified membrane conductance and the membrane conductance changes induced by 1 microM ionomycin in the presence of CaCl2 were found to be 186 +/- 3 nS/cm and 15 +/- 3 nS/cm, respectively.

Stochastic theory of singly occupied ion channels. II. Effects of access resistance and potential gradients extending into the bath

In a previous paper (Jakobsson, E., and S. W. Chiu. 1987. Biophys. J. 52:33-46), we presented the stochastic theory of the singly occupied ion channel as applied to sodium permeation of gramicidin channels, with the assumption of perfect equilibration between the bathing solutions and the ends of the ion channel. In the present paper we couple the previous theory to electrodiffusion of ions from the bulk of the bathing solution to the channel mouth. Our electrodiffusion calculations incorporate estimates of the potential gradients near the channel mouth due to image forces and due to the fraction of the applied potential that falls beyond the ends of the channel. To keep the diffusion calculation one-dimensional, we make the assumption that the electrical potentials in the bath exhibit hemispherical symmetry. As in the previous paper, the flux equations are fit to data on sodium permeation of normal gramicidin A, and gramicidins modified by the fluorination of the valine at the No. 1 position (Barrett Russell, E. W., L. B. Weiss, F. I. Navetta, R. E. Koeppe II, and O. S. Anderson. 1986. Biophys. J. 49:673-686). The conclusions of our previous paper with respect to the effect of fluorination on the mobility, surface potential well depth, and central barrier, are confirmed. However the absolute values of these quantities are somewhat changed when diffusive resistance to the mouth is taken into account, as in the present paper. Future possibilities for more accurate calculations by other methods are outlined.

Electrodiffusion of ions approaching the mouth of a conducting membrane channel

The movement of ions in the aqueous medium as they approach the mouth (radius a) of a conducting membrane channel is analyzed. Starting with the Nernst-Planck and Poisson equations, we derive a nonlinear integrodifferential equation for the electric potential, phi(r), a less than or equal to r less than infinity. The formulation allows deviations from charge neutrality and dependence of phi(r) on ion flux. A numerical solution is obtained by converting the equation to an integral equation that is solved by an iterative method for an assumed mouth potential, combined with a shooting method to adjust the mouth potential until the numerical solution agrees with an asymptotic expansion of the potential at r-a much greater than lambda (lambda = Debye length). Approximate analytic solutions are obtained by assuming charge neutrality (Läuger, 1976) and by linearizing. The linear approximation agrees with the exact solution under most physiological conditions, but the charge-neutrality solution is only valid for r much greater than lambda and thus cannot be used unless a much greater than lambda. Families of curves of ion flux vs. potential drop across the electrolyte, phi(infinity)-phi (a), and of permeant ion density at the channel mouth, n1(a), vs. flux are obtained for different values of a/lambda and S = a d phi/dr(a). If a much greater than lambda and S = O, the maximum flux (which is approached when n1(a)----0) is reduced by 50% compared to the value predicted by the charge-neutrality solution. Access resistance is shown to be a factor a/[2 (a + lambda)] times the published formula (Hille, 1968), which was derived without including deviations from charge neutrality and ion density gradients and hence does not apply when there is no counter-ion current. The results are applied to an idealized diffusion-limited channel with symmetric electrolytes. For S = O, the current/voltage curves saturate at a value dependent on a/lambda; for S greater than O, they increase linearly for large voltage.

Use of weak acids to determine the bulk diffusion limitation of H+ ion conductance through the gramicidin channel

The addition of 2 M formic acid at pH 3.75 increased the single channel H+ ion conductance of gramicidin channels 12-fold at 200 mV. Other weak acids (acetic, lactic, oxalic) produce a similar, but smaller increase. Formic acid (and other weak acids) also blocks the K+ conductance at pH 3.75, but not at pH 6.0 when the anion form predominates. This increased H+ conductance and K+ block can be explained by formic acid (HF) binding to the mouth of the gramicidin channel (Km = 1 M) and providing a source of H+ ions. A kinetic model is derived, based on the equilibrium binding of formic acid to the channel mouth, that quantitatively predicts the conductance for different mixtures of H+, K+, and formic acid. The binding of the neutral formic acid to the mouth of the gramicidin channel is directly supported by the observation that a neutral molecule with a similar structure, formamide (and malonamide and acrylamide), blocks the K+ conductance at pH 6.0. The H+ conductance in the presence of formic acid provides a lower bound for the intrinsic conductance of the gramicidin channel when there is no diffusion limitation at the channel mouth. The 12-fold increase in conductance produced by formic acid suggests that greater than 90% of the total resistance to H+ results from diffusion limitation in the bulk solution.

Biophysical properties of a chloride channel in the apical membrane of a secretory epithelial cell

1. Patch clamp studies on colonic tumor cell line T84 show the presence of chloride channels. 2. The channels are activated by forskolin, PGE2, or 8-Br-cAMP. 3. Single channel conductance was ca 40 pS at the reversal potential, increasing to 70 pS at +80 mV and decreasing to 25 pS at -80 mV. 4. Relative permeabilities were I greater than Br greater than Cl greater than F.

Electrostatic radius of the gramicidin channel determined from voltage dependence of H+ ion conductance

The results of Decker and Levitt (1987) suggest that the conductance of H+ ion through the gramicidin channel is limited primarily by diffusion in the bulk solution at the channel mouth. It is assumed in this paper that the H+ conductance is 100% diffusion limited. This means that all the factors that influence the H+ flux are external to the channel and are presumed to be known. In particular, the diffusion coefficient of H+ in this region is assumed to be equal to the bulk solution value and the only force acting on the ion is that due to the applied voltage. A model of the H+ flux is derived, based on the Nernst-Planck equation. It has three adjustable parameters: the electrostatic radius, the capture distance, and the radius of the H+ ion. The acceptable range of the parameters was determined by comparing the predictions of the model with the experimental measurements of the H+ conductance at pH 3.75. The best fit was obtained for an electrostatic radius in the range 2.3-2.7 A. This is in good agreement with earlier predictions (2.5 A) based on the assumption that the dielectric constant of the channel water is equal to that of bulk water. The addition of 1 M choline Cl- (an impermeant) increases the H+ current at low voltage and decreases it at high voltage. The increase can be explained by the small surface charge that results from the separation of charge produced by exclusion of the large choline cation (relative to Cl-) from the membrane surface. The decrease at high voltages can be accounted for by the change in the profile of the applied potential produced by the increase in ionic strength.

Stochastic theory of ion movement in channels with single-ion occupancy. Application to sodium permeation of gramicidin channels

The electrodiffusion equations were solved for the one-ion channel both by the analytical method due to Levitt and also by Brownian dynamic simulations. For both types of calculations equilibration of ion distribution between the bath and the ends of the channel was assumed. Potential profiles were found that give good fits to published data on Na+ permeation of gramicidin channels. The data were best fit by profiles that have no relative energy maximum at the mouth of the channel. This finding suggests that alignment of waters or channel charged groups inside the channel in response to an ion's approach may provide an energetically favorable situation for entry sufficient to overcome the energy required for removing bulk waters of hydration. An alternative possibility is that the barrier to ion entry is situated outside the region restricted to single-ion occupancy. Replacement of valine with more polar amino acids at the No. 1 location was found to correspond to a deepening of the potential minima near the channel mouths, an increase in height of the central barrier to ion translocation across the channel, and possibly a reduction in the mobility of the ion-water complex in the channel. The Levitt theory was extended to calculate passage times for ions to cross the channel and the blocking effects of ions that entered the channel but didn't cross. These quantities were also calculated by the Brownian dynamics method.

Gramicidin-mediated currents at very low permeant ion concentrations

Current-voltage relations have been measured for the fluxes of caesium ions through pores formed by gramicidin in lipid bilayer membranes. The ionic currents have been separated from capacitative currents using a bridge circuit with an integrator as null-detector. The conductances during brief voltage pulses were small enough to avoid the effects of diffusion polarization and the ionic strength was raised using choline chloride or magnesium sulfate to reduce the effects of double-layer polarization. Under these conditions the current-voltage relations have the same shape at 0.1 and 1 mM, but different shapes for higher concentrations. These data demonstrate that the fluxes do not obey independence for concentrations above 10 mM, but they cannot be used in isolation to support a particular value of the binding constant. The shape observed at low concentrations suggests that entry of ions into the pore remains weakly potential dependent even at 300 mV.

Effects of double-layer polarization on ion transport

It has been proposed that changes in ionic strength will alter the shape of current-voltage relations for ion transport across a lipid membrane. To investigate this effect, we measured currents across glyceryl monooleate membranes at applied potentials between 10 and 300 mV using either gramicidin and 1 mM NaCl or valinomycin and 1 mM KCl. A bridge circuit with an integrator as null detector was used to separate the capacitative and ionic components of the current. The changes in the current-voltage relations when ionic strength is varied between 1 and 100 mM are compared with predictions of Gouy-Chapman theory for the effects of these variations on polarization of the electrical diffuse double-layer. Double-layer polarization accounts adequately for the changes observed using membranes made permeable by either gramicidin or valinomycin.

Analysis of the ion transfer through the channel of 9,11,13,15-phenylalanylgramicidin A

The behavior of an analogue of gramicidin A in which all four tryptophanyl residues are substituted by phenylalanyl and which shows a strong voltage effect on the single channel conductance is analyzed on the basis of a 'three-barrier--two-site' model. It is shown that in the gramicidin family the side chains of some amino acids, in spite of their location, which point outside the channel can play a major role in the binding of ions in the channel and thus can significantly modify the energy profile of the channel.

Single-channel studies on linear gramicidins with altered amino acid side chains. Effects of altering the polarity of the side chain at position 1 in gramicidin A

The modulation of gramicidin A single-channel characteristics by the amino acid side chains was investigated using gramicidin A analogues in which the NH2 terminal valine was chemically replaced by other amino acids. The replacements were chosen such that pairs of analogues would have essentially isosteric side chains of different polarities at position 1 (valine vs. trifluorovaline or hexafluorovaline; norvaline vs. S-methyl-cysteine; and norleucine vs. methionine). Even though the side chains are not in direct contact with the permeating ions, the single-channel conductances for Na+ and Cs+ are markedly affected by the changes in the physico-chemical characteristics of the side chains. The maximum single-channel conductance for Na+ is decreased by as much as 10-fold in channels formed by analogues with polar side chains at position 1 compared with their counterparts with nonpolar side chains, while the Na+ affinity is fairly insensitive to these changes. The relative conductance changes seen with Cs+ were less than those seen with Na+; the ion selectivity of the channels with polar side chains at position 1 was increased. Hybrid channels could form between compounds with a polar side chain at position 1 and either valine gramicidin A or their counterparts with a nonpolar side chain at position 1. The structure of channels formed by the modified gramicidins is thus essentially identical to the structure of channels formed by valine gramicidin A. The polarity of the side chain at position 1 is an important determinant of the permeability characteristics of the gramicidin A channel. We discuss the importance of having structural information when interpreting the functional consequences of site-directed amino acid modifications.