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

Monte Carlo studies of a model for lipid-gramicidin A bilayers

This paper presents results of Monte Carlo simulations of a full bilayer of 200 lipid chains and one gramicidin A dimer. Simulations are described for systems with lipid chains of 14, 16, and 18 carbons, respectively. Using accepted potential functions to calculate interactions between all non-hydrogen atoms a Monte Carlo configuration sampling is generated from which order parameter profiles are calculated and specific configurations are displayed. Results are compared with experimental data for lipid-gramicidin bilayers.

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.

Ion-water and ion-polypeptide correlations in a gramicidin-like channel. A molecular dynamics study

This work describes a molecular dynamics study of ion-water and ion-polypeptide correlation in a model gramicidin-like channel (the polyglycine analogue) based upon interaction between polarizable, multipolar groups. The model suggests that the vicinity of the dimer junction and of the ethanolamine tail are regions of unusual flexibility. Cs+ binds weakly in the mouth of the channel: there it coordinates five water molecules and the #11CO group with which it interacts strongly and is ideally aligned. In the channel interior it is generally pentacoordinate; at the dimer junction, because of increased channel flexibility, it again becomes essentially hexacoordinate. The ion is also strongly coupled to the #13 CO but not to either #9 or #15, consistent with 13C NMR data. Water in the channel interior is strikingly different from bulk water; it has a much lower mean dipole moment. This correlates with our observation (which differs from that of previous studies) that water-water angular correlations do not persist within the channel, a result independent of ion occupancy or ionic polarity. In agreement with streaming potential measurements, there are seven single file water molecules associated with Cs+ permeation; one of these is always in direct contact with bulk water. At the mouth of an ion-free channel, there is a pattern of dipole moment alteration among the polar groups. Due to differential interaction with water, exo-carbonyls have unusually large dipole moments whereas those of the endo-carbonyls are low. The computed potential of mean force for CS+ translocation is qualitatively reasonable. However, it only exhibits a weakly articulated binding site and it does not quantitatively account for channel energetics. Correction for membrane polarization reduces, but does not eliminate, these problems.

Diffusion and kinetic approaches to describe permeation in ionic channels

Diffusion and reaction rate theories provide convenient approaches for describing permeation in ionic channels. Both approaches have strengths and weaknesses. Diffusion theories realistically approximate the physical process of ion movement within an aqueous pore, but those theories do not handle ionic interactions easily. Reaction rate theories are easy to use, and they provide a mathematical summarization of the data that is valuable for communicating experimental results. During ion permeation, however, the basic assumptions of reaction rate theory are not met. Therefore, rate theories do not provide true physical descriptions of ion permeation.

Gramicidin single-channel properties show no solvent-history dependence

The structure of membrane-associated gramicidins can depend on the solvent in which they were dissolved prior to membrane incorporation (LoGrasso, P. V., F. Moll, and T. A. Cross 1988. Biophys. J. 54:259-267; Killian, J. A., K. U. Prasad, D. Hains, and D. W. Urry. 1988. Biochemistry. 27:4848-4855). The peptide's solvent history might thus affect the functional characteristics of gramicidin channels (op. cit.). We tested this proposal by examining the properties (conductance, conductance dispersity, and average duration) of channels formed by [Val1]gramicidin A that had been dissolved in eight different solvents. The peptide was incorporated into lipid bilayers either by addition to the aqueous phase (and subsequent adsorption to the membrane) or by cosolubilization with the membrane-forming phospholipid. When the peptide was cosolubilized with the phospholipid, the channel properties did not vary with the solvent used. When the peptide was dissolved in chloroform, benzene, or trifluoroethanol and added through the aqueous phase, the channel properties differed from those found when gramidicin was dissolved in methanol, ethanol, dioxane, dimethylsulfoxide, or ethylacetate. The changes observed with the former three solvents were reproduced by adding them to the aqueous phase, and are therefore due to the ability of these solvents to partition into the membrane and alter the channels' behavior.

The 20-pS chloride channel of the human airway epithelium

The single-channel inside-out patch clamp technique was used to characterize chloride channels in the apical membranes of human airway epithelial cells maintained in primary culture. Patches were obtained from single isolated cells or from cells at the edges of confluent groups. The channel seen most often, in 24% of all patches, had a conductance of approximately 20 pS and had a linear current-voltage relationship in symmetric chloride solutions. The anion selectivity sequence for the channel was NO3- greater than Cl- greater than HCO3-, and it was impermeable to gluconate ions, indicating that the channel diameter lies between 4.7 and 5.5 A. Current through the channel saturated at high chloride concentrations, and the relationship between channel current and chloride concentration could be approximated by the Michaelis-Menten equation. Analysis of the channel's anion permeability and its current vs. concentration relationship indicates that it can be described by the one-ion channel theory, with a relatively weak binding site inside the channel. Histograms of channel open and closed durations were constructed using the log binning technique and could be well fitted by triple exponential distributions, suggesting that the channel has at least three open and three closed states.

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.

Application of Brownian motion theory to the analysis of membrane channel ionic trajectories calculated by molecular dynamics

This paper shows how Brownian motion theory can be used to analyze features of individual ion trajectories in channels as calculated by molecular dynamics, and that its use permits more precise determinations of diffusion coefficients than would otherwise be possible. We also show how a consideration of trajectories of single particles can distinguish between effects due to the magnitude of the diffusion coefficient and effects due to barriers and wells in the potential profile, effects which can not be distinguished by consideration of average fluxes.

Surmounting barriers in ionic channels

Biological cells are defined by the membrane that shields their vital molecules from the environment. The lipid bilayer of the membrane is an effective dielectric shield (Parsegian, 1969; Andersen, 1978; Honiget al.1986), preventing penetration by charged molecules: the lipid presents a large electrostatic energy barrier because it cannot neutralize the charge of solute molecules nearly as well as water. This energy barrier inhibits the permeation of solutes with local charge, even metabolites. Of course, metabolites do enter cells, and so physiologists have suspected (for a very long time, Hille, 1984, ch. 8) that the membrane shield is pierced by aqueous channels, through which solutes diffuse (with their local charge substantially neutralized) as they cross the membrane. These aqueous pores now have molecular reality (e.g. Nodaet al.1984; Miller, 1986). Each is formed by a specialized protein, integral to membranes, perhaps shaped like a thick-walled pipe, called ionic channels. Channels control the movement of many important molecules in and out of cells by the ‘gating’ mechanism that controls their opening and closing and by the selective properties of their open channel.