How shortening a channel may lower its conductance. The case of des-Val7-DVal8-gramicidin A.

A shortened analog of gramicidin A has been shown by Urry et al. (Biochim. Biophys. Acta 775, 115-119) to have lower conductance than native gramicidin A. They argue this suggests that the major current carrier is the doubly occupied channel. A different perspective is presented here. Channel formation does not alter bilayer width. In a shortened channel an ion approaching the binding site moves further toward the center of the lipid-pore system. The electrostatic contribution to the energy barrier near the constriction mouth is greater for the shorter channel. As long as entry to the channel is rate limiting singly occupied short channels should exhibit lower conductance. The data are not inconsistent with singly occupied channels being the major current carriers. Experiments on other gramicidin analogs are suggested to more clearly distinguish between singly and doubly occupied channels as the dominant conducting species.

Ionic interactions in multiply occupied channels.

A significant number of physiologically important ion channels function via multi-ion mechanisms where repulsion between ions at slightly separated locations is believed to be critical for permeation. We apply the semi-microscopic Monte Carlo approach and analyse how multiple occupancy affects permeation energetics and ion-water-peptide correlations. We consider double occupancy in idealized models of two systems: gramicidin A and the KcsA K+ channel. We focus on the excess repulsion energy due to ion-water and ion-peptide correlations (repulsion energy adjusted for direct ion-ion interaction). Gramicidin, where multiple occupancy is marginally important functionally, is ideal for correlating structure and ion interactions. Pair occupancy is stabilized by interaction with bulk solvent, destabilized by interaction with both the channel water and, as binding sites are far apart, the peptide backbone. In the KcsA K+ channel, double occupancy is promoted by the uneven spacing and the large ion-water separations in the selectivity filter. The carbonyls forming the binding cavities are equally important for pair stabilization. Due to the binding pocket's design, net ionic repulsion is approximately 25-30% of what it would be in a gramicidin-like structure with the same interionic spacing.

Current noise in transport of hydrophobic ions through lipid bilayer membranes including diffusion polarization in the aqueous phase.

An exact treatment of the current noise spectrum produced by transport of hydrophobic ions through membranes is presented, including the coupling of the diffusion processes through both the aqueous phase and the membrane. Both the equilibrium and the steady state noise spectra are computed. The theory contains previous results as limiting cases. The structure of the spectra is discussed with emphasis upon how noise measurements can be used to estimate kinetic parameters, especially the rate of desorption from the membrane. For this restricted model there is no low frequency divergence in the non-equilibrium current noise, i.e., for the model treated there is no 1/f noise.

Energy barriers for passage of ions through channels. Exact solution of two electrostatic problems.

Exact solutions are given to two electrostatic problems relevant to ion permeation through pores in membranes. The first assesses the importance of the pore forming molecule as a dielectric shield. It is shown on the basis of structural and dielectric considerations alone (neglecting effects attributable to possible charge distribution at the interior surface of the pre-former) that the minimum electrostatic barrier for monovalent ion passage through a gramicidin-like channel is 11 kT. It is further shown that given favorable circumstances, dielectric shielding might dramatically reduce the barrier to ion passage through potassium channels. The second problem considers the error introduced by treating ions as point charges. It is shown that for structureless pores the point charge approximation introduces no meaningful error, even if the ratio of ion radius to pore radius is as great as 0.95.

The interaction of Cl- with a gramicidin-like channel.

Molecular dynamics simulations have been used to study the interaction of Cl- with a gramicidin-like channel. The results suggest that there is a high-energy barrier at the entrance of the channel, which would correspond to a permeability 10(-9)-times that of a cation of the same size. This could account for the cationic selectivity of the gramicidin channel and indicates that valence selectivity is kinetically controlled.

Electrostatic modeling of ion pores. Multipolar sources.

We present calculations of the polarization energy required when a multipolar source enters a transmembrane ion channel. The polarization energy for polar, but uncharged, sources is nearly independent of channel length if the length/diameter ratio is greater than 1.25; however, it is strongly dependent on channel radius. All significant changes in the polarization energy occur within a distance of +/- one channel radius of the entrance to the channel. Our calculational method also provides a means of estimating the change in polarization energy that occurs when an ion is not located axially; this contribution can be significant for smaller ions, for which the binding sites may be far from the axis.

Ion-water and water-water interactions in a gramicidinlike channel: effects due to group polarizability and backbone flexibility.

In the gramicidin channel, ionic transport and water transport occur simultaneously. Gramicidin's transport properties are influenced by ionic interactions with both the polypeptide and the channel waters. We present results of molecular dynamics studies on a series of alkali metal ions interacting with a water-filled gramicidinlike channel (a configurationally constrained polyglycine analog) at the dimer junction, in mid-monomer, and near the channel entrance. We investigate details of both short and long range ion-water and water-water correlation; these are notably dependent on the explicit consideration of polarizability and the degree of backbone flexibility. The nature of ion-water and water-water correlations changes as ionic size decreases and these changes may be augmented or attenuated by manipulation of the two parameters under study. Incorporating polarizability generally shortens ion-water distances and enhances ion-induced electrostriction (decreased water-water separations), while simultaneously reducing the long range orientational correlation of the single filing waters within the channel. Increasing flexibility predictably results in a broadening of the distribution of water-water and ion-water separations and contributes to the loss of long range orientational correlations. Both effects are ion specific; Cs+ and Na+ interact with the channel in distinctly different ways, while K+ represents an intermediate case more closely resembling Cs+. Our results demonstrate that incorporation of polarizability in the potential function has significant effects on the properties of channel water and, consequently, on the ionic transport process. While ion-water and water-water distances are decreased due to this feature, thereby fostering longer ranged correlations within the channel, enhanced interactions between water molecules and peptide groups tend to mitigate this effect. Possible implications for the multiple occupancy states of gramicidin and long range information transfer via a single file water chain are considered.

Kinetics of transport of hydrophobic ions through lipid membranes including diffusion polarization in the aqueous phase.

Previous interpretations of the kinetics of transport of hydrophobic ions through membranes have been based on one of three limiting assumptions. Either diffusion in the aqueous phase was taken to be rapid, or ionic motion was constrained to the membrane or a steady state was presumed to be established within the membrane. We present a general treatment of the coupled diffusion process through both the aqueous phase and the membrane; our theory contains the previous results as limiting cases. It is applied to voltage jump-current relaxation experiments on black lipid membranes in the presence of dipicrylamine or sodium tetraphenylborate. We have attempted to establish the rate of desorption from the membrane. For the system phosphatidylserine/tetraphenylborate, the rate of desorption and the rate of translocation were found to be comparable.

A laser-temperature-jump method for the study of the rate of transfer of hydrophobic ions and carriers across the interface of thin lipid membranes.

The first application of a laser-temperature-jump apparatus for the study of ion transport through planar (artificial) lipid membranes is described. The relaxation of the electric current is detected, either continuously at a constant applied voltage or discontinuously by a series of short voltage pulses. The second technique, a combined voltage- and temperature-jump method, is especially appropriate to investigate the kinetics of the adsorption/desorption process of hydrophobic ions and neutral carriers of cations at the membrane interface and to separate this phenomenon from the diffusion process through the unstirred aqueous layers adjacent to the membrane. The aim is to determine the rate-limiting step of transport. The permeation rate of the hydrophobic anion 2,4,6-trinitrophenolate is limited by the inner membrane barrier. For tetraphenylberate the rate constant of translocation across the inner barrier and that of desorption from the membrane into water are found to be of comparable magnitude. The membrane permeability of the neutral macrocyclic ion carrier enniatin B is strongly interface limited by its comparatively small rate of desorption into water. These results show that the frequently used a priori assumption of partition equilibrium at the membrane interfaces during transport is not justified.

How pore mouth charge distributions alter the permeability of transmembrane ionic channels.

This paper investigates the effects that surface dipole layers and surface charge layers along the pore mouth-water interface can have on the electrical properties of a transmembrane channel. Three specific molecular sources are considered: dipole layers formed by membrane phospholipids, dipole layers lining the mouth of a channel-forming protein, and charged groups in the mouth of a channel-forming protein. We find, consistent with previous work, that changing the lipid-water potential difference only influences channel conduction if the rate-limiting step takes place well inside the channel constriction. We find that either mouth dipoles or mouth charges can act as powerful ion attractors increasing either cation or anion concentration near the channel entrance to many times its bulk value, especially at low ionic strengths. The effects are sufficient to reconcile the apparently contradictory properties of high selectivity and high conductivity, observed for a number of K+ channel systems. We find that localizing the electrical sources closer to the constriction entrance substantially increases their effectiveness as ion attractors; this phenomenon is especially marked for dipolar distributions. An approximate treatment of electrolyte shielding is used to discriminate between the various mechanisms for increasing ionic concentration near the constriction entrance. Dipolar potentials are far less sensitive to ionic strength variation than potentials due to fixed charges. We suggest that the K+ channel from sarcoplasmic reticulum does not have a fixed negative charge near the constriction entrance; we suggest further that the Ca+2-activated K+ channel from transverse tubule does have such a charge.

Effect of pore structure on energy barriers and applied voltage profiles. I. Symmetrical channels.

This paper presents calculations of the image potential for an ion in an aqueous pore spanning a lipid membrane and for the electric field produced in such a pore when a transmembrane potential is applied. The pore diameter may be variable. As long as the length-to-radius ratio in the narrow portion of a channel is large enough, the image potential for an ion in or near the mouth of a channel is determined by the geometry of the mouth. Within the constriction, the image potential of the ion-pore system may be reasonably approximated by constructing an "equivalent pore" of uniform diameter spanning a somewhat thinner membrane. When a transmembrane potential is applied the electric field within a constricted, constant radius, section of the model pore is constant. If the length-to-radius ratio of the narrow part of the channel is not too large or the channel ensemble has wide mouths, the field extends a significant distance into the aqueous region. The method is used to model features of the gramicidin A channel. The energy barrier for hydration (for exiting the channel) is identified with the activation energy for gramicidin conductance (Bamberg and Läuger, 1974, Biochim. Biophys. Acta. 367:127).

Effect of pore structure on energy barriers and applied voltage profiles. II. Unsymmetrical channels.

This paper examines "realistic" pores, i.e., ones that are neither symmetric nor of uniform diameter. Methods are described that permit estimation of the image potential for an ion in an aqueous pore spanning a lipid membrane and for the electric field produced in such a pore when a transmembrane potential is applied. They are used to model features of the delayed rectifier potassium channel. Constraints on the geometry of the exterior mouth, the dielectric properties of the narrow part of the pore and the conduction mechanism are determined for this channel.

Electrostatic modeling of ion pores. II. Effects attributable to the membrane dipole potential.

This paper presents calculations of the shielded dipole potential in the interior of a pore piercing a lipid membrane that is at a potential V0 with respect to the aqueous solution. Except in the case of long narrow pores, there is substantial shielding of the membrane dipole potential. The associated dipole field never extends a significant distance into the aqueous region. The fact that the single-channel conductance of gramicidin B is only twice as large in glyceryl monooleate membranes as in phosphatidyl choline (PC) membranes, even though PC is approximately 120 mV more positive with respect to water, is interpreted in terms of the potential energy profile calculated for a gramicidin-like channel. It is demonstrated that the membrane dipole potential can significantly affect channel conductance only if the pore is narrow and if the peak in the potential energy profile occurs in the pore interior.

Electrostatic modeling of ion pores. Energy barriers and electric field profiles.

This paper presents calculations of the image potential for an ion in an aqueous pore through lipid membrane and the electric field produced in such a pore when a transmembrane potential is applied. The method used is one introduced by Levitt (1978, Biophys. J. 22:209), who solved an equivalent problem, in which a surface charge density is placed at the dielectric boundary. It is shown that there are singularities in this surface charge density if the model system has sharp corners. Numerically accurate calculations require exact treatment of these singularities. The major result of this paper is the development of a projection method that explicitly accounts for this behavior. It is shown how this technique can be used to compute, both reliably and efficiently, the electrical potential within a model pore in response to any electrical source. As the length of a channel with fixed radius is increased, the peak in the image potential approaches that of an infinitely long channel more rapidly than previously believed. When a transmembrane potential is applied the electric field within a pore is constant over most of its length. Unless the channel is much longer than its radius, the field extends well into the aqueous domain. For sufficiently dissimilar dielectrics the calculated values for the peak in the image potential and for the field well within the pore can be summarized by simple empirical expressions that are accurate to within 5%.

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.

The channel properties of possible gramicidin dimers.

Extending previous work (Sung & Jordan, 1987 a, Biophys. J. 51, 661-672; 1988, Biophys. J.54, 519-526), we describe channel properties of five possible gramicidin dimers by studying dimerization energies and axial electrical potentials. Unlike the head-to-head dimer (the predominant channel former), both tail-to-tail and head-to-tail dimers with the same beta-helical monomer structure as the head-to-head dimer only form four intermonomer hydrogen bonds and are much less stable. Were channels formed from these dimers to be observed, their electrical potential profiles suggest that they should be cation selective, probably conduct less than the head-to-head dimer, have a central cation binding site, bind cations preferentially if crystallizable, and in the case of the head-to-tail dimer, rectify. Like the antiparallel double stranded helical dimer (a possible minor conducting pathway) the parallel double stranded helical dimer has 28 interstrand hydrogen bonds, but its hydrogen bond network is quite distorted and it is much less stable. If it formed, its electrical potential profile suggests that it would be cation selective, bind anions preferentially if crystallizable, rectify, and at high enough voltages, might exhibit a conductance greater than that of the antiparallel form.

Theoretical study of the antiparallel double-stranded helical dimer of gramicidin as an ion channel.

Recent experimental studies by Durkin, J. T., O. S. Andersen, F. Heitz, Y. Trudelle, and R. E. Koeppe II (1987. Biophys. J. 51:451a) have suggested that the antiparallel double-stranded helical (APDS) dimer of gramicidin can form a transmembrane cation channel. This article reports a theoretical study that successfully rationalizes the channel properties of the APDS dimer. As in the case of the head-to-head (HH) dimer, the APDS exhibits a high potential energy barrier as anions approach the channel mouth, according for the observation of valence selectivity. The calculated potential energies of cations show two binding sites near the channel mouths, a typical feature of the HH channel. The potential energies of hydrated cations in the APDS are generally higher than those in the HH channel and show a larger pseudoperiodicity and higher barriers, an observation which suggests that the APDS should exhibit lower single channel conductance.

Why is gramicidin valence selective? A theoretical study.

Calculations contrasting the channel solvation energy for cesium ions and chloride ions associated with water in gramicidin-like channels are presented. The energy profile for the cation exhibits a deep well at the channel entrance; within the single file region the solvation energy is roughly constant. The anion exhibits a totally different energy profile. There is an energy barrier at the channel entrance; if the ion could surmount this barrier, it would be quite stable within the channel. At the channel entrance, the calculated solvation energy difference between anion and cation is approximately 15 kcal mol-1. This is completely consistent with the observation that chloride neither permeates nor blocks the channel since the estimated rate of ion entry would be approximately 0.01-10(-5) s-1, far slower than the rate at which the channel dimer dissociates into monomers.

Molecular dynamics simulation of cation motion in water-filled gramicidinlike pores.

A model calculation is carried out to study the potential energy profile of a sodium ion with several water molecules inside a simplified model of the gramicidin ion channel. The sodium ion is treated as a Lennard-Jones sphere with a point charge at its center. The Barnes polarizable water model is used to mimic the water molecules. A polarizable and deformable gramicidinlike channel is constructed based on the model obtained by Koeppe and Kimura. Potential minima and saddle points are located and the static energy barriers are computed. The potential minima at the two mouths of the channel exhibit an aqueous solvation structure very different from that at any of the interior minima. These sites are approximately 23.6 and 24.4 A apart for binding of a sodium ion and a cesium ion, respectively. Ionic motion from these exterior sites to the first interior minimum requires substantial rearrangement of the waters of solvation; this rearrangement may be the hydration/dehydration step in ionic permeation through the channel. Based on these results, a mechanism by which the sodium ion moves from the exterior binding site to the interior of the channel is proposed. Our model channel accommodates about eight water molecules and the transport of the ion and water within the channel is found to be single file. Results of less extensive calculations for Cs+ and Li+ ions in a channel with or without water are also reported.