Ionic selectivity, saturation and block in gramicidin A channels: I. Theory for the electrical properties of ion selective channels having two pairs of binding sites and multiple conductance states.

A model for the gramicidin A channel is proposed which extends existing models by adding a specific cationic binding site at each entrance to the channel. The binding of ions to these outer channel sites is assumed to shift the energy levels of the inner sites and barriers and thereby alter the channel conductance. The resulting properties are analyzed theoretically for the simplest case of two inner sites and a single energy barrier. This for-site model (two outer and two inner) predicts that the membrane potential at zero current (Uo) should be a Goldman-Hodgkin-Katz equation with concentration-dependent permeability ratios. The coefficients of the concentration-dependent terms are shown to be related to the peak energy shifts of the barrier and to the binding constants of the outer sites. The thory also predicts the channel conductance in symmetrical solutions to exhibit three limiting behaviors, from which the properties of the outer and inner sites can be characterized. In two-cation symmetrical mixtures the conductance as a function of mole fraction is shown to have a minimum, and the related phenomenon of inhibition and block exerted by one ion on the other is explained explicitly by the theory. These various phenomena, having ion interactions in a multiply occupied channel as a common physical basis, are all related (by the theory) through a set of measurable parameters describing the properties of the system.     

Modulation of gramicidin A open channel lifetime by ion occupancy.

The hypothesis that the gramicidin A channel stability depends on the level of ion occupancy of the channel was used to derive a mathematical model relating channel lifetime to channel occupancy. Eyring barrier permeation models were examined for their ability to fit the zero-voltage conductance, current-voltage, as well as lifetime data. The simplest permeation model required to explain the major features of the experimental data consists of three barriers and four sites (3B4S) with a maximum of two ions occupying the channel. The average lifetime of the channel was calculated from the barrier model by assuming the closing rate constant to be proportional to the probability of the internal channel sites being empty. The link between permeation and lifetime has as its single parameter the experimentally determined averaged lifetime of gramicidin A channels in the limit of infinitely dilute solutions and has therefore no adjustable parameters. This simple assumption that one or more ions inside the channel completely stabilize the dimer conformation is successful in explaining the experimental data considering the fact that this model for stabilization is independent of ion species and configurational occupancy. The model is used to examine, by comparison with experimental data, the asymmetrical voltage dependence of the lifetime in asymmetrical solutions, the effects of blockers, and the effects of elevated osmotic pressure.     

Interactions in cation permeation through the gramicidin channel. Cs, Rb, K, Na, Li, Tl, H, and effects of anion binding.

As a prototype for binding and interaction in biological Na and K channels, the single channel conductances for Li, Na, K, Rb, Cs, H, and Tl and the membrane potentials for Tl-K mixtures are characterized for gramicidin A over wider concentration rangers than previously and analyzed using an "equilibrium domain" model that assumes a central rate-determining barrier. Peculiarities in the conductance-concentration relationship for TlF, TlNO3, and TlAc suggest that anions bind to Tl-loaded channels, and the theory is extended to allow for this. For concreteness, the selectivity of cation permeation is characterized in terms of individual binding and rate constants of this model, with the conclusions that the strongest site binds Cs greater than Rb greater than K greater than Na greater than Li, while the next strongest binds Na greater than K greater than Li greater than Rb greater than Cs. However, because Schagina, Grinfeldt, and Lev''s recent finding of single filing (personal communication) indicates that the channel sites in gramicidin cannot be at equilibrium with the solution, and work in progress with Hägglund and Enos (Biophys. J. 21:26a. [Abstr.]) indicates that the simplest model adequate to account for the observed concentration-dependences of flux-ratio, conductance, I--V characteristic, and permeability has three barriers and four sites, some implications of additional rate-determining barriers at the mouth of the channel are discussed. The results are summarized using phenomenological "experimental" parameters that provide a model-independent way to represent that data concisely and which can be interpreted physically in terms of any desired model.     

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.     

Gramicidin channel selectivity. Molecular mechanics calculations for formamidinium, guanidinium, and acetamidinium.

Empirical energy function calculations were used to evaluate the effects of minimization on the structure of a gramicidin A channel and to analyze the energies of interaction between three cations (guanidinium, acetamidinium, formamidinium) and the channel as a function of position along the channel axis. The energy minimized model of the gramicidin channel, which was based on the results of Venkatachalam and Urry (1983), has a constriction at the channel entrance. If the channel is not allowed to relax in the presence of the ions (rigid model), there is a large potential energy barrier for all three cations. The barrier varies with cation size and is due to high van der Waals and ion deformation energies. If the channel is minimized in the presence of the ions, the potential energy barrier to formamidinium entry is almost eliminated, but a residual barrier remains for guanidinium and acetamidinium. The residual barrier is primarily due, not to the expansion of the helix, but, to the disruption of hydrogen bonds between the terminal ethanoloamine and the next turn of the helix which occurs when the carbonyls of the outer turn of the helix librate inward toward the ion as it enters the channel. The residual potential energy barriers could be a possible explanation for the measured selectivity of gramicidin for formamidinium over guanidinium. The results of this full-atomic model address the applicability of the size-exclusion concept for the selectivity of the gramicidin channel.     

Simulation study of a gramicidin/lipid bilayer system in excess water and lipid. II. Rates and mechanisms of water transport

A gramicidin channel in a fluid phase DMPC bilayer with excess lipid and water has been simulated. By use of the formal correspondence between diffusion and random walk, a permeability for water through the channel was calculated, and was found to agree closely with the experimental results of Rosenberg and Finkelstein (Rosenberg, P.A., and A. Finkelstein. 1978. J. Gen. Physiol. 72:327-340; 341-350) for permeation of water through gramicidin in a phospholipid membrane. By using fluctuation analysis, components of resistance to permeation were computed for movement through the channel interior, for the transition step at the channel mouth where the water molecule solvation environment changes, and for the process of diffusion up to the channel mouth. The majority of the resistance to permeation appears to occur in the transition step at the channel mouth. A significant amount is also due to structurally based free energy barriers within the channel. Only small amounts are due to local friction within the channel or to diffusive resistance for approaching the channel mouth.     

Location of ion-binding sites in the gramicidin channel by X-ray diffraction.

We report the first X-ray diffraction on gramicidin in its membrane-active form by using uniformly aligned multilayer samples of membranes containing gramicidin and ions (T1+, K+, Ba2+, Mg2+ or without ions). From the difference electron density profiles, we found a pair of symmetrically located ion-binding sites for T1- at 9.6 (+/- 0.3) A and for Ba2+ at 13.0 (+/- 0.2) A from the midpoint of the gramicidin channel. The location of Ba(2+)-binding sites is near the ends of the channel, consistent with the experimental observation that divalent cations do not permeate but block the channel. The location of T1(+)-binding sites is somewhat of a surprise. It was generally thought that monovalent cations bind to the first turn of the helix from the mouth of the channel. (It is now generally accepted that the gramicidin channel is a cylindrical pore formed by two monomers, each a single-stranded beta 6.3 helix and hydrogen-bonded head-to-head at their N termini.) But our experiment shows that the T1(+)-binding site is either near the bottom of or below the first helix turn.     

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).     

Ion movement through gramicidin A channels. Studies on the diffusion-controlled association step

The permeability characteristics of gramicidin A channels are generally considered to reflect accurately the intrinsic properties of the channels themselves; i.e., the aqueous convergence regions are assumed to be negligible barriers for ion movement through the channels. The validity of this assumption has been examined by an analysis of gramicidin A single-channel current-voltage characteristics up to very high potentials (500 mV). At low permeant ion concentrations the currents approach a voltage-independent limiting value, whose magnitude is proportional to the permeant ion concentration. The magnitude of this current is decreased by experimental maneuvers that decrease the aqueous diffusion coefficient of the ions. It is concluded that the magnitude of this limiting current is determined by the diffusive ion movement through the aqueous convergence regions up to the channel entrance. It is further shown that the small-signal (ohmic) permeability properties also reflect the existence of the aqueous diffusion limitation. These results have considerable consequences for the construction of kinetic models for ion movement through gramicidin A channels. It is shown that the simple two-site-three-barrier model commonly used to interpret gramicidin A permeability data may lead to erroneous conclusions, as biionic potentials will be concentration dependent even when the channel is occupied by at most one ion. The aqueous diffusion limitation must be considered explicitly in the analysis of gramicidin A permeability characteristics. Some implications for understanding the properties of ion-conducting channels in biological membranes will be considered.     

Fluctuations of barrier structure in ionic channels

In rate-theory analysis of ion transport in channels, the energy of binding sites and the height of activation barriers are usually considered to be time-independent and not influenced by the movement of the ion. The assumption of a fixed barrier structure seems questionable, however, in view of the fact that proteins may exist in a large number of conformational states and may rapidly move from one state to the other. In this study, some of the effects of multiple conformational states of a channel on ion transport are analyzed. In the first part of the paper, the ion permeability of a channel with n binding sites is treated on the assumption that interconversion of channel states is much faster than ion transfer between binding sites. Under this condition, the form of the flux equation remains the same as for a channel with fixed barriers, provided that the rate constants for ion jumps are replaced by weighted averages over the rate constants for the individual conformational states. In the second part, a channel with two (main) barriers and a single (main) binding site is considered, with the rates of conformational transitions being arbitrary. This case, in particular, includes the situation where a jump of the ion is followed by a slow transition to a more polarized state of the binding site. Under this condition, the conductance of the channel exhibits a nonlinear dependence on ion concentration which is different from a simple saturation behavior. Under non-stationary conditions damped oscillations may occur.     

Formation of ion channels by a negatively charged analog of gramicidin A.

O-pyromellitylgramicidin is a derivative of gramicidin in which three carboxyl groups are introduced at the terminal hydroxyl end of the peptide. Experiments with artificial lipid membranes indicate that this negatively charged analog forms ion-permeable channels in a way similar to that of gramicidin. If O-pyromellitylgramicidin is added to only one aqueous solution, the membrane conductance remains small, but increases by several orders of magnitude if the same amount is also added to the other side. In accordance with the dimer model of the channel, the membrane conductance under symmetrical conditions is proportional to the square of the aqueous concentration of O-pyromellitylgramicidin over a wide range. The ratio lambdaPG/lambdaG of the single-channel conductance of O-pyromellitylgramicidin to that of gramicidin is close to unity at high ionic strength, but increases more than fivefold at smaller ionic strength (0.01 M). This observation is explained in terms of an electrostatic effect of the fixed negative charges localized near the mouth of the channel. In a mixture of O-pyromellitylgramicidin and gramicidin, unit conductance steps of intermediate size are observed in addition to the conductance steps corresponding to the pure compounds, indicating the formation of hybrid channels. Hybrid channels with preferred orientation may be formed if small amounts of gramicicin and O-pyromellitylgramicidin are added to opposite sides of the membrane. These hybrid channels show a distinct asymmetry in the current-voltage characteristic.     

Binding of thallium and other cations to the gramicidin A channel. Equilibrium dialysis study of gramicidin in phosphatidylcholine vesicles

Gramicidin A is a linear peptide antibiotic which forms dimer transmembrane channels selective for small monovalent cations, including thallium ions (Tl⁺) which are strongly bound. While there is great interest in the number of ion-binding sites per channel and the affinities of the sites for the various cations, measurements of the kinetics of ion permeation yield these equilibrium parameters only as indirect estimates dependent on the model assumed for the channel. Sonicated lipid vesicles. containing 1 mole of gramicidin per 30 moles of dimyristoylphosphatidylcholine. can be prepared with 5 mm-gramicidin. Evidence from our previous spectroscopic studies strongly supports the belief that this gramicidin is in the form of symmetrical dimer channels. Lipid vesicles containing gramicidin were dialyzed against control vesicles without gramicidin in the presence of a constant amount of radioactive ²⁰¹Tl⁺ and increasing amounts of non-radioactive Tl⁺. The ratio of ²⁰¹Tl⁺ free in solution to ²⁰¹Tl⁺ bound to the channel was measured after equilibrium (≥ 48 h) at 23 °C, and this ratio was plotted as a function of the free Tl⁺ concentration. The inverse of the slope yielded 0.8 to 1.1 for the maximum number of simultaneously occupied highest affinity sites per channel, and the inverse of the intercept yielded a highest affinity constant of 500 to 1000 m^?1 for each site. It appears that direct electrostatic repulsion prevents ions from binding simultaneously to the identical channel ends for thallium ion concentrations up to 20 mm. Estimates of the highest affinity constants for Rb⁺ and Na⁺ were also obtained.     

Study of interaction between cation fluxes in gramicidin A-modified bilayer phospholipid membranes. Determination of the number of ion-binding sites and their position in the gramicidin channel

Simultaneous studies were carried out of isotope and electric parameters of spheric bilayer membranes modified with gramicidin A and its analog O-pyromellithylgramicidin (PG) having three negative charges on the N-end of the molecule. The relationship between the electric coefficients of permeability and the isotope ones PG/P* = n was determined by two independent methods. It has been found that for the membranes modified with gramicidin A in RbCl concentrations from 2.2 x 10(-3) to 10(-1) M the value n is constant and approximates 2 and with RbCl concentration 1 M, n = 1.6. For the membranes modified with PG in 0.1 M solutions of PbCl n = 2. The results obtained in terms of the model of unilinear ion diffusion in a narrow pore indicate that in a gramicidin channel there are two sites of cation binding which are located near the channel mouth.     

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.     

Ion channels formed by chemical analogs of gramicidin A.

Channel-forming peptides such as gramicidin A offer the opportunity to study the relationship between chemical structure and transport properties of an ion channel. This article summarizes a number of recent experiments with chemical analogs and derivatives of gramicidin A using artificial lipid bilayer membranes. The introduction of negative charges near the channel mouth leads to an increase in the cation transport rate. Hybrid channels consisting of a neutral and a negatively charged or of a positively and a negatively charged half-channel may be formed. The current-voltage characteristic of these hybrid channels exhibits a pronounced asymmetry.Experiments with charged derivatives of gramicidin A have been used in order to distinguish between different structural models of the dimeric channel; these studies strongly support Urry's model of a single-stranded, head-to-head associated helical dimer. In a further set of experiments gramicidin analogs with modified amino acid sequence were studied. It was found that a single substitution (tryptophan replaced by phenylalanine) leads to marked changes in the conductance of the channel. Analogs with a simplified amino acid sequence such as (L-Trp-D-Leu)7-L-Trp or L-Trp-Gly-(L-Trp-D-Leu)6-L-Trp are able to form cation permeable channels with similar properties as gramicidin A.     

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.     

Single channel properties of D-Leu2-gramicidin A. Side chain modulation of channel lifetime

The channel forming properties of synthetic gramicidin A and DLeu2-gramicidin A were compared in black lipid membranes. The most probable single channel conductance was identical for both derivatives but in each case a distribution of smaller channel sizes was observed. However, the lifetime of the channel formed by DLeu2-gramicidin A was considerably shorter than for gramicidin A. The DLeu2 substitution is considered to interfere with the head to head hydrogen bonding which forms the conducting dimer, thus destabilizing the dimeric structure of the channel and reducing the lifetime. This represents the first demonstration of side-chain modulation of channel lifetime.     

The kinetics of ion movements in the gramicidin channel.

The main features of the ion permeability of gramicidin channels are summarized. The significance of maximums in the single channel conductance-concentration curves, of concentration-dependent permeability ratios, and or current-voltage curves with concentration-dependent form, as well as of other features, is discussed in terms of the mechanism of the ion transfer processes. The observations are then shown to be accounted for by rate theory expressions derived for a model pore consisting of two sites in series and in which ions are not permitted to pass each other. The status of other models is briefly reviewed.     

How electrolyte shielding influences the electrical potential in transmembrane ion channels.

The electrical potential due to fixed charge distributions is strongly altered in the vicinity of a membrane and notably dependent on aqueous electrolyte concentration. We present an efficient way to solve the nonlinear Poisson-Boltzmann equation applicable to general cylindrically symmetric dielectric geometries. It generalizes Gouy-Chapman theory to systems containing transmembrane channels. The method is applied to three channel systems: gramicidin, gap junction, and porin. We find that for a long, narrow channel such as gramicidin concentration variation has little influence on the electrical image barrier to ion permeation. However, electrolyte shielding reduces the image induced contribution to the energy required for multiple occupancy. In addition, the presence of electrolyte significantly affects the voltage profile due to an applied potential, substantially compressing the electric field to the immediate vicinity of the pore itself. In the large diameter channels, where bulk electrolyte may be assumed to enter the pore, the electrolyte greatly reduces the image barrier to ion permeation. At physiological ionic strengths this barrier is negligible and the channel may be readily multiply occupied. At all ionic strengths considered (l greater than 0.005 M) the image barrier saturates rapidly and is essentially constant more than one channel radius from the entrance to the pore. At lower ionic strengths (l less than 0.016 M) there are noticeable (greater than 20 mV) energy penalties associated with multiple occupancy.