John Sandblom

Gramicidin as an example of a single-filing ionic channel.

The cationic channel formed by the uncharged polypeptide backbone of the gramicidin A dimer is a simple and well characterizable prototype for the less easily studied types of ion-selective channels of the cell membrane. Excitable membranes are known to contain several types of ionic channels, each of which has come to be recogmzed’ to be a macromolecular pore capable of passing millions of ions per second and yet narrow enough to exhibit some selectivity as to the charge and size of the ions allowed to pass as well as to show signs of “singlefiling*’.’-3 A number of important conceptions about the general properties of channels have been confirmed by experimental findings in gramicidin A and by the theory that is developing to account for For example, recent findings on gramicidin channels indicate that such channels are able to contain several interacting permeant ions simultaneo~sly‘*’~.~ and are also SQ narrow that ions and water molecules are not permitted to pass each other?t.28*29 This supports the current view as to the likelihood of such behavior in the Na+ and K+ channels of The findings, in roughly chronological sequence, for excitable membranes and for gramicidin, are: single-filing flux coupling,20*2t concentrationdependent permeability ratio^.^-^^ block in mixture of cations’. ’% and coupling between ion-flux and water flu^.^*^ The conductanceconcentration behavior for the gramicidin channel in single salts also indicates the existence of at least two classes of sites with different binding constants for the group la cations: t % Here we will provide further evidence for multiple occupancy from the changes in shape that occur in the current-voltage relationshp of single gramicidin channels when the ionic concentration is changed. Finally, although the highly selective H+ permeation of the gramicidin channel has long been k n ~ w n : * ~ * ~ new, and surprising, data on the H+ permeation properties of the gramicidin channel, which we will present here, indicate that this channel may provide a much more %*

Multioccupancy models for single filing ionic channels: Theoretical behavior of a four-site channel with three barriers separating the sites

SummaryA procedure is developed for dealing with multioccupancy in single-filing channels having any number of sites internal to the barriers at the channel ends but having the outermost sites in equilibrium with the bathing solutions. Using this procedure, a general theory is developed for a single-filing channel having three barriers and four sites, the outermost of which are in equilibrium with the bathing solutions. By introducing a vectorial representation, it is shown that the four-site model can be reduced to an equivalent two-site model with respect to the number of possible transitions, thereby simplifying the algebraic steps required to solve transport equations for the system. The transport coefficients are derived and expressed in terms of the energy levels of the peaks and the wells for the different occupancy configurations. An explicit solution to the transport equations is given in a comprised form for a single permeable species. The solution allows some important properties for the system to be deduced, specifically with regard, to the conductance at zero current, the correlation factor between electrical conductance and tracer flux, and the current-voltage relationship. Examples are given for the use of the present results in a physical interpretation of the data from the gramicidin A channel.

Evaluation of surface tension and ion occupancy effects on gramicidin A channel lifetime

The surface tension of glycerylmonooleate-hexadecane lipid bilayer membranes and the lifetime of gramicidin A channels were measured at various concentrations of the surrounding solutions. For HCl the surface tension is essentially constant at approximately 5 mN/m up to approximately 1 M, whereas the average lifetime increases approximately 40-fold. At higher concentrations the surface tension decreases markedly. For CsCl the surface tension is constant up to about 1 M then increases with salt level. The average lifetime in this case increases about sixfold. In both cases the lifetime levels off and even decreases at higher salt levels. The increase in lifetime observed with ion activity is therefore qualitatively different from, and not explained by, the established dependence of lifetime on membrane properties (Elliot, J.R., D. Needham, J.P. Dilger, and D.A. Haydon. 1983. Biochim. Biophys. Acta. 735:95-103). We have previously proposed that ion occupancy is a determinant of channel stability, and to test this hypothesis the voltage dependence of channel lifetime was measured in asymmetrical solutions. For the case of a potassium chloride solution on one side of the membrane and a hydrogen chloride solution, on the other, the voltage dependence of the lifetime is asymmetrical. The asymmetry is such that when the electrical field is applied in the direction of the chemical gradient for each of the ions, the channel lifetime approaches, at increasing field strengths, that of a symmetrical solution of the respective ion. The voltage dependence of the surface tension, on the other hand, is negligible for the range of voltages used. These results, and the earlier findings that the order of the lifetimes for the alkali cations generally agree with the order of the permeability selectivity of the gramicidin A channel, support the hypothesis that ion occupancy is a major factor determining the lifetime of gramicidin A channels. The effects of multivalent blockers and osmotic agents were also tested. Ba2, La3+,and Mg2 decrease the lifetime and conductance markedly. Sucrose and urea increase the lifetime and decrease the conductance. The voltage dependence of the lifetime in symmetrical solutions was examined. Contrary to previous reports it was found that the lifetimes for K+, Cs, and H+ are voltage dependent. For 0.5 M HCI the lifetime decreases monotonically by .60% at 150 mV, and for 0.5 M KCI the lifetime increases by -60% at 200 mV. Below 10 mM there is no effect of voltage for H+, K+, and Cs+. These effects of blockers, osmotic agents, and voltage on the lifetime, as well as the lack of effect of voltage at low salt levels, are consistent with the occupancy hypothesis.

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.

Electrical relaxation processes in black lipid membranes in the presence of a cation-selective ionophore

SummaryThe time course of relaxation of the electric current following steps in the applied potential across lipid bilayer membranes has been measured. The membranes were made cation-selective by the addition of nonactin. To permit the measurement of very short time constants a voltage clamp device was developed in order to reduce the charging period to less than 1 μsec, regardless of the magnitude of the series resistances in the external solutions. It was possible by this method to establish the presence of two electric processes, which were found to behave differently with respect to temperature, applied potential and external solution conditions. The rapid process (τ≈10 μsec) was interpreted in terms of the electric parameters of the polar part of the membrane according to the theory developed by Hägglund and Sandblom (T.I.T.J. Life Sci.2: 107, 1972). The second process (τ≈100 μsec) showed a behavior consistent with the model of Stark, Ketterer, Benz and Läuger (Biophys. J.11:981, 1971), which considers the different rate constants involved in the net transfer of carriermediated ion transport across bilayer membranes.

The Current-voltage Behavior of Ion Channels: Important Features of the Energy Profile of the Gramicidin Channel Deduced from the Conductance-voltage Characteristic in the Limit of Low Ion Concentration

The conductance-voltage (G-V) characteristic of a single-filing, multi-barrier, multi-occupancy channel depends in the limit of low ion concentration upon only two parameters: the voltage dependence of the entry step and the ratio of the rate constant for leaving the channel to that for crossing its middle (14,17,20). We show that the G-V shape in this low concentration limit can be measured accurately using a triangular wave, many-channel technique and demonstrate that the observed shape is incompatible with that expected if the only important rate limiting barrier at low concentration were at the channel mouth. Instead the central barrier turns out, surprisingly, in view of the markedly sublinear I-V shape at low concentration, to be even slightly larger than the exit barrier. Additionally, we find that it is not possible to fit both the G-V shape and the concentration dependence of the zero-current conductance simultaneously with a 3-barrier 2-site model. However, by adding additional sites to yield a 3-barrier 4-site model either of the type 3B4S where the extra site in each channel half is external to the mouth of the channel or of the type 3B4S where the extra site is internal to the mouth of the channel, we obtain good agreement. Additionally, using the flux ratio data of Procopio and Andersen (19) to discriminate between 3B4S and 3B4S models, we find the 3B4S model to be the only satisfactory one.

Electrical Behavior of Single-Filing Channels

Several biological channels, as well as the model peptide channel formed by gramicidin, are believed to be capable of multiple occupancy by permeant ions (Hodgkin and Keynes, 1955; Hladky, 1972; Hille and Schwarz, 1978; Begenisich, 1979; Eisenman et al., 1978; Urban et al., 1980). Some of the peptide channels, such as those formed by Gramicidin A, have been estimated to be so narrow that ions and water molecules cannot pass each other (Schagina et al., 1978; Procopio and Andersen, 1979; Levitt et al., 1978; Finkelstein and Andersen, 1981). That such channels also have multiple barriers with different locations in the potential field is inferred from the finding of flux-ratio exponents greater than 1 and from the existence of an ion-concentration dependence of the current-voltage characteristic, which in the gramicidin channel was recognized quite early (Hladky, 1972; Lauger, 1973) to be concave toward the voltage axis at low salt concentrations (“sublinear”) and convex at high concentrations (“supralinear”).

Linear network representation of multistate models of transport

By introducing external driving forces in rate-theory models of transport we show how the Eyring rate equations can be transformed into Ohms law with potentials that obey Kirchhoffs second law. From such a formalism the state diagram of a multioccupancy multicomponent system can be directly converted into linear network with resistors connecting nodal (branch) points and with capacitances connecting each nodal point with a reference point. The external forces appear as emf or current generators in the network. This theory allows the algebraic methods of linear network theory to be used in solving the flux equations for multistate models and is particularly useful for making proper simplifying approximation in models of complex membrane structure. Some general properties of linear network representation are also deduced. It is shown, for instance, that Maxwells reciprocity relationships of linear networks lead directly to Onsagers relationships in the near equilibrium region. Finally, as an example of the procedure, the equivalent circuit method is used to solve the equations for a few transport models.

Measurement of channel lifetime in artificial lipid membranes: dimerization kinetics of gramicidin a

Abstract The autocorrelation function (acf) method has been used to evaluate the lifetime of gramicidin A channels in lipid bilayers. The accuracy of the method was evaluated using computer simulation techniques and experimentally by comparing the acf method with methods to extract the lifetime from single-channel recordings. It was found that a correct evaluation of the lifetime requires registrations for a period of 500-1000 lifetimes and that improving the accuracy of the method by increasing the event activity is not as effective as increasing the total registration time. The effects of noise and filters are examined and a method for constructing the survival-plot, in the case of overlapping channels, is presented. Experimental data for the dependence of lifetime and conductivity on salt activity are presented for CsCl, KCl and LiCl. The general finding is that the lifetime increases with ion concentration and for CsCl and KCl it passes through a maximum at about 1 M. A simple model relating the channel unit conductance and lifetime to the ion occupancy of the channel is described, and the best fit of the model to the data is presented.

Mechanisms of facilitation and blocking in gramicidin channels by impermeant ions

Abstract The mechanisms responsible for the facilitating effect of quarternary ammonium ions on the cation permeability of gramicidin A channels have been examined. Measurements of the current-voltage relationship have been carried out in diphytanoyl phosphatidylcholine (DPPC) membranes in the presence of HCl. It was found that the quarternary ammonium ions tetrabutylammonium tetramethylammonium (TMA), tetraethylammonium (TEA) and tetrapropylammonium (TPA) enhance the conductance whereas tetrabutylammonium (TBA) has little effect on the single channel conductance. When the concentration of quarternary ammonium ions (TEA) is increased (at constant pH) the conductance increases, passes through a maximum and then decreases. In asymmetric conditions, when quarternary ammonium ions (TMA) are placed on one side of the membrane only, the effect on the current is unidirectional, i.e. the current is unaffected in the direction towards the TMA side and enhanced in the direction away from the TMA side. This unidirectional effect on the current is similar to that found for Ca 2+ blocking in the sense that impermeant ions exert their effect on the positive side of the membrane only. The observed properties are explained in terms of a model with binding sites located near the outside for the impermeant ions. The differences between facilitating and blocking effects are then accounted for as a result of cooperative and noncooperative binding of permeant and impermeant ions.