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.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Influence of ion occupancy and membrane deformation on gramicidin A channel stability in lipid membranes.

The average lifetime of gramicidin A channels in monoolein/decane bilayer membranes was measured. The results support the hypothesis of channel stabilization by ion occupancy. The effects of electric field and salt concentration are consistent with the expected effects on both occupancy and membrane compression. The lifetime in asymmetric solutions with divalent cation blockers on one side of the membrane shows a voltage dependence such that the lifetime decreases for positive voltages applied from the blocking side and increases for negative voltages. This result strongly supports the occupancy hypothesis. The lifetime increases with permeant ion concentration, and at the one molar level it also increases with voltage. The voltage dependence of lifetime for a low concentration of permeant ion depends on the total salt level. The results for these conditions are consistent with the assumption that membrane compression also influences the lifetime, even for the "soft" solvent-containing membrane considered here. It is proposed that the channel nearest neighbor lipids need not be fixed in a plane at the channel end. Using a liquid crystal model it may then be shown that surface tension is the major component of the membrane deformation free energy, which may explain the significant effects of the membrane compression on the lifetime.     

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.     

Single-salt behavior of a symmetrical 4-site channel with barriers at its middle and ends

The theory of a symmetrical 3-barrier, 4-site, single-filing ionic channel is developed. The model goes beyond earlier models by including additional sites, as well as barriers which need not be symmetrical in the applied field, and contains the earlier models as special cases. It is itself a special case of the most general 4-site model, which has 5 barriers. By considering the barriers at the mouth and middle of the channel to be sufficiently larger than the barriers separating the sites in each channel half, these barriers can be neglected; thus this case reduces to a 3-barrier model where the sites in each channel half can then be assumed to be in equilibrium with each other. The alternative 3-barrier, 4-site case, where the barrier between the sites is considered to be larger than that at the mouth of the channel, is considered elsewhere. Pure cation permeation is considered and only single-salt properties of the system are analyzed, namely occupancy, conductance, flux ratio exponent and current-voltage relation. The concentration dependences of these properties are computed and interrelated and, where possible, also given in analytical form. The mathematical relations are obtained for a channel which is symmetrical around its middle, which is the appropriate assumption for the gramicidin channel. However, the barriers themselves are allowed to be asymmetric with respect to the potential dependence, which has been found to be essential for gramicidin. Mathematically, a straight-forward matrix formulation is used; but a general theoretical method is presented for reducing a complex model (with more than 2 sites) to a simpler cases when equilibrium exists across one or several barriers, as is often the cases. This method is a prototype which makes analytical solutions of complex barrier models possible in many cases.     

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.     

Ion permeation through a narrow channel: using gramicidin to ascertain all-atom molecular dynamics potential of mean force methodology and biomolecular force fields

We investigate methods for extracting the potential of mean force (PMF) governing ion permeation from molecular dynamics simulations (MD) using gramicidin A as a prototypical narrow ion channel. It is possible to obtain well-converged meaningful PMFs using all-atom MD, which predict experimental observables within order-of-magnitude agreement with experimental results. This was possible by careful attention to issues of statistical convergence of the PMF, finite size effects, and lipid hydrocarbon chain polarizability. When comparing the modern all-atom force fields of CHARMM27 and AMBER94, we found that a fairly consistent picture emerges, and that both AMBER94 and CHARMM27 predict observables that are in semiquantitative agreement with both the experimental conductance and dissociation coefficient. Even small changes in the force field, however, result in significant changes in permeation energetics. Furthermore, the full two-dimensional free-energy surface describing permeation reveals the location and magnitude of the central barrier and the location of two binding sites for K(+) ion permeation near the channel entrance--i.e., an inner site on-axis and an outer site off-axis. We conclude that the MD-PMF approach is a powerful tool for understanding and predicting the function of narrow ion channels in a manner that is consistent with the atomic and thermally fluctuating nature of proteins.     

Voltage-dependent formation of gramicidin channels in lipid bilayers.

The formation kinetics of gramicidin A channels in lipid bilayer membranes has been characterized as a function of voltage for different solution conditions and membrane composition. The frequency of channel events was measured during the application of voltage ramps and counted in given intervals, a procedure that eliminated the effects of drift in gramicidin concentration. The formation rate was found to increase strongly with voltages up to approximately 50 mV and then to level off slightly. The shape of the voltage dependence was independent of lipid solvent and ramp speed but differed for different ions and different solution concentrations. This suggested an ion occupancy effect on the formation rate that was further supported by the fact that the minimum of the formation rate was shifted toward the equilibrium potential in asymmetric solution concentrations. The effects are explained in terms of a model that contains two contributions to the voltage dependence, a voltage-dependent ion binding to the monomers and a polarization of monomers by the applied electric field and by the occupied ions. The theory is found to give a good fit to experimental data.     

Symmetry and asymmetry of permeation through toxin-modified Na+ channels.

Single Na+ channels from rat skeletal muscle were inserted into planar lipid bilayers in the presence of either 200 nM batrachotoxin (BTX) or 50 microM veratridine (VT). These toxins, in addition to their ability to shift inactivation of voltage-gated Na+ channels, may be used as probes of ion conduction in these channels. Channels modified by either of the toxins have qualitatively similar selectivity for the alkali cations (Na+ approximately Li+ greater than K+ greater than Rb+ greater than Cs+). Biionic reversal potentials, for example, were concentration independent for all ions studied. Na+/K+ and Na+/Rb+ reversal potentials, however, were dependent on the orientation of the ionic species with respect to the intra- or extracellular face of the channel, whereas Na+/Li+ biionic reversal potentials were not orientation dependent. A simple, four-barrier, three-well, single-ion occupancy model was used to generate current-voltage relationships similar to those observed in symmetrical solutions of Na, K, or Li ions. The barrier profiles for Na and Li ions were symmetric, whereas that for K ions was asymmetric. This suggests the barrier to ion permeation for K ions may be different than that for Na and Li ions. With this model, these hypothetical energy barrier profiles could predict the orientation-dependent reversal potentials observed for Na+/K+ and Na+/Rb+. The energy barrier profiles, however, were not capable of describing biionic Na/Li ion permeation. Together these results support the hypothesis that Na ions have a different rate determining step for ion permeation than that of K and Rb ions.     

Test of molecular dynamics force fields in gramicidin A

The force fields commonly used in molecular dynamics simulations of proteins are optimized under bulk conditions. Whether the same force fields can be used in simulations of membrane proteins is not well established, although they are increasingly being used for such purposes. Here we consider ion permeation in the gramicidin A channel as a test of the AMBER force field in a membrane environment. The potentials of mean force for potassium ions are calculated along the channel axis and compared with the one deduced from the experimental conductance data. The calculated result indicates a rather large central barrier similar to those obtained from other force fields, which are incompatible with the conductance data. We suggest that lack of polarizability is the most likely cause of this problem, and, therefore, urge development of polarizable force fields for simulations of membrane proteins.     

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.     

Semi-Markov models for brownian dynamics permeation in biological ion channels

Constructing accurate computational models that explain how ions permeate through a biological ion channel is an important problem in biophysics and drug design. Brownian dynamics simulations are large-scale interacting particle computer simulations for modeling ion channel permeation but can be computationally prohibitive. In this paper, we show the somewhat surprising result that a small-dimensional semi-Markov model can generate events (such as conduction events and dwell times at binding sites in the protein) that are statistically indistinguishable from brownian dynamics computer simulation. This approach enables the use of extrapolation techniques to predict channel conduction when performing the actual brownian dynamics simulation that is computationally intractable. Numerical studies on the simulation of gramicidin A ion channels are presented.     

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.     

Modeling ion permeation through batrachotoxin-modified Na+ channels from rat skeletal muscle with a multi-ion pore.

The mechanism of ion permeation through Na+ channels that have been modified by batrachotoxin (BTX) and inserted into planar bilayers has been generally described by models based on single-ion occupancy, with or without an influence of negative surface charge, depending on the tissue source. For native Na+ channels there is evidence suggestive of a multi-ion conduction mechanism. To explore the question of ion occupancy, we have reexamined permeation of Na+, Li+, and K+ through BTX-modified Na+ channels from rat skeletal muscle. Single-channel current-voltage (I-V) behavior was studied in neutral lipid bilayers in the presence of symmetrical Na+ concentrations ranging from 0.5 to 3,000 mM. The dependence of unitary current on the mole fraction of Na+ was also examined in symmetrical mixtures of Na(+)-Li+ and Na(+)-K+ at a constant total ionic strength of 206 and 2,006 mM. The dependence of unitary conductance on symmetrical Na+ concentration does not exhibit Michaelis-Menten behavior characteristic of single-ion occupancy but can be simulated by an Eyring-type model with three barriers and two sites (3B2S) that includes double occupancy and ion-ion repulsion. Best-fit energy barrier profiles for Na+, Li+, and K+ were obtained by nonlinear curve fitting of I-V data using the 3B2S model. The Na(+)-Li+ and Na(+)-K+ mole-fraction experiments do not exhibit an anomalous mole-fraction effect. However, the 3B2S model is able to account for the biphasic dependence of unitary conductance on symmetrical [Na+] that is suggestive of multiple occupancy and the monotonic dependence of unitary current on the mole fraction of Na+ that is compatible with single or multiple occupancy. The best-fit 3B2S barrier profiles also successfully predict bi-ionic reversal potentials for Na(+)-Li+ and Na(+)-K+ in both orientations across the channel. Our experimental and modeling results reconcile the dual personality of ion permeation through Na+ channels, which can display features of single or multiple occupancy under various conditions. To a first approximation, the 3B2S model developed for this channel does not require corrections for vestibule surface charge. However, if negative surface charges of the protein do influence conduction, the conductance behavior in the limit of low [Na+] does not correspond to a Gouy-Chapman model of planar surface charge.     

Interaction of ions and water in gramicidin A channels: streaming potentials across lipid bilayer membranes

For very narrow channels in which ions and water cannot overtake one another (single-file transport), electrokinetic measurements provide information about the number of water molecules within a channel. Gramicidin A is believed to form such narrow channels in lipid bilayer membranes. In 0.01 and 0.1 M solutions of CsCl, KCL, and NaCl, streaming potentials of 3.0 mV per osmolal osmotic pressure difference (created by urea, glycerol, or glucose) appear across gramicidin A-treated membranes. This implies that there are six to seven water molecules within a gramicidin channel. Electroosmotic experiments, in which the water flux assoicated with current flow across gramicidin-treated membranes is measured, corroborate this result. In 1 M salt solutions, streaming potentials are 2.35 mV per osmolal osmotic pressure difference instead of 3.0 mV. The smaller value may indicate multiple ion occupancy of the gramicidin channel at high salt concentrations. Apparent deviations from ideal cationic selectivity observed while attempting to measure single-salt dilution potentials across gramicidin-treated membranes result from streaming potential effects.     

Ion effects on gating of the Ca(2+)-activated K+ channel correlate with occupancy of the pore.

We studied the effects of permeant ions on the gating of the large conductance Ca(2+)-activated K+ channel from rat skeletal muscle. Rb+ blockade of inward K+ current caused an increase in the open probability as though Rb+ occupancy of the pore interferes with channel closing. In support of this hypothesis, we directly measured the occupancy of the pore by the impermeant ion Cs+ and found that it strongly correlates with its effect on gating. This is consistent with the "foot-in-the-door" model of gating, which states that channels cannot close with an ion in the pore. However, because Rb+ and Cs+ not only slow the closing rate (as predicted by the model), but also speed the opening rate, our results are more consistent with a modified version of the model in which the channel can indeed close while occupied, but the occupancy destabilizes the closed state. Increasing the occupancy of the pore by the addition of other permeant (K+ and Tl+) and impermeant (tetraethylammonium) ions did not affect the open probability. To account for this disparity, we used a two-site permeation model in which only one of the sites influenced gating. Occupancy of this "gating site" interferes with channel closing and hastens opening. Ions that directly or indirectly increase the occupancy of this site will increase the open probability.     

The gramicidin a channel: A review of its permeability characteristics with special reference to the single-file aspect of transport

Summary Gramicidin A forms univalent cation-selective channels of 4 Å diameter in phospholipid bilayer membranes. The transport of ions and water throughout most of the channel length is by a singlefile process; that is, cations and water molecules cannot pass each other within the channel. The implications of this single-file mode of transport for ion movement are considered. In particular, we show that there is no significant electrostatic barrier to ion movement between the energy wells at the two ends of the channel. The rate of ion translocation (e.g., Na⁺ or Cs⁺) through the channel between these wells is limited by the necessity for an ion to move six water molecules in single file along with it; this also limits the maximum possible value for channel conductance. At all attainable concentrations of NaCl, the gramicidin A channel never contains more than one sodium ion, whereas even at 0.1M CsCl, some channels contain two cesium ions. There is no necessity to postulate more than two ion-binding sites in the channel or occupancy of the channel by more than two ions at any time.     

短杆菌肽A-DMPC通道内离子输运的分子动力学模拟

用最近提出的构建膜体系初始构象的有效方法 ,构建了在DMPC脂膜环境下短杆菌肽A通道模型 (GA -DMPC)。通过对Na 、Ca2 、Cl-三种不同离子在GA -DMPC通道内不同位置的分子动力学模拟 ,研究离子在通道内输运过程中与通道及通道内水分子的相互作用 ,从分子动力学的角度阐明离子在通道内的输运机制。主要计算结果表明 :(1)离子在通道内的输运使GA的构象发生变化 ,GA的柔性是离子在通道内通透的重要因素 ;(2)Cl- 离子可扩大通道半径 ,Na 离子和Ca2 离子则减小通道半径。Cl-离子不能在GA通道内通透 ;(3)离子的出现使通道内水分子的偶极方向发生变化。上述结果均与实验相符。