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.     

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.     

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).     

Statistical mechanical equilibrium theory of selective ion channels.

A rigorous statistical mechanical formulation of the equilibrium properties of selective ion channels is developed, incorporating the influence of the membrane potential, multiple occupancy, and saturation effects. The theory provides a framework for discussing familiar quantities and concepts in the context of detailed microscopic models. Statistical mechanical expressions for the free energy profile along the channel axis, the cross-sectional area of the pore, and probability of occupancy are given and discussed. In particular, the influence of the membrane voltage, the significance of the electric distance, and traditional assumptions concerning the linearity of the membrane electric field along the channel axis are examined. Important findings are: 1) the equilibrium probabilities of occupancy of multiply occupied channels have the familiar algebraic form of saturation properties which is obtained from kinetic models with discrete states of denumerable ion occupancy (although this does not prove the existence of specific binding sites; 2) the total free energy profile of an ion along the channel axis can be separated into an intrinsic ion-pore free energy potential of mean force, independent of the transmembrane potential, and other contributions that arise from the interfacial polarization; 3) the transmembrane potential calculated numerically for a detailed atomic configuration of the gramicidin A channel embedded in a bilayer membrane with explicit lipid molecules is shown to be closely linear over a distance of 25 A along the channel axis. Therefore, the present analysis provides some support for the constant membrane potential field approximation, a concept that has played a central role in the interpretation of flux data based on traditional models of ion permeation. It is hoped that this formulation will provide a sound physical basis for developing nonequilibrium theories of ion transport in selective biological channels.     

Ionic permeation free energy in gramicidin: a semimicroscopic perspective

Ion permeation through the gramicidin channel is studied using a model that circumvents two major difficulties inherent to standard simulational methods. It exploits the timescale separation between electronic and structural contributions to dielectric stabilization, accounting for the influence of electronic polarization by embedding the channel in a dielectric milieu that describes this polarization in a mean sense. The explicit mobile moieties are the ion, multipolar waters, and the carbonyls and amides of the peptide backbone. The model treats the influence of aromatic residues and the membrane dipole potential. A new electrical geometry is introduced that treats long-range electrostatics exactly and avoids problems related to periodic boundary conditions. It permits the translocating ion to make a seamless transition from nearby electrolyte to the channel interior. Other degrees of freedom (more distant bulk electrolyte and nonpolar lipid) are treated as dielectric continua. Reasonable permeation free energy profiles are obtained for potassium, rubidium, and cesium; binding wells are shallow and the central barrier is small. Estimated cationic single-channel conductances are smaller than experiment, but only by factors between 2 (rubidium) and 50 (potassium). When applied to chloride the internal barrier is large, with a corresponding miniscule single-channel conductance. The estimated relative single-channel conductances of gramicidin A, B, and C agree well with experiment.     

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.     

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.     

Calcium channel selectivity for divalent and monovalent cations. Voltage and concentration dependence of single channel current in ventricular heart cells

Single channel and whole cell recordings were used to study ion permeation through Ca channels in isolated ventricular heart cells of guinea pigs. We evaluated the permeability to various divalent and monovalent cations in two ways, by measuring either unitary current amplitude or reversal potential (Erev). According to whole cell measurements of Erev, the relative permeability sequence is Ca2+ greater than Sr2+ greater than Ba2+ for divalent ions; Mg2+ is not measurably permeant. Monovalent ions follow the sequence Li+ greater than Na+ greater than K+ greater than Cs+, and are much less permeant than the divalents. These whole cell measurements were supported by single channel recordings, which showed clear outward currents through single Ca channels at strong depolarizations, similar values of Erev, and similar inflections in the current-voltage relation near Erev. Information from Erev measurements stands in contrast to estimates of open channel flux or single channel conductance, which give the sequence Na+ (85 pS) greater than Li+ (45 pS) greater than Ba2+ (20 pS) greater than Ca2+ (9 pS) near 0 mV with 110-150 mM charge carrier. Thus, ions with a higher permeability, judged by Erev, have lower ion transfer rates. In another comparison, whole cell Na currents through Ca channels are halved by less than 2 microM [Ca]o, but greater than 10 mM [Ca]o is required to produce half-maximal unitary Ca current. All of these observations seem consistent with a recent hypothesis for the mechanism of Ca channel permeation, which proposes that: ions pass through the pore in single file, interacting with multiple binding sites along the way; selectivity is largely determined by ion affinity to the binding sites rather than by exclusion by a selectivity filter; occupancy by only one Ca ion is sufficient to block the pore's high conductance for monovalent ions like Na+; rapid permeation by Ca ions depends upon double occupancy, which only becomes significant at millimolar [Ca]o, because of electrostatic repulsion or some other interaction between ions; and once double occupancy occurs, the ion-ion interaction helps promote a quick exit of Ca ions from the pore into the cell.     

Not only enthalpy: large entropy contribution to ion permeation barriers in single-file channels

The effect of channel length on the barrier for potassium ion permeation through single-file channels has been studied by means of all-atom molecular dynamics simulations. Using series of peptidic gramicidin-like and simplified ring-structured channels, both embedded in model membranes, we obtained two distinct types of behavior: saturation of the central free energy barriers for peptidic channels and a linear increase in simplified ring-structured channels with increasing channel length. The saturation of the central free energy barrier for the peptidic channels occurs at relatively short lengths, and it is correlated with the desolvation from the bulk water. Remarkably, decomposition of free energy barriers into enthalpic and entropic terms reveals an entropic cost for ion permeation. Furthermore, this entropic cost dominates the ion permeation free energy barrier, since the corresponding free energy contribution is higher than the enthalpic barrier. We conclude that the length dependence of the free energy is enthalpy-dominated, but the entropy is the major contribution to the permeation barrier. The decrease in rotational water motion and the reduction of channel mobility are putative origins for the overall entropic penalty.     

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.     

Electric field effects on membranes: gramicidin A as a test ground

Electric fields due to transmembrane potential differences or ionic gradients across the membrane are presumably crucial for many reactions across membranes or close to membranes like signal transduction, control of ion channels or the generation of neural impulses. Molecular dynamics simulations have been used to study the influence of external electric fields on a mixed gramicidin/phospholipid bilayer system. At high field strengths, formation of membrane electropores occurred both close and distal to the gramicidin. Gramicidin was found to stabilize the membrane adjacent to the protein but also at larger distances of up to 2-3 nm. As a result, membrane pore formation was found to be significantly suppressed for the mixed gramicidin/DMPC system. Moderate field strengths only weakly affected the structure and dynamics of the gramicidin. Spontaneous potassium passage events in external electric fields were observed for both the head-to-head helical conformation as well as for the double helical conformation of gramicidin A. The double-helical conformation was found to facilitate ion passage compared to the head-to-head helical dimer.     

Molecular dynamics - potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels

Ion channels catalyze the permeation of charged molecules across cell membranes and are essential for many vital physiological functions, including nerve and muscle activity. To understand better the mechanisms underlying ion conduction and valence selectivity of narrow ion channels, we have employed free energy techniques to calculate the potential of mean force (PMF) for ion movement through the prototypical gramicidin A channel. Employing modern all-atom molecular dynamics (MD) force fields with umbrella sampling methods that incorporate one hundred 1-2 ns trajectories, we find that it is possible to achieve semi-quantitative agreement with experimental binding and conductance measurements. We also examine the sensitivity of the MD-PMF results to the choice of MD force field and compare PMFs for potassium, calcium and chloride ions to explore the basis for the valence selectivity of this narrow and uncharged ion channel. A large central barrier is observed for both anions and divalent ions, consistent with lack of experimental conductance. Neither anion or divalent cation is seen to be stabilized inside the channel relative to the bulk electrolyte and each leads to large disruptions to the protein and membrane structure when held deep inside the channel. Weak binding of calcium ions outside the channel corresponds to a free energy well that is too shallow to demonstrate channel blocking. Our findings emphasize the success of the MD-PMF approach and the sensitivity of ion energetics to the choice of biomolecular force field.     

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.     

Determinants of Water Permeability through Nanoscopic Hydrophilic Channels

Naturally occurring pores show a variety of polarities and sizes that are presumably directly linked to their biological function. Many biological channels are selective toward permeants similar or smaller in size than water molecules, and therefore their pores operate in the regime of single-file water pores. Intrinsic factors affecting water permeability through such pores include the channel-membrane match, the structural stability of the channel, the channel geometry and channel-water affinity. We present an extensive molecular dynamics study on the role of the channel geometry and polarity on the water osmotic and diffusive permeability coefficients. We show that the polarity of the naturally occurring peptidic channels is close to optimal for water permeation, and that the water mobility for a wide range of channel polarities is essentially length independent. By systematically varying the geometry and polarity of model hydrophilic pores, based on the fold of gramicidin A, the water density, occupancy, and permeability are studied. Our focus is on the characterization of the transition between different permeation regimes in terms of the structure of water in the pores, the average pore occupancy and the dynamics of the permeating water molecules. We show that a general relationship between osmotic and diffusive water permeability coefficients in the single-file regime accounts for the time averaged pore occupancy, and that the dynamics of the permeating water molecules through narrow non single file channels effectively behaves like independent single-file columns.     

Theoretical studies of the M2 transmembrane segment of the glycine receptor: models of the open pore structure and current-voltage characteristics

The pentameric glycine receptor (GlyR), a member of the nicotinicoid superfamily of ligand-gated ion channels, is an inhibitory Cl(-) channel that is gated by glycine. Using recently published NMR data of the second transmembrane segment (M2) of the human alpha1 GlyR, structural models of pentameric assemblies embedded in a lipid bilayer were constructed using a combination of experimentally determined constraints coupled with all-atom energy minimization. Based on this structure of the pentameric M2 "pore", Brownian dynamics simulations of ion permeation through this putative conducting open state of the channel were carried out. Simulated I-V curves were in good agreement with published experimental current-voltage curves and the anion/cation permeability ratio, suggesting that our open-state model may be representative of the conducting channel of the full-length receptor. These studies also predicted regions of chloride occupancy and suggested residues critical to anion permeation. Calculations of the conductance of the cation-selective mutant A251E channel are also consistent with experimental data. In addition, both rotation and untilting of the pore helices of our model were found to be broadly consistent with closing of the channel, albeit at distinct regions that may reflect alternate gates of the receptor.     

Investigating the dielectric effects of channel pore water on the electrostatic barriers of the permeation ion by the finite difference Poisson-Boltzmann method

In this paper, the finite difference Poisson-Boltzmann (FDPB) method with four dielectric constants is developed to study the effect of dielectric saturation on the electrostatic barriers of the permeation ion. In this method, the inner shape of the channel pore is explicitly represented, and the fact that the dielectric constant inside the channel pore is different from that of bulk water is taken into account. A model channel system which is a right-handed twist bundle with four α-helical segments is provided for this study. From the FDPB calculations, it is found that the difference of the ionic electrostatic solvation energy for wider domains depends strongly on the pore radius in the vicinity of the ion when the pore dielectric constant is changed from 78 to 5. However, the electrostatic solvation energy of the permeation ion can not be significantly affected by the dielectric constant in regions with small pore radii. Our results indicate that the local electrostatic interactions inside the ion channel are of major importance for ion electrostatic solvation energies, and the effect of dielectric saturation on the electrostatic barriers is coupled to the interior channel dimensions. Received: 28 January 1997 / Accepted: 24 September 1997     

Dynamic properties of individual water molecules in a hydrophobic pore lined with acyl chains: a molecular dynamics study

Recently, a certain class of synthetic molecules has been shown to form ion channels, the pore of which is lined with hydrophobic acyl chains [M. Sokabe, in: F. Oosawa, H. Hayashi, T. Yoshioka (Eds.), Transmembrane Signaling and Sensation, JSSP/VNU Science Press BV, Tokyo, 1984, p. 119; F. Hayashi, M. Sokabe, M. Takagi, K. Hayashi, U. Kishimoto, Biochim. Biophys. Acta, 510 (1978) 305; M.J. Pregel, L. Jullien, J. Canceill, L. Lacombe, J.M. Lehn, J. Chem. Soc. Perkin Trans., 2 (1995) 417; Y. Tanaka, Y. Kobuke, M. Sokabe, Angew. Chem. Int. Ed. Engl., 34 (1995) 693; M. Sokabe, Z. Qi, K. Donowaki, H. Ishida, K. Okubo, Biophys. J., 70 (1996) A201; H. Ishida, K. Donowaki, Y. Inoue, Z. Qi, M. Sokabe, Chem. Lett. (1997) p. 953]. As an initial step towards understanding the physical mechanisms of ion permeation across such a hydrophobic pore, systematic molecular dynamics simulations were performed to investigate dynamic and energetic properties of water molecules inside the pore using a dimer of alanine-N'-acylated cyclic peptide as a channel model. Dynamic energy profiles for water molecules indicated that the energy barrier at the middle region of the pore is approximately 2-3 kcal/mol higher than that in the cap water region which was defined as a vicinity region of the channel entrance. Energetics analyses demonstrated that the mutual interactions among intrapore water molecules are the major factor to give favorable interaction (negative energy contribution) for themselves. The pore, despite being lined with acyl chains, has a favorable van der Waals interaction with intrapore water molecules. These results may help to explain why water-filled channels can be formed by the hydrophobic helices in natural channels.     

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.