The representation of membrane admittance.

An integral representation for the membrane admittance in terms of its known current response to a voltage step function is presented. It is demonstrated that the frequency-dependent terms in the contribution to the membrane admittance by the ion-selective conductance of the nerve membrane are proportional to the static conductances. The additional information contained in the real and imaginary parts of the membrane admittance should allow the parameters of the ion conductance to be determined. Eventually, these measurements should also give information about the electric dipole displacement currents of the conductance systems themselves, and about the metabolically supported active ion transport currents that maintain the ion concentration gradients.     

Norepinephrine stimulation of lymphocyte ATPase by an alpha adrenergic receptor mechanism.

The effects of norepinephrine in interaction with adrenergic blocking compounds were studied on membrane adenosine triphosphatase (ATPase) activities of human lymphocytes and lymphoblasts. Sodium-potassium ion exchange pump activity was assayed by 86-Rb uptake and ATPase activity of membrane fractions was assayed by ADP and inorganic phosphate generation. The results of these studies indicate that norepinephrine acts by an alpha adrenergic mechanism to enhance membrane sodium-potassium ion exchange pump activity and ATPase activity. The pharmacologic and ionic dissection of the adrenergic sensitivity of ATPase activity indicates that this alpha adrenergic mechanism is related to membrane ATPase activities in addition to that associated with the ion exchange pump. Analysis of fractions obtained by sucrose gradients indicates that the action of norepinephrine is localized in the plasma membrane. Beta adrenergic stimulation was observed to inhibit ATPase activity. The complexity of adrenergic effects on membrane ATPase suggests interactions of hormone modulation of membrane nucleotide cyclases and transport-related ATPase enzymes.     

Photogating of ionic currents across lipid bilayers. Hydrophobic ion conductance by an ion chain mechanism.

The photogating of hydrophobic ion currents across the lipid bilayer membrane allows the direct study of their kinetics by symmetrically forming charge within the membrane and across each interface, rather than across the membrane. We find that the photoinduced conductance continues to increase beyond the region where the tetraphenylboride charge density in the membrane exceeds the estimated porphyrin cation density. This photoconductance is proportional to the tetraphenylboride charge density raised to the second to third power. The risetime of the photogating effect increases with increasing concentration of tetraphenyl boride. The porphyrin cation mobility is increased when the tetraphenylboride anion is present, and low concentrations of tetraphenylphosphonium cation increase the dark conductivity while inhibiting the photoconductivity. The activation energy for both the porphyrin and phosphonium cation induced conductance is more positive than that of the tetraphenylboride conductance. From these results we conclude that in addition to some cancellation of space charge within the membrane, the mechanism of increased conductance involves the transport of these hydrophobic anions via an alternating anion-cation chain, analogous to the Grotthuss mechanism for excess proton conduction in water. This ion chain conductance can be viewed as an evolutionary prototype of an ion channel across the membrane. It also underscores the importance of the counter ion in the transport of large ions such as peptides across the lipid bilayer.     

Transmembrane electrical currents of spin-labeled hydrophobic ions.

When spin-labeled phosphonium ions are rapidly mixed with phospholipid vesicles, time-dependent changes in the electron paramagnetic resonance spectrum of the spin label are observed. These changes are interpreted in terms of transmembrane transport of the hydrophobic ion, and simple analysis of the data at different membrane potentials is shown to give the binding constant of the ion to both membrane surfaces, the permeability, and current-voltage relationship for the vesicle membrane in the presence of the hydrophobic ion. These results establish the time resolution for methods using the phosphonium ion as a probe of time-dependent potentials across vesicle membranes, as well as provide fundamental information regarding the binding and transport of hydrophobic cations across bilayers. This latter point is significant in view of the fact that hydrophobic cations have not been well characterized in planar bilayers due to their weak binding and low conductance.     

A molecular theory for nonohmicity of the ion leak across the lipid-bilayer membrane.

The current-voltage relationship of ion leak (i.e., ion transport involving neither special channels nor carriers) across the lipid-bilayer membrane has been observed to be log-linear above the ohmic regime. The coefficient of the linear term has been found to be universal for membranes and penetrants examined. This universality has been explained in terms of diffusion in an external field, where the ion position is described as a Markovian process. Such a diffusion picture can be questioned, however. It is also probable that a leaking ion gets over the potential barrier before experiencing sufficient random collision in the membrane, considering that each ion is surrounded with long lipid molecules aligned almost unidirectionally. As an alternative, we discuss this ion leak in terms of velocity distribution of the ions entering the membrane and density fluctuation of the lipids. We conclude that we can explain the universality without resorting to the diffusion picture.     

Surface potential of phosphatidylserine monolayers. I. Divalent ion binding effect

Surface potentials of phosphatidylserine monolayers have been measured in the presence of different divalent ion concentrations in order to determine the way in which divalent ions bind to the membrane surface. The association constants for divalent ions (Mg²⁺, Ca²⁺ and Mn²⁺) with the phosphatidylserine membrane have been obtained from the experimental data and simple ion binding theory. The order of divalent ion binding to the membrane is Mn²⁺ > Ca²⁺ > Mg²⁺. However, none of the divalent ions used completely neutralized the negative charge of phosphatidylserine even at relatively high concentrations. The amounts of the divalent ions bound depended upon the concentration of the monovalent ions present in the subphase. It is suggested that the amounts of bound ions obtained from the use of radioisotope tracer methods may include a considerable contribution from the excess free ions in the double layer region of the phosphatidylserine membrane.     

Measurement of diffusion potentials in liposomes. Origin and properties of the threshold level in the oxonol VI response

A model is presented for the response of the membrane potential probe oxonol VI on diffusion potentials in liposomes. In this model the dependence of the probe response on the initial ion gradient is explained in terms of internal volume, internal ion concentration, membrane capacity and initial membrane potential. It is found that in the presence of an initial membrane potential (positive outside) there is a threshold value of the ion gradient needed for a probe response, which increases when the internal volume or the internal ion concentration decrease. The model is confirmed by experiments with liposomes of different sizes and internal KCl concentrations, prepared from asolectin or lipids isolated from the thermophilic cyanobacterium Synechococcus 6716. The significance of the model for threshold values observed in other energy-dependent phenomena is discussed.     

The problem of nonstationary ion fluxes in excitable membranes.

Time-dependent electrodiffusion through a membrane is analysed within a simple model treating the boundary-layers in a consistent manner. It is shown that time-independent reversal potentials for the ion fluxes exist only under steady-state conditions. We argue that this result holds very generally. Therefore nonstationary effect like ion storage and depletion inside the membrane should not contribute to the phenomena of excitability.     

An analytical model of ionic movements in airway epithelial cells.

A new mathematical model of ion movements in airway epithelia is presented, which allows predictions of ion fluxes, membrane potentials and ion concentrations. The model includes sodium and chloride channels in the apical membrane, a Na/K pump and a cotransport system for Cl- with stoichiometry Na+:K+:2Cl- in the basolateral membrane. Potassium channels in the basolateral membrane are used to regulate cell volume. Membrane potentials, ion fluxes and intracellular ion concentration are calculated as functions of apical ion permeabilities, the maximum pump current and the cotransport parameters. The major predictions of the model are: (1) Cl- concentration in the cell is determined entirely by the intracellular concentration of negatively charged impermeable ions and the osmotic conditions; (2) changes in intracellular Na+ and K+ concentrations are inversely related; (3) cotransport provides the major driving force for Cl- flux, increases intracellular Na+ concentration, decreases intracellular K+ concentration and hyperpolarizes the cell interior; (4) the maximum rate of the Na/K pump, by contrast, has little effect on Na+ or Cl- transepithelial fluxes and a much less pronounced effect on cell membrane polarization; (5) an increase in apical Na+ permeability causes an increase in intracellular Na+ concentration and a significant increase in Na+ flux; (6) an increase in apical Cl- permeability decreases intracellular Na+ concentration and Na+ flux; (7) assuming Na+ and Cl- permeabilities equal to those measured in human nasal epithelia, the model predicts that under short circuit conditions, Na+ absorption is much higher than Cl- secretion, in agreement with experimental measurements.     

ON THE CAUSE OF THE INFLUENCE OF IONS ON THE RATE OF DIFFUSION OF WATER THROUGH COLLODION MEMBRANES. II

1. It had been shown in previous publications that when pure water is separated from a solution of an electrolyte by a collodion membrane the ion with the same sign of charge as the membrane increases and the ion with the opposite sign of charge as the membrane diminishes the rate of diffusion of water into the solution; but that the relative influence of the oppositely charged ions upon the rate of diffusion of water through the membrane is not the same for different concentrations. Beginning with the lowest concentrations of electrolytes the attractive influence of that ion which has the same sign of charge as the collodion membrane upon the oppositely charged water increases more rapidly with increasing concentration of the electrolyte than the repelling effect of the ion possessing the opposite sign of charge as the membrane. When the concentration exceeds a certain critical value the repelling influence of the latter ion upon the water increases more rapidly with a further increase in the concentration of the electrolyte than the attractive influence of the ion having the same sign of charge as the membrane. 2. It is shown in this paper that the influence of the concentration of electrolytes on the rate of transport of water through collodion membranes in electrical endosmose is similar to that in the case of free osmosis. 3. On the basis of the Helmholtz theory of electrical double layers this seems to indicate that the influence of an electrolyte on the rate of diffusion of water through a collodion membrane in the case of free osmosis is due to the fact that the ion possessing the same sign of charge as the membrane increases the density of charge of the latter while the ion with the opposite sign diminishes the density of charge of the membrane. The relative influence of the oppositely charged ions on the density of charge of the membrane is not the same in all concentrations. The influence of the ion with the same sign of charge increases in the lowest concentrations more rapidly with increasing concentration than the influence of the ion with the opposite sign of charge, while for somewhat higher concentrations the reverse is true.     

Semiconductor theory of ion transport in thin lipid membranes: I. Potential and field distributions

In the theory as presented in this paper and the following one, we shall attempt to apply the semiconductor principles and methods to the study of ion transport in thin lipid membranes. Detailed formulations are given on the potential energy barriers at the interfaces, voltage drops in the polar and non-polar regions, and potential and field distributions in the diffuse double layer and within a charged membrane. These results will be used mainly as the boundary conditions for the solution of ion flow as to be given in the following paper. The analysis clearly indicates that the ion transport is interface-limited and is profoundly influenced by the presence of surface charges. An explanation of Na⁺ extrusion in nerve membrane is given based on the field distribution analysis. The theory also suggests that the “membrane potential” depends mainly on surface charges but not necessarily on ion permeation through the membrane.     

Speculations on the evolution of ion transport mechanisms.

Primate cells evolved a plasma membrane to restrict the loss of important molecules. The osmotic problems that then arose were solved in one of several ways. Of major importance was the evolution of specific ion pumps, to actively extrude those salts whose inward diffusion would have led to swelling and lysis. In addition, these pumps allowed the cell to store energy in the form of ion gradients across the membrane. Thus, even in the earliest stages, the evolution of ion transport systems coincided with the development of mechanisms which catalyzes the energy transformations. It is postulated that an "ATP"-driven proton pump was one of the first ion transport systems. Such a proton pump would extrude hydrogen ions from the cell, establishing both a transmembrane pH gradient (alkaline inside) and a membrane potential (negative inside). This difference in electrochemical potential for protons (the proton-motive force) could then drive a variety of essential membrane functions, such as the active transport of ions and nutrients. A second major advance was the evolution of an ion transport system that converted light energy into a form which could be used by the cell. The modern model for this is the "purple membrane" of Halobacterium halobium, which catalyzes the extrusion of protons after the capture of light. The protonmotive force generated by such a light-driven proton pump could then power net synthesis of ATP by a reversal of the ATP-driven proton pump. A third important evolutionary step associated with ion transport was the development of a system to harness energy released by biological oxidations. Again, the solution of this problem was to conserve energy as a protonmotive force by coupling the activity of a respiratory chain to the extrusion of protons. Finally, with the development of animal cells a more careful regulation of internal and external pH was required. Thus, an ATP-driven Na+-K+ pump replaced the proton-translocating ATPase as the major ion pump found in plasma membranes.     

Nonlinear Electrical Effects in Lipid Bilayer Membranes: III. The Dissociation Field Effect

In the course of an analysis of nonlinear electrical effects in lipid bilayer membranes, the influence of the dissociation field (or Wien) effect on the membrane conductivity is investigated. It is shown that the theory of Onsager for the Wien effect in a macroscopic phase can be applied to a thin membrane when the proper boundary conditions at the membrane-solution interface are introduced. It is assumed that an activation energy is associated with the passage of the ion across the interface. The mathematical treatment of the model is restricted to the case for which cations and anions have identical properties except for the charge sign. The resulting differential equations for the ion concentration within the membrane are integrated numerically. The analysis shows that the influence of the Wien effect on the membrane conductivity is appreciable only if the energy barrier at the interface is sufficiently high, i.e. if the rate limiting step for the ion transport is the passage of the ion across the interface.     

Potassium uniport and ATP synthesis in Halobacterium halobium.

Light-driven potassium ion uptake in Halobacterium halobium is mediated by bacteriorhodopsin. This uptake is charge-balanced by sodium ions and not by proton release. Light-induced shifts in concentrations of divalent cations were found to be negligible. The transient changes in extracellular pH (alkaline overshoot) can be understood by the concomitant processes of ATP synthesis, proton/sodium exchange and potassium uptake. The driving force of potassium ion uptake is the membrane potential, no ATP-dependent potassium transport process is found. Fluorescence measurements indicate a high permeability of the membrane to potassium ions compared to sodium ions. Therefore the potassium ion diffusion potential contributes to the membrane potential (about 30 mV/decade) and thereby influences the ATP level. Sudden enhancement of the diffusion potential by the potassium ionophore monactin leads to the expected transient increase in cellular ATP level. Due to the large size (up to 100-fold) of the potassium ion gradient and its high capacity (intracellular concentration up to 3 M) the potassium ion gradient can well serve the cell as a long term storage form of energy.     

水分胁迫对木麻黄(Casuarina.Sp.)小枝活性氧伤害的定量分析

两种木麻黄在水分胁迫条件下水势、质膜相对透性、超氧离子、ＭＤＡ和ＳＯＤ之间都显著相关。但ＣＡＴ和ＰＯＤ与水势、质膜相对透性、超氧离子、ＭＤＡ和ＳＯＤ等指标之间的相关关系不一致,大部分不显著,水势对质膜相对透性、ＭＤＡ、超氧离子和ＳＯＤ的弹性系数均属于ＥＰ〈０,处于水势对这些生理指标的负效应阶段。ＳＯＤ对质膜相对透性、ＭＤＡ和超氧离子的弹性系数均小于１,属于０〈ＥＰ〈１,处于ＳＯＤ活性对质膜相对透性的效应的递减阶段。超氧离子对质膜相对透性和ＭＤＡ的弹性系数均小于１,属于０〈ＥＰ〈１,处于超氧离子对质膜相对透性的效应的递减阶段。抗旱能力不同的两种木麻黄弹性系数和相尖的边际量不同。     

Semiconductor theory of ion transport in thin lipid membranes: II. Surface recombination

Following the theory of surface recombination in semiconductors, we have derived an expression for the rate of ion recombination at the membrane surface. The surface recombination rate is used in the boundary conditions of current flows at the interfaces. Expressions for the ion fluxes are then derived as functions of environmental variables and membrane parameters. Our analysis strongly suggests that the ion flow through a thin lipid membrane consists of two major components: the surface barrier jumping current and the surface recombination current that are controlled decisively by surface barrier height, surface trap density and surface recombination rates. These general formulations are useful not only for the calculation but also for the understanding of ion transport in thin lipid membranes under a variety of experimental conditions. The implications of this theory to biological membranes and its possible extensions are discussed.     

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.     

Transduction of membrane tension by the ion channel alamethicin.

Mechanoelectrical transduction in biological cells is generally attributed to tension-sensitive ion channels, but their mechanisms and physiology remain controversial due to the elusiveness of the channel proteins and potential cytoskeletal interactions. Our discovery of membrane tension sensitivity in ion channels formed by the protein alamethicin reconstituted into pure lipid membranes has demonstrated two simple physical mechanisms of cytoskeleton-independent transduction. Single channel analysis has shown that membrane tension energizes mechanical work for changes of conductance state equal to tension times the associated increase in membrane area. Results show a approximately 40 A2 increase in pore area and transfer of an 80-A2 polypeptide into the membrane. Both mechanisms may be implicated in mechanical signal transduction by cells.     

Simple model can explain self-inhibition of red cell anion exchange.

Ion translocation in red cell anion exchange is assumed to occur by means of an alternating access mechanism, in which a critical binding site for the transported ion alternates between two conformational states, each accessible from only one side of the membrane. If this alternating site is located within the transport protein at some distance from one or both surfaces of the membrane, an access channel is required to connect the alternating site to the adjacent bulk solution. This automatically leads to inhibition of transport at high concentrations of the transported ion because release of the ion from the alternating site can occur only via unoccupied channel sites.