Modulation of properties of phospholipid membranes by the long-chain polyprenol (C(160))

The electrical measurements of phospholipid bilayers and the studies of phospholipid vesicles by using the transmission electron microscopy (TEM) showed that dotriacontaprenol (C(160)) isolated from leaves of Spermatophyta influences some properties of membranes. The current-voltage characteristics, the membrane conductance-temperature relationships, the membrane breakdown voltage and the membrane capacitance have been measured for different mixtures of C(160)/DOPC. The membrane conductance, the activation energy of ion migration across the membrane and the membrane thickness were determined. Dotriacontaprenol decreases the membrane breakdown voltage, the activation energy and the membrane capacitance, and increases the membrane conductance and the membrane hydrophobic thickness. The analysis of TEM micrographs shows several characteristic structures, which have been described. The results indicate that dotriacontaprenol increases the membrane elasticity and modulates the surface curvature of the membranes by the formation of fluid microdomains. We suggest that the long polyprenols facilitate the formation of transmembrane, ions-conductive pores.     

Current-Voltage Curves of Porous Membranes in the Presence of Pore-Blocking Ions: I. Narrow Pores Containing No More Than One Moving Ion

We propose a physical model for voltage-dependent conductance changes of excitable cell membranes. It is based on competition of uni- and bivalent ions for chains of stable sites extending through the membrane. These one-dimensional pathways (pores) have different profiles of chemical potential for the two ionic species so that bivalent ions can block the passage of univalent ions at large membrane potentials. We treat the special case that each pore is either empty or, because of electrostatic repulsion, contains no more than one uni- or bivalent ion at a time. A system of linear differential equations describes the time-dependent probabilities of the various possible pore states. The states are limited by transition rate constants involving the profile of the chemical potential, the membrane voltage, the ionic concentrations in the adjacent baths, and electrostatic interactions between the ions. The steady-state solutions (Kirchhoff-Hill theorem) yield expressions for the relationship between the small signal conductance of univalent ions and the concentration of these ions in the external bathing medium (a saturation curve) and for the ionic currents and the steady-state current-voltage curve (N-shaped). From the latter curve we compute the shift of theshold potential caused by concentration changes of the external bathing medium. The model yields a number of predictions which can be tested experimentally.     

Properties and modulation of alpha human atrial natriuretic peptide (alpha-hANP)-formed ion channels

Using the lipid bilayer technique we have optimized recording conditions and confirmed that alpha human atrial natriuretic peptide [alpha-hANP(1-28)] forms single ion channels. The single channel currents recorded in 250/50 mM KCl cis/trans chambers show that the ANP-formed channels were heterogeneous, and differed in their conductance, kinetic, and pharmacological properties. The ANP-formed single channels were grouped as: (i) H202- and Ba2+-sensitive channel with fast kinetics; the nonlinear current-voltage (I-V) relationship of this channel had a reversal potential (Erev) of -28.2 mV, which is close to the equilibrium potential for K+ (EK = -35 mV) and a maximal slope conductance (gmax) of 68 pS at positive potentials. Sequential ionic substitution (KCl, K gluconate and choline Cl) of the cis solution suggests that the current was carried by cations. The fast channel had three modes (spike mode, burst mode, and open mode) that differed in their kinetics but not in their conductance properties. (ii) A large conductance channel possessing several subconductance levels that showed time-dependent inactivation at positive and negative membrane potentials (Vm). The inactivation ratio of the current at the end of the voltage step (Iss) to the initial current (Ii) activated immediately after the voltage step, (Iss/Ii), was voltage dependent and described by a bell-shaped curve. The maximal current-voltage (I-V) relationship of this channel, which had an Erev of +17.2 mV, was nonlinear and the value of gmax was 273 pS at negative voltages. (iii) A transiently-activated channel: the nonlinear I-V relationship of this channel had an Erev of -29.8 mV and the value of gmax was 160 pS at positive voltages. We propose that the voltage-dependence of the ionic currents and the kinetic parameters of these channel types indicate that if they were formed in vivo and activated by cytosolic factors they could change the membrane potential and the electrolyte homeostasis of the cell.     

Study of ionic currents across a model membrane channel using Brownian dynamics.

Brownian dynamics simulations have been carried out to study ionic currents flowing across a model membrane channel under various conditions. The model channel we use has a cylindrical transmembrane segment that is joined to a catenary vestibule at each side. Two cylindrical reservoirs connected to the channel contain a fixed number of sodium and chloride ions. Under a driving force of 100 mV, the channel is virtually impermeable to sodium ions, owing to the repulsive dielectric force presented to ions by the vestibular wall. When two rings of dipoles, with their negative poles facing the pore lumen, are placed just above and below the constricted channel segment, sodium ions cross the channel. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength does not increase the channel conductance further. When only those ions that acquire a kinetic energy large enough to surmount a barrier are allowed to enter the narrow transmembrane segment, the channel conductance decreases monotonically with the barrier height. This barrier represents those interactions between an ion, water molecules, and the protein wall in the transmembrane segment that are not treated explicitly in the simulation. The conductance obtained from simulations closely matches that obtained from ACh channels when a step potential barrier of 2-3 kTr is placed at the channel neck. The current-voltage relationship obtained with symmetrical solutions is ohmic in the absence of a barrier. The current-voltage curve becomes nonlinear when the 3 kTr barrier is in place. With asymmetrical solutions, the relationship approximates the Goldman equation, with the reversal potential close to that predicted by the Nernst equation. The conductance first increases linearly with concentration and then begins to rise at a slower rate with higher ionic concentration. We discuss the implications of these findings for the transport of ions across the membrane and the structure of ion channels.     

Thickness dependence of monoglyceride bilayer membrane conductance.

We have studied the conductance properties of unmodified monoglyceride membranes as a function of monoglyceride chain length. As membrane thickness decreases from 31 to 20 nm, the steepness of the current-voltage (I-V) curve increases from 80 mV per e-fold current increase to 52 mV per e-fold current increase. The zero-voltage conductance increases more than 1,000-fold and the apparent activation energy of conductance decreases from 18.4 to 14.2 kcal/mol. We have analyzed our results using both the Nernst-Planck equation and absolute rate theory. Both approaches are consistent with our results and give consistent values for the parameters describing the I-V curves. We conclude that both the surface ion concentration and the distance from the surface of the membrane at which the energy of an ion rises appreciably above its value in solution (position of the barrier) are invariant with thickness.     

The Electrical Conductance of Semipermeable Membranes: I. A Formal Analysis

A kinetic analysis of membrane conductance under conditions of stationary flow is presented. The semipermeable membrane is idealized as a homogeneous laminar phase separating ionic solutions on either side. It is assumed, without consideration of the mechanisms involved, that some ion species permeate the membrane while others do not. The flux of a given species is taken to be linearly related to the gradient of its concentration and to the electric field. The resulting flow equations, when combined with Poisson's equation, permit the formulation of the conductance problem in terms of a set of non-linear differential equations. They describe the spatial variation of the electric displacement and contain the ion current densities as parameters. Their integration, subject to appropriate boundary conditions, fixes the values of these parameters and of the corresponding transmembrane potential. The solution of the conductance problem cannot, however, be carried through in analytic form. The numerical analysis of a number of special cases will be presented in subsequent publications.     

Strong electrolyte continuum theory solution for equilibrium profiles, diffusion limitation, and conductance in charged ion channels.

The solution for the ion flux through a membrane channel that incorporates the electrolyte nature of the aqueous solution is a difficult theoretical problem that, until now, has not been properly formulated. The difficulty arises from the complicated electrostatic problem presented by a high dielectric aqueous channel piercing a low dielectric lipid membrane. The problem is greatly simplified by assuming that the ratio of the dielectric constant of the water to that of the lipid is infinite. It is shown that this is a good approximation for most channels of biological interest. This assumption allows one to derive simple analytical expressions for the Born image potential and the potential from a fixed charge in the channel, and it leads to a differential equation for the potential from the background electrolyte. This leads to a rigorous solution for the ion flux or the equilibrium potential based on a combination of the Nernst-Planck equation and strong electrolyte theory (i.e., Gouy-Chapman or Debye-Huckel). This approach is illustrated by solving the system of equations for the specific case of a large channel containing fixed negative charges. The following characteristics of this channels are discussed: anion and mono- and divalent cation conductance, saturation of current with increasing concentration, current-voltage relationship, influence of location and valence of fixed charge, and interaction between ions. The qualitative behavior of this channel is similar to that of the acetylcholine receptor channel.     

Space charge-limited conductance in lipid bilayer membranes

Summary A mathematical treatment is given for the flux of ions of one charge sign across lipid bilayer membranes. This treatment is a generalization of a previous analysis of the membrane conductance by D. Walz, E. Bamberg and P. Läuger which was restricted to systems with negligible space charge in the membrane. The present theory includes space charge effects, and it is no longer assumed that the electric field strength in the membrane is constant. It is found that the ohmic membrane conductivity ₀ is reduced by space charges; if only ions of one charge sign are soluble in the membrane, ₀ approaches a limiting value for increasing concentration of the permeable ion in the aqueous solution. The theory also predicts the range in which the constant field approximation is valid. It is found that space charge effects become predominant when the mean concentration of the permeable ion in the membrane exceeds 5×10^–5 m. The currentvoltage characteristic of the membrane remains practically linear even in the presence of a high space charge. It is therefore concluded that the experimentally observed nonlinearity is caused mainly by the distortion of the potential energy profile of an ion due to image forces.     

Effect of ionic polarizability on electrodiffusion in lipid bilayer membranes.

Ion-carrier complexes and organic ions of similar size and shape have mobilities in lipid bilayer membranes which span several orders of magnitude. In this communication, an examination is made of the hypothesis that the basis for this unusually wide range of ionic mobilities is the potential energy barrier arising from image forces which selectively act on ions according to their polarizability. Using Poisson's equation to evaluate the electrostatic interaction between an ion and its surroundings, the potential energy barrier to ion transport due to image effects is computed, with the result that the potential energy barrier height depends strongly on ionic polarizability. Theoretical membrane potential energy profile calculations are used in conjunction with Nernst-Planck electrodiffusion equation to analyze the available mobility data for several ion-carrier complexes and lipid-soluble ions in lipid bilayer membranes. The variation among the mobilities of different ions is shown to be in agreement with theoretical predictions based on ionic polarizability and size. Furthermore, the important influence exerted by image forces on ion transport in lipid bilayer membranes compared to the frictional effect of membrane viscosity is established by contrasting available data on the activation energy of ionic conductivity with that for membrane fluidity.     

Single potassium channels of human glioma cells.

Single potassium channels in the membrane of human malignant glioma cells U-118MG were studied using the technique of patch clamp in cell-attached and inside-out configurations. Three types of potassium channels were found which differed from each other under conditions close to physiological in their conductance and gating characteristics. The lowest-conductance channel (20 pS near the reversal potential) showed a mild outward rectification up to 45 pS at positive voltages and spontaneous modes of high and low activity. At extreme values of potentials its activity was generally low. The intermediate conductance channel had an S-shaped I-V curve, giving a conductance of 63 pS at reversal, and a low and voltage independent opening probability. The high-conductance (215 pS) channel was found to be activated by both membrane potential and Ca2+ ions and blocked by internal sodium at high voltages. The current-voltage curves of all three channel types displayed saturation.     

Electrodiffusion of ions approaching the mouth of a conducting membrane channel.

The movement of ions in the aqueous medium as they approach the mouth (radius a) of a conducting membrane channel is analyzed. Starting with the Nernst-Planck and Poisson equations, we derive a nonlinear integrodifferential equation for the electric potential, phi(r), a less than or equal to r less than infinity. The formulation allows deviations from charge neutrality and dependence of phi(r) on ion flux. A numerical solution is obtained by converting the equation to an integral equation that is solved by an iterative method for an assumed mouth potential, combined with a shooting method to adjust the mouth potential until the numerical solution agrees with an asymptotic expansion of the potential at r-a much greater than lambda (lambda = Debye length). Approximate analytic solutions are obtained by assuming charge neutrality (Läuger, 1976) and by linearizing. The linear approximation agrees with the exact solution under most physiological conditions, but the charge-neutrality solution is only valid for r much greater than lambda and thus cannot be used unless a much greater than lambda. Families of curves of ion flux vs. potential drop across the electrolyte, phi(infinity)-phi (a), and of permeant ion density at the channel mouth, n1(a), vs. flux are obtained for different values of a/lambda and S = a d phi/dr(a). If a much greater than lambda and S = O, the maximum flux (which is approached when n1(a)----0) is reduced by 50% compared to the value predicted by the charge-neutrality solution. Access resistance is shown to be a factor a/[2 (a + lambda)] times the published formula (Hille, 1968), which was derived without including deviations from charge neutrality and ion density gradients and hence does not apply when there is no counter-ion current. The results are applied to an idealized diffusion-limited channel with symmetric electrolytes. For S = O, the current/voltage curves saturate at a value dependent on a/lambda; for S greater than O, they increase linearly for large voltage.     

Pore formation by the Bordetella adenylate cyclase toxin in lipid bilayer membranes: role of voltage and pH

The bifunctional adenylate cyclase toxin (ACT or CyaA) of Bordetella pertussis invades target cells via transport through the cytoplasmic membrane. The membrane potential represents thereby an important factor for the uptake in vivo. Previous studies demonstrated that adenylate cyclase (AC) delivery into cells requires a negative membrane potential inside the cells. The results of lipid bilayer experiments with ACT presented here indicated that two different types of pore-like structures are formed by ACT dependent on the orientation of the electrical potential across the membranes. Pore formation at a positive potential at the cis side of the membranes, the side of the addition of the toxin, was fast and its conductance had a defined size, whereas at negative potential the pores were not defined, had a reduced pore-forming activity and a very short lifetime. Fluctuations inserted at positive potentials showed asymmetric current-voltage relationships for positive and negative voltages. Positive potentials at the cis side resulted in an increasing current, whereas at negative potentials the current decreased or remained at a constant level. Calcium ions enhanced the voltage dependence of the ACT pores when they were added to the cis side. The single-pore conductance was strongly affected by the variation of the pH value and increased in 1M KCl with increasing pH from about 4 pS at pH 5 to about 60 pS at pH 9. The ion selectivity remained unaffected by pH. Experiments with ACT mutants revealed, that the adenylate cyclase (AC) and repeat (RT) domains were not involved in voltage and pH sensing.     

Pore formation by the Bordetella adenylate cyclase toxin in lipid bilayer membranes: Role of voltage and pH

The bifunctional adenylate cyclase toxin (ACT or CyaA) of Bordetella pertussis invades target cells via transport through the cytoplasmic membrane. The membrane potential represents thereby an important factor for the uptake in vivo. Previous studies demonstrated that adenylate cyclase (AC) delivery into cells requires a negative membrane potential inside the cells. The results of lipid bilayer experiments with ACT presented here indicated that two different types of pore-like structures are formed by ACT dependent on the orientation of the electrical potential across the membranes. Pore formation at a positive potential at the cis side of the membranes, the side of the addition of the toxin, was fast and its conductance had a defined size, whereas at negative potential the pores were not defined, had a reduced pore-forming activity and a very short lifetime. Fluctuations inserted at positive potentials showed asymmetric current-voltage relationships for positive and negative voltages. Positive potentials at the cis side resulted in an increasing current, whereas at negative potentials the current decreased or remained at a constant level. Calcium ions enhanced the voltage dependence of the ACT pores when they were added to the cis side. The single-pore conductance was strongly affected by the variation of the pH value and increased in 1M KCl with increasing pH from about 4 pS at pH 5 to about 60 pS at pH 9. The ion selectivity remained unaffected by pH. Experiments with ACT mutants revealed, that the adenylate cyclase (AC) and repeat (RT) domains were not involved in voltage and pH sensing.     

Equilibrium properties of a voltage-dependent junctional conductance

The conductance of junctions between amphibian blastomeres is strongly voltage dependent. Isolated pairs of blastomeres from embryos of Ambystoma mexicanum, Xenopus laevis, and Rana pipiens were voltage clamped, and junctional current was measured during transjunctional voltage steps. The steady-state junctional conductance decreases as a steep function of transjunctional voltage of either polarity. A voltage-insensitive conductance less than 5% of the maximum remains at large transjunctional voltages. Equal transjunctional voltages of opposite polarities produce equal conductance changes. The conductance is half maximal at a transjunctional voltage of approximately 15 mV. The junctional conductance is insensitive to the potential between the inside and outside of the cells. The changes in steady-state junctional conductance may be accurately modeled for voltages of each polarity as arising from a reversible two-state system in which voltage linearly affects the energy difference between states. The voltage sensitivity can be accounted for by the movement of about six electron charges through the transjunctional voltage. The changes in junctional conductance are not consistent with a current-controlled or ionic accumulation mechanism. We propose that the intramembrane particles that comprise gap junctions in early amphibian embryos are voltage-sensitive channels.     

Permeation in ionic channels: a statistical rate theory approach.

A novel way to model permeation through ionic channels is formulated. Our method does not require that equilibrium exists in the channel or at the channel interfaces. In addition, the potential profile does not need to be specified and the assumption of constant field across the membrane does not need to be made. Our formulation relies on statistical rate theory for its development and uses a form of the electrochemical potential which assumes that the ions are in solution. We show that the conductance and the degree of nonlinearity are dependent on the relative equilibrium exchange rates in the channel and at the interfaces. Nonlinear current-voltage plots can be obtained in symmetric solutions as well as a nonunity exponent for the Ussing flux ratio. Due to the dependence of the partition coefficient on solubility, it is highly unlikely that the intracellular and extracellular partition coefficients are the same. A manifestation of unequal partition coefficients is a current reversal at a membrane voltage that is different from the Nernst potential of the current-carrying ionic species.     

Constant fields and constant gradients in open ionic channels.

Ions enter cells through pores in proteins that are holes in dielectrics. The energy of interaction between ion and charge induced on the dielectric is many kT, and so the dielectric properties of channel and pore are important. We describe ionic movement by (three-dimensional) Nemst-Planck equations (including flux and net charge). Potential is described by Poisson's equation in the pore and Laplace's equation in the channel wall, allowing induced but not permanent charge. Asymptotic expansions are constructed exploiting the long narrow shape of the pore and the relatively high dielectric constant of the pore's contents. The resulting one-dimensional equations can be integrated numerically; they can be analyzed when channels are short or long (compared with the Debye length). Traditional constant field equations are derived if the induced charge is small, e.g., if the channel is short or if the total concentration gradient is zero. A constant gradient of concentration is derived if the channel is long. Plots directly comparable to experiments are given of current vs voltage, reversal potential vs. concentration, and slope conductance vs. concentration. This dielectric theory can easily be tested: its parameters can be determined by traditional constant field measurements. The dielectric theory then predicts current-voltage relations quite different from constant field, usually more linear, when gradients of total concentration are imposed. Numerical analysis shows that the interaction of ion and channel can be described by a mean potential if, but only if, the induced charge is negligible, that is to say, the electric field is spatially constant.     

Voltage-dependent block of anthrax toxin channels in planar phospholipid bilayer membranes by symmetric tetraalkylammonium ions. Single-channel analysis

Previous studies have shown that symmetric tetraalkylammonium ions affect, in a voltage-dependent manner, the conductance of membranes containing many channels formed by the PA65 fragment of anthrax toxin. In this paper we analyze this phenomenon at the single-channel level for tetrabutylammonium ion (Bu4N+). We find that Bu4N+ induces a flickery block of the PA65 channel when present on either side of the membrane, and this block is relieved by large positive voltages on the blocking-ion side. At high frequencies (greater than 2 kHz) we have resolved individual blocking events and measured the dwell times in the blocked and unblocked states. These dwell times have single-exponential distributions, with time constants tau b and tau u that are voltage dependent, consistent with the two-barrier, single-well potential energy diagram that we postulated in our previous paper. The fraction of time the channel spends unblocked [tau u/(tau u + tau b)] as a function of voltage is identical to the normalized conductance-voltage relation determined from macroscopic measurements of blocking, thus demonstrating that these single channels mirror the behavior seen with many (greater than 10,000) channels in the membrane. In going from large negative to large positive voltages (-100 to +160 mV) on the cis (PA65-containing) side of the membrane, one sees the mean blocked time (tau b) increase to a maximum at +60 mV and then steadily decline for voltages greater than +60 mV, thereby clearly demonstrating that Bu4N+ is driven through the channel by positive voltages on the blocking-ion side. In other words, the channel is permeable to Bu4N+. An interesting finding that emerges from analysis of the voltage dependence of mean blocked and unblocked times is that the blocking rate, with Bu4N+ present on the cis side of the membrane, plateaus at large positive cis voltages to a voltage-independent value consistent with the rate of Bu4N+ entry into the blocking site being diffusion limited.     

Ionic mechanisms of nonlinearity of the retinal horizontal cell membrane

Changes in ionic conductance lying at the basis of nonlinearity of the current-voltage characteristic curve of the cell (nonsynaptic) membrane of horizontal cells were studied in experiments on the goldfish and turtle retina. All measurements were made during blocking of synaptic transmission by bright light or Co⁺⁺. An increase in the K⁺ concentration led to depolarization and to a reduction of the steepness of the hyperpolarization branch of the current-voltage curve, whereas a decrease in K⁺ had the opposite effect. Changes in the Cl^– or Na⁺ concentrations had no significant effect on membrane potential or on the shape of the current-voltage curve. The principal potential-forming ion in the horizontal cells is thus K⁺; conductance for Cl^– is absent or very low, and conductance for Na⁺ also is evidently small. In the presence of Ba⁺⁺ (2–5 mM) the steepness of the hyperpolarization branch of the current-voltage curve was increased and the whole curve became more linear. It is concluded that nonlinearity of the current-voltage curve of the horizontal cell membrane is due mainly to potential-dependent potassium channels, whose conductance increases during hyperpolarization; this increase in conductance is blocked by Ba⁺⁺. An increase in the Ca⁺⁺ concentration to 20 mM led to an increase in steepness of the depolarization branch of the current-voltage curve, suggesting that depolarization increases membrane conductance for Ca⁺⁺.Institute for Problems in Information Transmission, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 13, No. 5, pp. 531–539, September–October, 1981.     

Leak Current Rectification in Myxicola Giant Axons : Constant field and constant conductance components

Early leak current, i.e. for times similar to the time to peak of the transient current was measured in Myxicola giant axons in the presence of tetrodotoxin. The leak current-voltage relation rectifies, showing more current for strong depolarizing pulses than expected from symmetry around the holding potential. A satisfactory practical approximation for most leak corrections is constant resting conductance. The leak current-voltage curve rectifies less than expected from the constant field equation. These curves cannot be reconstructed by summing the constant field currents for sodium and potassium using a P_Na/P_K ratio obtained in the usual way, from zero current constant field fits to resting membrane potential data. Nor can they be reconstructed by summing the constant field current for potassium with that for any other single ion. They can be reconstructed, however, by summing the constant field current for potassium with a constant conductance component. It is concluded that the leak current and the resting membrane potential, therefore, are determined by multiple ionic components, at least three and possibly many. Arguments are presented suggesting that ion permeability ratios obtained in the usual way, by fitting the constant field equation to resting membrane potential data should be viewed with skepticism.     

Influence of membrane thickness and ion concentration on the properties of the gramicidin a channel. Autocorrelation, spectral power density, relaxation and single-channel studies.

The properties of the gramicidin A channel in membranes made from a series of monoglycerides have been studied. In agreement with previous studies, the dissociation rate constant kD of the dimeric channel was found to increase strongly with increasing chain length of the monoglyceride, corresponding to a decrease of the mean life-time of the channel. The value of kD, however, was not strictly correlated with the membrane thickness, as seen from a comparison of membranes with different solvent content. Furthermore, the life-time of the channel increased with the concentration of the permeable ion. This effect was tentatively explained by an electrostatic stabilization of the channel. The single-channel conductance lambda was found to decrease with increasing membrane thickness d, if d was varied by increasing the chain length of the lipid. On the other hand, if d was changed by varying the solvent content of the membranes formed from one and the same lipid, lambda remained constant. These observations were explained by the assumption of local inhomogeneities in the membrane thickness. A striking difference between the lambda values obtained from autocorrelation analysis in the presence of many presence of many channels (lambda a) and those obtained from single-channel experiments (lambda sc) occurred with membranes from longer chain-length monoglycerides. This difference disappeared at low ion concentrations. Electrostatic interactions between channels in local clusters were proposed for an interpretation of these findings.