Energetics of permeation of thin lipid membranes by ions

The energy of an ion in a thin hydrocarbon membrane relative to its energy in a bulk aqueous phase is considered in terms of the electrostatic and surface components that may be expected to be involved. Except when diffusion activation energies are large compared to partition free energies, the latter will control permeation rate and the state of an ion having the lowest partition energy will be critical for its permeability. This minimum is found when an ion is surrounded with a thin layer of water. All ions of the same charge will tend to be at their lowest state in a sphere of water of the same size. It is concluded, therefore, that all ions of a given charge will have about the same permeability in lipid membranes.     

Proton transport via the membrane surface

Some proton pumps, such as cytochrome c oxidase (C(c)O), translocate protons across biological membranes at a rate that considerably exceeds the rate of proton transport to the entrance of the proton-conducting channel via bulk diffusion. This effect is usually ascribed to a proton-collecting antenna surrounding the channel entrance. In this paper, we consider a realistic phenomenological model of such an antenna. In our model, a homogeneous membrane surface, which can mediate proton diffusion toward the channel entrance, is populated with protolytic groups that are in dynamic equilibrium with the solution. Equations that describe coupled surface-bulk proton diffusion are derived and analyzed. A general expression for the rate constant of proton transport via such a coupled surface-bulk diffusion mechanism is obtained. A rigorous criterion is formulated of when proton diffusion along the surface enhances the transport. The enhancement factor is found to depend on the ratio of the surface and bulk diffusional constants, pK(a) values of surface protolytic groups, and their concentration. A capture radius for a proton on the surface and an effective size of the antenna are found. The theory also predicts the effective distance that a proton can migrate on the membrane surface between a source (such as CcO) and a sink (such as ATP synthase) without fully equilibrating with the bulk. In pure aqueous solutions, protons can travel over long distances (microns). In buffered solutions, the travel distance is much shorter (nanometers); still the enhancement effect of the surface diffusion on the proton flow to a target on the surface can be tens to hundreds at physiological buffer concentrations. These results are discussed in a general context of chemiosmotic theory.     

The effective size of mixed sexually and asexually reproducing populations

Using the transition matrix of inbreeding and coancestry coefficients, the inbreeding (N(eI)), variance (N(eV)), and asymptotic (N(e lambda)) effective sizes of mixed sexual and asexual populations are formulated in terms of asexuality rate (delta), variance of asexual (C) and sexual (K) reproductive contributions of individuals, correlation between asexual and sexual contributions (rho(ck)), selfing rate (beta), and census population size (N). The trajectory of N(eI) toward N(e lambda) changes crucially depending on delta, N, and beta, whereas that of N(eV) is rather consistent. With increasing asexuality, N(e lambda) either increases or decreases depending on C, K, and rho(ck). The parameter space in which a partially asexual population has a larger N(e lambda) than a fully sexual population is delineated. This structure is destroyed when N(1 - delta) < 1 or delta > 1 - 1/N. With such a high asexuality, tremendously many generations are required for the asymptotic size N(e lambda) to be established, and N(e lambda) is extremely large with any value of C, K, and rho(ck) because the population is dominated eventually by individuals of the same genotype and the allelic diversity within the individuals decays quite slowly. In reality, the asymptotic state would occur only occasionally, and instantaneous rather than asymptotic effective sizes should be practical when predicting evolutionary dynamics of highly asexual populations.     

Water transport and ion-water interaction in the gramicidin channel

The diffuse permeability and the diffusion coefficient of water (Dw) in the gramicidin channel is determined from the osmotic water permeability of the channel and "single file" pore theory. Dw is about 7% of the self-diffusion coefficient of bulk water. The diffusion coefficient of a single water molecule alone in the channel is also determined and is about equal to the value in bulk water. This provides an estimate of the mobility of water on the channel walls in the absence of water-water interaction. Since the gramicidin channel walls should be representative of uncharged polar protein surfaces, this result provides direct evidence that the presence of a cation in the channel reduces the hydraulic water permeability by a factor ranging from 60 for Tl+ to 5 for Na+. The diffusion coefficient of a cation (Dc) in the channel is estimated and compared with Dw. For Na+ it is found that Dc approximately equal to Dw, which implies that the movement of the row of water molecules through the channel determines the local mobility of Na+. Thus, it seems that short range ion-wall interactions are not important in determining the channel conductance for Na+. In contrast, for Li+, local ion-wall interactions probably do limit the conductance.     

Ion currents through pores. The roles of diffusion and external access steps in determining the currents through narrow pores.

External access steps, which may include restricted aqueous diffusion, are introduced into a kinetic model for ion transport through narrow pores. The conductance-concentration relation and the concentration dependence of the biionic permeability are calculated using two alternative assumptions: (a) access to the mouth of the pore is allowed only when no ion is within the lumen or at either mouth; (b) ions remain at the mouth only very transiently. With either assumption the concentration dependence of the fluxes is the same as in previous treatments in which all steps in access were lumped into a single process. Also as before, the biionic permeability ratio is independent of concentration so long as the lumen is never doubly occupied. For narrow pores, such as those formed by gramicidin A, the slowest external portion of the access process must occur close to the pore's mouth, and thus the region an ion must occupy to gain access is small. As a consequence, the probability of finding an ion within this region is also small. On this basis, it is argued that the second assumption is appropriate for these pores. The kinetic equations that result are identical to those used by Urban, B., S.B. Hladky, and D.A. Haydon (1980, Biochim. Biophys. Acta. 602:331-354).     

Thermodynamics of information transfer between subunits in oligomeric enzymes and kinetic cooperativity. 2. Thermodynamics of kinetic cooperativity

The principles of structural kinetics allow one to define the thermodynamic conditions that are sufficient to generate a certain type of kinetic behavior. If subunits are loosely coupled, that is if no quaternary constraint exists between them, the kinetic behavior of the polymeric enzyme is qualitatively defined by the behavior of an ideal dimer. The nature and the extent of the kinetic cooperativity are defined by the energy of interaction, delta G rho, between two subunits. This energy of interaction is that of an ideal dimer relative to that of the A2 and B2 states. This thermodynamic formulation of a given type of cooperativity holds whatever the degree of polymerization of the enzyme. Under these conditions of loose coupling between subunits, positive kinetic cooperativity cannot be associated with any sigmoidicity of the rate curve. The range of energy coupling where positive kinetic cooperativity must, of necessity, be observed becomes more and more narrow as the number of subunit interactions is increased. This range, however, is independent of the number of subunits. The same situation is not observed for negative cooperativity which appears to be independent of both the number of subunits and the number of subunit interactions. If the subunits are tightly coupled, that is if quaternary constraints exist between them, three thermodynamic parameters, delta G' rho, delta G lambda, delta G mu, are required to define the nature of kinetic cooperativity. delta G' rho is the free energy of an ideal strained dimer relative to that of strained A2 and B2 states. delta G lambda and delta G mu represent the difference of strain energies between conformations A and B and B and B relative to that existing between conformations A and A. One may determine in the parametric space (delta G' rho, delta G lambda, delta G mu) the boundaries between the sufficient conditions that generate a certain type of cooperativity and the lack of these conditions. The kinetic parameters of the rate equation are not all independent. A number of constraint conditions exist between them which depend upon the subunit design of the polymeric enzyme. The existence of these constraint conditions may be diagnostic of a certain type of subunit interactions.     

Aqueous pathways dominate permeation of solutes across Pisum sativum seed coats and mediate solute transport via diffusion and bulk flow of water

The permeability of seed coats to solutes either of biological or anthropogenic origin plays a major role in germination, seedling growth and seed treatment by pesticides. An experimental set‐up was designed for investigating the mechanisms of seed coat permeation, which allows steady‐state experiments with isolated seed coats of Pisum sativum. Permeances were measured for a set of organic model compounds with different physicochemical properties and sizes. The results show that narrow aqueous pathways dominate the diffusion of solutes across pea seed coats, as indicated by a correlation of permeances with the molecular sizes of the compounds instead of their lipophilicity. Further indicators for an aqueous pathway are small size selectivity and a small effect of temperature on permeation. The application of an osmotic water potential gradient across isolated seed coats leads to an increase in solute transfer, indicating that the aqueous pathways form a water‐filled continuum across the seed coat allowing the bulk flow of water. Thus, the uptake of organic solutes across pea testae has two components: (1) by diffusion and (2) by bulk water inflow, which, however, is relevant only during imbibition.     

Ion movement through gramicidin A channels. Studies on the diffusion-controlled association step

The permeability characteristics of gramicidin A channels are generally considered to reflect accurately the intrinsic properties of the channels themselves; i.e., the aqueous convergence regions are assumed to be negligible barriers for ion movement through the channels. The validity of this assumption has been examined by an analysis of gramicidin A single-channel current-voltage characteristics up to very high potentials (500 mV). At low permeant ion concentrations the currents approach a voltage-independent limiting value, whose magnitude is proportional to the permeant ion concentration. The magnitude of this current is decreased by experimental maneuvers that decrease the aqueous diffusion coefficient of the ions. It is concluded that the magnitude of this limiting current is determined by the diffusive ion movement through the aqueous convergence regions up to the channel entrance. It is further shown that the small-signal (ohmic) permeability properties also reflect the existence of the aqueous diffusion limitation. These results have considerable consequences for the construction of kinetic models for ion movement through gramicidin A channels. It is shown that the simple two-site-three-barrier model commonly used to interpret gramicidin A permeability data may lead to erroneous conclusions, as biionic potentials will be concentration dependent even when the channel is occupied by at most one ion. The aqueous diffusion limitation must be considered explicitly in the analysis of gramicidin A permeability characteristics. Some implications for understanding the properties of ion-conducting channels in biological membranes will be considered.     

Influence of blood flow on cutaneous permeability to inert gas

A thermally regulated Plexiglas chamber was designed for investigation of transcutaneous diffusion of N2 and helium (He) in the human hand. Influence of cutaneous blood flow in this process was studied simultaneously with gas diffusion measurements. Changes in cutaneous blood flow (Q, in ml X min-1 X 100 ml tissue-1) were effected by altering ambient temperature (T) from 20 to 40 degrees C (Q = 0.08 X 100.07T). We found that the rate of inert gas diffusion through human skin, expressed as conductance (G, in ml STPD X h-1 X m-2 X atm-1), increases exponentially as a function of blood flow, and was indistinguishable between He and N2 (G = 21.19 X 100.0124Q). The permeability, diffusion coefficient per unit diffusion distance (D/h, in cm/h), also rose exponentially as a function of blood flow. But permeability for He (D/h = 0.1748 X 100.0203Q) was greater than that for N2 (D/h = 0.1678 X 100.0114Q). As cutaneous blood flow rises, because of increased temperature, the apparent diffusion distance falls linearly for both N2 and He. The change is more prominent for He than for N2 diffusion. Estimated replacement time for the body stores of N2 by transcutaneous diffusion alone was shortened from 26.8 h at 31 degrees C to 15.1 h at 37 degrees C. It is suggested from this study that beneficial results may be derived during decompression procedure 1) by maintaining an appropriate transcutaneous pressure gradient of inert gases, and 2) by elevating ambient temperature.     

Interaction of Clostridium perfringens iota-toxin with lipid bilayer membranes. Demonstration of channel formation by the activated binding component Ib and channel block by the enzyme component Ia.

The interaction between model lipid membranes and the binding component (Ib) of the ADP-ribosylating iota-toxin of Clostridium perfringens was studied in detail. Ib had to be activated by trypsin to result in channel formation in artificial lipid bilayers. The channels formed readily by Ib had a small single-channel conductance of about 85 picosiemens in 1 m KCl. Channel function was blocked in single-channel and multichannel experiments by the enzymatic component Ia in a pH-dependent manner. The strong Ia-mediated channel block of Ib occurred only when the pH was at least lowered to pH 5.6. The single-channel conductance showed a linear dependence on the bulk aqueous KCl concentration, which indicated that the channel properties were more general than specific. Zero current membrane potential measurements suggested the Ib channel has an approximately 6-fold higher permeability for potassium ions than for chloride. The selectivity ratio changed for salts composed of cations and anions of different mobility in the aqueous phase, again suggesting that Ib formed a water-filled general diffusion pore. Asymmetric addition of activated Ib to lipid bilayer membranes resulted in an asymmetric voltage dependence, indicating its full orientation within the membrane. Titration experiments with chloroquine and different tetraalkylammonium ions suggested that the Ib channel was blocked by these compounds but had only a weak affinity to them. In vivo measurements using Vero cells demonstrate that chloroquine and related molecules also did not efficiently block intoxication of the cells by iota-toxin. The possible role of Ib in the translocation of iota-toxin across the target cell membrane is discussed.     

Proton diffusion along the membrane surface of thylakoids is not enhanced over that in bulk water

In photosynthesis and respiration ATP synthesis is powered by a transmembrane protonmotive force. Membrane bound proton pumps and proton translocating ATPsynthases are coupled by lateral proton flow. Whether it leads through the aqueous bulk phases (chemiosmotic theory) or whether it is confined to the membrane or the membrane water interface, is still controversial. Another related controversy is whether or not proton diffusion along the interface between a phospholipid membrane and water is enhanced over the one in bulk water. Thylakoid membranes of plant chloroplasts are intrinsically closely apposed (≈5 nm). To study lateral proton diffusion along the narrow interfacial domain between adjacent thylakoid membranes, we stimulated the proton pumps by a flash of light. This generates an alkalinization jump. In the absence of ADP the membrane is relatively proton tight. Therefore, the alkalinization jump relaxes into the medium. The relaxation kinetics as function of pH and added buffers were studied by flash spectrophotometry. The results were compared with a theory dealing with the diffusion of protons, hydroxyl ions, and mobile buffers plus the action of fixed buffers. We came to the conclusion that the lateral diffusion coefficient both, for H⁺ and for OH^- was less or of same magnitude as in bulk water.     

Electrostatic radius of the gramicidin channel determined from voltage dependence of H+ ion conductance.

The results of Decker and Levitt (1987) suggest that the conductance of H+ ion through the gramicidin channel is limited primarily by diffusion in the bulk solution at the channel mouth. It is assumed in this paper that the H+ conductance is 100% diffusion limited. This means that all the factors that influence the H+ flux are external to the channel and are presumed to be known. In particular, the diffusion coefficient of H+ in this region is assumed to be equal to the bulk solution value and the only force acting on the ion is that due to the applied voltage. A model of the H+ flux is derived, based on the Nernst-Planck equation. It has three adjustable parameters: the electrostatic radius, the capture distance, and the radius of the H+ ion. The acceptable range of the parameters was determined by comparing the predictions of the model with the experimental measurements of the H+ conductance at pH 3.75. The best fit was obtained for an electrostatic radius in the range 2.3-2.7 A. This is in good agreement with earlier predictions (2.5 A) based on the assumption that the dielectric constant of the channel water is equal to that of bulk water. The addition of 1 M choline Cl- (an impermeant) increases the H+ current at low voltage and decreases it at high voltage. The increase can be explained by the small surface charge that results from the separation of charge produced by exclusion of the large choline cation (relative to Cl-) from the membrane surface. The decrease at high voltages can be accounted for by the change in the profile of the applied potential produced by the increase in ionic strength.     

Effects of amphotericin B on membrane permeability--kinetics of spin probe reduction

The effect of the polyene antibiotic amphotericin B on the permeability of both unilamellar and multilamellar model membranes is investigated. The method measures the loss of the electron paramagnetic resonance signal of a spin probe, trapped in the aqueous compartment of a lipid dispersion, upon addition of ascorbate ions to the bulk aqueous phase. Amphotericin B causes large increases in the permeability of cholesterol-containing egg phosphatidylcholine membranes, whereas the effects are small in the absence of sterol and do not depend on surface charge. The effect of amphotericin depends upon the antibiotic:sterol mole ratio. The antibiotic appears to be unable to cross the membrane, acting only on the outermost bilayer of a multibilayer dispersion. When a phospholipid in the gel phase is used, amphotericin B causes large increases in permeability, independently of the presence or absence of sterol. It is suggested that the mechanism of action of amphotericin B is different for lipids in the liquid crystalline or gel states.     

Meningococcal PorA/C1, a channel that combines high conductance and high selectivity.

Class 1 porins (PorA/C1) from Neisseria meningitidis achieve both high selectivity and high conductance. The channel is highly selective (24:1 Na+ over Cl-), suggesting a highly negatively charged selectivity filter. The trimeric nature of PorA/C1 accounts for part of the enormous conductance in 200 mM NaCl (0.97nS). However, the currents that can be achieved exceed the simple infinite-sink calculation for a pore 0.7 nm in radius (estimated from nonelectrolyte permeability). The conductance is linear with salt activity from 20 mM to 2.0 M NaCl with no sign of saturation at low salt. Impermeant polymers reduce the conductance in a manner consistent with their ability to reduce bulk conductivity. Extrapolating from the known structure of homologous porins, the selectivity filter is likely to be small and localized. If small and highly negatively charged ( approximately 9 charges), the predicted conductance would be an order of magnitude higher than that observed. The rate at which ions reach the selectivity filter seems to limit overall ionic flux. PorA/C1 rectifies strongly, and this rectification can be accounted for by calculated differences in the voltage and concentration profiles in the access regions. Thus, it appears that the conductance of this channel is determined by the access resistance and the selectivity by a highly-conductive filter.     

An extended kinetic analysis of valinomycin-induced Rb-transport through monoglyceride membranes

Summary The time course of the current following a voltage jump, which is applied to monoglyceride bilayers in the presence of valinomycin, shows two relaxation times. This is basically in agreement with a simple carrier model which has been described in full detail formerly. Relaxation times and amplitudes allow a calculation of the rate constants of the transport model. The presented data supplement an analysis which was hitherto based only on the slower relaxation process and on information derived from the nonlinearity of currentvoltage characteristics. The additional resolution of the faster relaxation time allowed an approximate determination of the voltage dependence of the translocation rate constant for the carrier-ion-complex and provided evidence for a small voltage dependence of the interfacial reaction. The dependence of the relaxation parameters on the ion concentration in the aqueous phase was interpreted assuming a saturation of the ion concentration at the reaction plane at high bulk concentrations.     

An extended kinetic analysis of valinomycin-induced Rb-transport through monoglyceride membranes.

The time course of the current following a voltage jump, which is applied to monoglyceride bilayers in the presence of valinomycin, shows two relaxation times. This is basically in agreement with a simple carrier model which has been described in full detail formerly. Relaxation times and amplitudes allow a calculation of the rate constants of the transport model. The presented data supplement an analysis which was hitherto based only on the slower relaxation process and on information derived from the nonlinearity of current-voltage characteristics. The additional resolution of the faster relaxation time allowed an approximate determination of the voltage dependence of the translocation rate constant for carrier-ion-complex and provided evidence for a small voltage dependence of the interfacial reaction. The dependence of the relaxation parameters on the ion concentration in the aqueous phase was interpreted assuming a saturation of the ion concentration at the reaction plane at high bulk concentrations.     

ATP transport through a single mitochondrial channel, VDAC, studied by current fluctuation analysis.

The "molecular Coulter counter" concept has been used to study transport of ATP molecules through the nanometer-scale aqueous pore of the voltage-dependent mitochondrial ion channel, VDAC. We examine the ATP-induced current fluctuations and the change in average current through a single fully open channel reconstituted into a planar lipid bilayer. At high salt concentration (1 M NaCl), the addition of ATP reduces both solution conductivity and channel conductance, but the effect on the channel is several times stronger and shows saturation behavior even at 50 mM ATP concentration. These results and simple steric considerations indicate pronounced attraction of ATP molecules to VDAC's aqueous pore and permit us to evaluate the effect of a single ATP molecule on channel conductance. ATP addition also generates an excess noise in the ionic current through the channel. Analysis of this excess noise shows that its spectrum is flat in the accessible frequency interval up to several kilohertz. ATP exchange between the pore and the bulk is fast enough not to display any dispersion at these frequencies. By relating the low-frequency spectral density of the noise to the equilibrium diffusion of ATP molecules in the aqueous pore, we calculate a diffusion coefficient D = (1.6-3.3)10(-11) m2/s. This is one order of magnitude smaller than the ATP diffusion coefficient in the bulk, but it agrees with recent results on ATP flux measurements in multichannel membranes using the luciferin/luciferase method.     

The mechanism of restructuring of surfactant monolayer on mica surface in aqueous solution: molecular dynamics simulation

Molecular dynamics simulation was employed to investigate the restructuring process of CTAB monolayer at mica/water interface. The reversing process of CTAB monolayer was exploited by diffusion of water molecules, reversing of CTAB molecules with time evolution and restructuring of the surfactant monolayer. The results showed that bromide ions around surfactant head groups diffused into bulk water readily due to the electrostatic repulsion caused by negatively charged mica surface. Meanwhile, because of the electrostatic attraction between water molecules and mica surface, part of water molecules can penetrate the surfactant monolayer to form water channel which bridges bulk water and mica surface. The monolayer structure was disturbed by diffusion of bromide ions and formation of water channel. Few of the head groups of surfactants tended to reverse and enter into aqueous solution. The number of reversed surfactant molecules increased with time evolution. The monolayer restructured into bilayer structure gradually. Finally, a cylindrical aggregate was obtained.