Transmembrane electrical potential of excitable membranes: a pore analysis influence of surface charges and surface dipoles

A treatment is proposed in order to establish the general expression of the zero-current transmembrane potential of excitable membranes. The membrane model considered here is that of a hydrocarbon layer which is impermeable to ions and which represents the lipid bilayer matrix. In this matrix are incorporated ionic channels. The ion transport process through the channels is described by the absolute-rate theory applied to pores which are seen as chains of potential energy maxima and minima. Only one of the energy barriers corresponds to the gate step, and it is strongly dependent on the transmembrane potential. The kinetic equation is related to the zero current, to electrostatic boundary conditions and to the Gouy-Chapman equation for the aqueous diffuse layer.     

Theory for carrier-mediated zero-current conductance of bilayers extended to allow for nonequilibrium of interfacial reactions,spatially dependent mobilities and barrier shape

Summary A generalized form of the electrodiffusion equation, allowing for any shape of symmetrical energy barrier and any spatial dependence of the diffusion coefficient, is used to deduce theoretically the carrier-mediated conductance for thin (e.g., bilayer) membranes in the limit of low applied current. Both the Nernst-Planck and the Eyring single-barrier treatments are special cases of this more general approach, which allows for the effect of non-uniform properties of the lipid and non-uniform profiles of the forces acting within the membrane interior. Two independent mechanisms for ions to cross the membrane-solution interfaces are considered; namely, (1) the reaction at the interface between ions from solution and carriers from the membrane, and (2) the partition across the interfaces of complexes already formed in the solution. The rates of these reactions are taken into account using the rate equations of chemical kinetics; and the Poisson-Boltzmann equation is integrated in the aqueous solutions to evaluate the effect of charged polar head groups of the lipid. The analysis leads to an expression for the conductance, which, in the approximation of constant field, is an explicit function of such experimentally variable parameters as the concentrations and types of permeant ions and carriers in the aqueous phases, the total ionic strength and the nature of the polar head groups of the lipid. The functional relationship observable in an unknown membrane can, in principle, enable one to deduce such information as the mechanism of ion permeation across the interfaces, the magnitude of the surface charge, and the degree of ion-carrier complexation in the aqueous solutions.     

Permeability of lipid bilayers to water and ionic solutes

The lipid bilayer moiety of biological membranes is considered to be the primary barrier to free diffusion of water and solutes. This conclusion arises from observations of lipid bilayer model membrane systems, which are generally less permeable than biological membranes. However, the nature of the permeability barrier remains unclear, particularly with respect to ionic solutes. For instance, anion permeability is significantly greater than cation permeability, and permeability to proton-hydroxide is orders of magnitude greater than other monovalent inorganic ions. In this review, we first consider bilayer permeability to water and discuss proposed permeation mechanisms which involve transient defects arising from thermal fluctuations. We next consider whether such defects can account for ion permeation, including proton-hydroxide flux. We conclude that at least two varieties of transient defects are required to explain permeation of water and ionic solutes.     

A theory for the effects of neutral carriers such as the macrotetralide actin antibiotics on the electric properties of bilayer membranes

Summary To develop a quantitiative theoretical treatment for the effects of neutral macrocyclic antibiotics on the electrical properties of phospholipid bilayer membranes, this paper proceeds from the known ability of such molecules to form stoichiometric, lipid-soluble complexes with cations and deduces the electrical properties that a simple organic solvent phase would have if it were made into a membrane of the thinness of the phospholipid bilayer. In effect, we postulate that the essential barrier to ion movement across a bilayer membrane is its liquid-like hydrocarbon interior and that the neutral macrocyclic antibiotics bind monovalent cations and solubilize them in the membrane as mobile positively charged complexes. Using the Poisson-Boltzmann equation to describe the equilibrium profile of the electrical potential, it is shown that an excess of the positive complexes over all the other ions is expected in the membrane as a net space charge for appropriate conditions of membrane thickness and values of the partition coefficients of the various ionic species and without requiring the presence of fixed charges. Describing the fluxes of these complexes by the Nernst-Planck equation and neglecting the contribution to the electric current of uncomplexed ions, theoretical expressions are derived for the membrane potential in ionic mixtures, as well as for the limiting value of the membrane conductance at zero current when the membrane is interposed between identical solutions. The expressions are given in terms of the ionic activities and antibiotic concentrations in the aqueous solutions so as to be accessible to direct experimental test. Under suitable experimental conditions, the membrane potential is described by an equation recognizible as the Goldman-Hodgkin-Katz equation, in which the permeability ratios are combinations of parameters predicted from the present theory to be independently determinable from the ratio of membrane conductances in single salt solutions. Since this identity between permeability and conductance ratios is expected also for systems obeying the Independence Principle of Hodgkin and Huxley, the applicability of this principle to membranes exposed to antibiotics is discussed, and it is shown that this principle is compatible with the permeation mechanism proposed here.     

Influence of dolichyl phosphate on permeability and stability of bilayer lipid membranes

The ionic permeability coefficients, ionic transference numbers, activation energy of ion transport and breakdown voltage of bilayer lipid membranes made from dioleoylphosphatidylcholine or its mixtures with dolichyl 12-phosphate have been studied. The electrical measurements showed that dolichyl phosphate in phospholipid bilayers decreases membrane permeability, changes membrane ionic selectivity and increases membrane stability. These results are discussed in light of the aggregation behavior and the intramolecular clustering of a dolichyl phosphate molecule in phospholipid membranes. From our data we suggest that the hydrophilic part of dolichyl phosphate molecules regulates their behavior in membranes.     

Transport of oppositely charged lipophilic probe ions in lipid bilayer membranes having various structures

Summary A comparative study of the charge transport kinetics of oppositely charged lipophilic probe ions in lipid bilayer membranes of varying composition was carried out by using the charge pulse technique. The ions investigated were the chemical analogs tetraphenylborate, tetraphenylarsonium and tetraphenylphosphonium. Membrane structural aspects investigated were the type of solvent used in membrane formation, sterol content, and the nature of the principal lipid. The overall results indicate that the character of the transport process involving positive lipophilic probes is, in contrast to positively charged carrier complexes, very similar to that deduced in previous studies of negative lipophilic ions. The major effect on transport of lipophilic ions of both signs using differentn-alkane solvents appears to be due to changes in the thickness of the membrane hydrocarbon region. Positive ion transport is relatively sensitive to the inclusion of sterols of several types in both monoolein and lecithin membranes, as compared with negative ion transport, suggesting that a combination of sterol-induced dipolar field and fluidity changes are involved. Results involving several variations in lipid structure, with the possible exception of hydrocarbon tail saturation, when interpreted in terms of dipolar field changes deduced under the assumption of charge independent fluidity effects, are consistent with monolayer surface potential measurements.     

Modification of ion transport in lipid bilayer membranes in the presence of 2,4-dichlorophenoxyacetic acid. I. Enhancement of cationic conductance and changes of the kinetics of nonactin-mediated transport of potassium.

We have found that herbicide 2,4-dichlorophenoxyacetic acid (2,4-D) has the ability to increase the rate of transport of positive ions of several kinds, and to inhibit transport of negatively charged tetraphenylborate ions in lipid bilayer membranes. It has been found that only the neutral form of 2,4-D is transport active, whereas the ionized from of 2,4-D does not modify transport of ions, and does not by itself permeate through lipid membranes. The results suggest that the enhancement of transport of positively charged ions such as tetraphenylarsonium + and nonactin-K+ is dominated by the increase of the ion translocation rate constant. It has been shown that the enhancement of nonactin-mediated transport of K+ by 2,4-D can be accounted for by a simple carrier model. We have observed that a 2,4-D concentration above 3 X 10(-4) M the potassium ion transport in phosphatidylcholine-cholesterol as well as in cholesterol-free glycerolmonooleate membranes is enhanced to such a degree that, depending upon the concentration of potassium ions, it becomes limited by the rate of recombination of K+ with nonactin, and/or by backdiffusion of unloaded nonactin molecules. Furthermore, the effect of 2,4-D is enhanced by ionic strength of aqueous solution. From the changes of kinetic parameters of nonactin-K+ transport, as well as from the changes of membranes conductance due to tetraphenylarsonium + ions, we have estimated the changes of the electrical potential of the membrane interior. We have found that the potential of the interior of the membrane becomes more negative in the presence of 2,4-D, and that its change is proportional to the aqueous concentration of 2,4-D. The effect of 2,4-D on ion transport has been attributed to a layer of 2,4-D molecules absorbed within the interfacial region, and having a dipole moment directed toward the aqueous medium. The results of kinetic studied of nonactin-K+ transport suggest that this layer is located on the hydrocarbon side of the interface.     

A three-barrier model for the hemocyanin channel

Keyhole limpet hemocyanin forms ion-conducting channels in planar lipid bilayer membranes. Ionic current through the open hemocyanin channel presents the following characteristics: (a) it is carried mainly by cations; (b) it is a nonlinear function of membrane potential; (c) channel conductance is a saturating function of ion activity; (d) it shows ionic competition. A model for the open hemocyanin channel is developed from absolute reaction rate theory. The model calls for three energy barriers in the channel. Two energy barriers represent the entrance and exit of the ion into and out of the channel. The third barrier separates two energy minima that represent two binding sites. Furthermore, only one ion is allowed inside the channel at a given time. This model is able to recreate all the hemocyanin characteristics found experimentally in negatively charged and neutral membranes.     

The effect of hexadecaprenol on molecular organisation and transport properties of model membranes

The Langmuir monolayer technique and voltammetric analysis were used to investigate the properties of model lipid membranes prepared from dioleoylphosphatidylcholine (DOPC), hexadecaprenol (C80), and their mixtures. Surface pressure-molecular area isotherms, current-voltage characteristics, and membrane conductance-temperature were measured. Molecular area isobars, specific molecular areas, excess free energy of mixing, collapse pressure and collapse area were determined for lipid monolayers. Membrane conductance, activation energy of ion migration across the membrane, and membrane permeability coefficient for chloride ions were determined for lipid bilayers. Hexadecaprenol decreases the activation energy and increases membrane conductance and membrane permeability coefficient. The results of monolayer and bilayer investigations show that some electrical, transport and packing properties of lipid membranes change under the influence of hexadecaprenol. The results indicate that hexadecaprenol modulates the molecular organisation of the membrane and that the specific molecular area of polyprenol molecules depends on the relative concentration of polyprenols in membranes. We suggest that hexadecaprenol modifies lipid membranes by the formation of fluid microdomains. The results also indicate that electrical transmembrane potential can accelerate the formation of pores in lipid bilayers modified by long chain polyprenols.     

The partition and transport behavior of cytotoxic ionic liquids (ILs) through the DPPC bilayer: Insights from molecular dynamics simulation

A molecular dynamics (MD) simulation with atomistic details was performed to examine the partitioning and transport behavior of moderately cytotoxic ionic liquids (ILs), namely choline bis(2-ethylhexyl) phosphate (CBEH), choline bis(2,4,4-trimethylpentyl) phosphinate (CTMP) and choline O,O-diethyl dithiophosphate (CDEP) in a fully hydrated dipalmitoylphosphatidylcholine (DPPC) bilayer in the fluid phase at 323?K. The structure of ILs was so selected to understand if the role of dipole and dispersion forces in the ILs distribution in the membrane can be possible. Several analyses including mass density, electrostatic potential, order parameter, diffusion coefficients and hydrogen bond formation, was carried out to determine the precise location of the anionic species inside the membrane. Moreover, the potential of the mean force (PMF) method was used to calculate free energy profile for transferring anionic species from the DPPC membrane into the bulk water. While less cytotoxic DEP is located within the bulk water, more cytotoxic TMP and BEH ILs were found to remain in the membrane and the energy barrier for crossing through the bilayer center of BEH was higher. Various ILs have no significant effect on P–N vector. The thickness of lipid bilayer decreased in all systems comprising ILs, while area per lipid increased.     

Electrical noise from lipid bilayer membranes in the presence of hydrophobic ions

In the presence of the hydrophobic ion dipicrylamine, lipid bilayer membranes exhibit a characteristic type of noise spectrum which is different from other forms of noise described so far. The spectral density of current noise measured in zero voltage increases in proportion to the square of frequency at low frequencies and becomes constant at high frequencies. The observed form of the noise spectrum can be interpreted on the basis of a transport model for hydrophobic ions in which it is assumed that the ions are adsorbed in potential-energy minima at either membrane surface and are able to cross the central energy barrier by thermal activation. Accordingly, current-noise results from random fluctuations in the number of ions jumping over the barrier from right to left and from left to right. On the basis of this model the rate constant ki for the translocation of the hydrophobic ion across the barrier, as well as the mean surface concentration Nt of adsorbed ions may be calculated from the observed spectral intensity of current noise. The values of ki obtained in this way closely agree with the results of previous relaxation experiments. A similar, although less quantitative, agreement is also found for the surface concentration Nt.     

Monovalent ion permeability of model bilayer membranes based on lipids from tissues of various vertebrates

The ionic permeability of model bilayer membranes prepared from total lipids of the brain, heart, liver, and muscles of four species of higher vertebrates was studies. The electrical conductivity and potential of membranes breakdown were measured in KCl, NaCl, and LiCl solutions. It was found that the permeability for potassium ions of bilayer lipid membranes from the lipids of nervous tissue decreases in the row of poikilothermal vertebrates and increases in mammals. A reverse regularity was observed for membrane stability, which manifested itself as an increase in membrane breakdown in the order fish-amphibian-reptile and a decrease in membrane breakdown in mammalian membranes. It was shown that, in most cases, the the permeability of bilayer lipid membranes for K+ ions is higher than for Na+ and Li+.     

Exploring lipid-dependent conformations of membrane-bound α-synuclein with the VDAC nanopore

Regulation of VDAC by α-synuclein (αSyn) is a rich and instructive example of protein-protein interactions catalyzed by a lipid membrane surface. αSyn, a peripheral membrane protein involved in Parkinson's disease pathology, is known to bind to membranes in a transient manner. αSyn's negatively charged C-terminal domain is then available to be electromechanically trapped by the VDAC β-barrel, a process that is observed in vitro as the reversible reduction of ion flow through a single voltage-biased VDAC nanopore. Binding of αSyn to the lipid bilayer is a prerequisite of the channel-protein interaction; surprisingly, however, we find that the strength of αSyn binding to the membrane does not correlate in any simple way with its efficiency of blocking VDAC, suggesting that the lipid-dependent conformations of the membrane-bound αSyn control the interaction. Quantitative models of the free energy landscape governing the capture and release processes allow us to discriminate between several αSyn (sub-) conformations on the membrane surface. These results, combined with known structural features of αSyn on anionic lipid membranes, point to a model in which the lipid composition determines the fraction of αSyn molecules for which the charged C terminal domain is constrained to be close, but not tightly bound, to the membrane surface and thus readily captured by the VDAC nanopore. We speculate that changes in the mitochondrial membrane lipid composition may be key regulators of the αSyn-VDAC interaction and consequently of VDAC-facilitated transport of ions and metabolites in and out of mitochondria and, i.e. mitochondrial metabolism.     

Nonlinear Electrical Effects in Lipid Bilayer Membranes: II. Integration of the Generalized Nernst-Planck Equations

In this paper the ion transport across a thin lipid membrane is treated using a generalized form of the Nernst-Planck equations. An additional term is introduced into the flux equations to account for the image force acting on the ion. As the membrane thickness is of the same order of magnitude as the range of the image forces, the potential energy of the ion in the membrane is strongly dependent on position. The integration of the flux equations leads to a general expression for the integral membrane conductance lambda as a function of the voltage u. The ratio lambda(u)/lambda(0) (lambda(0) = membrane conductance in the limit u --> 0) depends on the dielectric constant and the thickness of the membrane, but is independent of the ionic radius. When the numerical values of the potential energy function, as calculated by the method of electrical images, are inserted into the expression for lambda(u)/lambda(0), a strongly non-linear current-voltage characteristic is obtained. The theoretical current-voltage curve agrees satisfactorily with the experimental data at a low ionic strength and at low voltages; at higher voltages the observed membrane conductance exceeds the predicted value.     

Life at the border: Adaptation of proteins to anisotropic membrane environment

This review discusses main features of transmembrane (TM) proteins which distinguish them from water‐soluble proteins and allow their adaptation to the anisotropic membrane environment. We overview the structural limitations on membrane protein architecture, spatial arrangement of proteins in membranes and their intrinsic hydrophobic thickness, co‐translational and post‐translational folding and insertion into lipid bilayers, topogenesis, high propensity to form oligomers, and large‐scale conformational transitions during membrane insertion and transport function. Special attention is paid to the polarity of TM protein surfaces described by profiles of dipolarity/polarizability and hydrogen‐bonding capacity parameters that match polarity of the lipid environment. Analysis of distributions of Trp resides on surfaces of TM proteins from different biological membranes indicates that interfacial membrane regions with preferential accumulation of Trp indole rings correspond to the outer part of the lipid acyl chain region—between double bonds and carbonyl groups of lipids. These “midpolar” regions are not always symmetric in proteins from natural membranes. We also examined the hydrophobic effect that drives insertion of proteins into lipid bilayer and different free energy contributions to TM protein stability, including attractive van der Waals forces and hydrogen bonds, side‐chain conformational entropy, the hydrophobic mismatch, membrane deformations, and specific protein–lipid binding.     

Electrogenic and nonelectrogenic ion fluxes across lipid and mitochondrial membranes mediated by monensin and monensin ethyl ester

Monensin is a carrier of cations through lipid membranes capable of exchanging sodium (potassium) cations for protons by an electroneutral mechanism, whereas its ethyl ester derivative ethyl-monensin is supposed to transport sodium (potassium) cations in an electrogenic manner. To elucidate mechanistic details of the ionophoric activity, ion fluxes mediated by monensin and ethyl-monensin were measured on planar bilayer lipid membranes, liposomes, and mitochondria. In particular, generation of membrane potential on liposomes was studied via the measurements of rhodamine 6G uptake by fluorescence correlation spectroscopy. In mitochondria, swelling experiments were expounded by the additional measurements of respiration, membrane potential, and matrix pH. It can be concluded that both monensin and ethyl-monensin can perform nonelectrogenic exchange of potassium (sodium) ions for protons and serve as electrogenic potassium ion carriers similar to valinomycin. The results obtained are in line with the predictions based on the crystal structures of the monensin complexes with sodium ions and protons (Huczyński et al., Biochim. Biophys. Acta, 1818 (2012) pp. 2108–2119). The functional activity observed for artificial membranes and mitochondria can be applied to explain the activity of ionophores in living systems. It can also be important for studying the antitumor activity of monensin.     

Energy of an ion crossing a low dielectric membrane: the role of dispersion self-free energy

The Born charging equation predicts that the permeability of a cell membrane to ions by the solubility-diffusion mechanism depends on the ionic radius and on the dielectric constant of the membrane. However, experiments, for example, on red blood cells and on lysosome membranes, show that the permeability depends strongly on the choice of salt anion in a way that cannot be accommodated by differences in ionic size. We demonstrate that one step towards understanding this ion specificity is to take account of the previously ignored dispersion self-free energy of the ion. This is the quantum electrodynamic analogue of the (electrostatic) Born self-energy of an ion. We show that the dispersion self-free energy contribution can be and often is of the same order of magnitude as the Born contribution. To understand the observed specificity, it is essential to take into account of both ionic size and ionic polarizability. In parallel and to reinforce these observations, we also give simple estimates for how self-free energy changes that occur when an ion moves into the air-water interface region (which has a density profile for water molecules) can influence the surface tension of salt solutions. Consistency can be found between the Hofmeister sequences observed in ion permeation and in surface tension of electrolytes when these previously ignored self-free energies are included properly.     

A theory for the effects of diffusion-reaction coupling on the carrier-mediated ionic permeability in lipid bilayers

The zero-current membrane potential and the current-voltage relations are discussed theoretically for the case in which ionic transport is mediated by carriers that form complexes with ions in the aqueous phase (‘solution complexation’ mechanism). Interest for this topic originated partly from the finding that gradients of the neutral cyclic peptide PV, cyclo (dVal-lPro-lVal-dPro)₃, commonly thought to act as a carrier via ‘solution complexation’, generate Nernstian potentials across lipid bilayers separating solutions of identical ion composition. It is shown that the general expression for the potential in a gradient of carriers reduces to the Nernst equation under any of the following conditions: slow aqueous reaction; impermeability of the membrane to the neutral carriers; high concentration of the complexing ions in solution; finite permeability of the membrane to the neutral carrier, but faster rate of movement from the membrane surface into the torus than across the middle or out of the membrane. In symmetrical solutions, the conductance is most typically characterized by a quantity that we designate by δ*, which has the dimensions of a length and is generally a complex function of ion activity. Comparing the thory with previous data on dioleoylphosphatidylcholine membranes in the presence of PV and K⁺, the order of magnitude of the rates of the aqueous reaction and of the membrane permeability to the neutral carriers is tentatively estimated.