Electrical capacitances of thin lipid films

Based on the considerations of surface charge and surface recombination (or ion binding), the capacitances of the diffused double layer and the polar region are calculated as functions of ionic strength, pH value and external bias. Electrical capacitances of thin lipid films were measured under various conditions. In all cases, the change in capacitance is not more than 5%. Agreement between theory and experiment is fairly good except for the capacitance-voltage relation. It is concluded that though the magnitude of the observed membrane capacitance is determined by the center hydrocarbon region, its constancy and stability are attributed to the largeness and guarding action of the interface capacitances.     

Elastic, electrostatic and electrokinetic forces influencing membrane curvature

Many cellular and intracellular processes critically depend on membrane shape, but the shape generating mechanisms are still to be fully understood. In this study we evaluate how electrostatic/electrokinetic forces contribute to membrane curvature. Membrane bilayer had finite thickness and was either elastically anisotropic or anisotropic overall, but isotropic per sections (heads and tails). The physics of the situation was evaluated using a coupled system of elastic and electrostatic/electrokinetic (Poisson-Nernst-Planck) equations. The fixed charges present only on the upper membrane surface lead to the accumulation of counter-ions and depletion of co-ions that decay spatially very rapidly (Debye length<1nm), as does the potential and electric field. Spatially uneven electric field and the permittivity mismatch also induce charges at the membrane-solution interface, which are not fixed but influence the electrostatics nevertheless. Membrane bends due to - Coulomb force (caused by fixed membrane charges in the electric field) and the dielectric force (due to the non-uniform electric field and the permittivity mismatch between the membrane and the solution). Both act as membrane surface forces, and both depend supra-linearly on the fixed charge density. Regardless of sign of the fixed charges, the membrane bends toward the charged (upper) surface owing to the action of the Coulomb force, but this is opposed by the smaller dielectric force. The spontaneous membrane curvature becomes very pronounced at high fixed charge densities, leading to very small spontaneous radii (<50nm). In conclusion the electrostatic/electrokinetic forces contribute significantly to the membrane curvature.     

Anatomical distribution of voltage-dependent membrane capacitance in frog skeletal muscle fibers

Components of nonlinear capacitance, or charge movement, were localized in the membranes of frog skeletal muscle fibers by studying the effect of 'detubulation' resulting from sudden withdrawal of glycerol from a glycerol-hypertonic solution in which the muscles had been immersed. Linear capacitance was evaluated from the integral of the transient current elicited by imposed voltage clamp steps near the holding potential using bathing solutions that minimized tubular voltage attenuation. The dependence of linear membrane capacitance on fiber diameter in intact fibers was consistent with surface and tubular capacitances and a term attributable to the capacitance of the fiber end. A reduction in this dependence in detubulated fibers suggested that sudden glycerol withdrawal isolated between 75 and 100% of the transverse tubules from the fiber surface. Glycerol withdrawal in two stages did not cause appreciable detubulation. Such glycerol-treated but not detubulated fibers were used as controls. Detubulation reduced delayed (q gamma) charging currents to an extent not explicable simply in terms of tubular conduction delays. Nonlinear membrane capacitance measured at different voltages was expressed normalized to accessible linear fiber membrane capacitance. In control fibers it was strongly voltage dependent. Both the magnitude and steepness of the function were markedly reduced by adding tetracaine, which removed a component in agreement with earlier reports for q gamma charge. In contrast, detubulated fibers had nonlinear capacitances resembling those of q beta charge, and were not affected by adding tetracaine. These findings are discussed in terms of a preferential localization of tetracaine-sensitive (q gamma) charge in transverse tubule membrane, in contrast to a more even distribution of the tetracaine-resistant (q beta) charge in both transverse tubule and surface membranes. These results suggest that q beta and q gamma are due to different molecules and that the movement of q gamma in the transverse tubule membrane is the voltage-sensing step in excitation-contraction coupling.     

Alamethicin adsorption to a planar lipid bilayer.

The effect of alamethicin and its derivatives on the voltage-dependent capacitance of phosphatidylethanolamine (squalane) membranes was measured using two different methods: lock-in detection and voltage pulse. Alamethicin and its derivatives modulate the voltage-dependent capacitance at voltages lower than the voltage at which alamethicin-induced conductance is detected. The magnitude and sign of this alamethicin-induced capacitance change depends on the aqueous alamethicin concentration and the kind of alamethicin used. Our experimental data can be interpreted as a potential-dependent pseudocapacitance associated with adsorbed alamethicin. Pseudocapacitance is expressed as a function of alamethicin charge, its concentration in the bathing solution and the applied electric field. The theory describes the dependence of the capacitance on applied voltage and alamethicin concentration. When alamethicin is neutral the theory predicts no change of the voltage-dependent capacitance with either sign of applied voltage. Experimental data are consistent with the model in which alamethicin molecules interact with each other while being adsorbed to the membrane surface. The energy of this interaction depends on the alamethicin concentration.     

Electrostatic potential and Born energy of charged molecules interacting with phospholipid membranes: calculation via 3-D numerical solution of the full Poisson equation.

Understanding the physicochemical basis of the interaction of molecules with lipid bilayers is fundamental to membrane biology. In this study, a new, three-dimensional numerical solution of the full Poisson equation including local dielectric variation is developed using finite difference techniques in order to model electrostatic interactions of charged molecules with a non-uniform dielectric. This solution is used to describe the electric field and electrostatic potential profile of a charged molecule interacting with a phospholipid bilayer in a manner consistent with the known composition and structure of the membrane. Furthermore, the Born interaction energy is then calculated by appropriate integration of the electric field over whole space. Numerical computations indicate that the electrostatic potential profile surrounding a charge molecule and its resultant Born interaction energy are a function of molecular position within the membrane and change most significantly within the polar region of the bilayer. The maximum interaction energy is observed when the charge is placed at the center of the hydrophobic core of the membrane and is strongly dependent on the size of the charge and on the thickness of the hydrocarbon core of the bilayer. The numerical results of this continuum model are compared with various analytical approximations for the Born energy including models established for discontinuous slab dielectrics. The calculated energies agree with the well-known Born analytical expression only when the charge is located near the center of a hydrocarbon core of greater than 60 A in thickness. The Born-image model shows excellent agreement with the numerical results only when modified to include an appropriate effective thickness of the low dielectric region. In addition, a newly derived approximation which considers the local mean dielectric provides a simple and continuous solution that also agrees well with the numerical results.     

Inner field compensation as a tool for the characterization of asymmetric membranes and Peptide-membrane interactions

Symmetric and asymmetric planar lipid bilayers prepared according to the Montal-Mueller method are a powerful tool to characterize peptide-membrane interactions. Several electrical properties of lipid bilayers such as membrane current, membrane capacitance, and the inner membrane potential differences and their changes can be deduced. The time-resolved determination of peptide-induced changes in membrane capacitance and inner membrane potential difference are of high importance for the characterization of peptide-membrane interactions. Intercalation and accumulation of peptides lead to changes in membrane capacitance, and membrane interaction of charged peptides induces changes in the charge distribution within the membrane and with that to changes in the membrane potential profile. In this study, we establish time-resolved measurements of the capacitance minimization potential DeltaPsi on various asymmetric planar lipid bilayers using the inner field compensation method. The results are compared to the respective ones of inner membrane potential differences DeltaPhi determined from ion carrier transport measurements. Finally, the time courses of membrane capacitances and of DeltaPsi have been used to characterize the interaction of cathelicidins with reconstituted lipid matrices of various Gram-negative bacteria.     

Effectiveness, active energy produced by molecular motors, and nonlinear capacitance of the cochlear outer hair cell

Cochlear outer hair cells are crucial for active hearing. These cells have a unique form of motility, named electromotility, whose main features are the cell's length changes, active force production, and nonlinear capacitance. The molecular motor, prestin, that drives outer hair cell electromotility has recently been identified. We reveal relationships between the active energy produced by the outer hair cell molecular motors, motor effectiveness, and the capacitive properties of the cell membrane. We quantitatively characterize these relationships by introducing three characteristics: effective capacitance, zero-strain capacitance, and zero-resultant capacitance. We show that zero-strain capacitance is smaller than zero-resultant capacitance, and that the effective capacitance is between the two. It was also found that the differences between the introduced capacitive characteristics can be expressed in terms of the active energy produced by the cell's molecular motors. The effectiveness of the cell and its molecular motors is introduced as the ratio of the motors'active energy to the energy of the externally applied electric field. It is shown that the effectiveness is proportional to the difference between zero-strain and zero-resultant capacitance. We analyze the cell and motor's effectiveness within a broad range of cellular parameters and estimate it to be within a range of 12%-30%.     

The medium reorganization energy for the charge transfer reactions in proteins

A low static dielectric permittivity of proteins causes the low reorganization energies for the charge transfer reactions inside them. This reorganization energy does not depend on the pre-existing intraprotein electric field. The charge transferred inside the protein interacts with its aqueous surroundings; for many globular proteins, the effect of this surroundings on the reorganization energy is comparable with the effect of reorganization of the protein itself while for the charge transfer in the middle of membrane the aqueous phase plays a minor role. Reorganization energy depends strongly on the system considered, and hence there is no sense to speak on the "protein reorganization energy" as some permanent characteristic parameter. We employed a simple algorithm for calculation of the medium reorganization energy using the numerical solution of the Poisson-Boltzmann equation. Namely, the reaction field energy was computed in two versions - all media having optical dielectric permittivity, and all the media with the static one; the difference of these two quantities gives the reorganization energy. We have calculated reorganization energies for electron transfer in cytochrome c, various ammine-ruthenated cytochromes c, azurin, ferredoxin, cytochrome c oxidase, complex of methylamine dehydrogenase with amicyanin, and for proton transfer in α-chymotrypsin. It is shown that calculation of the medium reorganization energy can be a useful tool in analysis of the mechanisms of the charge transfer reactions in proteins.     

Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems

Voltage-dependent ion channels determine the electric properties of axonal cell membranes. They not only allow the passage of ions through the cell membrane, but also contribute to an additional charging of the cell membrane resulting in the so-called capacitance loading. The switching of the channel gates between an open and a closed configuration is intrinsically related to the movement of gating charge within the cell membrane. At the beginning of an action potential, the transient gating current is opposite to the direction of the current of sodium ions through the membrane. Therefore, the excitability is expected to become reduced due to the influence of a gating current. Our stochastic Hodgkin-Huxley-like modeling takes into account both the channel noise-i.e. the fluctuations of the number of open ion channels-and the capacitance fluctuations that result from the dynamics of the gating charge. We investigate the spiking dynamics of membrane patches of a variable size and analyze the statistics of the spontaneous spiking. As a main result, we find that the gating currents yield a drastic reduction of the spontaneous spiking rate for sufficiently large ion channel clusters. Consequently, this demonstrates a prominent mechanism for channel noise reduction.     

Contribution of interfacial tension changes during cellular interaction to the energy balance

The energetics of cell-cell and cell-substrate interactions has been analyzed in terms of the lyophobic colloid stability theory adapted to biological conditions. Some important differences that exist between lyophobic particles and living cells are recognized and taken into account. The protein-aceous coat exterior to the lipid cell membrane (glycocalyx) is treated as a very thick Stern layer which has a constant electric capacitance. The cell itself is viewed as a fluid droplet due to the semi-fluid state of the cell membrane, and its outer boundary is assumed to have a constant electric charge density. When particles with constant surface charge density interact, their surface potential increases. Then the potential at the lipid-protein interface will also increase, hence the interfacial tension should decrease. The magnitude of the interfacial tension change at the lipid-protein interface occurring during the interaction of cells has been calculated for various thicknesses of the glycocalyx. This term, obtained for cells with a relatively thin proteinaceous coat, was found to dominate the energy balance, making the total energy of interaction negative.     

Electrostatic calculations for an ion channel. I. Energy and potential profiles and interactions between ions

The electrostatic energy profile of one, two, or three ions in an aqueous channel through a lipid membrane is calculated. It is shown that the previous solution to this problem (based on the assumption that the channel is infinitely long) significantly overestimates the electrostatic energy barrier. For example, for a 3-A radius pore, the energy is 16 kT for the infinite channel and 6.7 kT for an ion in the center of a channel 25 A long. The energy as a function of the position of the ion is also determined. With this energy profile, the rate of crossing the membrane (using the Nernst-Planck equation) was estimated and found to be compatible with the maximum conductance observed for the gramicidin A channel. The total electrostatic energy (as a function of position) required to place two or three ions in the channel is also calculated. The electrostatic interaction is small for two ions at opposite ends of the channel and large for any positioning of the three ions. Finally, the gradient through the channel of an applied potential is calculated. The solution to these problems is based on solving an equivalent problem in which an appropriate surface charge is placed on the boundary between the lipid and aqueous regions. The magnitude of the surface charge is obtained from the numerical solution for a system of coupled integral equations.     

The different screening of electric charges and dipoles near a dielectric interface

The electric fields within a planar slab of material due to both charges and dipoles within the slab and near to its surface are simply calculated using the method of images. If the slab is immersed in a fluid of high dielectric constant the electric field within the slab due to the charge is always reduced but that of a suitably oriented electric dipole is enhanced by as much as a factor of two.     

Alamethicin channel conductance modified by lipid charge

The membrane surface charge modifies the conductance of ion channels by changing the electric potential and redistributing the ionic composition in their vicinity. We have studied the effects of lipid charge on the conductance of a multi-state channel formed in planar lipid bilayers by the peptide antibiotic alamethicin. The channel conductance was measured in two lipids: in a neutral dioleoylphosphatidylethanolamine (DOPE) and a negatively charged dioleoylphosphatidylserine (DOPS). The charge state of DOPS was manipulated by the pH of the membrane-bathing solution. We find that at high salt concentrations (e.g., 2 M NaCl) the effect of the lipid charge is below the accuracy of our measurements. However, when the salt concentration in the membrane-bathing solution is decreased, the surface charge manifests itself as an increase in the conductance of the first two channel levels that correspond to the smallest conductive alamethicin aggregates. Our analysis shows that both the salt and pH dependence of the surface charge effect can be rationalized within the nonlinear Poisson-Boltzmann approach. Given channel conductance in neutral lipids, we use different procedures to account for the surface charge (e.g., introduce averaging over the channel aperture and take into account Na+ adsorption to DOPS heads), but only one adjustable parameter: an effective distance from the nearest lipid charge to the channel mouth center. We show that this distance varies by 0.3-0.4 nm upon channel transition from the minimal conducting aggregate (level L0) to the next larger one (level L1). This conclusion is in accord with a simple geometrical model of alamethicin aggregation.     

A Theoretical Analysis of the Capacitance of Muscle Fibers Using a Distributed Model of the Tubular System

A model is developed to predict the changes in total capacitance (i.e. total charge stored divided by surface membrane potential) of the tubular system of muscle fibers. The tubular system is represented as a punctated disc and the area of membrane across which current flows is represented as a punctated annulus, the capacitance of the muscle fiber being proportional to this area. The area can be determined from a distributed model of the tubular system, in which the only resistance to radial current flow is presumed to be in the lumen of the tubules. Calculations are made of the variation of capacitance expected as the conductivity of the bathing solution is varied. These calculations include the effects of fixed charge in the tubular lumen and the effects of changes in the shape and volume of the tubular system in solutions of low conductivity. The calculated results fail to fit comparable experimental data, although they do qualitatively account for the known variation of the radial spread of contraction with conductivity of the bathing medium. It is pointed out that the existence of a significant "access resistance" at the mouth of the tubules might explain the discrepancy between theory and experiment.     

Ion concentration and charge adjacent to electrically charged cell membrane

Equations describing ion concentration profiles and electric charge in electrolyte solutions adjacent to an electrically charged cell membrane model in the electrochemical equilibrium state are developed and completely solved. The membrane system model consists of an infinitely large planar sheet of finite thickness separating two electrolyte solutions. Electric charges in the membrane model consist of planes of charge parallel to the surfaces of the planar sheet. The charge in solution adjacent to each surface of the membrane is due to differences in the total anion and cation concentrations in each solution.Expressions of concentration and charge are functions of the quantity and location of charge in the membrane, the various permittivities and thickness of the membrane, and the ionic compositions, permittivities, and temperature of the electrolyte solutions.The validity and relation of the model to real membranes are discussed.     

Membrane electrostatics

In conclusion, charged membrane together with their adjacent electrolyte solution form a thermodynamic and physico-chemical entity. Their surfaces represent an exceptionally complicated interfacial system owing to intrinsic membrane complexity, as well as to the polarity and often large thickness of the interfacial region. Despite this, charged membranes can be described reasonably accurately within the framework of available theoretical models, provided that the latter are chosen on the basis of suitable criteria, which are briefly discussed in Section A. Interion correlations are likely to be important for the regular and/or rigid, thin membrane-solution interfaces. Lateral distribution of the structural membrane charge is seldom and charge distribution perpendicular to the membranes is nearly always electrostatically important. So is the interfacial hydration, which to a large extent determines the properties of the innermost part of the interfacial region, with a thickness of 2-3 nm. Fine structure of the ion double-layer and the interfacial smearing of the structural membrane charge decrease whilst the surface hydration increases the calculated value of the electrostatic membrane potential relative to the result of common Gouy-Chapman approximation. In some cases these effects partly cancel-out; simple electrostatic models are then fairly accurate. Notwithstanding this, it is at present difficult to draw detailed molecular conclusions from a large part of the published data, mainly owing to the lack of really stringent controls or calibrations. Ion binding to the membrane surface is a complicated process which involves charge-charge as well as charge-solvent interactions. Its efficiency normally increases with the ion valency and with the membrane charge density, but it is also strongly dependent on the physico-chemical and thermodynamic state of the membrane. Except in the case of the stereospecific ion binding to a membrane, the relatively easily accessible phosphate and carboxylic groups on lipids and integral membrane proteins are the main cation binding sites. Anions bind preferentially to the amine groups, even on zwitterionic molecules. Membrane structure is apt to change upon ion binding but not always in the same direction: membranes with bound ions can either expand or become more condensed, depending on the final hydrophilicity (polarity) of the membrane surface. The more polar membranes, as a rule, are less tightly packed and more fluid. Diffusive ion flow across a membrane depends on the transmembrane potential and concentration gradients, but also on the coulombic and hydration potentials at the membrane surface.(ABSTRACT TRUNCATED AT 400 WORDS)     

Poisson-Boltzmann calculations of nonspecific salt effects on protein-protein binding free energies

The salt dependence of the binding free energy of five protein-protein hetero-dimers and two homo-dimers/tetramers was calculated from numerical solutions to the Poisson-Boltzmann equation. Overall, the agreement with experimental values is very good. In all cases except one involving the highly charged lactoglobulin homo-dimer, increasing the salt concentration is found both experimentally and theoretically to decrease the binding affinity. To clarify the source of salt effects, the salt-dependent free energy of binding is partitioned into screening terms and to self-energy terms that involve the interaction of the charge distribution of a monomer with its own ion atmosphere. In six of the seven complexes studied, screening makes the largest contribution but self-energy effects can also be significant. The calculated salt effects are found to be insensitive to force-field parameters and to the internal dielectric constant assigned to the monomers. Nonlinearities due to high charge densities, which are extremely important in the binding of proteins to negatively charged membrane surfaces and to nucleic acids, make much smaller contributions to the protein-protein complexes studied here, with the exception of highly charged lactoglobulin dimers. Our results indicate that the Poisson-Boltzmann equation captures much of the physical basis of the nonspecific salt dependence of protein-protein complexation.     

Changes in physico-chemical properties of human large intestine tumour cells membrane

Tumour cells produce and excrete to blood many substances which are present in the cell itself in trace amounts only. Our work has been aimed at the determination of changes in electric charge and in phospholipid composition of large intestine normal mucosa and colorectal cancer cells.Surface charge density of tumour unaffected mucosa and of tissue sections from tumours, was measured by electrophoresis. The measurements were carried out at various pH of solution. Membrane isoelectric point was determined by measuring its electric charge in function of pH as well as total positive charge at low pH and total negative charge at high pH. Qualitative and quantitative composition of phospholipids in the membrane was determined by HPLC. Four phospholipid classes were identified: PI, PS, PE and PC and their surface concentrations were determined.The electric charge calculated from phospholipid concentrations is by three orders of magnitude higher than that determined electrophoretically. It indicates that the groups present in the membrane surface are involved in equilibria in which the charge is neutralized.The electric charge calculated from phospholipid concentrations is by three orders of magnitude higher than that determined electrophoretically. It indicates that the groups present in the membrane surface are involved in equilibria in which the charge is neutralized.Tumour changes provoke an increase in surface charge density of large intestine membrane, whereas the content of individual phospholipids increased or decreased depending on a patient.     

Charge pulse studies of transport phenomena in bilayer membranes. I. Steady-state measurements of actin- and valinomycin-mediated transport in glycerol monooleate bilayers.

A charge pulse technique has been applied to studies of transport phenomena in bilayer membranes. The membrane capacitance can be rapidly charged (in less than a microsecond). The charge then decays through the membrane's conductive mechanism-no current flows through the solution or external circuitry. The resulting voltage decay is thus a manifestation of membrane and boundary layer phenomena only. There are a number of advantages to this approach over conventional voltage or current-clamp techniques: the rise-time of the voltage perturbation is not limited by the time constant deriving from the membrane capacitance and solution resistance, thus permitting study of extremely rapid rate processes; the membrane is exposed to high voltage for relatively short times and thus can be subjected to higher voltages without breakdown; the steady-state current-voltage behavior of the membrane can be deduced from a single charge pulse experiment; the charge (and therefore the integral of the ion flux through the membrane) is monitored allowing detection of rate processes too rapid to follow directly. In this paper we present what is primarily a steady-state analysis of actin (non-, mon-, din-, trin-)-mediated transport of ammonium ion and valinomycin-mediated transport of cesium and potassium ions through glycerol monooleate bilayers. We introduce the concept of the "intercept discrepancy", a method for measuring charge lost through extremely rapid rate processes. Directly observable pre-steady-state phenomena are also discussed but will be the main subject of part II.     

Electrostatic modeling of ion pores. Energy barriers and electric field profiles

This paper presents calculations of the image potential for an ion in an aqueous pore through lipid membrane and the electric field produced in such a pore when a transmembrane potential is applied. The method used is one introduced by Levitt (1978, Biophys. J. 22:209), who solved an equivalent problem, in which a surface charge density is placed at the dielectric boundary. It is shown that there are singularities in this surface charge density if the model system has sharp corners. Numerically accurate calculations require exact treatment of these singularities. The major result of this paper is the development of a projection method that explicitly accounts for this behavior. It is shown how this technique can be used to compute, both reliably and efficiently, the electrical potential within a model pore in response to any electrical source. As the length of a channel with fixed radius is increased, the peak in the image potential approaches that of an infinitely long channel more rapidly than previously believed. When a transmembrane potential is applied the electric field within a pore is constant over most of its length. Unless the channel is much longer than its radius, the field extends well into the aqueous domain. For sufficiently dissimilar dielectrics the calculated values for the peak in the image potential and for the field well within the pore can be summarized by simple empirical expressions that are accurate to within 5%.