Effects of membrane potential and surface potential on the kinetics of solute transport

A theoretical study has been made of the influence of the transmembrane potential difference and the surface potential of living cells on the kinetics of carried-mediated solute transport. It is assumed that the form of the free energy barrier within the membrane may be approximated by one dominant symmetrical peak, and that the electrical field is constant. Both single-ion transport kinetics and cotransport of an ion with a neutral solute are dealt with. Provided that the surface potential and the transmembrane potential are constant, the concentration dependence of the uptake rate is given by the Michaelis-Menten equation. The kinetic parameters, the maximal rate of uptake and the K_m, depend on both the surface potential and the membrane potential in a rather complex way. It is shown that the intuitive notion, that the maximal rate of cation uptake will increase when the cell membrane is hyperpolarized, is wrong in its generallity. Both an increase or a decrease may occur, depending on the characteristics of the transport system involved. If the magnitude of the membrane potential and the surface potential depends on the substrate concentration, marked deviations from Michaelis-Menten kinetics may come to the fore. This may result in either apparent positive or apparent negative homotrope cooperative effects. Enhancement of the uptake rate of the substrate ion may occur on adding another cation, despite the fact that the membrane will become depolarized. The same type of complex transport kinetics as found for Rb⁺ and Na⁺ uptake in yeast cells can be simulated by using a single-site transport model and including effects of the membrane potential.     

Evaluation of membrane surface charge density: A discussion of some models

The theory of electrical double layer due to Gouy and Chapman, applied to the experimental data related to shifts of conductance-voltage curve along the voltage axis following changes in the external calcium concentration to derive values for the density of surface charges (σ) present on biomembranes, has been outlined. Similarly, the principal equations of resting membrane potential due to Kobatake and coworkers, also used for the first time by Lakshminarayanaiah to evaluate charges on biomembranes of several tissues, have been given. The values for σ derived by the first method have been considered to indicate the charge density at the channel region through which permeation of Na or K ion occurred. The values for σ derived by the second method are considered to represent the presence of charges smeared out uniformly over the membrane surface. Despite this difference in practical implementation of the concepts of the two theories which initially in their development are based on the assumption of charges covering the membrane surface uniformly, the ultimate values for σ derived by the two methods agree. The significance of this result in relation to different membrane models for surface charges is briefly discussed. Presented at the Society for Mathematical Biology Meeting, University of Pennsylvania, Philadelphia, August 19–21, 1976.     

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.     

A theory of charge separation,ion, electron and proton transport in photosynthetic membranes based on asymmetry of surface charges

We present a model for the light-induced charge separation, proton and ion transport across photosynthetic membranes based on an assumption of the transmembrane surface charge asymmetry. In dark equilibrium, this asymmetry gives rise to an internal membrane electric field whose direction is perpendicular to the membrane surfaces. The role of the field in the light-induced charge separation is similar to the function of the built-in electric field across a solid-state p-n junction. Light-generated free charge carriers in the membrane flow according to its direction and upon recombination on the surface give rise to an electrochemical potential difference for electrons across the membrane. The associated coupled electron-proton transport, and ion diffusion can be viewed as a response of the system to the light-induced redox and electric potential changes.     

Malate Uptake into Isolated Vacuoles from Catharanthus roseus Cells: Role of the Membrane Potential

The mechanisms involved in the transport of malate into isolated vacuoles of Catharanthus roseus (L.) cells were investigated with special reference to the effects of induced changes in membrane potential and surface charges of the tonoplast. For this purpose, thiocyanate (SCN^?), a highly permeant anion often used as a membrane potential probe, was extensively exploited. In the absence of Mg-ATP, the low accumulation ratio of ¹⁴C SCN^? could be related to the presence of negative charges at the outer surface of the tonoplast exerting a screening effect on the displacement of lipophilic anionic species. Nevertheless, malate was taken up continuously by vacuoles supporting the concept of a transport component which facilitates its transfer through the tonoplast. From experiments showing the pH dependence of malata uptake, it is suggested that the protonated form of the transporter is implicated in this process. Moreover, when the vacuoles are energized by Mg-ATP, the study of the equilibrium distribution of ¹⁴C SCN^? indicated an inside positive membrane potential difference. Advantage was taken of these results to modulate the membrane potential with high levels of thiocyanate. The data obtained demonstrate that malate uptake results from electrophoretic movement in response to the positive potential difference.     

The causal theory of the resting potential of cells

In this pedagogical article the causal theory of the resting potential of cells is presented, which for given extracellular ion concentrations predicts the intracellular ones simultaneously with the resting potential. In addition to the Na, K-pump, fixed charges on the membrane surfaces are taken into account. The equation determining the resting potential in the causal theory suggests a new explanation of the genesis of the resting potential. The usual criterion for an ion pump to be electrogenic is not relevant for the whole of the resting potential, and may therefore be misleading. The physical meaning of the Goldman-Hodgkin-Katz formula for the membrane potential as a diffusion potential is also explained and tested with numbers for the giant axon of the squid. A significant discrepancy between theory and experiment is found which calls for an experimental re-examination of the constitutive equations for passive potassium and sodium currents.     

Brownian dynamics study of ion transport in the vestibule of membrane channels.

Brownian dynamics simulations have been carried out to study the transport of ions in a vestibular geometry, which offers a more realistic shape for membrane channels than cylindrical tubes. Specifically, we consider a torus-shaped channel, for which the analytical solution of Poisson's equation is possible. The system is composed of the toroidal channel, with length and radius of the constricted region of 80 A and 4 A, respectively, and two reservoirs containing 50 sodium ions and 50 chloride ions. The positions of each of these ions executing Brownian motion under the influence of a stochastic force and a systematic electric force are determined at discrete time steps of 50 fs for up to 2.5 ns. All of the systematic forces acting on an ion due to the other ions, an external electric field, fixed charges in the channel protein, and the image charges induced at the water-protein boundary are explicitly included in the calculations. We find that the repulsive dielectric force arising from the induced surface charges plays a dominant role in channel dynamics. It expels an ion from the vestibule when it is deliberately put in it. Even in the presence of an applied electric potential of 100 mV, an ion cannot overcome this repulsive force and permeate the channel. Only when dipoles of a favorable orientation are placed along the sides of the transmembrane segment can an ion traverse the channel under the influence of a membrane potential. When the strength of the dipoles is further increased, an ion becomes detained in a potential well, and the driving force provided by the applied field is not sufficient to drive the ion out of the well. The trajectory of an ion navigating across the channel mostly remains close to the central axis of the pore lumen. Finally, we discuss the implications of these findings for the transport of ions across the membrane.     

Acidic lipids, H-ATPases, and mechanism of oxidative phosphorylation. Physico-chemical ideas 30 years after P. Mitchell's Nobel Prize award

Peter D. Mitchell, who was awarded the Nobel Prize in Chemistry 30 years ago, in 1978, formulated the chemiosmotic theory of oxidative phosphorylation. This review initially analyzes the major aspects of this theory, its unresolved problems, and its modifications. A new physico-chemical mechanism of energy transformation and coupling of oxidation and phosphorylation is then suggested based on recent concepts regarding proteins, including ATPases that work as molecular motors, and acidic lipids that act as hydrogen ion (H⁺) carriers. According to this proposed mechanism, the chemical energy of a redox substrate is transformed into nonequilibrium states of electron-transporting chain (ETC) coupling proteins. This leads to nonequilibrium pumping of H⁺ into the membrane. An acidic lipid, cardiolipin, binds with this H⁺ and carries it to the ATP-synthase along the membrane surface. This transport generates gradients of surface tension or electric field along the membrane surface. Hydrodynamic effects on a nanolevel lead to rotation of ATP-synthase and finally to the release of ATP into aqueous solution. This model also explains the generation of a transmembrane protonmotive force that is used for regulation of transmembrane transport, but is not necessary for the coupling of electron transport and ATP synthesis.     

Periaxonal surface calcium binding and distribution of charge on the faces of squid axon potassium channel molecules

Summary The calcium binding constant associated with external surface charge in a position to influence the voltage sensing charges for potassium channel gating appears to be 30 molar^–1, a value much larger than previously thought and in approximate agreement with that found for artificial membranes composed of the lipid brain phosphatidylserene. Fixed charge on the periaxonal membrane surface is distributed in such a way that much larger charges occur at a distance of at least 8 angstroms from the channel pore openings. The separation between the ion pathway and the channel gating charge appears to be greater than or equal to 8 angstroms. Periaxonal surface charge which is in a position to determine the surface potential for gating has a magnitude greater than or equal to one (negative) electronic charge per 182 square angstrom before calcium binding, which is reduced to –e/625 Å in a normal divalent ionic environment. With the normal divalent ionic composition of seawater the surface potential at a position to influence the gating voltage sensor is –15 millivolts relative to the bulk external potential. The external surface potential is –3 mV at the pore mouth. There appears to be a negligible amount of fixed charge on the axoplasmic surface in the vicinity of the ion channel opening. Further, our results confirm earlier measurements that have given a negligible amount of axoplasmic surface fixed charge whose field components would be in a position to influence the channel gating charges.     

Interaction of membrane surface charges with the reconstituted ADP/ATP-carrier from mitochondria

Various modulating influences of negative and positive membrane charges on binding and transport properties of the reconstituted ADP/ATP carrier from mitochondria were investigated. The results are interpreted in terms of functional and structural asymmetries of the adenine nucleotide carrier embedded in the liposomal membrane. The surface potential of liposomes was measured directly either by potential-dependent adsorption of the fluorescent dye $\text{2-p-}\text{toluidinylnaphthalene}$ 6-sulfonate (TNS) or by the $\text{p}\text{K}$ shift of the lipophilic pH indicator pentadecylumbelliferone. These results were correlated with the following observations. (1) Negative surface potentials increase the apparent dissociation constant, $\text{K}{}_{\mathrm{<mtext>d</mtext>}}$, for binding of the negatively charged inhbitor carboxyatractylate to the reconstituted carrier protein. (2) Surface potentials modulate the apparent transport affinity, $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$, of the reconstituted adenine nucleotide carrier for ADP and ATP. The interaction of surface charges with the transport function was investigated with carrier proteins oriented both right-side-out and inside-out. Thus the influence of the surface potential on the function of the ADP/ATP carrier could be determined for the internal and external active sites of the translocator on the outer side of the membrane. Large discrepancies were observed not only between the potentials measured directly (fluorescent dyes) and those measured indirectly (binding and transport affinities), but also between the different surface potentials determined from the influence on the alternatively oriented carrier proteins. The effect of surface charges was rather weak on the cytosolic side of the translocator, whereas there was a strong influence of surface charges on the active site at the matrix side. The most obvious explanation, i.e., screening of negative membrane charges by positively charged amino acid residues at the protein surface, could be ruled out. Besides the modulation of binding affinities for substrates and inhibitors, an additional side-specific effect of surface charges on the transport velocity was observed. Again, the influence on the internal active site of the ADP/ATP carrier was found to be much higher than that on the cytosolic site. The observed effects can be explained by a definite structural asymmetry of the carrier embedded in the liposomal membrane. That site which is physiologically exposed to the cytosol is located at a considerable distance from the plane of the membrane, whereas the opposite site seems to be in close proximity to the membrane surface. Moreover, a spatial equivalence of carboxyatractylate binding site and nucleotide binding site at the external side of the carrier protein was concluded.     

A theoretical analysis of pH dependence of sodium channel conductance

A new theory termed tunnel-acid-group-potential (TAGPT), which explains the effects of pHo and pHi on the ion conductance through different membrane channels, is presented. It is suggested that shifts in pHo and pHi change the values of negative charges generated by acid groups of side chains of some polar (Glu, Asp) amino acid residues lining the tunnel part of the channel. The resulting electrostatic field modification affects the heights of rate-limiting energy barriers (for ion transport) in the transition zones between the tunnel and the vestibules, which changes the channel conductance.     

A model for the stimulation of taste receptor cells by salt.

A taste cell mucosal surface is regarded as a planar region containing bound anionic sites and openings to ionic channels. It is assumed that the bulk aqueous properties of the exterior phase are not continuous with the surface but terminate at a plane near the surface. The region between the (Stern) plane and the membrane is regarded as having a lower dielectric constant than bulk water. This fact admits the possibility of ion pair formation between fixed sites and mobile cations. Mobile ion pairs entering the region may also bind to a fixed anionic site. Thus, it is assumed that mobile cations and ion pairs are potential determining species at the surface. Binding cations neutralizes surface charges, whereas binding mobile ion pairs does not. This competition accounts for the observed anion effect on stimulation of tast receptors by sodium salts. The potential profile is constructed by superimposing the phase boundary potentials with an ionic diffusion potential across the membrane. The model accounts for the anion effect on receptor potential, pH effects, the reversal of polarity when cells are treated with FeCl3, and the so-called "water reponse," depolarization of the taste cell upon dilution of the stimulant solution below a critical lower limit. The proposed model does not require both bound cationic and anionic receptors, and further suggests that limited access to a Stern-like region continuous with membrane channels may generally serve to control transport of ions.     

Ionic concentration profiles and charge distribution for the domain of a polarized spherical cell

Solutions of the Poisson-Boltzmann equation yield potential profiles and equilibrium distributions of ions on either side of a spherical shell membrane across which there exists a separation of ionic charges. For the special case in which the membrane is permeable to only one ion the total charge separation is analyzed in terms of the potential difference given by the Nernst equation. Potential profiles and ionic charge distributions are also given for situations involving a uniform distribution of fixed charges within the membrane.     

Generation of membrane potential beyond the conceptual range of Donnan theory and Goldman-Hodgkin-Katz equation

Donnan theory and Goldman-Hodgkin-Katz equation (GHK eq.) state that the nonzero membrane potential is generated by the asymmetric ion distribution between two solutions separated by a semipermeable membrane and/or by the continuous ion transport across the semipermeable membrane. However, there have been a number of reports of the membrane potential generation behaviors in conflict with those theories. The authors of this paper performed the experimental and theoretical investigation of membrane potential and found that (1) Donnan theory is valid only when the macroscopic electroneutrality is sufficed and (2) Potential behavior across a certain type of membrane appears to be inexplicable on the concept of GHK eq. Consequently, the authors derived a conclusion that the existing theories have some limitations for predicting the membrane potential behavior and we need to find a theory to overcome those limitations. The authors suggest that the ion adsorption theory named Ling’s adsorption theory, which attributes the membrane potential generation to the mobile ion adsorption onto the adsorption sites, could overcome those problems.     

Mechanism of neomycin stimulation of d-glucose uptake in rabbit intestinal brush border membrane

In order to study the effect of the antibiotic neomycin on the intestinal epithelium, d-glucose was used as a probe molecule and its transport into rabbit brush border membrane vesicles was measured by a rapid filtration method. Treatment of the epithelium with neomycin sulfate prior to the preparation of the brush border membrane enhanced the d-glucose uptake, whereas neutral N-acetylated neomycin did not. This action of neomycin was related to its polycationic character and not to its bactericidal action. No significant difference could be demonstrated between the protein content or disaccharidase-specific activities of the brush border fractions from treated or non-treated intestines. Electrophoretic protein patterns of SDS-solubilized membrane were not significantly different after neomycin treatment. To gain more information on the mechanism involved in the stimulation of d-glucose transport, experiments were conducted on phosphatidyl glycerol artificial membranes and the results compared with those obtained with brush border membrane. At a concentration of 10^?7 M, neomycin decreased the nonactin-induced K⁺ conductance by a factor of approx. 100. The membrane conductance was linearly dependent on the neomycin concentration and the conductance in 10^?2 M KCl was 10 times that in 10^?3 M KCl. The valence of neomycin was estimated, from the slope of these curves, to be between 6 and 4. In contrast, acetylated neomycin had no effect on the nonactin-induced K⁺ membrane conductance. Therefore, the effect of neomycin on artificial membrane is related to its 4 to 6 positive charges. It is proposed that the stimulation of sugar transport in brush border membrane is related to screening of the membrane negative charges by the positively-charged neomycin. Accumulation of anions at the membrane surface then occurs and their diffusion into the intravesicular space would increase the transmembrane potential which, in turn, stimulates the entry of d-glucose.     

Statistical mechanical equilibrium theory of selective ion channels.

A rigorous statistical mechanical formulation of the equilibrium properties of selective ion channels is developed, incorporating the influence of the membrane potential, multiple occupancy, and saturation effects. The theory provides a framework for discussing familiar quantities and concepts in the context of detailed microscopic models. Statistical mechanical expressions for the free energy profile along the channel axis, the cross-sectional area of the pore, and probability of occupancy are given and discussed. In particular, the influence of the membrane voltage, the significance of the electric distance, and traditional assumptions concerning the linearity of the membrane electric field along the channel axis are examined. Important findings are: 1) the equilibrium probabilities of occupancy of multiply occupied channels have the familiar algebraic form of saturation properties which is obtained from kinetic models with discrete states of denumerable ion occupancy (although this does not prove the existence of specific binding sites; 2) the total free energy profile of an ion along the channel axis can be separated into an intrinsic ion-pore free energy potential of mean force, independent of the transmembrane potential, and other contributions that arise from the interfacial polarization; 3) the transmembrane potential calculated numerically for a detailed atomic configuration of the gramicidin A channel embedded in a bilayer membrane with explicit lipid molecules is shown to be closely linear over a distance of 25 A along the channel axis. Therefore, the present analysis provides some support for the constant membrane potential field approximation, a concept that has played a central role in the interpretation of flux data based on traditional models of ion permeation. It is hoped that this formulation will provide a sound physical basis for developing nonequilibrium theories of ion transport in selective biological channels.     

Modeling Plasmalemma Ion Transport of the Aquatic Plant Egeria densa

Fresh-water plants generate extraordinarily high electric potential differences at the plasma membrane. For a deeper understanding of the underlying transport processes a mathematical model of the electrogenic plasmalemma ion transport was developed based on experimental data mainly obtained from Egeria densa. The model uses a general nonlinear network approach and assumes coupling of the transporters via membrane potential. A proton pump, an outward-rectifying K⁺ channel, an inward-rectifying K⁺ channel, a Cl⁻ channel and a (2H-Cl)⁺ symporter are considered to be elements of the system. The model takes into consideration the effects of light, external pH and ionic content of the bath medium on ion transport. As a result it does not only satisfactorily describe the membrane potential as a function of these external physiological factors but also succeeds in simulating the effects of specific inhibitors as well as I-V-curves obtained with the patch-clamp technique in the whole cell mode. The quality of the model was checked by stability and sensitivity analyses. Received: 18 March 1996/Revised: 17 July 1996     

Classical transport in a field reversed configuration

The transport of charged particles in a field reversed configuration (FRC) was previously considered to be turbulent because it is much faster than classical predictions. Classical transport has mainly been developed for plasmas in which the gyroradii of particles are small compared to the scale lengths of the variation of the density and magnetic field. This assumption is quite inappropriate for an FRC where the magnetic field vanishes on a surface within the plasma. Classical theory has been extended to include large ion gyroradii. A classical loss-cone process is revealed that is consistent with the transport experiments in which the ion gyroradii were comparable in size to the plasma radius.     

A Few Comments on Electrostatic Interactions in Cell Physiology

The role of fixed charges present at the surface of biological membranes is usually described by the Gouy-Chapman-Grahame theory of the electric double-layer where the Grahame equation is applied independently on each side of the membrane and where the capacitive charges (linked to the transmembrane ionic currents) are disregarded. In this article, we generalize the Gouy-Chapman-Grahame theory by taking into account both intrinsic charges (resulting from the dissociation of membrane constituents) and capacitive charges, in the density value of the membrane surface charges. In the first part, we show that capacitive charges couple electrostatic potentials present on both sides of the membrane. The intensity of this coupling depends both on the value of the membrane specific capacitance and the transmembrane electric potential difference. In the second part, we suggest some physiological implications of membrane electric double-layers.