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

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

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.     

Membrane Potentials and Ion Permeability in a Cation Exchange Membrane

The nonequilibrium electrical potentials across an artificial membrane bathed by solutions of a single salt have been measured and calculated using the Goldman-Hodgkin-Katz equation and the irreversible thermodynamic equation. The latter equation predicts the observed potential differences over a 2500-fold concentration range, while application of a modified Goldman-Hodgkin-Katz equation leads to difficulties.     

The reliability of relative anion-cation permeabilities deduced from reversal (Dilution) potential measurements in ion channel studies

Measurements of anion-cation permeability ratios (e.g., P _Cl/P _Na) are most readily made by measuring changes in zero-current reversal potential when the salt concentration on one side of the membrane (e.g., external NaCl) is decreased. This is particularly useful for measuring changes in ion selectivity in wild-type and mutant channels, such as those of the ligand-gated ion channel superfamily, and has shown that many of these channels have a significant permeability to counter-ions. One Brownian dynamics study of ion permeation through such narrow ion channels failed to observe such counter-ion movement, although later, another Brownian dynamics study did observe counter-ion movement through simulations of the same channels. The question has been raised as to the reliability of such reversal potential measurements for determining permeability ratios, particularly given the use of an equation such as the Goldman-Hodgkin-Katz (GHK) equation, which is often used to calculate such ratios. A new derivation of the GHK equation in terms of activity coefficients is also included. The application of irreversible thermodynamics will be shown to qualitatively support the reliability of such experimental anion-cation permeability values derived from reversal potential measurements. It will then be shown that for such zero-current situations, different electrodiffusion models, with very different underlying assumptions, produce almost identical relative permeabilities (and reversal potentials). Finally, the results of the two Brownian dynamics simulation studies and the relationship between reversal potentials and relative permeability will be discussed.     

Ionic selectivity, saturation and block in gramicidin A channels: I. Theory for the electrical properties of ion selective channels having two pairs of binding sites and multiple conductance states.

A model for the gramicidin A channel is proposed which extends existing models by adding a specific cationic binding site at each entrance to the channel. The binding of ions to these outer channel sites is assumed to shift the energy levels of the inner sites and barriers and thereby alter the channel conductance. The resulting properties are analyzed theoretically for the simplest case of two inner sites and a single energy barrier. This for-site model (two outer and two inner) predicts that the membrane potential at zero current (Uo) should be a Goldman-Hodgkin-Katz equation with concentration-dependent permeability ratios. The coefficients of the concentration-dependent terms are shown to be related to the peak energy shifts of the barrier and to the binding constants of the outer sites. The thory also predicts the channel conductance in symmetrical solutions to exhibit three limiting behaviors, from which the properties of the outer and inner sites can be characterized. In two-cation symmetrical mixtures the conductance as a function of mole fraction is shown to have a minimum, and the related phenomenon of inhibition and block exerted by one ion on the other is explained explicitly by the theory. These various phenomena, having ion interactions in a multiply occupied channel as a common physical basis, are all related (by the theory) through a set of measurable parameters describing the properties of the system.     

Effect of acetylcholine on postjunctional membrane permeability in eel electroplaque

Acetylcholine (ACh) was applied iontophoretically to the innervated face of isolated eel electroplaques while the membrane potential was being recorded intracellularly. At the resting potential (about -85 mV) application of the drug produced depolarizations (ACh potentials) of 20 mV or more which became smaller when the membrane was depolarized and reversed in polarity at about zero membrane potential. The reversal potential shifted in the negative direction when external Na+ was partially replaced by glucosamine. Increasing external K+ caused a shift of reversal potential in the positive direction. It was concluded that ACh increased the permeability of the postjunctional membrane to both ions. Replacement of Cl- by propionate had no effect on the reversal potential. In Na+-free solution containing glucosamine the reversal potential was positive to the resting potential, suggesting that ACh increased the permeability to glucosamine. Addition of Ca++ resulted in a still more positive reversal potential, indicating an increased permeability to Ca++ as well. Analysis of the results indicated that the increases in permeability of the postjunctional membrane to K+, Na+, Ca++, and glucosamine were in the ratios of approximately 1.0:0.9:0.7:0.2, respectively. With these permeability ratios, all of the observed shifts in reversal potential with changes in external ionic composition were predicted accurately by the constant field equation.     

Ion conductance and selectivity of single calcium-activated potassium channels in cultured rat muscle

The conductance and selectivity of the Ca-activated K channel in cultured rat muscle was studied. Shifts in the reversal potential of single channel currents when various cations were substituted for Ki+ were used with the Goldman-Hodgkin-Katz equation to calculate relative permeabilities. The selectivity was Tl+ greater than K+ greater than Rb+ greater than NH4+, with permeability ratios of 1.2, 1.0, 0.67, and 0.11. Na+, Li+, and Cs+ were not measurably permeant, with permeabilities less than 0.05 that of K+. Currents with the various ions were typically less than expected on the basis of the permeability ratios, which suggests that the movement of an ion through the channel was not independent of the other ions present. For a fixed activity of Ko+ (77 mM), plots of single channel conductance vs. activity of Ki+ were described by a two-barrier model with a single saturable site. This observation, plus the finding that the permeability ratios of Rb+ and NH+4 to K+ did not change with ion concentration, is consistent with a channel that can contain a maximum of one ion at any time. The empirically determined dissociation constant for the single saturable site was 100 mM, and the maximum calculated conductance for symmetrical solutions of K+ was 640 pS. TEAi+ (tetraethylammonium ion) reduced single channel current amplitude in a voltage-dependent manner. This effect was accounted for by assuming voltage-dependent block by TEA+ (apparent dissociation constant of 60 mM at 0 mV) at a site located 26% of the distance across the membrane potential, starting at the inner side. TEAo+ was much more effective in reducing single channel currents, with an apparent dissociation constant of approximately 0.3 mM.     

Membrane transport of polysialic acid chains: modulation of transmembrane potential

Polysialic acid (polySia) is a long polyanionic polymer (with the degree of polymerization, DP, up to 200) of negatively charged sialic acid monomers. PolySia chains are bound to the external surface of some neuroinvasive bacterial cells and neural cells. PolySia serves as a potent regulator of cell interactions via its unusual biophysical properties. In the present paper, the analysis, based on the Goldman-Hodgkin-Katz equation, of transmembrane potential changes resulting from transmembrane translocation of polySia is performed. The relationships between the transmembrane potential and the polySia DP (up to 200), the temperature, the cation/ anion permeability ratio, and the inner/outer concentration ratio of polySia has been plotted and discussed. The maximal membrane potential changes, up to 118 mV, were found for a permeability ratio greater than one. The increase of the polySia chain length resulted in the diminution of this effect. The temperature-dependent changes in membrane potential were less than 7 mV in the range 0-50 degrees C. The change in the concentration ratio (into its reciprocal) resulted in a mirror reflection of the membrane potential curves. The results show that the expression of polySia chains in bacterial cells can be responsible for the modulation of the transmembrane potential of the bacterial inner membrane. We suggest that the polySia chains can influence the transmembrane potential of neural cell membranes in a similar way. This analysis also describes the effect of the transmembrane translocation of negatively charged polyanionic polynucleotydes on the cell membrane potential.     

Highly permeant anions and glucose uptake as an alternative for quantitative generation and estimation of membrane potential differences in brush-border membrane vesicles

We have analyzed the combined utilization of highly permeant anions to induce membrane diffusion potentials and glucose uptake to probe the created potentials as a new approach to quantitative generation and estimation of membrane potential differences in vesicle studies. Rabbit jejunal brush-border membrane vesicles were used in our experiments so that membrane potential differences can be calculated from the Goldman-Hodgkin-Katz equation with the relative ion permeabilities recently reported for this preparation (Gunther, R.D., Schell, R.E. and Wright, E.M. (1984) J. Membrane Biol. 78, 119-127) or approximated by the Nernst potential for the anion. Iodide was selected as the highly permeant anion after showing its absence of effect on glucose uptake with equal concentrations of Na+ inside and outside the vesicles and the membrane potential clamped to zero with gramicidin D. Membrane potential was varied by altering the intra- and extravesicular iodide concentrations while keeping isosmolarity and isotonicity constant by chloride replacement. In these conditions, glucose uptake was sensitive and correlated to the expected membrane potentials. Moreover, a linear relationship between the log initial rate of glucose transport and membrane potential differences could be established. This linear relationship was quite insensitive to inside replacement of choline by potassium and to pH variations in the incubation medium, thus showing the reproducibility and the versatility of the method and the adequacy of glucose uptake as a probe for membrane potentials. However, no information can be gained on the stoichiometry of the Na+-glucose transporter as the slope of the straight line depends on both the charge carried by the fully loaded carrier and the point in the electric field at which the transition state of the carrier from cis to trans occurs. This new approach was compared with the more conventional one using valinomycin-induced K+-diffusion potentials and the Nernst potential for potassium as means for creating and estimating membrane potential differences. Both techniques were not equivalent, as linear relationships showing smaller slopes and sensitivity to pH were recorded with the latter. These differences are compatible with a potassium permeability in the presence of valinomycin that is lower than generally assumed, at least when compared to the permeability of the other ions present in the incubation medium.(ABSTRACT TRUNCATED AT 400 WORDS)     

Anion and cation permeability of a chloride channel in rat hippocampal neurons

The ionic permeability of a voltage-dependent Cl channel of rat hippocampal neurons was studied with the patch-clamp method. The unitary conductance of this channel was approximately 30 pS in symmetrical 150 mM NaCl saline. Reversal potentials interpreted in terms of the Goldman-Hodgkin-Katz voltage equation indicate a Cl:Na permeability ratio of approximately 5:1 for conditions where there is a salt gradient. Many anions are permeant; permeability generally follows a lyotropic sequence. Permeant cations include Li, Na, K, and Cs. The unitary conductance does not saturate for NaCl concentrations up to 1 M. No Na current is observed when the anion Cl is replaced by the impermeant anion SO4. Unitary conductance depends on the cation species present. The channel is reversibly blocked by extracellular Zn or 9-anthracene carboxylic acid. Physiological concentrations of Ca or Mg do not affect the Na:Cl permeability ratio. The permeability properties of the channel are consistent with a permeation mechanism that involves an activated complex of an anionic site, an extrinsic cation, and an extrinsic anion.     

The propagation of the nerve impulse.

A partial differential equation for the propagated action potential is derived using symmetry, charge conservation, and Ohm's law. Charge conservation analysis explicitly includes the gating charge when applied in the laboratory frame. When applied in the system of reference in which capacitive currents are zero, it yields a relation between orthogonal components of the ionic current allowing us to express the nonlinear ionic current in terms of the voltage-dependent membrane capacitance C(V) and the axial current that satisfies Ohm's law. The ionic current is shown to behave as C(V)V[C(V)V2]' at the foot of the action potential while the gating current behaves as C(V)V[Cg(V)V]' where Cg(V) is the capacitance associated with gating. Improved knowledge of the nonlinear current makes it possible to describe the propagated action potential in an approximated way with quasilinear partial differential equations. These equations have analytical solutions that travel with constant velocity, retain their shape, and account for other properties of the action potential. Furthermore, the quasilinear approximation is shown to be equivalent to the FitzHugh-Nagumo equation without recovery making apparent its physical content.     

A method to relate steady-state ionic currents, conductances, and membrane potential in ion exchange membranes with unknown thermodynamic properties

A method is presented by which the steady-state properties of an homogeneous, permselective membrane at uniform temperature can be predicted without knowledge of its thermodynamic properties other than assuming that they are functions only of local mole fractions in the membrane. By making this assumption, it is shown how the ionic conductances can be calculated at any point in the membrane from two sets of measurements, (a) R(symm), the steady-state resistance of the membrane measured between identical solutions and (b) V(0), the potential difference between nonidentical solutions for zero current. These two parameters are measured at different external solution compositions (e.g. a varying sodium-potassium ratio ranging from zero to infinity). From these measurements it is shown how the flux equations may be integrated without a knowledge of mobilities, activity coefficients, and other interior membrane parameters. The application of the method to fixed site membranes with variable mobilities is described and the theory for this particular case has also been verified experimentally in glass membranes.1 A possible application to biological membranes is discussed and a comparison is made between the present treatment and previous treatments used to calculate the steady-state properties of cell membranes, notably the theory of Teorell, Meyer, and Sievers and the constant field theory.     

An Analysis of the Surface Fixed-Charge Theory of the Squid Giant Axon Membrane

The observed shift in threshold potential, after perfusion of the squid giant axon with solutions of low ionic strength, can be predicted by assuming a fixed negative charge on the inside of the membrane. The constant field equation, together with the double-layer potential due to this charge, has been used to determine the change in resting potential during perfusion with solutions of low ionic strength. Neither the modified constant field equation nor Planck's diffusion equation can successfully predict the observed shift in resting potential. It is suggested that a positive charge distribution exists about the sodium channel on the outside of the membrane. The double-layer potential due to this positive charge, together with the independence principle, has been used to predict the relationship between sodium current and membrane potential when the ionic strength and sodium activity of the external solution are decreased. These predictions have been compared with the available experimental observations.     

The permeability of the endplate channel to organic cations in frog muscle

The relative permeability of endplate channels to many organic cations was determined by reversal-potential criteria. Endplate currents induced by iontophoretic "puffs" of acetylcholine were studied by a Vaseline gap, voltage clamp method in cut muscle fibers. Reversal potential changes were measured as the NaCl of the bathing medium was replaced by salts of organic cations, and permeability ratios relative to Na+ ions were calculated from the Goldman-Hodgkin-Katz equation. 40 small monovalent organic cations had permeability ratios larger than 0.1. The most permeant including NH4+, hydroxylamine, hydrazine, methylamine, guanidine, and several relatives of guanidine had permeability ratios in the range 1.3--2.0. However, even cations such as imidazole, choline, tris(hydroxymethyl)aminomethane, triethylamine, and glycine methylester were appreciably permeant with permeability ratios of 0.13--0.95. Four compounds with two charged nitrogen groups were also permeant. Molecular models of the permeant ions suggest that the smallest cross-section of the open pore must be at least as large as a square, 6.5 A x 6.5 A. Specific chemical factors seem to be less important than access or friction in determining the ionic selectivity of the endplate channel.     

Kinetic model of the effects of electrogenic enzymes on the membrane potential

Electrogenic enzymes contribute to the electrical field existing across biological membranes by using a source of free energy to generate an ionic current. The model introduced here permits one to evaluate this contribution. Since the model incorporates the electrogenic enzyme in the form of a sequential kinetic diagram, it permits one to study the kinetic effects of the concentration of the enzyme, the substrates and the different ligands on the membrane potential. Ionic electrodiffusion is expressed in terms of a chemical reaction; ionic permeabilities are thus treated as voltage-dependent rate constants. We use the condition of global electroneutrality to obtain an expression for the electrical potential difference across the membrane; such expression constitutes an extension of the Goldman-Hodgkin-Katz equation. The enzyme-related terms appear in the equation as functions of the rate constants and the diverse concentrations. The model is used to analyze the case of a cell membrane traversed by Na+ and K+ by simple diffusion, and by electrogenic transport mediated by a Na+-K+ ATPase. The enzyme reaction is represented by the six-step scheme proposed by Chapman et al. (1983, J. membr. Biol. 74, 139-153). The main results of the numerical calculations are that, within a certain interval, the membrane potential difference depends linearly on the enzyme density and hyperbolically on the ATP concentration. A similar behavior has been experimentally observed for the electrogenic proton pump of Neurospora crassa. Thus, the model here can be useful in the explanation and prediction of effects of electrogenic enzymes on the membrane potential.     

Application of the Goldman-Hodgkin-Katz current equation to membrane current-voltage data

A new approach for the analysis of current-voltage (IV) data is presented and applied to a variety of published data collected from various systems. Our analysis of published results shows that our method of analysis can account for the observed IV data. The calculated permeability coefficients are in reasonable agreement with those calculated from ion fluxes. In those cases where two ions are assumed to carry the current, the ratios of the calculated permeability coefficients are in agreement with those ratios determined from the Goldman-Hodgkin-Katz voltage equation. In most cases, the entire IV curve can be accounted for by using our method of analysis. In several examples, only a portion of the IV curve is in agreement with the predictions. We attribute the failure to account for the IV data to reflect the failure of one or more of the assumptions used by the GHK current equation. In other cases, assuming that an additional ion carries the current, the treatment can account for the IV data. However, the identity of the extra ion cannot be established from these published data without additional studies (e.g., ionic replacement studies).     

The Double Fixed Charge Membrane: Solution-Membrane Ion Partition Effects and Membrane Potentials

An analysis is made of the effect of solution-membrane partition of ions on the electrostatic potential and ion concentration profiles in fixed charge membranes. It is shown that the inclusion of partition effects gives rise to large solution-membrane “Donnan” potentials even when the concentration of fixed charges is of the same order as the concentration of the external solution. This effect renders the system and the simplified analysis of the double fixed charge membrane (FCM) previously given more applicable to biological membranes. An analysis is also given of the voltage dependence of the fluxes of individual ion species in the double FCM when it separates different ionic solutions and an expression is deduced for the membrane resting potential. Although the latter is similar in form to the Goldman-Hodgkin-Katz (GHK) equation the corresponding value of the permeability ratio P_C1/P_K is under certain specified conditions both concentration and potential dependent.     

Membrane potential dependency of glutamic acid transport in rabbit jejunal brush-border membrane vesicles: K+ and H+ effects

We have applied our recently developed approach for quantitative generation and estimation of membrane potential differences (Berteloot, A. (1986) Biochim. Biophys. Acta 857, 180-188) to the reevaluation of glutamic acid transport rheogenicity in rabbit jejunal brush-border membrane vesicles. Membrane diffusion-potentials were created by altering iodide concentrations in the intra- and extravesicular compartments while keeping isosmolarity, isotonicity and ionic strength constant by chloride replacement. The known value of ion permeabilities relative to sodium in this preparation also allows calculation of membrane potential differences using the Goldman-Hodgkin-Katz equation. This strategy appears superior to more classical methods involving ionophore-induced membrane diffusion-potentials of protons or potassium as both cations have been shown to participate in the transport mechanism. In this paper, we demonstrate that this approach is perfectly suitable for the investigation of membrane potential dependency of glutamic acid transport as our results showed that chloride replacement by iodide did not affect uptake in vesicles with membrane potential clamped to zero by gramicidin D (sodium conditions) or by gramicidin D plus valimonycin (sodium + potassium conditions). The method thus allows to dissociate membrane potential effects from possible effects that might be introduced by altering the anion species. In these conditions, our studies clearly demonstrate that glutamic acid uptake, whether analyzed over a 1 min time scale or under initial rate conditions, was sensitive to membrane potential differences. However, our results also show that the electrogenicity of the transport system varied depending upon the intravesicular presence or absence of potassium, its presence stimulating the membrane potential dependency of uptake. This effect is modulated by the internal pH and it is concluded that inside H+ and K+ are not equivalent as countertransported cations. The external pH also seems to modulate the response to potential by acting on the fully loaded form(s) of the transporter. The possibility that outside H+ competes for (an) external Na+ binding site(s) and/or precludes the attachment of (an) extra sodium ion(s) should be considered.     

The Non-Steady-State Membrane Potential of Ion Exchangers with Fixed Sites

A system of equations, based upon the assumption that the only force acting on each ionic species is due to the gradient of its electrochemical potential, is used to deduce, in the non-steady state for zero net current, the expression of the difference of electric potential between two solutions separated by an ion exchange membrane with fixed monovalent sites. The membrane is assumed to be solely permeable to cations or anions, depending on whether the charge of the sites is -1 or +1, and not to permit any flow of solvent. Under the assumptions that the difference of standard chemical potentials of any pair of permeant monovalent species and the ratio of their mobilities are constant throughout the membrane, even when the spacing of sites is variable, explicit expressions are derived for the diffusion potential and total membrane potential as functions of time and of solution activities. The expressions are valid for any number of permeant monovalent species having ideal behavior and for two permeant monovalent species having “n-type” non-ideal behavior. The results show that for a step change in solution composition the observable potential across a membrane having fixed, but not necessarily uniformly spaced, sites becomes independent of time once equilibria are established at the boundaries of the membrane and attains its steady-state value even while the ionic concentration profiles and the electric potential profile within the membrane are changing with time.     

Ion flow through membranes and the resting potential of cells

Summary A knowledge of the relationship between ion flow, both passive and active, ionic concentration, and membrane potential is essential to the understanding of cellular function. The problem has been analyzed on the basis of elementary physical and biophysical principles, providing a theoretical model of current flow and resting potential of cells, including those in epithelia. The model assumes that the permeability of the ion channets is not voltage dependent, but applies to gated channels when the gates are open. Two sources of nonlinearity of the current-voltage relationship are included in the analysis: ionic depletion and accumulation at the channels' mouths, and channel saturation at higher concentrations. The predictions of the model have been quantitative, validated by comparison with experiment, which has been limited to the only two cases in which adequate data was found. Application of the theory to the scala media of the mammalian cochlea has explained the source of its high positive potential and provided estimates of the Na⁺ and K⁺ permeabilities of the membranes of its marginel cess. This analysis provides a theoretically sound alternative to the widely used Goldman equation, the limited validity of which was emphasized by Goldman (D.E. Goldman, 1943,J. Gen. Physiol.27:37–60), as well as its derivatives, including the Goldman-Hodgkin-Katz equation for resting potentials.