Electrostatic repulsion of ion penetrable charged membranes: role of Donnan potential

A model is proposed for the electrostatic repulsion between two ion-penetrable charged membranes in which fixed charges are uniformly distributed. This model assumes that the electric potential far inside the membrane is always equal to the Donnan potential, independent of the membrane separation. In this respect the present model completely differs from usual models for the electrostatic interaction of colloidal particles which assume that the surface potential or the surface charge density remains constant during interaction. It is shown that the rise in potential in the interacting membranes caused by their approach is greatly suppressed so that the potential in the membrane does not exceed the Donnan potential. Numerical results of the calculation of the repulsion by the non-linear Poisson-Boltzmann equation are displayed as a function of the membrane separation and an approximate formula is also derived.     

Donnan potential and surface potential of a charged membrane.

A model is presented for the electrical potential distribution across a charged biological membrane that is in equilibrium with an electrolyte solution. We assume that a membrane has charged surface layers of thickness d on both surfaces of the membrane, where the fixed charges are distributed at a uniform density N within the layers, and that these charged layers are permeable to electrolyte ions. This model unites two different concepts, that is, the Donnan potential and the surface potential (or the Gouy-Chapman double-layer potential). Namely, the present model leads to the Donnan potential when d much greater than 1/k' (k' is the Debye-Hückel parameter of the surface charge layer) and to the surface potential as d----0, keeping the product Nd constant. The potential distribution depends significantly on the thickness d of the surface charge layer when d less than or approximately equal to 1/k'.     

Glycocalyx electrostatic potential profile analysis: ion, pH, steric, and charge effects

The Poisson-Boltzmann equation is modified to consider charge ionogenicity, steric exclusion, and charge distribution in order to describe the perimembranous electrostatic potential profile in a manner consistent with the known morphology and biochemical composition of the cell's glycocalyx. Exact numerical and approximate analytical solutions are given for various charge distributions and for an extended form of the Donnan potential model. The interrelated effects of ionic conditions, bulk pH, ion binding, local dielectric, steric volume exclusion, and charge distribution on the local potential, pH, and charge density within the glycocalyx are examined. Local charge-induced, potential-mediated pH reductions cause glycocalyx charge neutralization. Under certain conditions, local potentials may be insensitive to ionic strength or may decrease in spite of increasing charge density. The volume exclusion of the glycocalyx reduces the local ion concentration, thereby increasing the local potential. With neutral lipid membranes, the Donnan and surface potential agree if the glycocalyx charge distribution is both uniform and several times thicker than the Debye length (approximately 20 A in thickness under physiological conditions). Model limitations in terms of application to microdomains or protein endo- and ectodomains are discussed.     

Membrane potential and Donnan potential

The Nernst-Planck-Poisson equations for the potential profile across a membrane are exactly solved without recourse to the assumption of constant field within the membrane. It is assumed that the membrane core of thickness dc is covered by a surface layer of thickness ds in which the membrane-fixed charges are distributed at a uniform density N. The membrane boundary potentials as well as the diffusion potentials contribute to the membrane potential. It is shown that for ds greater or similar 1/k, k being the Debye-Hückel parameter, the potential in the membrane surface layer except in the region very near the membrane/solution boundary is effectively equal to the Donnan potential and that its contribution to the membrane potential becomes dominant as N increases. For low N, on the other hand, the membrane potential arises mostly from the diffusion potential.     

Electrostatic interaction between ion-penetrable multi-layered membranes

A theory of the double layer interaction regulated by the Donnan potential between two ion-penetrable membranes in an electrolyte solution developed previously by Ohshima and Kondo is extended to the case in which the membranes consist of many layers having different thickness and densities of membrane-fixed charges. The interaction force is found to be determined mainly by the contributions from layers located within the depth of 1/kappa (kappa, Debye-Hückel parameter) from the membrane surface. It is also predicted that the interaction force may alter its sign with changing electrolyte concentration.     

pH dependence of electrostatic interaction between ion-penetrable membranes

A theory on the electrostatic repulsion between ion-penetrable membranes proposed previously by us is extended by taking into account the degree of dissociation of the membrane-fixed ionizable groups. A system of equations which determines the pH dependence of the membrane interaction is presented. The density of membrane-fixed charges is consistently determined as a function of the electric potential so that both the membrane-fixed charge density and the potential are not constant but functions of the membrane separation. The pH at the surface of interacting membranes is also calculated as a function of the membrane separation.     

The net electric charge of proteins. A comparison of determinations by Donnan potential measurements and by gel electrophoresis

We compare a new method for the determination of the net charge of proteins based on Donnan potential measurements, as described briefly by Ojteg, G., Nygren, K. and Wolgast, M. (1987) Acta Physiol. Scand. 129, 277-286, with a conventional method using polyacrylamide gel electrophoresis. The new technique utilizes the Donnan potential, which develops over a semipermeable membrane that separates the non-permeating protein from the surrounding bath of the same ionic composition as the protein solution, to determine the net valency. The advantages of this method, besides its simplicity, are that it can determine the charge of, e.g., a protein in a free-fluid phase and that the pH and ionic composition of the bathing fluid can be varied over a broad range. The Donnan potential decreased to half its original value when the ionic strength was doubled. Usually a protein concentration of 1-10 mg.ml-1 must be used. The Donnan potential method was applied to determine the net charges of a series of proteins with different isoelectric points. The values showed close agreement with the data obtained by gel electrophoresis.     

Physical properties of the cell wall of photoautotrophic suspension cells fromChenopodium rubrum L.

Photoautotrophic suspension cells ofChenopodium rubrum were used to determine Donnan potential, charge density and pore-radius distribution in the cell wall. Experiments were done either with turgescent cells or with isolated cell walls. Titration of a cell-wall-generated 9-aminoacridine fluorescence quench with salts of mono- and divalent cations was used to determine Donnan potential and charge density. The experiments and theory were adapted from measurements of membrane surface charges. A tenfold increase in ionic strength, which decreases the repellant forces between charges of the same sign, led to an approximately threefold increase in the measured charge density, thus resulting in a much smaller decrease of the Donnan potential than would be expected if the charge density remained fixed. This decreased influence of ionic strength on the Donnan potential, resulting from the elasticity of the cell wall, was also measurable but less pronounced when the wall of intact cells was stretched by turgor. The porosity of the cell wall was determined by longterm uptake of polyethylene glycols of different molecular weights, and by gel filtration of polyethylene glycols and dextrans as well as mono- and disaccharides using intact suspension cells as matrix. Both methods gave a mean pore diameter of about 4.5 nm and a maximum pore size of 5.5 nm. The resulting pores-size distribution was slightly broader with the latter method.Abbreviations 9-AA 9-aminoacridine - DMBr₂ decamethoniumbromide=N,N,N,N,N,N hexamethyldecane-1,10-diaminebromide - DW dry weight after lyophilization - EDTA ethylene diaminetetra acetic acid - EGTA ethylene glycol-bis(-aminoethyl ether)-N,N,N,N-tetraacetic acid - FW fresh weight - Mops 3-(N-morpholino)propanesulfonic acid - MW molecular weight - PEG polyethylene glycol     

The relationship between the poisson-boltzmann model and the condensation hypothesis: an analysis based on the low salt form of the Donnan coefficient

Two common models for the interaction of counterions with cylindrical polyions are considered in the context of the Donnan membrane equilibrium. General analytic expressions are obtained from the Poisson-Boltzmann equation for the Donnan coefficient in terms of the potential at the surface of the polyion or the local concentration of unbound ions at the surface. Analysis based on these expressions shows that if, and only if, the polyion charge density exceeds a certain critical value a large local concentration of ions will persist near the polyion surface at low ionic strengths. We therefore conclude that this principal hypothesis of the condensation model is consistent with the characteristics of the Poisson-Boltzmann potential at the surface of the polyion.     

Donnan potentials from striated muscle liquid crystals. Lattice spacing dependence.

Electrochemical potentials were measured as a function of myofilament packing density in crayfish striated muscle. The A-band striations are supramolecular smectic B1 lattice assemblies of myosin filaments and the I-band striations are nematic liquid crystals of actin filaments. Both A- and I-bands generate potentials derived from the fixed charge that is associated with structural proteins. In the reported experiments, filament packing density was varied by osmotically reducing lattice volume. The electrochemical potentials were measured from the A- and I-bands in the relaxed condition over a range of lattice volumes. From the measurements of relative cross-sectional area, unit-cell volume (obtained by low-angle x-ray diffraction) and previously determined effective linear charge densities (Aldoroty, R.A., N.B. Garty, and E.W. April, 1985, Biophys. J., 47:89-96), Donnan potentials can be predicted for any amount of compression. In the relaxed condition, the predicted Donnan potentials correspond to the measured electrochemical potentials. In the rigor condition, however, a net increase in negative charge associated with the myosin filament is observed. The predictability of the data demonstrates the applicability of Donnan equilibrium theory to the measurement of electrochemical potentials from liquid-crystalline systems. Moreover, the relationship between filament spacing and the Donnan potential is consistent with the concept that surface charge provides the necessary electrostatic force to stabilize the myofilament lattice.     

Glycine transport by hemolysed and restored pigeon red cells. Effects of a Donnan-induced electrical potential on entry and exit kinetics.

The influence of a Donnan effect on the transport of glycine by hemolysed and restored pigeon red cells was examined. The Donnan effect was produced by replacing Cl- with 2,4-toluenedisulfonate or glutamate. The effects of the associated membrane potential and inside-outside pH difference on glycine entry and exit rates were examined. The effects of pH on entry and exit rates in the absence of a Donnan effect were also examined. In the absence of a Donnan effect, Na+-dependent glycine entry requires the protonated form of a group with a pKapp of 7.9 and the deprotonated form of another group with a pKapp of 6.8. Neither of these are required for exit but the deprotonated form of a group(s) with a pKapp of 6.2 is required. The pK 7.9 group and pK 6.2 group probably react with H+ at the inner face of the membrane and the pK 6.8 group probably reacts at the outer face. The V for glycine entry was determined for cells with their Cl- largely replaced by toluenedisulfonate and without such replacement. Between pH 6.1 and 7, the ratio of the respective V values, VT/VC1, was 1.5-1.7. VT/VC1 rose above pH 7 to near 4 at pH 8.3. At pH 6.9, with glutamate replacing cell Cl-, the analogous ratio (VGlu/VC1) was 1.7. The increase of VT/VC1 above pH 7 could be quantitatively accounted for by the increase in cell [H+]/medium [H+] caused by the Donnan effect together with the assumption that the pK 7.9 group reacts with H+ at the inner face of the membrane. When cell Cl- was replaced by toluenedisulfonate or glutamate there was a drop in the term in the glycine Km describing Na+ dependence of glycine entry. When cell Cl- was replaced by toluenedisulfonate therewas a rise in the Na+-independent term in the glycine entry Km. By replacing varying amounts of cell Cl- with either toluenedisulfonate or glutamate, plots were obtained of entry rates vs. the cell [Cl-]/ medium [Cl-] ratio consistent with the assumption that the Donnan-induced membrane potential acts on a "moving" charge. Glycine exit was only slightly accelerated by trans-toluenedisulfonate. The ratio, exit rate into toluenedisulfonate medium/exit rate into Cl- medium rose with decreasing pH. This rise could be accounted for by a Donnan-induced inside-outside pH difference which affects a pKapp 6.2 group reacting with internal H+. The observed influences of the Donnan effect on V (glycine entry), on both components of Km (glycine entry), on the shape of the plot of glycine entry rate vs. the cell [Cl-]/medium [Cl-] ratio and on glycine exit all fit the assumptions that when the empty porter reorients, one unit of negative charge accompanies it "across" the membrane and that no other steps involve charge movement. The properties of the system seem inconsistent with a translational ("ferry boat") mobile carrier.     

The surface potential on the purple membrane measured using a modified bacteriorhodopsin chromophore as the spectroscopic probe

The surface potential of the purple membrane was measured by a novel method by using an artificial bacteriorhodopsin whose chromophore was 13-CF₃ retinal instead of retinal. When attached to the apoprotein by a Schiff base, the intrinsic pK of the 13-CF₃ chromophore is around 7.3. The apparent p_K of this pigment depends on the surface potential and thus on the electrolyte concentration. This allowed us to determine the surface charge density using the Gouy-Chapman equation. The surface charge density was found to be −1.65 ± 0.15 × 10⁻³ electronic charges per Ų or about 2 negative charges/bacteriorhodopsin. This large value for the surface potential probably explains both part of the strong apparent association of divalent cations with the membrane and the effect of low salt concentrations on light-induced proton release from the purple membrane.     

Changes in the membrane surface charge density and/or membrane potential of the porcine intestinal brush-border membrane vesicles induced by treatment with neuraminidase

The effects of neuraminidase treatment on the membrane surface charge density and/or membrane potential of the porcine intestinal brush-border membrane vesicles were studied by using three fluorescent dyes, 1,6-diphenyl-1,3,5-hexatriene (DPH), 1-anilino-8-naphthalene sulfonate (ANS), and 3,3'-dipropyl-2,2'-thiadicarbocyanine iodide (DiS-C3(5]. The results of quenching studies of DPH-labeled membranes using cationic (T1+) and anionic (I-) quenchers suggested an increase of negative charge on the membrane surface by desialylation upon neuraminidase treatment. This interpretation was further supported by a decrease of ANS-binding affinity of the membranes after treatment with the enzyme. In addition, the degree of valinomycin-induced fluorescence change of DiS-C3(5)-probed membranes in the presence of various concentrations of KCl was reduced by treatment of the membranes with neuraminidase. This suggests that penetration of the dye molecules into the vesicle interior is facilitated by the treatment. The membrane potentials estimated from the null point of valinomycin-induced changes in the DiS-C3(5) fluorescence of the control and neuraminidase-treated membranes were -25 to -29.7 and -40 to -48.8 mV, respectively. From these results, it is suggested that the membrane surface charge density and/or membrane potential of the intestinal brush-border membranes are susceptible to modification of carbohydrate moieties on the membrane surface by neuraminidase treatment.     

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.     

Average electrostatic potential between the filaments in striated muscle and its relation to a simple Donnan potential.

An approximate analytical solution to the Poisson-Boltzmann equation for a cylindrical particle was used to calculate the relationship between the charge on the filaments and the average electrostatic potential. Both thick and then filaments were considered in the muscle lattice with a filament charge ratio of 4 to 1. Comparing this with a similar relationship obtained using simple Donnan theory showed a discrepancy at high charge where the Poisson-Boltzmann equation leads to saturation of the average potential. However, using two separate experiments from the literature, we have shown that at pH 7.0 muscle must not be close to saturation and thus is in a region of the curve where the two approaches agree.     

Surface potential determination in planar lipid bilayers: a simplification of the conductance-ratio method

One of the methods available for the measurement of surface potentials of planar lipid bilayers uses the conductance ratio between a charged and a neutral bilayer doped with ionophores to calculate the surface potential of the charged bilayer. We have devised a simplification of that method which does not require the use of an electrically neutral bilayer as control. The conductance of the charged bilayer is measured before and after the addition of divalent cations (Ba(2+)) to the bathing solution. Ba(2+) ions screen fixed surface charges, decreasing the surface potential. If the membrane is negatively charged the screening has the effect of decreasing the membrane conductance to cations. The resulting conductance ratio is used to calculate the surface potential change, which is fed into an iterative computer program. The program generates pairs of surface potential values and calculates the surface charge density for the two conditions. Since the surface charge density remains constant during this procedure, there is only one pair of surface potentials that satisfies the condition of constant charge density. Applying this method to experimental data from McLaughlin et al. [McLaughlin, S.G.A., Szabo, G. and Eisenman, G., Divalent ions and the surface potential of charged phospholipid membranes, J. Gen. Physiol., 58 (1971) 667-687.] we have found very similar results. We have also successfully used this method to determine the effect of palmitic acid on the surface potential of asolectin membranes.     

The surface membrane potential in a fluctuating medium]

Fluctuations of the surface membrane potential due to adsorbtion and desorbtion of ions when environmental fluctuations generate a fluctuation in the number of adsorbtion sites were investigated. The correlation functions of surface charge density, surface potential and the spectral density of surface potential fluctuations were calculated. The characteristic features of these fluctuations were determined.     

Analysis of electrophoretic mobility data for human erythrocytes according to sublayer models

An attempt was made to analyze the electrophoretic mobility data of human erythrocytes in media of different pH values and ionic strengths through cell surface models in which the surface charge layer consists of several ion-penetrable sublayers with a uniform charge distribution in each sublayer. As a result, the three-sublayer model was found to explain the mobility data much better than the two-sublayer model in a wide range of ionic strength at all pH values studied.