Investigation of ionic stability criteria for ion-permeable charged membranes

The flocculation criteria in the DLVO theory of colloid stability are applied to ion-permeable membranes containing ionizable fixed groups. These groups are not restricted to the membrane surface but are uniformly distributed throughout a thick surface layer. The flocculation concentrations for such membranes are calculated by using a numerical method to solve the nonlinear Poisson-Boltzmann equation. Results are compared with calculations previously carried out for more restrictive models of biological membranes. The flocculation concentrations are shown to depend on the density of ionizable groups, the dissociation constant of these groups, and the pH of the bulk solution.     

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.     

Electrostatic coupling across a membrane with titratable surface groups

The potential drop across a membrane is calculated for the case of ionizable groups on both membrane surfaces. The presence of both acid and amine groups on the membrane surfaces is considered. The membrane surface potential is obtained from the non-linear Poisson-Boltzmann equation by treating the fraction of dissociated ionizable surface groups as a self-consistent functional of the electrostatic potential. A discussion of the error due to ignoring the electrostatic coupling of the potential across the membrane is presented. The error turns out to be quite small for most membrane problems of biological interest. Finally, the conductance data of Mozhayeva & Naumov (1970) for the frog node are reanalyzed within the context of the diffuse double layer theory. It is shown to be unnecessary to invoke a specific binding of divalent cations to the membrane.     

Electrostatic effects in proteins: comparison of dielectric and charge models.

Two approaches for calculating electrostatic effects in proteins are compared and ana analysis is presented of the dependence of calculated properties on the model used to define the charge distribution. Changes in electrostatic free energy have been calculated using a screened Coulomb potential (SCP) with a distance-dependent effective dielectric permittivity to model bulk solvent effects and a finite difference approach to solve the Poisson-Boltzmann (FDPB) equation. The properties calculated include shifts in dissociation constants of ionizable groups, the effect of annihilating surface charges on the binding of metals, and shifts in redox potentials due to changes in the charge of ionizable groups. In the proteins considered the charged sites are separated by 3.5-12 A. It is shown that for the systems studied in this distance range the SCP yields calculated values which are at least as accurate as those obtained from solution of the FDPB equation. In addition, in the distance range 3-5 A the SCP gives substantially better results than the FDPB equation. Possible sources of this difference between the two methods are discussed. Shifts in binding constants and redox potentials were calculated with several standard charge sets, and the resulting values show a variation of 20-40% between the 'best' and 'worst' cases. From this study it is concluded that in most applications, changes in electrostatic free energies can be calculated economically and reliably using an SCP approach with a single functional form of the screening function.     

pH and excipient profiles during formulation of highly concentrated biotherapeutics using bufferless media

Several models have been developed to describe the shifts in pH and excipient concentrations seen during diafiltration of monoclonal antibody (mAb) products accounting for both Donnan equilibrium and electroneutrality constraints. However, these models have assumed that the mAb charge is either constant or only a function of pH, assumptions that will not be valid when formulating highly concentrated mAbs using bufferless or low-buffered media due to the change in local H⁺ concentration at the protein surface. The objective of this study was to incorporate the effects of both pH and ionic strength on the mAb charge, through the use of a charge regulation model based on the amino acid sequence of the mAb, into an appropriate mass balance model to describe the pH and excipient profiles during diafiltration. The model involves no adjustable parameters, with the protein charge evaluated directly from the protonation/deprotonation of the ionizable amino acids accounting for the electrostatic interactions between the charged mAb and the H⁺ ions. Model predictions are in excellent agreement with experimental data for the pH and ion concentrations during diafiltration of a mAb and fusion protein with different isoelectric points and different formulation conditions. Model simulations are then used to obtain fundamental insights into the factors controlling the diafiltration behavior as well as guidelines for development of diafiltration processes to achieve target bufferless formulation conditions.     

Membrane interactions in nerve myelin. I. Determination of surface charge from effects of pH and ionic strength on period.

We have used x-ray diffraction to study the interactions between myelin membranes in the sciatic nerve (PNS) and optic nerve (CNS) as a function of pH (2-10) and ionic strength (0-0.18). The period of myelin was found to change in a systematic manner with pH and ionic strength. PNS periods ranged from 165 to 250 A or more, while CNS periods ranged from 150 to 230 A. The native periods were observed only near physiological ionic strength at neutral or alkaline pH. The smallest periods were observed in the pH range 2.5-4 for PNS myelin and pH 2.5-5 for CNS myelin. The minimum period was also observed for PNS myelin after prolonged incubation in distilled water. At pH 4, within these acidic pH ranges, myelin period increased slightly with ionic strength; however, above these ranges, the period increased with pH and decreased with ionic strength. Electron density profiles calculated at different pH and ionic strength showed that the major structural alteration underlying the changes in period was in the width of the aqueous space at the extracellular apposition of membranes; the width of the cytoplasmic space was virtually constant. Assuming that the equilibrium myelin periods are determined by a balance of nonspecific forces/i.e., the electrostatic repulsion force and the van der Walls attractive force, as well as the short-range repulsion force (hydration force, or steric stabilization), then values in the period-dependency curve can be used to define the isoelectric pH and exclusion length of the membrane. The exclusion length, which is related to the minimum period at isoelectric pH, was used to calculate the electrostatic repulsion force given the other forces. The electrostatic repulsion was then used to calculate the surface potential, which in turn was used to calculate the surface charge density (at different pH and ionic strength). We found the negative surface charge increases with pH at constant ionic strength and with ionic strength at constant pH. We suggest that the former is due to deprotonation of the ionizable groups on the surface while the latter is due to ion binding. Interpretation of our data in terms of the chemical composition of myelin is given in the accompanying paper (Inouye and Kirschner, 1988). We also calculated the total potential energy functions for the different equilibrium periods and found that the energy minima became shallower and broader with increasing membrane separation. Finally, it was difficult to account directly for certain structural transitions from a balance of nonspecific forces.(ABSTRACT TRUNCATED AT 400 WORDS)     

Algal Flocculation with Synthetic Organic Polyelectrolytes

The feasibility of removing algae from water and wastewater by chemical flocculation techniques was investigated. Mixed cultures of algae were obtained from both continuous- and batch-fed laboratory reactors. Representative cationic, anionic, and nonionic synthetic organic polyelectrolytes were used as flocculants. Under the experimental conditions, chemically induced algal flocculation occurred with the addition of cationic polyelectrolyte, but not with anionic or nonionic polymers, although attachment of all polyelectrolyte species to the algal surface is shown. The mechanism of chemically induced algal flocculation is interpreted in terms of bridging phenomena between the discrete algal cells and the linearly extended polymer chains, forming a three-dimensional matrix that is capable of subsiding under quiescent conditions. The degree of flocculation is shown to be a direct function of the extent of polymer coverage of the active sites on the algal surface, although to induce flocculation by this method requires that the algal surface charge must concurrently be reduced to a level at which the extended polymers can bridge the minimal distance of separation imposed by electrostatic repulsion. The influence of pH, algal concentration, and algal growth phase on the requisite cationic flocculant dose is also reported.     

Comparison of double layer potentials in lipid monolayers and lipid bilayer membranes

Summary It is shown that the Gouy-Chapman double layer analysis adequately describes the variation of the surface potential of monolayers of acidic natural lipids over a wide range of surface charge density and salt concentration. It is also shown that the potential which initially appears when an electrolyte gradient is rapidly imposed across a bilayer membrane is due to a difference in the double layer potentials on the two sides of the membrane. This conclusion follows from the fact that the observed bilayer potentials arise much more rapidly than can be accounted for by charge migration across the membrane and from the observation that the bilayer membrane concentration potentials, when measured immediately after establishment of a gradient, are equal to the surface potential change observed when the subphase concentration of a monolayer of the same lipid is changed by an amount equal to the gradient across the bilayer. The bilayer potential and monolayer potential changes, so measured, agree in a number of different electrolyte solutions over a wide range of electrolyte concentrations and surface charge densities. Because of this agreement and the applicability of the Gouy theory to monolayers, initial bilayer potentials may be calculated if the composition of the mixture used to form the membrane is known, provided that the pK's and areas of such components are available. In the absence of this information, membrane potentials may be calculated from electrophoretic data on the membrane lipid mixture; the conditions under which the latter approach is possible have been determined. The experimental results indicate that the composition of monolyers and bilayers spread from the same lipid mixture in decane are very similar, that the composition of the two types of film closely resembles the composition of the solution used to generate them, and that bilayer membranes are close-packed. The evidence further indicates that if any hydrocarbon solvent remains in these bilayers, it must be so situated that it contributes little, if anything, to the surface area. The steady state potential in the bilayer membrane system is frequently not identical with the initial potential which supports the hypothesis that in many cases only a fraction of the electrical conductance of unmodified membranes is caused by the ions which constitute the bulk electrolyte. An expression for the relationship between diffusion and double layer potentials has been derived which shows that, in the absence of any intrinsic selectivity of the hydrocarbon region of the membrane for hydrogen, hydroxyl, or impurity, the two potentials should be identical.     

A simple electrostatic model can explain the effect of pH upon the force-pCa relation of skinned frog skeletal muscle fibers.

The relative force-pCa relation of skinned frog skeletal muscle fibers is shifted along the pCa axis by changes in pH. This shift has been interpreted as arising from competition between H+ and Ca2+ for a binding site on troponin. Unfortunately, binding studies have been unable to confirm such competition. Alternatively, however, the data fit a model where H+ influences the degree of dissociation of ionizable groups on the surface of the thin filaments, thus altering the electrostatic potential surrounding the filaments. Alterations in the potential will, in turn, change the concentration of Ca2+ near the troponin binding sites in accordance with the Boltzmann relation. A simple model, based upon the Gouy-Chapman relation between surface potential and charge density, provides a quantitative explanation for the shift of the relative force-pCa curve with pH, given a reasonable estimate of the surface charge density on the thin filament. A best fit is obtained when the ionizable groups giving rise to the potential have a log proton ionization constant (pKa) of 6.1, similar to that for the imidazole group on histidine, and when the density of these groups is near that estimated from amino acid analysis of thin filament proteins and from filament geometry. In preliminary experiments, reaction of skinned frog fibers with diethylpyrocarbonate (DEP) at pH 6 shifted the force-pCa curve toward lower Ca2+. This would be expected in the model since DEP at pH 6 is reported to specifically react with histidine imidazole groups and to irreversibly decrease their pKa, which would increase the net negative charge of the filaments.     

Changes in surface-charge density of blood cells after sudden unexpected death

The objective of the investigation was evaluation of postmortem changes of electric charge of human erythrocyte and thrombocyte membranes after sudden unexpected death. The surface charge density values were determined on the basis of the electrophoretic mobility measurements of the cells carried out at various pHs of electrolyte solution. The interactions between both erythrocyte and thrombocyte membranes and electrolyte ions were studied. Values of parameters characterizing the membrane--that is, the total surface concentrations of both acidic and basic groups and their association constants with solution ions--were calculated on the basis of a four-equilibria mathematical model. The model was validated by comparison of these values to experimental data. We established that examined electric properties of the cell membranes are affected by sudden unexpected death. Postmortem processes occurring in the cell membranes can lead to disorders of existing equilibria, which in turn result in changes in values of all the above-mentioned parameters.     

The Effect of Surface Charge on the Voltage-Dependent Conductance Induced in Thin Lipid Membranes by Monazomycin

Differences in the behavior of phosphatidylethanolamine (PE) and phosphatidylglycerol (PG) thin lipid membranes treated with monazomycin are shown to be due to the negative surface charge on PG membranes. We demonstrate that shifts of the conductance-voltage (g-V) characteristic of PG films produced by changes of univalent or divalent cation concentrations result from changes of the membrane surface potential on one or both sides. In particular, if divalent cations are added to the aqueous phase not containing monazomycin, the resulting asymmetry of the surface potentials results in an intramembrane potential difference not recordable by electrodes in the bulk phases. Nevertheless, this intramembrane potential difference is "seen" by the monazomycin, and consequently the g-V characteristic is shifted along the voltage axis. These changes are accounted for by diffuse double layer theory. Thus we find it unnecessary to invoke specific binding of Mg⁺⁺ or Ca⁺⁺ to the negative charges of PG membranes to explain the observation that concentrations of these ions some 100-fold lower than that of the univalent cation present produce large shifts of the g-V characteristic. We suggest that analogous shifts of g-V characteristics in axons produced by changes of divalent cation concentration are also best explained by diffuse double layer theory.     

Analysis of potentiometric titrations of heterogeneous natural polyelectrolytes in terms of counterion condensation theory: application to humic acid

A model, developed within the framework of the counterion condensation theory of linear polyelectrolytes, is presented in this paper to describe the acid-base properties of linear polyelectrolytes, consisting of several types of functional ionizable groups. This formalism has been successfully applied to Fluka humic acid under salt-free conditions, as well as in the presence of supporting simple 1:1 salt (KNO3) at three different concentrations. As part of this approach, the charge density of the humic acid is obtained from the activity coefficient measurements of potassium counterions at different humic acid concentrations at a constant degree of dissociation of the polyelectrolyte. The humic acid average charge density was found to be 0.80 +/- 0.05. Using the present model, we are able to satisfactorily describe the experimental data obtained from acid-base potentiometric titrations. Four main functional groups making up the polymer are determined through their fractional abundances (Xi) and intrinsic pK (pK0i) values. The fractional abundances remained constant and independent of the ionic strength, indicating that the humic acid constitution does not depend on the concentration of excess salts. The pK0i values show a small change with ionic strength, which can be explained by the polyelectrolytic behavior of the solution.     

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)     

Critical conditions for ferric chloride-induced flocculation of freshwater algae

The effects of algae concentration, ferric chloride dose, and pH on the flocculation efficiency of the freshwater algae Chlorella zofingiensis can be understood by considering the nature of the electrostatic charges on the algae and precipitate surfaces. Two critical conditions are identified which, when met, result in flocculation efficiencies in excess of 90% for freshwater algae. First, a minimum concentration of ferric chloride is required to overcome the electrostatic stabilization of the algae and promote bridging of algae cells by hydroxide precipitates. At low algae concentrations, the minimum amount of ferric chloride required increases linearly with algae concentration, characteristic of flocculation primarily through electrostatic bridging by hydroxide precipitates. At higher algae concentrations, the minimum required concentration of ferric chloride for flocculation is independent of algae concentration, suggesting a change in the primary flocculation mechanism from bridging to sweep flocculation. Second, the algae must have a negative surface charge. Experiments and surface complexation modeling show that the surface charge of C. zofingiensis is negative above a pH of 4.0 ± 0.3 which agrees well with the minimum pH required for effective flocculation. These critical flocculation criteria can be extended to other freshwater algae to design effective flocculation systems.     

A model for cation content of plants based on surface potentials and surface charge densities of plant membranes

The model presented takes into account the interaction between the negatively charged membranes and macromolecules and the cations. A central postulate is that a constant average surface charge density (σ) as well as a constant average surface potential (Ψ) is conserved under different ionic conditions. The model makes it possible to predict the size of σ and Ψ from measurements of Na, K, Mg and Ca content in plant tissues of the same age but grown under two different ionic conditions (e.g. high and low K⁺). Assumptions were made about the relative amounts of free and bound Ca²⁺ and σ and Ψ were calculated from values in the literature. In all cases σ (and Ψ) are predicted to be higher for shoot (−29 to −96 mC m⁻²) than for root membranes (−14 to −27 mC m⁻²). In most cases the predicted σ falls within the range determined experimentally for biological membranes.     

Biphasic voltage relaxation pattern observed in cells of Eremosphaera viridis after injection of charge-pulses of short duration: detection of tip clogging of intracellular microelectrodes by charge-pulse technique

Charge pulse experiments performed on the peat-bog alga Eremosphaera viridis revealed an unusual voltage relaxation behaviour. Injection of charge pulses of 1 microseconds duration resulted in an immediate charging of the membranes (time constant of the order of 40 ns). Nevertheless, the potential-measuring microelectrode recorded an exponential increase in membrane voltage with a time constant of about 1.3 ms. The maximum voltage value was recorded after about 3 ms, followed by an exponential decay with a time constant of about 9.6 ms. This biphasic time course was independent of the amplitude of the injected charge and of the location of the impaled microelectrodes in the vacuole. Centrifuged cells in which the chloroplasts and the other organelles were pelleted in one part of the cells showed the same electrical response. Electrical breakdown of the cell membranes resulted in the disappearance of the biphasic voltage response. In this case only the decaying relaxation process could be recorded with a time constant of 3 ms. After resealing of the membranes the original biphasic relaxation response was restored. Increasing concentrations of KCl in the bathing medium reduced both time constants almost correspondingly. The experimental findings were evaluated with an electrical equivalent circuit. Theoretical analysis with reference to the experimental data suggested that the delayed voltage response of the potential-recording electrode resulted from a membrane seal across the tip of this electrode. The resistance of this seal was calculated to be about 400 M omega. The specific resistances and capacitances of tonoplast and plasmalemma membranes were calculated from the decaying part of the biphasic relaxation curves. The average values were found to be 2.58 omega.m2 and 5 mF.m-2. The investigations reported here suggest that charge pulse experiments can be generally used for the detection of membrane and cytoplasmic material clogging of the tip of intracellular microelectrodes, a problem with which most electrophysiologists are faced when interpreting data obtained from impaled microelectrodes.     

The role of the carboxyl and amino groups of polyene macrolides in their interactions with sterols and their selective toxicity. A P-NMR study

The permeability induced by amphotericin B and vacidin A derivatives in large unilamellar lipidic vesicles containing various sterols has been studied using the proton-cation exchange method and ³¹P-NMR spectroscopy. Derivatives which have a free ionizable carboxyl group induce biphasic ‘all or none’ permeability typical of channel-forming ionophores, whatever the sterol present. In sterol-free membranes, they have no significant activity. Derivatives which lack a free ionizable carboxyl group exhibit this channel-like mode of action only in membranes containing ergosterol or sterols with an alkyl side like that of ergosterol. In membranes containing cholesterol or sterol whose side-chain is alike, a slow and progressive permeability is observed at high concentrations. This activity is observed in sterol-free membranes as well. Derivatives containing sugars with substituted amino groups always have lower ionophoric activity than those which are unsubstituted. The greatest decrease in activity was observed for N-acetyl derivatives. Substitution of the amino groups has no effect on the mode of action. A model of interaction of polyenes with sterols is presented accounting for the data obtained on vesicles and the observed selective toxicity of polyene derivatives in biological membranes.     

Electrostatic interactions among hydrophobic ions in lipid bilayer membranes.

We have shown that the absorption of tetraphenylborate into black lipid membranes formed from either bacterial phosphatidylethanolamine or glycerolmonooleate produces concentration-dependent changes in the electrostatic potential between the membrane interior and the bulk aqueous phases. These potential changes were studied by a variety of techniques: voltage clamp, charge pulse, and "probe" measurements on black lipid membranes; electrophroetic mobility measurements on phospholipid vesicles; and surface potential measurements on phospholipid monolayers. The magnitude of the potential changes indicates that tetraphenylborate absorbs into a region of the membrane with a low dielectric constant, where it produces substantial boundary potentials, as first suggested by Markin et al. (1971). Many features of our data can be explained by a simple three-capacitor model, which we develop in a self-consistent manner. Some discrepancies between our data and the simple model suggest that discrete charge phenomena may be important within these thin membranes.