Polyelectrolyte Charge Corrected Molecular Weight and Effective Charge by Sedimentation

Ionic charge on a macromolecule complicates the determination of its molecular weight in solution due to the Donnan effect. Compensation for it can be made if one knows the value of the effective charge, which can be found by dialysis equilibrium across a semipermeable membrane. A moving boundary of molecules sedimenting in a centrifugal field can act as a membrane, obviating some of the disadvantages (such as selective adsorption) of a real membrane. Interference optics are used to monitor the reverse gradient of the salt due to the Donnan effect, hence facilitating the determination of the effective charge. The apparent molecular weight obtained from a conventional sedimentation equilibrium can then be corrected to yield the true molecular weight. The effective charge is valuable in revealing macromolecular structural features when related to the titratable charge through the Manning counter-ion condensation theory. Agreement between the values of the backbone molecular weights for the Na, Cs, and Ca salts of heparin indicated the validity of the approach. The effective charge ratio and the axial charge spacing for the Na and Ca heparin agreed with the literature, whereas the results for Cs indicated a degree of binding in excess of that due to counter-ion condensation.     

Electric field dependence of alamethicin channels.

Circular dichroism (CD) of alamethicin embedded in vesicular membranes from outside, and its change, upon imposing Donnan potentials across the membrane, was measured. The changes in CD suggested a decrease in a helicity and increase in beta structure with the membrane potential positive inside and vice versa when the potential was positive on the outer side of the vesicles from where the alamethicin was inserted into the membrane. The Donnan potential was created by entrapping the polyacrylate (PA-) in the vesicles and changing the salt concentration outside or by adding different concentrations of PA- or polyethyleneimide (PEI+) at the outside of vesicles with 2 x 10(-5) M salt inside. The effect of the potential on the CD spectra and thus the alamethicin conformation is independent on the type of the polyelectrolyte employed for the Donnan potential generation.     

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.     

Computation of the Electrical Double Layer Properties of Semipermeable Membranes in Multicomponent Electrolytes

A methodology is presented for calculating of the surface potential, Donnan potential, and ion concentration profiles for semipermeable microbial membranes that is valid for an arbitrary electrolyte composition. This model for surface potential, Donnan potential, and charge density was applied to recently reported experimental data for gram-positive bacteria, including Bacillus brevis, Rhodococcus opacus, Rhodococcus erythropolis, and Corynebacterium species. These calculations show that previously unconsidered trace amounts of divalent and trivalent cations at very low concentrations (10⁻⁶ M) can have significant effects on the calculated surface and Donnan potentials, at ionic strengths of I ≤ 0.01 M, and that these effects need to be considered in accurate modeling of microbial surface. In addition, the calculated ion concentration profiles show that owing to the relatively high surface charges that can develop in microbial membranes, electrostatic effects can act to significantly concentrate divalent (factors of 5 × 10³) and trivalent (factors of 2 × 10⁴) cations within the bacterial cell wall. Comparison of the calculated concentration factors with those derived from experiments shows that a significant fraction of the uptake of metal by bacteria can be explained by the proposed electrostatic model.     

The Origin of Bioelectrical Potentials in Plant and Animal Cells

The electrical potential difference across a plant or animalcell membrane can be caused by at least three different mechanisms,acting alone or in concert. First, a Donnan equilibrium canaccount for a sizable membrane potential without the participationof any active transport process. In a Donnan equilibrium themembrane potential is generated by the diffusion of permeatingions down their concentration gradients. The asymmetric distributionof permeating ions is caused by the presence of charged, nondiffusibleions, e.g., proteins inside the cell. The second mechanism isan electrically neutral ion pump, e.g., the coupled sodium-potassiumpump found in many types of cells. An electrically neutral pumpcan generate a large membrane potential if the membrane hasa high passive permeability to one of the actively transportedions, usually potassium. The third mechanism is an electrogenicion pump, which makes a substantial contribution to the membranepotential in several types of plant and animal cells. An electrogenicpump directly causes a net movement of charge across the cellmembrane. The membrane voltage generated by the pump then causesa passive flow of diffusible ions which partially short circuitsthe potential difference generated by the pump.     

Porin channels in intact cells of Escherichia coli are not affected by Donnan potentials across the outer membrane

Donnan potential (interior negative) across the outer membrane of Escherichia coli was measured by the distribution of [14C]choline in a mutant with a deletion through the genes for the active transport of choline. Calculation showed that the presence of membrane-derived oligosaccharides in the periplasm could quantitatively explain the magnitude of the Donnan potential and the periplasmic volume. By measuring the permeability of porin channels in intact cells suspended in solutions of widely different ionic strengths, it was shown that changing Donnan potential from 5 mV to approximately 100 mV had no effect on the permeability of either OmpF or OmpC porin channel toward a zwitterionic compound, cephaloridine. Thus, the "voltage-dependent gating" of porin channel, previously reported from another laboratory, is likely to be an artifact of in vitro reconstitution. The influx of negatively charged compounds, however, was affected by the Donnan potential as expected from the electrolyte diffusion theory.     

Relationship among the surface potential, Donnan potential and charge density of ion-penetrable membranes

Calculation of the potential distribution across a uniformly charged ion-penetrable membrane that we developed previously is extended to derive a relationship among the surface potential, Donnan potential and charge density of an ion-penetrable membrane in a mixed solution of 2-1 and 1-1 electrolytes. We also present an approximate method for calculating the surface potential/Donnan potential/charge density relationship for membranes with an arbitrary distribution of membrane-fixed charges.     

The Donnan Equilibrium: A Theoretical Study of the Effects of Interionic Forces

We investigate the conditions under which nonideality in solution influences the Donnan equilibrium. Of the various parameters that characterize this equilibrium, the osmotic pressure established across the Donnan membrane is found to be particularly sensitive to intermolecular interactions between the diffusible and nondiffusible ionic species. Under physiologically appropriate conditions, we find that it is almost never valid to use Debye-Hückel theory to calculate ionic activities: it is important to take proper account of ion size. When the diffusible species is a 1-1 electrolyte, this can be done using the mean spherical approximation (MSA) for a mixture of ions of different diameters. For 2-2, or higher-valent, electrolytes one should also include the effects of the second ionic virial coefficient, which the MSA omits.     

Mass Balance Model with Donnan Equilibrium Accurately Describes Unusual pH and Excipient Profiles during Diafiltration of Monoclonal Antibodies

There is extensive experimental data showing that the final pH and buffer composition after protein diafiltration (DF), particularly with monoclonal antibodies, can be considerably different than that in the DF buffer due to electrostatic interactions between the charged protein and the charged ions. Previous models for this behavior have focused on the final (equilibrium) partitioning and are unable to explain the complex pH and concentration profiles during the DF process. The objective of this study is to develop a new model for antibody DF based on solution of the transient mass balance equations, with the permeate concentrations of the charged species evaluated assuming Donnan equilibrium across the semipermeable membrane in combination with electroneutrality constraints. Model predictions are in excellent agreement with experimental data obtained during DF of both acidic and basic monoclonal antibodies, with the protein charge determined from independent electrophoretic mobility measurements. The model is able to predict the entire pH/histidine concentration profiles during DF, providing a framework for the development of DF processes that yield the desired antibody formulation.     

Studies on Ion Accumulation in Muscle Cells

A comparison is made between the quantitative predictions of equilibrium ionic distribution in living cells according to the membrane theory (Donnan equilibrium) and according to the association-induction hypothesis. This comparison shows that both theories predict competitive effects of one permeant ion on the equilibrium concentration of another permeant ion; but within the limit of experimental accuracy only the association-induction model predicts quantitatively significant specific competition of one specified ion with the accumulation of another specified ion. The equilibrium distributions of K⁺, Rb⁺, and Cs⁺ ions in frog sartorius muscle were studied and quantitatively significant specific competition was demonstrated; these results favor the association-induction hypothesis (adsorption on cell proteins and protein complexes and partial exclusion from cell water). Based on this model we estimated that at 257deg;C, the apparent association constants for K⁺, Rb⁺, and Cs⁺ ion are 665, 756, and 488 (mole/liter)^-1. We found that the total concentration of adsorption sites (no less than 240 mmole/kg of fresh cells) agrees with the analytically determined concentrations of β- and γ-carboxyl groups of muscle cell proteins (260 to 288 mmole/kg).     

Theoretical evaluation of a possible nature of the outer membrane potential of mitochondria

A possibility of generation of the outer membrane potential in mitochondria has been suggested earlier in the literature, but the potential has not been directly measured yet. Even its nature, metabolic impact and a possible range of magnitudes are not clear, and require further theoretical and experimental analysis. Here, using simple mathematical model, we evaluated a possible contribution of the Donnan and metabolically derived potentials to the outer membrane potential, concluding that the superposition of both is most probable; exclusively Donnan origin of the potential is doubtful because unrealistically high concentrations of charged macromolecules are needed for maintaining its relatively high levels. Regardless of the mechanism(s) of generation, the maximal possible potential seems to be less than 30 mV because significant osmotic gradients, created at higher values, increase the probability of the outer membrane rupture. New experimental approaches for direct or indirect determination of true value of the outer membrane potential are suggested here to avoid a possible interference of the surface electrical potential of the inner membrane, which may change as a result of the extrusion of matrix protons under energization of mitochondria.     

THE COLLOIDAL BEHAVIOR OF SERUM GLOBULIN

1. The globulin prepared from ox serum by dilution and precipitation with carbon dioxide has been found, by electrometric titration experiments, to behave like an amphoteric electrolyte, reacting stoichiometrically with acids and bases. 2. The potential difference developed between a solution of globulin chloride, phosphate, or acetate and a solution of the corresponding acid, free from protein, separated from the globulin by a collodion membrane, was found to be influenced by hydrogen ion concentration and salt concentration in the way predicted by Donnan''s theory of membrane equilibrium. In experiments with sodium globulinate and sodium hydroxide it was found that the potential difference could be similarly explained. 3. The osmotic pressure of such solutions could be qualitatively accounted for by the Donnan theory, but exhibited a discrepancy which is explicable by analogy with certain experiments of Loeb on gelatin. 4. The application of Loeb''s theory of colloidal behavior, which had previously been found to hold in the case of gelatin, casein, egg albumin, and edestin, has thus been extended to another protein, serum globulin.     

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'.     

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.     

The theoretical distributions and diffusivities of small ions in chondroitin sulphate and hyaluronate

The electrostatic interactions between polyionic glycosaminoglycans and small mobile ions are investigated using the Poisson-Boltzmann equation and a rod-in-cell model of the polyelectrolyte. Calculations are made for the range of polyelectrolyte concentrations and buffer compositions for which measurements of ion distributions and diffusivities are reported in a companion paper (Maroudas et al., Biophys. Chem. 32 (1988) 257). We conclude that the distribution of mobile ions is largely determined by the 'far-field' potential and is adequately described by the Poisson-Boltzmann theory and also by more approximate theories such as ideal Donnan or 'condensation' theory. The measured variations in cation diffusivities, particularly the increase in diffusivity with increasing matrix concentration at low ionic strengths, are predicted qualitatively using an approximate diffusion theory together with the calculated potential fields. However, the same theory applied to anion diffusion gives qualitatively wrong results.     

Active Ion Transport Across Canine Blood Vessel Walls

Experiments giving evidence of active Na and Cl ion fluxes across large canine blood vessel walls (aorta, vena cava) in vitro have been presented. The information has been obtained using ion tracer techniques after Ussing and with diffusion cells of the Hogben type. The available data suggest that the membranes are satisfactorily oxygenated by the bathing solutions saturated with oxygen at atmospheric pressure. Evidence is offered which indicates that active ion transport does occur across the aorta and vena cava in in vitro experiments. Under the conditions of the experiment net Na and Cl flux takes place from intima to adventitia across the aorta, and from adventitia to intima across the vena cava at low measured potential differences. The possible relationships of derangement of active ion transport mechanisms, produced by electric currents and tissue injury potential differences, to intravascular thrombosis are alluded to. It would appear that sodium and chloride fluxes across large blood vessel walls in vitro occur at least in part as the result of metabolic processes and cannot be explained simply on the basis of diffusion across a semipermeable membrane.     

Low frequency changes in skin surface potentials by skin compression: experimental results and theories

Human living skin generates an increase in the skin potential when compressed. This was measured on eight subjects with a matrix of nine Ag/AgCl electrodes. The potential increased with the pressure until it reached a maximum. When the pressure was increased stepwise, the response showed an overshoot at each step. Human cadaver skin did not show these potential increments. Neither did pads of collagen, paper tissue soaked in a KCl solution, nor layers of cultured keratinocytes. Three theories are described that may explain the origin of the measured skin potentials. The first is based on the piezoelectric characteristics of proteins in the skin. The second theory assumes that the skin is a charged membrane which generates a streaming potential when deformed. A third theory is proposed in which deformation of absorbed charged protein layers on structures in the skin change the alignment of Donnan potentials in the surrounding tissue.     

Stem cell recovering effect of copper‐free GHK in skin

The peptide Gly‐His‐Lys (GHK) is a naturally occurring copper(II)‐chelating motifs in human serum and cerebrospinal fluid. In industry, GHK (with or without copper) is used to make hair and skin care products. Copper‐GHK plays a physiological role in the process of wound healing and tissue repair by stimulating collagen synthesis in fibroblasts. We also reported that copper‐GHK promotes the survival of basal stem cells in the skin. However, the effects of copper‐free GHK (GHK) have not been investigated well. In this study, the effects of GHK were studied using cultured normal human keratinocytes and skin equivalent (SE) models. In monolayer cultured keratinocytes, GHK increased the proliferation of keratinocytes. When GHK was added during the culture of SE models, the basal cells became more cuboidal than control model. In addition, there was linear and intense staining of α6 and β1 integrin along the basement membrane. The number of p63 and proliferating cell nuclear antigen positive cells was also significantly increased in GHK‐treated SEs than in control SEs. Western blot and slide culture experiment showed that GHK increased the expression of integrin by keratinocytes. All these results showed that GHK increased the stemness and proliferative potential of epidermal basal cells, which is associated with increased expression of integrin. In conclusion, copper‐free GHK showed similar effects with copper‐GHK. Thus, it can be said that copper‐free GHK can be used in industry to obtain the effects of copper‐GHK in vivo. Further study is necessary to explore the relationship between copper‐free GHK and copper‐GHK. Copyright © 2012 European Peptide Society and John Wiley & Sons, Ltd.     

Intracellular pH of Thermoplasma acidophila.

Thermoplasma acidophila, a mycoplasma-like organism, was grown at 56 degrees C and pH 2. The intracellular pH of this organism is close to neutral as measured by the distribution of a radioactive weak organic acid, 5,5-dimethyl-2,4-oxazolidinedione, across the plasma membrane. The cell can maintain the pH gradient when subjected to heat or to metabolic inhibitors. Our experiments seem to indicate that a major portion of the pH gradient is not maintained by active processes, but rather by a Donnan potential across the cell membrane.