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.     

ON THE INFLUENCE OF AGGREGATES ON THE MEMBRANE POTENTIALS AND THE OSMOTIC PRESSURE OF PROTEIN SOLUTIONS

1. It is shown that when part of the gelatin in a solution of gelatin chloride is replaced by particles of powdered gelatin (without change of pH) the membrane potential of the solution is influenced comparatively little. 2. A measurement of the hydrogen ion concentration of the gelatin chloride solution and the outside aqueous solution with which the gelatin solution is in osmotic equilibrium, shows that the membrane potential can be calculated from this difference of hydrogen ion concentration with an accuracy of half a millivolt. This proves that the membrane potential is due to the establishment of a membrane equilibrium and that the powdered particles participate in this membrane equilibrium. 3. It is shown that a Donnan equilibrium is established between powdered particles of gelatin chloride and not too strong a solution of gelatin chloride. This is due to the fact that the powdered gelatin particles may be considered as a solid solution of gelatin with a higher concentration than that of the weak gelatin solution in which they are suspended. It follows from the theory of membrane equilibria that this difference in concentration of protein ions must give rise to potential differences between the solid particles and the weaker gelatin solution. 4. The writer had shown previously that when the gelatin in a solution of gelatin chloride is replaced by powdered gelatin (without a change in pH), the osmotic pressure of the solution is lowered the more the more dissolved gelatin is replaced by powdered gelatin. It is therefore obvious that the powdered particles of gelatin do not participate in the osmotic pressure of the solution in spite of the fact that they participate in the establishment of the Donnan equilibrium and in the membrane potentials. 5. This paradoxical phenomenon finds its explanation in the fact that as a consequence of the participation of each particle in the Donnan equilibrium, a special osmotic pressure is set up in each individual particle of powdered gelatin which leads to a swelling of that particle, and this osmotic pressure is measured by the increase in the cohesion pressure of the powdered particles required to balance the osmotic pressure inside each particle. 6. In a mixture of protein in solution and powdered protein (or protein micellæ) we have therefore two kinds of osmotic pressure, the hydrostatic pressure of the protein which is in true solution, and the cohesion pressure of the aggregates. Since only the former is noticeable in the hydrostatic pressure which serves as a measure of the osmotic pressure of a solution, it is clear why the osmotic pressure of a protein solution must be diminished when part of the protein in true solution is replaced by aggregates.     

The Electrical Conductance of Semipermeable Membranes: II. Unipolar Flow, Symmetric Electrolytes

A general formulation of the problem of stationary ion flow through semipermeable membranes was presented in the first paper of this series. The formalism is applied here to the evaluation of membrane conductance for the special case of unipolar ion flow between symmetric electrolytes. Thus it is assumed that the permeant ions carry one sign of charge only. Furthermore, the valences of all ions in solution on both sides of the membrane are taken to be of equal absolute magnitude. Conductance results obtained by numerical methods are presented for several representative sets of the parameters which characterize the membrane system in equilibrium. These results are discussed qualitatively with emphasis upon the contribution of particular system parameters to the non-linearities observed. Approximate analytic conductance relations, valid for high current levels, are also given.     

THE ORIGIN OF THE ELECTRICAL CHARGES OF COLLOIDAL PARTICLES AND OF LIVING TISSUES

1. When a solution of a salt of gelatin or crystalline egg albumin is separated by a collodion membrane from a watery solution (free from protein) a potential difference is set up across the membrane in which the protein is positively charged in the case of protein-acid salts and in which the protein is negatively charged in the case of metal proteinates. The turning point is the isoelectric point of the protein. 2. Measurements of the pH of the (inside) protein solution and of the outside watery solution show that when equilibrium is established the value pH inside minus pH outside is positive in the case of protein-acid salts and negative in the case of metal proteinates. This is to be expected when the P.D. is caused by the establishment of a Donnan equilibrium, since in that case the pH should be lower outside than inside in the case of a protein-acid salt and should be higher outside than inside in the case of a metal proteinate. 3. At the isoelectric point where the electrical charge is zero the value of pH inside minus pH outside becomes also zero. 4. It is shown that a P.D. is established between suspended particles of powdered gelatin and the surrounding watery solution and that the sign of charge of the particles is positive when they contain gelatin-acid salts, while it is negative when the powdered particles contain metal gelatinate. At the isoelectric point the charge is zero. 5. Measurements of the pH inside the powdered particles and of the pH in the outside watery solution show that when equilibrium is established the value pH inside minus pH outside is positive when the powdered particles contain a gelatin-acid salt, while the value pH inside minus pH outside is negative when the powdered particles contain Na gelatinate. At the isoelectric point the value pH inside minus pH outside is zero. 6. The addition of neutral salts depresses the electrical charge of the powdered particles of protein-acid salts. It is shown that the addition of salts to a suspension of powdered particles of gelatin chloride also diminishes the value of pH inside minus pH outside. 7. The agreement between the values 58 (pH inside minus pH outside) and the P. D. observed by the Compton electrometer is not only qualitative but quantitative. This proves that the difference in the concentration of acid (or alkali, as the case may be) in the two phases is the only cause for the observed P.D. 8. The Donnan theory demands that the P.D. of a gelatin chloride solution should be 1½ times as great as the P.D. of a gelatin sulfate solution of the same pH and the same concentration (1 per cent) of originally isoelectric gelatin. This is found to be correct and it is also shown that the values of pH inside minus pH outside for the two solutions possess the ratio of 3:2. 9. All these measurements prove that the electrical charges of suspended particles of protein are determined exclusively by the Donnan equilibrium.     

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.     

THE INFLUENCE OF ELECTROLYTES ON THE SOLUTION AND PRECIPITATION OF CASEIN AND GELATIN

1. Colloids have been divided into two groups according to the ease with which their solutions or suspensions are precipitated by electrolytes. One group (hydrophilic colloids), e.g., solutions of gelatin or crystalline egg albumin in water, requires high concentrations of electrolytes for this purpose, while the other group (hydrophobic colloids) requires low concentrations. In the latter group the precipitating ion of the salt has the opposite sign of charge as the colloidal particle (Hardy''s rule), while no such relation exists in the precipitation of colloids of the first group. 2. The influence of electrolytes on the solubility of solid Na caseinate, which belongs to the first group (hydrophilic colloids), and of solid casein chloride which belongs to the second group (hydrophobic colloids), was investigated and it was found that the forces determining the solution are entirely different in the two cases. The forces which cause the hydrophobic casein chloride to go into solution are forces regulated by the Donnan equilibrium; namely, the swelling of particles. As soon as the swelling of a solid particle of casein chloride exceeds a certain limit it is dissolved. The forces which cause the hydrophilic Na caseinate to go into solution are of a different character and may be those of residual valency. Swelling plays no rôle in this case, and the solubility of Na caseinate is not regulated by the Donnan equilibrium. 3. The stability of solutions of casein chloride (requiring low concentrations of electrolytes for precipitation) is due, first, to the osmotic pressure generated through the Donnan equilibrium between the casein ions tending to form an aggregate, whereby the protein ions of the nascent micellum are forced apart again; and second, to the potential difference between the surface of a micellum and the surrounding solution (also regulated by the Donnan equilibrium) which prevents the further coalescence of micella already formed. This latter consequence of the Donnan effect had already been suggested by J. A. Wilson. 4. The precipitation of this group of hydrophobic colloids by salts is due to the diminution or annihilation of the osmotic pressure and the P.D. just discussed. Since low concentrations of electrolytes suffice for the depression of the swelling and P.D. of the micella, it is clear why low concentrations of electrolytes suffice for the precipitation of hydrophobic colloids, such as casein chloride. 5. This also explains why only that ion of the precipitating salt is active in the precipitation of hydrophobic colloids which has the opposite sign of charge as the colloidal ion, since this is always the case in the Donnan effect. Hardy''s rule is, therefore, at least in the precipitation of casein chloride, only a consequence of the Donnan effect. 6. For the salting out of hydrophilic colloids, like gelatin, from watery solution, sulfates are more efficient than chlorides regardless of the pH of the gelatin solution. Solution experiments lead to the result that while CaCl₂ or NaCl increase the solubility of isoelectric gelatin in water, and the more, the higher the concentration of the salt, Na₂SO₄ increases the solubility of isoelectric gelatin in low concentrations, but when the concentration of Na₂SO₄ exceeds M/32 it diminishes the solubility of isoelectric gelatin the more, the higher the concentration. The reason for this difference in the action of the two salts is not yet clear. 7. There is neither any necessity nor any room for the assumption that the precipitation of proteins is due to the adsorption of the ions of the precipitating salt by the colloid.     

ELECTRICAL CHARGES OF COLLOIDAL PARTICLES AND ANOMALOUS OSMOSIS

1. It has been shown in previous publications that when solutions of different concentrations of salts are separated by collodion-gelatin membranes from water, electrical forces participate in addition to osmotic forces in the transport of water from the side of the water to that of the solution. When the hydrogen ion concentration of the salt solution and of the water on the other side of the membrane is the same and if both are on the acid side of the isoelectric point of gelatin (e.g. pH 3.0), the electrical transport of water increases with the valency of the cation and inversely with the valency of the anion of the salt in solution. Moreover, the electrical transport of water increases at first with increasing concentration of the solution until a maximum is reached at a concentration of about M/32, when upon further increase of the concentration of the salt solution the transport diminishes until a concentration of about M/4 is reached, when a second rise begins, which is exclusively or preeminently the expression of osmotic forces and therefore needs no further discussion. 2. It is shown that the increase in the height of the transport curves with increase in the valency of the cation and inversely with the increase in the valency of the anion is due to the influence of the salt on the P.D. (E) across the membrane, the positive charge of the solution increasing in the same way with the valency of the ions mentioned. This effect on the P.D. increases with increasing concentration of the solution and is partly, if not essentially, the result of diffusion potentials. 3. The drop in the transport curves is, however, due to the influence of the salts on the P.D. (ε) between the liquid inside the pores of the gelatin membrane and the gelatin walls of the pores. According to the Donnan equilibrium the liquid inside the pores must be negatively charged at pH 3.0 and this charge is diminished the higher the concentration of the salt. Since the electrical transport is in proportion to the product of E x ε and since the augmenting action of the salt on E begins at lower concentrations than the depressing action on ε, it follows that the electrical transport of water must at first rise with increasing concentration of the salt and then drop. 4. If the Donnan equilibrium is the sole cause for the P.D. (ε) between solid gelatin and watery solution the transport of water through collodion-gelatin membranes from water to salt solution should be determined purely by osmotic forces when water, gelatin, and salt solution have the hydrogen ion concentration of the isoelectric point of gelatin (pH = 4.7). It is shown that this is practically the case when solutions of LiCl, NaCl, KCl, MgCl₂, CaCl₂, BaCl₂, Na₂SO₄, MgSO₄ are separated by collodion-gelatin membranes from water; that, however, when the salt has a trivalent (or tetravalent?) cation or a tetravalent anion a P.D. between solid isoelectric gelatin and water is produced in which the wall assumes the sign of charge of the polyvalent ion. 5. It is suggested that the salts with trivalent cation, e.g. Ce(NO₃)₃, form loose compounds with isoelectric gelatin which dissociate electrolytically into positively charged complex gelatin-Ce ions and negatively charged NO₃ ions, and that the salts of Na₄Fe(CN)₆ form loose compounds with isoelectric gelatin which dissociate electrolytically into negatively charged complex gelatin-Fe(CN)₆ ions and positively charged Na ions. The Donnan equilibrium resulting from this ionization would in that case be the cause of the charge of the membrane.     

DONNAN EQUILIBRIUM AND THE PHYSICAL PROPERTIES OF PROTEINS : I. MEMBRANE POTENTIALS.

1. It is shown that a neutral salt depresses the potential difference which exists at the point of equilibrium between a gelatin chloride solution contained in a collodion bag and an outside aqueous solution (without gelatin). The depressing effect of a neutral salt on the P.D. is similar to the depression of the osmotic pressure of the gelatin chloride solution by the same salt. 2. It is shown that this depression of the P.D. by the salt can be calculated with a fair degree of accuracy on the basis of Nernst''s logarithmic formula on the assumption that the P.D. which exists at the point of equilibrium is due to the difference of the hydrogen ion concentration on the opposite sides of the membrane. 3. Since this difference of hydrogen ion concentration on both sides of the membrane is due to Donnan''s membrane equilibrium this latter equilibrium must be the cause of the P.D. 4. A definite P.D. exists also between a solid block of gelatin chloride and the surrounding aqueous solution at the point of equilibrium and this P.D. is depressed in a similar way as the swelling of the gelatin chloride by the addition of neutral salts. It is shown that the P.D. can be calculated from the difference in the hydrogen ion concentration inside and outside the block of gelatin at equilibrium. 5. The influence of the hydrogen ion concentration on the P.D. of a gelatin chloride solution is similar to that of the hydrogen ion concentration on the osmotic pressure, swelling, and viscosity of gelatin solutions, and the same is true for the influence of the valency of the anion with which the gelatin is in combination. It is shown that in all these cases the P.D. which exists at equilibrium can be calculated with a fair degree of accuracy from the difference of the pH inside and outside the gelatin solution on the basis of Nernst''s logarithmic formula by assuming that the difference in the concentration of hydrogen ions on both sides of the membrane determines the P.D. 6. The P.D. which exists at the boundary of a gelatin chloride solution and water at the point of equilibrium can also be calculated with a fair degree of accuracy by Nernst''s logarithmic formula from the value pCl outside minus pCl inside. This proves that the equation x² = y ( y + z) is the correct expression for the Donnan membrane equilibrium when solutions of protein-acid salts with monovalent anion are separated by a collodion membrane from water. In this equation x is the concentration of the H ion (and the monovalent anion) in the water, y the concentration of the H ion and the monovalent anion of the free acid in the gelatin solution, and z the concentration of the anion in combination with the protein. 7. The similarity between the variation of P.D. and the variation of the osmotic pressure, swelling, and viscosity of gelatin, and the fact that the Donnan equilibrium determines the variation in P.D. raise the question whether or not the variations of the osmotic pressure, swelling, and viscosity are also determined by the Donnan equilibrium.     

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

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

VALENCY RULE AND ALLEGED HOFMEISTER SERIES IN THE COLLOIDAL BEHAVIOR OF PROTEINS : I. THE ACTION OF ACIDS.

1. The action of a number of acids on four properties of gelatin (membrane potentials, osmotic pressure, swelling, and viscosity) was studied. The acids used can be divided into three groups; first, monobasic acids (HCl, HBr, HI, HNO₃, acetic, propionic, and lactic acids); second, strong dibasic acids (H₂SO₄ and sulfosalicylic acid) which dissociate as dibasic acids in the range of pH between 4.7 and 2.5; and third, weak dibasic and tribasic acids (succinic, tartaric, citric) which dissociate as monobasic acids at pH 3.0 or below and dissociate increasingly as dibasic acids, according to their strength, with pH increasing above 3.0. 2. If the influence of these acids on the four above mentioned properties of gelatin is plotted as ordinates over the pH of the gelatin solution or gelatin gel as abscissæ, it is found that all the acids have the same effect where the anion is monovalent; this is true for the seven monobasic acids at all pH and for the weak dibasic and tribasic acids at pH below 3.0. The two strong dibasic acids (the anion of which is divalent in the whole range of pH of these experiments) have a much smaller effect than the acids with monovalent anion. The weak dibasic and tribasic acids act, at pH above 3.0, like acids the anion of which is chiefly monovalent but which contain also divalent anions increasing with pH and with the strength of the acid. 3. These experiments prove that only the valency but not the other properties of the anion of an acid influences the four properties of gelatin mentioned, thus absolutely contradicting the Hofmeister anion series in this case which were due to the failure of the earlier experimenters to measure properly the pH of their protein solutions or gels and to compare the effects of acids at the same pH of the protein solution or protein gel after equilibrium was established. 4. It is shown that the validity of the valency rule and the non-validity of the Hofmeister anion series for the four properties of proteins mentioned are consequences of the fact that the influence of acids on the membrane potentials, osmotic pressure, swelling, and viscosity of gelatin is due to the Donnan equilibrium between protein solutions or gels and the surrounding aqueous solution. This equilibrium depends only on the valency but not on any other property of the anion of an acid. 5. That the valency rule is determined by the Donnan equilibrium is strikingly illustrated by the ratio of the membrane potentials for divalent and monovalent anions of acids. Loeb has shown that the Donnan equilibrium demands that this ratio should be 0.66 and the actual measurements agree with this postulate of the theory within the limits of accuracy of the measurements. 6. The valency rule can be expected to hold for only such properties of proteins as depend upon the Donnan equilibrium. Properties of proteins not depending on the Donnan equilibrium may be affected not only by the valency but also by the chemical nature of the anion of an acid.     

The donnan equilibrium

A complete solution has been obtained for the distribution of ions and for the electrostatic potential in a simple Donnan equilibrium, namely, where the membrane is permeable to two ions, but not to the third. Electrical neutrality is shown to be an extremely good approximation everywhere except close to the membrane.     

Biological and artificial ion exchangers: Electrical measurements with glass microelectrodes

Summary Biological (stratum corneum) and artificial (cation-exchange resin beads, Bio-Rad AG 50W-X2) ion exchangers were impaled by glass microelectrodes filled with KCl solution. The electrical potential difference recorded in these structures in reference to the external bathing medium was shown to be dependent on the KCl concentration of both the external and the microelectrode filling solutions. The potentials were interpreted on the grounds of the fixed charge theory of membrane potentials as a consequence of two phase boundary potentials (Donnan potentials), one at the matrix-external solution interface and the other at the matrix-microelectrode solution interface. The contribution of a diffusion component for the recorded potential was considered.     

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 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.     

An Ion Displacement Membrane Model

The usual assumption in treating the diffusion of ions in an electric field has been that the movement of each ion is independent of the movement of the others. The resulting equation for diffusion by a succession of spontaneous jumps has been well stated by Parlin and Eyring. This paper will consider one simple case in which a different assumption is reasonable. Diffusion of monovalent positive ions is considered as a series of jumps from one fixed negative site to another. The sites are assumed to be full (electrical neutrality). Interaction occurs by the displacement of one ion by another. An ion leaves a site if and only if another ion, not necessarily of the same species, attempts to occupy the same site. Flux ratios and net fluxes are given as functions of the electrical potential, concentration ratios, and number of sites encountered in crossing the membrane. Quantitative comparisons with observations of Hodgkin and Keynes are presented.     

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.     

THE EFFECT OF PURE PROTEIN SOLUTIONS AND OF BLOOD SERUM ON THE DIFFUSIBILITY OF CALCIUM

1. A comparative study has been made of the diffusibility of calcium in solutions of crystalline egg albumin, serum globulin, and human blood serum. 2. In all three of these solutions, at pH 7.4, molal Ca concentrations within the membrane are greater than the calcium concentrations in the outside solutions, quite in accordance with the Donnan theory. 3. At pH 7.4, the ratio of See PDF for Structure varies directly with the protein concentration whether the solution be one of egg albumin, serum globulin, or blood serum. This is also in accordance with the Donnan theory. 4. On the acid side of the isoelectric point of the proteins, the concentration of Ca outside becomes greater than the concentration in the solution of blood serum or pure protein, as is demanded by the Donnan theory. 5. The magnitude of the Ca ratios on the alkaline and acid sides of the isoelectric points is probably the resultant of the Donnan equilibrium and the formation of complex Ca-protein ions. Northrop and Kunitz have shown the probability of the existence of such ions in the case of Zn⁺⁺, K⁺, and Li⁺, where satisfactory electrodes have been developed for E.M.F. measurements.     

Direct Measurement of Potential Difference across the Human Red Blood Cell Membrane

The electrical potential difference across the human red cell membrane has been measured directly. A biological amplifier with neutralized input capacity was used. Human red cells in modified Ringer solution were impaled individually with 3 M KCl-filled glass microelectrodes. Movements of the microelectrodes were effected by Leitz micromanipulators. Results showed a potential difference of -8.0 ± 0.21 (SEM) mv, the inside being negative with respect to the outside. This value is approximately that calculated by using the Nernst equation considering the intracellular and extracellular chloride concentrations.

As a control, similar measurements were made on nylon microcapsules containing hemoglobin. The measured potential of -0.52 ± 0.02 (SEM) mv, which agreed very well with the value calculated on the basis of Donnan equilibrium, was much smaller in magnitude as compared to the results for the red cell, and there was evidence of fixed charges on the microcapsule membrane. There was no evidence of this in the case of the red cell.