IONIC RADIUS AND IONIC EFFICIENCY

1. It has been shown in preceding papers that when we separate solutions of electrolytes from pure water by collodion membranes the ions with the same sign of charge as the membrane increase while the ions with the opposite sign of charge diminish the rate of diffusion of water from the side of pure water to the side of solution; and that the accelerating and depressing effects of these ions on the rate of diffusion of water increase with their valency. 2. It is shown in this paper that aside from the valency a second quantity of the ion plays a rôle in this effect, namely the radius, which in a monatomic ion means the distance between the central positive nucleus and the outermost ring or shell of electrons of the ion. In monatomic, monovalent anions the radius increases in the order Cl< Br< I (being largest in I), while for monatomic, monovalent cations it increases in the order Li< Na< K< Rb (being largest in Rb). 3. It is shown that the accelerating as well as the depressing effect of the anions mentioned increases directly with the order of magnitude of their radius and that the efficiency is greatest in the case of I which has the largest radius; while the accelerating as well as the depressing effect of cations increases inversely with the order of magnitude of their radius, Li with the smallest radius having the greatest efficiency. 4. This is intelligible on the assumption that the action of the ions is electrostatic in character, in the case of cations due to the electrostatic effect of the excess charge of their positive nucleus, and in the case of anions due to the excess charge of their captured electron. The electrostatic effect of the positive nucleus of a cation on the membrane (or any other body) will be the greater the smaller the ionic radius of the cation; and the electrostatic effect of an excess electron will be the greater the further its distance from its own positive nucleus. 5. It is suggested that this rule may possibly include polyatomic, monovalent ions (e.g. NO₃, CNS, etc.) when we replace these polyatomic ions by monatomic models in which the radius is calculated in such a way as to give the model the same electrostatic effect which the polyatomic ion possesses. 6. These conclusions are in harmony with the fact that the efficiency of ions increases also with their valency. 7. It is suggested that these rules concerning the influence of the ionic radius can possibly be demonstrated in other phenomena, depending on the electrostatic effect of ions.     

Physical descriptions of experimental selectivity measurements in ion channels

Three experiments that quantify the amount of selectivity exhibited by a biological ion channel are examined with Poisson-Nernst-Planck (PNP) theory. Conductance ratios and the conductance mole fraction experiments are examined by considering a simple model ion channel for which an approximate solution to the PNP equations with Donnan boundary conditions is derived. A more general result is derived for the Goldman-Hodgkin-Katz permeability ratio. The results show that (1) the conductance ratio measures the ratio of the diffusion coefficients of the ions inside the channel, (2) the mole fraction experiment measures the difference of the excess chemical potentials of the ions inside the channel, and (3) the permeability ratio measures both diffusion coefficients and excess chemical potentials. The results are used to divide selectivity into two components: partitioning, an equilibrium measure of how well the ions enter the channel, and diffusion, a nonequilibrium measure of how well the ions move through the channel.     

IONIC EFFECTS ON LIGNIFICATION AND PEROXIDASE IN TISSUE CULTURES

Crown-gall tumor tissue cultures release peroxidase into the medium in response to the concentration of specific ions in the medium. This release is not due to diffusion from cut surfaces or injured cells. Calcium, magnesium, and ammonium were, in that order, most effective in increasing peroxidase release. The enzyme was demonstrated cytochemically on the cell walls and in the cytoplasm. Cell wall fractions, exhaustively washed in buffer, still contained bound peroxidase. This bound peroxidase could be released by treating the wall fractions with certain divalent cations or ammonium. The order of effectiveness for removing the enzyme from the washed cell walls is: Ca⁺⁺ ≈ Sr⁺⁺ > Ba⁺⁺ > Mg⁺⁺ > NH₄⁺. These data support the thesis presented that specific ions can control the deposition of lignin on cell walls by affecting the peroxidase levels on these walls.     

Ion-specific diffusion rates through transmembrane protein channels. A molecular dynamics study

The migration of different alkali metal cations through a transmembrane model channel is simulated by means of the molecular dynamics technique. The parameters of the model are chosen in close relation to the gramicidin A channel. Coulomb- and van der Waals-type potentials between the ions and flexible carbonyl groups of the pore-forming molecule are used to describe the ion channel interaction. The diffusion properties of the ions are obtained from three-dimensional trajectory calculations. The diffusion rates for the different ions Li+, Na+, K+ and Rb+ are affected not only by the mass of the particles but also very strongly by their size. The latter effect is more pronounced for rigid channels, i.e., for binding vibrational frequencies of the CO groups with v greater than 400 cm-1. In this range the selectivity sequence for the diffusion rates is the inverse of that expected from normal rate theory but agrees with that found in experiments for gramicidin A.     

INFLUENCE OF IONIC CONDITIONS ON CELL DIFFERENTIATION AND MORPHOGENESIS OF THE CELLULAR SLIME MOLDS

Effects of various ionic conditions on the development of the cellular slime molds D. discoideum and D. mucoroides were studied. A certain concentration of lithium ions (7 mM) promoted differentiation of the stalk cells and conversely inhibited formation of the spores. The presence of calcium and magnesium ions was needed for Li to manifest its specific effect. A high concentration of Ca (100-120 mM) also facilitated differentiation of the stalk cells. On the other hand, fluoride ions stimulated considerable formation of spores at 15 mM. In the absence of divalent cations, sodium ions inhibited morphogenesis and cell differentiation proportionately with its concentration, and complete inhibition was obtained at 20 mM. The inhibitory effect of Na was nullified by addition of small amounts of Ca. Possible mechanisms by which these ions exert their influences on development of this organism were discussed.     

Molecular dynamics estimates of ion diffusion in model hydrophobic and KcsA potassium channels

Molecular dynamics simulations are carried out to obtain estimates of diffusion coefficients of biologically important Na+, K+, Ca2+ and Cl- ions in hydrophobic cylindrical channels with varying radii and large reservoirs. Calculations for the cylindrical channels are compared to those for the KcsA potassium channel, for which the protein structure has recently been determined from X-ray diffraction experiments. Our results show that ion diffusion is maintained at reasonably high levels even within narrow channels, and does not support the very small diffusion coefficients used in some continuum models in order to fit experimental data. The present estimates of ion diffusion coefficients are useful in the calculation of channel conductance using the Poisson-Nernst-Planck theory, or Brownian dynamics.     

IONIC TRANSFERENCE NUMBERS IN CELLOPHANE MEMBRANES

The "apparent" cation transference number within cellophane is determined for HCl, KCl, NH₄Cl, NaCl, and LiCl. The method consists in measuring the E.M.F. in a concentration chain employing Ag:AgCl electrodes or calomel electrodes and calculating from formulas derived for cases of simple, unconstrained diffusion. The transference numbers and the cation mobilities relative to the chloride ion were found to be higher in the cellophane (relative cation mobilities increased about 40 per cent). The effect of the membrane is discussed. It is emphasized that with the introduction of a membrane as a liquid junction new factors are introduced, which are not considered in the formulas ordinarily used. Such factors may be activity changes due to dimensional or other reasons and particularly electrical effects exhibited by the membrane upon the ionic diffusion. Accordingly the transference number, as determined, may lack well defined physical significance.     

THE ROLE OF CARBONIC ANHYDRASE IN CERTAIN IONIC EXCHANGES INVOLVING THE ERYTHROCYTE

1. The acceleration by bicarbonates of the swelling and hemolysis of erythrocytes in solutions of ammonium salts, first reported by Ørskov, is strikingly dependent upon carbonic anhydrase, being almost abolished by inhibitors of this enzyme such as KCN and sulfanilamide, and under suitable conditions being enhanced by its addition to the external solution. This behavior gives support to the theory of "catalyzed diffusion" as an explanation of the Ørskov effect. 2. The inhibitory effects of both sulfanilamide and KCN seem to be capable of complete reversal on washing the erythrocytes in isotonic salt solutions. The full effect of KCN appears almost instantly; that of sulfanilamide requires a period measured in seconds, or possibly even in minutes, to reach its maximum, the delay presumably being due to the slower penetration of the erythrocyte by this substance. Under favorable conditions the effect of concentrations of sulfanilamide of a few hundredths of a milligram per cent can be demonstrated. No similar effects have been obtained with sulfapyridine. 3. Bicarbonates also have a "catalytic" effect on the response of the internal pH of erythrocytes to changes in that of their surroundings. The resulting volume changes of the cell, which otherwise frequently require many minutes for their completion, may take place within a few seconds in the presence of low concentrations of bicarbonates. At a given pH value the effect of the latter substances is chiefly on the rate of the change and only to a minor extent on its magnitude. It may be further accelerated under appropriate conditions by the addition to the cell suspension of carbonic anhydrase, and can be almost abolished by KCN and by sulfanilamide. 4. Volume changes of erythrocytes associated with exchanges of Cl'' for SO₄'''' ions are greatly accelerated by low concentrations of bicarbonates, this effect being likewise dependent upon carbonic anhydrase. There is some evidence that in this case the exchange takes place, at least in part, in two steps: Cl'' for HCO₃'' and HCO₃'' for SO₄''''.     

Kinetics of transport of hydrophobic ions through lipid membranes including diffusion polarization in the aqueous phase

Previous interpretations of the kinetics of transport of hydrophobic ions through membranes have been based on one of three limiting assumptions. Either diffusion in the aqueous phase was taken to be rapid, or ionic motion was constrained to the membrane or a steady state was presumed to be established within the membrane. We present a general treatment of the coupled diffusion process through both the aqueous phase and the membrane; our theory contains the previous results as limiting cases. It is applied to voltage jump-current relaxation experiments on black lipid membranes in the presence of dipicrylamine or sodium tetraphenylborate. We have attempted to establish the rate of desorption from the membrane. For the system phosphatidylserine/tetraphenylborate, the rate of desorption and the rate of translocation were found to be comparable.     

ON THE PERMEABILITY OF THE STOMACH MUCOSA FOR ACIDS AND SOME OTHER SUBSTANCES

1. Solutions approximately isotonic with blood of strong and weak acids, several salts, glucose, and glycine were introduced in the resting stomachs of cats. The concentration and volume changes were recorded. 2. It was found that the stomach mucosa was permeable to the majority of the ions tested. There was also a permeability in the opposite direction from the blood (mucosa) to the stomach content, particularly of alkali chlorides. Poorly permeable substances were glucose, glycine, and sodium iodate. Pure weak acids such as acetic acid penetrated very rapidly. 3. The electrolyte concentration changes in the stomach content (or gastric juice) are pictured as an exchange diffusion; for instance, the hydrogen ions of an acid are exchanged against alkali ions of the mucosa or blood. 4. It is pointed out that the concept of the mucosa as an ion permeable membrane could be used as the foundation of a "diffusion theory," which can explain the acidity and chloride variations of the gastric juice without postulating neutralizing or diluting secretions.     

Simulate the diffusion of hydrated ions by nanofiltration membrane process with random walk

We propose a new diffusion model describing the diffusion behaviours of hydrated ions in the process of nanofiltration (NF) based on the random walk (RW) theory when the NF membrane is uncharged or low charged. In this model, the hydration of ions and their deformation capacity are considered. The structure of the membrane is idealised into a lozenge shape and the diameter of membrane pore is defined as gapsize. A computer program named RW system in chemistry is developed to simulate based on this model. Six familiar ions Li⁺, Na⁺, Mg²⁺, Al³⁺, K⁺ and Ca²⁺ are investigated. Their characteristics are calculated by Gaussian 03, Pople, Inc., Wallingford, CT. The diffusivities of hydrated ions are calculated and discussed. The results show that the hydration of ions cannot be ignored in NF process when the membrane pore size is near the dimensions of the hydrated ions.     

KINETICS OF PENETRATION : VII. MOLECULAR VERSUS IONIC TRANSPORT

In some living cells the order of penetration of certain cations corresponds to that of their mobilities in water. This has led to the idea that electrolytes pass chiefly as ions through the protoplasmic surface in which the order of ionic mobilities is supposed to correspond to that found in water. If this correspondence could be demonstrated it would not prove that electrolytes pass chiefly as ions through the protoplasmic surface for such a correspondence could exist if the movement were mostly in molecular form. This is clearly shown in the models here described. In these the protoplasmic surface is represented by a non-aqueous layer interposed between two aqueous phases, one representing the external solution, the other the cell sap. The order of penetration through the non-aqueous layer is Cs > Rb > K > Na > Li. This will be recognized as the order of ionic mobilities in water. Nevertheless the movement is mostly in molecular form in the nonaqueous layer (which is used in the model to represent the protoplasmic surface) since the salts are very weak electrolytes in this layer. The chief reason for this order of penetration lies in the fact that the partition coefficients exhibit the same order, that of cesium being greatest and that of lithium smallest. The partition coefficients largely control the rate of entrance since they determine the concentration gradient in the non-aqueous layer which in turn controls the process of penetration. The relative molecular mobilities (diffusion constants) in the non-aqueous layer do not differ greatly. The ionic mobilities are not known (except for K⁺ and Na⁺) but they are of negligible importance, since the movement in the non-aqueous layer is largely in molecular form. They may follow the same order as in water, in accordance with Walden''s rule. Ammonium appears to enter faster than its partition coefficient would lead us to expect, which may be due to rapid penetration of NH₃. This recalls the apparent rapid penetration of ammonium in living cells which has also been explained as due to the rapid penetration of NH₃. Both observation and calculation indicate that the rate of penetration is not directly proportional to the partition coefficient but increases somewhat less rapidly. Many of these considerations doubtless apply to living cells.     

Leaching of zinc sulfide by Thiobacillus ferrooxidans: bacterial oxidation of the sulfur product layer increases the rate of zinc sulfide dissolution at high concentrations of ferrous ions

This paper reports the results of leaching experiments conducted with and without Thiobacillus ferrooxidans at the same conditions in solution. The extent of leaching of ZnS with bacteria is significantly higher than that without bacteria at high concentrations of ferrous ions. A porous layer of elemental sulfur is present on the surfaces of the chemically leached particles, while no sulfur is present on the surfaces of the bacterially leached particles. The analysis of the data using the shrinking-core model shows that the chemical leaching of ZnS is limited by the diffusion of ferrous ions through the sulfur product layer at high concentrations of ferrous ions. The analysis of the data shows that diffusion through the product layer does not limit the rate of dissolution when bacteria are present. This suggests that the action of T. ferrooxidans in oxidizing the sulfur formed on the particle surface is to remove the barrier to diffusion by ferrous ions.     

ON THE CAUSE OF THE INFLUENCE OF IONS ON THE RATE OF DIFFUSION OF WATER THROUGH COLLODION MEMBRANES. II

1. It had been shown in previous publications that when pure water is separated from a solution of an electrolyte by a collodion membrane the ion with the same sign of charge as the membrane increases and the ion with the opposite sign of charge as the membrane diminishes the rate of diffusion of water into the solution; but that the relative influence of the oppositely charged ions upon the rate of diffusion of water through the membrane is not the same for different concentrations. Beginning with the lowest concentrations of electrolytes the attractive influence of that ion which has the same sign of charge as the collodion membrane upon the oppositely charged water increases more rapidly with increasing concentration of the electrolyte than the repelling effect of the ion possessing the opposite sign of charge as the membrane. When the concentration exceeds a certain critical value the repelling influence of the latter ion upon the water increases more rapidly with a further increase in the concentration of the electrolyte than the attractive influence of the ion having the same sign of charge as the membrane. 2. It is shown in this paper that the influence of the concentration of electrolytes on the rate of transport of water through collodion membranes in electrical endosmose is similar to that in the case of free osmosis. 3. On the basis of the Helmholtz theory of electrical double layers this seems to indicate that the influence of an electrolyte on the rate of diffusion of water through a collodion membrane in the case of free osmosis is due to the fact that the ion possessing the same sign of charge as the membrane increases the density of charge of the latter while the ion with the opposite sign diminishes the density of charge of the membrane. The relative influence of the oppositely charged ions on the density of charge of the membrane is not the same in all concentrations. The influence of the ion with the same sign of charge increases in the lowest concentrations more rapidly with increasing concentration than the influence of the ion with the opposite sign of charge, while for somewhat higher concentrations the reverse is true.     

Effect of hydrodynamic interactions on the diffusion of integral membrane proteins: tracer diffusion in organelle and reconstituted membranes.

A persistent discrepancy exists between theoretical predictions and experimental observations for the diffusion coefficients of integral membrane proteins in lipid bilayers free of immobilized proteins. Current thermodynamic theories overestimate tracer diffusion coefficients at high area fractions. We explore the hypothesis that the combined effect of hydrodynamic and thermodynamic interactions reconciles theory with experiment. We have determined previously the short- and long-time tracer diffusivities, Ds and Dl, respectively, of integral membrane proteins in lipid bilayers as a function of their area fraction, phi. The results are based on two-particle hydrodynamic and thermodynamic interactions and are precise to O(phi). Here we extend the results for Dl to high phi by combining the hydrodynamic results for Ds into theories for Dl based on many-particle thermodynamic interactions. The results compare favorably with the experimental measurements of Dl as a function of protein area fraction for bacteriorhodopsin in reconstituted membranes and for complex III of the mitochondrial inner membrane. The agreement suggests that both hydrodynamic and thermodynamic interactions are important determinants of diffusion coefficients of proteins in lipid bilayers. Additional experiments are required to verify the role of hydrodynamic interactions in protein diffusion in reconstituted systems.     

CHANGES OF APPARENT IONIC MOBILITIES IN PROTOPLASM : I. EFFECTS OF GUAIACOL ON VALONIA

In normal cells of Valonia the order of the apparent mobilities of the ions in the non-aqueous protoplasmic surface is K > Cl > Na. After treatment with 0.01 M guaiacol (which does not injure the cell) the order becomes Na > Cl > K. As it does not seem probable that such a reversal could occur with simple ions we may assume provisionally that in the protoplasmic surface we have to do with charged complexes of the type (KX _I)⁺, (KX _II)⁺, where X _I and X _II are elements or radicals, or with chemical compounds formed in the protoplasm. When 0.01 M guaiacol is added to sea water or to 0.6 M NaCl (both at pH 6.4, where the concentration of the guaiacol ion is negligible) the P.D. of the cell changes (after a short latent period) from about 10 mv. negative to about 28 mv. positive and then slowly returns approximately to its original value (Fig. 1, p. 14). This appears to depend chiefly on changes in the apparent mobilities of organic ions in the protoplasm. The protoplasmic surface is capable of so much change that it does not seem probable that it is a monomolecular layer. It does not behave like a collodion nor a protein film since the apparent mobility of Na⁺ can increase while that of K⁺ is decreasing under the influence of guaiacol.     

Leaching of Zinc Sulfide by Thiobacillus ferrooxidans: Bacterial Oxidation of the Sulfur Product Layer Increases the Rate of Zinc Sulfide Dissolution at High Concentrations of Ferrous Ions

This paper reports the results of leaching experiments conducted with and without Thiobacillus ferrooxidans at the same conditions in solution. The extent of leaching of ZnS with bacteria is significantly higher than that without bacteria at high concentrations of ferrous ions. A porous layer of elemental sulfur is present on the surfaces of the chemically leached particles, while no sulfur is present on the surfaces of the bacterially leached particles. The analysis of the data using the shrinking-core model shows that the chemical leaching of ZnS is limited by the diffusion of ferrous ions through the sulfur product layer at high concentrations of ferrous ions. The analysis of the data shows that diffusion through the product layer does not limit the rate of dissolution when bacteria are present. This suggests that the action of T. ferrooxidans in oxidizing the sulfur formed on the particle surface is to remove the barrier to diffusion by ferrous ions.     

STUDIES ON THE PERMEABILITY OF MEMBRANES : IV. VARIATIONS OF TRANSFER NUMBERS WITH THE DRIED COLLODION MEMBRANE PRODUCED BY THE ELECTRIC CURRENT.

The transfer number of Cl in a KCl solution within the pores of a dried collodion membrane is always lower than 0.5. It depends on the concentration of the solution and decreases in general with decreasing concentration. However, the transfer number for any given KCl concentration has the significance of a definite and constant figure only when an infinitely small amount of coulombs is allowed to pass through the system. For finite durations of electric transfer experiments a polarization effect will always change the original transfer number. This polarization consists in an accumulation of the salt at the one boundary and a diminution at the other boundary of the membrane. Again, as the transfer number strongly depends on concentration, this change in concentration will bring about in its turn a gradual change in the transfer number too. It is shown under what conditions the transfer numbers for the anion as obtained by electic transfer experiments are higher or lower than the ones expected without polarization effect. Thus, by changing the character and magnitude of the force driving the ions across the membranes, and according to the history of previous treatment of the membrane, the whole character of what we may call the specific permeablity for ions of the membrane may be varied without any substantial change of the membrane itself concerning its structure, its chemical composition, or its pore size. Contemplation of the results obtained in this series of experiments in the light of the theoretical considerations just outlined has impressed us with the fallacy of speaking of the definite permeability of any type of membrane for electrolytes. The behavior of the membrane toward the passage of electrolytes depends on a variety of conditions. It may be recalled that different investigators have reported widely varying results concerning the permeability of certain physiological membranes for electrolytes. Such experiments as have been described in this paper may lead to an understanding of some of the factors responsible for such variations. We are aware that the collodion membrane in its simplicity is scarcely comparable to the extremely complicated biological membranes. Nevertheless any attempts to understand better the behavior of biological membranes may wisely begin with a study of the simplest prototypes.     

Investigation of Factors Affecting the Bioregeneration Process for Perchlorate-Laden Gel-Type Anion-Exchange Resin

Ion exchange is the most common process for perchlorate removal from waters. Selective ion-exchange resins are widely used for perchlorate removal from waters, but are incinerated after one-time use, making the ion-exchange process incomplete for perchlorate removal. As perchlorate ions are readily biodegradable, direct contact of spent ion-exchange resins with perchlorate-reducing bacteria for its regeneration has been studied recently. In this research, some factors affecting the bioregeneration of perchlorate-laden gel-type anion-exchange resin were investigated. Bioregeneration is a sustainable process when compared to one-time use of resin and disposal by incineration. Batch bioregeneration experiments were performed to determine (a) the effect of initial perchlorate load in the resin, (b) the effect of microbial concentration, and (c) the effect of nitrate load on the degradation of perchlorate in the resin bead. The results of the bioregeneration tests suggested that the bioregeneration process may be controlled by both kinetics and diffusion. Higher perchlorate load in the resin had a positive effect on perchlorate degradation rates, whereas varying microbial concentration did not have a significant effect on perchlorate degradation in gel-type resin. The presence of nitrate suppressed perchlorate degradation initially, but once all nitrate was utilized, perchlorate degradation took place.