Thermoosmosis through charged membranes

Thermoosmosis through oxidized collodion and collodion-sulfonated polystyrene interpolymer membranes has been observed in KCl solutions of various concentrations. The effective temperature difference acting for thermoosmosis was determined by measuring the thermal membrane potential appearing on both sides of membrane. It was found that the velocity of thermoosmosis is proportional to the effective temperature difference and the proportionality constant (thermoosmotic coefficient) is a function of electrolyte concentration. The dependence of the thermoosmotic coefficient of charged membranes on the electrolyte concentration is found to have a characteristic feature.     

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.     

The osmotic flow of an electrolyte through a charged porous membrane

A pore model in which the pore wall has a continuous distribution of electrical charge is used to investigate the osmotic flow through a charged permeable membrane separating electrolyte solutions of unequal concentrations. The pore is treated as a long, circular, cylindrical duct. The analysis is based on a continuum formulation in which a dilute electrolyte solution is described by the coupled Nernst-Planck/Poisson creeping flow equations. Account is taken of the significant size of the electrolyte ions (assumed to be rigid spheres) when compared with the diameter of the membrane pores. Analytical solutions for the ion concentrations, hydrostatic pressure and electrostatic potential in the electrolyte solutions are given and an intra-pore flow solution is derived. A mathematical expression for the osmotic reflection coefficient as a function of the solute ion: pore diameter ratio λ and the solute fluxes is obtained. Approximate solutions are quoted which relate the solute fluxes and the solution electrostatic potentials at the membrane surfaces to the bulk solution concentrations, the membrane pore charge and pore geometry. The osmotic reflection coefficient is thus determined as a function of these parameters.     

THE INFLUENCE OF ELECTROLYTES ON THE ELECTRIFICATION AND THE RATE OF DIFFUSION OF WATER THROUGH COLLODION MEMBRANES

1. When pure water is separated by a collodion membrane from a watery solution of an electrolyte the rate of diffusion of water is influenced not only by the forces of gas pressure but also by electrical forces. 2. Water is in this case attracted by the solute as if the molecules of water were charged electrically, the sign of the charge of the water particles as well as the strength of the attractive force finding expression in the following two rules, (a) Solutions of neutral salts possessing a univalent or bivalent cation influence the rate of diffusion of water through a collodion membrane, as if the water particles were charged positively and were attracted by the anion and repelled by the cation of the electrolyte; the attractive and repulsive action increasing with the number of charges of the ion and diminishing inversely with a quantity which we will designate arbitrarily as the "radius" of the ion. The same rule applies to solutions of alkalies. (b) Solutions of neutral or acid salts possessing a trivalent or tetravalent cation influence the rate of diffusion of water through a collodion membrane as if the particles of water were charged negatively and were attracted by the cation and repelled by the anion of the electrolyte. Solutions of acids obey the same rule, the high electrostatic effect of the hydrogen ion being probably due to its small "ionic radius." 3. The correctness of the assumption made in these rules concerning the sign of the charge of the water particles is proved by experiments on electrical osmose. 4. A method is given by which the strength of the attractive electric force of electrolytes on the molecules of water can be roughly estimated and the results of these measurements are in agreement with the two rules. 5. The electric attraction of water caused by the electrolyte increases with an increase in the concentration of the electrolyte, but at low concentrations more rapidly than at high concentrations. A tentative explanation for this phenomenon is offered. 6. The rate of diffusion of an electrolyte from a solution to pure solvent through a collodion membrane seems to obey largely the kinetic theory inasmuch as the number of molecules of solute diffusing through the unit of area of the membrane in unit time is (as long as the concentration is not too low) approximately proportional to the concentration of the electrolyte and is the same for the same concentrations of LiCl, NaCl, MgCl₂, and CaCl₂.     

THE COLLOIDAL BEHAVIOR OF EDESTIN

1. It has been shown by titration experiments that the globulin edestin behaves like an amphoteric electrolyte, reacting stoichiometrically with acids and bases. 2. The potential difference developed between a solution of edestin chloride or acetate separated by a collodion membrane from an acid solution free from protein was found to be influenced by salt concentration and hydrogen ion concentration in the way predicted by Donnan''s theory of membrane equilibrium. 3. The osmotic pressure of such edestin-acid salt solutions was found to be influenced by salt concentration and by hydrogen ion concentration in the same way as is the potential difference. 4. The colloidal behavior of edestin is thus completely analogous to that observed by Loeb with gelatin, casein, and egg albumin, and may be explained by Loeb''s theory of colloidal behavior, which is based on the idea that proteins react stoichiometrically as amphoteric electrolytes and on Donnan''s theory of membrane equilibrium.     

The study of volt-ampere characteristics of ionic channels formed by gramicidin A

A method of measurement of the non-linearity coefficient of volt-ampere characteristics of the type i(U) approximately = U(1 + beta U2) has been developed for ionic channels formed by gramicidin A, using the third harmonic of the membrane current. The shape of the volt-ampere characteristics (VA) of ionic channels formed by gramicidin A did not depend on the antibiotic concentration in the membrane. The coefficient beta of non-linearity of VA of membranes modified by gramicidin A depended on electrolyte concentration "c" and it increased proportionally with the lg c from -17 V-2 at 0.03 mol/l KC1 to 8 V-2 at 3.4 mol/l KCl, and it was zero at co = 0.3 - 1 mol/l KCl. Egg lecithin and glycerol monooleate (GMO) membranes differ in their co values. The substitution of K+ for Li+ of the membrane solvent (n-heptane for n-hexadecane) did not influence the value of beta; the same applied for GMO membranes without any solvent. In a number of membranes, spontaneous change of the non-linearity coefficient with time observed after the membrane formation, as well as jumps of the non-linearity coefficient at a practically unchanged membrane conductivity. An analysis of some theoretical models of the ion transport through the channel has shown that, at voltages above 200 mV, these models provide rather small values of beta, or extremely high VA non-linearity.     

Isoelectric point of an ion-penetrable membrane.

The surface potential of an ion-penetrable planar membrane is calculated for the case in which acidic and basic groups are present in the membrane. It is found that when both acidic and basic groups are not uniformly distributed in the direction normal to the membrane, the isoelectric point (the pH value at which the surface potential becomes zero) of the membrane varies with the electrolyte concentration, whereas if both groups are uniformly distributed, the isoelectric point is independent of the electrolyte concentration. As a simple example, we treat a membrane consisting of two layers, in which acidic groups are distributed in the outer layer and basic groups are in the inner layer. Simple equations determining the membrane surface potential as a function of pH and electrolyte concentration and the dependence of the isoelectric point on the electrolyte concentration are presented.     

Electrostatic interaction between ion-penetrable multi-layered membranes

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

Partial purification of human parathyroid hormone 1-84 as a thioredoxin fusion form in recombinant Escherichia coli by thermoosmotic shock

A modified purification method, thermoosmotic shock (osmotic shock coupled with heat-treatment) for heat-stable proteins, was devised in the purification of Trx-hPTH (1-84) (human parathyroid hormone coupled with thioredoxin as a fusion partner) from E. coli. Thermoosmotic shock can integrate the functions of extraction and crude separation of fusion protein Trx-hPTH (1-84). To improve the purification efficiency, thermoosmotic shock conditions were optimized and achieved as follows: the optimized high osmotic solution containing 20mM Tris-HCl buffer (pH 8.0), 1mM EDTA, and 25% sucrose; the low osmotic solution containing 20mM Tris-HCl buffer (pH 8.0), 1mM EDTA, and the heat-treatment temperature of 100 degrees C for 10 min. Using this method, the purity of Trx-hPTH (1-84) was up to 73% and the yield was up to 72%, respectively. In addition, the two separation methods of both thermoosmotic shock and affinity chromatography have been compared, indicating that thermoosmotic shock is an economical and feasible way for the fusion protein separation. Besides, the thermoosmotic shock method may be used for the purification of some proteins of thermal stability without N-terminal His-tag.     

Osmotic flow caused by polyelectrolytes

Osmotic flow of water caused by high concentrations of anionic polyelectrolytes across semipermeable membranes, permeable only to solvent and simple electrolyte, has been measured in a newly designed flow cell. The flow cell features small solution and solvent compartments and an efficient stirring mechanism. We have demonstrated that, while the osmotic pressure of the anionic polyelectrolytes is determined primarily by micro-counterions, the osmotic flow is determined by solution-dependent properties as embodied in the hydrodynamic frictional coefficient which is determined by the polymer backbone segment of the polyelectrolyte. The variation of the osmotic permeability coefficient, L(p)(o), with concentration and osmotic pressure closely correlated with the concentration dependence of this frictional coefficient. These studies confirm previous work that the kinetics of osmotic flow across a membrane impermeable to the osmotically active solute is primarily determined by the diffusive mobility of the solute.     

Strong electrolyte continuum theory solution for equilibrium profiles, diffusion limitation, and conductance in charged ion channels.

The solution for the ion flux through a membrane channel that incorporates the electrolyte nature of the aqueous solution is a difficult theoretical problem that, until now, has not been properly formulated. The difficulty arises from the complicated electrostatic problem presented by a high dielectric aqueous channel piercing a low dielectric lipid membrane. The problem is greatly simplified by assuming that the ratio of the dielectric constant of the water to that of the lipid is infinite. It is shown that this is a good approximation for most channels of biological interest. This assumption allows one to derive simple analytical expressions for the Born image potential and the potential from a fixed charge in the channel, and it leads to a differential equation for the potential from the background electrolyte. This leads to a rigorous solution for the ion flux or the equilibrium potential based on a combination of the Nernst-Planck equation and strong electrolyte theory (i.e., Gouy-Chapman or Debye-Huckel). This approach is illustrated by solving the system of equations for the specific case of a large channel containing fixed negative charges. The following characteristics of this channels are discussed: anion and mono- and divalent cation conductance, saturation of current with increasing concentration, current-voltage relationship, influence of location and valence of fixed charge, and interaction between ions. The qualitative behavior of this channel is similar to that of the acetylcholine receptor channel.     

Dielectric saturation of the aqueous boundary layers adjacent to charged bilayer membranes

Summary The surface charge density resulting from the adsorption of hydrophobic anions of dipicrylamine onto dioleyl-lecithin bilayer membranes has been measured directly using a high field pulse method. The surface charge density increases linearly with adsorbate concentration in the water until electrostatic repulsion of impinging hydrophobic ions by those already adsorbed becomes appreciable. Then Gouy-Chapman theory predicts that surface charge density will increase sublinearly, with the power [z ⁺/(z ⁺+2)] of the adsorbate concentration, wherez ⁺ is the cation valence of the indifferent electrolyte screening the negatively charged membrane surface. The predicted 1/3 and 1/2 power laws for univalent and divalent cations, respectively, have been observed in these experiments using Na⁺, Mg⁺⁺, and Ba⁺⁺ ions. Gouy-Chapman theory predicts further that the change from linear to sublinear dependence takes place at a surface charge density governed by the static dielectric constant of water and the concentration of indifferent electrolyte. Quantitative agreement with experiment is obtained at electrolyte concentrations of 10^–4 m and 10^–3 m, but can be maintained at higher concentrations only if the aqueous dielectric constant is decreased. A transition field model is proposed in which the Gouy-Chapman theory is modified to take account of dielectric saturation of water in the intense electric fields adjacent to charged membrane surfaces.     

Ion concentration and charge adjacent to electrically charged cell membrane

Equations describing ion concentration profiles and electric charge in electrolyte solutions adjacent to an electrically charged cell membrane model in the electrochemical equilibrium state are developed and completely solved. The membrane system model consists of an infinitely large planar sheet of finite thickness separating two electrolyte solutions. Electric charges in the membrane model consist of planes of charge parallel to the surfaces of the planar sheet. The charge in solution adjacent to each surface of the membrane is due to differences in the total anion and cation concentrations in each solution.Expressions of concentration and charge are functions of the quantity and location of charge in the membrane, the various permittivities and thickness of the membrane, and the ionic compositions, permittivities, and temperature of the electrolyte solutions.The validity and relation of the model to real membranes are discussed.     

Ion transfer during electrolyte osmosis through a charged porous membrane

In an earlier investigation (I) concerning the osmotic flow of an electrolyte through a charged porous membrane it was shown that in order to determine the osmotic reflection coefficient for the process a solution of the associated ion transfer equations is required. In I, previously unpublished approximate formulae for the required variables were quoted. The current paper presents the derivation of these solutions. The investigation considers the solution of the one-dimensional form of the coupled Poisson/convection-free Nernst-Planck equations subject to boundary conditions derived in I. Both equations and boundary conditions contain unknown parameters which are evaluated as part of the solution. Exact numerical and approximate analytical solutions are derived for the intrapore electrostatic potential and ion concentrations and for the unknown ion fluxes. Formulae are given for the electric current generated in the process and for the electrolyte factor in the osmotic reflection coefficient.     

NaCl胁迫对毛竹叶片的电阻抗图谱参数及膜透性的影响

以NaCl胁迫下毛竹（Phyllostachys edulis）实生苗叶片为材料,测定其电阻抗图谱参数和膜透性的变化,通过膜透性与电阻抗图谱参数间的相关性,来证明电阻抗图谱法研究竹子受胁迫程度的有效性。结果表明：随着盐浓度的升高,胞外电阻、胞内电阻和弛豫时间呈现先减小、后增加、再减小的特征,而弛豫时间分布系数表现恰好相反;叶片细胞膜相对透性逐渐增大,脯氨酸的含量先逐渐增大,然后减小。相关分析表明：胞内电阻、胞外电阻、弛豫时间与脯氨酸含量呈极显著负相关（p〈0.01）;胞外电阻、弛豫时间与膜相对透性呈显著负相关（p〈0.05）。电阻抗图谱参数能够有效地表示毛竹受NaCl胁迫的程度,电阻抗图谱法将是竹子逆境胁迫研究的一种有效方法。     

Temperature gradients and prebiological evolution

Thermodiffusive transport of trace elements that play important roles in living organisms, such as molybdenum, nickel, copper, and vanadium, was studied in a nonisothermal biphasic system comprised of a liquid solution and jelly layers. Our intent was to mimic the effects of temperature gradients on prebiological evolution. Conditions were found, similar to those probably existing during development of early eobionts, under which all the elements tested were concentrated within the heated jelly. Nonisothermal matter transport through grossly porous artificial membranes--the process of thermodialysis--was next investigated to assess the behavior of compartmentalized, i.e., membrane bound, eobionts. Particular interest was dedicated to the continuity of nonisothermal transport phenomena in the homogeneous and heterogeneous (membrane) systems and to the ability of compartmentalized eobionts to withstand osmotic swelling by means of thermoosmotic transport. Interestingly enough, under the experimental conditions adopted, sodium/potassium countertransport is also found, suggesting a very early physicochemical origin of the sodium-potassium pump. Surprisingly enough, evidence of teleonomic behavior appears in those very simple analogs of prebiological systems.     

Volume osmotic flows of non-homogeneous electrolyte solutions through horizontally mounted membrane

Results of an experimental study of volume osmotic flows in a single-membrane osmotic-diffusive cell, which contains a horizontal, microporous, symmetrical polymer membrane separating water and binary or ternary electrolyte solutions are presented. In the experimental set-up, water was placed on one side of the membrane. The opposite side of the membrane was exposed to binary or ternary solutions. As binary solutions, aqueous potassium chloride or ammonia solutions were used, whereas potassium chloride in 0.25 mol x l(-1) aqueous ammonia solution or ammonia in 0.1 mol x l(-1) aqueous potassium chloride solution were used as ternary solutions. Two (A and B) configurations of a single-membrane osmotic-diffusive cell in a gravitational field were studied. In configuration A, water was placed in a compartment above the membrane and the solution below the membrane. In configuration B the position of water and solution was reversed. Furthermore, the effect of amplification of volume osmotic flows of electrolyte solutions in the single-membrane osmotic-diffusive electrochemical cell was demonstrated. The thermodynamic models of the flux graviosmotic and amplification effects were developed, and the volume flux graviosmotic effect for configurations A and B of a single-membrane osmotic-diffusive cell was calculated. The results were interpreted within the conventional instability category, increasing the diffusion permeability coefficient value for the system: concentration boundary layer/membrane/concentration boundary layer.     

Electrostatic interactions at charged lipid membranes. Calcium binding

A quantitative study of calcium-ion binding by the negatively-charged phospholipid methylphosphatidic acid is presented. Experimental results are compared with the predictions of the Gouy-Chapman theory, taking into account both the ions bound at the membrane surface and the ions held in the diffuse layer. This theory suffices to explain the titration of the calcium/lipid system, but fails to explain completely the behaviour of the ordered-fluid transition temperature, which shows a splitting that according to electrostatic theory alone should not occur. The dependence of the calcium-lipid binding constant. upon 1: 1 electrolyte concentration is correctly predicted by the theory; the latter however gives equations which can only be solved numerically. A simple, approximate equation is therefore given (in the text, eq. 34) for the prediction of the degree of calcium binding to a negatively-charged lipid membrane.     

Intrinsic electric fields and proton diffusion in immobilized protein membranes. Effects of electrolytes and buffers.

We present a theory for proton diffusion through an immobilized protein membrane perfused with an electrolyte and a buffer. Using a Nernst-Planck equation for each species and assuming local charge neutrality, we obtain two coupled nonlinear diffusion equations with new diffusion coefficients dependent on the concentration of all species, the diffusion constants or mobilities of the buffers and salts, the pH-derivative of the titration curves of the mobile buffer and the immobilized protein, and the derivative with respect to ionic strength of the protein titration curve. Transient time scales are locally pH-dependent because of protonation-deprotonation reactions with the fixed protein and are ionic strength-dependent because salts provide charge carriers to shield internal electric fields. Intrinsic electric fields arise proportional to the gradient of an "effective" charge concentration. The field may reverse locally if buffer concentrations are large (greater to or equal to 0.1 M) and if the diffusivity of the electrolyte species is sufficiently small. The "ideal" electrolyte case (where each species has the same diffusivity) reduces to a simple form. We apply these theoretical considerations to membranes composed of papain and bovine serum albumin (BSA) and show that intrinsic electric fields greatly enhance the mobility of protons when the ionic strength of the salts is smaller than 0.1 M. These results are consistent with experiments where pH changes are observed to depend strongly on buffer, salt, and proton concentrations in baths adjacent to the membranes.