Osmosis: a macroscopic phenomenon,a microscopic view

At present, physical chemistry employs the tools of thermodynamics to treat osmosis across a semipermeable membrane. We propose a model in terms of momentum transfer, the inherent asymmetry of which leads quantitatively to the van't Hoff relationship; qualitatively, the solute molecules can be looked upon as micropumps that suck solvent through the pores in the membrane.     

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.     

Osmotic Flow of Water across Permeable Cellulose Membranes

Direct measurements have been made of the net volume flow through cellulose membranes, due to a difference in concentration of solute across the membrane. The aqueous solutions used included solutes ranging in size from deuterated water to bovine serum albumin. For the semipermeable membrane (impermeable to the solute) the volume flow produced by the osmotic gradient is equal to the flow produced by the hydrostatic pressure RT ΔC, as given by the van't Hoff relationship. In the case in which the membrane is permeable to the solute, the net volume flow is reduced, as predicted by the theory of Staverman, based on the thermodynamics of the steady state. A means of establishing the amount of this reduction is given, depending on the size of the solute molecule and the effective pore radius of the membrane. With the help of these results, a hypothetical biological membrane moving water by osmotic and hydrostatic pressure gradients is discussed.     

The Kinetics of Osmotic Transport through Pores of Molecular Dimensions

This paper presents a theoretical analysis of the kinetics of osmotic transport across a semipermeable membrane. There is a thermodynamic connection between the rate of flow under a hydrostatic pressure difference and the rate of flow due to a difference in solute concentration on the two sides. One might therefore attempt to calculate the osmotic transport coefficient by applying Poiseuille's equation to the flow produced by a difference in hydrostatic pressure. Such a procedure is, however, inappropriate if the pores in the membrane are too small to allow molecules to “overtake.” It then becomes necessary to perform a statistical calculation of the transport coefficient, and such a calculation is described in this paper. The resulting expression for the number of solvent molecules passing through a pore per second is J = m D₁ δn₁/l² where m is the number of solvent molecules in the pore, l is the length of the pore, D₁ is the self-diffusion coefficient of the solute, and δn₁ the difference in solvent mole fraction on the two sides of the membrane. This equation is used for estimating the number of pores per unit area of the squid axon membrane; the result is 6 × 10⁹ pores/cm².     

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.     

A kinetic theory of diffusion forces in metabolizing systems

The development of a molecular theory of the diffusion drag forces in liquids is attempted by considering the liquids as limiting cases of very dense gases. An expression is derived for the force on a small particle suspended in a nonuniform mixture of such gases on the basis of kinetic theory. Another expression for the order of magnitude of the force on a larger particle is obtained by introducing certain hydrodynamical considerations. These results are compared with an expression previously derived by N. Rashevsky, and estimates are made of the order of magnitude of the volume force on the granules and particles within a typical cell due to the diffusion of metabolites. It is found that the drag forces, exerted by a diffusing solute, depend to a very large extent on the physical properties of the solvent.     

Effects of solvent and solute drag on transmembrane diffusion

The present study compares and quantitates both solvent drag and solute drag forces in a system with both heteropore and homopore membranes. It is shown that tracer solute permeability can be increased if solution flow or driver solute flux is in the direction of tracer diffusion. Either force can decrease tracer permeability if the force can decrease tracer permeability if the force is opposite to the direction of tracer diffusion. The two forces can be additive or one force may reduce the effect of the other force. In the particular system quantitated, solute drag is shown to be some 300 times more effective than solvent drag on a mole-to-mole basis. The use of a number of solute pairs on other homopore and heteropore membranes confirms the finding that the two drag forces can be analyzed or manipulated in a variety of systems.     

Molecular Simulations of Membrane Based Separations of Supercritical Electrolyte Solutions

Abstract

Computer simulations of solutions of electrolytes (NaCl and KCl) in supercritical water undergoing membrane based separations have been carried out. These studies used a technique developed recently, in which the system is maintained at steady state by periodically recycling the solvent molecules that permeated the membrane. Our results showed that ionic clusters, formed as a result of water molecules surrounding the ions, play a significant role in these separations. The effect of the main osmotic driving forces, such as pressure, temperature, concentration, and electric fields on the rate of permeation across the membrane was studied. In addition, we also looked at the effect of changes in the pore size and the attractive force between the membrane and solvent/solute. Finally, we examined the stability of the ionic clusters in these simulations.     

Further Observations on Asymmetrical Solute Movement across Membranes

The permeability of frog skin under the influence of urea hyperosmolarity has been studied. Flux ratio asymmetry has been demonstrated again for tracer mannitol. The inhibitors DNP, CN^-, and ouabain have been used to eliminate active sodium transport and it was found that urea hyperosmolarity produces asymmetrical mannitol fluxes on frog skins having no short-circuit current. These findings suggest that flux ratio asymmetry is due to solute interaction and is unrelated to sodium transport. Studies with a synthetic membrane show clearly that bulk flow of fluid can produce a "solvent drag" effect and change flux ratios. When bulk flow is blocked and solute gradients allowed their full expression, then solute interaction "solute drag" is easily demonstrable in a synthetic system.     

Interrelation of ethylene glycol,urea and water transport in the red cell

The reflection coefficient, σ_j, which measures the coupling between the jth solute and water transport across a semipermeable membrane, varies between 0 and 1.0. Values of σ_j significantly less than 1.0 provide irreversible thermodynamic proof that there is coupling between the transport of solute and solvent and thus that they share a common pathway. We have developed an improved method for measuring σ and have used it to determine that σ_{ethylene glycol} = 0.71 ± 0.03 and σ_urea = 0.65 ± 0.03, in agreement with many, but not all, previous determinations. Since both of these values are significantly lower than 1.0, they show that there is a common ethylene glycol/water pathway and a common urea/water pathway. Addition of first one and then two methyl groups to urea increases σ to 0.89 ± 0.04 for methylurea and 0.98 ± 0.4 for 1,3-dimethylurea, consistent with passage through an aqueous pore with a sharp cutoff in the 6–7 Å region.     

MEMBRANE POTENTIALS AND CATAPHORETIC POTENTIALS OF PROTEINS

1. It has been shown in preceding publications that the membrane potentials of protein solutions or gels are determined by differences in the concentration of a common ion (e.g. hydrogen ion) inside a protein solution or protein gel and an outside aqueous solution free from protein, and that the membrane potentials can be calculated with a good degree of accuracy from Donnan''s equation for membrane equilibria. 2. On the basis of the theory of electrical double layers developed by Helmholtz, we are forced to assume that the cataphoretic potentials of protein particles are determined by a difference in the concentration of the two oppositely charged ions of the same electrolyte in the two strata of an electrical double layer surrounding the protein particle but situated entirely in the aqueous solution. 3. The membrane potentials of proteins agree with the cataphoretic potentials in that the sign of charge of the protein is negative on the alkaline side and positive on the acid side of the isoelectric point of the protein in both membrane potentials and cataphoretic potentials. The two types of potential of proteins disagree, especially in regard to the action of salts with trivalent and tetravalent ions on the sign of charge of the protein. While low concentrations of these salts bring about a reversal of the sign of the cataphoretic potentials of protein particles (at least in the neighborhood of the isoelectric point), the same salts can bring the membrane potentials of proteins only to zero, but call bring about no or practically no reversal of the sign of charge of the protein. Where salts seem to bring about a reversal in the membrane potential of protein solutions, the reversal is probably in reality always due to a change in the pH. 4. We may state, as a result of our experiments, that the cataphoretic migration and the cataphoretic P.D. of protein particles or of suspended particles coated with a protein are the result of two groups of forces; namely, first, forces inherent in the protein particles (these forces being linked with the membrane equilibrium between protein particles and the outside aqueous solution); and second, forces inherent entirely in the aqueous solution surrounding the protein particles. The forces inherent in the protein particles and linked with the membrane equilibrium prevail to such an extent over the forces inherent in the water, that the sense of the cataphoretic migration of protein particles is determined by the forces resulting from the membrane equilibrium.     

Geometric and potential driving formation and evolution of biomolecular surfaces

This paper presents new geometrical flow equations for the theoretical modeling of biomolecular surfaces in the context of multiscale implicit solvent models. To account for the local variations near the biomolecular surfaces due to interactions between solvent molecules, and between solvent and solute molecules, we propose potential driven geometric flows, which balance the intrinsic geometric forces that would occur for a surface separating two homogeneous materials with the potential forces induced by the atomic interactions. Stochastic geometric flows are introduced to account for the random fluctuation and dissipation in density and pressure near the solvent–solute interface. Physical properties, such as free energy minimization (area decreasing) and incompressibility (volume preserving), are realized by some of our geometric flow equations. The proposed approach for geometric and potential forces driving the formation and evolution of biological surfaces is illustrated by extensive numerical experiments and compared with established minimal molecular surfaces and molecular surfaces. Local modification of biomolecular surfaces is demonstrated with potential driven geometric flows. High order geometric flows are also considered and tested in the present work for surface generation. Biomolecular surfaces generated by these approaches are typically free of geometric singularities. As the speed of surface generation is crucial to implicit solvent model based molecular dynamics, four numerical algorithms, a semi-implicit scheme, a Crank–Nicolson scheme, and two alternating direction implicit (ADI) schemes, are constructed and tested. Being either stable or conditionally stable but admitting a large critical time step size, these schemes overcome the stability constraint of the earlier forward Euler scheme. Aided with the Thomas algorithm, one of the ADI schemes is found to be very efficient as it balances the speed and accuracy.      

Effect of frictional force on urea and thiourea during an intramembrane transport: an explicit solvent Langevin dynamics simulation method

An explicit solvent Langevin dynamics (LD) simulation method is employed to investigate the effect of frictional force on the solute–solvent interactions in urea and thiourea, which are subjected to varied degree of frictional forces akin to diffusional transport across the membrane system. Utilizing the frictional force concept in LD method, the effect of increasing frictional coefficient is studied on the microscopic properties such as single-point energy and N–C–N bond angle of urea and thiourea in aqueous solutions. The present work follows a self-conscious approach by explicitly including the solvent molecules in the LD simulations. The results are further compared with the standard Langevin approach without explicitly specifying solvent molecules. An analysis of the results reveals that the two cases differ strongly in the intermediate (Brownian) regime of frictional coefficient.     

Coupling of Solute and Solvent Flows in Porous Lipid Bilayer Membranes

The present experiments were designed to evaluate coupling of water and nonelectrolyte flows in porous lipid bilayer membranes (i.e., in the presence of amphotericin B) in series with unstirred layers. Alterations in solute flux during osmosis, with respect to the flux in the absence of net water flow, could be related to two factors: first, changes in the diffusional component of solute flux referable to variations in solute concentrations at the membrane interfaces produced by osmotic flow through the unstirred layers; and second, coupling of solute and solvent flows within the membrane phase. Osmotic water flow in the same direction as solute flow increased substantially the net fluxes of glycerol and erythritol through the membranes, while osmotic flow in the opposite direction to glycerol flow reduced the net flux of that solute. The observed effects of osmotic water flow on the fluxes of these solutes were in reasonable agreement with predictions based on a model for coupling of solute and solvent flows within the membrane phase, and considerably in excess of the prediction for a diffusion process alone.     

Interfacial interaction between methyl parathion-degrading bacteria and minerals is important in biodegradation

In the present study, the influence of kaolinite and goethite on microbial degradation of methyl parathion was investigated. We observed that the biodegradation process was improved by kaolinite and depressed by goethite. Calorimetric data further showed that the metabolic activities of degrading cells (Pseudomonas putida) were enhanced by the presence of kaolinite and depressed by the presence of goethite. A semipermeable membrane experiment was performed and results supported the above observations: the promotive effect of kaolinite and the inhibition of goethite for microbial degradation was not found when the bacteria was enclosed by semipermeable membrane and had no direct contact with these minerals, suggesting the important function of the contact of cellular surfaces with mineral particles. The relative larger particles of kaolinite were loosely attached to the bacteria. This attachment made the cells easy to use the sorbed substrate and then stimulated biodegradation. For goethite, small particles were tightly bound to bacterial cells and limited the acquisition of substrate and nutrients, thereby inhibiting biodegradation. These results indicated that interfacial interaction between bacterial cells and minerals significantly affected the biodegradation of pesticides.     

Role of solute drag in intestinal transport

This study presents experiments related to the role of solvent drag and solute drag in the transmembrane movement of nonelectrolytes in a perfused rat intestine preparation. Conditions were chosen to simulate the effects of luminal hyperosmolarity on the permeability of tracer solutes. Data are presented on net water flux, transepithelial potentials, and lumen-to-blood and blood-to-lumen tracer solute movements during control electrolyte perfusion and after making the perfusate hyperosmotic. The results indicate that both solvent drag and solute drag can play significant roles in the transepithelial movement of solute and solute permeabilities in the rat ileum preparation. It is suggested that the potential roles of solvent drag and solute drag should be accounted for or considered during the characterization of the mechanisms of biological membrane function.     

Molecular dynamics simulation study of the static and dynamic properties of a model colloidal suspension with explicit solvent

Molecular dynamics simulation was used to study a colloidal suspension with explicit solvent to determine how inclusion of the solvent affects the structure and dynamics of the system. The solute was modelled as a hard-core particle enclosed in a Weeks–Chandler–Andersen (WCA) potential shell, while the solvent was modelled as a simple WCA fluid. We found that when the solute–solvent interaction included a hard core equal to half of the solute hard-core diameter, large depletion effects arose, leading to an effective attraction and large deviations from hard-sphere structure for the colloidal component. It was found that these effects could be eliminated by reducing the hard-core distance parameter in the solute–solvent interaction, thus allowing the solvent to penetrate closer to the colloidal particles. Three different values for the solute–solvent hard-core parameter were systematically studied by comparing the static structure factor and radial distribution function to the predictions of the Percus–Yevick theory for hard spheres. When the optimal value of the solute–solvent hard-core interaction parameter was found, this model was then used to study the dynamical behaviour of the colloidal suspension. This was done by first measuring the velocity autocorrelation function (VACF) over a large range of packing fractions. We found that this model predicted the sign of the long-time tail in the VACF in agreement with experimental values, something that single component hard-sphere systems have failed to do. The intermediate scattering functions at low wavevector were briefly studied to determine their behaviour in a dilute system. It was found that they could be modelled using a simple diffusion equation with a wavevector independent diffusion coefficient, making this model an excellent analogue of experimentally studied hard-sphere colloids.     

A mathematical model of solute coupled water transport in toad intestine incorporating recirculation of the actively transported solute

A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241-251), computations predict that 60-80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived.     

Effect of dielectric constant of medium on protonation equilibria of ethylenediamine

Abstract

The effect of dielectric constant of medium on protonation equilibria has been studied by determining protonation constants of ethylenediamine pH metrically in various concentrations (0–60%v/v) of acetoni-trile– and ethylene glycol–water mixtures, at an ionic strength of 0.16mol L^?1 and at 303.0 K. MINIQUAD75 computer program has been used for the calculation of protonation constants. Linear and non-linear variations of step-wise protonation constants with reciprocal of dielectric constant of the solvent mixtures have been attributed to the dominance of the electrostatic and non-electrostatic forces, respectively. The trend is explained on the basis of solute–solute and solute–solvent interactions, solvation, proton transfer processes and dielectric constants of the media.