Transport parameters in the human red cell membrane: solute-membrane interactions of amides and ureas

We have studied the permeability of a series of hydrophilic amides and ureas through the red cell membrane by determining the three phenomenological coefficients which describe solute-membrane interaction: the hydraulic permeability (Lp), the phenomenological permeability coefficient (omega i) and the reflection coefficient (sigma i). In 55 experiments on nine solutes, we have determined that the reflection coefficient (after a small correction for solute permeation by membrane dissolution) is significantly less than 1.0 (P less than 0.003, t-test), which provides very strong evidence that solute and water fluxes are coupled as they cross the red cell membrane. It is proposed that the aqueous channel is a tripartite assembly, comprising H-bond exchange regions at both faces of the membrane, joined by a narrower sieve-specific region which crosses the lipid. The solutes bind to the H-bond exchange regions to exchange their solvation shell with the H-bonds of the channel; the existence of these regions is confirmed by the finding that the permeation of all the amides and ureas requires binding to well-characterized sites with Km values of 0.1-0.5 M. The sieve-specific regions provide the steric restraints which govern the passage of the solutes according to their size; their existence is shown by the findings that: (1) the reflection coefficient (actually the function [1-corrected sigma i]) is linearly dependent upon the solute molecular diameter; and (2) the permeability coefficient is linearly dependent upon solute molar volume. These several observations, taken together, provide strong arguments which lead to the conclusion that the amides and urea cross the red cell membrane in an aqueous pore.     

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.     

Network thermodynamic analysis and stimulation of isotonic solute-coupled volume flow in leaky epithelia: an example of the use of network theory to provide the qualitative aspects of a complex system and its verification by stimulation

A network thermodynamic model was developed to provide insights into the nature of isotonic solute-coupled volume flow in "leaky" epithelia, where the transepithelial volume flow is assumed to be primarily through the cellular pathway. The coupled flows of solute and volume at each membrane in this four membrane model are described by the practical phenomenological equations as developed by Kedem & Katchalsky (1958). The model contains one permeable non-electrolyte solute (s) and a fixed amount of an impermeable non-electrolyte (i) inside the cell. The cell is assumed to be capable of volume regulation under the steady-state experimental conditions simulated. A solute-pump, located in the basolateral membrane, uses feedback regulation to adjust Cs in the cell in order to maintain cell volume at or near control levels in all simulations. Model behavior is, in general, very consistent with experimental observations with respect to tonicity and magnitude of volume flow over a wide range of experimental conditions. Examination of the parameter space suggests the following important features when isotonic solute-coupled volume flow moves primarily through the cellular pathway: (1) the apical membrane reflection coefficient must be less than that of the basolateral membrane; (2) the basement membrane reflection coefficient must be small; (3) the apical membrane solute permeability and reflection coefficient are the two most "sensitive" parameters and need to vary in an inverse manner in order to maintain isotonicity when both solute and volume flows increase; and (4) relationships (1) and (3) above imply the need for at least two separate solute pathways in the apical membrane, one that is shared with volume flow and one that is not.     

Hydrostatic pressures developed by osmotically swelling vesicles bound to planar membranes

When phospholipid vesicles bound to a planar membrane are osmotically swollen, they develop a hydrostatic pressure (delta P) and fuse with the membrane. We have calculated the steady-state delta P, from the equations of irreversible thermodynamics governing water and solute flows, for two general methods of osmotic swelling. In the first method, vesicles are swollen by adding a solute to the vesicle-containing compartment to make it hyperosmotic. delta P is determined by the vesicle membrane's permeabilities to solute and water. If the vesicle membrane is devoid of open channels, then delta P is zero. When the vesicle membrane contains open channels, then delta P peaks at a channel density unique to the solute permeability properties of both the channel and the membrane. The solute enters the vesicle through the channels but leaks out through the region of vesicle-planar membrane contact. delta P is largest for channels having high permeabilities to the solute and for solutes with low membrane permeabilities in the contact region. The model predicts the following order of solutes producing pressures of decreasing magnitude: KCl greater than urea greater than formamide greater than or equal to ethylene glycol. Differences between osmoticants quantitatively depend on the solute permeability of the channel and the density of channels in the vesicle membrane. The order of effectiveness is the same as that experimentally observed for solutes promoting fusion. Therefore, delta P drives fusion. When channels with small permeabilities are used, coupling between solute and water flows within the channel has a significant effect on delta P. In the second method, an impermeant solute bathing the vesicles is isosmotically replaced by a solute which permeates the channels in the vesicle membrane. delta P resulting from this method is much less sensitive to the permeabilities of the channel and membrane to the solute. delta P approaches the theoretical limit set by the concentration of the impermeant solute.     

Configurational effect on the reflection coefficient for rigid solutes in capillary pores

Osmosis-driven flow through a leaky porous membrane is analyzed by combining the relevant equations describing spatial and orientational distributions of rigid non-spherical solute particles with the equations of fluid flow in a single capillary which is very narrow compared to its length. The capillary cross-section is either circular or rectangular and connects two bulk solution reservoirs having equal pressures but unequal concentrations of solute (osmotic pressure). The objective of this analysis is to study the effect of particle and pore shape on the reflection coefficient (σ₀). The most significant result is that for solute particles of any eccentricity from one (sphere) to infinity (needle) in either the circular or rectangular pores, σ₀ ≈ (1?K)², where K is the pore-bulk equilibrium partition coefficient. A corollary of this result is that, comparing solute particles of equal volume, the more elongated a solute is the higher is its reflection coefficient; furthermore, for a given solute, the reflection coefficient is higher for pores that are more eccentric compared to a circle of equal area.     

Solute concentration effect on osmotic reflection coefficient

A theory for the effect of concentration on osmotic reflection coefficient, correct to first order, was developed at the molecular level by considering the effect of solute-solute interactions on solute concentration and the fluid stress tensor within a solvent-filled pore. The solvent was modeled as a continuous fluid and potential energies between solute molecules and the pore wall were assumed to be pairwise additive. Although the theory is more general, calculations are presented only for excluded volume effects (hard-sphere for solute, hard-wall for pore). The relationship between the first-order concentration effect and the infinite dilution value of reflection coefficient appears to be geometry independent. The theory is discussed in light of experimental studies of osmotic flow that have recently appeared in the literature.     

Analysis of lateral diffusion from a spherical cell surface to a tubular projection.

Cell surfaces are often heterogeneous with respect to the lateral distribution and mobility of membrane components. Because lateral mobility is related to membrane structure, measurement of a particular component's local diffusion coefficient within a distinct surface region provides useful information about the formation and maintenance of that region. Many structurally interesting cell surface features can be described as narrow tubular projections from the body of the cell. In a companion paper, we consider the thin "tethers" that can be mechanically drawn from the red blood cell membrane, and we measure the transport of fluorescent integral proteins from the surface of the cell body onto the tether. In this paper we present an analysis to describe the surface diffusion of membrane particles from a spherical shell onto a thin cylindrical process. Provision is made for different rates of diffusion within the two morphologically distinct regions. The relative role of each region in controlling the diffusive flux between regions is determined primarily by a single dimensionless parameter. This parameter incorporates the ratio of the two diffusion coefficients as well as the dimensions of each region. The analysis can be applied to a fluorescence photobleaching experiment in which the extended process is bleached. If the dimensions of the spherical cell body and the cylindrical extension are known, then the diffusion coefficients of both regions can be determined from the experimental fluorescence recovery curve.     

OZONE-INDUCED MEMBRANE PERMEABILITY CHANGES

The effect of 0.5 ppm ozone for 0.5-1 hr on plant cell membrane permeability was ascertained. Permeabilities to both water and solutes were estimated by measuring leaf disc weight changes and following tritiated water and ⁸⁶Rb fluxes. Measurements were made immediately after ozone exposure and 24 hr after exposure. The reflection coefficient, σ, an index of solute permeability, decreased in ozone-treated primary leaves of pinto bean (Phaseolus vulgaris). The latter indicates an increase in membrane solute permeability or internal solute leakage. Water and THO flux estimates both indicated a decrease in membrane permeability to water; both the hydraulic conductivity (L_p) and the water diffusional coefficient (L_D) apparently decreased, an anomaly which is discussed. These data indicate that ozone has a direct effect on membrane function by altering permeability characteristics. We assume from these data that cell membranes are primary target sites for ozone injury.     

Membrane Permeability: Generalization of the Reflection Coefficient Method of Describing Volume and Solute Flows

The reflection coefficient method for describing volume and solute fluxes through membranes is generalized to take into account the nonideality of the solutions bathing the membrane and/or multicomponent systems. The reflection coefficient of the impermeable species in these systems is less than unity by a coefficient γ. The reflection coefficient obtained solely from the volume flow equation, σ^v, will always be less than the reflection coefficient obtained from the solute flow equation, σ^8v. These two coefficients are related by σ^8v = σ^v + γ.     

The permeability of the frog choroid plexus to nonelectrolytes

Summary Anin vitro preparation of the frog choroid plexus has been used to measure the permeability of the choroidal epithelium to 50 nonelectrolytes by an osmotic method. The method involves the measurement of nonelectrolyte reflection coefficients () by a rapid electrical procedure. For the majority of compounds tested, there was a good correlation between the rate of solute permeation and the solute's bulk-phase lipid: water partition coefficients; i.e., the higher the partition coefficient the greater the permeability. The membrane lipids of the choroid plexus differ from the membrane lipids of the gall bladder in at least three ways: (1) the lipids of the choroid plexus cannot distinguish between branched chain solutes and their straight chain isomers; (2) small polar solutes such as urea and acetamide permeate via the membrane lipids to a significant extent; and (3) the smaller selectivity ratios suggest that the lipids of the choroid plexus contain more hydrogen bonding sites (i.e., there are stronger solute: lipid intermolecular forces in the choroid plexus). The permeability characteristics of the choroid plexus are qualitatively similar to those of most other cell membranes. In addition, there is evidence for the presence of a special mechanism for the transport of sugar across this epithelium.     

Non-electrolyte permeability as a tool for studying membrane fluidity

1. The reflection coefficient for the permeation of thiourea through bilayers of phosphatidylcholine is a function of the fatty-acid composition of the lipid molecules. By means of these reflection coefficients an index for membrane fluidity has been given to each of those lipids, relative to that of egg phosphatidylcholine. 2. The maximum number of water molecules that can copermeate with each molecule of solute by means of solute-solvent interaction is a function of the packing of the lipid molecules in the bilayer. This parameter has been used in this paper for characterizing the fluidity of cholesterol-containing membranes and for membranes with their lipids in the gel state.     

Transport Parameters in a Porous Cellulose Acetate Membrane

The transport parameters of a cellulose acetate membrane prepared from a mixture of cellulose acetate, formamide, and acetone, 25:25:50 by weight, were studied. The membrane consists of a thin, porous layer, the skin, in series with a thick, highly porous layer, the coarse support. In the skin the diffusional permeability coefficient, ω, of a number of small amides and alcohols depends critically upon the partition coefficient, K_s, the size of the molecule, and the apparent hydrogen-bonding ability, N_s, of the solute. These observations are in general agreement with our earlier conclusions on the properties of nonporous membranes. On the other hand, the corrected reflection coefficient, σ', is not a very sensitive function of either N_s or K_s taken separately. The correlation between σ' and molecular diameter is reasonably good; however, it is much improved when both N_s and K_s are taken into consideration. Isotope interaction was also studied in the present preparation and was found to provide only a small (5–8%) contribution to the diffusional permeability coefficient of ethylene glycol. The contribution of solute-water friction was found to be less than 24% of the total solute friction.     

Analysis of the introduction and removal of glycerol in rabbit kidneys using a Krogh cylinder model

In 1982, Rubinsky and Cravalho described a Krogh cylinder model for the analysis of cryoprotectant transport in a perfused organ. By application of the Kedem-Katchalsky equations, changes in tissue volume caused by movements of water and solute were used to predict changes in capillary radius (Cryobiology 19, 70-82, 1982). We have now measured the changes in vascular resistance that are produced when sucrose or glycerol is introduced into the perfusate flowing through rabbit kidneys at 10 degrees C, and have analyzed these data by means of the Rubinsky-Cravalho semiempirical model. The sucrose data provided an estimate of hydraulic conductivity and the dimensions of the Krogh tissue units. Three rates of addition of glycerol, 10, 30, and 90 mM/min to a final concentration of 3 M, were studied. The vascular resistance fell to approximately 40% of its initial value (radius approximately 128% of initial value) with all three rates of addition, and then returned toward its normal value while the glycerol concentration was still increasing. This behavior could be explained either by a sudden change in solute permeability at that capillary radius, or by an inverse dependence of reflection coefficient upon solute concentration. Evidence is presented that favors the latter interpretation. The best fits for the apparent hydraulic conductivity and apparent solute permeability for glycerol are 1 X 10(-6) cm/sec atm and 6 X 10(-8) cm/sec, respectively, with the reflection coefficient falling from 1.0 when the glycerol concentration is zero to 0.1 when it is 3 M. The model is used to predict tissue concentrations of glycerol throughout each experiment.     

Permeability characteristics of the basement membrane (basal lamella) of the intestine of Ascaris suum

Permeability characteristics have been determined for isolated ribbons of the basement membrane of the intestine ofAscaris suum. The solute permeability coefficient (P_c) was measured for a series of hydrophobic, nonionic molecules of graded molecular size. The geometric pore area per unit path length (A_o/Δx) was estimated to be 24.0 cm from the diffusion rates for the various solute molecules. A filtration coefficient (L_p) of 18.1×10^?12 cm⁵/dyne-sec was determined by a method that employs osmotic pressure. The preceding values were used to calculate an average pore radius of 24.0 A for the membrane. The unstirred layer was estimated to be 30μm thick from measurements of the change in the rate of diffusion of water across the membrane with change in the rate of perfusion. The preceding values were used to calculate a reflection coefficien (σ), effective permeability coefficient (ω′), and a permeability coefficient (ω). The results support the view that this basement membrane functions as a filter and selective barrier to diffusion of constituents of the worm's body fluid.     

Role of the F1 region in the Escherichia coli aerotaxis receptor Aer

In Escherichia coli, the aerotaxis receptor Aer is an atypical receptor because it senses intracellular redox potential. The Aer sensor is a cytoplasmic, N-terminal PAS domain that is tethered to the membrane by a 47-residue F1 linker. Here we investigated the function, topology, and orientation of F1 by employing random mutagenesis, cysteine scanning, and disulfide cross-linking. No native residue was obligatory for function, most deleterious substitutions had radically different side chain properties, and all F1 mutants but one were functionally rescued by the chemoreceptor Tar. Cross-linking studies were consistent with the predicted α-helical structure in the N-terminal F1 region and demonstrated trigonal interactions among the F1 linkers from three Aer monomers, presumably within trimer-of-dimer units, as well as binary interactions between subunits. Using heterodimer analyses, we also demonstrated the importance of arginine residues near the membrane interface, which may properly anchor the Aer protein in the membrane. By incorporating these data into a homology model of Aer, we developed a model for the orientation of the Aer F1 and PAS regions in an Aer lattice that is compatible with the known dimensions of the chemoreceptor lattice. We propose that the F1 region facilitates the orientation of PAS and HAMP domains during folding and thereby promotes the stability of the PAS and HAMP domains in Aer.     

A biophysical analysis of stem and root diameter variations in woody plants

A comprehensive model of stem and root diameter variation was developed. The stem (or root) was represented using two coaxial cylinders corresponding with the mature xylem and the extensible tissues. The extensible tissues were assumed to behave as a single cell separated from the mature xylem by a virtual membrane. The mature xylem and the extensible tissues are able to dilate with temperature and grow. Moreover, the extensible tissues are able to shrink and swell according to water flow intensity. The model is mainly based on the calculation of water volume flows in the "single cell" that are described using the principles of irreversible thermodynamics. The elastic response to storage volume and plastic extension accompanying growth are described. The model simulates diameter variation due to temperature, solute accumulation, and xylem, water potential. The model was applied to the peach (Prunus persica) stem and to the plum (Prunus domestica x Prunus spinosa) root. The simulation outputs corresponded well with the diameter variation observed. The model predicts that variations of turgor pressure and osmotic potential are smaller than the variations of xylem water potential. It also demonstrates correlations between the xylem water potential, the turgor pressure, the elastic modulus, and the osmotic potential. The relationship between the diameter and the xylem water potential exhibits a substantial hysteresis, as observed in field data. A sensitivity analysis using the model parameters showed that growth and shrinkage were highly sensitive to the initial values of the turgor pressure and to the reflection coefficient of solutes. Shrinkage and growth were sensitive to elastic modulus and wall-yielding threshold pressure, respectively. The model was not sensitive to changes in temperature.     

Predicted permeability parameters of human ovarian tissue cells to various cryoprotectants and water

This study presents a generic numerical model to simulate the coupled solute and solvent transport in human ovarian tissue sections during addition and removal of chemical additives or cryoprotective agents (CPA). The model accounts for the axial and radial diffusion of the solute (CPA) as well as axial convection of the CPA, and a variable vascular surface area (A) during the transport process. In addition, the model also accounts for the radial movement of the solvent (water) into and out of the vascular spaces. Osmotic responses of various cells within an human ovarian tissue section are predicted by the numerical model with three model parameters: permeability of the tissue cell membrane to water (L(p)), permeability of the tissue cell membrane to the solute or CPA (omega) and the diffusion coefficient of the solute or CPA in the vascular space (D). By fitting the model results with published experimental data on solute/water concentrations within an human ovarian tissue section, I was able to determine the permeability parameters of ovarian tissue cells in the presence of 1.5M solutions of each of the following: dimethyl sulphoxide (DMSO), propylene glycol (PROH), ethylene glycol (EG), and glycerol (GLY), at two temperatures (4 degrees C and 27 degrees C). Modeling Approach 1: Assuming a constant value of solute diffusivity (D = 1.0 x 10(-9) m(2)/sec), the best fit values of L(p) ranged from 0.35 x 10(-14) to 1.43 x 10(-14) m(3)/N-sec while omega ranged from 2.57 x 10(-14) to 70.5 x 10(-14) mol/N-sec. Based on these values of L(p) and omega, the solute reflection coefficient, sigma defined as sigma = 1-omega v(CPA)/L(P) ranged from 0.9961 to 0.9996. Modeling Approach 2: The relative values of omega and sigma from our initial modeling suggest that the embedded ovarian tissue cells are relatively impermeable to all the CPAs investigated (or omega approximately 0 and sigma approximately 1.0). Consequently the model was modified and used to predict the values of L(p) and D assuming omega = 0 and sigma = 1.0. The best fit values of L(p) ranged from 0.44 x 10(-14) to 1.2 x 10(-14) m(3)/N-sec while D ranged from 0.85 x 10(-9) to 2.08 x 10(-9) m(2)/sec. Modeling Approach 3: Finally, the best fit values of D from modeling approach 2 were incorporated into model 1 to re-predict the values of L(p) and omega. It is hoped that the ovarian tissue cell parameters reported here will help to optimize chemical loading and unloading procedures for whole ovarian tissue sections and consequently, tissue cryopreservation procedures.