The permeability coefficient of the wall of a villous membrane

Summary The equations hitherto used to correct the permeability coefficient for the unstirred layer influence are valid only for flat membranes. Therefore, appropriate equations for membranes with a villous surface (e.g., small intestine) have been derived. They take into account the non-linear concentration gradient in the intervillous part of the unstirred layer. Quantitative information about the geometry of the villous surface and the unstirred layer thickness are needed to calculate the permeability coefficient of the membrane wall (e.g., intestinal epithelium). The concentration of highly permeable substances drops sharply already in the upper part of the intervillous space, so that the tips of the villi function as effective absorbing area. The intervillous concentration gradient of a substance with a low permeability coefficient is so small, that such a substance is absorbed by the total surface area of the villous membrane. The effective absorbing area of substances with intermediate permeability coefficient lies between the described limits.     

Determination of the membrane permeability coefficient and the reflection coefficient by the two-dimensional laminar flow model for intestinal perfusion experiments

We performed single perfusion experiments in the small intestine of rats in order to prove that the two-dimensional laminar flow model is suitable to determine the membrane permeability coefficient and the reflection coefficient. We used progesterone as an aqueous-diffusion-limited drug, urea as a membrane transport-limited drug and the tritiated water as an intermediate substance. The membrane permeability coefficient for progesterone was calculated to be 3.6 X 10(-4) cm/s. This value did not change when the thickness of the aqueous diffusion layer was altered by increasing the perfusion rate 10-fold. It was directly demonstrated that the two-dimensional laminar flow model was suitable to analyze the data of intestinal perfusion experiments. Membrane permeability coefficients for urea and tritiated water were determined to be 3.4 X 10(-5) cm/s and 8.9 X 10(-5) cm/s, respectively. In the presence of water absorption with the hypotonic perfusion solution, the reflection coefficient for urea was 0.84. This value is thought to be theoretically reasonable, suggesting the usefullness of the two-dimensional laminar flow model to obtain the reflection coefficient in the intestinal membrane.     

Diffusion with memory in two cases of biological interest

The complexity of a biological structure, such as membrane where the transport process may carry solid particles which may obstruct some of the pores, diminishing their size and making the permeability dependent on the local structure of the medium, suggests the introduction of a space-dependent diffusion constant. In this note, the profile concentration of diffusing solutes inside a cell membrane has been calculated on the basis of the Fick diffusion equation modified by introducing a memory formalism (diffusion with memory). This approach has been employed to describe the concentration profile inside the membrane when a sudden change of the concentration in the medium bathing one of its face is applied for a limited interval of time. A further application of the method concerns the so-called concentration boundary layer that occurs at the membrane-aqueous medium interface, where the solute concentration depends, even at considerable depth, on the local structure of the interface. These profiles are compared to some recent experiments concerning the diffusion of ethanol in a layer close to a nephrophane membrane. This approach generalizes the diffusion models based on the Fick equation to more complex systems, where a space-independent diffusion coefficient could be inappropriate to take into account the large variety of diffusion processes in biological systems.     

A new diffusion chamber system for the determination of drug permeability coefficients across the human intestinal epithelium that are independent of the unstirred water layer.

A new method for determining permeability coefficients, that are independent of the unstirred water layer (UWL), has been developed. The method was used to determine the cellular permeability coefficient of the rapidly absorbed drug testosterone in monolayers of the human intestinal epithelial cell line, Caco-2. Using a new diffusion cell with an effective stirring system based on a gas lift, the cellular permeability coefficient for testosterone was (1.98 +/- 0.13).10(-4) cm/s which is 3.5-times higher than the permeability coefficient obtained in the unstirred system. The thickness of the UWL obtained with the well stirred diffusion cell was 52 +/- 4 microns. This value is much lower than those previously reported in various well stirred in vitro models. The calculated cellular permeability of testosterone was 13-23-times lower than that for an UWL of the same thickness as the epithelial cell (17-30 microns). We conclude that the permeability of the epithelial monolayer must be included in calculations of the thickness of the UWL.     

The water permeability of toad urinary bladder. I. Permeability of barriers in series with the luminal membrane

Antidiuretic hormone (ADH) induces a large increase in the water permeability of the luminal membrane of toad urinary bladder. Measured values of the diffusional water permeability coefficient, Pd(w), are spuriously low, however, because of barriers within the tissue, in series with the luminal membrane, that impede diffusion. We have now determined the water permeability coefficient of these series barriers in fully stretched bladders and find it to be approximately 6.3 X 10(- 4) cm/s. This is equivalent to an unstirred aqueous layer of approximately 400 microns. On the other hand, the permeability coefficient of the bladder to a lipophilic molecule, hexanol, is approximately 9.0 X 10(-4) cm/s. This is equivalent to an unstirred aqueous layer of only 100 microns. The much smaller hindrance to hexanol diffusion than to water diffusion by the series barriers implies a lipophilic component to the barriers. We suggest that membrane-enclosed organelles may be so tightly packed within the cytoplasm of granular epithelial cells that they offer a substantial impediment to diffusion of water through the cell. Alternatively, the lipophilic component of the barrier could be the plasma membranes of the basal cells, which cover most of the basement membrane and thereby may restrict water transport to the narrow spaces between basal and granular cells.     

A multiscale theoretical model for diffusive mass transfer in cellular biological media

An integrated methodology is developed for the theoretical analysis of solute transport and reaction in cellular biological media, such as tissues, microbial flocs, and biofilms. First, the method of local spatial averaging with a weight function is used to establish the equation which describes solute conservation at the cellular biological medium scale, starting with a continuum-based formulation of solute transport at finer spatial scales. Second, an effective-medium model is developed for the self-consistent calculation of the local diffusion coefficient in the cellular biological medium, including the effects of the structural heterogeneity of the extra-cellular space and the reversible adsorption to extra-cellular polymers. The final expression for the local effective diffusion coefficient is: D(Abeta)=lambda(beta)D(Aupsilon), where D(Aupsilon) is the diffusion coefficient in water, and lambda(beta) is a function of the composition and fundamental geometric and physicochemical system properties, including the size of solute molecules, the size of extra-cellular polymer fibers, and the mass permeability of the cell membrane. Furthermore, the analysis sheds some light on the function of the extra-cellular hydrogel as a diffusive barrier to solute molecules approaching the cell membrane, and its implications on the transport of chemotherapeutic agents within a cellular biological medium. Finally, the model predicts the qualitative trend as well as the quantitative variability of a large number of published experimental data on the diffusion coefficient of oxygen in cell-entrapping gels, microbial flocs, biofilms, and mammalian tissues.     

Potassium ion accumulation at the external surface of the nodal membrane in frog myelinated fibers.

Potassium accumulation associated with outward membrane potassium current was investigated experimentally in myelinated fibers and analyzed in terms of two models-three-compartment and diffusion in an unstirred layer. In the myelinated fibers, as in squid giant axons, the three-compartment model satisfactorily describes potassium accumulation. Within this framework the average space thickness, theta, in frog was 5,900 +/- 700 A, while the permeability coefficient of the external barrier, PK, was (1.5 +/- 0.1) X 10(-2) cm/s. The model of ionic diffusion in an unstirred aqueous layer adjacent to the axolemma, as an alternative explanation for ion accumulation, was also consistent with the experimental data, provided that D, the diffusion constant, was (1.8 +/- 0.2) X 10(-6) cm/s and l, the unstirred layer thickness, was 1.4 +/- 0.1 micron, i.e., similar to the depth of the nodal gap. An empirical equation relating the extent of potassium accumulation to the amplitude and duration of depolarization is given.     

Water transport across isolated term human amnion

Summary The hydrodynamic permeability of normal term human amnion is measured using pressure-driven bulk flows. The permeability coefficient is found to vary widely, variations between tissues taken from different subjects being significantly greater than those from samples taken from one subject. No correlation is observed between this coefiicient and either tissue thickness or the diffusional permeability coefficient measured using tritiated water; it is, however, found to be very sensitive to epithelial damage.The results indicate that the bulk transport of water through amnion is largely controlled by the amniotic epithelium alone. This contrasts with water diffusion which is a function of total membrane thickness. The two permeability coefficients cannot therefore be employed to formulate an equivalent pore model of the whole tissue. An equivalent pore model of the epithelial layer only is considered and the results assessed in the light of other evidence bearing on the structure of amnion. It is concluded that the epithelial layer is intersected by a large number of pores with radius 10 to 30 Å, and a smaller number of much broader pores.     

The water permeability of basement membrane under increasing pressure: evidence for a new theory of permeability

The water permeability and physical characteristics of the basement membrane (lens capsule) of the crystalline lens of the adult rat have been investigated. The hydraulic conductivity of the basement membrane at low pressure is 50 +/- 9.5 X 10(-12) m s-1 Pa-1 and at high pressure 17 +/- 7.5 X 10(-12) m s-1 Pa-1. This decrease in permeability occurs despite a 75% increase in area of the membrane and a 65% reduction in its thickness. Conventional theories of a membrane possessing pores or of a fibre matrix of filaments of a constant diameter fail to explain the decreasing permeability of the membrane with increasing hydrostatic pressure. The present data suggest that the structure of the membrane is changed by pressure and the coiled filaments of which it is composed are extended as stress is applied to the membrane. If allowance is made both for thinning and for compaction of the membrane and the extension of its area the permeability of the membrane can be predicted satisfactorily at varying pressures. Thus the hydraulic conductivity of basement membrane at a given pressure can be adequately described by the product of a constant and a dimensionless 'deformation coefficient'. This deformation coefficient is equal to the square of the product of the thickness ratio and elongation ratio of the membrane at the given filtration pressure.     

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.     

On the Problem of Diffusivity in Heterogeneous Biological Materials with Random Structure

Biological tissues are multicompartmental heterogeneous media composed of cellular and subcellular domains. Randomly walking water molecules may have different diffusion coefficients and densities (concentrations) in different domains, namely within cells and within the outer medium. Results of the proposed effective media scale-averaging iterative scheme are used to explore the effects of a large range of microstructural and compositional parameters on the apparent (effective) diffusion coefficient. A self-consistent modelling framework for predicting the steady-state effective diffusion coefficient is presented; the framework reveals the strong dependence of the apparent diffusion coefficient on the ratio of the microscopic diffusion coefficients of the comprising phases, permeability of the cells, and their volume fractions.     

Diffusion of 133Xe through frog skins, toad bladders, and water boundary layers.

We have measured the total permeability coefficients P as a function of stirring frequency omega for 133Xe through frog skins and toad bladders. The permeability coefficients for the frog skins and toad bladders proper are, respectively, Pm = (3.9 +/- 0.8) X 10(-4) cm/s and (7.4 +/- 4.2) X 10(-4) cm/s. "Unstirred" water layer thickness delta is determined concurrently, from the frequency dependence of P(omega); the result for frog skin is delta = (0.060 +/- 0.016) square root of omega(rad/s) cm. The stirring frequency range is from omega = 7.5 rad/s (72 rpm) to 55 rad/s (530 rpm). The results support the conclusions that the principal barrier to Xe diffusion in these epithelia is inter- and intracellular water, and that the diffusion is passive and rapid. The experimental method may be straightforwardly adapted to the measurement of diffusion or counterdiffusion of any gamma-radioactive soluble or partly soluble solute through any flat membrane or through a solvent. We estimate the amount of total body-absorbed radioactivity due to environmental 133Xe to be 50 fCi for an ambient concentration of 2.6 pCi/m3 of air.     

Significant potassium ion accumulation at the external surface of Myxicola giant axons

Potassium accumulation associated with outward membrane potassium current was investigated experimentally in Myxicola giant axon. During prolonged voltage-clamp pulses to positive transmembrane potentials, the K+ equilibrium potential may approach zero mV, suggesting massive K+ accumulation outside the axonal membrane to concentrations many-fold higher than those in the bathing medium. The potassium accumulation can be satisfactorily described by a three-compartment model, consisting of the nerve fiber, a restricted physiological periaxonal space and the bulk solution. The average thickness, theta, of the periaxonal space is calculated as 177 +/- 59 A, i.e., comparable to that in the squid, while the permeability coefficient of the external barrier, PKs, was calculated to be (1.4 +/- 0.4) X 10(-4) cm/s. These conclusions are well supported by morphological study.     

A model for the diffusion of fluorescent probes in the septate giant axon of earthworm. Axoplasmic diffusion and junctional membrane permeability.

The diffusion of the three fluorescent probes dichlorofluorescein, carboxyfluorescein, and Lucifer Yellow within the septate median giant axon of the earthworm was monitored using fluorometric methods. A diffusion model was derived that allowed computation of the apparent axoplasmic diffusion coefficient, junctional membrane permeability (septal membranes), and plasma membrane permeability for each probe. Dichlorofluorescein and carboxyfluorescein have similar apparent axoplasmic diffusion coefficients, which were reduced by a factor of eight relative to that predicted from the Einstein-Stokes equation. Nonspecific reversible binding appears to be the major cause of the retarded diffusion coefficients. Junctional membrane permeability for dichlorofluorescein was 4.7 to 73-fold greater than that for carboxyfluorescein. This difference could not be explained on the basis of molecular size but can be explained by the difference in charge between the two molecules. Diffusion coefficients and junctional membrane permeabilities remained constant with time for both dyes. The diffusion of Lucifer Yellow within the axoplasm and permeability through the junctional membranes did not remain constant with time but declined. From this it was inferred that Lucifer Yellow experienced a slow, irreversible binding to axoplasmic elements. All three probes had finite plasma membrane permeabilities.     

Interaction of enkephalin peptides with anionic model membranes.

According to the model for passive transport across the membranes, the total flow of permeant molecules is related to the product of the water-membrane partition coefficient and the diffusion coefficient, and to the water-membrane interfacial barrier. The effect of membrane surface charge on the permeability and interaction of analgesic peptide ligands with model membranes was investigated. A mixture of zwitterionic phospholipids with cholesterol was used as a model membrane. The lipid membrane charge density was controlled by the addition of anionic 1-palmitoyl-2-oleoylphosphatidylserine. Two classes of highly potent analgesic peptides were studied, c[D-Pen(2),D-Pen(5)]enkephalin (DPDPE) and biphalin, a dimeric analog of enkephalin. The effect of increased surface charge on the permeability of the zwitterionic DPDPE is a relatively modest decrease, that appears to be due to a diminished partition coefficient. On the other hand the binding of the dicationic biphalin ligands to membranes increases proportionally with increased negative surface charge. This effect translates into a significant reduction of biphalin permeability by reducing the diffusion of the peptide across the bilayer. These experiments show the importance of electrostatic effects on the peptide-membrane interactions and suggest that the negative charge naturally present in cell membranes may hamper the membrane transport of some peptide drugs, especially cationic ones, unless there are cationic transporters present.     

Anomalous Diffusion Induced by Cristae Geometry in the Inner Mitochondrial Membrane

Diffusion of inner membrane proteins is a prerequisite for correct functionality of mitochondria. The complicated structure of tubular, vesicular or flat cristae and their small connections to the inner boundary membrane impose constraints on the mobility of proteins making their diffusion a very complicated process. Therefore we investigate the molecular transport along the main mitochondrial axis using highly accurate computational methods. Diffusion is modeled on a curvilinear surface reproducing the shape of mitochondrial inner membrane (IM). Monte Carlo simulations are carried out for topologies resembling both tubular and lamellar cristae, for a range of physiologically viable crista sizes and densities. Geometrical confinement induces up to several-fold reduction in apparent mobility. IM surface curvature per se generates transient anomalous diffusion (TAD), while finite and stable values of projected diffusion coefficients are recovered in a quasi-normal regime for short- and long-time limits. In both these cases, a simple area-scaling law is found sufficient to explain limiting diffusion coefficients for permeable cristae junctions, while asymmetric reduction of the junction permeability leads to strong but predictable variations in molecular motion rate. A geometry-based model is given as an illustration for the time-dependence of diffusivity when IM has tubular topology. Implications for experimental observations of diffusion along mitochondria using methods of optical microscopy are drawn out: a non-homogenous power law is proposed as a suitable approach to TAD. The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes.     

Effect of membrane tension on the physical properties of DOPC lipid bilayer membrane

Molecular dynamics simulations of a dioleoylphosphocholine (DOPC) lipid bilayer were performed to explore its mechanosensitivity. Variations in the bilayer properties, such as area per lipid, volume, thickness, hydration depth (HD), hydration thickness (HT), lateral diffusion coefficient, and changes in lipid structural order were computed in the membrane tension range 0 to 15dyn/cm. We determined that an increase in membrane tension results in a decrease in the bilayer thickness and HD of ~5% and ~5.7% respectively, whereas area per lipid, volume, and HT/HD increased by 6.8%, 2.4%, and 5% respectively. The changes in lipid conformation and orientation were characterized using orientational (S(2)) and deuterium (S(CD)) order parameters. Upon increase of membrane tension both order parameters indicated an increase in lipid disorder by 10-20%, mostly in the tail end region of the hydrophobic chains. The effect of membrane tension on lipid lateral diffusion in the DOPC bilayer was analyzed on three different time scales corresponding to inertial motion, anomalous diffusion and normal diffusion. The results showed that lateral diffusion of lipid molecules is anomalous in nature due to the non-exponential distribution of waiting times. The anomalous and normal diffusion coefficients increased by 20% and 52% when the membrane tension changed from 0 to 15dyn/cm, respectively. In conclusion, our studies showed that membrane tension causes relatively significant changes in the area per lipid, volume, polarity, membrane thickness, and fluidity of the membrane suggesting multiple mechanisms by which mechanical perturbation of the membrane could trigger mechanosensitive response in cells.     

Water permeability of Betula periderm

The water permeability of periderm membranes stripped from mature trees of Betula pendula Roth was investigated. The diffusion of water was studied using the system water/membrane/water, and transpiration was measured using the system water/membrane/water vapor. Betula periderm consists of successive periderm layers each made up of about 5 heavily suberized cell layers and a varying number of cell layers that are little suberized, if at all. It is shown that these layers act as resistances in series. The permeability coefficient of the diffusion of water (P _d) can be predicted with 79% accuracy from the reciprocal of the membrane weight (x in mg cm^-2) by means of the linear equation P _d=14.69·10^-7 x-0.73·10^-7. For example, the P _d of a periderm membrane having a weight of 10 mg cm^-2 (approx. 250 m thick) is 7.4·10^-8 cm s^-1, which is comparable to the permeability of cuticles. This comparison shows that on a basis of unit thickness, Betula periderm is quite permeable to water as cuticles have the same resistance with a thickness of only 0.5 to 3 m. It is argued that this comparatively high water permeability of birch periderm is due to the fact that middle lamellae and the primary walls of periderm cells are not at all, or only incompletely suberized and, therefore, form a hydrophilic network within which the water can flow. This conclusion is based on the following observations: (1) Middle lamellae and primary walls stain strongly with toluidine blue, which shows them to be polar. (2) If silver ions are added as tracer for the flow of water, they are found only in the middle lamellae, primary walls, and in plasmodesmata, while no silver can be detected in the suberized walls. (3) Permeability coefficients of transpiration strongly depend on water activity. This shows conclusively that water flows across Betula periderm via a polar pathway. It is further argued that liquid continuity is likely to be maintained under all physiological conditions in the network formed by middle lamellae and primary walls. On the other hand, the lumina of periderm cells, intercellular air spaces in the lenticels, and even the pores in the suberized walls (remainders of plasmodesmata) will drain at a humidity of 95% and below. Due to the presence of intercellulars the permeability coefficient of lenticels is much greater than that of the periderm. A substantial amount of the total water, therefore, flows as vapor through lenticels even though they cover only 3% of the surface.Abbreviations PM perideron membrane - P _d permeability coefficient for diffusion of water - P _tt permeability coefficient of transpiration - MES (N-morpholino)ethane sulfonic acid     

Development of a novel microperfusion chamber for determination of cell membrane transport properties.

A novel microperfusion chamber was developed to measure kinetic cell volume changes under various extracellular conditions and to quantitatively determine cell membrane transport properties. This device eliminates modeling ambiguities and limitations inherent in the use of the microdiffusion chamber and the micropipette perfusion technique, both of which have been previously validated and are closely related optical technologies using light microscopy and image analysis. The resultant simplicity should prove to be especially valuable for study of the coupled transport of water and permeating solutes through cell membranes. Using the microperfusion chamber, water and dimethylsulfoxide (DMSO) permeability coefficients of mouse oocytes as well as the water permeability coefficient of golden hamster pancreatic islet cells were determined. In these experiments, the individual cells were held in the chamber and perfused at 22 degrees C with hyperosmotic media, with or without DMSO (1.5 M). The cell volume change was videotaped and quantified by image analysis. Based on the experimental data and irreversible thermodynamics theory for the coupled mass transfer across the cell membrane, the water permeability coefficient of the oocytes was determined to be 0.47 micron. min-1. atm-1 in the absence of DMSO and 0.65 microns. min-1. atm-1 in the presence of DMSO. The DMSO permeability coefficient of the oocyte membrane and associated membrane reflection coefficient to DMSO were determined to be 0.23 and 0.85 micron/s, respectively. These values are consistent with those determined using the micropipette perfusion and microdiffusion chamber techniques. The water permeability coefficient of the golden hamster pancreatic islet cells was determined to be 0.27 microns. min-1. atm-1, which agrees well with a value previously determined using an electronic sizing (Coulter counter) technique. The use of the microperfusion chamber has the following major advantages: 1) This method allows the extracellular condition(s) to be readily changed by perfusing a single cell or group of cells with a prepared medium (cells can be reperfused with a different medium to study the response of the same cell to different osmotic conditions). 2) The short mixing time of cells and perfusion medium allows for accurate control of the extracellular osmolality and ensures accuracy of the corresponding mathematical formulation (modeling). 3) This technique has wide applicability in studying the cell osmotic response and in determining cell membrane transport properties.