Water permeability of plant cuticles: permeance,diffusion and partition coefficients

Summary Using isolated cuticular membranes from ten woody and herbaceous plant species, permeance and diffusion coefficients for water were measured, and partition coefficients were calculated. The cuticular membranes of fruit had much higher permeance and diffusion coefficients than leaf cuticular membranes from either trees or herbs. Both diffusion and partition coefficients increased with increasing membrane thickness. Thin cuticles, therefore, tend to be better and more efficient water barriers than thick cuticles. We compared the diffusion coefficients and the water content of cuticles as calculated from transport measurements with those obtained from water vapor sorption. There is good to fair agreement for cuticular membranes with a low water content, but large discrepancies appear for polymer matrix membranes with high permeance. This is probably due to the fact that diffusion coefficients obtained from transport measurements on membranes with high permeance and water content are underestimated. Water permeabilities of polyethylene and polypropylene membranes are similar to those of leaf cuticular membranes. However, leaf cuticles have much lower diffusion coefficients and a much greater water content than these synthetic polymers. This suggests that cuticles are primarily mobility barriers as far as water transport is concerned.     

Experimental Study of the Independence of Diffusion and Hydrodynamic Permeability Coefficients in Collodion Membranes

The two parameters usually invoked when discussing transport across membranes are the "diffusion permeability coefficient" and the "hydrodynamic permeability coefficient." In this study the magnitude of these two coefficients is established experimentally for collodion membranes of differing porosities. The hydrodynamic permeability is predominant while convergence of the two permeabilities tends to obtain as the membranes become less coarse. The flux data obtained are used to calculate "average pore diameter" and the meaningfulness of these calculations is interpreted. The relationship between the two coefficients and transport across membranes as treated by the system of irreversible thermodynamics is discussed.     

Effects of spatial variation in membrane diffusibility and solubility on the lateral transport of membrane components.

There exist many examples of membrane components (e.g. receptors) accumulating in special domains of cell membranes. We analyze how certain variations in lateral diffusibility and solubility of the membrane would increase the efficiency of transport to these regions. A theorem is derived to show that the mean-time-of capture, tc, for particles diffusing to a trap from an annular region surrounding it, is intermediate to the tc values that correspond to the minimum and maximum diffusion coefficients that obtain in this region. An analytical solution for tc as a function of the gradient of diffusivity surrounding a trap is derived for circular geometry. Since local diffusion coefficients can be increased dramatically by reducing the concentration of intra-membrane particles and/or allowing them to form aggregates, such mechanisms could greatly enhance the diffusion-limited transport of particular membrane components to a trap (e.g. coated pit). If the trap is surrounded by an annular region in which the probe particles' partition function is increased, say, by the local segregation of certain phospholipids, tc is shown to vary inversely with the logarithm of the relative partition function. We provide some conjectural examples to illustrate the magnitude of the effects which heterogeneities in diffusibility and solubility may have in biological membranes.     

A probabilistic approach for estimating water permeability in pressure-driven membranes

A probabilistic approach is proposed to estimate water permeability in a cellulose triacetate (CTA) membrane. Water transport across the membrane is simulated in reverse osmosis mode by means of non-equilibrium molecular dynamics (MD) simulations. Different membrane configurations obtained by an annealing MD simulation are considered and simulation results are analyzed by using a hierarchical Bayesian model to obtain the permeability of the different membranes. The estimated membrane permeability is used to predict full-scale water flux by means of a process-level Monte Carlo simulation. Based on the results, the parameters of the model are observed to converge within 5-ns total simulation time. The results also indicate that the use of unique structural configurations in MD simulations is essential to capture realistic membrane properties at the molecular scale. Furthermore, the predicted full-scale water flux based on the estimated permeability is within the same order of magnitude of bench-scale experimental measurement of 1.72×10^?5 m/s.     

Effect of protein adsorption on the transport characteristics of asymmetric ultrafiltration membranes.

The effects of bovine serum albumin adsorption on the transport characteristics of asymmetric poly(ether sulfone) ultrafiltration membranes were determined using polydisperse dextrans with gel permeation chromatography. Actual dextran sieving coefficients were evaluated from observed sieving data for both the clean and preadsorbed membranes using a stagnant film model. The flux dependence of the actual dextran sieving coefficients was used to evaluate the intrinsic membrane hindrance factors for convective (i.e., sieving) and diffusive transport for the different molecular weight dextrans using classical membrane transport theory. Protein adsorption caused a reduction in both dextran sieving and diffusion, with the magnitude of the reduction a function of the dextran molecular weight and pore size. The effects of adsorption on the specific pore area and the membrane porosity were then determined using a recent model for solute transport through asymmetric ultrafiltration membranes. The data indicate that protein adsorption occurs preferentially in the larger membrane pores, causing a greater reduction in solute sieving compared to the membrane hydraulic permeability and porosity than would be predicted on the basis of either a simple pore blockage or pore constriction model.     

Multispectral imaging of ion transport in neutral carrier-based cation-selective membranes.

BACKGROUND: High-resolution spectroscopic imaging of the cross section of ion-selective membranes during real-time electrochemical measurements is termed spectroelectrochemical microscopy (SpECM). SpECM is aimed for optimizing the experimental conditions in mass transport controlled ion-selective electrode (ISE) membranes for improved detection limit. METHODS: The SpECM measurements are performed in a thin layer electrochemical cell. The key element of the cell is a membrane strip spacer ring assembly which forms a two compartment electrochemical cell. The cell is placed onto the stage of a microscope and the membrane strip is positioned in the center of the field of view. A slice of the image is focused onto the entrance slit of the imaging spectrometer. RESULTS: SpECM has been used for the determination of the diffusion coefficients of different membrane ingredients and for the quantitative assessment of the charged site concentrations in ISE membranes and membrane plasticizers. In addition, changes in the concentration profiles of the ionophore (free and complexed) and charged mobile sites inside the ISE membranes are documented upon the application of large external voltages. CONCLUSIONS: This account demonstrates the power and advantages of SpECM, a multispectral imaging method for investigations of mass transport processes in ISE membranes during electrochemical measurements.     

A Physical Interpretation of the Phenomenological Coefficients of Membrane Permeability

A "translation" of the phenomenological permeability coefficients into friction and distribution coefficients amenable to physical interpretation is presented. Expressions are obtained for the solute permeability coefficient ω and the reflection coefficient σ for both non-electrolytic and electrolytic permeants. An analysis of the coefficients is given for loose membranes as well as for dense natural membranes where transport may go through capillaries or by solution in the lipoid parts of the membrane. Water diffusion and filtration and the relation between these and capillary pore radius of the membrane are discussed. For the permeation of ions through the charged membranes equations are developed for the case of zero electrical current in the membrane. The correlation of σ with ω and L_p for electrolytes resembles that for non-electrolytes. In this case ω and σ depend markedly on ion concentration and on the charge density of the membrane. The reflection coefficient may assume negative values indicating anomalous osmosis. An analysis of the phenomena of anomalous osmosis was carried out for the model of Teorell and Meyer and Sievers and the results agree with the experimental data of Loeb and of Grim and Sollner. A set of equations and reference curves are presented for the evaluation of ω and σ in the transport of polyvalent ions through charged membranes.     

Enzymatic production of L-tryptophan in liquid membrane systems

Tryptophan synthesis was investigated in a two-phase system employing an organic liquid membrane. A diffusion cell was constructed to study the transport of the various components of the reaction through an organic layer of cyclohexane. The organic phase was supported by two polymeric membranes, and Aliquat-336 was used as the anion exchanger. A differential in pH was maintained between the aqueous phases to facilitate extraction of the product from the reaction phase. A mathematical model was developed to estimate effective diffusivities and predict the sensitivity of the system to changes in the partition coefficients and liquid membrane thickness. The use of liquid membrane emulsion-type reactors is discussed.     

Single-molecule analysis of PIP2;1 dynamics and partitioning reveals multiple modes of Arabidopsis plasma membrane aquaporin regulation

PIP2;1 is an integral membrane protein that facilitates water transport across plasma membranes. To address the dynamics of Arabidopsis thaliana PIP2;1 at the single-molecule level as well as their role in PIP2;1 regulation, we tracked green fluorescent protein-PIP2;1 molecules by variable-angle evanescent wave microscopy and fluorescence correlation spectroscopy (FCS). Single-particle tracking analysis revealed that PIP2;1 presented four diffusion modes with large dispersion of diffusion coefficients, suggesting that partitioning and dynamics of PIP2;1 are heterogeneous and, more importantly, that PIP2;1 can move into or out of membrane microdomains. In response to salt stress, the diffusion coefficients and percentage of restricted diffusion increased, implying that PIP2;1 internalization was enhanced. This was further supported by the decrease in PIP2;1 density on plasma membranes by FCS. We additionally demonstrated that PIP2;1 internalization involves a combination of two pathways: a tyrphostin A23-sensitive clathrin-dependent pathway and a methyl-β-cyclodextrin-sensitive, membrane raft-associated pathway. The latter was efficiently stimulated under NaCl conditions. Taken together, our findings demonstrate that PIP2;1 molecules are heterogeneously distributed on the plasma membrane and that clathrin and membrane raft pathways cooperate to mediate the subcellular trafficking of PIP2;1, suggesting that the dynamic partitioning and recycling pathways might be involved in the multiple modes of regulating water permeability.     

Lateral diffusion as a rate-limiting step in ubiquinone-mediated mitochondrial electron transport

Data are presented which indicate that the diffusion-based collisions of ubiquinone with its redox partners in the mitochondrial inner membrane are a rate-limiting step for maximum (uncoupled) rates of succinate-linked electron transport. Data were obtained from experimental analysis of a comparison of the apparent activation energies of lateral diffusion rates, collision frequencies, and electron transport rates in native and protein-diluted (phospholipid-enriched) inner membranes. Diffusion coefficients for Complex III (ubiquinol:cytochrome c oxidoreductase) and ubiquinone redox components were determined as a function of temperature using fluorescence recovery after photobleaching, and collision frequencies of appropriate redox partners were subsequently calculated. The data reveal that 1) the apparent activation energies for both diffusion and electron transport were highest in the native inner membrane and decreased with decreasing protein density, 2) the apparent activation energy for the diffusion step of ubiquinone made up the most significant portion of the activation energy for the overall kinetic activity, i.e. electron transport steps plus the diffusion steps, 3) the apparent activation energies for both diffusion and electron transport decreased in a proportionate manner as the membrane protein density was decreased, and 4) Arrhenius plots of the ratio of experimental electron transport productive collisions (turnovers) to calculated theoretically predicted, diffusion-based collisions for ubiquinone with its redox partners had little or no temperature dependence, indicating that as temperature increases, increases in electron transport rate are accounted for by the increases in diffusion-based collisions. These data support the Random Collision Model of mitochondrial electron transport in which the rates of diffusion and appropriate concentrations of redox components limit the maximum rates of electron transport in the inner membrane.     

Nuclear envelope permeability measured by fluorescence microphotolysis of single liver cell nuclei

Fluorescence microphotolysis ("photobleaching") has been widely used to measure translational diffusion coefficients of lipids and proteins in cell membranes. This communication shows that fluorescence microphotolysis can be also employed for measurement of membrane transport in single cells and organelles. The influx of fluorescently labeled dextrans of graded molecular size into leaky human erythrocyte ghosts and isolated rat liver cell nuclei has been measured. For the nuclear envelope, a functional pore radius of 56-59 A is derived.     

Molecular modeling and simulation of Mycobacterium tuberculosis cell wall permeability

The low permeability of the mycobacterial cell wall is thought to contribute to the intrinsic drug resistance of mycobacteria. In this study, the permeability of the Mycobacterium tuberculosis cell wall is studied by computer simulation. Thirteen known drugs with diverse chemical structures were modeled as solutes undergoing transport across a model for the M. tuberculosis cell wall. The properties of the solute-membrane complexes were investigated by means of molecular dynamics simulation, especially the diffusion coefficients of the solute molecules inside the cell wall. The molecular shape of the solute was found to be an important factor for permeation through the M. tuberculosis cell wall. Predominant lateral diffusion within, as opposed to transverse diffusion across, the membrane/cell wall system was observed for some solutes. The extent of lateral diffusion relative to transverse diffusion of a solute within a biological cell membrane may be an important finding with respect to absorption distribution, metabolism, elimination, and toxicity properties of drug candidates. Molecular similarity measures among the solutes were computed, and the results suggest that compounds having high molecular similarity will display similar transport behavior in a common membrane/cell wall environment. In addition, the diffusion coefficients of the solute molecules across the M. tuberculosis cell wall model were compared to those across the monolayers of dipalmitoylphosphatidylethanolamine and dimyristoylphosphatidylcholine, are two common phospholipids in bacterial and animal membranes. The differences among these three groups of diffusion coefficients were observed and analyzed.     

Effects of unstirred layers or transport number discontinuities on the transient and steady-state current-voltage relationships of membranes

The effects of current-induced electrolyte accumulation and depletion on the electrical properties of a two-layered membrane system have been examined. The membrane consisted of a charged, ion permselective layer and an uncharged, non-selective layer. The model was designed to reveal the properties of membranes possessing long pores with ionic charges at one end or of ion-selective membranes bounded by highly unstirred aqueous layers. Electrolyte concentration profiles in the inert layer and their time-dependent changes were obtained from solutions of the diffusion equation under the condition of constant current. The profiles were then used to calculate the voltage developed across the membrane at various times after the current is switched on. The theoretical results are presented in the form of $\text{i-V}$ curves with reduced coordinates that can be used to obtain time-current-voltage relationships for membranes of the type considered having any thickness of the non-selective layer and bathed in any concentration of any 1:1 electrolyte. Experimental results on a model composite membrane were in good agreement with calculations that assume that ion transport occurs only under the influence of electrical potential and concentration gradients, suggesting that in such systems, the combined effects of convection, osmosis, electro-osmosis, and concentration-dependence of diffusion coefficients, activity coefficients, and transference numbers are small. Voltage fluctuations in the form of periodic spikes were observed experimentally at the limiting current density (the current density at which the electrolyte concentration at one surface of the selective layer goes to 0). These phenomena were not seen when the current was in the direction leading to accumulation of electrolyte in the non-selective (unstirred) layer. Such composite membranes can exhibit S-shaped and N-shaped $\text{i-V}$ curves under ramp-voltage and ramp-current clamps, respectively.     

Extracting Curvature Preferences of Lipids Assembled in Flat Bilayers Shows Possible Kinetic Windows for Genesis of Bilayer Asymmetry and Domain Formation in Biological Membranes

Studies on the assembly of pure lipid components allow mechanistic insights toward understanding the structural and functional aspects of biological membranes. Molecular dynamic (MD) simulations on membrane systems provide molecular details on membrane dynamics that are difficult to obtain experimentally. A large number of MD studies have remained somewhat disconnected from a key concept of amphipathic assembly resulting in membrane structures—shape parameters of lipid molecules in those structures in aqueous environments. This is because most of the MD studies have been done on flat lipid membranes. With the above in view, we analyzed MD simulations of 26 pure lipid patches as a function of (1) lipid type(s) and (2) time of MD simulations along with 35–40 ns trajectories of five pure lipids. We report, for the first time, extraction of curvature preferences of lipids from MD simulations done on flat bilayers. Our results may lead to mechanistic insights into the possible origins of bilayer asymmetries and domain formation in biological membranes.     

A method for estimating lateral diffusion coefficients in membranes from steady-state fluorescence quenching studies.

The Stern-Volmer theory, in which the quantum yield ratio (Io/I) depends linearly on the quencher concentration, will typically be inapplicable to fluorescence quenching in membranes. Numerical analysis shows that diffusion-controlled quenching results in a nonlinear concentration dependence for diffusion coefficients less than or of the order of 10(-6) cm2 s-1 and probe fluorescence lifetimes in the region of 10-100 ns. Lateral diffusion coefficients in membranes are typically overestimated an order of magnitude or more by the Stern-Volmer theory. An alternative empirical method is presented, which represents nonlinear concentration curves by a single parameter linear approximation determined by a least-squares analysis. The fitting parameter, P, depends on the interaction distance, the membrane thickness, the maximum extent of quenching and, in the case of biexponential probe fluorescence decay, the fluorescence kinetic parameters. P is presented in tabular form for a useful range of these parameters. The method is used to estimate diffusion coefficients for plastoquinone and plastoquinol from pyrene fluorescence quenching in soya bean phosphatidylcholine liposomes. It is found that the diffusion coefficients are nearly equal and in the region of 1.3-3.5 X 10(-7) cm2 s-1 for interaction radii of 1.5-0.5 nm, respectively.     

The lack of relationship between fluorescence polarization and lateral diffusion in biological membranes

An investigation has been carried out of the relationship between changes in the fluorescence polarization of 1,6-diphenyl-1,3,5-hexatriene (DPH) and concomittant changes in the lateral diffusion of proteins and lipid probes in membranes. Plasma membranes from lymphocytes and a CH1 mouse lymphoma line were treated with up to 70 mol% (relative to the total membrane phospholipid) of oleic or linoleic fatty acids. Under these conditions the fluorescence polarization of DPH decreased by between 8 and 15% which, in the framework of the microviscosity approach, suggests a membrane fluidity change of between 20 and 50%. The lateral diffusion coefficients of surface immunoglobin and the lipid probes 3,3′-dioctadecylindocarbocyanine and pyrene were also measured in these membranes using the fluorescence photobleaching recovery technique and the rate of pyrene excimer formation. The diffusion rates were found to be unaffected by the presence of free fatty acids. Hence despite large ‘microviscosity’ changes as reported by depolarization of DPH fluorescence, lateral diffusion coefficients are essentially unchanged. This finding is consistent with the idea that perturbing agents such as free fatty acids do not cause a general fluidization of the membrane but act locally to alter, for example, protein function. It is also consistent with the suggestion that lateral mobility of membrane proteins is not modulated by the lipid viscosity.     

Carrier facilitated diffusion

The concept of a mobile carrier combining reversibly with a substrate is considered as a possible mechanism for facilitated transport across biological membranes. The mathematical model is a system of three reaction diffusion equations with certain boundary conditions. Two limiting cases are discussed in detail: The case of a "thin" membrane where the diffusion of bound and unbound carrier from one surface to the other may be simulated by a single jump. If the diffusion rate of the substance to be transported is small, then an approximate stationary solution is derived using singular perturbation theory. Finally, the results of numerical simulations are presented for a wide range of parameters.     

Calculation of diffusion coefficient for supercritical carbon dioxide and carbon dioxide+naphthalene system by molecular dynamics simulation using EPM2 model

NVT ensemble molecular dynamics (MD) simulation has been applied to calculate the self-diffusion coefficients of carbon dioxide and the tracer diffusion coefficients of naphthalene in supercritical carbon dioxide. The simulation was carried out in the pressure range from 8 to 40 MPa. The elementary physical model proposed by Harris and Yung was adopted for carbon dioxide and some approximation models were used for naphthalene. The systems of MD simulation for carbon dioxide consist of 256 particles. One naphthalene molecule was added for carbon dioxide+naphthalene system. The system can be assumed to be an infinite dilution condition for carbon dioxide+naphthalene system and the mutual diffusion coefficients are equal to the tracer diffusion coefficients of naphthalene. The self-diffusion coefficients of carbon dioxide and the tracer diffusion coefficients of naphthalene in supercritical carbon dioxide can be calculated by mean square displacement. The calculated results of diffusion coefficients showed good agreement with the experimental data without adjustable parameters.