Computer Simulation of Isothermal Mass Transport in Graphite Slit Pores

Abstract

Results are presented from a simulation study of the mass transport of oxygen and nitrogen through graphite slit pores. The work is motivated by an attempt to understand the molecular origins of the kinetic selectivity displayed when air is separated into its major components using pressure swing adsorption. A combination of non-equilibrium molecular dynamics (NEMD), equilibrium molecular dynamics (EMD) and grand canonical Monte Carlo methods has been employed in our study to extract the maximum information. Transport diffusivities, self-diffusivities, permeabilities and Darken thermodynamic factors have been calculated as a function of pore width and temperature for pure component oxygen and nitrogen. In addition, new EMD simulation data for an 80:20 mixture of nitrogen and oxygen is reported, including a direct calculation of the Stefan-Maxwell coefficients. The results are discussed in terms of the oxygen selectivity and the possible mechanisms, which increase or decrease this quantity.

We find that the pore width behaviour of the diffusion coefficients consists of three distinct regimes: a regime at larger pore widths in which single component diffusion coefficients are largely independent of pore width, an optimum pore width at which both diffusivities increase substantially but the slit pore is selective towards nitrogen, and a regime at very low pore widths at which the diffusivities decrease sharply, but the slits are selective towards oxygen. The mechanism behind each of these regimes is discussed in terms of “entropic” effects and potential barrier heights.

We have also found that permeability selectivity is substantially reduced in a mixture of the two gases with a composition similar to that of air. Cross diffusion coefficients in the mixture have been calculated and shown to be non-negligible.     

Kinetics of Diffusion and Convection in 3.2-Å Pores: Exact Solution by Computer Simulation

The kinetics of transport in pores the size postulated for cell membranes has been investigated by direct computer simulation (molecular dynamics). The simulated pore is 11 Å long and 3.2 Å in radius, and the water molecules are modeled by hard, smooth spheres, 1 Å in radius. The balls are given an initial set of positions and velocities (with an average temperature of 313° K) and the computer then calculates their exact paths through the pore. Two different conditions were used at the ends of the pore. In one, the ends are closed and the balls are completely isolated. In the other, the ball density in each end region is fixed so that a pressure difference can be established and a net convective flow produced. The following values were directly measured in the simulated experiments: net and diffusive (oneway) flux; pressure, temperature, and diffusion coefficients in the pore; area available for diffusion; probability distribution of ball positions in the pore; and the interaction between diffusion and convection. The density, viscosity, and diffusion coefficients in the bulk fluid were determined from the theory of hard sphere dense gases. From these values, the “equivalent” pore radius (determined by the same procedure that is used for cell membranes) was computed and compared with the physical pore radius of the simulated pore.     

Adsorption and diffusion of CO2 and CH4 in covalent organic frameworks: an MC/MD simulation study

Covalent organic frameworks (COFs) are a promising gas separation material which have been developed recently. In this work, we have used grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations to investigate the adsorption and diffusion properties of CO₂ and CH₄ in five recent synthesised COF materials. We have also considered the properties of amino-modified COFs by adding –NH₂ group to the five COFs. The adsorption isotherm, adsorption/diffusion selectivity, self/transport diffusion coefficients have been examined and discussed. All of the five COFs exhibit promising adsorption selectivity which is higher than common nanoporous materials. An S-shaped adsorption isotherm can be found for CO₂ instead of CH₄ adsorption. The introduction of –NH₂ group is effective at low pressure region (<200?kPa). The diffusion coefficients are similar for TS-COFs but increase with the pore size for PI-COFs, and the diffusion coefficients seem less dependent on the –NH₂ groups.     

Diffusion and redistribution of lipid-like molecules between membranes in virus-cell and cell-cell fusion systems.

The kinetics of redistribution of lipid-like molecules between the membranes of two fused spherical vesicles is studied by solving the time-dependent diffusion equation of the system. The effects on the probe redistribution rate of pore size at the fusion junction and the relative sizes of the vesicles are examined. It is found that the redistribution rate constant decreases significantly, but not drastically, as the relative size of the pore to that of the vesicles decreases (the bottleneck effect). In general, the time scale of the probe redistribution rate is determined by the size of the vesicles that is loaded with the probe before the activation of the fusion. For a pore size 50 A in diameter and a typical diffusion coefficient of 10(-8) cm2/s for lipids, the mixing half times for typical virus-cell and cell-cell fusion systems are less than 30 ms and above 200 s, respectively. Thus, although the redistribution of lipid-like probes by diffusion is not rate limiting in virus-cell fusion, redistribution by diffusion is close to rate limiting in spike-protein mediated cell-cell fusion.     

Dynamic light scattering measurements of the diffusion of probes in filamentous actin solutions

The diffusion coefficients of monodisperse polystyrene latex spheres in solutions of polymerized actin were measured using dynamic light scattering. Four different probes with radii R, ranging from 50 to 500 nm, were separately used in actin solutions with concentrations c, ranging from 1.5 to 21 microM, which had been polymerized with either 1 mM MgCl2, 1 mM CaCl2, or 100 mM KCl. Under all conditions, and at four different scattering angles in the range of 30 degrees-90 degrees, the measured average diffusion coefficients D of the probes were systematically smaller for samples of increased actin concentration or of increased probe radius. Control experiments indicated that the probes did not bind to the actin. These data for Mg2+- and Ca2+-polymerized actin agree and were found to be quite well summarized by the scaling relation D/D0 = exp[-alpha R delta c nu], where D0 is the measured diffusion coefficient of the probes in water (and, as also measured, in the starting actin solutions prior to polymerization with added salt), with values of delta = 0.73 +/- 0.05, nu = 1.08 +/- 0.09, and alpha = (1.1 +/- 0.6) x 10(-3) (with c in microM and R in nm). Data for KCl-polymerized actin show much more restricted diffusivities of the probes at comparable actin concentrations. Inhomogeneities in the solution are reflected in the "effective polydispersity" of the probe diffusion coefficients, which depend on local microviscosity differences.     

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.     

Conformational studies of BSA using laser light scattering

The usefulness of laser light scattering as a technique for determining protein conformation has been investigated by studying the self-association and drug binding of bovine serum albumin (BSA). The diffusion coefficients of BSA monomers and dimers have been measured and the ratio of these two quantities indicates that in the dimer, the subunit separation is 2.2 times the monomeric hydrodynamic radius. The binding of salicylate to BSA causes an increase in its diffusion coefficient corresponding to a reduction in the frictional drag of the solvent on the protein molecules. It has been found that data obtained using laser light scattering may be interpreted confidently only when proper care has been taken in sample preparation and the scattered intensity autocorrelation function has been appropriately analyzed.     

Mass transport parameters of aspen wood chip beds via stimulus-response tracer techniques

A stimulus-response tracer technique has been used to characterize packed beds of untreated, as well as acid prehydrolyzed, and enzymatically hydrolyzed aspen wood chips. Glucose was used as the tracer. Bulk liquid phase dispersion, interphase mass transfer, and intraparticle diffusion coefficients were determined for these materials as well as effective porosities and tortuosities. The untreated and prehydrolyzed aspen wood chips were found to have effective coid fractions of ca. 0.8, while the enzymatically hydrolyzed wood chips exhibited a void fraction of 0.37. Intraparticle diffusion was approximately twice as rapid in the prehydrolyzed and enzymatically hydrolyzed wood chips as in the untreated wood chips. Also, under the current experimental conditions, intraparticle diffusional transport resistance accounted for roughly half of the total tracer pulse dispersion. It is demonstrated that stimulus-response tracer techniques can be useful and convenient probes for beds of lignocellulosic, or other conversion and/or treatment. (c) 1993 John Wiley & Sons, Inc.     

Kinetic models and phenomenological analysis of passive lipid translocation in single-file

Passive movement of lipids through a membrane-embedded pore is analysed with kinetic equations of transport in single-file. The number of lipids arranged along the translocation coordinate in the pore is not limited in the calculations. The assumption is made that the energetic state of a pore is independent of the sequence of lipids contained in it. The results are valid for an arbitrary number of species with identical kinetic constants. It is shown that infinitely fast diffusion of one vacant site is equivalent to the filled pore approximation, which has been used here. We introduce the concept of non-strict single-file, which allows also for exchanges of neighbouring lipids inside the pore at specified rates. The model successfully simulates the redistribution of lipids between the monolayers of red blood cell plasma membranes under operation of an active aminophospholipid translocase. Kinetic equations are related to linear flux force relations. Phenomenological coefficients are expressed and analysed in terms of kinetic constants. Plausible kinetic pore model parameters are derived from comparison with a reference simulation of a thermodynamic model of the erythrocyte transmembrane lipid distribution. Mechanical forces due to differences in compressions of the lipid molecules between the monolayers are incorporated in kinetic rate constants. It is seen how the active inward transport of aminophospholipids causes an unsymmetrical passive redistribution of the other components due to mechanical effects and cross-coupling of fluxes.     

Lipid mono- and bilayer supported on polymer films: composite polymer-lipid films on solid substrates.

We report the deposition of lipid monolayers and bilayers on polyacrylamide films deposited by radical chain reaction onto solid substrates in aqueous solutions. Polymer films of various degrees of monomer density and cross-linking are prepared. Lateral diffusion and fluorescent probe permeation measurements yield insight into the continuity of the lipid layers and show that monolayers exposed to air are much less sensitive towards polymer heterogeneities than bilayers below water, which is explained in terms of the wetting laws. The diffusion studies of lipid and lipopeptide probes yield absolute values of the frictional coefficients between the lipid layer and the polymer films and allow one to estimate the surface viscosity of the polymer film. The potential applications of supported membranes on soft thin polymer films for the preparation of biofunctionalized surfaces or biocompatible receptive surfaces for biosensors are discussed.     

Comparative study of diffusion coefficients of alpha-lactalbumins and lysozyme using polarization interferometer

The method of macroscopic diffusion with polarization optics has been applied to compare the translational diffusion coefficients for three proteins with similar three-dimensional structures in different conformational states. It has been shown that the values of diffusion coefficients obtained by the method are almost the same as those obtained by quasielastic light scattering. However this method is more available since it is less sensitive to aggregation and requires less amount of protein for investigation.     

Adsorption of rutin with a novel β-cyclodextrin polymer adsorbent: Thermodynamic and kinetic study

The adsorption properties toward rutin of a cyclodextrin polymer adsorbent CroCD-TuC 3 have been studied. The adsorption capacity is reduced as temperature and pH of solution rises, but increases with the increase of solvent polarity. Compared with Sephadex? G-15 dextran gel beads, CroCD-TuC 3 shows dramatically higher isosteric enthalpy due to a significant contribution of rutin/β-cyclodextrin inclusion complex formation in CroCD-TuC 3 skeleton. A highlight in our study is that the pore diffusion model has been employed to describe the mass transfer inside the adsorbent pores. It reveals that the diffusion inside the pores is the rate-restricting step in the whole adsorption process. The effective pore diffusivity of rutin in CroCD-TuC 3 calculated is much lower than the diffusivity in diluted solution. The pore diffusion model is an available tool to investigate the profile of mass transfer inside the pores, and provides an effective method to describe adsorption kinetics.     

Transport rates of proteins in porous materials with known microgeometry.

Many biological and biotechnological systems involve the diffusion of macromolecules through complicated macroporous (pore size on the order of 10-100 microns) environments. In this report, we present and evaluate an experimental system for measuring the rate of protein transport in an inert, macroporous membrane. For this particular membrane system, the microgeometry was characterized in terms of distribution of pore size, position, and orientation. Although the rate of protein desorption was much less than expected based on continuum diffusion models, we demonstrate that the measured transport rates are consistent with diffusion of protein in a complex, interconnected network of water-filled pores. The porous systems exhibit transitional behavior in quantitative agreement with the behavior of percolation lattices (mean square error 7%, n = 29). Predictive mathematical models of the diffusion process were developed: these models used percolation concepts to describe pore topology, continuum models of diffusion/dissolution to describe protein movement at each single pore, and measured pore size distributions. Effective diffusion coefficients for protein transport in aqueous, constricted macropores were predicted by this technique. Predicted diffusion coefficients, based on measured and derived microstructural parameters, agree with experimentally measured diffusion coefficients within a factor of 2. This approach may be useful in the design of porous polymer systems for biological applications and for evaluating other biological systems where conduction of mass, heat, momentum, or charge occurs in a heterogeneous environment.     

GEOGRAPHIC VARIATION WITHIN AN ISLAND: UNIVARIATE AND MULTIVARIATE CONTOURING OF SCALATION,SIZE, AND SHAPE OF THE LIZARD GALLOTIA GALLOTI

Microgeographic variation of the vegetarian lizard Gallotia galloti within the island of Tenerife is described using univariate analysis, correlation, multiple group principal component analysis, canonical analysis, transects, and contours. The size varies locally in a mosaic pattern while head shape shows a WNW–ESE cline in the south. The scalation (scale and femoral pore counts) has two facets to its geographic variation, both of which are incongruent with the primary variation in the size and shape. The scalation shows categorical variation (stepped cline) between northern and southern populations and also a strong clinal relationship with altitude. The possible causes of this variation are considered and adaptation to current ecological conditions appears to be implicated for at least the altitudinal variation, although the pertinent factors are not obvious. It is apparent that vertebrate populations distributed across small islands do not necessarily offer the advantage of a discrete homogeneous unit for evolutionary studies but can offer the opportunity for studying microgeographic variation.     

Electron spin resonance and electron-spin-echo study of oriented multilayers of L alpha-dipalmitoylphosphatidylcholine water systems.

A detailed electron spin resonance (ESR) study of spin-labeled-oriented multilayers of L alpha-dipalmitoylphosphatidylcholine (DPPC) water systems for low water content (2-10% by weight) is reported with the purpose of characterizing the dynamical and structural properties of model membrane systems. Emphasis is placed on the value of combining such experiments with detailed simulations based on current slow-motional theories. Information is obtained regarding ordering and anisotropic rotational diffusion rates via ESR lineshape analysis over the entire motional range, from the fast motional region through the moderately slow and slow to the rigid limit. This includes the low-temperature gel phase, the liquid crystalline L alpha (1) phase and what appears to be a third high-temperature phase above the L alpha phase. Cholestane (CSL) and spin-labeled DPPC (5-PC, 8-PC, and 16-PC) have been used to probe different depths of the bilayer. While CSL and 5-PC both reflect the high ordering of the bilayer close to the lipid-water interface, CSL appears to be located close enough to the water for the nitroxide to be involved in hydrogen bonding with water molecules. 16-PC reflects the relatively low ordering near the tail of the hydrocarbon chain in the bilayer. Quantitative estimates of ordering and motion are obtained for these cases. The results from CSL indicate that close to the lipid-water interface the DPPC molecule is oriented approximately perpendicular to the bilayer in these low water-content systems. However, all three labeled lipid probes indicate that the hydrocarbon chain of DPPC may be bent away from the bilayer normal by as much as 30 degrees and this evidence is stronger at low temperatures. When cholesterol is added to the DPPC-water system at a concentration greater than or equal to 2.5 mol %, the ordering is greatly increased although the rotational diffusion rate remains almost unaffected in the gel phase. Electron spin echoes (ESE) are observed for the first time from oriented lipid-water multilayers. Results obtained from cw ESR lineshape analysis are correlated with data from ESE experiments, which give a more direct measurement of relaxation times. These results indicate that for detection of very slow motions (close to the rigid limit) ESE experiments are more sensitive to dynamics than continuous wave ESR for which inhomogeneous broadening becomes a major problem.     

An NMR study of the temperature dependence of the coefficient of water self-diffusion through lipid bilayer membranes

The temperature dependence of the coefficient of water self-diffusion through plane-parallel lipid multilayers of the phospholipid dioleoylphosphatidylcholine oriented on a glass support has been studied in the temperature range of 20-60 degrees C by the method of NMR with magnetic field pulse gradient. The values of the coefficients of transbilayer water diffusion are by four orders of magnitude less than for bulky water and ten times less than the coefficients of lateral diffusion of the lipid under the same conditions. The temperature dependence of the coefficient of water diffusion is described by the Arrhenius law with an apparent activation energy of about 41 kJ/mol, which far exceeds the activation energy for the diffusion of bulky water (18 kJ/mol). The experimental data were analyzed using a "dissolving-diffusion" model, by simulating the passage of water through membrane channels, and by analyzing the exchange of water molecules in states with different modes of translation mobility, including pore channels and bilayer "defects". Each of the approaches used made it possible to take the significance of bilayer permeability for the apparent energy of activation of water diffusion into account and estimate the energies of activation of water diffusion in the hydrophobic moiety of the bilayer, which were found to be close to the values for bulky water. The coefficients of water diffusion in the system under examination and the coefficients of permeation of water through the bilayer were estimated, and the effect of bilayer "defects" on the coefficients of water diffusion along and across bilayers was studied.     

Determination of partition and lateral diffusion coefficients of ubiquinones by fluorescence quenching of n-(9-anthroyloxy)stearic acids in phospholipid vesicles and mitochondrial membranes

The quenching of fluorescence of n-(9-anthroyloxy)stearic acids and other probes by different ubiquinone homologues and analogues has been exploited to assess the localization and lateral mobility of the quinones in lipid bilayers of model and mitochondrial membranes. The true bimolecular collisional quenching constants in the lipids together with the lipid/water partition coefficients were obtained from Stern-Volmer plots at different membrane concentrations. A monomeric localization of the quinone in the phospholipid bilayer is suggested for the short side-chain ubiquinone homologues and for the longer derivatives when cosonicated with the phospholipids. The diffusion coefficients of the ubiquinones, calculated from the quenching constants either in three dimensions or in two dimensions, are in the range of (1-6) X 10(-6) cm2 s-1, both in phospholipid vesicles and in mitochondrial membranes. A careful analysis of different possible locations of ubiquinones in the phospholipid bilayer, accounting for the calculated diffusion coefficients and the viscosities derived therefrom, strongly suggests that the ubiquinone 10 molecule is located within the lipid bilayer with the quinone ring preferentially adjacent to the polar head groups of the phospholipids and the hydrophobic tail largely accommodated in the bilayer midplane. The steady-state rates of either ubiquinol 1-cytochrome c reductase or NADH:ubiquinone 1 reductase are proportional to the concentration of the quinol or quinone substrate in the membrane. The second-order rate constants appear to be at least 3 orders of magnitude lower than the second-order constants for quenching of the fluorescent probes; this is taken as a clear indication that ubiquinone diffusion is not the rate-determining step in the quinone-enzyme interaction.(ABSTRACT TRUNCATED AT 250 WORDS)     

The maximal size of protein to diffuse through the nuclear pore is larger than 60kDa

It has generally been believed that the diffusion limit set by the nuclear pore for protein is 60kDa. We here studied the cellular localization of several artificial proteins and found that the diffusion limit set by the nuclear pore is not as small as previously thought. The results indicate that the maximal size of protein to diffuse through the nuclear pore complex could be quite larger than 60kDa, thus greatly extending the diffusion limit that the nuclear pore can accommodate.     

Depletion of calcium from the lumen of endoplasmic reticulum reversibly inhibits passive diffusion and signal-mediated transport into the nucleus

Nuclear pore complexes provide channels for molecular transport across the nuclear envelope. Translocation of most proteins and RNAs through the pore complex is mediated by signal- and ATP-dependent mechanisms, while transport of small molecules is accomplished by passive diffusion. We report here that depletion of calcium from the lumen of the endoplasmic reticulum and nuclear envelope with ionophores or the calcium pump inhibitor thapsigargin rapidly and potently inhibits signal mediated transport of proteins into the nucleus. Lumenal calcium depletion also inhibits passive diffusion through the pore complex. Signal-mediated protein import and passive diffusion are rapidly restored when the drugs depleting lumenal calcium are removed and cells are incubated at 37 degrees C in calcium-containing medium. These results indicate that loss of calcium from the lumen of the endoplasmic reticulum and nuclear envelope reversibly affects properties of pore complex components located on the nuclear/cytoplasmic membrane surfaces, and they provide direct functional evidence for conformational flexibility of the pore complex. These methods will be useful for achieving reversible inhibition of nucleocytoplasmic trafficking for in vivo functional studies, and for studying the structure of the passive diffusion channel(s) of the pore complex.