Forces and stresses acting on fusion pore membrane during secretion

To assess the forces and stresses present in fusion pore during secretion the stationary convective flux of lipid through a fusion pore connecting two planar membranes under different tensions was investigated through computer simulations. The physics of the problem is described by Navier-Stokes equations, and the convective flux of lipid was evaluated using finite element method. Each of the membrane monolayer is considered separately as an isotropic, homogeneous and incompressible viscous medium with the same viscosity. The difference in membrane tensions, which is simulated as the pressure difference at two ends of each monolayer, is the driving force of the lipid flow. The two monolayers interact by sliding past each other with inter-monolayer frictional viscosity. Fluid velocity, pressure, shear and normal stresses, viscous and frictional dissipations and forces were calculated to evaluate where the fusion pore will deform, extend (or compress) and dilate. The pressure changes little in the planar sections, whereas in the toroidal section the change is rapid. The magnitude of lipid velocity peaks at the pore neck. The radial lipid velocity is zero at the neck, has two peaks one on each side of the pore neck, and diminishes without going to zero in planar parts of two monolayers. The peaks are of opposite signs due to the change of direction of lipid flow. The axial velocity is confined to the toroidal section, peaks at the neck and is clearly greater in the outer monolayer. As a result of the spatially highly uneven lipid flow the membrane is under a significant stress, shear and normal. The shear stress, which indicates where the membrane will deform without changing the volume, has two peaks placed symmetrically about the neck. The normal stress shows where the membrane may extend or compress. Both, the radial and axial normal stresses are negative (extensive) in the upper toroidal section and positive (compressive) in the lower toroidal section. The pressure difference determines lipid velocity and velocity dependent variables (shear as well as normal axial and radial stresses), but also contributes directly to the force on the membranes and critically influences where and to what extent the membrane will deform, extend or dilate. The viscosity coefficient (due to friction of one element of lipid against neighboring ones), and frictional coefficient (due to friction between two monolayers sliding past each other) further modulate some variables. Lipid velocity rises as pressure difference increases, diminishes as the viscosity coefficient rises but is unaffected by the frictional coefficient. The shear and normal stresses rise as pressure difference increases, but the change of the viscosity coefficients has no effect. Both the viscous dissipation (which has two peaks placed symmetrically about the neck) and much smaller frictional dissipation (which peaks at the pore neck) rise with pressure and diminish if the viscosity coefficient rises, but only the frictional dissipation increases if the frictional coefficient increases. Finally, the radial force causing pore dilatation, and which is significant only in the planar section of the vesicular membrane, is governed almost entirely by the pressure, whereas the viscosity and frictional coefficients have only a marginal effect. Many variables are altered during pore dilatation. The lipid velocity and dissipations (viscous and frictional) rise approximately linearly with pore radius, whereas the lipid mass flow increases supra-linearly owing to the combined effects of the changes in pore radius and greater lipid velocity. Interestingly the radial force on the vesicular membrane increases only marginally.     

Model Pores of Molecular Dimension: The Preparation and Characterization of Track-Etched Membranes

Extremely uniform pores of near molecular dimension can be formed by the irradiation-etching technique first demonstrated by Price and Walker. The technique has now been developed to the stage where it can be used to fabricate model membranes for examining the various steric, hydrodynamic, and electrodynamic phenomena encountered in transport through molecular-size pores. Methods for preparing and characterizing membranes with pores as small as 25 A (radius) are described in this paper. Results on pore size determination via Knudsen gas flow and electrolyte conduction are compared. Pore wall modification by monolayer deposition is also discussed.     

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.     

Lipid flow through fusion pores connecting membranes of different tensions.

When two membranes fuse, their components mix; this is usually described as a purely diffusional process. However, if the membranes are under different tensions, the material will spread predominantly by convection. We use standard fluid mechanics to rigorously calculate the steady-state convective flux of lipids. A fusion pore is modeled as a toroid shape, connecting two planar membranes. Each of the membrane monolayers is considered separately as incompressible viscous media with the same shear viscosity, etas. The two monolayers interact by sliding past each other, described by an intermonolayer viscosity, etar. Combining a continuity equation with an equation that balances the work provided by the tension difference, Deltasigma, against the energy dissipated by flow in the viscous membrane, yields expressions for lipid velocity, upsilon, and area of lipid flux, Phi. These expressions for upsilon and Phi depend on Deltasigma, etas, etar, and geometrical aspects of a toroidal pore, but the general features of the theory hold for any fusion pore that has a roughly hourglass shape. These expressions are readily applicable to data from any experiments that monitor movement of lipid dye between fused membranes under different tensions. Lipid velocity increases nonlinearly from a small value for small pore radii, rp, to a saturating value at large rp. As a result of velocity saturation, the flux increases linearly with pore radius for large pores. The calculated lipid flux is in agreement with available experimental data for both large and transient fusion pores.     

Osmotic flow in membrane pores of molecular size

Water transfer by osmosis through pores occurs either by viscous flow or diffusion depending on whether the driving osmolyte is able to enter the pore. Analysis of osmotic permeabilities (P _os )measured in antibiotic and cellular pore systems supports this distinction, showing that P _os approaches either the viscous value (P _f ) or the diffusive value (P _d )depending on the size of the osmolyte in relation to the pore radius. Macroscopic hydrodynamics and diffusion theory, when used with drag and steric coefficients within an appropriate osmotic model, apply with remarkable accuracy to channels of molecular dimensions where water molecules cannot pass each other, without the need to postulate any special flow regimes. It becomes apparent that the true viscous to diffusive flow ratio, P _f /P _d , can be separated from the effects of tracer filing by osmotic measurements alone. It does not monotonically decrease with the pore radius but rises steeply at the smaller radii which would apply to pores in cell membranes. Consequently, the application of the theory to osmotic and diffusive flow data for the red cell predicts a pore radius of 0.2 nm in agreement with other recent measurements on isolated components of the system, showing that the viscous-diffusive distinction applies even in molecular pores.     

Characterization of a continuous supermacroporous monolithic matrix for chromatographic separation of large bioparticles

A continuous supermacroporous monolithic chromatographic matrix has been characterized using a capillary model, experimental breakthrough curves, and pressure drop experiments. The model describes the convective flow and its dispersive mixing effects, mass transfer resistance, pore size distribution, and the adsorption behavior of the monolithic matrix. It is possible to determine an effective pore size distribution by fitting the capillary model to experimental breakthrough curves and pressure drop experiments. The model is able to describe the flow rate dependence of the experimental breakthrough curves. Mass transport resistance was due to: (i) dispersive mixing effects in the convective flow in the pores; and (ii) slow diffusion in the stagnant film covering the surface within each pore, under adsorption conditions. The monolithic matrix can be described by a very narrow pore size distribution, illustrating one of the advantages of the gel. A broader pore size distribution results in increased band broadening. This can be studied easily using the model developed in this investigation.     

Mechanism of methane adsorption on groove space in organic matter surface

Organic matter plays an important role in methane adsorption in shale. Pore surface of organic matter is usually rough and uneven, which results in a large amount of groove space on the pore surface. Thus, the influence of groove space on the adsorption capacity of methane in shale cannot be neglected. Nanoscale pore structures of the organic-rich shale in the Longmaxi Formation were investigated by low-pressure nitrogen gas adsorption as a basis for constructing models. We simplified the internal groove space into triangular prisms with different angles. The grand canonical Monte Carlo simulation and molecular dynamics simulation were used to analyse the methane molecule adsorption behaviour in pores. The results showed that the pore morphology of organic-rich shale in the Longmaxi Formation was mainly slit-shaped pores. The excess adsorption isotherms showed good agreement between experiment and simulation, indicating that the model is suitable and reliable. Methane molecules can enter into the groove space with an opening size of 0.738 nm, while they fail to enter into groove spaces with an opening size less than 0.492 nm. This understanding has important significance for the study of the adsorption characteristics of organic pores which have undergone multiple evolutions in geological history.     

Combined Diffusive and Viscous Transport of Methane in a Carbon Slit Pore

Abstract

The transport of mass through porous materials can occur by essentially two different mechanisms: (1) diffusion and (2) viscous flow. The former occurs when there is a gradient in chemical potential of the pore fluid, while the latter occurs in the presence of a pressure gradient. In general, fluid transport occurs by both of these mechanisms and their respective contributions to the total intra-pore flux are approximately additive. Experimentally, there is no unambiguous way of determining the individual contributions to the total flux of these two modes of transport. Fortunately, molecular simulations does provide a solution.

We present a novel simulation method in which the separate contributions to the total flux are determined. The method involves the use of two non-equilibrium molecular dynamics techniques: dual control volume grand canonical molecular dynamics (DCV GCMD) and an algorithm for simulating planar Poiseuille flow. We apply this technique to study the combined (viscous and diffusive) transport of methane through single slit-shaped graphite pores of width 2.5, 5.0 and 10.0 methane diameters. We find that the viscous contribution to the total intrapore flux through each of these pores is 10%, 15% and 34%, respectively.     

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.     

Numerical Simulation of CO2 Flooding of Coalbed Methane Considering the Fluid-Solid Coupling Effect

CO₂ flooding of coalbed methane (CO₂-ECBM) not only stores CO₂ underground and reduces greenhouse gas emissions but also enhances the gas production ratio. This coupled process involves multi-phase fluid flow and coal-rock deformation, as well as processes such as competitive gas adsorption and diffusion from the coal matrix into fractures. A dual-porosity medium that consists of a matrix and fractures was built to simulate the flooding process, and a mathematical model was used to consider the competitive adsorption, diffusion and seepage processes and the interaction between flow and deformation. Due to the effects of the initial pressure and the differences in pressure variation during the production process, permeability changes caused by matrix shrinkage were spatially variable in the reservoir. The maximum value of permeability appeared near the production well, and the degree of rebound decreased with increasing distance from the production well.     

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.     

Model‐Based Investigation on the Mass Transfer and Adsorption Mechanisms of Mono‐Pegylated Lysozyme in Ion‐Exchange Chromatography

Recent studies highlighted the potential of PEGylated proteins to improve stabilities and pharmacokinetics of protein drugs. Ion‐exchange chromatography (IEX) is among the most frequently used purification methods for PEGylated proteins. However, the underlying physical mechanisms allowing for a separation of different PEGamers (proteins with a varying number of attached PEG molecules) are not yet fully understood. In this work, mechanistic chromatography modeling is applied to gain a deeper understanding of the mass transfer and adsorption/desorption mechanisms of mono‐PEGylated proteins in IEX. Using a combination of the general rate model (GRM) and the steric mass action (SMA) isotherm, simulation results in good agreement with the experimental data are achieved. During linear gradient elution of proteins attached with PEG of different molecular weight, similar peak heights, and peak shapes at constant gradient length are observed. A superimposed effect of increased desorption rate and reduced diffusion rate as a function of the hydrodynamic radius of PEGylated proteins is identified to be the reason of this anomaly. That is why the concept of the diffusion‐desorption‐compensation effect is proposed. In addition to the altered elution orders, PEGylation results in a considerable decrease of maximum binding capacity. By using the SMA model in a kinetic formulation, the adsorption behavior of PEGylated proteins in the highly concentrated state is described mechanistically. An exponential increase in the steric hindrance effect with increasing PEG molecular weight is observed. This suggests the formation of multiple PEG layers in the interstitial space between bound proteins and an associated shielding of ligands on the adsorber surface to be the cause of the reduced maximum binding capacity. The presented in silico approach thus complements the hitherto proposed theories on the binding mechanisms of PEGylated proteins in IEX.     

Insulin transport within skeletal muscle transverse tubule networks

It has recently been observed in situ in mice that insulin takes approximately 10 min to be transported 20 microm into the t-tubule networks of skeletal muscle fibers. The mechanisms for this slow transport are unknown. It has been suggested that the biochemical composition of the t-tubular space that may include large molecules acting as gels and increased viscosity in the narrow tubules may explain this slow diffusion. In this article, we construct a mathematical model of insulin transport within the t-tubule network to determine potential mechanisms responsible for this slow insulin transport process. Our model includes insulin diffusion, insulin binding to insulin receptors, t-tubule network tortuosity, interstitial fluid viscosity, hydrodynamic wall effects, and insulin receptor internalization and recycling. The model predicted that depending on fiber type there is a 2-15 min delay in the arrival time of insulin between the sarcolemma and inner t-tubules (located 20 microm from the sarcolemma) after insulin injection. This is consistent with the experimental data. Increased viscosity in the narrow t-tubules and large molecules acting as gels are not the primary mechanisms responsible for the slow insulin diffusion. The primary mechanisms responsible for the slow insulin transport are insulin binding to insulin receptors and network tortuosity.     

Modeling and analysis of elution stage of biospecific adsorption in finite bath

A model is developed and used to predict the dynamic behavior of the elution stage of biospecific adsorption (affinity chromatography) in a finite bath. Both nonselective and selective elution of monovalent adsorbates is considered. The model expressions account for film and pore diffusion resistances for the adsorbate(s) and the eluent, and various rate expressions for the desorption of the adsorbate from the adsorbate-ligand complex are constructed and studied. The results indicate that the duration of the elution stage depends significantly on the Sherwood number of the adsorbate and the rate of the interaction step between the ligand and the adsorbate relative to the diffusion of the adsorbate in the pore during elution. In nonselective elution, when the value of the effective pore diffusivity of the eluent is significantly larger than that of the adsorbate, the results suggest that it would be advantageous to use an initial eluent concentration in the finite bath that is only slightly higher than the critical eluent concentration in order to minimize the risk of product and ligand damage. In selective elution the amount of adsorbate recovered in the elution stage is greatly influenced by the initial concentration of the eluent and the equilibrium dissociation constants of the adsorbate-ligand and adsorbate-eluent complexes.     

Pore network modelling of affinity chromatography: determination of the dynamic profiles of the pore diffusivity of beta-galactosidase and its effect on column performance as the loading of beta-galactosidase onto anti-beta-galactosidase varies with time.

A three-dimensional pore network model for diffusion in porous adsorbent particles was employed in a dynamic adsorption model that simulates the adsorption of a solute in porous particles packed in a chromatographic column. The solution of the combined model yielded the dynamic profiles of the pore diffusion coefficient of beta-galactosidase along the radius of porous adsorbent particles and along the length of the column as the loading of beta-galactosidase onto anti-beta-galactosidase immobilized on the surface of the pores of the particles occurred, and, the dynamic adsorptive capacity of the chromatographic column as a function of the design and operational parameters of the chromatographic system. It was found that for a given column length the dynamic profiles of the pore diffusion coefficient were influenced by (a) the superficial fluid velocity in the column, (b) the diameter of the adsorbent particles, and (c) the pore connectivity of the porous structure of the adsorbent particles. The effect of the magnitude of the pore connectivity on the dynamic profiles of the pore diffusion coefficient of beta-galactosidase increased as the diameter of the adsorbent particles and the superficial fluid velocity in the column increased. The dynamic adsorptive capacity of the column increased as (i) the particle diameter and the superficial fluid velocity in the column decreased, and (ii) the column length and the pore connectivity increased. In preparative affinity chromatography, it is desirable to obtain high throughputs within acceptable pressure gradients, and this may require the employment of larger diameter adsorbent particles. In such a case, longer column lengths satisfying acceptable pressure gradients with adsorbent particles having higher pore connectivity values could provide high dynamic adsorptive capacities. An alternative chromatographic system could be comprised of a long column packed with large particles which have fractal pores (fractal particles) that have high pore connectivities and which allow high intraparticle diffusional and convective flow mass transfer rates providing high throughputs and high dynamic adsorptive capacities. If large scale monoliths could be made to be reproducible and operationally stable, they could also offer an alternative mode of operation that could provide high throughputs and high dynamic adsorptive capacities.     

Apolipoprotein A-I(Milano) anion exchange chromatography: mass transfer and adsorption kinetics

The mass transfer and adsorption kinetics of self-associating apolipoprotein A-I(Milano) (apoA-I(M)) was investigated for the two anion exchangers Q-Sepharose-HP and Macro-Prep-HQ. At high salt where no protein binding occurs and without urea, mass transfer was controlled by hindered pore diffusion of multiple associated forms for both materials. Adding urea suppressed self-association, but resulted in higher viscosity and caused unfolding. As a consequence, the effective diffusivity decreased as urea was added and was greater for the larger pore Macro-Prep-HQ resin. At low salt, under strong binding conditions, the adsorption kinetics followed a more complex mechanism. In this case, the kinetics was very slow for both stationary phases up to 2 M urea. However, at higher urea concentrations, the adsorption kinetics for the smaller pore Q-Sepharose-HP matrix became much faster, suggesting a transition from pore- to surface-dominated diffusion. Microscopic observations confirmed that different transport mechanisms were in play below and above 2 M urea, which marked the approximate boundary above which self-association was suppressed and unfolding occurred. The net result was enhanced uptake kinetics at high urea concentrations (e.g., 4 M) where protein unfolding is thought to lead to a more flexible structure that can reptate along the pore surface. Although the observed enhancement was dependent on the pore size and, thus, the surface area of the resin, it was not limited to apoA-I(M). BSA showed a similar trend as a function of urea when its disulfide bonds were reduced.     

Fluidics-resolved estimation of protein adsorption kinetics in a biomicrofluidic system

Protein adsorption on surfaces is a complex phenomenon that is described by the balance of convective/diffusive transport of the protein species to the surface and its adsorption/desorption at the surface. The extent of binding depends on a variety of factors such as protein/surface interactions, availability of binding sites, localized concentrations of protein near biomaterial surfaces and flow characteristics of the protein in that region. Factors such as time-varying flows, complex device geometries, presence of multiple competitive species, or possible denaturing of proteins when they attach to the surface make it extremely difficult to quantitatively analyze protein interactions with surfaces. Adsorption/desorption rate constants are often inferred using simplistic models which neglect mass transport and have limited use across different microfluidic systems and flow protocols. In this work, we have developed and demonstrated a fluidics-resolved model that evaluates protein adsorption, accounting for both the fluidic transport and the biochemical kinetics in complex biomicrofluidic devices. The model is valid for both flow and static conditions. An automated procedure was also developed to extract the "intrinsic" mass-transport-independent adsorption kinetic rate constants from experimental data using a least squares optimization method. The automated data extraction methodology is applied to two proteins (alkaline phosphatase and glucose oxidase) that have been brought into contact with poly(etheretherketone) and Teflon capillaries. The applicability of the procedure in analyzing flow and adsorption in complex microfluidic structures is also demonstrated.     

Aqueous viscosity is the primary source of friction in lipidic pore dynamics

A new theory, to our knowledge, is developed that describes the dynamics of a lipidic pore in a liposome. The equations of the theory capture the experimentally observed three-stage functional form of pore radius over time—stage 1, rapid pore enlargement; stage 2, slow pore shrinkage; and stage 3, rapid pore closure. They also show that lipid flow is kinetically limited by the values of both membrane and aqueous viscosity; therefore, pore evolution is affected by both viscosities. The theory predicts that for a giant liposome, tens of microns in radius, water viscosity dominates over the effects of membrane viscosity. The edge tension of a lipidic pore is calculated by using the theory to quantitatively account for pore kinetics in stage 3, rapid pore closing. This value of edge tension agrees with the value as standardly calculated from the stage of slow pore closure, stage 2. For small, submicron liposomes, membrane viscosity affects pore kinetics, but only if the viscosity of the aqueous solution is comparable to that of distilled water. A first-principle fluid-mechanics calculation of the friction due to aqueous viscosity is in excellent agreement with the friction obtained by applying the new theory to data of previously published experimental results.     

Breakthrough performance of linear-DNA on ion-exchange membrane columns

Breakthrough performance of linear-DNA adsorption on ion-exchange membrane columns was theoretically and experimentally investigated using batch and fixed-bed systems. System dispersion curves showed the absence of flow non-idealities in the experimental arrangement. Breakthrough curves were not significantly affected by flow-rate or inlet solution concentration. In the theoretical analysis a model was integrated by the serial coupling of the membrane transport model and the system dispersion model. A transport model that considers finite kinetic rate and column dispersed flow was used in the study. A simplex optimization routine coupled to the solution of the partial differential model equations was employed to estimate the maximum adsorption capacity constant, the equilibrium desorption constant and the forward interaction rate-constant, which are the parameters of the membrane transport model. Through this approach a good prediction of the adsorption phenomena is obtained for inlet concentrations and flow rates greater than 0.2 mg/ml and 0.16 ml/min.