Simulation of diffusion of O 2 and CO 2 in amorphous poly(ethylene terephthalate) and related alkylene and isomeric polyesters

The diffusion of small molecules through polymers is important in many areas of polymer science, such as gas barrier and separation membrane materials, polymeric foams, and in the processing and properties of polymers. Molecular simulation techniques have been applied to study the diffusion of oxygen and carbon dioxide as small molecule penetrants in models of bulk amorphous poly(ethylene terephthalate) (PET) and related alkylene and isomeric polyesters. A bulk amorphous configuration with periodic boundary conditions made into a unit cell whose dimensions were determined for each of the simulated polyesters in the cell having the experimental density. The diffusion coefficients for O 2 and CO 2 were determined via NVE molecular dynamics simulations using the Dreiding 2.21 molecular mechanics force field over a range of temperatures (300, 500 and 600 K) using up to 3 ns simulation time. We have focussed on the influence of the temperature, polymer dynamics, number of CH 2 groups, density and free volume distribution on the diffusion properties. Correlation of diffusion coefficients with free volume and number of CH 2 groups was found.     

Polymers of intrinsic microporosity for gas permeation: a molecular simulation study

We report a molecular simulation study for gas permeation in two membranes constructed from polymers of intrinsic microporosity (PIM-1 and PIM-7). With rigid ladder polymer chains, the membranes posses approximately 47.7 and 46.6% fractional free volumes (FFVs) in PIM-1 and PIM-7, respectively. The voids in the membranes have a diameter up to 9 Å and are largely interconnected. The sorption and diffusion of four gases (H₂, O₂, CH₄ and CO₂) were calculated by Monte Carlo and molecular dynamics simulations. The solubility coefficients increase in the order of H₂ < O₂ < CH₄ < CO₂, while the diffusion coefficients increase in the following order: CH₄ < CO₂ < O₂ < H₂. The simulation results agree well with experimental data, particularly for the solubility coefficients. The solubility and diffusion coefficients correlate well separately with the critical temperatures and effective diameters of gases. These molecular-based correlations can be used in the prediction for other gases. As attributed to the microporous structure, PIM-1 and PIM-7 outperform most glassy polymeric membranes in sorption and diffusion. PIM-1 has larger solubility and diffusion coefficients than PIM-7 because the cyano groups in PIM-1 lead to a stronger affinity and a larger FFV. The simulated solubility, diffusivity and permeation selectivities of CO₂/H₂, CO₂/O₂ and CO₂/CH₄ are consistent with experimental data. The quantitative microscopic understanding of gas permeation in the PIM membranes is useful for the new development of high-performance membranes.     

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.     

Towards mimicking natural protein channels with aligned carbon nanotube membranes for active drug delivery

AimsCarbon nanotube (CNT) membranes offer an exciting opportunity to mimic natural protein channels due to 1) a mechanism of dramatically enhanced fluid flow 2) ability to place ‘gatekeeper’ chemistry at the entrance to pores 3) the ability for biochemical reactions to occur on gatekeeper molecules and 4) an ability to chemically functionalize each side of the membrane independently.Main methodsAligned CNT membranes were fabricated and CNT pore entrances modified with gatekeeper chemistry. Pressure driven fluid flow and diffusion experiments were performed to study the mechanisms of transport through CNTs.Key findingsThe transport mechanism through CNT membranes is primarily 1) ionic diffusion near bulk expectation 2) gas flow enhanced 1–2 orders of magnitude primarily due to specular reflection 3) fluid flow 4–5 orders of magnitude faster than conventional materials due to a nearly ideal slip-boundary interface. The transport can be modulated by ‘gatekeeper’ chemistry at the pore entrance using steric hindrance, electrostatic attraction/repulsion, or biochemical state. The conformation of charged tethered molecules can be modulated by applied bias setting the stage for programmable drug release devices.SignificanceThe membrane structure is mechanically far more robust than lipid bilayer films, allowing for large-scale chemical separations, delivery or sensing based on the principles of protein channels. The performance of protein channels is several orders of magnitude faster than conventional membrane materials. The fundamental requirements of mimicking protein channels are present in the CNT membrane system.     

A new technique for measurement of water permeability of stomatous cuticular membranes isolated from Hedera helix leaves

Transpiration of cuticular membranes isolated from the lower stomatous surface of Hedera helix (ivy) leaves was measured using a novel approach which allowed a distinction to be made between gas phase diffusion (through stomatal pores) and solid phase diffusion (transport through the polymer matrix membrane and cuticular waxes) of water molecules. This approach is based on the principle that the diffusivity of water vapour in the gas phase can be manipulated by using different gases (helium, nitrogen, or carbon dioxide) while diffusivity of water in the solid phase is not affected. This approach allowed the flow of water across stomatal pores ('stomatal transpiration') to be calculated separately from the flow across the cuticle (cuticular transpiration) on the stomatous leaf surface. As expected, water flux across the cuticle isolated from the astomatous leaf surface was not affected by the gas composition since there are no gas-filled pores. Resistance to flux of water through the solid cuticle on the stomatous leaf surface was about 11 times lower than cuticular resistance on the astomatous leaf surface, indicating pronounced differences in barrier properties between cuticles isolated from both leaf surfaces. In order to check whether this difference in resistance was due to different barrier properties of cuticular waxes on both leaf sides, mobility of 14C-labelled 2,4-dichlorophenoxy-butyric acid 14C-2,4-DB) in reconstituted cuticular wax isolated from both leaf surfaces was measured separately. However, mobility of 14C-2,4-DB in reconstituted wax isolated from the lower leaf surface was 2.6 times lower compared with the upper leaf side. The significantly higher permeability of the ivy cuticle on the lower stomatous leaf surface compared with the astomatous surface might result from lateral heterogeneity in permeability of the cuticle covering normal epidermal cells compared with the cuticle covering the stomatal cell surface.     

Structural and functional insights into nucleocytoplasmic transport

The cell nucleus is surrounded by a double membrane system, the nuclear envelope (NE), with the outer nuclear membrane being continuous with the endoplasmic reticulum. Nuclear pore complexes (NPCs) fuse the inner and outer nuclear membranes, forming aqueous channels that allow free diffusion of small molecules but that also mediate the energy-dependent transport of large macromolecules. The NPC represents the largest known molecular complex and is composed of about 30 different proteins, termed nucleoporins (Nups). Here, we review recent studies that provide novel insight into the structural and functional organization of nucleocytoplasmic transport. In addition, prospects towards a high resolution model of the nuclear pore are discussed.     

Transmembrane molecular transport during versus after extremely large, nanosecond electric pulses

Recently there has been intense and growing interest in the non-thermal biological effects of nanosecond electric pulses, particularly apoptosis induction. These effects have been hypothesized to result from the widespread creation of small, lipidic pores in the plasma and organelle membranes of cells (supra-electroporation) and, more specifically, ionic and molecular transport through these pores. Here we show that transport occurs overwhelmingly after pulsing. First, we show that the electrical drift distance for typical charged solutes during nanosecond pulses (up to 100 ns), even those with very large magnitudes (up to 10 MV/m), ranges from only a fraction of the membrane thickness (5 nm) to several membrane thicknesses. This is much smaller than the diameter of a typical cell (∼16 μm), which implies that molecular drift transport during nanosecond pulses is necessarily minimal. This implication is not dependent on assumptions about pore density or the molecular flux through pores. Second, we show that molecular transport resulting from post-pulse diffusion through minimum-size pores is orders of magnitude larger than electrical drift-driven transport during nanosecond pulses. While field-assisted charge entry and the magnitude of flux favor transport during nanosecond pulses, these effects are too small to overcome the orders of magnitude more time available for post-pulse transport. Therefore, the basic conclusion that essentially all transmembrane molecular transport occurs post-pulse holds across the plausible range of relevant parameters. Our analysis shows that a primary direct consequence of nanosecond electric pulses is the creation (or maintenance) of large populations of small pores in cell membranes that govern post-pulse transmembrane transport of small ions and molecules.     

Molecular dynamics simulation of proton transport near the surface of a phospholipid membrane

The structural and dynamical properties of a hydrated proton near the surface of DMPC membrane were studied using a molecular dynamics simulation. The proton transport between water molecules was modeled using the second generation multistate empirical valence bond model. The proton diffusion was found to be inhibited at the membrane surface. The potential of mean force for the proton adsorption to the membrane surface and its release back into the bulk water was also determined, yielding a small barrier in each direction. An efficient algorithm for Ewald summation calculations for the multistate empirical valence bond model is also introduced.     

Dynamic loading of deformable porous media can induce active solute transport

Active solute transport mediated by molecular motors across porous membranes is a well-recognized mechanism for transport across the cell membrane. In contrast, active transport mediated by mechanical loading of porous media is a non-intuitive mechanism that has only been predicted recently from theory, but not yet observed experimentally. This study uses agarose hydrogel and dextran molecules as a model experimental system to explore this mechanism. Results show that dynamic loading can enhance the uptake of dextran by a factor greater than 15 over passive diffusion, for certain combinations of gel concentration and dextran molecular weight. Upon cessation of loading, the concentration reverts back to that achieved under passive diffusion. Thus, active solute transport in porous media can indeed be mediated by cyclical mechanical loading.     

Comparative study of molecular dynamics,diffusion, and permeability for ligands in biomembranes of different lipid composition

A comparative study of several model lipid bilayers of different composition, which included analysis of kinetic parameters of model lipid bilayers and permeability of bilayer membranes for small molecules, has been carried out. The conformity of results of numeric experiments to experimental data (structure of membrane lipid bilayers, lateral diffusion coefficients, and relative permeability of biomembranes for ligands) is discussed in the framework of a standard molecular dynamics protocol.     

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.     

Effect of alkyl chain unsaturation and cholesterol intercalation on oxygen transport in membranes: a pulse ESR spin labeling study.

Transport and diffusion of molecular oxygen in phosphatidylcholine (PC)-cholesterol membranes and their molecular mechanism were investigated. A special attention was paid to the molecular interaction involving unsaturated alkyl chains and cholesterol. Oxygen transport was evaluated by monitoring the bimolecular collision rate of molecular oxygen and the lipid-type spin labels, tempocholine phosphatidic acid ester, 5-doxylstearic acid, and 16-doxylstearic acid. The collision rate was determined by measuring the spin-lattice relaxation times (T1's) in the presence and absence of molecular oxygen with long-pulse saturation-recovery ESR techniques. In the absence of cholesterol, incorporation of either a cis or trans double bond at the C9-C10 position of the alkyl chain decreases oxygen transport at all locations in the membrane. The activation energy for the translational diffusion of molecular oxygen in the absence of cholesterol is 3.7-6.5 kcal/mol, which is comparable to the activation energy theoretically estimated for kink migration or C-C bond rotation of alkyl chains [Tr?uble, H. (1971) J. Membr. Biol. 4, 193-208; Pace, R. J., & Chan, S. I. (1982) J. Chem. Phys. 76, 4241-4247]. Intercalation of cholesterol in saturated PC membranes reduces oxygen transport in the headgroup region and the hydrophobic region near the membrane surface but little affects the transport in the central part of the bilayer. In unsaturated PC membranes, intercalation of cholesterol also reduces oxygen transport in and near the headgroup regions. In contrast, it increases oxygen transport in the middle of the bilayer. On the basis of these observations, a model for the mechanism of oxygen transport in the membrane is proposed in which oxygen molecules reside in vacant pockets created by gauche-trans isomerization of alkyl chains and the structural nonconformability of neighboring lipids, unsaturated PC and cholesterol in particular, and oxygen molecules jump from one pocket to the adjacent one or move along with the movement of the pocket itself. The presence of cholesterol decreases oxygen permeability across the membrane in all membranes used in this work in spite of the increase in oxygen transport in the central part of unsaturated PC-cholesterol membranes because cholesterol decreases oxygen transport in and near the headgroup regions, where the major barriers for oxygen permeability are located. Oxygen gradients across the membranes of the cells and the mitochondria are evaluated. Arguments are advanced that oxygen permeation across the protein-rich mitochondrial membranes can be a rate-limiting step for oxygen consumption under hypoxic conditions in vivo.     

Evaluation of the Membrane Permeability (PAMPA and Skin) of Benzimidazoles with Potential Cannabinoid Activity and their Relation with the Biopharmaceutics Classification System (BCS)

The permeability of five benzimidazole derivates with potential cannabinoid activity was determined in two models of membranes, parallel artificial membrane permeability assay (PAMPA) and skin, in order to study the relationship of the physicochemical properties of the molecules and characteristics of the membranes with the permeability defined by the Biopharmaceutics Classification System. It was established that the PAMPA intestinal absorption method is a good predictor for classifying these molecules as very permeable, independent of their thermodynamic solubility, if and only if these have a Log P _oct value <3.0. In contrast, transdermal permeability is conditioned on the solubility of the molecule so that it can only serve as a model for classifying the permeability of molecules that possess high solubility (class I: high solubility, high permeability; class III: high solubility, low permeability).     

The Physics of Cell Membranes

An overview is given of the fundamental physics underlying the self-assembly, molecular organisation and electrical properties of the membranes that envelop living cells. These ultra thin (∼ 6 nm) membranes act as a diffusion barrier between the cell interior (cytoplasm) and the external medium. They consist basically of a bi-molecular film of lipid molecules in which are embedded functional proteins that perform a variety of functions, including energy transduction, signalling, transport of ions (and othermolecules), etc. Some examples are also presented of the fascinating and socially and commercially important applications of membrane biophysics. This revised version was published online in July 2006 with corrections to the Cover Date.     

Molecular simulation study on sorption and diffusion processes in polymeric pervaporation membrane materials

Since MD simulations of membrane separation processes of aqueous/organic solutions lead to reasonable results that are in good agreement with experimental investigations an approach has been made to apply this method also for organic/organic membrane separation. In this connection the separation of a model feed mixture of 20 wt% benzene and 80 wt% n-heptane with dense amorphous polymer membranes was simulated utilising molecular modelling techniques. Special modifications of standard polymers such as polymethacrylates and polysiloxanes were investigated. It could be demonstrated that MD simulations of polymer–feed interface models can reproduce at least qualitatively important experimental results from related membrane pervaporation processes. These models are therefore suited in principle to obtain a better insight in the atomistic mechanisms of pervaporation. In addition, the knowledge about the underlying diffusion mechanism could be improved.     

The effect of hexadecaprenol on molecular organisation and transport properties of model membranes

The Langmuir monolayer technique and voltammetric analysis were used to investigate the properties of model lipid membranes prepared from dioleoylphosphatidylcholine (DOPC), hexadecaprenol (C80), and their mixtures. Surface pressure-molecular area isotherms, current-voltage characteristics, and membrane conductance-temperature were measured. Molecular area isobars, specific molecular areas, excess free energy of mixing, collapse pressure and collapse area were determined for lipid monolayers. Membrane conductance, activation energy of ion migration across the membrane, and membrane permeability coefficient for chloride ions were determined for lipid bilayers. Hexadecaprenol decreases the activation energy and increases membrane conductance and membrane permeability coefficient. The results of monolayer and bilayer investigations show that some electrical, transport and packing properties of lipid membranes change under the influence of hexadecaprenol. The results indicate that hexadecaprenol modulates the molecular organisation of the membrane and that the specific molecular area of polyprenol molecules depends on the relative concentration of polyprenols in membranes. We suggest that hexadecaprenol modifies lipid membranes by the formation of fluid microdomains. The results also indicate that electrical transmembrane potential can accelerate the formation of pores in lipid bilayers modified by long chain polyprenols.     

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.     

Molecular dynamics simulations of the interaction of phospholipid bilayers with polycaprolactone

The molecular interaction between common polymer chains and the cell membrane is unknown. Molecular dynamics simulations offer an emerging tool to characterise the nature of the interaction between common degradable polymer chains used in biomedical applications, such as polycaprolactone, and model cell membranes. Herein we characterise with all-atomistic and coarse-grained molecular dynamics simulations the interaction between single polycaprolactone chains of varying chain lengths with a phospholipid membrane. We find that the length of the polymer chain greatly affects the nature of interaction with the membrane, as well as the membrane properties. Furthermore, we next utilise advanced sampling techniques in molecular dynamics to characterise the two-dimensional free energy surface for the interaction of varying polymer chain lengths (short, intermediate, and long) with model cell membranes. We find that the free energy minimum shifts from the membrane-water interface to the hydrophobic core of the phospholipid membrane as a function of chain length. Finally, we perform coarse-grained molecular dynamics simulations of slightly larger membranes with polymers of the same length and characterise the results as compared with all-atomistic molecular dynamics simulations. These results can be used to design polymer chain lengths and chemistries to optimise their interaction with cell membranes at the molecular level.     

How cholesterol interacts with proteins and lipids during its intracellular transport

Sterols, as cholesterol in mammalian cells and ergosterol in fungi, are indispensable molecules for proper functioning and nanoscale organization of the plasma membrane. Synthesis, uptake and efflux of cholesterol are regulated by a variety of protein–lipid and protein–protein interactions. Similarly, membrane lipids and their physico-chemical properties directly affect cholesterol partitioning and thereby contribute to the highly heterogeneous intracellular cholesterol distribution. Movement of cholesterol in cells is mediated by vesicle trafficking along the endocytic and secretory pathways as well as by non-vesicular sterol exchange between organelles. In this article, we will review recent progress in elucidating sterol–lipid and sterol–protein interactions contributing to proper sterol transport in living cells. We outline recent biophysical models of cholesterol distribution and dynamics in membranes and explain how such models are related to sterol flux between organelles. An overview of various sterol-transfer proteins is given, and the physico-chemical principles of their function in non-vesicular sterol transport are explained. We also discuss selected experimental approaches for characterization of sterol–protein interactions and for monitoring intracellular sterol transport. Finally, we review recent work on the molecular mechanisms underlying lipoprotein-mediated cholesterol import into mammalian cells and describe the process of cellular cholesterol efflux. Overall, we emphasize how specific protein–lipid and protein–protein interactions help overcoming the extremely low water solubility of cholesterol, thereby controlling intracellular cholesterol movement. This article is part of a Special Issue entitled: Lipid–protein interactions.     

Key roles of enzyme positions and membrane surface potentials in the properties of biomimetic membranes

The coupling of diffusion, reaction, and electrostatic interactions existing in the microenvironment of permeable and charged bi-enzymatic membranes has led to the concept of biomimetic membranes. These membranes permit the active and specific transport of small hydrophilic molecules against their concentration gradients, at constant temperature and pressure. This study shows that such membranes behave in totally different ways, depending both on the relative position of the two enzymes, either within or outside the ionic double layer, and on the membrane surface potentials.