Free Area Model Research Articles

Quantitative Relationship between Monolayer Domain Structure and Interfacial Shear Rheology

With micro-disc rheometry, we have been able to map out the viscosity of dipalmitoylphosphatidylcholine monolayers, and determine how the viscosity changes with additions of cholesterol and/or palmitic acid, which are common additives to clinical lung surfactants. We find that 1-3 wt% cholesterol (similar to that found in Infasurf, a clinical replacement surfactant) induces a two-three order of magnitude drop in the interfacial rheology. This drop correlates very well with the decrease in molecular coherence of the DPPC lattice as measure with synchrotron X-ray diffraction when used in a free-area model of the viscosity. However, palmitic acid induces a two order of magnitude increase in the viscosity of DPPC which is only partly correlated with the increase in molecular coherence of DPPC. Instead, a better explanation of the effects of PA on DPPC is the formation of a highly organized, low tilt phase that is about 1:1 DPPC:PA that appears at low surface pressure. For mixtures in which the PA fraction is below equimolar, we obtain a mixed solid phase of the 1:1 DPPC:PA cocrystal and a liquid phase of nearly pure DPPC. This phase separation is exacerbated by the presence of cholesterol, which segregates to the liquid phase. As the surface pressure increases, a second crystal forms of nearly pure DPPC. This is accompanied by a dramatic change in the rate of change of the surface viscosity vs surface pressure. This solid-solid phase coexistence is likely common in many complex biological monolayers.

Monitoring phases and phase transitions in phosphatidylethanolamine monolayers using active interfacial microrheology.

Active interfacial microrheology is a sensitive tool to detect phase transitions and headgroup order in phospholipid monolayers. The re-orientation of a magnetic nickel nanorod is used to explore changes in the surface rheology of 1,2-dilauroyl-sn-glycero-3-phosphoethanolamine (DLPE) and 1,2-dimyristoyl-sn-glycero-3-phosphoethanolamine (DMPE), which differ by two CH2 groups in their alkyl chains. Phosphatidylethanolamines such as DLPE and DMPE are a major component of cell membranes in bacteria and in the nervous system. At room temperature, DLPE has a liquid expanded (LE) phase for surface pressure, Π < ∼38 mN m(-1); DMPE has an LE phase for Π < ∼7 mN m(-1). In their respective LE phases, DLPE and DMPE show no measurable change in surface viscosity with Π, consistent with a surface viscosity <10(-9) N s m(-1), the resolution of our technique. However, there is a measurable, discontinuous change in the surface viscosity at the LE to liquid condensed (LC) transition for both DLPE and DMPE. This discontinuous change is correlated with a significant increase in the surface compressibility modulus (or isothermal two-dimensional bulk modulus). In the LC phase of DMPE there is an exponential increase in surface viscosity with Π consistent with a two-dimensional free area model. The second-order LC to solid (S) transition in DMPE is marked by an abrupt onset of surface elasticity; there is no measurable elasticity in the LC phase. A measurable surface elasticity in the S phase suggests a change in the molecular ordering or interactions of the DMPE headgroups that is not reflected in isotherms or in grazing incidence X-ray diffraction. This onset of measurable elasticity is also seen in DLPE, even though no indication of a LC-S transition is visible in the isotherms.

Effect of cholesterol nanodomains on monolayer morphology and dynamics.

At low mole fractions, cholesterol segregates into 10- to 100-nm-diameter nanodomains dispersed throughout primarily dipalmitoylphosphatidylcholine (DPPC) domains in mixed DPPC:cholesterol monolayers. The nanodomains consist of 6:1 DPPC:cholesterol "complexes" that decorate and lengthen DPPC domain boundaries, consistent with a reduced line tension, λ. The surface viscosity of the monolayer, ηs, decreases exponentially with the area fraction of the nanodomains at fixed surface pressure over the 0.1- to 10-Hz range of frequencies common to respiration. At fixed cholesterol fraction, the surface viscosity increases exponentially with surface pressure in similar ways for all cholesterol fractions. This increase can be explained with a free-area model that relates ηs to the pure DPPC monolayer compressibility and collapse pressure. The elastic modulus, G', initially decreases with cholesterol fraction, consistent with the decrease in λ expected from the line-active nanodomains, in analogy to 3D emulsions. However, increasing cholesterol further causes a sharp increase in G' between 4 and 5 mol% cholesterol owing to an evolution in the domain morphology, so that the monolayer is elastic rather than viscous over 0.1-10 Hz. Understanding the effects of small mole fractions of cholesterol should help resolve the controversial role cholesterol plays in human lung surfactants and may give clues as to how cholesterol influences raft formation in cell membranes.

Cholesterol Nanodomains: their Effect on Monolayer Morphology and Dynamics

Small mole fractions of cholesterol segregate into 10 - 100 nm diameter nanodomains in dipalmitoylphosphatidylcholine (DPPC) monolayers. The nanodomains segregate to DPPC domain boundaries, reducing the line tension, Δ, which alters domain shapes. The nanodomains consist of a 6:1 lipid: cholesterol “complex” and the surface viscosity, ηs, decreases exponentially with the area fraction of the complex at a given surface pressure. ηs increases exponentially with surface pressure, independent of cholesterol content, as predicted by a free area model that relates ηs to monolayer compressibility and collapse pressure. G', the elastic modulus, decreases with Δ at low cholesterol fractions, in analogy to 3-D emulsions. Increasing cholesterol further causes a sharp increase in G', likely due to a transition from a tilted to untilted molecular packing. Understanding the effects of small mole fractions of cholesterol should resolve the role of cholesterol in human lung surfactants and may give clues as to how cholesterol influences raft formation in cell membranes.

The Nano-Free Trade Territory (NFTT) Model

This paper is interested to introduce an alternative free trade area model to promote fast economic growth at the least developed countries (LDC’s). This new model of free trade area is called “The Nano-Free Trade Territory (NFTT) Model”. The idea is to generate jobs and indirect technological transfer to LDC’s. Basically, this paper is divided in two sections follow by: First section is about the introduction to regionalism and multilateralism. Second section is about how NFTT model works and its effects on the rest of host country.

Diffusion and Partitioning of Fluorescent Lipid Probes in Phospholipid Monolayers

The pressure-dependent diffusion and partitioning of single lipid fluorophores in DMPC and DPPC monolayers were investigated with the use of a custom-made monolayer trough mounted on a combined fluorescence correlation spectroscopy (FCS) and wide-field microscopy setup. It is shown that lipid diffusion, which is essential for the function of biological membranes, is heavily influenced by the lateral pressure and phase of the lipid structure. Both of these may change dynamically during, e.g., protein adsorption and desorption processes. Using FCS, we measured lipid diffusion coefficients over a wide range of lateral pressures in DMPC monolayers and fitted them to a free-area model as well as the direct experimental observable mean molecular area. FCS measurements on DPPC monolayers were also performed below the onset of the phase transition (Π < 5 mN/m). At higher pressures, FCS was not applicable for measuring diffusion coefficients in DPPC monolayers. Single-molecule fluorescence microscopy and differential scanning calorimetry clearly showed that this was due to heterogeneous partitioning of the lipid fluorophores in condensed phases. The results were compared with dye partitioning in giant lipid vesicles. These findings are significant in relation to the application of lipid fluorophores to study diffusion in both model systems and biological systems.

A Theoretical Model for Transdermal Drug Delivery from Emulsions and its Dependence upon Formulation

This article presents a theoretical model of transdermal drug delivery from an emulsion-type vehicle that addresses the vehicle heterogeneity and incorporates the prediction of drug transport parameters as function of the vehicle composition. The basic mass transfer model considers interfacial and diffusion resistances within the emulsion and partition/diffusion phenomena across two skin compartments in series. Drug transport parameters are predicted as follows: partition coefficients are derived from regular solutions theory, drug diffusivity in the continuous phase is computed from a free volume theory with segmental motion, and permeability of the surfactant layer around droplets is estimated based on a free surface area model. These relationships are incorporated within the basic mass transfer model, so that the overall model is able to predict temporal profiles of drug release from the vehicle and of drug concentration in plasma, as a function of vehicle composition. In this way, the proposed model provides a sound physicochemical basis to support the development of new formulations and the planning of experiments. A simulated case study regarding a nitroglycerin ointment is presented in detail, illustrating how thermodynamic and kinetic factors inherent to the emulsion vehicle can modulate drug release and subsequent systemic absorption.

Peripheral Protein Adsorption to Lipid-Water Interfaces: The Free Area Theory

In fluid monolayers approaching collapse, phospholipids and their complexes with diacylglycerols hinder adsorption to the monolayer of the amphipathic protein, colipase. Herein, a statistical, free-area model, analogous to that used to analyze two-dimensional lipid diffusion, is developed to describe regulation by lipids of the initial rate of protein adsorption from the bulk aqueous phase to the lipid-water interface. It is successfully applied to rate data for colipase adsorption to phospholipid alone and yields realistic values of the two model parameters; the phospholipid excluded area and the critical free surface area required to initiate adsorption. The model is further developed and applied to analyze colipase adsorption rates to mixed monolayers of phospholipid and phospholipid-diacylglycerol complexes. The results are consistent with complexes being stably associated over the physiologically relevant range of lipid packing densities and being randomly distributed with uncomplexed phospholipid molecules. Thus, complexes should form in fluid regions of cellular membranes at sites of diacylglycerol generation. If so, by analogy with the behavior of colipase, increasing diacylglycerol may not trigger translocation of some amphipathic peripheral proteins until its abundance locally exceeds its mole fraction in complexes with membrane phospholipids.

Membrane Lateral Mobility Obstructed by Polymer-Tethered Lipids Studied at the Single Molecule Level

Obstructed long-range lateral diffusion of phospholipids (TRITC-DHPE) and membrane proteins (bacteriorhodopsin) in a planar polymer-tethered 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer is studied using wide-field single molecule fluorescence microscopy. The obstacles are well-controlled concentrations of hydrophobic lipid-mimicking dioctadecylamine moieties in the polymer-exposed monolayer of the model membrane. Diffusion of both types of tracer molecules is well described by a percolating system with different percolation thresholds for lipids and proteins. Data analysis using a free area model of obstructed lipid diffusion indicates that phospholipids and tethered lipids interact via hard-core repulsion. A comparison to Monte Carlo lattice calculations reveals that tethered lipids act as immobile obstacles, are randomly distributed, and do not self-assemble into large-scale aggregates for low to moderate tethering concentrations. A procedure is presented to identify anomalous subdiffusion from tracking data at a single time lag. From the analysis of the cumulative distribution function of the square displacements, it was found that TRITC-DHPE and W80i show normal diffusion at lower concentrations of tethered lipids and anomalous diffusion at higher ones. This study may help improve our understanding of how lipids and proteins in biomembranes may be obstructed by very small obstacles comprising only one or very few molecules.

Shear viscosity of langmuir monolayers in the low-density limit.

We have measured the shear viscosity in the liquid phase of several Langmuir monolayers with an accuracy better than 30%. The method is based on the optical monitoring of the Brownian diffusion of submicron latex spheres floating at the air-water interface. The values are between 1 and 11x10(-10) N s m(-1), which is 10 to 100 times lower than previous data on similar systems. For N-palmitoyl-6-n-penicillanic acid and L-alpha-dipalmitoylphosphatidylcholine, the variation of the shear viscosity with surface density agrees with a classical free area model, whereas for pentadecanoic acid we observe a compensation effect.

The Lateral Diffusion of Selectively Aggregated Peptides in Giant Unilamellar Vesicles

We have systematically investigated the effect of aggregation of a transmembrane peptide on its diffusion in dimyristoylphosphatidylcholine and in palmitoyloleoylphosphatidylcholine model membranes. The hydrophobic segment of the b subunit from E. coli F 1F 0-ATP synthase was modified with a histidine tag at the carbonyl terminus and was aggregated selectively by using a series of multivalent, dendritic chelating agents with nitrilotriacetic acid functional groups. Peptide complexes ranging from monomers to hexamers were formed and studied in giant unilamellar vesicles. The rate of diffusion for the transmembrane peptide complexes were found to depend on the size of the complex. The results agree with predictions from the free area model for monomers and dimers, and the hydrodynamic continuum model for tetramers, pentamers, and hexamers. Comparisons with diffusion of lipids confirm that the diffusion of a transmembrane peptide is enhanced by coupling of density fluctuations between the two monolayers.

Single Molecule Fluorescence Imaging of Phospholipid Monolayers at the Air−Water Interface

Langmuir films of amphiphilic biomolecules represent promising systems to study diffusional properties in model membranes under controlled area conditions. Here, we present for the first time single molecule fluorescence imaging experiments on phospholipid monolayers at the air−water interface. The technique is used to track the lateral diffusion of single molecules of N-(6-tetramethylrhodaminethiocarbamoyl)-1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine, triethylammonium salt (TRITC−DHPE), in phospholipid monolayers of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dimyristoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (sodium salt) (DMPG) at different areas per phospholipid molecule. Our tracking data of the averaged mean-square displacement indicate for both phospholipids that surface flow could be suppressed significantly. The diffusion behavior of TRITC−DHPE in DMPC and DMPG monolayers is characterized by unobstructed diffusion and can be described well by a free area model. Our experiments show that single molecule fluorescence imaging can be successfully applied to monolayers of amphiphiles at the air−water interface. This opens the door to future studies of hindered diffusion in monolayers of specific heterogeneity.

Characterizing the Glassy Phase of a Statistical Copolymer Monolayer

Monolayers of a statistical copolymer with a poly(methacrylate) chain and hydrophilic and hydrophobic side groups are investigated at the air/water interface. The isotherms suggest a fluid and a frozen phase. With in-situ X-ray reflectivity the monolayer thickness is determined to be 2.5 nm or less. The shear viscosity in the fluid phase is extremely high yet can be described in the framework of the free area model. However, the parameter which characterizes the overlap of holes available for a diffusing monomer unit is a factor of 2 higher than expected, suggesting local diffusion barriers formed by nanosized clusters. In the glassy phase single-molecule fluorescence shows anomalous diffusion in an ≈140 nm cage (cf. ref 1), indicating that the clusters touch. The aggregates are mainly formed by the hydrophilic monomers, as both the X-ray data and the isotherms suggest.

Lipid Lateral Diffusion in Dilauroylphosphatidylcholine/Cholesterol Mixed Monolayers at the Air/Water Interface

Binary monolayers of l-α-dilauroylphosphatidylcholine (DLPC) and cholesterol were formed at the air/water interface by the successive addition method with chloroform as the spreading solvent at 296 K. Translational diffusion of a probe lipid in the monolayers as a function of cholesterol fraction was examined by the technique of fluorescence recovery after photobleaching in conjunction with epifluorescence microscopy and the Wilhelmy plate method. A transition from biphasic morphology to a visually homogeneous uniphasic monolayer occurred at surface pressures between 13 and 20 mN·m-1, depending on the cholesterol fraction in the monolayer. The lateral diffusion coefficient was found to decrease when surface pressure and/or cholesterol fraction were/was increased. The diffusion coefficients of the probe lipid in the homogeneous monolayers were analyzed on the basis of the free area model. The observed retardation of the diffusion is ascribed to an increase in the in-plane surface viscosity of monolayers. In the case of biphasic binary monolayers, the retardation with increasing cholesterol fraction is attributed to the obstacle mediated diffusion as in the effective medium analysis as well as to increasing surface viscosity.

Surface Self-Diffusion in L3 Phases

The self-diffusion coefficient of amphiphilic probes in the L3 phases of a surfactant system has been measured by fringe pattern photobleaching (FRAPP) experiments. The variation of the diffusion coefficients with the surfactant volume fraction is in agreement with a model for diffusion in cubic phases, which allows to determine approximately the topology of the phases. The observed variation of the diffusion coefficients with the probe lengths agrees with the free-area model for surfactant diffusion.

Surface Shear Viscosity and Phase Transitions of Monolayers at the Air-Water Interface

― The canal method has been employed to measure the in-plane steady shear viscosity of monolayers of bolaform lipids extracted from the membrane of the thermophilic microorganism Sulfolobus solfataricus. Monolayers were formed with the polar lipid extract (PLE), which is a mixture of several bolaform lipids, each one endowed with two nonequivalent polar headgroups. Viscosities were obtained from the measured flows by using the equation introduced by Joly; this equation contains a semiempirical parameter A, which takes into account the monolayer-subphase mechanical coupling. Measuring the flows for two different substances (PLE and oleic acid) and channel widths, the monolayer viscosities and the parameter A were determined at the same time. The analysis of the viscosity data according to the free area model shows evidences of the molecular conformational changes matching monolayer phase transitions.

Lateral diffusion and percolation in two-phase, two-component lipid bilayers. Topology of the solid-phase domains in-plane and across the lipid bilayer.

Fluorescence recovery after photobleaching (FRAP) has recently been used to examine the percolation properties of coexisting phases in two-component, two-phase phosphatidylcholine bilayers [Vaz, W. L. C., Melo, E. C. C., & Thompson, T. E. (1989) Biophys. J. 56, 869-876]. We now report the use of FRAP to study two additional problems in similar systems. The first is the effect of solid-phase obstacles on the lateral diffusion in the fluid phase. The second is the question of whether or not, in a single bilayer, solid-phase domains in one monolayer are exactly superimposed on solid domains in the apposing monolayer. To address the first problem, the lateral diffusion of N-(7-nitrobenzoxa-2,3-diazol-4-yl)-1-palmitoyl-2-oleoylphosp hatidylethanolamine (NBD-POPE), a probe soluble only in the fluid phase when solid and fluid phases coexist, has been studied in the mixture N-lignoceroyldihydrogalactosylceramide (LigGalCer)/dipalmitoylphosphatidylcholine (DPPC). Percolation of the fluid phase occurs at a high mass fraction of solid phase. This indicates that the solid domains have a centrosymmetric shape, a characteristic which makes this a good experimental system to test theoretical simulations of diffusion in an archipelago. It is shown that agreement between theory and experiment is poor, a result that had already been observed when the obstacles were integral membrane proteins. We develop an effective-medium model for diffusion in two-phase systems which explains both our results and those obtained with integral proteins. The distinctive feature of the model is the consideration of an annular region around the obstacles where the lipids are more ordered than in the bulk fluid phase. The diffusion coefficient is then calculated by extending the free area model to two-phase systems, taking these annuli into account. The second question, the organization of the solid-phase domains across the lipid bilayer, is examined in the systems LigGalCer/DPPC and dimyristoylphosphatidylcholine (DMPC)/distearoylphosphatidylcholine (DSPC) by comparing the diffusion of a fluid-phase-soluble, gel-phase-insoluble lipid derivative which spans the two monolayers of a bilayer (NBD-membrane-spanning-phosphatidylethanolamine, NBD-msPE) with that of a probe which is restricted to a single monolayer. In LigGalCer/DPPC, 20:80, the distribution of solid domains in one of the monolayers is independent of the distribution in the apposing monolayer. In contrast, in DMPC/DSPC, 50:50, the solid domains in one monolayer are exactly superimposed upon the solid domains existing in the apposing monolayer.

Lateral diffusion of amphiphiles and macromolecules at the air/water interface

We report a lateral diffusion study on the air/water interface of a surface-active protein, bacterial lipase from Pseudomonas fluorescens, and a vinyl polymer, poly(tert-butyl methacrylate), with the technique of fluorescence recovery after photobleaching. For the validation of implementing the technique and the calibration of our instrument, we relied on a phospholipid system that Peters and Beck have used earlier and found that our results were in accord with theirs within 20% in absolute magnitude. For both the phospholipid and lipase, we analyzed the lateral diffusion data in terms of the free area model of Sackmann and Trauble

Rigid Disks at High Density. II

As shown in a previous publication, the Helmholtz free energy per particle (divided by kBT) for a rigid disk system has the following asymptotic form in the limit of the reduced density θ=A0/A→1:F/NkBT∼2ln(λ/a)−2ln(θ−1−1)+C+D(θ−1−1)+···, in which C and D are appropriate numerical constants, λ is the mean thermal de Broglie wavelength, a is the disk diameter, and A0 is the close-packed value of the area, A, of a system of N particles. Moreover, a technique for estimating the value of C was developed. This technique was based upon a product representation for the partition function which considered a sequence of correlated motion of larger and larger sets of contiguous particles. An approximate value of C was previously obtained from all contributions for four or fewer correlated disks. This article extends these calculations to fifth order (contributions of all sets of five particles) with the summary result: C=0.14384–0.013857+0.014322–0.0073211–0.004222+···=0.14384–0.011078+···, in which the first number is the value of C obtained from the one-particle free-area model, and the remaining terms are the corrections from two-, three-, etc., particle correlations. These results are in slight disagreement with the estimate of C obtained by Hoover and Alder from molecular dynamics calculations, namely C≅0.14384–0.06±0.02. The sequential approximation scheme for estimating C is applied to the tunnel model (where the exact value is known) and shows a rapid convergence. An analysis of the most compact clusters or sets also supports the fifth-order estimate of C.