Intrinsic molecules in lipid membranes change the lipid-domain interfacial area: cholesterol at domain interfaces

A theoretical analysis of the effects of intrinsic molecules on the lateral density fluctuations in lipid bilayer membranes is carried out by means of computer simulations on a microscopic interaction model of the gel-to-fluid chain-melting phase transition. The inhomogeneous equilibrium structures of gel and fluid domains, which in previous work (Cruzeiro-Hansson, L. and Mouritsen, O.G. (1988) Biochim. Biophys. Acta 944, 63-72) were shown to characterize the transition region of pure lipid membranes, are here shown to be enhanced by intrinsic molecules such as cholesterol. Cholesterol is found to increase the interfacial area and to accumulate in the interfaces. The interfacial area, the average cluster size, the lateral compressibility, and the membrane area are calculated as functions of temperature and cholesterol concentration. It is shown that the enhancement by cholesterol of the lateral density fluctuations and the lipid-domain interfacial area is most pronounced away from the transition temperature. The implications of the results are discussed in relation to passive ion permeability and function of interfacially active enzymes such as phospholipase.     

Kinetics of cold-set diffusion-limited aggregations of denatured whey protein isolate colloids

The CaCl2-induced cold-set aggregation kinetics of the denatured whey protein isolate (WPI) colloids has been investigated under dilute diffusion-limited cluster aggregation (DLCA) conditions, using small-angle light scattering. In particular, the structure factor, the scattered intensity at zero angle and the average radius of gyration have been measured for the aggregating system as a function of time. It is found that the fractal dimension of the clusters is df= 1.85, in the range typical of clusters aggregated under DLCA conditions. The aggregation kinetics in this transition region can be described by a power law relation in the initial stage of the aggregation, but the exponent of the power law is equal to 0.7, i.e., significantly larger than 1/df= 0.54, which is the typical value of the DLCA kinetics. Since it is found that the average gyration radius of the clusters has reached a value of 80 microm, leading to a cumulative volume fraction of clusters equal to 0.25, it is legitimate to expect that the process is in the region of transition from aggregation to gelation. This confirmed by the fact that, at the later stage of the aggregation, the growth of the average cluster size further accelerates with time and eventually becomes explosive, leading to gelation. The observed aggregation kinetics has been compared with that reported in the literature from DLCA Monte Carlo simulations, and a good agreement has been found with the data corresponding to the transition region from aggregation to gelation. Numerical simulations using the Smoluchowski kinetic model have also been carried out in order to support the experimental findings.     

Geometrical properties of gel and fluid clusters in DMPC/DSPC bilayers: Monte Carlo simulation approach using a two-state model

In this paper the geometrical properties of gel and fluid clusters of equimolar dimyristoylphosphatidylcholine/distearoylphosphatidylcholine (DMPC/DSPC) lipid bilayers are calculated by using an Ising-type model (Sugar, I. P., T. E. Thompson, and R. L. Biltonen. 1999. Biophys. J. 76:2099-2110). The model is able to predict the following properties in agreement with the respective experimental data: the excess heat capacity curves, fluorescence recovery after photobleaching (FRAP) threshold temperatures at different mixing ratios, the most frequent center-to-center distance between DSPC clusters, and the fractal dimension of gel clusters. In agreement with the neutron diffraction and fluorescence microscopy data, the simulations show that below the percolation threshold temperature of gel clusters many nanometer-size gel clusters co-exist with one large gel cluster of size comparable with the membrane surface area. With increasing temperature the calculated effective fractal dimension and capacity dimension of gel and fluid clusters decrease and increase, respectively, within the (0, 2) interval. In the region of the gel-to-fluid transition the following geometrical properties are independent from the temperature and the state of the cluster: 1) the cluster perimeter linearly increases with the number of cluster arms at a rate of 8.2 nm/arm; 2) the average number of inner islands in a cluster increases with increasing cluster size, S, according to a power function of 0.00427 x S(1.3); 3) the following exponential function describes the average size of an inner island versus the size of the host cluster, S: 1 + 1.09(1 - e(-0.0072xS)). By means of the equations describing the average geometry of the clusters the process of the association of clusters is investigated.     

Detection of structural defects in phosphatidylcholine membranes by small-angle neutron scattering. The cluster model of a lipid bilayer

The oriented DPPC multilayers hydrated by D2O have been studied by a small-angle neutron scattering method in the Guinier range, and the gyration radius of the structural inhomogeneities has been estimated at about 29 A. They are interpreted as the annular defects between adjacent clusters uniting the all-trans chain 'segments' adjacent to the polar head group regions. The angle of the 'segment' tilt is determined by the hydrated polar group area (59.2 A2 for DPPC bilayers) and has been estimated to be about 44 degrees under the given experimental conditions. The hydrocarbon interior of a bilayer can be suggested as a 'sandwich' that is formed by two clustered layers (approx. 7 A of the thickness) and the central disordered (liquid) layer. The average cluster size along the bilayer surface is estimated to be approx. 24 A which correlates with the estimations of the short order region dimensions from the halfwidth of the X-ray 'packing' reflex (4.6 A)-1. The average interchain separation of approx. 5 A and the average cross-section area of a chain in a cluster (21.4 A2) were estimated from the reflex position and the chain cross-section geometry. The total volume of defects and the fraction of a bilayer surface occupied by them were estimated too.     

Influence of the local anesthetic tetracaine on the phase behavior and the thermodynamic properties of phospholipid bilayers.

We investigated the influence of the local anesthetic tetracaine on the thermodynamic properties and the temperature- and pressure-dependent phase behavior of the model biomembrane 1,2-dimyristoyl-sn-glycero-3-phosphocholine by using volumetric measurements at temperatures ranging from 0 degrees to 40 degrees C and at pressures from ambient up to 1000 bar. The pVT measurements were complemented by temperature-dependent differential scanning calorimetric measurements. Information about the influence of different concentrations of the local anesthetic on the thermodynamic changes accompanying the lipid phase transitions, and on the thermal expansion coefficient, the isothermal compressibility, and the volume fluctuations of the lipids in their different phases, could be obtained from these experiments. The incorporation of tetracaine leads to an overall disordering of the membrane, as can be inferred from the depression of the main transition temperature and the reduction of the volume change at the main lipid phase transition. The expansion coefficient alpha p and the isothermal compressibility chi T of the lipid bilayer are enhanced by the addition of tetracaine and strongly enhanced values of alpha p and chi T, and the lipid volume fluctuations are found in the direct neighborhood of the main phase transition region. As tetracaine can be viewed as a model system for amphiphilic molecules, these results also provide insight into the general understanding of the physicochemical action of amphiphilic molecules on membranes. The experimental results are compared with recent theoretical predictions for the phase behavior of anesthetic-lipid systems, and the biological relevance of this study is discussed.     

Maximum-entropy determination of self-association distribution functions; daunorubicin and ATP.

In the present paper we show how one can use the perturbation of some molecular optical property (for example circular dichroism or chemical shift) as a function of concentration to construct cluster distribution functions describing the self-association of molecules in solution. The optical data are first converted into data giving the variation of the average extent of clustering as a function of the total concentration and then, using straightforward thermodynamics, a set of moments of the cluster distribution function can be obtained. Utilizing the maximum-entropy method, the moments are then used to calculate approximate distribution functions, where the more moments that are used the better the approximation obtained. Given the probability distribution for clusters of different sizes one can then calculate the equilibrium constant for each stage of association. Thus one converts average degree of association into equilibrium constants without having to use any specific model. By this method one can clearly tell whether the equilibrium constants remain constant, increase, or decrease with the number of molecules in a cluster. We apply the method to literature data for two systems, namely daunorubicin, which has a strong tendency to cluster in solution, and Mg(ATP)(2-) which forms weaker clusters. We find that the successive equilibrium constants for adding a monomer to a cluster are approximately constant for daunorubicin but clearly decrease as a function of increasing cluster size for Mg(ATP)(2-).     

Development and initial evaluation of PEG-stabilized bilayer disks as novel model membranes

We show in this study that stable dispersions dominated by flat bilayer disks may be prepared from a carefully optimized mixture of 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC), cholesterol, and 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[methoxy(polyethyleneglycol)-5000] [PEG-DSPE(5000)]. By varying the content of the latter component, the average diameter of the disks can be changed in the interval from about 15 to 60 nm. The disks show excellent long-term stability, and their size and structure remain unaltered in the temperature range between 25 and 37 degrees C. The utility of the disks as artificial model membranes was confirmed and compared to uni- and multilamellar liposomes in a series of drug partition studies. Data obtained by isothermal titration calorimetry and drug partition chromatography (also referred to as immobilized liposome chromatography) indicate that the bilayer disks may serve as an attractive and sometimes superior alternative to liposomes in studies aiming at the investigation of drug-membrane interactions. The disks may, in addition, hold great potential for structure/function studies of membrane-bound proteins. Furthermore, we suggest that the sterically stabilized bilayer disks may prove interesting as carriers for in vivo delivery of protein/peptide, as well as conventional amphiphilic and/or hydrophobic, drugs.     

Influence of torus on the capacitance of asymmetrical phospholipid bilayers

We have measured the specific capacitance of phosphatidylethanolamine/phosphatidylserine membranes formed from monolayers. The membranes were built across Teflon films whose thickness varied from 6 to 25 mum. The building up of the membranes was followed by recording the capacitance of the membranes during the entire process of their formation. It is observed that the specific capacitance increases by about 10% as the thickness of the film is increased. Furthermore, during formation of the membrane it is observed that the capacitance values increased markedly immediately before the membranes are completely formed and then suddenly decrease to their normal values when formed (closing-off phenomenon). These results have led us to propose that the transition region known to surround membranes formed from monolayers may affect the capacitance values measured for such membranes. However, this effect is indirect in the sense that the composition (most likely in the form of inverted micelles) of the transition region will ultimately modify the hydrophobic/hydrophilic barrier in the bilayer by affecting the lateral tension known to exist in such membranes and, as a consequence, the average molecular area occupied by a phospholipid molecule in the bilayer. By such a mechanism, one can rationalize our experimental finding that the membrane capacitance varies as a function of the partition thickness across which they are prepared. It also rationalizes the large fluctuations in capacitance values usually found in the literature for such membranes as well as, at least in part, the closing-off phenomenon.     

Sample Size Estimation in Cluster Randomized Studies with Varying Cluster Size

Cluster randomized studies are common in community trials. The standard method for estimating sample size for cluster randomized studies assumes a common cluster size. However often in cluster randomized studies, size of the clusters vary. In this paper, we derive sample size estimation for continuous outcomes for cluster randomized studies while accounting for the variability due to cluster size. It is shown that the proposed formula for estimating total cluster size can be obtained by adding a correction term to the traditional formula which uses the average cluster size. Application of these results to the design of a health promotion educational intervention study is discussed.     

Nucleation and relaxation from meta-stability in spatial ecological models.

We study a model for competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. If a species does better locally than the other by an amount epsilon, the global outcome depends on the initial densities (uniformly distributed in space), epsilon and the size of the system. The transition point moves to lower values of the initial density of the superior species with increasing system size. Away from the transition point, the dynamics can be described by a mean-field approximation. The transition zone is dominated by formation of clusters and is characterized by nucleation effects and relaxation from meta-stability. Following cluster formation, the dynamics are dominated by motion of cluster interfaces through a combination of planar wave motion and motion through mean curvature. Clusters of the superior species bigger than a certain critical threshold grow whereas smaller clusters shrink. The reaction-diffusion system obtained from the mean-field dynamics agrees well with the particle system. The statistics of clusters at an early time soon after cluster-formation follow a percolation-like diffusive scaling law. We derive bounds on the time-to-extinction based on cluster properties at this early time. We also deduce finite-size scaling from infinite system behavior.     

Adsorption Behavior of Polydisperse Polymeric Systems

Adsorption behavior of polydisperse polymers at interfaces is studied by the Monte Carlo simulation method based on a lattice model. Effects of temperature and adsorption energies on the polymer density profile, cluster distributions and adsorption layer thickness are evaluated in two different polydisperse systems. It is found that adsorption properties are greatly different in these two systems. In normal distribution polydisperse systems, polymers are more sensitive to the excluded volume effects while in average distribution polymers are more inclined to adsorb on adsorbing interfaces. As higher temperature and lower attraction constrain the polymer adsorption, more clusters are found under these conditions. When temperature approaches the critical temperature of monodisperse systems, stable and large clusters exist in these two polydisperse systems. These results suggest that micro phase transition may exist in polydisperse systems. Polydisperse systems take little change of phase transition temperatures but altered the clusters morphology to some extent. The adsorption layer thickness changes are more sensitive to both temperature and polymer–interface interactions in average distribution systems when the whole polymer concentration increases slightly. This work also suggests significant differences between the polydisperse and the monodisperse systems in adsorption behavior. Therefore, quantitative system errors may exist when the monodisperse system models are used in simulation to evaluate polymer adsorption properties.     

The effects of density fluctuations on the partitioning of foreign molecules into lipid bilayers: application to anaesthetics and insecticides

An extensive computer-simulation study is performed on a simple but general molecular model recently proposed (J?rgensen et al. (1991) Biochem. Biophys. Acta 1062, 277-238) to describe foreign molecules interacting with lipid bilayers. The model is a multi-state lattice model of the main bilayer transition in which the foreign molecules are assumed to intercalate at interstitial lattice positions. Specific as well as non-specific interactions between the foreign molecules and the lipid acyl chains are considered. Particular attention is paid to the fluctuating properties of the membrane and how the presence of the foreign molecules modulates these fluctuations in the transition region. By means of computer-stimulation techniques, a detailed account is given of the macroscopic as well as microscopic consequences of the fluctuations. The macroscopic consequences of the fluctuations are seen in the thermal anomalies of the specific heat and the passive trans-membrane permeability. Microscopically, the fluctuations manifest themselves in lipid-domain formation in the transition region which implies an effective dynamic membrane heterogeneity. Within the model it is found that certain anaesthetics and insecticides which are characterised by specific interactions with the lipids have a strong effect on the heterogeneity of the membrane inducing regions of locally very high concentration of the foreign molecules. This leads to a broadening of the specific heat peak and a maximum in the membrane/water partition coefficient. These results are in accordance with available experimental data for volatile general anaesthetics like halothane, local anaesthetics like cocain derivatives, and insecticides like lindane.     

Partition of amphiphilic molecules to lipid bilayers by isothermal titration calorimetry

The partition of the amphiphile sodium dodecyl sulfate (SDS) between an aqueous solution and a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayer was followed by isothermal titration calorimetry (ITC) as a function of the total concentration of SDS. It was found that the obtained partition coefficient is strongly affected by the ligand concentration, even after correction for the charge imposed in the bilayer by the bound SDS. The partition coefficient decreased as the total concentration of SDS increased, with this effect being significant for local concentrations of SDS in the lipid bilayer above 5 molar%. At those high local concentrations, the properties of the lipid bilayer are strongly affected, leading to nonideal behavior and concentration-dependent apparent partition coefficients. It is shown that with the modern ITC instruments available, the concentrations of SDS can be drastically reduced while maintaining a good signal-to-noise ratio. The intrinsic parameters of the interaction with unperturbed membranes can be obtained from the asymptotic behavior of the apparent parameters as a function of the ligand concentration for both nonionic and ionic solutes. A detailed analysis is performed, and a spreadsheet is provided to obtain the interaction parameters with and without correction for electrostatics.     

The binding capacity is a probability density function.

The binding capacity of a system, or equivalently, the fluctuations of the number of ligands bound around the average value defined by the binding isotherm, can be regarded as a probability density function for the chemical potential of the ligand. The first moment of this density function is the mean ligand activity as defined by Wyman and gives the average free energy (in kT units) of binding per site. The second moment is directly related to the cooperativity of the system. These and higher moments can be obtained from numerical integration of experimental data in a direct way. An analytical expression for the moment generating function shows that the N independent coefficients of the partition function of a system containing N sites are uniquely defined by the first N moments of the binding capacity.     

Imaging fluorescence correlation spectroscopy: nonuniform IgE distributions on planar membranes.

Fluorescence correlation spectroscopy is useful for detecting and characterizing molecular clusters that are smaller than or approximately equal to optical resolution in size. Here, we report the development of an approach in which the pixel-to-pixel fluorescence fluctuations from a single fluorescence image are spatially autocorrelated. In these measurements, tetramethylrhodamine-labeled, anti-trinitrophenyl IgE antibodies were specifically bound to substrate-supported planar membranes composed of trinitrophenyl-aminocaproyldipalmitoylphosphatidylethanolamine and dipalmitoylphosphatidylcholine. The antibody-coated membranes were illuminated with the evanescent field from a totally internally reflected laser beam, and the fluorescence arising from the IgE-coated membranes was recorded with a cooled CCD camera. The image was corrected for the elliptical Gaussian shape of the evanescent illumination after background subtraction. The spatial autocorrelation functions of the resulting images generated two useful parameters: the extrapolated initial values, which were related to the average cluster intensity and density; and the correlation distances, which were related to the average cluster size. These parameters varied with the IgE density, and unlabeled polyclonal anti-IgE enhanced the nonuniform IgE distributions. The autocorrelation functions calculated from images of planar membranes containing fluorescently labeled lipids rather than bound, labeled IgE demonstrated that the spatial nonuniformities were prominent only in the presence of IgE. Fluorescent beads were used to demonstrate the principles and the methods.     

Clusters in a liquid-crystalline lipid bilayer

From analysis of the position and width of the diffuse maximum from X-ray scattering on hydrocarbon chains of phospholipid molecules, the average distance between neighbour chains in a bilayer and the values of interaction (correlation) radia were estimated. Comparison with the results of other methods applied shows that the cluster model of molecule packing in lipid bilayers explains the experimental data in the best way. The minimal dimensions of the clusters, average areas per molecule and approximate fraction of molecules in the clusters were estimated.     

Preparation and characteristics of lipid vesicles

Summary As determined by electron microscopy, lipid sonicated in buffer initially forms large vesicles which may be multilamellar. Prolonged sonication results in a population of vesicles of smaller, but not uniform diameters. These vesicles are bounded by only one bilayer. The lipid suspension can be partially fractionated according to size by column chromatography. A fraction of the eluate has been selected for further study. The weight-average vesicle weight and average radius of gyration are obtained by lightscattering measurements. The volume of buffer enclosed by the vesicles is determined using¹⁴C- or³H-labelled sugars as a marker. These values are in reasonable agreement with the corresponding values calculated from the size distribution of the vesicle fraction obtained by electron microscopy.     

Logistic growth in the presence of non-white environmental noise

A method is given for studying realistic random fluctuations in the carrying capacity of the logistic population growth model. This method is then applied using an environmental noise based on a Poisson process, and the time-dependent moments of the population probability density calculated. These moments are expressed in terms of a parameter obtained by dividing the correlation time of the environmental fluctuations by the characteristic response time of the population. When this quotient is large (very slow fluctuations tracked by the population) or small (very rapid fluctuations which are averaged), exact solutions are obtained for the probability density itself. It is also shown that at equilibrium, the average population sizes given by these two exact solutions bound all other cases.Numerical simulations confirm these developments and point to a trade-off between population stability and average population size. Additional simulations show that the probability of becoming extinct in a given time is greatest for populations intermediate between tracking and averaging the carrying capacity fluctuations. In addition to specifying when environmental noise can be ignored, these results indicate the direction in which growth parameters evolve in a fluctuating environment.     

Mixing of perfluorinated carboxylic acids with dipalmitoylphosphatidylcholine

Perfluorinated acids are emerging as an important class of persistent environmental pollutant, thus raising human health concerns. To understand the behavior of these compounds in biological systems, the mixing behavior of two perfluorinated acids, perfluorododecanoic and perfluorotetradecanoic acid, with dipalmitoylphosphatidylcholine (DPPC) was studied in monolayers at the air-water interface and in fully hydrated DPPC bilayers. The mixing behavior of both acids was indicative of an attractive interaction and partial miscibility with DPPC at the air-water interface. In the bilayer studies, the fluorinated acids cause peak broadening and elimination of the pretransition of DPPC. The onset temperature of the main phase transition remains constant in the presence of the fluorinated acids suggesting immiscibilities in the gel phase. Below X(DPPC)=0.97 significant peak broadening of the main phase transition can be observed. These results suggest strong interaction between the respective acid and DPPC, and that both acids are able to partition into the lipid bilayer. However, their mixing behavior is far from ideal, thus suggesting the presence of domains or lipid aggregates with high acid concentrations which may (adversely) impact the function of biological mono- and bilayers.