Free energy potential for aggregation of giant, neutral lipid bilayer vesicles by Van der Waals attraction

On the control of dispersion interactions between biological membranes and protein coated biointerfaces

HYPOTHESIS

Interaction of cellular membranes with biointerfaces is of vital importance for a number of medical devices and implants. Adhesiveness of these surfaces and cells is often regulated by depositing a layer of bovine serum albumin (BSA) or other protein coatings. However, anomalously large separations between phospholipid membranes and the biointerfaces in various conditions and buffers have been observed, which could not be understood using available theoretical arguments.

METHODS

Using the Lifshitz theory, we here evaluate the distance-dependent Hamaker coefficient describing the dispersion interaction between a biointerface and a membrane to understand the relative positioning of two surfaces. Our theoretical modeling is supported by experiments where the biointerface is represented by a glass substrate with deposited BSA and protein layers. These biointerfaces are allowed to interact with giant unilamellar vesicles decorated with polyethylene glycol (PEG) using PEG lipids to mimic cellular membranes and their pericellular coat.

RESULTS

We demonstrate that careful treatment of the van der Waals interactions is critical for explaining the lack of adhesiveness of the membranes with protein-decorated biointerfaces. We show that BSA alone indeed passivates the glass, but depositing an additional protein layer on the surface BSA, or producing multiple layers of proteins and BSA results in repulsive dispersion forces responsible for 100 nm large equilibrium separations between the two surfaces.

Giant Vesicles and Their Use in Assays for Assessing Membrane Phase State, Curvature, Mechanics, and Electrical Properties

Giant unilamellar vesicles represent a promising and extremely useful model biomembrane system for systematic measurements of mechanical, thermodynamic, electrical, and rheological properties of lipid bilayers as a function of membrane composition, surrounding media, and temperature. The most important advantage of giant vesicles over other model membrane systems is that the membrane responses to external factors such as ions, (macro)molecules, hydrodynamic flows, or electromagnetic fields can be directly observed under the microscope. Here, we briefly review approaches for giant vesicle preparation and describe several assays used for deducing the membrane phase state and measuring a number of material properties, with further emphasis on membrane reshaping and curvature.

Structure and behaviour of vesicles in the presence of colloidal particles

This review highlights recent studies that investigate the structural changes and behaviour of synthetic vesicles when they are exposed to colloidal particles. We will show examples to demonstrate the power of combining particles and vesicles in generating exciting supracolloidal structures. These suprastructures have a wide range of often responsive behaviours that take advantage of both the mechanical and morphological support provided by the vesicles and the associated particles with preset functionality. This review includes applications spanning a variety of disciplines, including chemistry, biology, physics and medicine.

Shape Transformation of the Nuclear Envelope during Closed Mitosis

The nuclear envelope (NE) in lower eukaryotes such as Schizosaccharomyces pombe undergoes large morphology changes during closed mitosis. However, which physical parameters are important in governing the shape evolution of the NE, and how defects in the dividing chromosomes/microtubules are reflected in those parameters, are fundamental questions that remain unresolved. In this study, we show that improper separation of chromosomes in genetically deficient cells leads to membrane tethering or asymmetric division in contrast to the formation of two equal-sized daughter nuclei in wild-type cells. We hypothesize that the poleward force is transmitted to the nuclear membrane through its physical contact with the separated sister chromatids at the two spindle poles. A theoretical model is developed to predict the morphology evolution of the NE where key factors such as the work done by the poleward force and bending and surface energies stored in the membrane have been taken into account. Interestingly, the predicted phase diagram, summarizing the dependence of nuclear shape on the size of the load transmission regions, and the pole-to-pole distance versus surface area relationship all quantitatively agree well with our experimental observations, suggesting that this model captures the essential physics involved in closed mitosis.

Effects of Surfactants and Polyelectrolytes on the Interaction between a Negatively Charged Surface and a Hydrophobic Polymer Surface

We have measured and characterized how three classes of surface-active molecules self-assemble at, and modulate the interfacial forces between, a negatively charged mica surface and a hydrophobic end-grafted polydimethylsiloxane (PDMS) polymer surface in solution. We provide a broad overview of how chemical and structural properties of surfactant molecules result in different self-assembled structures at polymer and mineral surfaces, by studying three characteristic surfactants: (1) an anionic aliphatic surfactant, sodium dodecyl sulfate (SDS), (2) a cationic aliphatic surfactant, myristyltrimethylammonium bromide (MTAB), and (3) a silicone polyelectrolyte with a long-chain PDMS midblock and multiple cationic end groups. Through surface forces apparatus measurements, we show that the separate addition of three surfactants can result in interaction energies ranging from fully attractive to fully repulsive. Specifically, SDS adsorbs at the PDMS surface as a monolayer and modifies the monotonic electrostatic repulsion to a mica surface. MTAB adsorbs at both the PDMS (as a monolayer) and the mica surface (as a monolayer or bilayer), resulting in concentration-dependent interactions, including a long-range electrostatic repulsion, a short-range steric hydration repulsion, and a short-range hydrophobic attraction. The cationic polyelectrolyte adsorbs as a monolayer on the PDMS and causes a long-range electrostatic attraction to mica, which can be modulated to a monotonic repulsion upon further addition of SDS. Therefore, through judicious selection of surfactants, we show how to modify the magnitude and sign of the interaction energy at different separation distances between hydrophobic and hydrophilic surfaces, which govern the static and kinetic stability of colloidal dispersions. Additionally, we demonstrate how the charge density of silicone polyelectrolytes modifies both their self-assembly at polymer interfaces and the robust adhesion of thin PDMS films to target surfaces.

Direct measurement of interaction forces between charged multilamellar vesicles†

Depletion-attraction induced adhesion of two giant (∼ 40 μm), charged multilamellar vesicles is studied using a new Cantilevered-Capillary Force Apparatus, developed in this laboratory. The specific goal of this work is to investigate the role of dynamics in the adhesion and de-adhesion processes when the vesicles come together or are pulled apart at a constant velocity. Hydrodynamic effects are found to play an important role in the adhesion and separation of vesicles at the velocities that are studied. Specifically, a period of hydrodynamically controlled drainage of the thin film between vesicles is observed prior to adhesion, and it is shown that the force required to separate a pair of tensed, adhering vesicles increases with increasing separation velocity and membrane tension. It is also shown that the work done to separate the vesicles increases with separation velocity, but exhibits a maximum as the membrane tension is varied.

Adhesion and merging of lipid bilayers: a method for measuring the free energy of adhesion and hemifusion

Lipid bilayers can be induced to adhere to each other by molecular mediators, and, depending on the lipid composition, such adhesion can lead to merging of the contacting monolayers in a process known as hemifusion. Such bilayer-bilayer reactions have never been systematically studied. In the course of our studies of membrane-active molecules, we encountered such reactions. We believe that they need to be understood whenever bilayer-bilayer interactions take place, such as during membrane fusion. For illustration, we discuss three examples: spontaneous adhesion between phospholipid bilayers induced by low pH, polymer-induced osmotic depletion attraction between lipid bilayers, and anionic lipid bilayers cross-bridged by multicationic peptides. Our purpose here is to describe a general method for studying such interactions. We used giant unilamellar vesicles, each of which was aspirated in a micropipette so that we could monitor the tension of the membrane and the membrane area changes during the bilayer-bilayer interaction. We devised a general method for measuring the free energy of adhesion or hemifusion. The results show that the energies of adhesion or hemifusion of lipid bilayers could vary over 2 orders of magnitude from -1 to -50 × 10(-5) J/m(2) in these examples alone. Our method can be used to measure the energy of transition in each step of lipid transformation during membrane fusion. This is relevant for current research on membrane fusion, which focuses on how fusion proteins induce lipid transformations.

Adhesive interactions between vesicles in the strong adhesion limit

We consider the adhesive interaction energy between a pair of vesicles in the strong adhesion limit, in which bending forces play a negligible role in determining vesicle shape compared to forces due to membrane stretching. Although force−distance or energy−distance relationships characterizing adhesive interactions between fluid bilayers are routinely measured using the surface forces apparatus, the atomic force microscope, and the biomembrane force probe, the interacting bilayers in these methods are supported on surfaces (e.g., mica sheet) and cannot be deformed. However, it is known that, in a suspension, vesicles composed of the same bilayer can deform by stretching or bending, and can also undergo changes in volume. Adhesively interacting vesicles can thus form flat regions in the contact zone, which will result in an enhanced interaction energy as compared to rigid vesicles. The focus of this paper is to examine the magnitude of the interaction energy between adhesively interacting, deformed vesicles relative to free, undeformed vesicles as a function of the intervesicle separation. The modification of the intervesicle interaction energy due to vesicle deformability can be calculated knowing the undeformed radius of the vesicles, R0, the bending modulus, k(b), the area expansion modulus, k(a), and the adhesive minimum, W(P)(0), and separation, D(P)(0), in the energy of interaction between two flat bilayers, which can be obtained from the force−distance measurements made using the above supported-bilayer methods. For vesicles with constant volumes, we show that adhesive potentials between nondeforming bilayers such as |W(P)(0)| 5 × 10(−4) mJ/m2, which are ordinarily considered weak in the colloidal physics literature, can result in significantly deep (>10×) energy minima due to increase in vesicle area and flattening in the contact region. If the osmotic expulsion of water across the vesicles driven by the tense, stretched membrane in the presence of an osmotically active solute is also taken into account, the vesicles can undergo additional deformation (flattening), which further enhances the adhesive interaction between them. Finally, equilibration of ions and solutes due to the concentration differences created by the osmotic exchange of water can lead to further enhancement of the adhesion energy. Our result of the progressively increasing adhesive interaction energy between vesicles in the above regimes could explain why suspensions of very weakly attractive vesicles may undergo flocculation and eventual instability due to separation of vesicles from the suspending fluid by gravity. The possibility of such an instability is an extremely important issue for concentrated vesicle-based products and applications such as fabric softeners, hair therapeutics and drug delivery.

Quantification of phase transitions of lipid mixtures from bilayer to non-bilayer structures: Model, experimental validation and implication on membrane fusion

Lipid bilayers provide a solute-proof barrier that is widely used in living systems. It has long been recognized that the structural changes of lipids during the phase transition from bilayer to non-bilayer have striking similarities with those accompanying membrane fusion processes. In spite of this resemblance, the numerous quantitative studies on pure lipid bilayers are difficult to apply to real membranes. One reason is that in living matter, instead of pure lipids, lipid mixtures are involved and there is currently no model that establishes the connection between pure lipids and lipid mixtures. Here, we make this connection by showing how to obtain (i) the short-range repulsion between bilayers made of lipid mixtures and, (ii) the pressure at which transition from bilayer phase to non-bilayer phases occur. We validated our models by fitting the experimental data of several lipid mixtures to the theoretical data calculated based on our model. These results provide a useful tool to quantitatively predict the behavior of complex membranes at low hydration.

DNA as membrane-bound ligand-receptor pairs: duplex stability is tuned by intermembrane forces

We use membrane-anchored DNA as model adhesion receptors between lipid vesicles. By studying the thermal stability of DNA duplex formation, which tethers the vesicles into superstructures, we show that the melting temperature of a 10-base DNA sequence is dependent on the lipid composition of the tethered vesicles. We propose a simple model that describes how the intermembrane interactions tilt the free energy landscape for DNA binding. From our model, we estimate the area per DNA in the binding sites between vesicles and also the total area of the adhesion plaques. We find that vesicles containing a small proportion of cationic lipid that are modified with membrane-anchored DNA can be reversibly tethered by specific DNA interactions and that the DNA also induces a small attraction between these membranes, which stabilizes the DNA duplex. By increasing the equilibrium intermembrane distance on binding, we show that intermembrane interactions become negligible for the binding thermodynamics of the DNA and hence the thermal stability of vesicle aggregates becomes independent of lipid composition at large enough intervesicle separations. We discuss the implications of our findings with regards to cell adhesion and fusion receptors, and the programmable self-assembly of nano-structured materials by DNA hybridization.

The adhesion kinetics of sticky vesicles in tension: the distinction between spreading and receptor binding

We investigate the kinetics of spreading and adhesion between polymer vesicles decorated with avidin and biotin, held in micropipettes to maintain fixed tension and suppress membrane bending fluctuations. In this study, the density of avidin (actually Neutravidin) and biotin was varied, but was always sufficiently high so that lateral diffusion in the membrane was unimportant to the adhesive mechanism or rate. For a stunning result, we report a concentration-dependent distinction between adhesion and spreading: At low surface densities of avidin and biotin, irreversible vesicle adhesion is strong enough to break the membrane when vesicle separation is attempted, yet there is no spreading or "wetting". By this we mean that there is no development of an adhesion plaque beyond the initial radius of contact and there is no development of a meaningful contact angle. Conversely, at 30% functionalization and greater, membrane adhesion is manifest through a spreading process in which the vesicle held at lower tension partially engulfs the second vesicle, and the adhesion plaque grows, as does the contact angle. Generally, when spreading occurs, it starts abruptly, following a latent contact period whose duration decreases with increasing membrane functionality. A nucleation-type rate law describes the latency period, determined by competition between bending and sticking energy. The significance of this result is that, not only are membrane mechanics important to the development of adhesion in membranes of nanometer-scale thickness, mechanics can dominate and even mask adhesive features such as contact angle. This renders contact angle analyses inappropriate for some systems. The results also suggest that there exist large regions of parameter space where adhesive polymeric vesicles will behave qualitatively differently from their phospholipid counterparts. This motivates different strategies to design polymeric vesicles for applications such as targeted drug delivery and biomimetic scavengers.

Novel method for measuring the adhesion energy of vesicles

Adhering vesicles with osmotically stabilized volume are studied with Monte Carlo simulations and optical microscopy. The simulations are used to determine the dependence of the adhesion area on the vesicle volume, the surface area, the bending rigidity, the adhesion energy per membrane area, and the adhesion potential range. The simulation results lead to a simple functional expression that is supplemented by a correction term for gravity effects. The obtained equation provides a new tool to analyze optical microscopy data and, thus, to measure the adhesion energy per area by analyzing the geometry of the adhering vesicle. The method can be applied in the weak and ultra-weak adhesion regime, where the adhesion energy per area is below 10(-6) J/m(2). By comparing the shapes of adhering vesicles with different reduced volumes, the bending rigidity can be estimated as well. The new approach is applied to experimental data for lipid vesicles on (i) an untreated and (ii) a monolayer-coated glass surface, providing ultra-weak and weak adhesion strength, respectively.

Size and stability of liposomes: a possible role of hydration and osmotic forces

Dynamic light scattering and electrophoretic mobility measurements have been used to characterize the size, size distribution and zeta potentials (zeta-potentials) of egg yolk phosphatidylcholine (EYPC) liposomes in the presence of monovalent ions ( Na(+) and K(+)). To study the stability of liposomes the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory has been extended by introducing the hydrated radius of the adsorbed ions onto the liposome surfaces. The decrease of liposome size is explained on the basis of the membrane impermeability to some ions which generate osmotic forces, which leads to evacuate water from liposome inside.

Strength of thermal undulations of phospholipid membranes

The temperature dependence of intermembrane interactions in freely suspended multilamellar membranes of dimiristoylphosphatidylcholine in D2O was studied using small-angle neutron scattering (SANS) and high-resolution x-ray diffraction (HRXRD). The study reveals that the Helfrich's undulation force is the dominating repulsion force at temperatures above 48.6 degrees C and intermembrane distances larger than 20.5 A. At approximately 77 degrees C the onset of the unbinding transition in the multilamellar membranes is observed. This transition has a continuous behavior in agreement with theoretical predictions and proceeds in accordance with a two-state model. Complimentary analysis of SANS and HRXRD data permits accurate calculation of the fundamental undulation force constant cfl. The obtained value of cfl=0.111+/-0.005 is in good agreement with theoretical calculations. The results of this work demonstrate a key role of Helfrich's undulations in the balance of intermembrane interactions of lipid membranes under physiological temperatures and suggest that thermal undulations play an important part in the interactions of biological membranes. The agreement of the predictions with the experimental data confirms that lipid membranes can be considered as random fluctuating surfaces that can be described well by current theoretical models and that they can serve as a powerful tool for studying behavior of such surfaces.

Groove-spanning behavior of lipid membranes on microfabricated silicon substrates

We report on a spreading behavior of phospholipid membranes that arise from a lump of phospholipid (a lipid source) on topographically patterned substrates immersed in an aqueous solution. Microgrooves with well-defined shapes were prepared on Si111 surfaces by anisotropic etching in an alkaline solution. A spreading front that consists of membrane lobes and a single lipid bilayer was observed on the patterned silicon substrates by utilizing fluorescence interference contrast (FLIC) microscopy. FLIC images indicate that the membrane lobes span the microgrooves, while the underlying single lipid bilayer spread along the surface of the microgrooves. In fact, fluorescent polystyrene nanoparticles could be encapsulated in the microgrooves that were completely covered with the membrane lobes. The groove-spanning behavior of membrane lobes is discussed in terms of a balance between adhesion and bending energies of lipid bilayers.

The binding energy of two nitrilotriacetate groups sharing a nickel ion

Among the various molecular interactions used to construct supramolecular self-assembling systems, homoliganded metallic NTA-Ni-NTA complexes have received little attention despite their considerable potential applications, such as the connection of different biochemical functions. The stability of this complex is investigated here by using two concordant nanotechniques (surface forces apparatus and vesicle micromanipulation) that allow direct measurements of adhesion energies due to the chelation of nickel ions by nitrilotriacetate (NTA) groups grafted on surfaces. We show that two NTA groups can share a nickel ion, and that the association of a Ni-NTA complex with an NTA group has a molecular binding energy of 1.4 kcal/mol. Binding measurements in bulk by isothermal titration calorimetry experiments give the same value and, furthermore, indicate that the Ni-NTA chelation bond is about five times stronger than the NTA-Ni-NTA one. This first direct proof and quantification of the simultaneous chelation of a nickel ion by two NTA groups sheds new light on association dynamics involving chelation processes and offers perspectives for the development of new supramolecular assemblies and anchoring strategies.

Determination of the Encapsulation Efficiency of Individual Vesicles Using Single-Vesicle Photolysis and Confocal Single-Molecule Detection

This paper describes a new method to measure the encapsulation efficiency of individual lipid vesicles. Single vesicles were first optically trapped (with a CW Nd:YAG laser at 1064 nm) and then photolyzed with a single 3-ns UV laser pulse (from a N(2) laser at 337 nm) to release the molecules encapsulated within the vesicle; confocal detection with single-molecule sensitivity (laser excitation at 488 nm from a CW Ar(+) laser) was used to measure the number of released molecules. By placing the confocal probe volume a few micrometers from the vesicle and by monitoring the transit times and the number of released molecules that crossed this probe volume, we could calculate the total number of molecules released from the vesicle using a three-dimensional diffusion equation. Unlike traditional definitions of encapsulation efficiencies based on bulk assays, because we can measure the contents of and release from individual vesicles, we can define the encapsulation efficiency by dividing the concentration of molecules encapsulated in each vesicle over the original concentration of the molecules present in the loading solution. We characterized the encapsulation efficiency of carboxyfluorescein for vesicles prepared by rotary evaporation and found oligolamellar vesicles have an encapsulation efficiency of 36.3 +/- 18.9%, while multilamellar vesicles have an encapsulation efficiency of 17.5 +/- 8.9%.

Using the atomic force microscope to study the interaction between two solid supported lipid bilayers and the influence of synapsin I

To measure the interaction between two lipid bilayers with an atomic force microscope one solid supported bilayer was formed on a planar surface by spontaneous vesicle fusion. To spontaneously adsorb lipid bilayers also on the atomic force microscope tip, the tips were first coated with gold and a monolayer of mercapto undecanol. Calculations indicate that long-chain hydroxyl terminated alkyl thiols tend to enhance spontaneous vesicle fusion because of an increased van der Waals attraction as compared to short-chain thiols. Interactions measured between dioleoylphosphatidylcholine, dioleoylphosphatidylserine, and dioleoyloxypropyl trimethylammonium chloride showed the electrostatic double-layer force plus a shorter-range repulsion which decayed exponentially with a decay length of 0.7 nm for dioleoylphosphatidylcholine, 1.2 nm for dioleoylphosphatidylserine, and 0.8 nm for dioleoyloxypropyl trimethylammonium chloride. The salt concentration drastically changed the interaction between dioleoyloxypropyl trimethylammonium chloride bilayers. As an example for the influence of proteins on bilayer-bilayer interaction, the influence of the synaptic vesicle-associated, phospholipid binding protein synapsin I was studied. Synapsin I increased membrane stability so that the bilayers could not be penetrated with the tip.

Controlling and measuring local composition and properties in lipid bilayer membranes

Local composition, structure, morphology, and phase are interrelated in lipid bilayer membranes. This gives us the opportunity to control one or more of these properties by manipulating others. We investigate theserelationships with combinations of simultaneous two-color widefield fluorescence imaging, three-dimensional rendering of vesicle domains, andmanipulation of the vesicle morphology via optical trapping and micropipetteaspiration. We describe methods to modulate, to measure, and to probe thelocal structure of model membranes through control of membrane curvature inliposomes.

PEG-covered lipid surfaces: bilayers and monolayers

In this review paper we survey the ways in which various micropipet techniques have been used to study the mechanochemical and interactive features of lipid bilayer vesicles and monolayer-coated gas bubbles. Special emphasis will be made on characterizing the barrier properties of grafted PEG layers and how a hierarchical approach that uses a short barrier and extended ligand allows us to start to mimic nature's own solution to the problem of ubiquitous repulsion and specific attraction. The information gained from such studies not only characterizes the membrane and other lipid surfaces and their intersurface interactions from a fundamental materials science perspective, but also provides essential materials property data that are required for the successful design and deployment of lipid-based carriers and other capsules in applications involving this so-called 'stealthy' surface.

Formation of giant liposomes promoted by divalent cations: critical role of electrostatic repulsion

Spontaneous formation of giant unilamellar liposomes in a gentle hydration process, as well as the adhesion energy between liposomal membranes, has been found to be dependent on the concentration of divalent alkali cations, Ca2+ or Mg2+, in the medium. With electrically neutral phosphatidylcholine (PC), Ca2+ or Mg2+ at 1-30 mM greatly promoted liposome formation compared to low yields in nonelectrolyte or potassium chloride solutions. When negatively charged phosphatidylglycerol (PG) was mixed at 10%, the yield was high in nonelectrolytes but liposomes did not form at 3-10 mM CaCl2. In the adhesion test with micropipette manipulation, liposomal membranes adhered to each other only in a certain range of CaCl2 concentrations, which agreed with the range where liposome did not form. The adhesion range shifted to higher Ca2+ concentrations as the amount of PG was increased. These results indicate that the divalent cations bind to and add positive charges to the lipids, and that membranes are separated and stabilized in the form of unilamellar liposomes when net charges on the membranes produce large enough electrostatic repulsion. Under the assumption that the maximum of adhesion energy within an adhesive range corresponds to exact charge neutralization by added Ca2+, association constants of PC and PG for Ca2+ were estimated at 7.3 M(-1) and 86 M(-1), respectively, in good agreement with literature values.

Renormalization of the tension and area expansion modulus in fluid membranes

Renormalization of the membrane tension and elastic area expansion modulus by thermally induced bending fluctuations is treated in terms of the formalism of Brochard, De Gennes, and Pfeuty (J. de Phys. (France). 37:1099-1104, 1976). The dependence of the renormalized tension on the bare membrane tension parallels the dependence on the fractional area extension of giant vesicles found experimentally by Evans and Rawicz (Physiol. Rev. Lett. 64:2094-2097, 1990), and suggests conditions for molecular dynamics simulations with membrane patches of limited size that might best represent the properties of macroscopic vesicles.

Micropipette manipulation technique for the monitoring of pH-dependent membrane lysis as induced by the fusion peptide of influenza virus

We have assembled a micropipette aspiration assay to measure membrane destabilization events in which large (20-30 microns diameter) unilamellar vesicles are manipulated and exposed to membrane destabilizing agents. Single events can be seen with a light microscope and are recorded using both a video camera and a photomultiplier tube. We have performed experiments with a wild-type fusion peptide from influenza virus (X31) and found that it induces pH-dependent, stochastic lysis of large unilamellar vesicles. The rate and extent of lysis are both maximum at pH 5; the maximum rate of lysis is 0.018 s-1 at pH 5. An analysis of our data indicates that the lysis is not correlated either to the size of the vesicles or to the tension created in the vesicle membranes by aspiration.

Critical temperature for unilamellar vesicle formation in dimyristoylphosphatidylcholine dispersions from specific heat measurements

Using a heat conduction calorimeter with very high resolution (+/- 0.00005 J/degrees C.cm3), we have measured the specific heat CpL between 25 and 35 degrees C of dimyristoylphosphatidylcholine (DMPC) in aqueous dispersions. Previous studies of the temperature dependence of the chemical potential of DMPC in the L alpha phase (lamellar, liquid crystalline) indicated that a dispersion consisting only of unilamellar vesicles forms spontaneously at a critical temperature T* of 29.0 degrees C. Our present measurements show an anomaly in CpL between 28.70 and 29.50 degrees C: the curve for CpL versus T first decreases and then exhibits an inflection point at 28.96 degrees C before it flattens. This anomaly is attributed to the transformation from multilamellar dispersion to unilamellar vesicles at T* = 28.96 degrees C. Two independent properties of the CpL data also indicate T* is a critical point for the formation of unilamellar vesicles: (a) the time to reach equilibrium upon changing temperature increased dramatically between 28.7 and 28.96 degrees C, increasing as (T* - T)-1; at T > T* the dramatic "slowing-down" phenomenon was not observed. This slowing-down near T* is a general characteristic of critical phenomena. (b) The free energy change for the multilamellar-unilamellar transformation was obtained from the CpL-T data over this temperature interval and found to be 3.2 J/mol or 0.016 ergs/cm2 of bilayer, in agreement with other estimates of the interaction energy between neutral bilayers. We conclude with a discussion of the implications for membrane bilayer stability of these newly identified dynamic properties of the transformation.

Contributions of hydration and steric (entropic) pressures to the interactions between phosphatidylcholine bilayers: experiments with the subgel phase

The total repulsive interaction between electrically neutral, fluid bilayer membranes is thought to have a number of components, including a hydration pressure, due to the reorientation of water by the bilayer, and steric (entropic) pressures due to bilayer undulations, head group motion, and molecular protrusions. For fully hydrated, crystalline bilayers these three steric pressures should be relatively small, and the major repulsive pressure present should be the hydration pressure. Therefore, to isolate the contribution of hydration pressure to the total interbilayer interaction, we have measured pressure-distance data by X-ray diffraction analysis of osmotically stressed dipalmitoylphosphatidylcholine (DPPC) multilayers in the subgel phase, where wide-angle and low-angle X-ray data show the bilayers are crystalline. As applied pressure was increased from 0 to 1 x 10(6) dyn/cm2, the interbilayer fluid space (df) decreased less than 1 A from its value at full hydration of 8.4 A. As the pressure was increased from 1 x 10(6) to 3 x 10(7) dyn/cm2, df decreased from about 8 to 4 A. For this range of df, the repulsive pressure decayed exponentially with df with a decay length of 1.4 A. Further increases in applied pressure did not appreciably decrease df, so that there was a sharp upward break in the pressure-distance curve at an interbilayer spacing of about 3 A. In contrast, pressure-distance relations for gel (L beta') phase and liquid-crystalline (L alpha) phase bilayers had much softer upward breaks at df < 5 A and extended to larger df at zero applied pressure. However, the pressure-distance curves for all three phases decayed exponentially with approximately the same decay length for 4 < df < 8 A. We interpret these data to mean the following: (1) the repulsion observed for df < 5 A is primarily a steric pressure whose range depends on head group motion; (2) the steric undulation pressure plays an important role in determining the hydration properties and the range of the total repulsive pressure for fluid membranes; (3) the same underlying mechanisms govern the repulsive pressure for all phases for 4 < df < 8 A; (4) these mechanisms include a pressure due to reorientation of water molecules; and (5) the hydration pressure component extents a maximum of about two water molecules from the bilayer surface for the subgel phase.

A differential heat-conduction microcalorimeter for heat-capacity measurements of fluids

A heat-conduction calorimeter has been developed for measuring small changes in heat capacity of milligram samples of membrane lipid dispersed in water as a function of temperature. The operation of the instrument is based on the principle that the thermal response of the sample to a short (10 s), electrically generated heat burst is a function of the diffusivity of the sample. Modeling studies of the instrument's performance have revealed that the output response after the heat burst is a function of only the heat capacity, rho Cp. Calibration of the instrument experimentally confirmed this behavior. This feature obviated the need to measure the thermal conductivity in order to determine rho Cp from the diffusivity equation, eta = lambda/rho Cp. The calorimeter has the following characteristics: reproducibility of loading: +/- 400 microJ/C degrees.cm3; baseline stability: +/- 10 microJ/C degrees.cm3 per 36 h; resolution (+/- 1 S.D.): +/- 50 microJ/C degrees.cm3; sample size 600 microliters.

Role of hydrophobic forces in bilayer adhesion and fusion

With the aim of gaining more insight into the forces and molecular mechanisms associated with bilayer adhesion and fusion, the surface forces apparatus (SFA) was used for measuring the forces and deformations of interacting supported lipid bilayers. Concerning adhesion, we find that the adhesion between two bilayers can be progressively increased by up to two orders of magnitude if they are stressed to expose more hydrophobic groups. Concerning fusion, we find that the most important force leading to direct fusion is the hydrophobic attraction acting between the (exposed) hydrophobic interiors of bilayers; however, the occurrence of fusion is not simply related to the strength of the attractive interbilayer forces but also to the internal bilayer stresses (intrabilayer forces). For all the bilayer systems studied, a single basic fusion mechanism was found in which the bilayers do not "overcome" their short-range repulsive steric-hydration forces. Instead, local bilayer deformations allow these repulsive forces to be "bypassed" via a mechanism that is like a first-order phase transition, with a sudden instability occurring at some critical surface separation. Some very slow relaxation processes were observed for fluid bilayers in adhesive contact, suggestive of constrained lipid diffusion within the contact zone.

Membrane interactions in nerve myelin. I. Determination of surface charge from effects of pH and ionic strength on period

We have used x-ray diffraction to study the interactions between myelin membranes in the sciatic nerve (PNS) and optic nerve (CNS) as a function of pH (2-10) and ionic strength (0-0.18). The period of myelin was found to change in a systematic manner with pH and ionic strength. PNS periods ranged from 165 to 250 A or more, while CNS periods ranged from 150 to 230 A. The native periods were observed only near physiological ionic strength at neutral or alkaline pH. The smallest periods were observed in the pH range 2.5-4 for PNS myelin and pH 2.5-5 for CNS myelin. The minimum period was also observed for PNS myelin after prolonged incubation in distilled water. At pH 4, within these acidic pH ranges, myelin period increased slightly with ionic strength; however, above these ranges, the period increased with pH and decreased with ionic strength. Electron density profiles calculated at different pH and ionic strength showed that the major structural alteration underlying the changes in period was in the width of the aqueous space at the extracellular apposition of membranes; the width of the cytoplasmic space was virtually constant. Assuming that the equilibrium myelin periods are determined by a balance of nonspecific forces/i.e., the electrostatic repulsion force and the van der Walls attractive force, as well as the short-range repulsion force (hydration force, or steric stabilization), then values in the period-dependency curve can be used to define the isoelectric pH and exclusion length of the membrane. The exclusion length, which is related to the minimum period at isoelectric pH, was used to calculate the electrostatic repulsion force given the other forces. The electrostatic repulsion was then used to calculate the surface potential, which in turn was used to calculate the surface charge density (at different pH and ionic strength). We found the negative surface charge increases with pH at constant ionic strength and with ionic strength at constant pH. We suggest that the former is due to deprotonation of the ionizable groups on the surface while the latter is due to ion binding. Interpretation of our data in terms of the chemical composition of myelin is given in the accompanying paper (Inouye and Kirschner, 1988). We also calculated the total potential energy functions for the different equilibrium periods and found that the energy minima became shallower and broader with increasing membrane separation. Finally, it was difficult to account directly for certain structural transitions from a balance of nonspecific forces. Such transitions included the abrupt appearance of the native period at alkaline pH and physiological ionic strength and the discontinuous compaction after prolonged treatment in distilled water. Possibly, in PNS myelin conformational modification of PO glycoprotein occurs under these conditions. The invariance of the cytoplasmic space suggests the presence of specific short-range interactions between surfaces at this apposition.

Thermal-mechanical fluctuations enhance repulsion between bimolecular layers

Beginning with the free energy potential for long-range interactions between parallel flat sheets and the mechanical energy of bending those sheets, we have derived an upper bound for repulsion enhanced by thermal undulations of sheets in a multilamellar array. Through a self-consistent (mean-field) potential, we cover the full range of layer separations from close-in to far-apart, where the enhanced repulsion approaches the weak steric interaction derived previously by Helfrich [Helfrich, W. (1978) Z. Naturforsch. 33a, 305-315]. We have examined the effect of the fluctuation-enhanced repulsion in experimental studies of osmotic (and mechanical) compression of multilamellar lipid arrays, mechanical compression of bilayers immobilized on mica substrates, and controlled adhesion of giant bilayer membrane vesicles.

Glycolipid modulation of membrane adhesion

A novel test of carbohydrate-mediated adhesion has been developed. At the tips of two syringes, large spherical model membranes have been made from phosphatidylcholine and varying amounts of mixed brain gangliosides dissolved in n-decane. The apposition of two such membranes resulted in adhesion, not fusion, as judged by the absence of fluorescence mixing in the junction with NBD-phosphatidylethanolamine in one membrane and perylene in the other. Adhesion was observed without gangliosides. The rate of formation of the adhesion area ("rate" of adhesion) was unchanged from 0 to 0.8 mol% gangliosides. A slightly lower but constant rate was observed within the physiological range from 2 to 10 mol%. Adhesion was frequently blocked at 11 to 15 mol% gangliosides. The rate of adhesion with pure gangliosides increased with the number of sialic acid residues: GT greater than GD1a greater than GM1. These results are interpreted in terms of a sialic acid-dependent segregation of gangliosides into the adhesion zone.

Detailed mechanics of membrane-membrane adhesion and separation. II. Discrete kinetically trapped molecular cross-bridges

In general, membrane-membrane adhesion involves specific molecular binding and cross-bridging reactions. The ideal, classical view is that near equilibrium the forces required to separate adhesive contacts are essentially equal to those induced in the membrane when the contact is formed. In contrast to the classical view, experimental observations often show that negligible levels of tension are induced by the adhesive contact even though the tension required to separate the contact is large enough to rupture the membrane. The deviation in tension levels associated with contact formation and separation appears to be due to the sparse distribution of strong molecular cross-bridges. Here, the mechanics of membrane-membrane adhesion and separation is developed for the case of discrete, kinetically trapped cross-bridges. The solution is obtained by numerical computation of the membrane contour that minimizes the total free energy (membrane elastic energy of deformation plus cross-bridge energies) in the contact zone. This solution is matched with the analytical solution for membrane stresses and geometry derived for the adjacent, unbridged zone. The results yield specific values of the macroscopic tension applied to the membrane in the plane region away from the contact zone and the microscopic angle at the edge of the contact zone. Two disparate values of the macroscopic tension are found: (a) the minimum tension required to separate the adherent membranes; and (b) the maximum tension induced in the membranes when the contact is formed (i.e., the level of tension at which the contact will just begin to spread). The results show that the deviation between these two tensions can be very large and depends strongly on the surface density of cross-bridges. In addition, the results provide an estimate of the restraining forces that anchor receptors within the plane of the membrane.