Formation of supported membranes from vesicles

Using a combination of the quartz crystal microbalance and surface plasmon resonance techniques, we have studied the spontaneous formation of supported lipid bilayers from small (approximately 25 nm) unilamellar vesicles. Together these experimental methods measure the amount of lipid adsorbed on the surface and the amount of water trapped by the lipid. With this approach, we have, for the first time, been able to observe in detail the progression from the adsorption of intact vesicles to rupture and bilayer formation. Monte Carlo simulations reproduce the data.     

Dynamic model and stationary shapes of fluid vesicles

A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find stationary shapes of vesicles with different topologies and the dynamic evolution towards them. The results are in agreement with those found by minimization of the Canham-Helfrich free energy. This fact shows that our phase-field model could be applied to more complex problems of instabilities.     

Dynamic strength of fluid membranes

Rupturing fluid membrane vesicles with a steady ramp of micropipette suction yields a tension distribution that images the kinetic process of membrane failure. When plotted on a log scale of tension loading rate, the distribution peaks (membrane strengths) define a dynamic tension spectrum with distinct regimes that reflect passage of prominent energy barriers along the pathway to rupture. Demonstrated here by tests on giant PC lipid vesicles over loading rates from 0.06–60 mN/m/s, the stochastic process of rupture can be modelled as a causal sequence of two thermally-activated transitions where each transition governs membrane strength on separate scales of loading rate. Under fast ramps of tension, a steep linear regime appears in each spectrum at high strengths which implies that failure requires nucleation of a rare nanoscale defect. The slope and projected intercept yield defect size and spontaneous production rate respectively. However, under slow ramps of loading, the spectrum crosses over to a shallow-curved regime at lower strength, which is consistent with the kinetic impedance to opening an unstable hole in a fluid film. The dependence of rupture tension on rate reveals hole edge energy and frequency scale for thermal fluctuations in size. To cite this article: E. Evans, V. Heinrich, C. R. Physique 4 (2003).     

A fluid generalization of membranes

In a certain sense a perfect fluid is a generalization of a point particle. This leads to the question as to what is the corresponding generalization for extended objects. Here the lagrangian formulation of a perfect fluid is much generalized by replacing the product of the co-moving vector which is a first fundamental form by higher dimensional first fundamental forms; this has as a particular example a fluid which is a classical generalization of a membrane; however there is as yet no indication of any relationship between their quantum theories.     

Swinging and tumbling of fluid vesicles in shear flow

The dynamics of fluid vesicles in simple shear flow is studied using mesoscale simulations of dynamically triangulated surfaces, as well as a theoretical approach based on two variables: a shape parameter and the inclination angle, which has no adjustable parameters. We show that, between the well-known tank-treading and tumbling states, a new "swinging" state can appear. We predict the dynamic phase diagram as a function of the shear rate, the viscosities of the membrane and the internal fluid, and the reduced vesicle volume. Our results agree well with recent experiments.     

Fluid vesicles with viscous membranes in shear flow

The effect of membrane viscosity on the dynamics of vesicles in shear flow is studied. We present a new simulation technique, which combines three-dimensional multiparticle collision dynamics for the solvent with a dynamically triangulated membrane model. Vesicles are found to transit from steady tank treading to unsteady tumbling motion with increasing membrane viscosity. Depending on the reduced volume and membrane viscosity, shear can induce both discocyte-to-prolate and prolate-to-discocyte transformations. This behavior can be understood from a simplified model.     

Adhesion of fluid vesicles at chemically structured substrates

The adhesion of fluid vesicles at chemically structured substrates is studied theoretically via Monte Carlo simulations. The substrate surface is planar and repels the vesicle membrane apart from a single surface domain γ , which strongly attracts this membrane. If the vesicle is larger than the attractive γ domain, the spreading of the vesicle onto the substrate is restricted by the size of this surface domain. Once the contact line of the adhering vesicle has reached the boundaries of the γ domain, further deflation of the vesicle leads to a regime of low membrane tension with pronounced shape fluctuations, which are now governed by the bending rigidity. For a circular γ domain and a small bending rigidity, the membrane oscillates strongly around an average spherical cap shape. If such a vesicle is deflated, the contact area increases or decreases with increasing osmotic pressure, depending on the relative size of the vesicle and the circular γ domain. The lateral localization of the vesicle's center of mass by such a domain is optimal for a certain domain radius, which is found to be rather independent of adhesion strength and bending rigidity. For vesicles adhering to stripe-shaped surface domains, the width of the contact area perpendicular to the stripe varies nonmonotonically with the adhesion strength.     

Dynamics of multicomponent vesicles in a viscous fluid

We develop and investigate numerically a thermodynamically consistent model of two-dimensional multicomponent vesicles in an incompressible viscous fluid. The model is derived using an energy variation approach that accounts for different lipid surface phases, the excess energy (line energy) associated with surface phase domain boundaries, bending energy, spontaneous curvature, local inextensibility and fluid flow via the Stokes equations. The equations are high-order (fourth order) nonlinear and nonlocal due to incompressibility of the fluid and the local inextensibility of the vesicle membrane. To solve the equations numerically, we develop a nonstiff, pseudo-spectral boundary integral method that relies on an analysis of the equations at small scales. The algorithm is closely related to that developed very recently by Veerapaneni et al. [81] for homogeneous vesicles although we use a different and more efficient time stepping algorithm and a reformulation of the inextensibility equation. We present simulations of multicomponent vesicles in an initially quiescent fluid and investigate the effect of varying the average surface concentration of an initially unstable mixture of lipid phases. The phases then redistribute and alter the morphology of the vesicle and its dynamics. When an applied shear is introduced, an initially elliptical vesicle tank-treads and attains a steady shape and surface phase distribution. A sufficiently elongated vesicle tumbles and the presence of different surface phases with different bending stiffnesses and spontaneous curvatures yields a complex evolution of the vesicle morphology as the vesicle bends in regions where the bending stiffness and spontaneous curvature are small.     

Dynamics of domain growth in self-assembled fluid vesicles

The dynamics of phase separation in multicomponent bilayer fluid vesicles is investigated by means of large-scale dissipative particle dynamics. The model explicitly accounts for solvent particles, thereby allowing for the very first numerical investigation of the effects of hydrodynamics and area-to-volume constraints. We observed regimes corresponding to coalescence of flat patches, budding and vesiculation, and coalescence of caps. We point out that the area-to-volume constraint has a strong influence on crossovers between these regimes.     

Advanced flicker spectroscopy of fluid membranes

The bending elasticity of a fluid membrane is characterized by its modulus and spontaneous curvature. We present a new method, advanced flicker spectroscopy of giant nonspherical vesicles, which makes it possible to simultaneously measure both parameters for the first time. Our analysis is based on the generation of a large set of reference data from Monte Carlo simulations of randomly triangulated surfaces. As an example of the potential of the procedure, we monitor thermal trajectories of vesicle shapes and discuss the elastic response of zwitterionic membranes to transmembrane pH gradients. Our technique makes it possible to easily characterize membrane curvature as a function of environmental conditions.     

Elastic energy of tilt and bending of fluid membranes

Tilt of hydrocarbon chains of lipid molecules with respect to membrane plane is commonly considered to characterize the internal structure of a membrane in the crystalline state. However, membranes in the liquid state can also exhibit tilt resulting from packing constraints imposed on the lipid molecules in diverse biologically relevant structures such as intermediates of membrane fusion, pores in lipid bilayers and others. We analyze the energetics of tilt in liquid membranes and its coupling with membrane bending. We consider three contributions to the elastic energy: constant tilt, variation of tilt along the membrane surface and membrane bending. The major assumption of the model is that the core of a liquid membrane has the common properties of an elastic continuum. We show that the variation of tilt and membrane bending are additive and that their energy contributions are determined by the same elastic coefficient: the Helfrich bending modulus, the modulus of Gaussian curvature and the spontaneous curvature known from previous studies of pure bending. The energy of a combined deformation of bending and varying tilt is determined by an effective tensor accounting for the two factors. In contrast, the deformation of constant tilt does not couple with bending and its contribution to the elastic energy is determined by an independent elastic constant. While accurate determination of this constant requires additional measurements, we estimate its value using a simplified approach. We discuss the relationships between the obtained elastic Hamiltonian of a membrane and the previous models of membrane elasticity. Received 10 February 2000 and Received in final form 19 June 2000     

Macroion-induced compositional instability of binary fluid membranes

Macroion adsorption on a mixed, fluid, lipid membrane containing oppositely charged lipids induces local changes in lipid composition at the interaction zones, and gradients at their boundaries. Including these effects in the free energy of the macroion-dressed membrane we derive its spinodal equation, and show that nonideal lipid mixing can lead to (lipid-mediated) attraction between macroions and lateral phase separation in the composite membrane. The critical nonideality for this transition is substantially smaller than that of the bare lipid membrane, decreasing with macroion size and charge. That is, the lipid membrane is destabilized by macroion adsorption.     

Undulations,steric interaction and cohesion of fluid membranes

Summary The theory of undulations of fluid membranes is reviewed and in some parts extended. The functional dependences of the steric interaction of undulating membranes are derived in a new way from simple physical arguments. Discussing the competition between steric repulsion and van der Waals attraction, one finds that membranes which usually separate (e.g. giant egg lecithin vesicles) should cohere if under lateral tension. The contours of two cohering vesicles observed when egg lecithin was swelling are analysed to show that the net energy of cohesion can be extremely small (≲10⁻⁵ erg cm⁻²). Paper presented at the ?Meeting on Lyotropics and Related Fields?, held in Rende, Cosenza, September 13–18, 1982.     

Configurations of points and strings

Let X$X$ be a smooth projective variety of dimension n≥2$n\ge 2$. It is shown that a finite configuration of points on X$X$ subject to certain geometric conditions possesses rich inner structure. On the mathematical level this inner structure is a variation of Hodge-like structure. As a consequence one can attach to such point configurations:

(i)

Lie algebras and their representations;     

Exploring PDA Configurations

This paper reviews the principle of the phase-Doppler particle sizer by means of examples of the effects of varying the various experimental parameters. The examples are computed by means of a comprehensive numerical model of a complete phase-Doppler system including many practical aspects such as aperture size, polarization filters and detector properties. First the phase-Doppler principle is explained as a logical development of an interferometric measurement of the phase of the light scattered from a particle. Then the standard phase-Doppler analyzer (PDA) is decribed followed by some newer or less known variations of the principle intended to measure, e.g., in the backscatter direction, to size very small particles or to determine the refractive index of a particle. Finally, the trajectory problem in PDA measurements is briefly discussed.