Specific biomembrane adhesion --Indirect lateral interactions between bound receptor molecules

We studied biomembrane adhesion using the micropipet aspiration technique. Adhesion was caused by contact site A, a laterally mobile and highly specific cell adhesion molecule from Dictyostelium discoideum, reconstituted in lipid vesicles of DOPC (L-α-dioleoylphosphatidylcholine) with an addition of 5 mol % DOPE-PEG₂₀₀₀ (1,2-diacyl-sn-glycero-3-phosphatidylethanolamine-N-[poly(ethyleneglycol) 2000]). The “fuzzy” membrane mimics the cellular plasma membrane including the glycocalyx. We found adhesion and subsequent receptor migration into the contact zone. Using membrane tension jumps to probe the equation of state of the two-dimensional “gas” of bound receptor pairs within the contact zone, we found strong, attractive lateral interactions. Received 16 February 2001     

Structure and interaction potentials in solid-supported lipid membranes studied by X-ray reflectivity at varied osmotic pressure

Highly oriented solid-supported lipid membranes in stacks of controlled number N ≃ 16 (oligo-membranes) have been prepared by spin-coating using the uncharged lipid model system 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). The samples have been immersed in aqueous polymer solutions for control of osmotic pressure and have been studied by X-ray reflectivity. The bilayer structure and fluctuations have been determined by modelling the data over the full q-range. Thermal fluctuations are described using the continuous smectic Hamiltonian with the appropriate boundary conditions at the substrate and at the free surface of the stack. The resulting fluctuation amplitudes and the pressure-distance relation are discussed in view of the inter-bilayer potential.     

Surfaces with quenched and annealed disordered charge distributions

We consider surfaces with disordered charge distribution. The disorder can be caused by mobile charges, as for example in mixed lipid bilayers, or by weakly charged surfaces where charge regulation takes place (e.g. carboxyl groups). Using Monte-Carlo simulation methods we find for quenched as well as annealed disordered charge distributions counterion densities close to the surface that are significantly larger than for ordered regularly spaced surface ions. Our field-theoretic results agree well with results obtained from Monte-Carlo simulations of the system. Furthermore, we obtain expressions for the effective interaction between charged colloids and charged rods close to a charged surface and discuss the effect of the surface-ion mobility and polarization charges on the interaction. In general, polarization effects as well as surface-ion mobility lead to a weakening of the effective interaction between charged objects.     

Effect of an electric field on a floating lipid bilayer: A neutron reflectivity study

We present here a neutron reflectivity study of the influence of an alternative electric field on a supported phospholipid double bilayer. We report for the first time a reproducible increase of the fluctuation amplitude leading to the complete unbinding of the floating bilayer. Results are in good agreement with a semi-quantitative interpretation in terms of negative electrostatic surface tension.     

Domain-induced budding in buckling membranes

We present a phase field model on buckling membranes to analyze phase separation and budding on soft membranes. By numerically integrating dynamic equations, it turns out that the formation of caps is greatly influenced by the presence of a little excess area due to the surface area constraint. When cap-shaped domains are created, domain coalescence is mainly observed not between domains with same budding directions, but between domains with opposite budding directions, because the bending energy between two domains is larger in the former case. Although we do not introduce spontaneous curvature like Helfrich model, we obtain some suggestions related to the slow dynamics of the phase separation on vesicles.     

Elasticity and shape equation of a liquid membrane

The density of the elastic energy of a deformed membrane in a liquid state is calculated. The thermodynamic equilibrium of its different parts is taken into account. The shape equation of a closed membrane is deduced. The quantity which keeps its value, when the variations of the energy of the system are calculated, is not the area of the deformed membrane, but its area in the flat tension free state. Because of this, additional terms appear in the second variation around the stable state. The case of a lipid bilayer and its fluctuations is examined for both free and blocked exchange of molecules between the monolayers, comprising the bilayer. Received 4 February 2002 / Received in final form 15 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: bivas@issp.bas.bg     

Membrane-mediated interactions of rod-like inclusions

Inclusions embedded in lipid membranes undergo a mediated force, due to the tendency of the membrane to relax its excess of elastic energy. In this paper we determine the exact shape of a two-dimensional vesicle hosting two different inclusions, and we analyse how the inclusion conformation influences the mediated interaction. We find non-trivial equilibrium configurations for the inclusions along the hosting membrane, and we derive the complete phase diagram of the mediated interaction. In particular, we find a non-vanishing mediated force even when the distance between the inclusions is much greater than their size. Our model can be applied to describe the mediated interactions of parallel, elongated inclusions embedded in three-dimensional membranes. Received 22 October 2001 and Received in final form 8 March 2002     

Active membranes studied by X-ray scattering

In view of recent theories of “active” membranes, we have studied multilamellar phospholipid membrane stacks with reconstituted transmembrane protein bacteriorhodopsin (BR) under different illumination conditions by X-ray scattering. The light-active protein is considered as an active constituent which drives the system out of equilibrium and is predicted to change the collective fluctuation properties of the membranes. Using X-ray reflectivity, X-ray non-specular (diffuse) scattering, and grazing incidence scattering, we find no detectable change in the scattering curves when changing the illumination condition. In particular the intermembrane spacing d remains constant, after eliminating hydration-related artifacts by design of a suitable sample environment. The absence of any observable non-equilibrium effects in the experimental window is discussed in view of the relevant parameters and recent theories.     

Fractal aggregates induced by liposome-liposome interaction in the presence of Ca2+

We present a study of the fractal dimension of clusters of large unilamellar vesicles (LUVs) formed by egg yolk phosphatidylcholine (EYPC), dimyristoylphosphocholine (DMPC) and dipalmitoylphosphocholine (DPPC) induced by Ca²⁺ . Fractal dimensions were calculated by application of two methods, measuring the angular dependency of the light scattered by the clusters and following the evolution of the cluster size. In all cases, the fractal dimensions fell in the range from 2.1 to 1.8, corresponding to two regimes: diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA). Whereas DMPC clusters showed a typical transition from the RLCA to the DLCA aggregation, EYPC exhibited an unusual behaviour, since the aggregation was limited for a higher concentration than the critical aggregation concentration. The behaviour of DPPC was intermediate, with a transition from the RLCA to the DLCA regimes with cluster sizes depending on Ca²⁺ concentration. Studies on the reversibility of the aggregates show that EYPC and DPPC clusters can be re-dispersed by dilution with water. DMPC does not present reversibility. Reversibility is evidence of the existence of secondary minima in the DLVO potential between two liposomes. To predict these secondary minima, a correction of the DLVO model was necessary taking into account a repulsive force of hydration.     

Vesicle self-reproduction: The involvement of membrane hydraulic and solute permeabilities

Conditions for self-reproduction are sought for a growing vesicle with its growth defined by an exponential increase of vesicle membrane area and by adequate flow of the solution across the membrane. In the first step of the presumed vesicle self-reproduction process, the initially spherical vesicle must double its volume in the doubling time of the membrane area and, through the appropriate shape transformations, attain the shape of two equal spheres connected by an infinitesimally thin neck. The second step involves separation of the two spheres and relies on conditions that cause the neck to be broken. In this paper we consider the first step of this self-reproduction process for a vesicle suspended in a solution whose solute can permeate the vesicle membrane. It is shown that vesicle self-reproduction occurs only for certain combinations of the values of membrane hydraulic and solute permeabilities and the external solute concentration, these quantities being related to the mechanical properties of the membrane and the membrane area doubling time. The analysis includes also the relaxation of a perturbed system towards stationary self-reproduction behavior and the case where the final shape consists of two connected spheres of different radii.     

Local entropic effects of polymers grafted to soft interfaces

In this paper, we study the equilibrium properties of polymer chains end-tethered to a fluid membrane. The loss of conformational entropy of the polymer results in an inhomogeneous pressure field that we calculate for Gaussian chains. We estimate the effects of excluded volume through a relation between pressure and concentration. Under the polymer pressure, a soft surface will deform. We calculate the deformation profile for a fluid membrane and show that close to the grafting point, this profile assumes a cone-like shape, independently of the boundary conditions. Interactions between different polymers are also mediated by the membrane deformation. This pair-additive potential is attractive for chains grafted on the same side of the membrane and repulsive otherwise. Received 20 April 2000     

On coupling between the orientation and the shape of a vesicle under a shear flow

A simple 2D model of deformable vesicles tumbling in a shear under flow is introduced in order to account for the main qualitative features observed experimentally as shear rates are increased. The simplicity of the model allows for a full analytical tractability while retaining the essential physical ingredients. The model reveals that the main axes of the vesicle undergo oscillations which are coupled to the vesicle orientation in the flow. The model reproduces and sheds light on the main novel features reported in recent experiments [M. Mader et al., Eur. Phys. J. E. 19, 389 (2006)], namely that both coefficients A and B that enter the Keller-Skalak equation, dψ/dt = A+Bcos(2 ψ) (ψ is the vesicle orientation angle in the shear flow), undergo a collapse upon increasing shear rate.     

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     

Wetting of phospholipid membranes on hydrophilic surfaces - Concepts towards self-healing membranes

We report on the wetting behavior of phospholipid membranes on solid surfaces immersed in aqueous solution. Using fluorescence microscopy, the spreading velocity of fluid bilayers advancing from a lipid source is investigated. The kinetic spreading coefficient was measured as a function of temperature for pure DMPC membranes and as a function of charge density and cholesterol content for binary membranes. A theoretical model for the membrane flow is presented, which takes into account the liquid crystalline bilayer architecture of the lipid membrane. The spreading power results from the membrane-solid VdW interaction and is dissipated in hydrodynamic shear flow as well as by inter-monolayer friction within the bilayer. The frictional drag causes a dynamic tension gradient in the spreading membrane, which is manifested by a single exponential decay of the fluorescence intensity profile along the spreading direction. Obstacles are shown to act as pinning centers deforming the advancing line interface. However, no depinning was observed, since the centers are circumflown without abrupt relaxation. Received 6 November 1998     

Bilayers of neutral lipids bear a small but significant charge

Many experiments done on neutral lipid bilayers in pure water show weak repulsions. These weak forces prevent vesicles from adhering and are generally overcome by adding some salt in the aqueous medium. They also appear as stray repulsions in surface forces measurements made on lipid bilayers. Using a surface forces apparatus in pure water and in salt solution, we have measured the forces between two stearoyl-oleoyl-phosphatidyl-choline (SOPC) bilayers and between two dimiristoyl-phosphatidyl-ethanolamine (DMPE) bilayers. The results show that the repulsions are due to a small amount of negative charges coming from impurities in SOPC. This was quantitatively confirmed by electrophoretic measurements. There are 3 times less charges in the case of DMPE layers. The effect of these charges which is negligible at high salt concentration may significantly affect the adhesion energy and behaviour of neutral lipid bilayers between 0 and salt. Received 18 December 1998     

X-ray reflectivity of solid-supported, multilamellar membranes

We have investigated the structure of solid-supported, multilamellar membranes by X-ray reflectivity. The density profile is obtained by fitting the full q-range to a model using the bilayer Fourier coefficients as fitting parameters. The effect of hydration and the substrate boundary condition are discussed in view of the well-known Landau-Peierls effect and its implications for structure determination. The resulting bilayer density profile agrees remarkably well with previously published data of a molecular dynamics (MD) simulation for 1,2-oleoyl-palmitoyl-sn-glycero-3-phosphocholine (OPPC). Received 1 October 2001 and Received in final form 21 December 2001     

Fluctuation spectra of free and supported membrane pairs

Fluctuation spectra of fluid compound membrane systems are calculated. The systems addressed contain two (or more) almost parallel membranes that are connected by harmonic tethers or by a continuous, harmonic confining potential. Additionally, such a compound system can be attached to a supporting substrate. We compare quasi-analytical results for tethers with analytical results for corresponding continuous models and investigate under what circumstances the discrete nature of the tethers actually influences the fluctuations. A tethered, supported membrane pair with similar bending rigidities and stiff tethers can possess a nonmonotonic fluctuation spectrum with a maximum. A nonmonotonic spectrum with a maximum and a minimum can occur for an either free or supported membrane pair of rather different bending rigidities and for stiff tethers. Typical membrane displacements are calculated for supported membrane pairs with discrete or continuous interacting potentials. Thereby an estimate of how close the constituent two membranes and the substrate typically approach each other is given. For a supported membrane pair with discrete or continuous interactions, the typical displacements of each membrane are altered with respect to a single supported membrane, where those of the membrane near the substrate are diminished and those of the membrane further away are enhanced.     

Dynamics of viscous vesicles in shear flow

The dynamics of giant lipid vesicles under shear flow is experimentally investigated. Consistent with previous theoretical and numerical studies, two flow regimes are identified depending on the viscosity ratio between the interior and the exterior of the vesicle, and its reduced volume or excess surface. At low viscosity ratios, a tank-treading motion of the membrane takes place, the vesicle assuming a constant orientation with respect to the flow direction. At higher viscosity ratios, a tumbling motion is observed in which the whole vesicle rotates with a periodically modulated velocity. When the shear rate increases, this tumbling motion becomes increasingly sensitive to vesicle deformation due to the elongational component of the flow and significant deviations from simpler models are observed. A good characterization of these various flow regimes is essential for the validation of analytical and numerical models, and to relate microscopic dynamics to macroscopic rheology of suspensions of deformable particles, such as blood.     

Elastica hypoarealis

We examine the equilibria of a rigid loop in the plane, characterized by an energy functional quadratic in the curvature, subject to the constraints of fixed length and fixed enclosed area. Whereas the only non self-intersecting equilibrium corresponding to the fixed length constraint is the circle, the area constraint gives rise to distinct equilibria labeled by an integer. These configurations exhibit self-intersections and bifurcations as the area is reduced. In addition, not only can the Euler-Lagrange equation be integrated to provide a quadrature for the curvature but the embedding itself can be expressed as a local function of the curvature. Perturbations connecting equilibria are shown to satisfy a first order ODE which is readily solved. Analytical expressions for the energy as a function of the area are obtained in the limiting regimes. Received 18 October 2001 / Received in final form 31 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: capo@fis.cinvestav.mx RID="b" ID="b"e-mail: chryss@nuclecu.unam.mx RID="c" ID="c"e-mail: jemal@nuclecu.unam.mx