Polymers grafted to a fluid and flexible membrane: Extreme sensitivity to the grafting density

Equilibrium phase coexistence between two chemical species implies the equality of the chemical potentials and of the osmotic pressures. We study this problem on a deformable membrane when one type of the molecules serves as anchor for polymeric chains immersed in the surrounding medium (considered as a good solvent). We derive the general conditions for phase coexistence when both the curvature of the membrane and the density field of the anchor molecule are free to adjust themselves. We show that curvature favors phase segregation. Our model predicts that membranes decorated with polymeric chains exhibit new shape bifurcations without equivalent in fixed density systems. Received: 26 November 2002 / Accepted: 2 April 2003 / Published online: 12 May 2003 RID="a" ID="a"e-mail: nicolas@drfmc.ceng.cea.fr RID="b" ID="b"e-mail: bfourcade@cea.fr     

Polymer brushes near the crystallization density

In this paper, polymer brushes are studied via molecular-dynamics simulations at very high grafting densities, where the crossover between the brush regime and the polymer-crystal regime is taking place. This crossover is directly observed with the structure factor and pair-correlation function. With increasing grafting density, this crystallization is progressing from the core layer of the brush towards the surface layer. The same process is analyzed using the lateral fluctuations of the monomers as a signature of their diminishing mobility. Additionally, bond forces and the chain excess free energy indicate a transition from the brush regime to the overstretched regime, which is in agreement with predictions of a modified self-consistent field theory.     

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     

Dewetting of solid-supported multilamellar lipid layers

Thin multilamellar assemblies of neutral lipid bilayers deposited on silicon substrates are shown to be unstable upon hydration. We analyze the stability of these systems taking into account a reduction of the fluctuation-related components of the bilayer interaction potential. The sizes of the patterns observed are consistent with a spinodal dewetting process. Received 27 November 2001     

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     

Shapes of nearly cylindrical, axisymmetric bilayer membranes

Shapes of nearly cylindrical sections of axisymmetric phospholipid membranes are studied theoretically. Describing the shape of such sections by their deviation from a reference cylinder, the well-established shape equation for axisymmetric bilayer membranes is expanded in terms of this deviation, and it is then solved analytically. The phase diagram shows the resulting stationary shapes as functions of system parameters and external conditions, i.e., the pressure difference across the membrane, the membrane tension, the difference between the tensions of the two monolayers, and the axial force acting on the vesicle. The accuracy of the approximate analytical solution is demonstrated by comparison with numerical results. The obtained analytical solution allows to extend the analysis to include shapes where numerical methods have failed. Received 27 September 2000 and Received in final form 26 March 2001     

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     

Theory of gel point in real polymer solutions

We develop a new theory of gelation which takes into account (i) delay of the gel point and (ii) change of functionality due to ring formation. We show that the problem of finding the gel point in real polymer solutions reduces to the problem of calculating the total ring concentration and the extent of reaction of intermolecular reaction at the gel point. In this paper, we solve a special case of this problem, on the basis of the independence assumption between intermolecular reaction and cyclization which takes into account only (i) the delay of the gel point: making use of the asymptotic equality of the total ring concentration, we acquire an approximate solution for the gel point D_c as a function of the inverse concentration , the relative frequency of cyclization and dimension d. Applying the observed values of in linear polyesters, the theoretical result reproduces well the Wile and the Gordon-Scantlebury observations, showing the existence of a critical dilution beyond which gelation can not occur, and an asymptote . As the classical gel point is approached, the present theory reduces to the linear equation, which makes one-to-one correspondence with the real slope , suggesting the inequality which is just what polymer chemists have quested for so far, with the physical meaning having remained unknown. Receveid: 30 December 1997 / Revised: 28 May 1998 / Accepted: 12 June 1998     

Radial distribution function of rod-like polyelectrolytes

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in the rod-like limit. The extent to which the radial distribution function of a polyelectrolyte is reproduced by that of a wormlike chain with an adjusted effective persistence length is investigated. Strong evidence is found for a universal scaling formula connecting the effective persistence length of a polyelectrolyte with the strength of the electrostatic interaction and the Debye screening length. Received 4 March 2002 and Received in final form 1 July 2002 RID="a" ID="a"e-mail: jrudnick@physics.ucla.edu     

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     

Polyelectrolyte chains in poor solvent. A variational description of necklace formation

We study the properties of polyelectrolyte chains under different solvent conditions, using a variational technique. The free energy and the conformational properties of a polyelectrolyte chain are studied by minimizing the free energy F_N, depending on N(N - 1)/2 trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length 2⁴ < N < 2⁸ and for an open chain of length 50 < N < 200 in poor- and theta-solvent conditions, including a Coulomb repulsion between the monomers. In theta-solvent conditions the blob size is measured and found in agreement with scaling theory, including charge depletion effects, expected for the case of an open chain. In poor-solvent conditions, a globule instability, driven by electrostatic repulsion, is observed. We notice also inhomogeneous behavior of the monomer-monomer correlation function, reminiscence of necklace formation in poor-solvent polyelectrolyte solutions. A global phase diagram in terms of solvent quality and inverse Bjerrum length is presented. Received 7 June 2001 and Received in final form 17 October 2001     

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     

On the organization of self-assembled actin networks in giant vesicles

We studied the formation of actin scaffolds in giant vesicles of dimyristoylphosphatidylcholine (DMPC). Polymerization of actin was induced at low ionic strength through ionophore-mediated influx of Mg²⁺ (2 mM). The spatial organization of the filamentous actin was visualized by confocal and epifluorescence microscopy as a function of the filaments length and membrane composition, by including various amounts of cholesterol or lipids with neutral and positively charged polyethyleneglycol headgroups (PEG lipopolymers). In vesicles of pure DMPC, the newly polymerized actin adsorbs to the membrane and forms a thin shell. In the presence of 2.5 mol% lipopolymers or of cholesterol at a molar fraction x = 0.37, formation of a thin adsorbed film is impeded. A fuzzy cortex is predominantly formed in vesicles of diameter d smaller than the filament persistence length ( d ⩽ 15μm) while for larger vesicles a homogeneous network formation is favoured in the bulk of the vesicle. The fuzzy-cortex formation is interpreted as a consequence of the reduction of the bending energy if the actin filaments accumulate close to the vesicle wall. Received: 17 January 2002 / Accepted: 21 March 2003 / Published online: 24 April 2003 RID="a" ID="a"e-mail: Laurent_Limozin@ph.tum.de     

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     

Adsorption of polymers anchored to membranes

Polymers, which are attached to a membrane at one of their ends, exert an entropic pressure, which curves the membrane away from the polymers. It is shown that adsorption which arises from a short-ranged potential between the polymer and the membrane has a large influence on the curvature of the membrane, leading to a decrease of the entropically induced curvature. If one ignores the finite size of the anchor segment, the polymer-induced curvature does not change sign and vanishes in the limit of strong adsorption and a pure contact potential. If one includes the finite size of the anchor segment, the membrane bends towards the polymer for sufficiently strong adsorption. Received 20 October 2000     

Adhesion of membranes with competing specific and generic interactions

Biomimetic membranes in contact with a planar substrate or a second membrane are studied theoretically. The membranes contain specific adhesion molecules (stickers) which are attracted by the second surface. In the absence of stickers, the trans-interaction between the membrane and the second surface is assumed to be repulsive at short separations. It is shown that the interplay of specific attractive and generic repulsive interactions can lead to the formation of a potential barrier. This barrier induces a line tension between bound and unbound membrane segments which results in lateral phase separation during adhesion. The mechanism for adhesion-induced phase separation is rather general, as is demonstrated by considering two distinct cases involving: i) stickers with a linear attractive potential, and ii) stickers with a short-ranged square-well potential. In both cases, membrane fluctuations reduce the potential barrier and, therefore, decrease the tendency of phase separation. Received 24 January 2002 and Received in final form 24 April 2002     

Universality classes of self-avoiding fixed-connectivity membranes

We present an analysis of extensive large-scale Monte Carlo simulations of self-avoiding fixed-connectivity membranes for sizes (number of faces) ranging from 512 to 17672 (triangular) plaquettes. Self-avoidance is implemented via impenetrable plaquettes. We simulate the impenetrable plaquette model in both three and four bulk dimensions. In both cases we find the membrane to be flat for all temperatures: the size exponent in three dimensions is ν = 0.95(5) (Hausdorff dimension d _H = 2.1(1)). The single flat phase appears, furthermore, to be equivalent to the large bending rigidity phase of non-self-avoiding fixed-connectivity membranes --the roughness exponent in three dimensions is ξ = 0.63(4). This suggests that there is a unique universality class for flat fixed-connectivity membranes without attractive interactions. Finally, we address some theoretical and experimental implications of our work. Received 23 June 2000 and Received in final form 25 October 2000     

Confinement-induced differences between dielectric normal modes and segmental modes of an ion-conducting polymer

Dielectric measurement in the range 0.1 Hz to 1 MHz were used to study the motions of polymers and ions in an ion-conducting polymer, polypropylene oxide containing small quantities (on the order of 1%) of lithium ions (LiClO₄), confined as a sandwich of uniform thickness between parallel insulating mica surfaces. In the dielectric loss spectrum, we observed three peaks; they originated from the normal mode of the polymer, segmental mode of the polymer, and ion motions. With decreasing film thickness, the peak frequencies corresponding to the normal mode and ion motion shifted to lower frequencies, indicating retardation due to confinement above 30 nm. This was accompanied by diminished intensity of the dielectric normal-mode relaxation, suggesting that confinement diminished the fluctuations of the end-to-end vector of the chain dipole in the direction between the confining surfaces. On the contrary, the segmental mode was not affected at that thickness. Finally, significant retardation of the segmental mode was observed only for the thinnest film (14 nm). The different dynamical modes of the polymer (segmental and slowest normal modes) respond with different thickness and temperature dependence to confinement. Received 31 August 2001 and Received in final form 30 October 2001     

Molecular mobility of confined phases in model mesoporous (MCM-41) and microporous (AlPO4-5 zeolite) host materials

This paper discusses the self-assembly of block copolymers into vesicular morphology. After a brief state of art of the field, a system based on an amphiphilic poly(butadiene)-b-poly(-L-glutamic acid) (PB-b-PGA) diblock copolymer in aqueous solution is discussed in detail. The aggregation behavior of this block copolymer has been investigated by means of fluorescence spectroscopy, dynamic (DLS) and static (SLS) light scattering as well as transmission electron microscopy (TEM). The diblock copolymer was found to form well-defined vesicles in water. The size of these so-called polymersomes or peptosomes could be reversibly manipulated as a function of both pH and ion strength. Depending on the pH of the aqueous solution, the hydrodynamic radii of these vesicles were found to vary from 100 nm to 150 nm. By cross-linking the 1,2-vinyl double bonds present in the polybutadiene block, the ability to transform a transient supramolecular self-organized aggregate into a permanent “shape-persistent stimuli-responsive nanoparticle” has been demonstrated. Received 25 June 2002 and Received in final form 22 October 2002 Published online: 11 March 2003