Gravity-Induced Shape Transformations of Vesicles

We theoretically study the behavior of vesicles filled with a liquid of higher density than the surrounding medium, a technique frequently used in experiments. In the presence of gravity, these vesicles sink to the bottom of the container, and eventually adhere even on non - attractive substrates. The strong size-dependence of the gravitational energy makes large parts of the phase diagram accessible to experiments even for small density differences. For relatively large volume, non-axisymmetric bound shapes are explicitly calculated and shown to be stable. Osmotic deflation of such a vesicle leads back to axisymmetric shapes, and, finally, to a collapsed state of the vesicle.Comment: 11 pages, RevTeX, 3 Postscript figures uuencode

Lateral diffusion of receptor-ligand bonds in membrane adhesion zones: Effect of thermal membrane roughness

The adhesion of cells is mediated by membrane receptors that bind to complementary ligands in apposing cell membranes. It is generally assumed that the lateral diffusion of mobile receptor-ligand bonds in membrane-membrane adhesion zones is slower than the diffusion of unbound receptors and ligands. We find that this slowing down is not only caused by the larger size of the bound receptor-ligand complexes, but also by thermal fluctuations of the membrane shape. We model two adhering membranes as elastic sheets pinned together by receptor-ligand bonds and study the diffusion of the bonds using Monte Carlo simulations. In our model, the fluctuations reduce the bond diffusion constant in planar membranes by a factor close to 2 in the biologically relevant regime of small bond concentrations.Comment: 6 pages, 5 figures; to appear in Europhysics Letter

Segregation of receptor-ligand complexes in cell adhesion zones: Phase diagrams and role of thermal membrane roughness

The adhesion zone of immune cells, the 'immunological synapse', exhibits characteristic domains of receptor-ligand complexes. The domain formation is likely caused by a length difference of the receptor-ligand complexes, and has been investigated in experiments in which T cells adhere to supported membranes with anchored ligands. For supported membranes with two types of anchored ligands, MHCp and ICAM1, that bind to the receptors TCR and LFA1 in the cell membrane, the coexistence of domains of TCR-MHCp and LFA1-ICAM1 complexes in the cell adhesion zone has been observed for a wide range of ligand concentrations and affinities. For supported membranes with long and short ligands that bind to the same cell receptor CD2, in contrast, domain coexistence has been observed for a rather narrow ratio of ligand concentrations. In this article, we determine detailed phase diagrams for cells adhering to supported membranes with a statistical-physical model of cell adhesion. We find a characteristic difference between the adhesion scenarios in which two types of ligands in a supported membrane bind (i) to the same cell receptor or (ii) to two different cell receptors, which helps to explain the experimental observations. Our phase diagrams fully include thermal shape fluctuations of the cell membranes on nanometer scales, which lead to a critical point for the domain formation and to a cooperative binding of the receptors and ligands.Comment: 23 pages, 6 figure

Coexistence of dilute and densely packed domains of ligand-receptor bonds in membrane adhesion

We analyze the stability of micro-domains of ligand-receptor bonds that mediate the adhesion of biological model membranes. After evaluating the effects of membrane fluctuations on the binding affinity of a single bond, we characterize the organization of bonds within the domains by theoretical means. In a large range of parameters, we find the commonly suggested dense packing to be separated by a free energy barrier from a regime in which bonds are sparsely distributed. If bonds are mobile, a coexistence of the two regimes should emerge, which agrees with recent experimental observations.Comment: 6 pages, 6 figures, accepted by EP

Lateral phase separation in mixtures of lipids and cholesterol

In an effort to understand "rafts" in biological membranes, we propose phenomenological models for saturated and unsaturated lipid mixtures, and lipid-cholesterol mixtures. We consider simple couplings between the local composition and internal membrane structure, and their influence on transitions between liquid and gel membrane phases. Assuming that the gel transition temperature of the saturated lipid is shifted by the presence of the unsaturated lipid, and that cholesterol acts as an external field on the chain melting transition, a variety of phase diagrams are obtained. The phase diagrams for binary mixtures of saturated/unsaturated lipids and lipid/cholesterol are in semi-quantitative agreement with the experiments. Our results also apply to regions in the ternary phase diagram of lipid/lipid/cholesterol systems

First order wetting of rough substrates and quantum unbinding

Replica and functional renormalization group methods show that, with short range substrate forces or in strong fluctuation regimes, wetting of a self-affine rough wall in 2D turns first-order as soon as the wall roughness exponent exceeds the anisotropy index of bulk interface fluctuations. Different thresholds apply with long range forces in mean field regimes. For bond-disordered bulk, fixed point stability suggests similar results, which ultimately rely on basic properties of quantum bound states with asymptotically power-law repulsive potentials.Comment: 11 pages, 1 figur

Efficiency of Energy Transduction in a Molecular Chemical Engine

A simple model of the two-state ratchet type is proposed for molecular chemical engines that convert chemical free energy into mechanical work and vice versa. The engine works by catalyzing a chemical reaction and turning a rotor. Analytical expressions are obtained for the dependences of rotation and reaction rates on the concentrations of reactant and product molecules, from which the performance of the engine is analyzed. In particular, the efficiency of energy transduction is discussed in some detail.Comment: 4 pages, 4 fugures; title modified, figures 2 and 3 modified, content changed (pages 1 and 4, mainly), references adde

Nonequilibrium wetting transitions with short range forces

We analyze within mean-field theory as well as numerically a KPZ equation that describes nonequilibrium wetting. Both complete and critical wettitng transitions were found and characterized in detail. For one-dimensional substrates the critical wetting temperature is depressed by fluctuations. In addition, we have investigated a region in the space of parameters (temperature and chemical potential) where the wet and nonwet phases coexist. Finite-size scaling analysis of the interfacial detaching times indicates that the finite coexistence region survives in the thermodynamic limit. Within this region we have observed (stable or very long-lived) structures related to spatio-temporal intermittency in other systems. In the interfacial representation these structures exhibit perfect triangular (pyramidal) patterns in one (two dimensions), that are characterized by their slope and size distribution.Comment: 11 pages, 5 figures. To appear in Physical Review

Adhesion of surfaces via particle adsorption: Exact results for a lattice of fluid columns

We present here exact results for a one-dimensional gas, or fluid, of hard-sphere particles with attractive boundaries. The particles, which can exchange with a bulk reservoir, mediate an interaction between the boundaries. A two-dimensional lattice of such one-dimensional gas `columns' represents a discrete approximation of a three-dimensional gas of particles between two surfaces. The effective particle-mediated interaction potential of the boundaries, or surfaces, is calculated from the grand-canonical partition function of the one-dimensional gas of particles, which is an extension of the well-studied Tonks gas. The effective interaction potential exhibits two minima. The first minimum at boundary contact reflects depletion interactions, while the second minimum at separations close to the particle diameter results from a single adsorbed particle that crosslinks the two boundaries. The second minimum is the global minimum for sufficiently large binding energies of the particles. Interestingly, the effective adhesion energy corresponding to this minimum is maximal at intermediate concentrations of the particles.Comment: to appear in Journal of Statistical Mechanics: Theory and Experimen

Hamilton's equations for a fluid membrane: axial symmetry

Consider a homogenous fluid membrane, or vesicle, described by the Helfrich-Canham energy, quadratic in the mean curvature. When the membrane is axially symmetric, this energy can be viewed as an `action' describing the motion of a particle; the contours of equilibrium geometries are identified with particle trajectories. A novel Hamiltonian formulation of the problem is presented which exhibits the following two features: {\it (i)} the second derivatives appearing in the action through the mean curvature are accommodated in a natural phase space; {\it (ii)} the intrinsic freedom associated with the choice of evolution parameter along the contour is preserved. As a result, the phase space involves momenta conjugate not only to the particle position but also to its velocity, and there are constraints on the phase space variables. This formulation provides the groundwork for a field theoretical generalization to arbitrary configurations, with the particle replaced by a loop in space.Comment: 11 page