Bundles of Interacting Strings in Two Dimensions

Bundles of strings which interact via short-ranged pair potentials are studied in two dimensions. The corresponding transfer matrix problem is solved analytically for arbitrary string number N by Bethe ansatz methods. Bundles consisting of N identical strings exhibit a unique unbinding transition. If the string bundle interacts with a hard wall, the bundle may unbind from the wall via a unique transition or a sequence of N successive transitions. In all cases, the critical exponents are independent of N and the density profile of the strings exhibits a scaling form that approaches a mean-field profile in the limit of large N.Comment: 8 pages (latex) with two figure

Membrane adhesion and domain formation

We review theoretical results for the adhesion-induced phase behavior of biomembranes. The focus is on models in which the membranes are represented as discretized elastic sheets with embedded adhesion molecules. We present several mechanism that lead to the formation of domains during adhesion, and discuss the time-dependent evolution of domain patterns obtained in Monte-Carlo simulations. The simulated pattern dynamics has striking similarities to the pattern evolution observed during T cell adhesion.Comment: 68 pages, 29 figure

Critical behavior of interacting surfaces with tension

Wetting phenomena, molecular protrusions of lipid bilayers and membrane stacks under lateral tension provide physical examples for interacting surfaces with tension. Such surfaces are studied theoretically using functional renormalization and Monte Carlo simulations. The critical behavior arising from thermally-excited shape fluctuations is determined both for global quantities such as the mean separation of these surfaces and for local quantities such as the probabilities for local contacts.Comment: 13 pages, 17 figures; accepted for publication in The European Physical Journa

Wetting between structured surfaces: Liquid bridges and induced forces

Wetting phenomena are theoretically studied for a slab geometry consisting of a wetting phase confined between two chemically patterned substrates. Each of these is decorated by an array of stripes whose composition alternates between two different surface phases. For a single pair of opposing stripes, the wetting phase may either form a bridge spanning from one surface to the other or it may break up into two separate channels. The bridge state induces an effective interaction between the two substrates. This leads to the bridge itself having a preferred contact angle and the substrates having a preferred separation. In the case of many stripes, one has a whole sequence of morphological transitions with the number of bridges decreasing as the surface separation grows

Membrane adhesion via competing receptor/ligand bonds

The adhesion of biological membranes is controlled by various types of receptor and ligand molecules. In this letter, we present a statistical-mechanical model for membranes that interact via receptor/ligand bonds of two different lengths. We show that the equilibrium phase behavior of the membranes is governed by an effective double-well potential. The depths of the two potential wells depend on the concentrations and binding energies of the receptors and ligands. The membranes are unbound for small, and bound for larger potential depths. In the bound state, the length mismatch of the receptor/ligand bonds can lead to lateral phase separation. We derive explicit scaling laws for the critical points of unbinding and phase separation, and determine the prefactors by comparison with Monte Carlo results.Comment: 7 pages, 3 figures; to appear in Europhys. Let

B cell activation and affinity discrimination by receptor segregation?

n/

Solvent free model for self-assembling fluid bilayer membranes: Stabilization of the fluid phase based on broad attractive tail potentials

We present a simple and highly adaptable method for simulating coarse-grained lipid membranes without explicit solvent. Lipids are represented by one head-bead and two tail-beads, with the interaction between tails being of key importance in stabilizing the fluid phase. Two such tail-tail potentials were tested, with the important feature in both cases being a variable range of attraction. We examined phase diagrams of this range versus temperature for both functional forms of the tail-tail attraction and found that a certain threshold attractive width was required to stabilize the fluid phase. Within the fluid phase region we find that material properties such as area per lipid, orientational order, diffusion constant, inter-leaflet flip-flop rate and bilayer stiffness all depend strongly and monotonically on the attractive width. For three particular values of the potential width we investigate the transition between gel and fluid phases via heating or cooling and find that this transition is discontinuous with considerable hysteresis. We also investigated the stretching of a bilayer to eventually form a pore and found excellent agreement with a recently published analytic theory.Comment: 14 pages 12 figure

Lateral phase separation of confined membranes

We consider membranes interacting via short, intermediate and long stickers. The effects of the intermediate stickers on the lateral phase separation of the membranes are studied via mean-field approximation. The critical potential depth of the stickers increases in the presence of the intermediate sticker. The lateral phase separation of the membrane thus suppressed by the intermediate stickers. Considering membranes interacting with short and long stickers, the effect of confinement on the phase behavior of the membranes is also investigated analytically

Barrier crossing of semiflexible polymers

We consider the motion of semiflexible polymers in double-well potentials. We calculate shape, energy, and effective diffusion constant of kink excitations, and in particular their dependence on the bending rigidity of the semiflexible polymer. For symmetric potentials, the kink motion is purely diffusive whereas kink motion becomes directed in the presence of a driving force on the polymer. We determine the average velocity of the semiflexible polymer based on the kink dynamics. The Kramers escape over the potential barriers proceeds by nucleation and diffusive motion of kink-antikink pairs, the relaxation to the straight configuration by annihilation of kink-antikink pairs. Our results apply to the activated motion of biopolymers such as DNA and actin filaments or synthetic polyelectrolytes on structured substrates.Comment: 7 pages, 3 figure