Vesicle shapes of low energy are studied for two variants of a continuum model for the bending energy of the bilayer: (i) the spontaneous-curvature model and (ii) the bilayer-coupling model, in which an additional constraint for the area difference of the two monolayers is imposed. We systematically investigate four branches of axisymmetric shapes: (i) the prolate-dumbbell shapes; (ii) the pear-shaped vesicles, which are intimately related to budding; (iii) the oblate-discocyte shapes; and (iv) the stomatocytes. These branches end up at limit shapes where either the membrane self-intersects or two (or more) shapes are connected by an infinitesimally narrow neck. The latter limit shape requires a certain condition between the curvatures of the adjacent shape and the spontaneous curvature. For both models, the phase diagram is determined, which is given by the shape of lowest bending energy for a given volume-to-area ratio and a given spontaneous curvature or area difference, respectively. The transitions between different shapes are continuous for the bilayer-coupling model, while most of the transitions are discontinuous in the spontaneous-curvature model. We introduce trajectories into these phase diagrams that correspond to a change in temperature and osmotic conditions. For the bilayer-coupling model, we find extreme sensitivity to an asymmetry in the monolayer expansivity. Both models lead to different predictions for typical trajectories, such as budding trajectories or oblate-stomatocyte transitions. Our study thus should provide the basis for an experimental test of both variants of the curvature model.

Liquid microchannels on structured surfaces are built up using a wettability pattern consisting of hydrophilic stripes on a hydrophobic substrate. These channels undergo a shape instability at a certain amount of adsorbed volume, from a homogeneous state with a spatially constant cross section to a state with a single bulge. This instability is quite different from the classical Rayleigh Plateau instability and represents a bifurcation between two different morphologies of constant mean curvature. The bulge state can be used to construct channel networks that could be used as fluid microchips or microreactors.

Intracellular transport is based on molecular motors that pull cargos along cytoskeletal filaments. One motor species always moves in one direction, e.g., conventional kinesin moves to the microtubule plus end, whereas cytoplasmic dynein moves to the microtubule minus end. However, many cellular cargoes are observed to move bidirectionally, involving both plus-and minusend-directed motors. The presumably simplest mechanism for such bidirectional transport is provided by a tug-of-war between the two motor species. This mechanism is studied theoretically using the load-dependent transport properties of individual motors as measured in single-molecule experiments. In contrast to previous expectations, such a tug-of-war is found to be highly cooperative and to exhibit seven different motility regimes depending on the precise values of the single motor parameters. The sensitivity of the transport process to small parameter changes can be used by the cell to regulate its cargo traffic.bidirectional movement ͉ cytoskeletal motor ͉ intracellular transport ͉ stochastic processes

The transport of cargo particles that are pulled by several molecular motors in a cooperative manner is studied theoretically in this article. The transport properties depend primarily on the maximal number N of motor molecules that may pull simultaneously on the cargo particle. Because each motor must unbind from the filament after a finite number of steps but can also rebind to it again, the actual number of pulling motors is not constant but varies with time between zero and N. An increase in the maximal number N leads to a strong increase of the average walking distance (or run length) of the cargo particle. If the cargo is pulled by up to N kinesin motors, for example, the walking distance is estimated to be 5 N؊1 ͞N micrometers, which implies that seven or eight kinesin molecules are sufficient to attain an average walking distance in the centimeter range. If the cargo particle is pulled against an external load force, this force is shared between the motors, which provides a nontrivial motor-motor coupling and a generic mechanism for nonlinear force-velocity relationships. With increasing load force, the probability distribution of the instantaneous velocity is shifted toward smaller values, becomes broader, and develops several peaks. Our theory is consistent with available experimental data and makes quantitative predictions that are accessible to systematic in vitro experiments.active transport ͉ bionanosystems ͉ load force ͉ run length ͉ walking distance

Membranes composed of amphiphilic molecules are highly flexible surfaces that determine the architecture of biological systems and provide a basic structural element for complex fluids such as microemulsions. Physical theories have been developed to describe many aspects of their conformational behaviour, such as the preferred shapes and shape transformations of closed vesicles, and the shape fluctuations, random-surface configurations, and adhesion and unbinding of interacting membranes. Understanding of these phenomena has been much improved through fruitful interactions between theory and experiment.

A simple model for the adhesion of vesicles to interfaces and membranes is introduced and theoretically studied. It is shown that adhering {or bound) vesicles can exhibit a large variety of dift'erent shapes. The notion of a contact angle governed by tension is found to be applicable only for a restricted subset of these shapes. Furthermore, the vesicle undergoes a nontrivial adhesion transition from a free to a bound state. This transition is governed by the balance between the overall bending and adhesion energies, and occurs even in the absence of shape fluctuations.Light and electron microscopy have revealed an astonishing complexity of the spatial organization of biological systems. ' There are two basic problems if one tries to un-

Binary Lennard-Jones fluids consisting of ''solvent'' and ''surfactant'' molecules are studied as simplified model systems for amphiphilic molecules in solution. Using Monte Carlo and molecular dynamics simulations, we observe the self-assembly of the surfactant molecules into bilayer membranes. These bilayers are fluid since the surfactants exhibit rapid lateral diffusion. We also measure the interfacial tension and the compressibility modulus of these bilayers. We show that they exhibit a tensionless state and characterize the corresponding stress profile. In this way, we bridge the gap between previous theoretical studies which were based ͑i͒ on discrete models with atomic resolution and ͑ii͒ on continuum models in which the bilayer membrane is treated as a smooth surface.

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