Interactions between proteins bound to biomembranes

We study a physical model for the interaction between general inclusions bound to fluid membranes that possess finite tension, as well as the usual bending rigidity. We are motivated by an interest in proteins bound to cell membranes that apply forces to these membranes, due to either entropic or direct chemical interactions. We find an exact analytic solution for the repulsive interaction between two similar circularly symmetric inclusions. This repulsion extends over length scales of order tens of nanometers, and contrasts with the membrane-mediated contact attraction for similar inclusions on tensionless membranes. For non circularly symmetric inclusions we study the small, algebraically long-ranged, attractive contribution to the force that arises. We discuss the relevance of our results to biological phenomena, such as the budding of caveolae from cell membranes and the striations that are observed on their coats.Comment: 22 pages, 2 figure

Public International Law: Environmental Law

Noteworthy international activity relating to the environment occurred in a wide variety of fora in 2000. This chapter provides brief updates on some of the most significant developments. Though by no means a comprehensive review, the chapter reflects the wide sweep of issues and large number of entities now involved in the development of international environmental law, at the start of this new century. It also reflects how critical and complex this international work is, and how much remains to be done

Dynamic phase separation of fluid membranes with rigid inclusions

Membrane shape fluctuations induce attractive interactions between rigid inclusions. Previous analytical studies showed that the fluctuation-induced pair interactions are rather small compared to thermal energies, but also that multi-body interactions cannot be neglected. In this article, it is shown numerically that shape fluctuations indeed lead to the dynamic separation of the membrane into phases with different inclusion concentrations. The tendency of lateral phase separation strongly increases with the inclusion size. Large inclusions aggregate at very small inclusion concentrations and for relatively small values of the inclusions' elastic modulus.Comment: 6 pages, 6 figure

The shape of polymer-decorated membranes

Flexible membranes with anchored polymers are studied using both analytical methods and Monte Carlo simulations. The anchored polymers exert an entropically induced pressure on the membrane which is calculated explicitly using a small-gradient expansion. Likewise, we are able to determine both the shape profile of the membrane, which approaches a cone-like shape close to the anchor and a catenoid far away from it, and the profile of the induced mean curvature. We also consider membranes decorated by many polymers and identify two coverage regimes; one of which is governed by polymer/membrane and the other by polymer/polymer interactions

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