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.