Pressure patches for membranes: the induced pinch of a grafted polymer

Achieving control of membrane shape and topology is of crucial importance to regulate function and performance of many systems in the realms of biology, physics, and chemical sciences. The design of a kit of versatile microscopic tools for tuning the shapes of fluid membranes relies ultimately on the possibility of tailoring molecules for applying a given, well-chosen force, to the self-assembled interfaces. Here we discuss theoretically the ability of grafted polymers to perform as mesoscopic pressure patches. We compute the pressure that a grafted polymer applies to the supporting surface. We also show that this entropic pressure leads to a well-defined pinched form of the membranes. Moreover, new membrane-mediated forces result from the action of these pressure tools, enabling action upon their spatial distribution along the membrane surface.