Bending of Membranes by Anchored Polymers

Polymers which are attached to a fluid membrane by a single anchor exhibit a dilute mushroom regime and a semi-dilute brush regime. Scaling arguments and explicit calculations for ideal polymers show that the membrane is bent by the anchored polymer: For smooth bends, an anchored mushroom with linear size R po induces a spontaneous curvature of order ≃ T /κ R po , where T and κ are the temperature and the bending rigidity, respectively; for sharp cone-like bends, it induces a bending angle ≃ T /2πκ. A brush with mean anchor separation ξ an leads to a curvature of order ≃ ( R po /ξ an ) 2/ν T /κξ an .