Rigid rod anchored to infinite membrane

We investigate the shape deformation of an infinite membrane anchored by a rigid rod. The density profile of the rod is calculated by the self-consistent-field theory and the shape of the membrane is predicted by the Helfrich membrane elasticity theory W. Helfrich, Z. Naturforsch. 28c, 693 (1973)]. It is found that the membrane bends away from the rigid rod when the interaction between the rod and the membrane is repulsive or weakly attractive (adsorption). However, the pulled height of the membrane at first increases and then decreases with the increase of the adsorption strength. Compared to a Gaussian chain with the same length, the rigid rod covers much larger area of the membrane, whereas exerts less local entropic pressure on the membrane. An evident gap is found between the membrane and the rigid rod because the membrane's curvature has to be continuous. These behaviors are compared with that of the flexible-polymer-anchored membranes studied by previous Monte Carlo simulations and theoretical analysis. It is straightforward to extend this method to more complicated and real biological systems, such as infinite membrane/multiple chains, protein inclusion, or systems with phase separation.