Nonlinear response of membranes to pinning sites

Bound membranes respond to pinning sites by locally unbinding and overshooting their equilibrium spacing. This nonlinear response can lead to long-ranged interactions between these sites. We introduce a theory which incorporates bending elasticity, fluctuations, and intermembrane interactions to calculate the profiles of bound membranes subject to local pinning. This theory predicts several scaling regimes where the overshoot scales both with the pinning strength and site size. We also calculate the effective, membrane induced interaction between the sites, and predict aggregation properties. Aggregation and reversibility of pinning sites leads to interesting collective phenomena.