Membrane-mediated interactions of rod-like inclusions

Inclusions embedded in lipid membranes undergo a mediated force. due to the tendency of the membrane to relax its excess of elastic energy. In this paper we determine the exact shape of a two-dimensional vesicle hosting two different inclusions. and we analyse how the inclusion conformation influences the mediated interaction. We find non-trivial equilibrium configurations for the inclusions along the hosting membrane, and we derive the complete phase diagram of the mediated interaction. In particular, we find a non-vanishing mediated force even when the distance between the inclusions is much greater than their size. Our model can be applied to describe the mediated interactions of parallel, elongated inclusions embedded in three-dimensional membranes.