We calculate the membrane-mediated interaction between two cylindrical inclusions in a symmetric lipid bilayer. Our theory takes two contributions to the free energy into account, the elastic behavior of the membrane and the conformational restrictions that the flexible hydrocarbon chains of the lipids experience in the vicinity of a rigid inclusion. The description of the elastic behavior is based on two order parameters, the hydrophobic thickness of the membrane and a director field that characterizes the average tilt of the lipid chains. Conformational restrictions of the lipid chains are taken into account by a simple director model. We show that the short-range interaction potential between two inclusions sensitively depends on the degree of hydrophobic mismatch and on the spontaneous curvature of the lipid layers. In particular, we find pronounced attraction if the hydrophobic mismatch is positive. For negative mismatch the attraction is much less pronounced and, additionally, an energetic barrier appears. The inclusions prefer a small but notable negative hydrophobic mismatch. Positive spontaneous curvature amplifies these behaviors.

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