Many-body interactions between curvature-inducing membrane inclusions with arbitrary cross-sections.

Abstract

By means of a multipolar expansion, we study analytically and numerically the interaction, in tensionless membranes, between multiple identical curvature-inducing membrane inclusions having arbitrary cross sections but uniform small detachment angles. In particular, for <i>N</i> circular inclusions forming regular polygons, we obtain analytical expressions for the total asymptotic interaction, up to <i>N</i> = 6, and we numerically compute the different multi-body contributions at arbitrary separations. We find that the latter are comparable to the sum of the two-body contributions. For <i>N</i> = 5 inclusions, the analytical asymptotic interaction scales as the inverse sixth power of the nearest neighbors distance <i>d</i>, weaker than the <i>d</i>^-4 power for <i>N</i> ≠ 5. The analytical interactions are always repulsive and in good agreement with the numerical results. In the case of noncircular cross sections, we consider the case of two identical inclusions having a given number of equally shaped lobes. Depending on the number of lobes and their amplitude, we find that the interaction is asymptotically either repulsive as <i>d</i>^-4 or attractive as <i>d</i>^-2, and always repulsive at short distances. We also characterize how the interaction depends on the inclusion rotation angles in the membrane plane.