Orientational dependence of fluctuation-induced interactions in biological membranes

Abstract

We study fluctuation-induced interactions between inclusions, such as membrane proteins, on a fluctuating membrane by using the functional integral formulation. Thermal fluctuations of the membrane are modified by the existence of inclusions, and those modified fluctuations lead to a force between them. Expanding the bending stiffness of membrane inclusions in multipoles and using symmetry to determine the coupling between the inclusion's multipole moments and membrane curvature, we find that the fluctuation-induced interactions fall off as 1/R4 with the separation R. In addition, we obtain a novel behavior for the orientational dependence between noncircular inclusions: For a small ratio of the monopole to the quadrupole moments, the stable configuration is given by θ1 + θ2 = (2n + 1)π/4, where θ1 and θ2 are the angles between the principal axes of inclusions and the separation vector, whereas for large ratio, the free energy is minimized when each angle is respectively (2n + 1)π/4 with n being an integer.