  Symmetry is closely intertwined with the function, genetics, and chemical
properties of multiprotein complexes. Here, we explore the relation between
structural symmetry and the ability of membrane proteins to sense and induce
membrane curvature, which is a key factor for modulating the shape and
organization of cell membranes. Using coarse-grained simulations and elasticity
theory, we show that the potential for direction-dependent membrane curvature
sensing is limited to asymmetric proteins, dimers, and tetramers, and argue
that one should expect this anisotropy to be strongest for dimers. Odd and
higher-order symmetries strongly suppress directional curvature sensing. This
classification gives a new perspective on the structure-function relation for
membrane proteins, and simplifies the task of translating between molecular
sensing mechanisms and their large-scale cellular consequences.
