Physical limits to membrane curvature sensing by a single protein

Membrane curvature sensing plays an important role during biological processes such as cell division. Recent experiments have revealed that nanometer-sized proteins such as septins can distinguish between micron-sized membrane-coated glass beads of different diameters, despite being orders of magnitude smaller. Membranes are also subject to local curvatures that vary spatiotemporally due to thermal fluctuations, leading to discrepancies between the instantaneously measured curvature and the bead’s curvature. Using continuum models of fluctuating membranes, we investigate whether it is feasible for a protein to sense deviations in bilayer lipid densities as a proxy for local curvature to infer the membrane’s overall shape. With concepts from estimation theory, we quantify how the sensing efficacy of a single protein depends on parameters such as protein size, bilayer thickness, membrane bending modulus, membrane-substrate adhesion strength, and bead size. Proteins can better distinguish between a pair of membrane-adhered beads if the beads are small; however, when the beads are sufficiently different in size, the sensing efficacy is appreciable even for micron-sized beads.