  Membrane curvature sensing is essential for a diverse range of biological
processes. Recent experiments have revealed that a single nanometer-sized
septin protein can distinguish between membrane-coated glass beads of one
micron and three micron diameters, even though the septin is orders of
magnitude smaller than the beads. This sensing ability is especially surprising
since curvature-sensing proteins must deal with persistent thermal fluctuations
of the membrane, leading to discrepancies between the bead's curvature and the
local membrane curvature sensed instantaneously by a protein. Using continuum
models of fluctuating membranes, we investigate whether it is feasible for a
protein acting as a perfect observer of the membrane to sense micron-scale
curvature either by measuring local membrane curvature or by using bilayer
lipid densities as a proxy. To do this, we develop algorithms to simulate lipid
density and membrane shape fluctuations. We derive physical limits to the
sensing efficacy of a protein in terms of protein size, membrane thickness,
membrane bending modulus, membrane-substrate adhesion strength, and bead size.
To explain the experimental protein-bead association rates, we develop two
classes of predictive models: i) for proteins that maximally associate to a
preferred curvature, and ii) for proteins with enhanced association rates above
a threshold curvature. We find that the experimentally observed sensing
efficacy is close to the theoretical sensing limits imposed on a septin-sized
protein, and that the variance in membrane curvature fluctuations sensed by a
protein determines how sharply the association rate depends on the curvature of
the bead.
