  The biophysical consequences of nanoscale curvature have been challenging to
resolve due to size-dependent membrane behavior and the experimental resolution
limits imposed by optical diffraction. Recent advances in nanoengineering and
super-resolution techniques have enabled new capabilities for creating and
observing curvature. In particular, draping supported lipid bilayers over
lithographically patterned substrates provides a model system for endocytic
pits. The experiments and simulations presented below describe the possible
detection of membrane curvature through fluorescence recovery after
photobleaching (FRAP), fluorescence correlation spectroscopy (FCS), single
particle tracking (SPT), and polarized localization microscopy (PLM). FRAP and
FCS depend on diffraction-limited illumination and detection. In particular, a
simulation of FRAP shows no effects on lipids diffusion due to a 50 nm diameter
membrane bud at any stage in the budding process. Simulated FCS demonstrated
small effects due to a 50 nm radius membrane bud that was amplified with
curvature-dependent lipid mobility changes. However, PLM and SPT achieve
sub-diffraction-limited resolution of membrane budding and lipid mobility
through the identification of the single-lipid positions with <15 nm spatial
and <20 ms temporal resolution. By mapping the single-lipid step lengths to
locations on the membrane, the effects of curvature on lipid behavior have been
resolved.
