  Colloids and proteins alike can bind to lipid bilayers and move laterally in
these two-dimensional fluids. Inspired by proteins that generate membrane
curvature, sense the underlying membrane geometry, and migrate to high
curvature sites, we explore the question: Can colloids, adhered to lipid
bilayers, also sense and respond to membrane geometry? We report the curvature
migration of Janus microparticles adhered to giant unilamellar vesicles
elongated to present well defined curvature fields. However, unlike proteins,
which migrate to minimize membrane bending energy, colloids migrate by an
entirely different mechanism. By determining the energy dissipated along a
trajectory, the energy field mediating these interactions is inferred to be
linear in the local deviatoric curvature, as reported previously for colloids
trapped at curved interfaces between immiscible fluids. In this latter system,
however, the energy gradients are far larger, so particles move
deterministically, whereas the colloids on vesicles move with significant
fluctuations in regions of weak curvature gradient. By addressing the role of
Brownian motion, we show that the observed curvature migration of colloids on
bilayers is indeed a case of curvature capillary migration, with membrane
tension playing the role of interfacial tension. Furthermore, since this motion
is mediated by membrane tension and shape, it can be modulated, or even turned
"on" and "off", by simply varying these parameters. While particle-particle
interactions on lipid membranes have been considered in many contributions, we
report here an exciting and previously unexplored modality to actively direct
the migration of colloids to desired locations on lipid bilayers.
