  Lipid membranes regulate the flow of materials and information between cells
and their organelles. Further, lipid composition and morphology can play a key
role in regulating a variety of biological processes. For example, viral
uptake, plasma membrane tension regulation, and the formation of caveolae all
require the creation and control of groups of lipids that adopt specific
morphologies. In this paper, we use a simplified model mixture of lipids and
cholesterol to examine the interplay between lipid phase-separation and bilayer
morphology. We observe and theoretically analyze three main features of
phase-separated giant unilamellar vesicles. First, by tracking the motion of
`dimpled' domains, we measure repulsive, elastic interactions that create
short--range translational and orientational order, leading to a stable
distribution of domain sizes, and hence maintaining lateral heterogeneity on
relatively short length scales and long time scales. Second, we examine the
transition to `budded' domain morphologies, showing that the transition is
size-selective, and has two kinetic regimes, as revealed by a calculated phase
diagram. Finally, using observations of the interactions between dimpled and
budded domains, we build a theoretical framework with an elastic model that
maps the free energies and allowed transitions in domain morphology upon
coalescence, to serve as an interpretive tool for understanding the algebra of
domain morphology. In all three cases, the two major factors that regulate
domain morphology and morphological transitions are the domain size and
membrane tension.
