  The mammalian cell membrane is embedded with biomolecular condensates of
protein and lipid clusters, which interact with an underlying viscoelastic
cytoskeleton network to organize the cell surface and mechanically interact
with the extracellular environment. However, the mechanical and thermodynamic
interplay between the viscoelastic network and liquid-liquid phase separation
of 2-dimensional (2D) lipid condensates remains poorly understood. Here, we
engineer materials composed of 2D lipid membrane condensates embedded within a
thin viscoelastic actin network. The network generates localized anisotropic
stresses that deform lipid condensates into triangular morphologies with sharp
edges and corners, shapes unseen in 3D composite gels. Kinetic coarsening of
phase-separating lipid condensates accelerates the viscoelastic relaxation of
the network, leading to an effectively softer composite material over
intermediate timescales. We dynamically manipulate the membrane composition to
control the elastic-to-viscous crossover of the network. Such viscoelastic
composite membranes may enable the development of coatings, catalytic surfaces,
separation membranes, and other interfaces with tunable spatial organization
and plasticity mechanisms.
