  We study phase behaviours of lipid--bilayer vesicles functionalised by
ligand--receptor complexes made of synthetic DNA by introducing a modelling
framework and a dedicated experimental platform. In particular, we perform
Monte Carlo simulations that combine a coarse grained description of the lipid
bilayer with state of art analytical models for multivalent ligand--receptor
interactions. Using density of state calculations, we derive the partition
function in pairs of vesicles and compute the number of ligand--receptor bonds
as a function of temperature. Numerical results are compared to microscopy and
fluorimetry experiments on Large Unilamellar Vesicles decorated by DNA linkers
carrying complementary overhangs. We find that vesicle aggregation is
suppressed when the total number of linkers falls below a threshold value.
Within the model proposed here, this is due to the higher configurational costs
required to form inter--vesicle bridges as compared to intra-vesicle loops,
which are in turn related to membrane deformability. Our findings and our
numerical/experimental methodologies are applicable to the rational design of
liposomes used as functional materials and drug delivery applications, as well
as to study inter-membrane interactions in living systems, such as cell
adhesion.
