  Multivalent interactions between deformable mesoscopic units are ubiquitous
in biology, where membrane macromolecules mediate the interactions between
neighbouring living cells and between cells and solid substrates. Lately,
analogous artificial materials have been synthesised by functionalising the
outer surface of compliant Brownian units, for example emulsion droplets and
lipid vesicles, with selective linkers, in particular short DNA sequences. This
development extended the range of applicability of DNA as a selective glue,
originally applied to solid nano and colloidal particles. On very deformable
lipid vesicles, the coupling between statistical effects of multivalent
interactions and mechanical deformation of the membranes gives rise to complex
emergent behaviours, as we recently contributed to demonstrate [Parolini et
al., Nature Communications, 2015, 6, 5948]. Several aspects of the complex
phenomenology observed in these systems still lack a quantitative experimental
characterisation and fundamental understanding. Here we focus on the
DNA-mediated multivalent interactions of a single liposome adhering to a flat
supported bilayer. This simplified geometry enables the estimate of the
membrane tension induced by the DNA-mediated adhesive forces acting on the
liposome. Our experimental investigation is completed by morphological
measurements and the characterisation of the DNA-melting transition, probed by
in-situ F\"{o}rster Resonant Energy Transfer spectroscopy. Experimental results
are compared with the predictions of an analytical theory that couples the
deformation of the vesicle to a full description of the statistical mechanics
of mobile linkers. With at most one fitting parameter, our theory is capable of
semi-quantitatively matching experimental data, confirming the quality of the
underlying assumptions.
