Floppy microscale spring networks are widely studied in theory and
simulations, but no well-controlled experimental system currently exists. Here,
we show that square lattices consisting of colloid-supported lipid bilayers
functionalized with DNA linkers act as microscale floppy spring networks. We
extract their normal modes by inverting the particle displacement correlation
matrix, showing the emergence of a spectrum of soft modes with low effective
stiffness in addition to stiff modes that derive from linker interactions.
Evaluation of the softest mode, a uniform shear mode, reveals that shear
stiffness decreases with lattice size. Experiments match well with Brownian
particle simulations and we develop a theoretical description based on mapping
interactions onto linear response to describe the modes. Our results reveal the
importance of entropic steric effects, and can be used for developing
reconfigurable materials at the colloidal length scale