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Just like atoms combine into molecules, colloids can self-organize intopredetermined structures according to a set of design principles. Controllingvalence -- the number of inter-particle bonds -- is a prerequisite for theassembly of complex architectures. The assembly can be directed via solid`patchy' particles with prescribed geometries to make, for example, a colloidaldiamond. We demonstrate here that the nanoscale ordering of individualmolecular linkers can combine to program the structure of microscopicassemblies. Specifically, we experimentally show that covering initiallyisotropic microdroplets with $N$ mobile DNA linkers results in spontaneous andreversible self-organization of the DNA into $Z(N)$ binding patches, selectinga predictable valence. We understand this valence thermodynamically, deriving afree energy functional for droplet-droplet adhesion that accurately predictsthe equilibrium size of and molecular organization within patches, as well asthe observed valence transitions with $N$. Thus, microscopic self-organizationcan be programmed by choosing the molecular properties and concentration ofbinders. These results are widely applicable to the assembly of any particlewith mobile linkers, such as functionalized liposomes or protein interactionsin cell-cell adhesion.

DNA self-organization controls valence in programmable colloid design