Increasing valence pushes DNA nanostar networks to the isostatic point

Significance Maxwell (1864) predicted that 3D networks of beams fixed to junctions through freely rotating joints will be rigid only if at least six beams emanate from each junction. This concept is key to macroscopic design of trussed structures, but its relevance to microscopic networks, where thermal fluctuations are large, such as in biomolecular gels, is not as clear. Here, we exploit DNA nanotechnology to create gels of defined connectivity and demonstrate that gel mechanics are controlled by an interplay between entropic effects, network structure, and Maxwell’s rigidity criterion.