Dynamic transistion to isostaticity induces complex stress response in DNA nanostar networks

Transiently cross-linked biopolymer networks (e.g. actin-actinin networks) exhibit a complex stress response markedly different from that of a simple Maxwell material. They both flow and support stress over several decades of low to intermediate frequencies. Here, we perform oscillatory rheology on networks made of 6-armed DNA nanostars (NS) whose designable interactions allow us to investigate the role of cross-linker lifetime on the complex stress response. When three of the arms have short-lived bonds (α-bonds) and the other three have longer-lived bonds (β-bonds) (e.g., α₃β₃ NS), the network exhibits a complex stress response persisting over a broad range of frequencies determined by the respective short-lifetime and long-lifetime bonds. We hypothesize the existence of a dynamic transition from a sub-isostatic network at low frequencies to an isostatic one at high frequencies to explain the complex stress response.