Cooperativity, entropy, and effective concentration in DNA origami self-replication.

Many new structures, machines, active materials, and devices have been produced in the rapidly growing field of DNA nanotechnology. However, the thermodynamics of complex DNA assemblies remains not well understood. Here, we treat the assembly, melting, and activation of more complex structures where interactions are generally cooperative. We abandon a rigorous theory involving a complex landscape in favor of a two-state (open-close) scenario with effective concentration and entropy effects. We test our model with self-replication of DNA origami motifs of increasing sizes and with FRET on a single DNA pair held in proximity, and it predicts melting temperatures to ~2°C where there is a 50°C shift arising from cooperativity. The model is especially useful for designing interactions between large objects programmed to open and close and is readily adaptable to assembly and activation in systems other than DNA.