ABSTRACT:
DNA origami is one of the most popular techniques for designing self-assembled DNA nanostructures. This approach involves the folding of a long “scaffold” strand of DNA by a set of much shorter “staple” strands, which pin parts of the scaffold in close proximity. With this technique, a huge variety of structures that are predictable and functionalizable on the nanoscale level have been assembled. Nonetheless, important open questions relating to the folding process, such as general principles for optimizing yield and assembly rate, remain open.
We present a modelling framework and basic parametrization for studying the folding of DNA origami. The model is based on treating the partially-folded origami as a graph, with each new staple adding additional arcs to said graph. Each staple arc represents a geometrical constraint, as the staple constrains non-adjacent domains of the origami in close proximity. The thermodynamic cost of this constraint is estimated from the length of the loop that is closed by the staple arc. We show that de?signing a rigorous thermodynamic model is challenging due to combinatorial issues associated with assigning loops to each staple arc, and present a solution to this problem for planar origami. We also present a simpler approach that can be used for non-planar origami. We demonstrate that this simpler methodology is generally consistent with the more rigorous model, opening up the potential for studying a wider range of systems. We compare the performance of the model to experimental results for the folding of simple origami, and use it to predict yields of various structures in a system in which more than one outcome is possible.