From toroids to helical tubules: Kirigami design of programmable tilings for 2-periodic, self-closing assemblies

Biology is full of intricate molecular structures whose geometries are inextricably linked to their function. Many of these structures are self-closing and exhibit varying curvature, such as the toroidal donut-like structure of the torovirus and the helical structure of spirochetes and bacterial flagella. Synthetic analogs of these structures could provide new ways to target viruses, deliver drugs, and develop synthetic molecular machines. However, the design and self-assembly of structures with varying curvature poses a challenge because they require multiple inequivalent particle types with different interactions and geometric specificity. Here, we develop a kirigami-based strategy for designing programmable tilings, which we use to determine the interaction and geometric specificity necessary to guide the self-assembly of 2-periodic, self-closing structures. We illustrate this strategy by designing a class of toroids and helical tubules and demonstrate that we can guide the self-assembly of a toroid using DNA origami subunits with 12 unique species. This work illustrates one route to using kirigami for designing curved, self-closing assemblies, which invites new designs that leverage kirigami for self-assembly, such as for helicoids and porous 2D surfaces.