Predicting the Free-Form Shape of Structured DNA Assemblies from Their Lattice-Based Design Blueprint.

Structured DNA assemblies have been designed primarily on a three-dimensional lattice because it is easy to arrange and cross-link the helices there. However, when we design free-form structures including wireframes and topologically closed circular objects on a lattice, artificially stretched bonds connecting bases are inevitably and arbitrarily formed. They often lead to nonconvergence or convergence to a wrong configuration in computational analysis to predict the equilibrium shape of the structure when started from its lattice-based configuration, which hinders the design process of free-form structures. Here, we present a computational procedure enabling the shape prediction of free-form structures from their lattice-based design blueprint without any convergence issue. It automatically partitions the structure into substructures and relocates them into a new configuration. When the analysis for calculating the equilibrium shape begins from this configuration, no convergence issue occurs because substructures and stretched bonds connecting them do not overlap and intertwine each other during analysis. Using the proposed approach, we could obtain the free-form shape of a comprehensive set of wireframe and circular structures accurately and quickly. We further demonstrated that it also facilitated a design of wireframe structures with nonstraight edges.