Construction of geometric structure by oritatami system

Self-assembly is the process where smaller components autonomously assemble to form a larger and more complex structure. One of the application areas of self-assembly is engineering and production of complicated nanostructures. Recently, researchers proposed a new folding model called the oritatami model (OM) that simulates the cotranscriptional self-assembly, based on the kinetics on the final shape of folded molecules. Nanostructures in oritatami system (OS) are represented by a sequence of beads and interactions on the lattice. We propose a method to design a general OS, which we call GEOS, that constructs a given geometric structure. The main idea is to design small modular OSs, which we call hinges, for every possible pair of adjacent points in the target structure. Once a shape filling curve for the target structure is ready, we construct an appropriate primary structure that follows the curve by a sequence of hinges. We establish generalized guidelines on designing a GEOS, and propose two GEOSs.