Self-Assembly of 3-d Structures Using 2-d Folding Tiles.

International audienceSelf-assembly is a process which is ubiquitous in natural, es-pecially biological systems. It occurs when groups of relatively simplecomponents spontaneously combine to form more complex structures.While such systems have inspired a large amount of research into design-ing theoretical models of self-assembling systems, and even laboratory-based implementations of them, these artificial models and systems oftentend to be lacking in one of the powerful features of natural systems (e.g.the assembly and folding of proteins), which is dynamic reconfigurabil-ity of structures. In this paper, we present a new mathematical modelof self-assembly, based on the abstract Tile Assembly Model (aTAM),called the Flexible Tile Assembly Model (FTAM). In the FTAM, the in-dividual components are 2-dimensional tiles as in the aTAM, but in theFTAM, bonds between the edges of tiles can be flexible, allowing bondsto flex and entire structures to reconfigure, thus allowing 2-dimensionalcomponents to form 3-dimensional structures. We analyze the powersand limitations of FTAM systems by (1) demonstrating how flexibilitycan be controlled to carefully build desired structures, and (2) showinghow flexibility can be beneficially harnessed to form structures whichcan “efficiently” reconfigure into many different configurations and/orgreatly varying configurations. We also show that with such power comesa heavy burden in terms of computational complexity of simulation andprediction by proving that for important properties of FTAM systems,determining their existence is intractable, even for properties which areeasily computed for systems in less dynamic models