AF: Small: RUI: Unifying Self-Assembly Through Tile Automata

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Self-assembly is the bottom-up process by which simple unorganized components autonomously combine to form large complex structures. This process is abundant in nature as a key underlying mechanism for the construction of biological organisms. The local interactions of simple self-assembling systems are often capable of simulating general purpose computation as well, leading researchers to begin using self-assembly technology as a tool for the precise algorithmic manipulation of matter at nano-scales. This project introduces and explores the Tile Automata abstract model of self-assembly to serve as a framework for unifying the diverse set of established and experimentally motivated models of self-assembly. The work develops fundamental theoretical results within this framework, and connects various established experimental models using Tile Automata as a central hub - yielding surprising connections between previously disparate models. Beyond providing a foundation for a theory of self-assembly, this framework also provides an important tool to influence and simplify experimental work. Some aspects of the DNA-based model are implausible, but by using the connections with Tile Automata, the work will show that the power of the unrealistic features may be attained within a more plausible limited version of the model, thus providing a guide for experimental implementation. A major goal of this work is to provide undergraduate research opportunities and increase Computer Science research participation among underrepresented groups. Another outcome of this work will be the continued development of software simulators for various models as well as the implementation of new models. The project introduces a mathematical model termed Tile Automata that combines the local interaction rules from Cellular Automata systems with self-assembly properties from tile-based self-assembly models. Although the majority of self-assembly models are motivated by experimental techniques, the abstractions may unintentionally limit or unrealistically extend the power of the system. Part of the research is to identify and remove these properties. The first focus of this work is on the DNA based signal tile model where unrealistic aspects of when signals fire may be exploited to achieve results within the model that are impossible experimentally. The investigators address these issues by proposing multiple small variations to signal passing, which each remove the issue with the original model. Each variation is then tied to the unifying framework and equality is achieved within a scale factor for each variation and for the original signal tile model, thereby providing an experimentally feasible path for achieving the full power of the model. The second focus is on repulsive forces within self-assembly models, which provide an enormous amount of power and allow for unrealistic communication across arbitrary distance within the model. The project seeks to show that repulsive forces may be simulated within the Tile Automata framework if assemblies are allowed to temporarily connect to check compatibility and then disconnect if not, which shows equivalent capabilities can be achieved without the improbable communication. The third focus is on other common self-assembly models and active or movement-based models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.