AF: Small: Using Notions of Simulation to Explore the Power of Self-Assembling Systems

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A wide variety of self-assembling systems exist in nature. These are systems in which complex structures are formed from individual molecules that combine with each other autonomously, obeying only local rules of behavior and without any external guidance or placement. This process is responsible for the formation of a huge diversity of inorganic structures (such as crystals like snowflakes), as well as numerous biological structures (including cellular membranes and viruses). Hoping to harness the power of self-assembly to create advanced materials, complex nanoscale structures, and perform molecular computing, researchers have begun developing artificial self-assembling systems. This work has consisted of laboratory implementations as well as mathematical and computational modeling.Theoretical computer science has provided numerous insights into the creation and understanding of theoretical models of self-assembly, and these models have provided valuable understanding which has productively guided laboratory experiments. In this project, the body of work in defining, developing, and comparing the relative powers of theoretical models of self-assembling systems will be extended by the PI. In particular, the relative powers of various models will be studied by comparing their abilities to simulate each other. Additionally, the abilities of systems within existing and new models to mimic biological processes such as evolution and immune system behavior will be investigated.This project is divided into two main components. The first consists of a series of studies of the abilities of various theoretical models to simulate each other when certain parameters are fixed, especially the so-called "temperature" parameter fixed at 1, making cooperative behaviors difficult or impossible. Whether or not certain models, again with fixed parameters, are intrinsically universal will also be explored. Additionally, while most current theoretical work comparing the relative powers of models is concerned with a strong notion of simulation which includes both the productions and dynamics of the simulating systems, relaxed notions which focus solely on the structures produced (i.e. the productions) of simulating systems will be investigated. While the previous method has produced great theoretical understanding, this new approach is geared toward a more practical understanding which can guide experimentalists desiring to build predefined structures.The second main component of this project involves work related to studying the abilities of various self-assembling systems to simulate complex and important biological activities such as protein folding, the formation of prion-like structures, self-replication, evolution, and immune system behaviors. For much of this, an existing model utilizing dynamically changing basic components, the Signal Tile Assembly Model, will be employed. Further, a new model based on square 2D components which can fold along their boundaries, allowing for the formation of 3D structures by "foldable" 2D building blocks, will be developed and studied, with special focus on their abilities to abstractly mimic protein-like behaviors.The work will consist of mathematical modeling as well as computational modeling in the form of simulation software. Results and software, will be made freely available with already existing software and content on www.self-assembly.net.