Molecules computing: self-assembled nanostructures, molecular automata, and chemical reaction networks

Abstract

Many endeavors of molecular-level engineering either rely on biological material such as nucleic acids and restriction enzymes, or are inspired by biological processes such as self-assembly or cellular regulatory networks. This thesis develops theories on three such topics: self-assembled nanostructures, molecular automata, and chemical reaction networks. The abstractions and underlying methods of the theories presented herein are based on computer science and include Turing machines and circuits. Toward engineering self-assembled nanostructures, we create a theory of scale-free shapes in which the complexity of their self-assembly is connected to the shapes' descriptional complexity. Further, we study patterns in terms of whether they can be self-assembled robustly without an increase in scale to accommodate redundancy. We also describe a new method of ensuring resilience to more types of error simultaneously. Toward creating molecular automata we study the computational power of a restriction enzyme-based automaton. Toward designing chemical reaction networks, we develop a technique of storing and processing information in molecular counts, which is capable of achieving Turing universal computation. We also study the computational complexity of simulating stochastic chemical reaction networks and formally connect robustness and simulation efficiency. Lastly, we describe nucleic acid implementations of Boolean logic circuits and arbitrary mass-action kinetics. The three areas of this thesis are promising realizations of molecular-level engineering, and the theories presented here inform the range of possibility or delineate inherent difficulties in these areas.