Graduation Year

2015

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mathematics & Statistics

Major Professor

Natasha Jonoska, Ph.D.

Co-Major Professor

Matthew Patitz, Ph.D.

Committee Member

Matthew Patitz, Ph.D.

Committee Member

Brian Curtin, Ph.D.

Committee Member

Gregory McColm, Ph.D.

Committee Member

Masahico Saito, Ph.D.

Committee Member

Dmytro Savchuk, Ph.D.

Keywords

Active aTAM, Cellular automata, DNA self-assembly, DNA tiling, Simulation, Temperature 1 assembly

Abstract

Algorithmic self-assembly has been an active area of research at the intersection of computer science, chemistry, and mathematics for almost two decades now, motivated by the natural self-assembly mechanism found in DNA and driven by the desire for precise control of nanoscale material manufacture and for the development of nanocomputing and nanorobotics. At the theoretical core of this research is the Abstract Tile Assembly Model (aTAM), the original abstract model of DNA tile self-assembly. Recent advancements in DNA nanotechnology have been made in developing strand displacement mechanisms that could allow DNA tiles to modify themselves during the assembly process by opening or closing certain binding sites, introducing new dynamics into tile self-assembly.

We focus on one way of incorporating such signaling mechanisms for binding site activation and deactivation into the theoretical model of tile self-assembly by extending the aTAM to create the Active aTAM. We give appropriate definitions first for incorporating activation signals and then for incorporating deactivation signals and tile detachment into the aTAM. We then give a comparison of Active aTAM to related models, such as the STAM, and take a look at some theoretical results.

The goal of the work presented here is to define and demonstrate the power of the Active aTAM with and without deactivation. To this end, we provide four constructions of temperature 1 (also known as "non-cooperative") active tile assembly systems that can simulate other computational systems. The first construction concerns the simulation of an arbitrary temperature 2 (also known as "cooperative") standard aTAM system in the sense of producing equivalent structures with a scaling factor of 2 in each dimension; the second construction generates the time history of a given 1D cellular automaton. The third and fourth constructions make use of tile detachment in order to dynamically simulate arbitrary 1D and 2D cellular automata with assemblies that record only the current state updates and not the entire computational history of the specified automaton.

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