||<p>The control of matter and phenomena at the nanoscale is fast becoming one of the
most important challenges of the 21st century with wide-ranging applications from
energy and health care to computing and material science. Conventional top-down approaches
to nanotechnology, having served us well for long, are reaching their inherent limitations.
Meanwhile, bottom-up methods such as self-assembly are emerging as viable alternatives
for nanoscale fabrication and manipulation.</p><p>A particularly successful bottom
up technique is DNA self-assembly where a set of carefully designed DNA strands form
a nanoscale object as a consequence of specific, local interactions among the different
components, without external direction. The final product of the self-assembly process
might be a static nanostructure or a dynamic nanodevice that performs a specific function.
Over the past two decades, DNA self-assembly has produced stunning nanoscale objects
such as 2D and 3D lattices, polyhedra and addressable arbitrary shaped substrates,
and a myriad of nanoscale devices such as molecular tweezers, computational circuits,
biosensors and molecular assembly lines. In this dissertation we study multiple problems
in the theory, simulations and experiments of DNA self-assembly. </p><p>We extend
the Turing-universal mathematical framework of self-assembly known as the Tile Assembly
Model by incorporating randomization during the assembly process. This allows us to
reduce the tile complexity of linear assemblies. We develop multiple techniques to
build linear assemblies of expected length N using far fewer tile types than previously
possible.</p><p>We abstract the fundamental properties of DNA and develop a biochemical
system, which we call meta-DNA, based entirely on strands of DNA as the only component
molecule. We further develop various enzyme-free protocols to manipulate meta-DNA
systems and provide strand level details along with abstract notations for these mechanisms.
</p><p>We simulate DNA circuits by providing detailed designs for local molecular
computations that involve spatially contiguous molecules arranged on addressable substrates
via enzyme-free DNA hybridization reaction cascades. We use the Visual DSD simulation
software in conjunction with localized reaction rates obtained from biophysical modeling
to create chemical reaction networks of localized hybridization circuits that are
then model checked using the PRISM model checking software.</p><p>We develop a DNA
detection system employing the triggered self-assembly of a novel DNA dendritic nanostructure.
Detection begins when a specific, single-stranded target DNA strand triggers a hybridization
chain reaction between two distinct DNA hairpins. Each hairpin opens and hybridizes
up to two copies of the other, and hence each layer of the growing dendritic nanostructure
can in principle accommodate an exponentially increasing number of cognate molecules,
generating a nanostructure with high molecular weight. </p><p>We build linear activatable
assemblies employing a novel protection/deprotection strategy to strictly enforce
the direction of tiling assembly growth to ensure the robustness of the assembly process.
Our system consists of two tiles that can form a linear co-polymer. These tiles, which
are initially protected such that they do not react with each other, can be activated
to form linear co-polymers via the use of a strand displacing enzyme.</p>