As a rapidly evolving field, nucleic acid nanotechnology focuses on creating functional nanostructures or dynamic devices through harnessing the programmbility of nucleic acids including deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), enabled by the predictable Watson-Crick base pairing. The precise control over the sequence and structure, along with the development of simulation softwares for the prediction of the experimental implementation provides the base of designing structures or devices with arbitrary topology and operational logic at nanoscale. Over the past 40 years, the thriving field has pushed the boundaries of nucleic acids, from originally biological macromolecules to functional building blocks with applications in biomedicine, molecular diagnostics and imaging, material science, electronics, crystallography, and more have emerged through programming the sequences and generating the various structures or devices. The underlying logic of nucleic acid programming is the base pairing rule, straightforward and robust. While for the complicated design of sequences and quantitative understanding of the programmed results, computational tools will markedly reduced the level of difficulty and even meet the challenge not available with manual effort. With this thesis three individual projects are presented, with all of them interweaving theory/computation and experiments. In a higher level abstraction, this dissertation covers the topic of biophysical understanding of the dynamic reactions, designing and realizing complex self-assembly systems and finally super-resolutional imaging. More specifically, Chapter 2 describes the study of RNA strand displacement kinetics with dedicated model extracting the reaction rates, providing guidelines for the rational design and regulation of the strand displacement reactions and eventually biochemical processes. In chapter 3 the platform for the design of complex symmetry of the self-assembly target and first experimental implementation of the assembly of pyrochlore lattices with DNA origamis are presented, which potentially can be applied to manipulate lights as optical materials. Chapter 4 focuses on the in solution characterization of the periodicity of DNA origami lattices with super-resolutional microscopy, with algorithms in development for three dimensional structural reconstruction.

Carbohydrates are one of the four main building blocks of life, and are categorized as monosaccharides (sugars), oligosaccharides and polysaccharides. Each sugar can exist in two alternative anomers (in which a hydroxy group at C-1 takes different orientations) and each pair of sugars can form different epimers (isomers around the stereocentres connecting the sugars). This leads to a vast combinatorial complexity, intractable to mass spectrometry and requiring large amounts of sample for NMR characterization. Combining measurements of collision cross section with mass spectrometry (IM–MS) helps, but many isomers are still difficult to separate. Here, we show that recognition tunnelling (RT) can classify many anomers and epimers via the current fluctuations they produce when captured in a tunnel junction functionalized with recognition molecules. Most importantly, RT is a nanoscale technique utilizing sub-picomole quantities of analyte. If integrated into a nanopore, RT would provide a unique approach to sequencing linear polysaccharides.

Rabies disease remains enzootic among raccoons, skunks, foxes and bats in the United States. It is of primary concern for public-health agencies to control spatial spread of rabies in wildlife and its potential spillover infection of domestic animals and humans. Rabies is invariably fatal in wildlife if untreated, with a non-negligible incubation period. Understanding how this latency affects spatial spread of rabies in wildlife is the concern of chapter 2 and 3. Chapter 1 deals with the background of mathematical models for rabies and lists main objectives. In chapter 2, a reaction-diffusion susceptible-exposed-infected (SEI) model and a delayed diffusive susceptible-infected (SI) model are constructed to describe the same epidemic process -- rabies spread in foxes. For the delayed diffusive model a non-local infection term with delay is resulted from modeling the dispersal during incubation stage. Comparison is made regarding minimum traveling wave speeds of the two models, which are verified using numerical experiments. In chapter 3, starting with two Kermack and McKendrick's models where infectivity, death rate and diffusion rate of infected individuals can depend on the age of infection, the asymptotic speed of spread $c^\ast$ for the cumulated force of infection can be analyzed. For the special case of fixed incubation period, the asymptotic speed of spread is governed by the same integral equation for both models. Although explicit solutions for $c^\ast$ are difficult to obtain, assuming that diffusion coefficient of incubating animals is small, $c^\ast$ can be estimated in terms of model parameter values. Chapter 4 considers the implementation of realistic landscape in simulation of rabies spread in skunks and bats in northeast Texas. The Finite Element Method (FEM) is adopted because the irregular shapes of realistic landscape naturally lead to unstructured grids in the spatial domain. This implementation leads to a more accurate description of skunk rabies cases distributions.

Single molecule DNA Sequencing technology has been a hot research topic in the recent decades because it holds the promise to sequence a human genome in a fast and affordable way, which will eventually make personalized medicine possible. Single molecule differentiation and DNA translocation control are the two main challenges in all single molecule DNA sequencing methods. In this thesis, I will first introduce DNA sequencing technology development and its application, and then explain the performance and limitation of prior art in detail. Following that, I will show a single molecule DNA base differentiation result obtained in recognition tunneling experiments. Furthermore, I will explain the assembly of a nanofluidic platform for single strand DNA translocation, which holds the promised to be integrated into a single molecule DNA sequencing instrument for DNA translocation control. Taken together, my dissertation research demonstrated the potential of using recognition tunneling techniques to serve as a general readout system for single molecule DNA sequencing application.