Networks, (K)nots, Nucleotides, and Nanostructures

Designing self-assembling DNA nanostructures often requires the identification of a route for a scaffolding strand of DNA through the target structure. When the target structure is modeled as a graph, these scaffolding routes correspond to Eulerian circuits subject to turning restrictions imposed by physical constraints on the strands of DNA. Existence of such Eulerian circuits is an NP-hard problem, which can be approached by adapting solutions to a version of the Traveling Salesperson Problem. However, the author and collaborators have demonstrated that even Eulerian circuits obeying these turning restrictions are not necessarily feasible as scaffolding routes by giving examples of nontrivially knotted circuits which cannot be traced by the unknotted scaffolding strand. Often, targets of DNA nanostructure self-assembly are modeled as graphs embedded on surfaces in space. In this case, Eulerian circuits obeying the turning restrictions correspond to A-trails, circuits which turn immediately left or right at each vertex. In any graph embedded on the sphere, all A-trails are unknotted regardless of the embedding of the sphere in space. We show that this does not hold in general for graphs on the torus. However, we show this property does hold for checkerboard-colorable graphs on the torus, that is, those graphs whose faces can be properly 2-colored, and provide a partial converse to this result. As a consequence, we characterize (with one exceptional family) regular triangulations of the torus containing unknotted A-trails. By developing a theory of sums of A-trails, we lift constructions from the torus to arbitrary n-tori, and by generalizing our work on A-trails to smooth circuit decompositions, we construct all torus links and certain sums of torus links from circuit decompositions of rectangular torus grids. Graphs embedded on surfaces are equivalent to ribbon graphs, which are particularly well-suited to modeling DNA nanostructures, as their boundary components correspond to strands of DNA and their twisted ribbons correspond to double-helices. Every ribbon graph has a corresponding delta-matroid, a combinatorial object encoding the structure of the ribbon-graph\u27s spanning quasi-trees (substructures having exactly one boundary component). We show that interlacement with respect to quasi-trees can be generalized to delta-matroids, and use the resulting structure on delta-matroids to provide feasible-set expansions for a family of delta-matroid polynomials, both recovering well-known expansions of this type (such as the spanning-tree expansion of the Tutte polynnomial) as well as providing several previously unknown expansions. Among these are expansions for the transition polynomial, a version of which has been used to study DNA nanostructure self-assembly, and the interlace polynomial, which solves a problem in DNA recombination

Inference of single-cell phylogenies from lineage tracing data using Cassiopeia.

The pairing of CRISPR/Cas9-based gene editing with massively parallel single-cell readouts now enables large-scale lineage tracing. However, the rapid growth in complexity of data from these assays has outpaced our ability to accurately infer phylogenetic relationships. First, we introduce Cassiopeia-a suite of scalable maximum parsimony approaches for tree reconstruction. Second, we provide a simulation framework for evaluating algorithms and exploring lineage tracer design principles. Finally, we generate the most complex experimental lineage tracing dataset to date, 34,557 human cells continuously traced over 15 generations, and use it for benchmarking phylogenetic inference approaches. We show that Cassiopeia outperforms traditional methods by several metrics and under a wide variety of parameter regimes, and provide insight into the principles for the design of improved Cas9-enabled recorders. Together, these should broadly enable large-scale mammalian lineage tracing efforts. Cassiopeia and its benchmarking resources are publicly available at www.github.com/YosefLab/Cassiopeia

Analysis, Design, and Construction of Nucleic Acid Devices

Nucleic acids present great promise as building blocks for nanoscale devices. To achieve this potential, methods for the analysis and design of DNA and RNA need to be improved. In this thesis, traditional algorithms for analyzing nucleic acids at equilibrium are extended to handle a class of pseudoknots, with examples provided relevant to biologists and bioengineers. With these analytical tools in hand, nucleic acid sequences are designed to maximize the equilibrium probability of a desired fold. Upon analysis, it is concluded that both affinity and specificity are important when choosing a sequence; this conclusion holds for a wide range of target structures and is robust to random perturbations to the energy model. Applying the intuition gained from these studies, a process called hybridization chain reaction (HCR) is invented, and sequences are chosen that experimentally verify this phenomenon. In HCR, a small number of DNA or RNA molecules trigger a system wide configurational change, allowing the amplification and detection of specific, nucleic acid sequences. As an extension, HCR is combined with a pre-existing aptamer domain to successfully construct an ATP sensor, and the groundwork is laid for the future development of sensors for other small molecules. In addition, recent studies on multi-stranded algorithms and improvements to HCR are included in the appendices. Not only will these advancements increase our understanding of biological RNAs, but they will also provide valuable tools for the future development of nucleic acid nanotechnologies

Promised streaming algorithms and finding pseudo-repetitions

As the size of data available for processing increases, new models of computation are needed. This motivates the study of data streams, which are sequences of information for which each element can be read only after the previous one. In this work we study two particular types of streaming variants: promised graph streaming algorithms and combinatorial queries on large words. We give an &omega(n) lower bound for working memory, where n is the number of vertices of the graph, for a variety of problems for which the graphs are promised to be forests. The crux of the proofs is based on reductions from the field of communication complexity. Finally, we give an upper bound for two problems related to finding pseudo-repetitions on words via anti-/morphisms, for which we also propose streaming versions

Extensive Genetic Diversity, Unique Population Structure and Evidence of Genetic Exchange in the Sexually Transmitted Parasite Trichomonas vaginalis

The human parasite Trichomonas vaginalis causes trichomoniasis, the world's most common non-viral sexually transmitted infection. Research on T. vaginalis genetic diversity has been limited by a lack of appropriate genotyping tools. To address this problem, we recently published a panel of T. vaginalis-specific genetic markers; here we use these markers to genotype isolates collected from ten regions around the globe. We detect high levels of genetic diversity, infer a two-type population structure, identify clinically relevant differences between the two types, and uncover evidence of genetic exchange in what was believed to be a clonal organism. Together, these results greatly improve our understanding of the population genetics of T. vaginalis and provide insights into the possibility of genetic exchange in the parasite, with implications for the epidemiology and control of the disease. By taking into account the existence of different types and their unique characteristics, we can improve understanding of the wide range of symptoms that patients manifest and better implement appropriate drug treatment. In addition, by recognizing the possibility of genetic exchange, we are more equipped to address the growing concern of drug resistance and the mechanisms by which it may spread within parasite populations

Spatial Cluster Analysis by the Adleman-Lipton DNA Computing Model and Flexible Grids

Spatial cluster analysis is an important data-mining task. Typical techniques include CLARANS, density- and gravity-based clustering, and other algorithms based on traditional von Neumann’s computing architecture. The purpose of this paper is to propose a technique for spatial cluster analysis based on DNA computing and a grid technique. We will adopt the Adleman-Lipton model and then design a flexible grid algorithm. Examples are given to show the effect of the algorithm. The new clustering technique provides an alternative for traditional cluster analysis

Global genomic diversity of a major wildlife pathogen: Ranavirus, past and present

Ranavirus is a genus of large double-stranded DNA viruses (family Iridoviridae) that parasitise three taxonomic classes of poikilothermic vertebrates. They are important wildlife pathogens of conservation and economic concern, posing significant threat to amphibian biodiversity and aquaculture commerce. Despite substantial advances since their discovery in the 1960s, the evolutionary history of ranaviruses remains poorly characterised. The aim of this thesis is to advance the characterisation of Ranavirus evolutionary dynamics to contemporary standards. A large whole-genome dataset was collated and scrutinised, combining all publicly available material with a novel collection of isolate genomes. Cutting-edge microbial genomics tools were applied to gain insight into ranavirus genetic diversity, phylogeography, and genome evolution. Delineation of the Ranavirus pan-genome served as a foundation to conduct phylogenetic and population genetic analyses. Where the limitations of alignment-based methodologies were met, alignment-free techniques were employed to make full use of all genomic information. Phylogenetic reconstructions uncovered unique genetic diversity incompatible with current taxonomic demarcations amongst several lineages of Ranavirus. Pervasive genetic recombination was detected across the genus, and certain lineages contained a high degree of ancestral polyphyly. Recurrent patterns linked to animal trade and aquaculture were detected. Extensively polyphyletic viruses were isolated from captive animals, and population genetic analysis revealed ancestry components shared by ranaviruses isolated from farmed animals on separate continents. Finally, phylodynamic analysis suggests human-mediated translocation of FV3-like ranaviruses began more than a century before present. The inadequacies of current Ranavirus taxonomy are highlighted by this work, and suggests a substantial diversity remains to be characterised. The processes by which ranaviral genetic diversity is generated appears particularly dynamic, with significant contributions made via recombination between distinct linages. Altogether, this thesis underscores the vital impact trade and captive rearing of fish and herpetofauna have had on the global spread of ranaviruses and their processes of genetic diversification. Finally, these results suggest that anthropogenic influences commenced decades earlier than previously thought, likely upon the acceleration of modern globalisation

Modeling HIV Drug Resistance

Despite the development of antiviral drugs and the optimization of therapies, the emergence of drug resistance remains one of the most challenging issues for successful treatments of HIV-infected patients. The availability of massive HIV drug resistance data provides us not only exciting opportunities for HIV research, but also the curse of high dimensionality. We provide several statistical learning methods in this thesis to analyze sequence data from different perspectives. We propose a hierarchical random graph approach to identify possible covariation among residue-specific mutations. Viral progression pathways were inferred using an EM-like algorithm in literature, and we present a normalization method to improve the accuracy of parameter estimations. To predict the drug resistance from genotypic data, we also build a novel regression model utilizing the information from progression pathways. Finally, we introduce a computational approach to determine viral fitness, for which our initial computational results closely agree with experimental results. Work on two other topics are presented in the Appendices. Latent class models find applications in several areas including social and biological sciences. Finding explicit maximum likelihood estimation has been elusive. We present a positive solution to a conjecture on a special latent class model proposed by Bernd Sturmfels from UC Berkeley. Monomial ideals provide ubiquitous links between combinatorics and commutative algebra. Irreducible decomposition of monomial ideals is a basic computational problem and it finds applications in several areas. We present two algorithms for finding irreducible decomposition of monomial ideals