Amyotrophic Lateral Sclerosis (ALS) is a fatal neurodegenerative disease characterized by the progressive loss of motor function. Pathological mechanisms and clinical measures vary extensively from patient to patient, creating a spectrum of disease phenotypes with a poorly understood influence on individual outcomes like disease duration. The inability to ascertain patient phenotype has hindered clinical trial design and the development of more personalized and effective therapeutics. Wholistic analytical methods (‘-omics’) have provided unprecedented molecular resolution into cellular and system level disease processes and offer a foundation to better understand ALS disease variability. Building off initiatives by the New York Genome Center ALS Consortium and Target ALS groups, the goal of this work was to stratify a large patient cohort utilizing a range of bioinformatic strategies and bulk tissue gene expression (transcriptomes) from the brain and spinal cord. Central Hypothesis: Variability in the onset and progression of ALS is partially captured by molecular subgroups (subtypes) with distinct gene expression profiles and implicated pathologies. Work presented in this dissertation addresses the following: (Chapter 2): The use of unsupervised clustering and gene enrichment methods for the identification and characterization of patient subtypes in the postmortem cortex and spinal cord. Results obtained from this Chapter establish three ALS subtypes, identify uniquely dysregulated pathways, and examine intra-patient concordance between regions of the central nervous system. (Chapter 3): Patient subtypes from Chapter 2 are considered in the context of clinical outcomes, leveraging multiple survival models and gene co-expression analyses. Results from this Chapter establish a weak association between ALS subtype and clinical outcomes including disease duration and age at symptom onset. (Chapter 4): Utilizing differential expression analysis, ‘marker’ genes are defined and leveraged with supervised classification (“machine learning”) methods to develop a suite of classifiers design to stratify patients by subtype. Results from this Chapter provide postmortem marker genes for two of the three ALS subtypes and offer a foundation for clinical stratification. Significance: Knowledge gained from this research provides a foundation to stratify patients in the clinic and prior to enrollment in clinical trials, offering a path toward improved therapies.

Predicting nonlinear dynamical systems has been a long-standing challenge in science. This field is currently witnessing a revolution with the advent of machine learning methods. Concurrently, the analysis of dynamics in various nonlinear complex systems continues to be crucial. Guided by these directions, I conduct the following studies. Predicting critical transitions and transient states in nonlinear dynamics is a complex problem. I developed a solution called parameter-aware reservoir computing, which uses machine learning to track how system dynamics change with a driving parameter. I show that the transition point can be accurately predicted while trained in a sustained functioning regime before the transition. Notably, it can also predict if the system will enter a transient state, the distribution of transient lifetimes, and their average before a final collapse, which are crucial for management. I introduce a machine-learning-based digital twin for monitoring and predicting the evolution of externally driven nonlinear dynamical systems, where reservoir computing is exploited. Extensive tests on various models, encompassing optics, ecology, and climate, verify the approach’s effectiveness. The digital twins can extrapolate unknown system dynamics, continually forecast and monitor under non-stationary external driving, infer hidden variables, adapt to different driving waveforms, and extrapolate bifurcation behaviors across varying system sizes. Integrating engineered gene circuits into host cells poses a significant challenge in synthetic biology due to circuit-host interactions, such as growth feedback. I conducted systematic studies on hundreds of circuit structures exhibiting various functionalities, and identified a comprehensive categorization of growth-induced failures. I discerned three dynamical mechanisms behind these circuit failures. Moreover, my comprehensive computations reveal a scaling law between the circuit robustness and the intensity of growth feedback. A class of circuits with optimal robustness is also identified. Chimera states, a phenomenon of symmetry-breaking in oscillator networks, traditionally have transient lifetimes that grow exponentially with system size. However, my research on high-dimensional oscillators leads to the discovery of ’short-lived’ chimera states. Their lifetime increases logarithmically with system size and decreases logarithmically with random perturbations, indicating a unique fragility. To understand these states, I use a transverse stability analysis supported by simulations.

Ecology has been an actively studied topic recently, along with the rapid development of human microbiota-based technology. Scientists have made remarkable progress using bioinformatics tools to identify species and analyze composition. However, a thorough understanding of interspecies interactions of microbial ecosystems is still lacking, which has been a significant obstacle in the further development of related technologies. In this work, a genetic circuit design principle with synthetic biology approaches is developed to form two-strain microbial consortia with different inter-strain interactions. The microbial systems are well-defined and inducible. Co-culture experiment results show that our microbial consortia behave consistently with previous ecological knowledge and thus serves as excellent model systems to simulate ecosystems with similar interactions. Colony patterns also emerge when co-culturing multiple species on solid media. With the engineered microbial consortia, image-processing based methods were developed to quantify the shape of co-culture colonies and distinguish microbial consortia with different interactions. Factors that affect the population ratios were identified through induction and variations in the inoculation process. Further time-lapse experiments revealed the basic rules of colony growth, composition variation, patterning, and how spatial factors impact the co-culture colony.

The advent of CRISPR/Cas9 revolutionized the field of genetic engineering and gave rise to the development of new gene editing tools including prime editing. Prime editing is a versatile gene editing method that mediates precise insertions and deletions and can perform all 12 types of point mutations. In turn, prime editing represents great promise in the design of new gene therapies and disease models where editing was previously not possible using current gene editing techniques. Despite advancements in genome modification technologies, parallel enrichment strategies of edited cells remain lagging behind in development. To this end, this project aimed to enhance prime editing using transient reporter for editing enrichment (TREE) technology to develop a method for the rapid generation of clonal isogenic cell lines for disease modeling. TREE uses an engineered BFP variant that upon a C-to-T conversion will convert to GFP after target modification. Using flow cytometry, this BFP-to-GFP conversion assay enables the isolation of edited cell populations via a fluorescent reporter of editing. Prime induced nucleotide engineering using a transient reporter for editing enrichment (PINE-TREE), pairs prime editing with TREE technology to efficiently enrich for prime edited cells. This investigation revealed PINE-TREE as an efficient editing and enrichment method compared to a conventional reporter of transfection (RoT) enrichment strategy. Here, PINE-TREE exhibited a significant increase in editing efficiencies of single nucleotide conversions, small insertions, and small deletions in multiple human cell types. Additionally, PINE-TREE demonstrated improved clonal cell editing efficiency in human induced pluripotent stem cells (hiPSCs). Most notably, PINE-TREE efficiently generated clonal isogenic hiPSCs harboring a mutation in the APOE gene for in vitro modeling of Alzheimer’s Disease. Collectively, results gathered from this study exhibited PINE-TREE as a valuable new tool in genetic engineering to accelerate the generation of clonal isogenic cell lines for applications in developmental biology, disease modeling, and drug screening.

The mutual inhibition between synthetic gene circuits and cell growth produces growth feedback in the host-circuit system. Previous studies have demonstrated that the growth feedback has an marked impact on the molecular dynamics of the host-circuit system. However, the complexity of the growth feedback effect is not fully understood. A theoretical framework was developed to study the dynamics of the coupling between growth feedback and synthetic gene circuits. The study’s results reveal three major points about the impact of growth feedback. First, a nonlinear emergent behavior mediated by growth feedback. The unexpected behavior depends on the dynamic ribosome allocation between gene circuit expression and host cell growth. Second, the emergence and loss of unexpected qualitative states on the host-circuit system generated by ultrasensitive growth feedback. Third, the growth feedback-induced cooperativity behavior in synthetic gene modules competing for resources. In addition, growth feedback attenuated the winner-takes-all rules on resource competition between the two self-activating modules. These results demonstrate that growth feedback plays an important role in the host-circuit system’s molecular dynamics. Characterizing general principles from the effect of growth facilitates the ability to minimize or even harness unexpected gene expression behaviors derived from the effect of growth feedback.

A notable challenge when assembling synthetic gene circuits is that modularity often fails to function as intended. A crucial underlying reason for this modularity failure is the existence of competition for shared and limited gene expression resources. By designing a synthetic cascading bistable switches (Syn-CBS) circuit in a single strain with two coupled self-activation modules to achieve successive cell fate transitions, nonlinear resource competition within synthetic gene circuits is unveiled. However, in vivo it can be seen that the transition path was redirected with the activation of one switch always prevailing over that of the other, contradictory to coactivation theoretically expected. This behavior is a result of resource competition between genes and follows a ‘winner-takes-all’ rule, where the winner is determined by the relative connection strength between the two modules. Despite investigation demonstrating that resource competition between gene modules can significantly alter circuit deterministic behaviors, how resource competition contributes to gene expression noise and how this noise can be controlled is still an open issue of fundamental importance in systems biology and biological physics. By utilizing a two-gene circuit, the effects of resource competition on protein expression noise levels can be closely studied. A surprising double-edged role is discovered: the competition for these resources decreases noise while the constraint on resource availability adds its own term of noise into the system, denoted “resource competitive” noise. Noise reduction effects are then studied using orthogonal resources. Results indicate that orthogonal resources are a good strategy for eliminating the contribution of resource competition to gene expression noise. Noise propagation through a cascading circuit has been considered without resource competition. It has been noted that the noise from upstream genes can be transmitted downstream. However, resource competition’s effects on this cascading noise have yet to be studied. When studied, it is found that resource competition can induce stochastic state switching and perturb noise propagation. Orthogonal resources can remove some of the resource competitive behavior and allow for a system with less noise.

Extrachromosomal circular DNA (eccDNA) has become an increasingly popular subject of study in eukaryotic cell biology due to its prevalence in human cancer. Though the literature reports a consensus regarding DNA break repair as a driver of eccDNA formation, there remains a lack of knowledge surrounding the exact mechanisms for eccDNA formation and the selective dynamics that promote their retainment in a cell or population. A central issue to studying eccDNA is the inability to distinguish between linear and circular DNA of homologous sequence. The work presented here describes an adapted eccDNA enrichment and detection assay, specifically for investigating the effects of manipulating a known eccDNA-forming locus in the budding yeast Saccharomyces cerevisiae. First, a galactose inducible GFP reporter was integrated within the copper inducible CUP1 tandem repeat locus of yeast cells. The eccDNA enrichment and detection assay was first applied to wildtype yeast to demonstrate the presence of CUP1 eccDNA in copper induced cells by qPCR. Although subsequent sequencing analysis failed to validate this result, it indicated the presence of various other known and previously un-reported eccDNA species. Finally, application of the enrichment protocol and qPCR detection assay to CUP1-GFP reporter cells yielded inconclusive results, suggesting the assay requires further optimization to sensitively detect eccDNA from this altered locus. While more work is necessary to draw conclusions regarding the limits of eccDNA production at a manipulated eccDNA-forming locus, this knowledge will lend to the potential for therapeutically targeting eccDNA at the point of de novo formation.

Synthetic biology (SB) has become an important field of science focusing on designing and engineering new biological parts and systems, or re-designing existing biological systems for useful purposes. The dramatic growth of SB throughout the past two decades has not only provided us numerous achievements, but also brought us more timely and underexplored problems. In SB's entire history, mathematical modeling has always been an indispensable approach to predict the experimental outcomes, improve experimental design and obtain mechanism-understanding of the biological systems. \textit{Escherichia coli} (\textit{E. coli}) is one of the most important experimental platforms, its growth dynamics is the major research objective in this dissertation. Chapter 2 employs a reaction-diffusion model to predict the \textit{E. coli} colony growth on a semi-solid agar plate under multiple controls. In that chapter, a density-dependent diffusion model with non-monotonic growth to capture the colony's non-linear growth profile is introduced. Findings of the new model to experimental data are compared and contrasted with those from other proposed models. In addition, the cross-sectional profile of the colony are computed and compared with experimental data. \textit{E. coli} colony is also used to perform spatial patterns driven by designed gene circuits. In Chapter 3, a gene circuit (MINPAC) and its corresponding pattern formation results are presented. Specifically, a series of partial differential equation (PDE) models are developed to describe the pattern formation driven by the MINPAC circuit. Model simulations of the patterns based on different experimental conditions and numerical analysis of the models to obtain a deeper understanding of the mechanisms are performed and discussed. Mathematical analysis of the simplified models, including traveling wave analysis and local stability analysis, is also presented and used to explore the control strategies of the pattern formation. The interaction between the gene circuit and the host \textit{E. coli} may be crucial and even greatly affect the experimental outcomes. Chapter 4 focuses on the growth feedback between the circuit and the host cell under different nutrient conditions. Two ordinary differential equation (ODE) models are developed to describe such feedback with nutrient variation. Preliminary results on data fitting using both two models and the model dynamical analysis are included.

The Hippo-YAP/TAZ signaling pathway plays a critical role in tissue homeostasis, tumorigenesis, and degeneration disorders. The regulation of YAP/TAZ levels is controlled by a complex regulatory network, where several feedback loops have been identified. However, it remains elusive how these feedback loops contain the YAP/TAZ levels and maintain the system in a healthy physiological state or trap the system into pathological conditions. Here, a mathematical model was developed to represent the YAP/TAZ regulatory network. Through theoretical analyses, three distinct states that designate the three physiological and pathological outcomes were found. The transition from the physiological state to the two pathological states is mechanistically controlled by coupled bidirectional bistable switches, which are robust to parametric variation and stochastic fluctuations at the molecular level. This work provides a mechanistic understanding of the regulation and dysregulation of YAP/TAZ levels in tissue state transitions.