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Breast cancer is the second leading cause of death among women in the United States. Several advances have been made in early detection and treatment of breast cancer in the last few decades, in particular with the widespread adoption of screening mammography and the identification of molecular targets that have enabled the development of therapies for specific subtypes. In light of the changing landscape of available interventions, there is an urgent need to develop approaches that integrate molecular and population-level data to evaluate the efficacy of current and emerging screening and treatment technologies in order to support the development of clinical guidelines that reduce the burden of breast cancer. Population modeling is a comparative effectiveness paradigm capable of linking the complex dynamics of adopting new interventions and their net effects on breast cancer incidence and mortality. Although several population-level models of breast cancer have been constructed, there are several challenges that must be addressed in order to construct estrogen receptor (ER) and human growth epidermal factor 2 (HER2) subtype-specific models. In this dissertation, I present several methodologies developed to enable the construction of molecular-specific population models of breast cancer progression, screening and treatment. I propose to achieve this goal through the following specific aims: 1) develop a framework to model breast cancer incidence in the U.S from 1975 to 2010, explicitly accounting for the effects of screening and menopausal hormonal therapy (MHT), 2) develop an approach to estimate parameters that characterize progression and baseline survival by estrogen receptor (ER) and human epidermal growth factor 2 (HER2) status in the absence of any intervention, and 3) use these results to construct an ER and HER2-specific breast cancer population model to evaluate the effects of screening and treatment on breast cancer incidence and mortality trends. Finally, I will also discuss an implementation of our model to characterize breast and ovarian cancer among women with a BRCA1 or BRCA2 mutation, and how it was used to quantify the benefits of risk-reducing interventions, such as prophylactic surgery and screening, to support women choosing to undergo these procedures at different ages.

The advent of RNA-Seq initially suggested that a complete and precise reconstruction of transcriptomes, with low false positive splice site identification, would be feasible and straightforward. Although numerous RNA-Seq analysis algorithms have been developed and much progress has been made on this task, recent benchmarks by multiple groups demonstrate that significant conceptual and computational improvements are needed to improve accuracy. Highlighting the insufficiency of existing algorithms, Dr. Salzman recently discovered a new class of RNA, circular RNA, which was overlooked in spite of intensive searches for novel alternative splicing using a variety of computational approaches to analyze RNA-Seq data. Simple statistical models have improved quantification of the known transcriptome and enabled the identification of circular RNA formed from annotated exons. In this work, we developed computational and statistical algorithms for accurate detection of novel splicing events from RNA-Seq. We have developed an algorithm for the identification of annotated and novel splicing events which enabled the discovery of new features of circular RNA biology. We also developed a novel split-read approach to annotation-independent junction discovery which identifies a broad range of genomic events detectable in RNA-Seq and includes the reporting of additional features for candidate junctions that are essential for downstream statistical analysis.

There has been an influx of novel single cell data acquisition and analysis methods promising to deepen our understanding of the variation within organ systems in healthy and diseased states. These methods are still in their infancy. Herein, I describe two respective innovations I developed for the acquisition and analysis methods. For the former, I describe an adaption of Proximity Ligation Assay to mass cytometry to add protein-protein and protein-nucleic acid interactions to this type of single cell analysis. For the latter, I describe a computational approach to make continuous comparisons between biological conditions across high-dimensional feature space. These methods provide new avenues of research available within the high-throughput high-parameter single cell analysis paradigm.

This thesis extends the theory and applications of two standard tools of applied algebraic topology, namely zigzag persistence and the MAPPER algorithm. On the theory side, we provide new stability results that support the application of these tools to point-cloud data. On the applications side, we apply these tools toward efficient shape matching of point clouds and for a novel analysis of gene-interaction networks. The levelset zigzag is a special case of zigzag persistence and is a powerful summary of a real-valued function. The stability of the levelset zigzag is one of its most important properties, since it provides justification for its usage in a continuous setting. We extend this stability of levelset zigzags to both zigzags that are in and not in the so-called pyramid family. The latter class are the coarsened levelset zigzags that are developed in this work, primarily to ease the application of levelset zigzags to point cloud data. MAPPER is the standard algorithm to calculate Reeb graphs from point-cloud data. Reeb graphs are graph-based summaries of topological spaces equipped with functions and have extensive applications in shape matching, surface compression and reconstruction, cancer sub-population discovery etc. As such, MAPPER has been successfully used in many applications. However, a missing piece till date is that there have been no guarantees on the stability of or error bounds on MAPPER. In the current work, we propose one notion of what it means for a Reeb graph calculation algorithm to be stable. Using the language of zigzag persistence, we are able to succinctly formalize the difference between calculated and ideal Reeb graphs. A worst case bound on the Reeb graph reconstruction error is then derived under fairly general conditions. A direct application of this result toward shape matching is demonstrated. We also demonstrate how Reeb graphs summarize vital information about datasets, beyond just point clouds. We apply MAPPER to gene expression networks constructed on cancer datasets. This gives us valuable insights about the structure of these networks. We compare our approach favorably to other state of the art methodologies. We outline the various biological insights that stem from our analysis.

Cell-cell interactions are crucial for the maintenance and progression of normal and diseased tissue regions. The cells within the regions typically communicate with one another via a ligand-receptor (LR) interaction to induce downstream pleiotropic phenotypic responses. In cancer, substantial work has been done to identify disease-specific malignant and immune cell interactions, leading to the development of innovative cancer checkpoint inhibitor immunotherapies. Despite these advances, disease recurrence remains an issue. We hypothesize that global cell-cell crosstalk adapts to the new microenvironment and enables the cancer cells to develop drug resistance. Mapping disease-specific interactomes remain a challenge due to the underlying heterogeneity of microenvironments since a single cell-cell interaction can have system-wide effects. This large combinatorial problem is difficult to test efficiently \textit{in-vitro} or \textit{in-vivo}. Instead, we aim to computationally infer potential cellular crosstalk patterns for hypothesis testing using transcriptomics data. This type of data provides us with a snapshot of the transcriptional abundance of all ligands and receptors within the system. Current computational approaches for inferring cellular crosstalk involve thresholding and correlation-based approaches, but do not capture the systems-level affect cell-cell interactions have upon one another. In addition, most transcriptomics datasets are high-dimensional but low sample size, which dampens the predictive power of many statistical approaches. In this dissertation, I present my work developing computational approaches to reconstruct complex cellular crosstalk networks within high-dimensional datasets of low sample size. I developed a novel network-based algorithm, REMI (REgularized Microenvironment Interactome), that predicts conditionally-dependent cell-cell interactions using transcriptomics data. I then applied REMI to a lung adenocarcinoma (LUAD) bulk flow-sorted RNA-sequencing dataset and identified disease progression-related cellular crosstalk signatures. I found that accounting for multi-cellular crosstalk interactions reduced false positives in predicted interactions through simulation analysis. To confirm the generalizability of REMI, I applied REMI to a head and neck squamous cell carcinoma (HNSCC) single-cell RNA-seq (scRNA-seq) atlas that performed with high specificity. In the last part of my thesis, I applied REMI to a bulk targeted-sequencing dataset from COVID-19 patients and identified cellular crosstalk patterns specific to early and late-stage SARS-CoV-2 disease progression. I also measured spatial crosstalk between cells by accounting for pairwise distances between cell types and multi-cellular neighborhood patterns. I conclude that spatial crosstalk is complex and the effect of all surrounding cell types should be accounted for to increase the accuracy of predictions of spatial crosstalk. My work demonstrates that cellular crosstalk exists in a group-wise manner and that extending our analysis beyond pairwise comparisons will greatly increase the accuracy of our predictions. These approaches will increase the accuracy of crosstalk inference, which will reduce misrepresented biological conclusions and accelerates the promise of precision medicine

Cancer screening is critical in clinical practice and public health in order to improve patient prognosis and reduce cancer mortality. In this dissertation, we propose a new approach of assessing the potential of cancer screening, based on estimation of the characteristics of cancer progression. We developed a novel stochastic model of cancer progression and applied this model to lung cancer and breast cancer separately. Model parameters were estimated using data from the Surveillance, Epidemiology and End Results (SEER) cancer registry. The model reproduces SEER, validates against external clinical trials and produces estimates of tumor volume doubling times, likelihood of cure, and mortality reduction that are consistent with empirical data. When applied to lung cancer, the model suggests that under the current treatment regimes, only 6% of patients can be cured in the absence of screening. Despite the high mortality rates from lung cancer, we predict that the majority of lung cancer patients who develop lethal disease could be cured if their primary tumor were detected and treated while it is smaller than 1 cm. To attain a lung cancer mortality reduction of 20% or greater from annual screening, our model estimates that a screen detection threshold of 1.2 cm or lower is necessary, provided there were little to no delay between initial detection and treatment. When applied to breast cancer, our results indicate that likelihood of cure from breast cancer has been improved from 44% in 1975 to 67% in 1993, and a greater fraction of the improvement is attributed to adjuvant therapy than screening. In addition, we found a synergy between adjuvant therapy and screening, which suggests that patients receiving adjuvant therapies would benefit more from screening than those who were not treated by adjuvant therapy, even if there were no improvement in the screening technology. We found that this synergy enables a biannual mammographic screening program to provide benefits that are comparable to an annual program for women age 50 to 69 years. Our model achieves validity and generalizability across different disease types, different cancer characteristics, and different patient cohorts. In this dissertation, we demonstrate the usefulness of this model on estimation of cancer progression timeline and likelihood of cure and its ability to quantify the benefit of screening and treatment. Our approach can be used to provide useful insight for decision making in screening policy, facilitate the design of screening trials, and prioritize novel screening tests based on their potential benefits.

Treatment of metastatic cancer utilizes chemotherapies or newer targeted therapies. However, treatment is thwarted by drug resistance where some cancer cells can survive and lead to relapse. Recent studies suggest that cancer cells can evade cell death after treatment through non-genetic means such as distinct signaling or differentiation states. To better understand these resistance mechanisms, we must study the dynamics of the anti-cancer drug response across time. We use high-dimensional single-cell platforms like mass cytometry and novel algorithms to visualize and trace the trajectories of subpopulations with different fates upon drug exposure. We present the development of a free, open-source R package known as FLOWMAPR that can represent complex timecourse datasets as a single, interpretable 2D graph. We apply this analytical approach to two novel studies of drug resistance: treatment of multiple myeloma using bortezomib and dexamethasone and response to BRAF inhibition in melanoma. Through visualization and computational modeling, we identify specific signaling or metabolic features that distinguish drug-resistant cells in models of both cancer subtypes. Moreover, through combination treatments with inhibitors directed against these features, we demonstrate the ability to reduce the fraction of drug-resistant cells present in both cell lines and in patients. Taken together, these studies demonstrate the potential for computational analysis of high-dimensional single-cell data to reveal mechanistic insights into cancer drug resistance, paving the way for the design of new treatments or more effective combination regimens.

Cellular differentiation is a continuous and coordinated process that integrates outputs from complex cell signaling networks to make decisions about cell identity, proliferation, and death. Traditionally, cellular differentiation has been described as a series of discrete populations. More recently, emerging technologies for deep single-cell phenotyping, such as mass cytometry by time-of-flight (CyTOF), have enabled us to describe cellular differentiation as a continuous process, where individual cells are aligned onto a trajectory based on their phenotypes. In Chapter 2, I build on prior work from our and other labs to develop experimental and computational methods in order to: (1) build a single-cell map of human naïve T-cell differentiation during expansion for adoptive cell transfer therapy for cancer as a model system; (2) discern division state-dependent from time-dependent processes on this map; (3) examine regulatory signaling on this map to rationally define a strategy to steer differentiation towards a clinically desirable T stem cell memory subset. In Chapter 3, I demonstrate the clinical utility of a known cell differentiation trajectory. Specifically, by aligning single leukemic cells onto a scaffold of human B-cell development, in collaboration with Profs. Kara L. Davis and Robert Tibshirani, we identify a signaling state at a developmental transition from late pro-B to early pre-B cells that predicts relapse based on a diagnostic bone marrow biopsy. Notably, such signaling behavior pre-exists at diagnosis and persists at relapse. In Chapters 4 and 5, in collaboration with Dr. Nikolay Samusik, we perform a comparative study and develop novel software for single-cell embedding, clustering, and visualization. Chapter 6 contains concluding remarks and future direction. Further, in collaboration with Prof. Purvesh Khatri, Prof. Mark M. Davis, and other Computational and Systems Immunology PhD students, we share advice on equipping a modern immunology graduate student with the computational skills they may need on their journey towards a career as a scientist.

Cancer screening is critical in clinical practice and public health in order to improve patient prognosis and reduce cancer mortality. In this dissertation, we propose a new approach of assessing the potential of cancer screening, based on estimation of the characteristics of cancer progression. We developed a novel stochastic model of cancer progression and applied this model to lung cancer and breast cancer separately. Model parameters were estimated using data from the Surveillance, Epidemiology and End Results (SEER) cancer registry. The model reproduces SEER, validates against external clinical trials and produces estimates of tumor volume doubling times, likelihood of cure, and mortality reduction that are consistent with empirical data. When applied to lung cancer, the model suggests that under the current treatment regimes, only 6% of patients can be cured in the absence of screening. Despite the high mortality rates from lung cancer, we predict that the majority of lung cancer patients who develop lethal disease could be cured if their primary tumor were detected and treated while it is smaller than 1 cm. To attain a lung cancer mortality reduction of 20% or greater from annual screening, our model estimates that a screen detection threshold of 1.2 cm or lower is necessary, provided there were little to no delay between initial detection and treatment. When applied to breast cancer, our results indicate that likelihood of cure from breast cancer has been improved from 44% in 1975 to 67% in 1993, and a greater fraction of the improvement is attributed to adjuvant therapy than screening. In addition, we found a synergy between adjuvant therapy and screening, which suggests that patients receiving adjuvant therapies would benefit more from screening than those who were not treated by adjuvant therapy, even if there were no improvement in the screening technology. We found that this synergy enables a biannual mammographic screening program to provide benefits that are comparable to an annual program for women age 50 to 69 years. Our model achieves validity and generalizability across different disease types, different cancer characteristics, and different patient cohorts. In this dissertation, we demonstrate the usefulness of this model on estimation of cancer progression timeline and likelihood of cure and its ability to quantify the benefit of screening and treatment. Our approach can be used to provide useful insight for decision making in screening policy, facilitate the design of screening trials, and prioritize novel screening tests based on their potential benefits.