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Metastatic breast cancer (MBC) is the leading cause of breast cancer (BC) related morbidity and mortality. Treatment resistance and tumor evolution and heterogeneity are major challenges of managing MBC. This thesis set out to investigate MBC evolution and heterogeneity through the lens of multi-omics to uncover drivers and mechanisms of endocrine resistance and guide precision treatment of BC bone metastasis (BoM). We previously identified the overexpression of FGFR4 in endocrine resistant samples. Further in this thesis, we demonstrated that high FGFR4 predicts poorer survival of patients with ER+ BC and ER suppresses FGFR4 expression. However, FGFR4 cannot drive endocrine resistance in ER+ BC cell lines in vitro. FGFR4 inhibitor had a minimal effect on HER2 non-amplified cell growth but a stronger inhibition of HER2 amplified cell growth and FGFR4 showed the highest expression in HER2-enriched BC, suggesting HER2 expression may be required for FGFR4 function in BC which should be further explored. To verify FGFR4 overexpression post endocrine therapy in vivo and investigate tumor microenvironment (TME) contribution to endocrine resistance, an ER+ SSM3 syngeneic murine homograft model was utilized. Results showed an increase of myeloid cell infiltration post endocrine therapy. To investigate the potential of multi-omics guided precision MBC treatment, we performed DNA/RNA/single cell RNA (scRNA) analyses of bilateral BoM, with matched primary invasive lobular breast carcinoma and patient derived organoids (PDO). BoM lost estrogen receptor expression, gained BRCA1 (D1834H) mutation, and upregulated multiple targetable cancer hallmark pathways. scRNA analysis uncovered a complicated microenvironment of BoM consisting of multiple epithelial cell subclones communicating extensively with TME. PDO faithfully retained features of originating BoM and were responsive to targeting driver mutations in vitro and in vivo. In summary, I performed a comprehensive analysis of MBC evolution and heterogeneity in ER+ breast cancer. These studies have identified FGFR4 as a potential driver of endocrine resistance, however, more studies are necessary as its role in breast cancer tumorigenesis might be strictly context dependent. In addition, I have shown that multi-omics profiling of BoM and organoids modeling represent a promising approach for precision medicine for patients with breast cancer.

As the principal pro-inflammatory prostanoid, prostaglandin E2 (PGE2) serves as mediator of pain and fever in inflammatory reactions. The biosynthesis of PGE2 starts from arachidonic acid (AA). Cyclooxygenase (COX)-1 and/or COX-2 converts AA to prostaglandin H2 (PGH2), and PGE2 synthases transform PGH2 to PGE2. Current mainstream approach for treating inflammation-related symptoms remains the application of traditional non-steroidal anti-inflammatory drugs (tNSAIDs) and selective COX-2 inhibitors (coxibs). As both categories shut down the biosynthesis of all downstream prostanoids, their application renders several deleterious effects including gastrointestinalulceration and cardiovascular risk. Microsomal prostaglandin E2 synthase-1 (mPGES-1) inhibitors, specifically blocking the production of inflammation-related PGE2, are expected to reduce the adverse effects while retain the anti-inflammation activity. Although several compounds have been reported, only a few have entered clinical trials and none was on the market. Particularly, most of the reported human mPGES-1 inhibitors were not active for wild-type mouse/rat mPGES-1 enzymes, which prevents using the well-established mouse/rat models of inflammation in preclinical studies. Therefore, we expect our designed inhibitors to also be potent against mouse mPGES-1 and thus is suitable for preclinical testing in wild-type mice.

Establishing robust connectivity in heterogeneous networks (HetNets) is an important yet challenging problem. For a heterogeneous network accommodating a large number of nodes, establishing perturbation-invulnerable connectivity is of utmost importance. This dissertation provides a robust advantaged node placement strategy best suited for sparse network graphs. In order to offer connectivity robustness, this work models the communication range of an advantaged node with a hexagon embedded within a circle representing the physical range of a node. Consequently, the proposed node placement method in this dissertation is based on a so-called hexagonal coordinate system (HCS) in which we develop an extended algebra. We formulate a class of geometric distance optimization problems aiming at establishing robust connectivity of a graph of multiple clusters of nodes. After showing that our formulated problem is NP-hard, we provide a heuristic algorithm based on HCS that efficiently solves the problem. Performance evaluation on different aspects of the algorithm is given. The results show that our algorithm is most effective in sparse networks for which we derive classification thresholds.After connectivity is established, we consider the problem that when some nodes are exposed to mobility, how to maintain connectivity. In this part, the network of interest consists of two types of nodes, pre-deployed (client) and intermediate nodes. We assume full control on the intermediate nodes but not the pre-deployed nodes. In such networks, on which we have only partial control, two types of node mobility scenarios are investigated. The first scenario analyzes the bounds of mobility when pre-deployed nodes move at small scales. The bounds of node mobility preserving connectivity are derived through analysis and verified by simulations.The second scenario considers the movement of pre-deployed nodes beyond the bounds of the first scenario thereby breaking connected links and partitioning the connected network. This scenario then considers relocating the existing intermediate nodes in order to reestablish connectivity. A general formulation is proposed in the form of an optimization problem. We prove that the general formulation of the problem is NP-hard. Next, we turn our attention to a practical scenario in which the location of nodes is made available using GPS signals. We solve the problem of the practical scenario in polynomial time and analyze the complexity of our solution.We also present comprehensive performance evaluation results of our proposed algorithm.

This dissertation consists of two essays. In the first essay, Enoch Hill and I develop a dynamic general equilibrium model in which an increase in the importance of firm-specific human capital is able to account for two key changes in business cycle patterns in the U.S. since mid-1980s: jobless recoveries and the reversal in the cyclicality of labor productivity. Additionally, we present empirical support that the importance of firm-specific human capital has indeed increased in importance for recent recessions. In the second essay, Zhifeng Cai and I develop a macroeconomic model of financial frictions in order to account for the investment and cash holding behavior of self-financing corporations during the Great Recession. Unlike standard models of financial frictions which impose collateral or borrowing constraints on firms, the financial frictions in our model work through the liquidity channel. In our model, corporate investment is subject to liquidity shocks. Bank credit line and liquid assets are substitutes for financing liquidity shocks. In our model, a tightening of the bank credit line forces firms to hold more liquid assets, increasing the effective cost of capital expenditure hence reducing corporate investment.