In this dissertation we discuss the construction and convergence of high order structure preserving numerical methods for problems in Lagrangian mechanics. Specifically, we make use of the discrete mechanics framework to construct symplectic integrators which have convergence which is optimal, in a certain sense. We then demonstrate how this optimal convergence can be leveraged to construct integrators of arbitrarily high order or with geometric convergence. We further show how these methods can be used to construct continuous approximations to the dynamics of a Lagrangian system, and show that these approximations are also very high order and have excellent structure preserving properties. We discuss the formulation of symplectic integrators on both vector spaces and Lie groups, using a Galerkin construction to induce a variational integrator. We begin with the formulation for vector spaces, and then extend this construction to Lie groups through the use of a convenient coordinate chart. We provide the necessary conditions for optimal convergence for both the vector space and Lie group constructions, and demonstrate that many canonical systems automatically satisfy these conditions. We close with several numerical experiments demonstrating the predicted convergence, and discuss further extensions of this work

In the peripheral nerve, mechanosensitive axons are insulated by myelin, a multilamellar membrane formed by Schwann cells. Here, we offer first evidence that a myelin degradation product induces mechanical hypersensitivity and global transcriptomics changes in a sex-specific manner. Focusing on downstream signaling events of the functionally active 84-104 myelin basic protein (MBP(84-104)) fragment released after nerve injury, we demonstrate that exposing the sciatic nerve to MBP(84-104) via endoneurial injection produces robust mechanical hypersensitivity in female, but not in male, mice. RNA-seq and systems biology analysis revealed a striking sexual dimorphism in molecular signatures of the dorsal root ganglia (DRG) and spinal cord response, not observed at the nerve injection site. Mechanistically, intra-sciatic MBP(84-104) induced phospholipase C (PLC)-driven (females) and phosphoinositide 3-kinase-driven (males) phospholipid metabolism (tier 1). PLC/inositol trisphosphate receptor (IP3R) and estrogen receptor co-regulation in spinal cord yielded Ca²⁺-dependent nociceptive signaling induction in females that was suppressed in males (tier 2). IP3R inactivation by intrathecal xestospongin C attenuated the female-specific hypersensitivity induced by MBP(84-104). According to sustained sensitization in tiers 1 and 2, T cell-related signaling spreads to the DRG and spinal cord in females, but remains localized to the sciatic nerve in males (tier 3). These results are consistent with our previous finding that MBP(84-104)-induced pain is T cell-dependent. In summary, an autoantigenic peptide endogenously released in nerve injury triggers multisite, sex-specific transcriptome changes, leading to neuropathic pain only in female mice. MBP(84-104) acts through sustained co-activation of metabolic, estrogen receptor-mediated nociceptive, and autoimmune signaling programs.

Inflammatory bowel disease (IBD) is prevalent, but the mechanisms underlying disease development remain elusive. We identify a role for the E3 ubiquitin ligase RNF5 in IBD. Intestinal epithelial cells (IECs) express a high level of RNF5, while the colon of Rnf5^-/- mice exhibits activated dendritic cells and intrinsic inflammation. Rnf5^-/- mice exhibit severe acute colitis following dextran sodium sulfate (DSS) treatment. S100A8 is identified as an RNF5 substrate, resulting in S100A8 ubiquitination and proteasomal-dependent degradation that is attenuated upon inflammatory stimuli. Loss of RNF5 from IECs leads to enhanced S100A8 secretion, which induces mucosal CD4⁺ T cells, resulting in Th1 pro-inflammatory responses. Administration of S100A8-neutralizing antibodies to DSS-treated Rnf5^-/- mice attenuates acute colitis development and increases survival. An inverse correlation between RNF5 and S100A8 protein expression in IECs of IBD patients coincides with disease severity. Collectively, RNF5-mediated regulation of S100A8 stability in IECs is required for the maintenance of intestinal homeostasis.

The prevalence of "long COVID" is just one of the conundrums highlighting how little we know about the lung's response to viral infection, particularly to syndromecoronavirus-2 (SARS-CoV-2), for which the lung is the point of entry. We used an in vitro human lung system to enable a prospective, unbiased, sequential single-cell level analysis of pulmonary cell responses to infection by multiple SARS-CoV-2 strains. Starting with human induced pluripotent stem cells and emulating lung organogenesis, we generated and infected three-dimensional, multi-cell-type-containing lung organoids (LOs) and gained several unexpected insights. First, SARS-CoV-2 tropism is much broader than previously believed: Many lung cell types are infectable, if not through a canonical receptor-mediated route (e.g., via Angiotensin-converting encyme 2(ACE2)) then via a noncanonical "backdoor" route (via macropinocytosis, a form of endocytosis). Food and Drug Administration (FDA)-approved endocytosis blockers can abrogate such entry, suggesting adjunctive therapies. Regardless of the route of entry, the virus triggers a lung-autonomous, pulmonary epithelial cell-intrinsic, innate immune response involving interferons and cytokine/chemokine production in the absence of hematopoietic derivatives. The virus can spread rapidly throughout human LOs resulting in mitochondrial apoptosis mediated by the prosurvival protein Bcl-xL. This host cytopathic response to the virus may help explain persistent inflammatory signatures in a dysfunctional pulmonary environment of long COVID. The host response to the virus is, in significant part, dependent on pulmonary Surfactant Protein-B, which plays an unanticipated role in signal transduction, viral resistance, dampening of systemic inflammatory cytokine production, and minimizing apoptosis. Exogenous surfactant, in fact, can be broadly therapeutic.

The novel coronavirus SARS-CoV-2, which emerged in late 2019, has since spread around the world and infected hundreds of millions of people with coronavirus disease 2019 (COVID-19). While this viral species was unknown prior to January 2020, its similarity to other coronaviruses that infect humans has allowed for rapid insight into the mechanisms that it uses to infect human hosts, as well as the ways in which the human immune system can respond. Here, we contextualize SARS-CoV-2 among other coronaviruses and identify what is known and what can be inferred about its behavior once inside a human host. Because the genomic content of coronaviruses, which specifies the virus's structure, is highly conserved, early genomic analysis provided a significant head start in predicting viral pathogenesis and in understanding potential differences among variants. The pathogenesis of the virus offers insights into symptomatology, transmission, and individual susceptibility. Additionally, prior research into interactions between the human immune system and coronaviruses has identified how these viruses can evade the immune system's protective mechanisms. We also explore systems-level research into the regulatory and proteomic effects of SARS-CoV-2 infection and the immune response. Understanding the structure and behavior of the virus serves to contextualize the many facets of the COVID-19 pandemic and can influence efforts to control the virus and treat the disease. IMPORTANCE COVID-19 involves a number of organ systems and can present with a wide range of symptoms. From how the virus infects cells to how it spreads between people, the available research suggests that these patterns are very similar to those seen in the closely related viruses SARS-CoV-1 and possibly Middle East respiratory syndrome-related CoV (MERS-CoV). Understanding the pathogenesis of the SARS-CoV-2 virus also contextualizes how the different biological systems affected by COVID-19 connect. Exploring the structure, phylogeny, and pathogenesis of the virus therefore helps to guide interpretation of the broader impacts of the virus on the human body and on human populations. For this reason, an in-depth exploration of viral mechanisms is critical to a robust understanding of SARS-CoV-2 and, potentially, future emergent human CoVs (HCoVs).

Solar-powered electrochemical production of hydrogen through water electrolysis is an active and important research endeavor. However, technologies and roadmaps for implementation of this process do not exist. In this perspective paper, we describe potential pathways for solar-hydrogen technologies into the marketplace in the form of photoelectrochemical or photovoltaic-driven electrolysis devices and systems. We detail technical approaches for device and system architectures, economic drivers, societal perceptions, political impacts, technological challenges, and research opportunities. Implementation scenarios are broken down into short-term and long-term markets, and a specific technology roadmap is defined. In the short term, the only plausible economical option will be photovoltaic-driven electrolysis systems for niche applications. In the long term, electrochemical solar-hydrogen technologies could be deployed more broadly in energy markets but will require advances in the technology, significant cost reductions, and/or policy changes. Ultimately, a transition to a society that significantly relies on solar-hydrogen technologies will benefit from continued creativity and influence from the scientific community.