Determinantal hypersurface from a geometric perspective

In this paper, we give a geometric interpretation of determinantal forms, both in the case of general matrices and symmetric matrices. We will prove irreducibility of the determinantal singular loci and state its dimension. We also provide detailed description of the singular locus for small dimensions.

Coupled plasmonic systems and devices : applications in visible metamaterials, nanophotonic circuits, and CMOS imaging

With the size of transistors approaching the sub-nanometer scale and Si-based photonics pinned at the micrometer scale due to the diffraction limit of light, we are unable to easily integrate the high transfer speeds of this comparably bulky technology with the increasingly smaller architecture of state-of-the-art processors. However, we find that we can bridge the gap between these two technologies by directly coupling electrons to photons through the use of dispersive metals in optics. Doing so allows us to access the surface electromagnetic wave excitations that arise at a metal/dielectric interface, a feature which both confines and enhances light in subwavelength dimensions - two promising characteristics for the development of integrated chip technology. This platform is known as plasmonics, and it allows us to design a broad range of complex metal/dielectric systems, all having different nanophotonic responses, but all originating from our ability to engineer the system surface plasmon resonances and interactions. In this thesis, we demonstrate how plasmonics can be used to develop coupled metal-dielectric systems to function as tunable plasmonic hole array color filters for CMOS image sensing, visible metamaterials composed of coupled negative-index plasmonic coaxial waveguides, and programmable plasmonic waveguide network systems to serve as color routers and logic devices at telecommunication wavelengths.

Coupled effects of mechanics, geometry, and chemistry on bio-membrane behavior

Lipid bilayer membranes are models for cell membranes--the structure that helps regulate cell function. Cell membranes are heterogeneous, and the coupling between composition and shape gives rise to complex behaviors that are important to regulation. This thesis seeks to systematically build and analyze complete models to understand the behavior of multi-component membranes.

We propose a model and use it to derive the equilibrium and stability conditions for a general class of closed multi-component biological membranes. Our analysis shows that the critical modes of these membranes have high frequencies, unlike single-component vesicles, and their stability depends on system size, unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We compare these results with experimental observations.

We also study open membranes to gain insight into long tubular membranes that arise for example in nerve cells. We derive a complete system of equations for open membranes by using the principle of virtual work. Our linear stability analysis predicts that the tubular membranes tend to have coiling shapes if the tension is small, cylindrical shapes if the tension is moderate, and beading shapes if the tension is large. This is consistent with experimental observations reported in the literature in nerve fibers. Further, we provide numerical solutions to the fully nonlinear equilibrium equations in some problems, and show that the observed mode shapes are consistent with those suggested by linear stability. Our work also proves that beadings of nerve fibers can appear purely as a mechanical response of the membrane.

Chemical-scale studies of G protein-coupled receptors and ligand-gated ion channels

This dissertation describes studies of G protein-coupled receptors (GPCRs) and ligand-gated ion channels (LGICs) using unnatural amino acid mutagenesis to gain high precision insights into the function of these important membrane proteins.

Chapter 2 considers the functional role of highly conserved proline residues within the transmembrane helices of the D2 dopamine GPCR. Through mutagenesis employing unnatural α-hydroxy acids, proline analogs, and N-methyl amino acids, we find that lack of backbone hydrogen bond donor ability is important to proline function. At one proline site we additionally find that a substituent on the proline backbone N is important to receptor function.

In Chapter 3, side chain conformation is probed by mutagenesis of GPCRs and the muscle-type nAChR. Specific side chain rearrangements of highly conserved residues have been proposed to accompany activation of these receptors. These rearrangements were probed using conformationally-biased β-substituted analogs of Trp and Phe and unnatural stereoisomers of Thr and Ile. We also modeled the conformational bias of the unnatural Trp and Phe analogs employed.

Chapters 4 and 5 examine details of ligand binding to nAChRs. Chapter 4 describes a study investigating the importance of hydrogen bonds between ligands and the complementary face of muscle-type and α4β4 nAChRs. A hydrogen bond involving the agonist appears to be important for ligand binding in the muscle-type receptor but not the α4β4 receptor.

Chapter 5 describes a study characterizing the binding of varenicline, an actively prescribed smoking cessation therapeutic, to the α7 nAChR. Additionally, binding interactions to the complementary face of the α7 binding site were examined for a small panel of agonists. We identified side chains important for binding large agonists such as varenicline, but dispensable for binding the small agonist ACh.

Chapter 6 describes efforts to image nAChRs site-specifically modified with a fluorophore by unnatural amino acid mutagenesis. While progress was hampered by high levels of fluorescent background, improvements to sample preparation and alternative strategies for fluorophore incorporation are described.

Chapter 7 describes efforts toward a fluorescence assay for G protein association with a GPCR, with the ultimate goal of probing key protein-protein interactions along the G protein/receptor interface. A wide range of fluorescent protein fusions were generated, expressed in Xenopus oocytes, and evaluated for their ability to associate with each other.

Charge symmetry in ^(13)N and ^(13)C a coupled-channel model

A set of coupled-channel differential equations based on a rotationally distorted optical potential is used to calculate the wave functions required to evaluate the gamma ray transition rate from the first excited state to the ground state in ^(13)C and ^(13)N. The bremsstrahlung differential cross section of low energy protons is also calculated and compared with existing data. The marked similarity between the potentials determined at each resonance level in both nuclei supports the hypothesis of the charge symmetry of nuclear forces by explaining the deviation of the ratios of the experimental E1 transition strengths from unity.

Iridium and rhodium analogues of the Shilov cycle catalyst; and the investigation and applications of the Reduction-Coupled Oxo Activation (ROA) mechanistic motif towards alkane upgrading

This dissertation will cover several disparate topics, with the overarching theme centering on the investigation of organometallic C-H activation and hydrocarbon transformation and upgrading. Chapters 2 and 3 discuss iridium and rhodium analogues of the Shilov cycle catalyst for methane to methanol oxidation, and Chapter 4 on the recently discovered ROA mechanistic motif in catalysts for various alkane partial oxidation reactions. In addition, Chapter 5 discusses the mechanism of nickel pyridine bisoxazoline Negishi catalysts for asymmetric and stereoconvergent C-C coupling, and the appendices discuss smaller projects on rhodium H/D exchange catalysts and DFT method benchmarking.