Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.

Identification of Genes Involved in the C. elegans VAB-1 Eph Receptor Tyrosine Kinase Signaling Pathway

The generation of a functional nervous system requires that neuronal cells and axons navigate precisely to their appropriate targets. The Eph Receptor Tyrosine Kinases (RTKs) and their ephrin ligands have emerged as one of the important guidance cues for neuronal and axon navigation. However, the molecular mechanisms of how Eph RTKs regulate these processes are still incomplete. The purpose of this work was to contribute to the understanding of how Eph receptors regulate axon guidance by identifying and characterizing components of the Caenorhabditis elegans Eph RTK (VAB-1) signaling pathway. To achieve this objective I utilized a hyper active form of the VAB-1 Eph RTK (MYR-VAB-1) that caused penetrant axon guidance defects in the PLM mechanosensory neurons, and screened for suppressors of the MYR-VAB-1 phenotype. Through a candidate gene approach, I identified the adaptor NCK-1 as a downstream effector of VAB-1. Molecular and genetic analysis revealed that the nck-1 gene encodes for two isoforms (NCK-1A and NCK-1B) that share similar expression patterns in parts of the nervous system, but also have independent expression patterns in other tissues. Genetic rescue experiments showed that both NCK-1 isoforms can function in axon guidance, but each isoform also has specific functions. In vitro binding assays showed that NCK-1 binds to VAB-1 in a kinase dependent manner. In addition to NCK-1, WSP-1/N-WASP was also identified as an effector of VAB-1 signaling. Phenotypic analysis showed that nck-1 and wsp-1 mutants had PLM axon over extension defects similar to vab-1 animals. Furthermore, VAB-1, NCK-1 and WSP-1 formed a complex in vitro. Intriguingly, protein binding assays showed that NCK-1 can also bind to the actin regulator UNC-34/Ena, but genetic experiments suggest that unc-34 is an inhibitor of nck-1 function. Through various genetic and biochemical experiments, I provide evidence that VAB-1 can disrupt the NCK-1/UNC-34 complex, and negatively regulate UNC-34. Taken together, my work provides a model of how VAB-1 RTK signaling can inhibit axon extension. I propose that activated VAB-1 can prevent axon extension by inhibiting growth cone filopodia formation. This is accomplished by inhibiting UNC-34/Ena activity, and simultaneously activating Arp2/3 through a VAB-1/NCK-1/WSP-1 complex.

Targeting the actin cytoskeleton in HER2+ metastatic cancer cells using a macrolide toxin

Breast and ovarian cancers are among the leading causes of cancer related deaths in women worldwide. In a subset of these cancers, dysregulation of the human epidermal growth factor receptor 2 (HER2) leads to overexpression of the receptor on the cell surface. Previous studies have found that these HER2+ cancers show high rates of progression to metastatic disease. Metastasis is driven by cytoskeletal rearrangements that produce filamentous actin (F-actin) based structures that penetrate and degrade extracellular matrix to facilitate tumour invasion. Advancements in targeted therapy have made F-actin an attractive target for the development of new cancer therapies. In this thesis, we tested the actin-depolymerizing macrolide toxin, Mycalolide B (MycB), as a potential warhead for a novel antibody drug conjugate (ADC) to target highly metastatic HER2+ breast and ovarian cancers. We found that MycB treatment of HER2+ breast (SKBR3, MDA-MB-453) and ovarian (SKOV3) cancer cells led to loss of viability (IC50 values ≤ 64 nM). Sub-lethal doses of MycB treatment caused potent suppression of leading edge protrusions, migration and invasion potential of HER2+ cancer cells (IC50 ≤ 32 nM). In contrast, other F-actin based processes such as receptor endocytosis were less sensitive to MycB treatment. MycB treatment skewed the size of endocytic vesicles, which may reflect defects in F-actin based vesicle motility or maturation. Given that HER2+ cancers have been effectively targeted by Trastuzumab and Trastuzumab-based ADCs, we tested the effects of a combination of Trastuzumab and MycB on cell migration and invasion. We found that MycB/ Trastuzumab combination treatments inhibited motility of SKOV3 cells to a greater degree than either treatment alone. Altogether, our results provide proof-of-principle that actin toxins such as MycB can be used as a novel class of warheads for ADCs to target and combat highly metastatic cancers.