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.

Ice-binding proteins adsorb to their ligand via anchored clathrate waters

The main success of my thesis has been to establish the mechanism by which antifreeze proteins (AFPs) bind irreversibly to ice crystals, and hence prevent their growth. AFPs organize ice-like water on their ice-binding site, which then merges and freezes with the quasi-liquid layer of ice. This was revealed from studying the exceptionally large (ca. 1.5-MDa) Ca 2+-dependent AFP from the Antarctic bacterium Marinomonas primoryensis (MpAFP). The 34-kDa antifreeze- active region of MpAFP was predicted to fold as a novel Ca 2+-binding β-helix. Site-directed mutagenesis confirmed the model and demonstrated that its ice-binding site (IBS) consisted of solvent-exposed Thr and Asx parallel arrays on the Ca 2+-binding turns. The X-ray crystal structure of the antifreeze region was solved to a resolution of 1.7 Å. Two of the four molecules within the unit cell of the crystal had portions of their IBSs freely exposed to solvent. Identical clathrate-like cages of water molecules were present on each IBS. These waters were organized by the hydrophobic effect and anchored to the protein via hydrogen bonds. They matched the spacing of water molecules in an ice lattice, demonstrating that anchored clathrate waters bind AFPs to ice. This mechanism was extended to other AFPs including the globular type III AFP from fishes. Site-directed mutagenesis and a modified ice-etching technique demonstrated this protein uses a compound ice-binding site, comprised of two flat and relatively hydrophobic surfaces, to bind at least two planes of ice. Reinvestigation of several crystal structures of type III AFP identified anchored clathrate waters on the solvent-exposed portion of its compound IBS that matched the spacing of waters on the primary prism plane of ice. Ice nucleation proteins (INPs), which can raise the temperature at which ice forms in solution to just slightly below 0oC, have the opposite effect to AFPs. A novel dimeric β-helical model was proposed for the INP produced by the bacterium Pseudomonas borealis. Molecular dynamics simulations showed that INPs are also capable of ordering water molecules into an ice- like lattice. However, their multimerization brings together sufficient ordered waters to form an ice nucleus and initiate freezing.

A structural basis for different antifreeze protein roles

Antifreeze proteins (AFPs) are produced by a variety of organisms to either protect them from freezing or help them tolerate being frozen. Recent structural work has shown that AFPs bind to ice using ordered surface waters on a particular surface of the protein called the ice-binding site (IBS). These 'anchored clathrate' waters fuse to particular planes of an ice crystal and hence irreversibly bind the AFP to its ligand. An AFP isolated from the perennial ryegrass, Lolium perenne (LpAFP) was previously modelled as a right-handed beta helix with two proposed IBSs. Steric mutagenesis, where small side chains were replaced with larger ones, determined that only one of the putative IBSs was responsible for binding ice. The mutagenesis work also partly validated the fold of the computer-generated model of this AFP. In order to determine the structure of the protein, LpAFP was crystallized and solved to 1.4 Å resolution. The protein folds as an untwisted left-handed beta-helix, of opposite handedness to the model. The IBS identified by mutagenesis is remarkably flat, but less regular than the IBS of most other AFPs. Furthermore, several of the residues constituting the IBS are in multiple conformations. This irregularity may explain why LpAFP causes less thermal hysteresis than many other AFPs. Its imperfect IBS is also argued to be responsible for LpAFP's heightened ice-recrystallization inhibition activity. The structure of LpAFP is the first for a plant AFP and for a protein responsible for providing freeze tolerance rather than freeze resistance. To help understand what constitutes an IBS, a non-ice-binding homologue of type III AFP, sialic acid synthase (SAS), was engineered for ice binding. Point mutations were made to the germinal IBS of SAS to mimic key features seen in type III AFP. The crystal structures of some of the mutant proteins showed that the potential IBS became less charged and flatter as the mutations progressed, and ice affinity was gained. This proof-of-principle study highlights some of the difficulties in AFP engineering.