Isolation of DNA sequences with homology to a degenerate FaRP oligonucleotide from the crayfish Procambarus clarkii

The neuropeptide Th1RFamide with the sequence Phe-Met-Arg-Phe-amide was originally isolated in the clam Macrocallista nimbosa (price and Greenberg, 1977). Since its discovery, a large family ofFl\1RFamide-related peptides termed FaRPs have been found to be present in all major animal phyla with functions ranging from modulation of neuronal activity to alteration of muscular contractions. However, little is known about the genetics encoding these peptides, especially in invertebrates. As FaRP-encoding genes have yet to be investigated in the invertebrate Malacostracean subphylum, the isolation and characterization ofFaRP-encoding DNA and mRNA was pursued in this project. The immediate aims of this thesis were: (1) to amplify mRNA sequences of Procambarus clarkii using a degenerate oligonucleotide primer deduced from the common amino acid sequence ofisolated Procambarus FaRPS, (2) to determine if these amplification products encode FaRP gene sequences, and (3) to create a selective cDNA library of sequences recognized by the degenerate oligonucleotide primer. The polymerase chain reaction - rapid amplification of cDNA ends (PCR-RACE) is a procedure in which a single gene-specific primer is used in conjunction with a generalized 3' or 5' primer to amplify copies ofthe region between a single point in the transcript and the 3' or 5' end of cDNA of interest (Frohman et aI., 1988). PCRRACE reactions were optimized with respect to primers used, buffer composition, cycle number, nature ofgenetic substrate to be amplified, annealing, extension and denaturation temperatures and times, and use of reamplification procedures. Amplification products were cloned into plasmid vectors and recombinant products were isolated, as were the recombinant plaques formed in the selective cDNA library. Labeled amplification products were hybridized to recombinant bacteriophage to determine ligated amplification product presence. When sequenced, the five isolated PCR-RACE amplification products were determined not to possess FaRP-encoding sequences. The 200bp, 450bp, and 1500bp sequences showed homology to the Caenorhabditis elegans cosmid K09A11, which encodes for cytochrome P450; transfer-RNA; transposase; and tRNA-Tyr, while the 500bp and 750bp sequences showed homology with the complete genome of the Vaccinia virus. Under the employed amplification conditions the degenerate oligonucleotide primer was observed to bind to and to amplify sequences with either 9 or 10bp of 17bp identity. The selective cDNA library was obselVed to be of extremely low titre. When library titre was increased, white. plaques were isolated. Amplification analysis of eight isolated Agt11 sequences from these plaques indicated an absence of an insertion sequence. The degenerate 17 base oligonucleotide primer synthesized from the common amino acid sequence ofisolated Procambarus FaRPs was thus determined to be non-specific in its binding under the conditions required for its use, and to be insufficient for the isolation and identification ofFaRP-encoding sequences. A more specific primer oflonger sequence, lower degeneracy, and higher melting temperature (TJ is recommended for further investigation into the FaRP-encoding genes of Procambarlls clarkii.

Planar Topological Defects in Unconventional Superconductors

In this work, we consider the properties of planar topological defects in unconventional superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper- Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.

Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.