No description available.

It is well known that, as a consequence of the Identity Theorem, we cannot "glue" together two analytic functions to create a new globally analytic function. In this paper we will both introduce and investigate special homeomorphisms, called quasiconformal maps, that are generalizations of the well known conformal maps. We will show that quasiconformal maps make this "gluing," up to conjugation, possible. Quasiconformal maps are a valuable tool in the field of complex dynamics. We will see how quasiconformal maps of infinitesimal circles have an image of an infinitesimal ellipse. Although quasiconformal maps are nice homeomorphisms, they might only be differentiable in the real sense almost everywhere and, surprisingly, complex differentiable nowhere. We shall rely on the work of Lehto and Virtanen as well as Shishikura in exploring these interesting complex valued functions. / Department of Mathematical Sciences

Complete and accurate DNA replication is essential to maintain the genetic integrity in all organisms. In eukaryotes, the minichromosome maintenance (MCM) complex forms the catalytic core of the CMG helicase that unwinds DNA at the replication fork. We have previously identified a conserved MCM complex binding protein (MCM-BP) through a proteomic screen in human cells. In chapter two of this thesis, I show that MCM-BP makes an important contribution to nuclear morphology in human cells by affecting centrosome duplication. I also show that MCM-BP depletion results in G2 checkpoint signaling and the induction of replication stress. A recent study in Xenopus egg extracts has suggested that MCM-BP functions to unload the MCM complex from chromatin during S-phase. However, the mechanism of this process remains enigmatic. In chapter three of this thesis, I show that MCM-BP directly binds the de-ubiquitylating enzyme, USP7 and that this interaction is mediated by S158 on MCM-BP and the USP7 TRAF domain. Furthermore, I indicate a novel role for USP7 in DNA replication that involves unloading of the MCM complex during S-phase. Finally, my data suggest that MCM-BP tethers an interaction between the USP7 and the MCM complex to facilitate MCM complex unloading at the end of S-phase.

2-Cyanoethyldiphenylphosphine (L) was synthesized from diphenylphosphine and acrylonitrile using an aqueous base as a catalyst. This ligand reacted with Pt(II) and Pd(II) salts to yield complexes of the stoichioretry MX2L2 (X = Cl, Br, NCS). In these complexes the ligand was found to function as a monodentate phosphine. infrared spectroscopic evidence suggested that the platinum complexes are of cis and the palladium complexes of trans geometries.A complex of the stoichiometry Pd2Cl4L2 was isolated from a 1:1. mole ratio of PdCl2 to L. Spectroscopic evidence suggested that the complex is a ligand bridged dieter which utilizes the phosphorus and nitrogen lone pairs of L. The nitrile groups in this complex reacted rapidly with alcohols to yield coordinated imino-ether groups.

Kinetic studies are reported of the reactions of 1,3,5-trinitrobenzene with aniline in dimethyl sulfoxide (DMSO). In the presence of buffers containing 1,4- diazabicyclo(2.2.2)octane, (Dabco), and its acid salt, DabcoH(^+), the anilide σ-adduct is formed. The reaction of ethyl 2,4,6-trinitrophenyI ether with aniline in DMSO containing Dabco occurs in two stages. The first gives σ-adduct intermediate on the substitution pathway, which has been identified spectroscopically. The second yields 2,4,6-trinitrodiphenyIamine, the substitution product. Kinetic studies show that proton transfer is rate-limiting both in the formation of the intermediate and in its subsequent acid-catalysed decomposition. Phenoxide is a considerably better leaving group than ethoxide and the substitution reactions of phenyl 2,4,6- trinitrophenyl ethers and phenyl 2,4-dinitronaphthyI ether with aniline in DMSO occur without the accumulation of intermediates. The kinetics indicate both uncatalysed and base catalysed pathways. Values have been determined for the pK(_a) in DMSO of several ammonium ions derived from amines which have previously been widely used as nucleophiles in nucleophilic aromatic substitution reactions; values are also given for four polynitrodiphenylamines used as indicators. Second order rate constants (K(_s)) are presented for the reaction of substituted phenyl 2,4,6-trinitrophenyl ethers with a series of phenolate ions having pK(_a) values both higher and lower than that of the respective leaving groups in aqueous solution. The rate constants for the reverse reaction (k(_-s)) have also been measured. The Brømsted diagram formed when plotting log k(_s) versus pK(_a) shows a change in slope when ΔpK(_a) = 0 (ΔpK(_a) being the difference in pK(_a) values of the leaving group and nucleophile). This is consistent with a two step process involving a discrete σ-adduct intermediate. From the measured β values effective charges have been determined and the overall effective charge map constructed. Kinetic studies have been made for the reactions of substituted phenyl 2,4,6- trinitrophenyl ethers with substituted phenolate ions in 74% DMSO-water (v/v). Two reactions are observed. The evidence suggests that the more rapid involves formation of a 1,1 σ-adduct between the substrate and the phenolate ions. The slower reaction is attributed to hydroxide attack at the 3-position of the substrate.

No description available.

The development of dimetallic metal complexes into functional and selective recognition agents for monophosphorylated peptides is described. The development of dimetallic metal complexes into functional and selective phosphopeptide recognition agents is described. Scaffold functionalization was conducted to assess whether binding affinity for phosphate monoesters could be modulated. A protocol for the facile synthesis of symmetric and asymmetric pyridine-functionalized bis-dipicolylamine (BDPA) scaffolds was thus first optimized. Zn(II) complexes were screened for the ability to bind to various phosphate monoesters of biological relevance using isothermal titration calorimetry (ITC). An expanded family of compounds was then screened using a variety of biophysicial and biological techniques for the ability to bind to disrupt Stat3 dimer both in biophysical assays and in whole cells. Several compounds displayed the ability to potently disrupt Stat3 dimer formation at low micromolar doses. Moreover, one compound emerged as having potent anti-cancer activity against MDA468, a solid breast cancer tumor line. Efforts were subsequently redirected towards the development of Zn(II)-BDPA receptors which mimicked the pY, pY+X recognition motif displayed by human SH2 domains. A family of ditopic biphenyl-based receptors, computationally predicted to adopt this binding mode, were synthesized and screened against a family of high-profile pY-containing phosphopeptides. The reported family of mimetics displayed a wide variance in cytotoxicity against common cancer cell lines, supporting our structure-activity hypothesis. Selectivity observed in our fluorescence intensity assay did not hold in a cellular context. We next pursued the development of selective receptors for phosphopeptides containing pS instead of pY. A diverse family of Zn(II)-BDPA receptors featuring a 2’ substituted benzothiazole core were synthesized, and their binding affinities toward model phosphopeptides assessed. A central conclusion of this project is that development of potent, selective receptors for anionic and hydrophobic peptides will likely be possible only by using receptors with cationic or hydrophobic pendants, and by maximizing phosphopeptide-specific interactions. Lastly, investigations into the use of bowl-type receptors as phosphopeptide recognition agents are presented. Synthesis of a prototype bowl receptor and early efforts to characterize the receptor’s binding preferences using ITC are reported. Progress-to-date in the development of a FRET system, which will be used to measure the receptor’s affinity for different dephosphorylation motifs, is also reported.

The development of dimetallic metal complexes into functional and selective recognition agents for monophosphorylated peptides is described. The development of dimetallic metal complexes into functional and selective phosphopeptide recognition agents is described. Scaffold functionalization was conducted to assess whether binding affinity for phosphate monoesters could be modulated. A protocol for the facile synthesis of symmetric and asymmetric pyridine-functionalized bis-dipicolylamine (BDPA) scaffolds was thus first optimized. Zn(II) complexes were screened for the ability to bind to various phosphate monoesters of biological relevance using isothermal titration calorimetry (ITC). An expanded family of compounds was then screened using a variety of biophysicial and biological techniques for the ability to bind to disrupt Stat3 dimer both in biophysical assays and in whole cells. Several compounds displayed the ability to potently disrupt Stat3 dimer formation at low micromolar doses. Moreover, one compound emerged as having potent anti-cancer activity against MDA468, a solid breast cancer tumor line. Efforts were subsequently redirected towards the development of Zn(II)-BDPA receptors which mimicked the pY, pY+X recognition motif displayed by human SH2 domains. A family of ditopic biphenyl-based receptors, computationally predicted to adopt this binding mode, were synthesized and screened against a family of high-profile pY-containing phosphopeptides. The reported family of mimetics displayed a wide variance in cytotoxicity against common cancer cell lines, supporting our structure-activity hypothesis. Selectivity observed in our fluorescence intensity assay did not hold in a cellular context. We next pursued the development of selective receptors for phosphopeptides containing pS instead of pY. A diverse family of Zn(II)-BDPA receptors featuring a 2’ substituted benzothiazole core were synthesized, and their binding affinities toward model phosphopeptides assessed. A central conclusion of this project is that development of potent, selective receptors for anionic and hydrophobic peptides will likely be possible only by using receptors with cationic or hydrophobic pendants, and by maximizing phosphopeptide-specific interactions. Lastly, investigations into the use of bowl-type receptors as phosphopeptide recognition agents are presented. Synthesis of a prototype bowl receptor and early efforts to characterize the receptor’s binding preferences using ITC are reported. Progress-to-date in the development of a FRET system, which will be used to measure the receptor’s affinity for different dephosphorylation motifs, is also reported.

The reach control problem (RCP) characterizes a control design approach, based on computer science notions of object triangulation, that has been extensively developed as a means of guiding the complete transient response of a system, entirely within a desired polytopic region of state-space operation characterized by linear constraints on its states. This thesis expands upon results achieved in the area of RCP problem solvability under continuous feedback, identifying new necessary conditions. It accomplishes this using algebraic topology constructs, mapping the reach control problem to an equivalent topological one to successfully demonstrate conditions under which topological obstructions are generated. These obstructions, which render the RCP unsolvable by continuous feedback are then used to characterize equivalent conditions necessary for solvability of the problem. This thesis also serves to formally demonstrate the substantial advantages of the RCP design approach over more conventional industry techniques, by solving real-world problems with complex specifications.

The course of pathogenic bacterial infection is dependent on the interactions between the host immune response and the bacterial virulence mechanisms. Our lab previously discovered that the Survival of Motor Neuron (SMN) protein complex undergoes a change in subcellular localization during infection with invasive Shigella bacteria, forming novel cytoplasmic aggregates called "U bodies". Similar results were obtained with other intracellular bacterial pathogens suggesting that these U bodies are a fundamental entity in microbial pathogenesis. Notably, the SMN complex normally plays a key role in the assembly of the spliceosomal U snRNA. We have shown during infection that there are changes in U snRNA maturation and splicing patterns. Importantly, we have found that U bodies are downstream of a stress pathway involving the stress-inducible ATF3 protein. Altogether, intracellular bacterial infection induces novel cellular stress pathways that disrupt normal SMN complex function and leads to changes in U snRNA associated functions.