Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

The study of genetic diversity and population structure of the Korean fleshy shrimp, Fenneropenaeus chinensis, using newly developed microsatellite markers

The fleshy shrimp, Fenneropenaeus chinensis, is the family of Penaeidae and one of the most economically important marine culture species in Korea. However, its genetic characteristics have never been studied. In this study, a total of 240 wild F. chinensis individuals were collected from four locations as follows: Narodo (NRD, n = 60), Beopseongpo (BSP, n = 60), Chaesukpo (CSP, n = 60), and Cheonsuman (CSM, n = 60). Genetic variability and the relationships among four wild F. chinensis populations were analyzed using 13 newly developed microsatellite loci. Relatively high levels of genetic variability (mean allelic richness = 16.87; mean heterozygosity = 0.845) were found among localities. Among the 52 population loci, 13 showed significant deviation from the Hardy–Weinberg equilibrium. Neighbor-joining, principal coordinate, and molecular variance analyses revealed the presence of three subpopulations (NRD, CSM, BSP and CSP), which was consistent with clustering based on genetic distance. The mean observed heterozygosity values of the NRD, CSM, BSP, and CSP populations were 0.724, 0.821, 0.814, and 0.785 over all loci, respectively. These genetic variability and differentiation results of the four wild populations can be applied for future genetic improvement using selective breeding and to design suitable management guidelines for Korean F. chinensis culture.

Weinstein-Levin family trees 1862-1987

2 volumes each containing the geneaelogy of the family of Jack Weinstein: the Weinstein and the Levin families. Volumes contain photographs, newspaper clippings and other materials relevant to history of the two families.

Characterization of Mycobacterium leprae RecA intein, a LAGLIDADG homing endonuclease, reveals a unique mode of DNA-binding, helical distortion and cleavage, compared to a canonical LAGLIDADG homing endonuclease

Mycobacterium leprae, which has undergone reductive evolution leaving behind a minimal set of essential genes, has retained intervening sequences in four of its genes implicating a vital role for them in the survival of the leprosy bacillus. A single in-frame intervening sequence has been found embedded within its recA gene. Comparison of M. leprae recA intervening sequence with the known intervening sequences indicated that it has the consensus amino acid sequence necessary for being a LAGLIDADG-type homing endonuclease. In light of massive gene decay and function loss in the leprosy bacillus, we sought to investigate whether its recA intervening sequence encodes a catalytically active homing endonuclease. Here we show that the purified M. leprae RecA intein (PI-MleI) binds to cognate DNA and displays endonuclease activity in the presence of alternative divalent cations, Mg2+ or Mn2+. A combination of approaches including four complementary footprinting assays such as DNase I, Cu/phenanthroline, methylation protection and KMnO4, enhancement of 2-aminopurine fluorescence and mapping of the cleavage site revealed that PI-MleI binds to cognate DNA flanking its insertion site, induces helical distortion at the cleavage site and generates two staggered double-strand breaks. Taken together, these results implicate that PI-MleI possess a modular structure with separate domains for DNA target recognition and cleavage, each with distinct sequence preferences. From a biological standpoint, it is tempting to speculate that our findings have implications for understanding the evolution of LAGLIDADG family of homing endonucleases

Hoffman Family collection.

Offprint on the "Jews in Altenmuhr" by Wielfried Jung. Manuscript commissioned by Richard Hoffman "A History of the Hoffman Family in Germany and the United States (1988). Pictures of Kleinbardorf and Massbach. Biographical material on Benjamin Hoffman. Democratic Party leaflet for Rebecca Hoffman. Report on family of David Louis Hoffman. Notes on the Heinemann branch. Manuscript by Douglas Hoffman "A History of Economic and Social Change in the Hoffman Family."

Simson Wolf Oppenheimer Family.

Translation of part of family history about the family of Simon Wolf Oppenheimer from Frankfurt am Main

Wolf family chronicle.

A chronicle of the Wolf family of Schluechtern in Hesse (Germany), reacing back to 1680

Optic-phonon-magnetoplasmons at the interface of two polar semiconductors semiconductors

An interface between two polar semiconductors can support a whole new family of seven type of optic-phonon magnetoplasmons. Six of these arise due to nonequivalence property of propagation introduced by the magnetic field in Voigt configuration and one mainly due to finite plasma density ratio at the interface.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

Enzymes with radical tendencies: the PFL family

The first glycyl radical in an enzyme was described 20 years ago and since then the family of glycyl radical enzymes (GREs) has expanded to include enzymes catalysing five chemically distinct reactions. The type enzymes of the family, anaerobic ribonucleotide reductase (RNRIII) and pyruvate formate lyase (PFL) had been studied long before it was known that they are GREs. Spectroscopic measurements on the radical and an observation that exposure to oxygen irreversibly inactivates the enzymes by cleavage of the protein proved that the radical is located on a particular glycine residue, close to the C-terminus of the protein. Both anaerobic RNRIII and PFL, are important for many anaerobic and facultative anaerobic bacteria as RNRIII is responsible for the synthesis of DNA precursors and PFL catalyses a key metabolic reaction in glycolysis. The crystal structures of both were solved in 1999 and they revealed that, although the enzymes do not share significant sequence identity, they share a similar structure - the radical site and residues necessary for catalysis are buried inside a ten stranded $\ualpha $/$\ubeta $-barrel. GREs are synthesised in an inactive form and are post-translationally activated by an activating enzyme which uses S-adenosyl methionine and an iron-sulphur cluster to generate the radical. One of the goals of this thesis work was to crystallise the activating enzyme of PFL. This task is challenging as, like GREs, the activating component is inactivated by oxygen. The experiments were therefore carried out in an oxygen free atmosphere. This is the first report of a crystalline GRE activating enzyme. Recently several new GREs have been characterised, all sharing sequence similarity to PFL but not to RNRIII. Also, the genome sequencing projects have identified many PFL-like GREs of unknown function, usually annotated as PFLs. In the present thesis I describe the grouping of these PFL family enzymes based on the sequence similarity and analyse the conservation patterns when compared to the structure of E. coli PFL. Based on this information an activation route is proposed. I also report a crystal structure of one of the PFL-like enzymes with unknown function, PFL2 from Archaeoglobus fulgidus. As A. fulgidus is a hyperthermophilic organism, possible mechanisms stabilising the structure are discussed. The organisation of an active site of PFL2 suggests that the enzyme may be a dehydratase. Keywords: glycyl radical, enzyme, pyruvate formate lyase, x-ray crystallography, bioinformatics

ORP1L, a new Rab7 effector and regulator of late endosome functions

Oxysterol binding protein (OSBP) homologues have been found in eukaryotic organisms ranging from yeast to humans. These evolutionary conserved proteins have in common the presence of an OSBP-related domain (ORD) which contains the fully conserved EQVSHHPP sequence motif. The ORD forms a barrel structure that binds sterols in its interior. Other domains and sequence elements found in OSBP-homologues include pleckstrin homology domains, ankyrin repeats and two phenylalanines in an acidic tract (FFAT) motifs, which target the proteins to distinct subcellular compartments. OSBP homologues have been implicated in a wide range of intracellular processes, including vesicle trafficking, lipid metabolism and cell signaling, but little is known about the functional mechanisms of these proteins. The human family of OSBP homologues consists of twelve OSBP-related proteins (ORP). This thesis work is focused on one of the family members, ORP1, of which two variants were found to be expressed tissue-specifically in humans. The shorter variant, ORP1S contains an ORD only. The N-terminally extended variant, ORP1L, comprises a pleckstrin homology domain and three ankyrin repeats in addition to the ORD. The two ORP1 variants differ in intracellular localization. ORP1S is cytosolic, while the ankyrin repeat region of ORP1L targets the protein to late endosomes/lysosomes. This part of ORP1L also has profound effects on late endosomal morphology, inducing perinuclear clustering of late endosomes. A central aim of this study was to identify molecular interactions of ORP1L on late endosomes. The morphological changes of late endosomes induced by overexpressed ORP1L implies involvement of small Rab GTPases, regulators of organelle motility, tethering, docking and/or fusion, in generation of the phenotype. A direct interaction was demonstrated between ORP1L and active Rab7. ORP1L prolongs the active state of Rab7 by stabilizing its GTP-bound form. The clustering of late endosomes/lysosomes was also shown to be linked to the minus end-directed microtubule-based dynein-dynactin motor complex through the ankyrin repeat region of ORP1L. ORP1L, Rab7 and the Rab7-interacting lysosomal protein (RILP) were found to be part of the same effector complex recruiting the dynein-dynactin complex to late endosomes, thereby promoting minus end-directed movement. The proteins were found to be physically close to each other on late endosomes and RILP was found to stabilize the ORP1L-Rab7 interaction. It is possible that ORP1L and RILP bind to each other through their C-terminal and N-terminal regions, respectively, when they are bridged by Rab7. With the results of this study we have been able to place a member of the uncharacterized OSBP-family, ORP1L, in the endocytic pathway, where it regulates motility and possibly fusion of late endosomes through interaction with the small GTPase Rab7.

Functional studies of purified transmembrane proteases, omptins, of Yersinia pestis and Salmonella enterica.

Surface proteolysis is important in migration of cells through tissue barriers. In the case of prokaryotes, surface proteolysis has been associated with invasiveness of pathogenic bacteria from the primary infection site into circulation and secondary infection sites in the host. This study addressed surface proteases of two important bacterial pathogens, Yersinia pestis which is the causative agent of the lethal systemic zoonosis, plague, and Salmonella enterica serovar Typhimurium which is an oral-faecal pathogen that annually causes millions of cases of gastoenteritis that may develop to septicaemia. Both bacterial species express an ortholog of the omptin family of transmembrane β-barrel, outer membrane proteases/adhesins. This thesis work addressed the functions of isolated plasminogen activator Pla of Y. pestis and the PgtE omptin of S. enterica. Pla and PgtE were isolated as His6-fusion proteins in denaturing conditions from recombinant Escherichia coli and activated by adding lipopolysaccharide (LPS). The structural features in LPS that enhance plasminogen activation by His6-Pla were determined, and it was found that the lack of O-specifi c chain, the presence of outer core oligosaccharide, the presence of phosphates in lipid A, as well as a low level of acylation in lipid A influence the enhancement of Pla activity by LPS. A conserved lipid A phosphate binding motif in Pla and PgtE was found important for the enhancement of enzymatic activity by LPS. The results help to explain the biological signifi cance of the genetic loss of the O-specifi c chain biosynthesis in Y. pestis as well as the variations in LPS structure upon entry of Y. pestis into the human host. Expression of Pla in Y. pestis is associated with adhesiveness to lamin of basement membranes. Here, isolated and LPS-activated His6-Pla was coated onto fluorescent microparticles. The coating conferred specifi c adhesiveness of the particles to laminin and reconstituted basement membrane, thus confi rming the intrinsic adhesive characteristics of the Pla protein. The adhesiveness is thought to direct plasmin proteolysis at tissue barriers, thus increasing tissue damage and bacterial spread. Gelatinase activity has not been previously reported in enteric bacteria. Expression of PgtE in S. enterica was associated with cleavage of porcine skin gelatin, denaturated human type I collagen, as well as DQ-gelatin. Purifi ed His6-PgtE also degraded porcine skin gelatin and human type I gelatin but did not react with DQ-gelatin, indicating that minor differences are seen in proteolysis by isolated and cell-bound PgtE. Pla was less effective in gelatin degradation. The novel gelatinase activity in S. enterica is likely to enhance bacterial dissemination during infection.

Membrane Insertion of C-tail Anchored Proteins

The correct localization of proteins is essential for cell viability. In order to achieve correct protein localization to cellular membranes, conserved membrane targeting and translocation mechanisms have evolved. The focus of this work was membrane targeting and translocation of a group of proteins that circumvent the known targeting and translocation mechanisms, the C-tail anchored protein family. Members of this protein family carry out a wide range of functions, from protein translocation and recognition events preceding membrane fusion, to the regulation of programmed cell death. In this work, the mechanisms of membrane insertion and targeting of two C-tail anchored proteins were studied utilizing in vivo and in vitro methods, in yeast and mammalian cell systems. The proteins studied were cytochrome b(5), a well characterized C-tail anchored model protein, and N-Bak, a novel member of the Bcl-2 family of regulators of programmed cell death. Membrane insertion of cytochrome b(5) into the endoplasmic reticulum membrane was found to occur independently of the known protein conducting channels, through which signal peptide-containing polypeptides are translocated. In fact, the membrane insertion process was independent of any protein components and did not require energy. Instead membrane insertion was observed to be dependent on the lipid composition of the membrane. The targeting of N-Bak was found to depend on the cellular context. Either the mitochondrial or endoplasmic reticulum membranes were targeted, which resulted in morphological changes of the target membranes. These findings indicate the existence of a novel membrane insertion mechanism for C-tail anchored proteins, in which membrane integration of the transmembrane domain, and the translocation of C-terminal fragments, appears to be spontaneous. This mode of membrane insertion is regulated by the target membrane fluidity, which depends on the lipid composition of the bilayer, and the hydrophobicity of the transmembrane domain of the C-tail anchored protein, as well as by the availability of the C-tail for membrane integration. Together these mechanisms enable the cell to achieve spatial and temporal regulation of sub-cellular localization of C-tail anchored proteins.

The Gerbera cDNA Microarray: A Tool for Large-Scale Identification of Genes Involved in Flower Development

During the past ten years, large-scale transcript analysis using microarrays has become a powerful tool to identify and predict functions for new genes. It allows simultaneous monitoring of the expression of thousands of genes and has become a routinely used tool in laboratories worldwide. Microarray analysis will, together with other functional genomics tools, take us closer to understanding the functions of all genes in genomes of living organisms. Flower development is a genetically regulated process which has mostly been studied in the traditional model species Arabidopsis thaliana, Antirrhinum majus and Petunia hybrida. The molecular mechanisms behind flower development in them are partly applicable in other plant systems. However, not all biological phenomena can be approached with just a few model systems. In order to understand and apply the knowledge to ecologically and economically important plants, other species also need to be studied. Sequencing of 17 000 ESTs from nine different cDNA libraries of the ornamental plant Gerbera hybrida made it possible to construct a cDNA microarray with 9000 probes. The probes of the microarray represent all different ESTs in the database. From the gerbera ESTs 20% were unique to gerbera while 373 were specific to the Asteraceae family of flowering plants. Gerbera has composite inflorescences with three different types of flowers that vary from each other morphologically. The marginal ray flowers are large, often pigmented and female, while the central disc flowers are smaller and more radially symmetrical perfect flowers. Intermediate trans flowers are similar to ray flowers but smaller in size. This feature together with the molecular tools applied to gerbera, make gerbera a unique system in comparison to the common model plants with only a single kind of flowers in their inflorescence. In the first part of this thesis, conditions for gerbera microarray analysis were optimised including experimental design, sample preparation and hybridization, as well as data analysis and verification. Moreover, in the first study, the flower and flower organ-specific genes were identified. After the reliability and reproducibility of the method were confirmed, the microarrays were utilized to investigate transcriptional differences between ray and disc flowers. This study revealed novel information about the morphological development as well as the transcriptional regulation of early stages of development in various flower types of gerbera. The most interesting finding was differential expression of MADS-box genes, suggesting the existence of flower type-specific regulatory complexes in the specification of different types of flowers. The gerbera microarray was further used to profile changes in expression during petal development. Gerbera ray flower petals are large, which makes them an ideal model to study organogenesis. Six different stages were compared and specifically analysed. Expression profiles of genes related to cell structure and growth implied that during stage two, cells divide, a process which is marked by expression of histones, cyclins and tubulins. Stage 4 was found to be a transition stage between cell division and expansion and by stage 6 cells had stopped division and instead underwent expansion. Interestingly, at the last analysed stage, stage 9, when cells did not grow any more, the highest number of upregulated genes was detected. The gerbera microarray is a fully-functioning tool for large-scale studies of flower development and correlation with real-time RT-PCR results show that it is also highly sensitive and reliable. Gene expression data presented here will be a source for gene expression mining or marker gene discovery in the future studies that will be performed in the Gerbera Laboratory. The publicly available data will also serve the plant research community world-wide.