Properties of Toeplitz operators on analytic function spaces : from function symbols to distributions

Toeplitz operators are among the most important classes of concrete operators with applications to several branches of pure and applied mathematics. This doctoral thesis deals with Toeplitz operators on analytic Bergman, Bloch and Fock spaces. Usually, a Toeplitz operator is a composition of multiplication by a function and a suitable projection. The present work deals with generalizing the notion to the case where the function is replaced by a distributional symbol. Fredholm theory for Toeplitz operators with matrix-valued symbols is also considered. The subject of this thesis belongs to the areas of complex analysis, functional analysis and operator theory. This work contains five research articles. The articles one, three and four deal with finding suitable distributional classes in Bergman, Fock and Bloch spaces, respectively. In each case the symbol class to be considered turns out to be a certain weighted Sobolev-type space of distributions. The Bergman space setting is the most straightforward. When dealing with Fock spaces, some difficulties arise due to unboundedness of the complex plane and the properties of the Gaussian measure in the definition. In the Bloch-type spaces an additional logarithmic weight must be introduced. Sufficient conditions for boundedness and compactness are derived. The article two contains a portion showing that under additional assumptions, the condition for Bergman spaces is also necessary. The fifth article deals with Fredholm theory for Toeplitz operators having matrix-valued symbols. The essential spectra and index theorems are obtained with the help of Hardy space factorization and the Berezin transform, for instance. The article two also has a part dealing with matrix-valued symbols in a non-reflexive Bergman space, in which case a condition on the oscillation of the symbol (a logarithmic VMO-condition) must be added.

Functional Mimics of Glutathione Peroxidase: Bioinspired Synthetic Antioxidants

Oxidative stress is caused by an imbalance between the production of reactive oxygen species (ROS) and the biological system's ability to detoxify these reactive intermediates. Mammalian cells have elaborate antioxidant defense mechanisms to control the damaging effects of ROS. Glutathione peroxidase (GPx), a selenoenzyme, plays a key role in protecting the organism from oxidative damage by catalyzing the reduction of harmful hydroperoxides with thiol a ``catalytic triad'' with tryptophan and glutamine, which cofactors. The selenocysteine residue at the active site forms activates the selenium moiety for an efficient reduction of peroxides. After the discovery that ebselen, a synthetic organoselenium compound, mimics the catalytic activity of GPx both in vitro and in vivo, several research groups developed a number of small-molecule selenium compounds as functional mimics of GPx, either by modifying the basic structure of ebselen or by incorporating some structural features of the native enzyme. The synthetic mimics reported in the literature can be classified in three major categories: (i) cyclic selenenyl amides having a Se-N bond, (ii) diaryl diselenides, and (iii) aromatic or aliphatic monoselenides. Recent studies show that ebselen exhibits very poor GPx activity when aryl or benzylic thiols such as PhSH or BnSH are used as cosubstrates. Because the catalytic activity of each GPx mimic largely depends on the thiol cosubstrates used, the difference in the thiols causes the discrepancies observed in different studies. In this Account, we demonstrate the effect of amide and amine substituents on the GPx activity of various organoselenium compounds. The existence of strong Se ... O/N interactions in the selenenyl sulfide intermediates significantly reduces the GPx activity. These interactions facilitate an attack of thiol at selenium rather than at sulfur, leading to thiol exchange reactions that hamper the formation of catalytically active selenol. Therefore, any substituent capable of enhancing the nucleophilic attack of thiol at sulfur in the selenenyl sulfide state would enhance the antioxidant potency of organoselenium compounds. Interestingly, replacement of the sec-amide substituent by a tert-amide group leads to a weakening of Se ... 0 interactions in the selenenyl sulfide intermediates. This modification results in 10- to 20-fold enhancements in the catalytic activities. Another strategy involving the replacement of tert-amide moieties by tert-amino substituents further increases the activity by 3- to 4-fold. The most effective modification so far in benzylamine-based GPx mimics appears to be either the replacement of a tert-amino substituent by a sec-amino group or the introduction of an additional 6-methoxy group in the phenyl ring. These strategies can contribute to a remarkable enhancement in the GPx activity. In addition to enhancing catalytic activity, a change in the substituents near the selenium moiety alters the catalytic mechanisms. The mechanistic investigations of functional mimics are useful not only for understanding the complex chemistry at the active site of GPx but also for designing and synthesizing novel antioxidants and anti-inflammatory agents.

Functional outcome and health-related quality of life after traumatic brain injury in the framework of the International Classification of Functioning, Disability and Health (ICF)

Traumatic brain injury (TBI) affects people of all ages and is a cause of long-term disability. In recent years, the epidemiological patterns of TBI have been changing. TBI is a heterogeneous disorder with different forms of presentation and highly individual outcome regarding functioning and health-related quality of life (HRQoL). The meaning of disability differs from person to person based on the individual s personality, value system, past experience, and the purpose he or she sees in life. Understanding of all these viewpoints is needed in comprehensive rehabilitation. This study examines the epidemiology of TBI in Finland as well as functioning and HRQoL after TBI, and compares the subjective and objective assessments of outcome. The frame of reference is the International Classification of Functioning, Disability and Health (ICF). The subjects of Study I represent the population of Finnish TBI patients who experienced their first TBI between 1991 and 2005. The 55 Finnish subjects of Studies II and IV participated in the first wave of the international Quality of life after brain injury (QOLIBRI) validation study. The 795 subjects from six language areas of Study III formed the second wave of the QOLIBRI validation study. The average annual incidence of Finnish hospitalised TBI patients during the years 1991-2005 was 101:100 000 in patients who had TBI as the primary diagnosis and did not have a previous TBI in their medical history. Males (59.2%) were at considerably higher risk of getting a TBI than females. The most common external cause of the injury was falls in all age groups. The number of TBI patients ≥ 70 years of age increased by 59.4% while the number of inhabitants older than 70 years increased by 30.3% in the population of Finland during the same time period. The functioning of a sample of 55 persons with TBI was assessed by extracting information from the patients medical documents using the ICF checklist. The most common problems were found in the ICF components of Body Functions (b) and Activities and Participation (d). HRQoL was assessed with the QOLIBRI which showed the highest level of satisfaction on the Emotions, Physical Problems and Daily Life and Autonomy scales. The highest scores were obtained by the youngest participants and participants living independently without the help of other people, and by people who were working. The relationship between the functional outcome and HRQoL was not straightforward. The procedure of linking the QOLIBRI and the GOSE to the ICF showed that these two outcome measures cover the relevant domains of TBI patients functioning. The QOLIBRI provides the patients subjective view, while the GOSE summarises the objective elements of functioning. Our study indicates that there are certain domains of functioning that are not traditionally sufficiently documented but are important for the HRQoL of persons with TBI. This was the finding especially in the domains of interpersonal relationships, social and leisure activities, self, and the environment. Rehabilitation aims to optimize functioning and to minimize the experience of disability among people with health conditions, and it needs to be based on a comprehensive understanding of human functioning. As an integrative model, the ICF may serve as a frame of reference in achieving such an understanding.

Consumers' attitudes towards food prices

High food prices can be a barrier to healthy eating because some of the food products may be perceived as expensive. Understanding the role of price in food purchase situations is important, but only a few studies document attitudes towards expensiveness or cheapness in foods. In this thesis, the role of food price in food choice and consumers attitudes towards food prices were investigated and the aim was to measure the food price attitudes. Food price attitudes were hypothesized to have an impact on consumers willingness to pay judgements and their willingness to buy premium-priced food products. First, using qualitative data consisting of 40 thematic interviews the experiences of the expensiveness and cheapness in foods were explored by using functional food products as a target product category. Second, a Food Price Attitude Scale was developed using four quantitative surveys representing Finnish consumers (2001 N=1158; 2002 N=1156; 2004a N=1113; 2004b N=1027). Food price attitudes were confirmed to compose a multidimensional construct and consumers may perceive positive and negative attitudes towards both high and low food prices. Finnish consumers were clustered into four groups based on their food price attitudes. In the first group, 29% of respondents were negative towards high food prices and they were willing to seek low food prices, whereas respondents in another group (22%) were positive towards high food prices. Additionally, in the third group consumers (17%) were willing to pay for high quality but still looked for low food prices. In the fourth group, consumers (32%) were willing to look for low food prices, unwilling to pay for high quality, but high-priced food was appreciated if offered to others. It was found in qualitative data that consumers willingness to accept high prices in foods was connected to price fairness and to justifications. Feelings of fairness or unfairness might be a core element of food price attitudes. Using quantitative methods, it was confirmed that positive attitudes towards high food prices in terms of high quality enhanced consumers willingness to buy food products with certain benefits (e.g., a health claim). Additionally, the favourable attitude towards low food prices lowered the willingness to pay estimates. This type of tendency, however, can create a possible bias in small convenient samples. In the food price-related research, it is advisable to take into account food price attitudes as possible background variables. The Food Price Attitude Scale needs further development to increase construct validity even though, in the present study, it was shown to be a reliable measure with good predictive and discriminant validity. The theoretical and managerial implications of the results for a better understanding of the role of price in consumers food purchases are discussed.

A functional style of programming with CSP-like communication mechanisms

This paper introduces CSP-like communication mechanisms into Backus’ Functional Programming (FP) systems extended by nondeterministic constructs. Several new functionals are used to describe nondeterminism and communication in programs. The functionals union and restriction are introduced into FP systems to develop a simple algebra of programs with nondeterminism. The behaviour of other functionals proposed in this paper are characterized by the properties of union and restriction. The axiomatic semantics of communication constructs are presented. Examples show that it is possible to reason about a communicating program by first transforming it into a non-communicating program by using the axioms of communication, and then reasoning about the resulting non-communicating version of the program. It is also shown that communicating programs can be developed from non-communicating programs given as specifications by using a transformational approach.

Purification and functional characteristics of an endocellulase from Chaetomium thermophile var. coprophile

An endocellulase (1→4)-β-d-glucan 4-glucanohydrolase was isolated from the culture filtrates of Chaetomium thermophile. The enzyme was homogeneous by PAGE and SDS-PAGE. The molecular weight was 36 000 by SDS-PAGE and 38 000 by gel filtration. It was a glycoprotein. From the amino acid composition, it was found to be rich in glycine, threonine, and aspartic and glutamic acids, but contained only low proportions of histidine and sulfur-containing amino acids. It was optimally active at pH 6 and at 60°. The enzyme did not hydrolyze cellobiose and cellotriose, but hydrolyzed cello-tetraose, -pentaose, and -hexaose at comparable rates. It was specific for molecules containing β-(1→4) linkages. It showed high activity towards amorphous cellulose, and the reaction products contained cellobiose to cellopentaose, showing that it effects random cleavage of cellulose.

Functional regulation of the Neurofibromatosis 2 tumor suppressor merlin

Neurofibromatosis 2 (NF2) is an autosomal dominant disorder manifested by the formation of multiple benign tumors of the nervous system. Affected individuals typically develop bilateral vestibular schwannomas which lead to deafness and balance disorders. The syndrome is caused by inactivation of the NF2 tumor suppressor gene, and mutation or loss of the NF2 product, merlin, is sufficient for tumorigenesis in both hereditary and sporadic NF2-associated tumors. Merlin belongs to the band 4.1 superfamily of cytoskeletal proteins, which also contain the related ezrin, radixin, and moesin (ERM) proteins. The ERM members provide a link between the cell cytoskeleton and membrane by connecting membrane-associated proteins to actin filaments. By stabilizing complexes in the cell cortex, the ERMs modulate morphology, growth, and migration of cells. Despite their structural homology, overlapping subcellular distribution, direct molecular association, and partial overlap of molecular interactions, merlin and ezrin exert opposite effects on cell proliferation. Merlin suppresses cell proliferation, whereas ezrin expression is linked to oncogenic activity. We hypothesized that the regions which differ between the proteins might explain merlin s specificity as a tumor suppressor. We therefore analyzed the regions, which are most diverse between merlin and ezrin; the N-terminal tail and the C-terminus. To determine the properties of the C-terminal region, we studied the two most predominant merlin isoforms together with truncation variants similar to those found in patients. We also focused on the evolutionally conserved C-terminal residues, E545-E547, that harbor disease causing mutations in its corresponding DNA sequence. In addition to inhibiting cell proliferation, merlin regulates cytoskeletal organization. The morphogenic properties of merlin may play a role in tumor suppression, since patient-derived tumor cells demonstrate cytoskeletal abnormalities. We analyzed the mechanisms of merlin-induced extension formation and determined that the C-terminal region of amino acids 538-568 is particularly important for the morphogenic activity. We also characterized the role of C-terminal merlin residues in the regulation of proliferation, phosphorylation, and intramolecular associations. In contrast to previous reports, we demonstrated that both merlin isoforms are able to suppress cell proliferation, whereas C-terminally mutated merlin constructs showed reduced growth inhibition. Phosphorylation serves as a mechanism to regulate the tumor suppressive activity of merlin. The C-terminal serine 518 is phosphorylated in response to both p21-activated kinase (PAK) and protein kinase A (PKA), which inactivates the growth inhibitory function of merlin. However, at least three differentially phosphorylated forms of the protein exist. In this study we demonstrated that also the N-terminus of merlin is phosphorylated by AGC kinases, and that both PKA and Akt phosphorylate merlin at serine 10 (S10). We evaluated the impact of this N-terminal tail phosphorylation, and showed that the phosphorylation state of S10 is an important regulator of merlin s ability to modulate cytoskeletal organization but also regulates the stability of the protein. In summary, this study describes the functional effect of merlin specific regions. We demonstrate that both S10 in the N-terminal tail and residues E545-E547 in the C-terminus are essential for merlin activity and function.

Hemiorchidectomy leads to dramatic and immediate alterations in pituitary follicle-stimulating hormone secretion and the functional activity of the remaining testis in the adult male bonnet monkey (Macaca radiata)

The aim of the present study was to examine the effect of hemiorchidectomy (HO) on serum FSH, LH, testosterone (T), and inhibin (INH) concentrations as well as on the testicular volume (TV) and on changes in the kinetics of germ cell turnovers in the remaining testis of adult male bonnet monkeys. Blood samples collected at 2200 h at various times before and after HO and testicular biopsies obtained at different periods were subjected to hormone analysis and DNA flow cytometry. Though serum T levels were lowered (p < 0.05) at 12 h after HO, T levels rapidly returned to intact control concentrations by Day 5. While serum LH remained unaltered, serum FSH increased markedly within 2 days of HO and remained significantly (p < 0.05) elevated over the next 90 days. Though serum INH showed a significant decrease (p < 0.05) by 15 min of HO, it returned to approximately 80% of intact levels within one week. The TV of the remaining testis showed maximal increment by Day 30 (p < 0.05) of HO. DNA flow cytometric analysis 24 days after HO showed increases (p < 0.05) in spermatogonia (2C) and primary spermatocytes (4C). These cell types by Day 45 had transformed to round (1C) and elongate (HC) (by 38%, p < 0.001) spermatids. Overall spermatogenesis (conversion of 2C to 1C and HC) showed significant enhancement at Days 110 and 175, suggesting that the spurt in spermatogenic activity is not confined to a single spermatogenic cycle.

Functional Analysis of an Acid Adaptive DNA Adenine Methyltransferase from Helicobacter pylori 26695

HP0593 DNA-(N-6-adenine)-methyltransferase (HP0593 MTase) is a member of a Type III restriction-modification system in Helicobacter pylori strain 26695. HP0593 MTase has been cloned, overexpressed and purified heterologously in Escherichia coli. The recognition sequence of the purified MTase was determined as 5'-GCAG-3' and the site of methylation was found to be adenine. The activity of HP0593 MTase was found to be optimal at pH 5.5. This is a unique property in context of natural adaptation of H. pylori in its acidic niche. Dot-blot assay using antibodies that react specifically with DNA containing m6A modification confirmed that HP0593 MTase is an adenine-specific MTase. HP0593 MTase occurred as both monomer and dimer in solution as determined by gel-filtration chromatography and chemical-crosslinking studies. The nonlinear dependence of methylation activity on enzyme concentration indicated that more than one molecule of enzyme was required for its activity. Analysis of initial velocity with AdoMet as a substrate showed that two molecules of AdoMet bind to HP0593 MTase, which is the first example in case of Type III MTases. Interestingly, metal ion cofactors such as Co2+, Mn2+, and also Mg2+ stimulated the HP0593 MTase activity. Preincubation and isotope partitioning analyses clearly indicated that HP0593 MTase-DNA complex is catalytically competent, and suggested that DNA binds to the MTase first followed by AdoMet. HP0593 MTase shows a distributive mechanism of methylation on DNA having more than one recognition site. Considering the occurrence of GCAG sequence in the potential promoter regions of physiologically important genes in H. pylori, our results provide impetus for exploring the role of this DNA MTase in the cellular processes of H. pylori.

DNA Binding, Coprotease, and Strand Exchange Activities of Mycobacterial RecA Proteins: Implications for Functional Diversity among RecA Nucleoprotein Filaments

One of the fundamental questions concerning homologous recombination is how RecA or its homologues recognize several DNA sequences with high affinity and catalyze all the diverse biological activities. In this study, we show that the extent of single-stranded DNA binding and strand exchange (SE) promoted by mycobacterial RecA proteins with DNA substrates having various degrees of GC content was comparable with that observed for Escherichia coli RecA. However, the rate and extent of SE promoted by these recombinases showed a strong negative correlation with increasing amounts of sequence divergence embedded at random across the length of the donor strand. Conversely, a positive correlation was seen between SE efficiency and the degree of sequence divergence in the recipient duplex DNA. The extent of heteroduplex formation was not significantly affected when both the pairing partners contained various degrees of sequence divergence, although there was a moderate decrease in the case of mycobacterial RecA proteins with substrates containing larger amounts of sequence divergence. Whereas a high GC content had no discernible effect on E. coli RecA coprotease activity, a negative correlation was apparent between mycobacterial RecA proteins and GC content. We further show clear differences in the extent of SE promoted by E. coli and mycobacterial RecA proteins in the presence of a wide range of ATP:ADP ratios. Taken together, our findings disclose the existence of functional diversity among E. coli and mycobacterial RecA nucleoprotein filaments, and the milieu of sequence divergence (i.e., in the donor or recipient) exerts differential effects on heteroduplex formation, which has implications for the emergence of new genetic variants.

Glass Transition in the Density Functional Theory of Freezing

A mean-field description of the glass transition in the hard-sphere system is obtained by numerically locating "glassy" minima of a model free-energy functional. These minima, characterized by inhomogeneous but aperiodic density distributions, appear as the average density is increased above the value at which equilibrium crystallization takes place. Investigations of the density distribution and local bond-orientational order at these minima yield results similar to those obtained from simulations.

Diversity in Functional Organization of Class I and Class II Biotin Protein Ligase

The cell envelope of Mycobacterium tuberculosis (M. tuberculosis) is composed of a variety of lipids including mycolic acids, sulpholipids, lipoarabinomannans, etc., which impart rigidity crucial for its survival and pathogenesis. Acyl CoA carboxylase (ACC) provides malonyl-CoA and methylmalonyl-CoA, committed precursors for fatty acid and essential for mycolic acid synthesis respectively. Biotin Protein Ligase (BPL/BirA) activates apo-biotin carboxyl carrier protein (BCCP) by biotinylating it to an active holo-BCCP. A minimal peptide (Schatz), an efficient substrate for Escherichia coli BirA, failed to serve as substrate for M. tuberculosis Biotin Protein Ligase (MtBPL). MtBPL specifically biotinylates homologous BCCP domain, MtBCCP87, but not EcBCCP87. This is a unique feature of MtBPL as EcBirA lacks such a stringent substrate specificity. This feature is also reflected in the lack of self/promiscuous biotinylation by MtBPL. The N-terminus/HTH domain of EcBirA has the selfbiotinable lysine residue that is inhibited in the presence of Schatz peptide, a peptide designed to act as a universal acceptor for EcBirA. This suggests that when biotin is limiting, EcBirA preferentially catalyzes, biotinylation of BCCP over selfbiotinylation. R118G mutant of EcBirA showed enhanced self and promiscuous biotinylation but its homologue, R69A MtBPL did not exhibit these properties. The catalytic domain of MtBPL was characterized further by limited proteolysis. Holo-MtBPL is protected from proteolysis by biotinyl-59 AMP, an intermediate of MtBPL catalyzed reaction. In contrast, apo-MtBPL is completely digested by trypsin within 20 min of co-incubation. Substrate selectivity and inability to promote self biotinylation are exquisite features of MtBPL and are a consequence of the unique molecular mechanism of an enzyme adapted for the high turnover of fatty acid biosynthesis.

Can one electrochemically measure the statistical morphology of a rough electrode

We have developed a theory for an electrochemical way of measuring the statistical properties of a nonfractally rough electrode. We obtained the expression for the current transient on a rough electrode which shows three times regions: short and long time limits and the transition region between them. The expressions for these time ranges are exploited to extract morphological information about the surface roughness. In the short and long time regimes, we extract information regarding various morphological features like the roughness factor, average roughness, curvature, correlation length, dimensionality of roughness, and polynomial approximation for the correlation function. The formulas for the surface structure factors (the measure of surface roughness) of rough surfaces in terms of measured reversible and diffusion-limited current transients are also obtained. Finally, we explore the feasibility of making such measurements.