Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

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.

IP Mobility in Wireless Operator Networks

Wireless network access is gaining increased heterogeneity in terms of the types of IP capable access technologies. The access network heterogeneity is an outcome of incremental and evolutionary approach of building new infrastructure. The recent success of multi-radio terminals drives both building a new infrastructure and implicit deployment of heterogeneous access networks. Typically there is no economical reason to replace the existing infrastructure when building a new one. The gradual migration phase usually takes several years. IP-based mobility across different access networks may involve both horizontal and vertical handovers. Depending on the networking environment, the mobile terminal may be attached to the network through multiple access technologies. Consequently, the terminal may send and receive packets through multiple networks simultaneously. This dissertation addresses the introduction of IP Mobility paradigm into the existing mobile operator network infrastructure that have not originally been designed for multi-access and IP Mobility. We propose a model for the future wireless networking and roaming architecture that does not require revolutionary technology changes and can be deployed without unnecessary complexity. The model proposes a clear separation of operator roles: (i) access operator, (ii) service operator, and (iii) inter-connection and roaming provider. The separation allows each type of an operator to have their own development path and business models without artificial bindings with each other. We also propose minimum requirements for the new model. We present the state of the art of IP Mobility. We also present results of standardization efforts in IP-based wireless architectures. Finally, we present experimentation results of IP-level mobility in various wireless operator deployments.

Electron and proton transfer in NADH:ubiquinone oxidoreductase (Complex I) from Escherichia coli

Cells of every living organism on our planet − bacterium, plant or animal − are organized in such a way that despite differences in structure and function they utilize the same metabolic energy represented by electrochemical proton gradient across a membrane. This gradient of protons is generated by the series of membrane bound multisubunit proteins, Complex I, II, III and IV, organized in so-called respiratory or electron transport chain. In the eukaryotic cell it locates in the inner mitochondrial membrane while in the bacterial cell it locates in the cytoplasmic membrane. The function of the respiratory chain is to accept electrons from NADH and ubiquinol and transfer them to oxygen resulting in the formation of water. The free energy released upon these redox reactions is converted by respiratory enzymes into an electrochemical proton gradient, which is used for synthesis of ATP as well as for many other energy dependent processes. This thesis is focused on studies of the first member of the respiratory chain − NADH:ubiquinone oxidoreductase or Complex I. This enzyme has a boot-shape structure with hydrophilic and hydrophobic domains, the former of which has all redox groups of the protein, the flavin and eight to nine iron-sulfur clusters. Complex I serves as a proton pump coupling transfer of two electrons from NADH to ubiquinone to the translocation of four protons across the membrane. So far the mechanism of energy transduction by Complex I is unknown. In the present study we applied a set of different methods to study the electron and proton transfer reactions in Complex I from Escherichia coli. The main achievement was the experiment that showed that the electron transfer through the hydrophilic domain of Complex I is unlikely to be coupled to proton transfer directly or to conformational changes in the protein. In this work for the first time properties of all redox centers of Complex I were characterized in the intact purified bacterial enzyme. We also probed the role of several conserved amino acid residues in the electron transfer of Complex I. Finally, we found that highly conserved amino acid residues in several membrane subunits form a common pattern with a very prominent feature – the presence of a few lysines within the membrane. Based on the experimental data, we suggested a tentative principle which may govern the redox-coupled proton pumping in Complex I.

Electron cryo-microscopy studies of bacteriophage phi8 and archaeal virus SH1

Symmetry is a key principle in viral structures, especially the protein capsid shells. However, symmetry mismatches are very common, and often correlate with dynamic functionality of biological significance. The three-dimensional structures of two isometric viruses, bacteriophage phi8 and the archaeal virus SH1 were reconstructed using electron cryo-microscopy. Two image reconstruction methods were used: the classical icosahedral method yielded high resolution models for the symmetrical parts of the structures, and a novel asymmetric in-situ reconstruction method allowed us to resolve the symmetry mismatches at the vertices of the viruses. Evidence was found that the hexameric packaging enzyme at the vertices of phi8 does not rotate relative to the capsid. The large two-fold symmetric spikes of SH1 were found not to be responsible for infectivity. Both virus structures provided insight into the evolution of viruses. Comparison of the phi8 polymerase complex capsid with those of phi6 and other dsRNA viruses suggests that the quaternary structure in dsRNA bacteriophages differs from other dsRNA viruses. SH1 is unusual because there are two major types of capsomers building up the capsid, both of which seem to be composed mainly of single beta-barrels perpendicular to the capsid surface. This indicates that the beta-barrel may be ancestral to the double beta-barrel fold.

Molecular details of phage phi6 RNA-dependent RNA synthesis

For most RNA viruses RNA-dependent RNA polymerases (RdRPs) encoded by the virus are responsible for the entire RNA metabolism. Thus, RdRPs are critical components in the viral life cycle. However, it is not fully understood how these important enzymes function during viral replication. Double-stranded RNA (dsRNA) viruses perform the synthesis of their RNA genome within a proteinacous viral particle containing an RdRP as a minor constituent. The phi6 bacteriophage is the best-studied dsRNA virus, providing an excellent background for studies of its RNA synthesis. The purified recombinant phi6 RdRP is highly active in vitro and it possesses both RNA replication and transcription activities. The crystal structure of the phi6 polymerase, solved in complex with a number of ligands, provides a working model for detailed in vitro studies of RNA-dependent RNA polymerization. In this thesis, the primer-independent initiation of the phi6 RdRP was studied in vitro using biochemical and structural methods. A C-terminal, four-amino-acid-long loop protruding into the central cavity of the phi6 RdRP has been suggested to stabilize the incoming nucleotides of the initiation complex formation through stacking interactions. A similar structural element has been found from several other viral RdRPs. In this thesis, this so-called initiation platform loop was subjected to site-directed mutagenesis to address its role in the initiation. It was found that the initiation mode of the mutants is primer-dependent, requiring either an oligonucleotide primer or a back-priming initiation mechanism for the RNA synthesis. The crystal structure of a mutant RdRP with altered initiation platform revealed a set of contacts important for primer-independent initiation. Since phi6 RdRP is structurally and functionally homologous to several viral RdRPs, among them the hepatitis C virus RdRP, these results provide further general insight to understand primer-independent initiation. In this study it is demonstrated that manganese phasing could be used as a practical tool for solving structures of large proteins with a bound manganese ion. The phi6 RdRP was used as a case study to obtain phases for crystallographic analysis. Manganese ions are naturally bound to the phi6 RdRP at the palm domain of the enzyme. In a crystallographic experiment, X-ray diffraction data from a phi6 RdRP crystal were collected at a wavelength of 1.89 Å, which is the K edge of manganese. With this data an automatically built model of the core region of the protein could be obtained. Finally, in this work terminal nucleotidyl transferase (TNTase) activity of the phi6 RdRP was documented in the isolated polymerase as well as in the viral particle. This is the first time that such an activity has been reported in a polymerase of a dsRNA virus. The phi6 RdRP used uridine triphosphates as the sole substrate in a TNTase reaction but could accept several heterologous templates. The RdRP was able to add one or a few non-templated nucleotides to the 3' end of the single- or double-stranded RNA substrate. Based on the results on particle-mediated TNTase activity and previous structural information of the polymerase, a model for termination of the RNA-dependent RNA synthesis is suggested in this thesis.

Lipid-Containing Icosahedral dsDNA Bacteriophages: Entry, Exit and Structure

In this thesis three icosahedral lipid-containing double-stranded (ds) deoxyribonucleic acid (DNA) bacteriophages have been studied: PRD1, Bam35 and P23-77. The work focuses on the entry, exit and structure of the viruses. PRD1 is the type member of the Tectiviridae family, infecting a variety of Gram-negative bacteria. The PRD1 receptor binding complex, consisting of the penton protein P31, the spike protein P5 and the receptor binding protein P2 recognizes a specific receptor on the host surface. In this study we found that the transmembrane protein P16 has an important stabilization function as the fourth member of the receptor binding complex and protein P16 may have a role in the formation of a tubular membrane structure, which is needed in the ejection of the genome into the cell. Phage Bam35 (Tectiviridae), which infects Gram-positive hosts, has been earlier found to resemble PRD1 in morphology and genome organization The uncharacterized early and late events in the Bam35 life cycle were studied by electrochemical methods. Physiological changes in the beginning of the infection were found to be similar in both lysogenic and nonlysogenic cell lines, Bam35 inducing a temporal decrease of membrane voltage and K+ efflux. At the end of the infection cycle physiological changes were observed only in the nonlysogenic cell line. The strong K+ efflux 40 min after infection and the induced premature cell lysis propose that Bam35 has a similar holin-endolysin lysis system to that of PRD1. Thermophilic icosahedral dsDNA Thermus phages P23-65H, P23-72 and P23-77 have been proposed to belong to the Tectiviridae family. In this study these phages were compared to each other. Analysis of structural protein patterns and stability revealed these phages to be very similar but not identical. The most stable of the studied viruses, P23-77, was further analyzed in more detail. Cryo-electron microscopy and three-dimensional image reconstruction was used to determine the structure of virus to 14 Å resolution. Results of thin layer chromatography for neutral lipids together with analysis of the three dimensional reconstruction of P23-77 virus particle revealed the presence of an internal lipid membrane. The overall capsid architecture of P23-77 is similar to PRD1 and Bam35, but most closely it resembles the structure of the capsid of archaeal virus SH1. This complicates the classification of dsDNA, internal lipid-containing icosahedral viruses.

Molecular mechanisms of bacteriophage phi6 RNA-dependent RNA polymerase and its utilization in biotechnology

Double-stranded RNA (dsRNA) viruses encode only a single protein species that contains RNA-dependent RNA polymerase (RdRP) motifs. This protein is a central component in the life cycle of a dsRNA virus, carrying out both RNA transcription and replication. The architecture of viral RdRPs resembles that of a 'cupped right hand' with fingers, palm and thumb domains. Those applying de novo initiation have additional structural features, including a flexible C-terminal domain that constitutes the priming platform. Moreover, viral RdRPs must be able to interact with the incoming 3'-terminus of the template and position it so that a productive binary complex is formed. Bacteriophage phi6 of the Cystoviridae family is to date one of the best studied dsRNA viruses. The purified recombinant phi6 RdRP is highly active in vitro and possesses both RNA replication and transcription activities. The extensive biochemical observations and the atomic level crystal structure of the phi6 RdRP provides an excellent platform for in-depth studies of RNA replication in vitro. In this thesis, targeted structure-based mutagenesis, enzymatic assays and molecular mapping of phi6 RdRP and its RNA were used to elucidate the formation of productive RNA-polymerase binary complexes. The positively charged rim of the template tunnel was shown to have a significant role in the engagement of highly structured ssRNA molecules, whereas specific interactions further down in the template tunnel promote ssRNA entry to the catalytic site. This work demonstrated that by aiding the formation of a stable binary complex with optimized RNA templates, the overall polymerization activity of the phi6 RdRP can be greatly enhanced. Furthermore, proteolyzed phi6 RdRPs that possess a nick in the polypeptide chain at the hinge region, which is part of the extended loop, were better suited for catalysis at higher temperatures whilst favouring back-primed initiation. The clipped C-terminus remains associated with the main body of the polymerase and the hinge region, although structurally disordered, is involved in the control of C-terminal domain displacement. The accumulated knowhow on bacteriophage phi6 was utilized in the development of two technologies for the production of dsRNA: (i) an in vitro system that combines the T7 RNA polymerase and the phi6 RdRP to generate dsRNA molecules of practically unlimited length, and (ii) an in vivo RNA replication system based on restricted infection with phi6 polymerase complexes in bacterial cells to produce virtually unlimited amounts of dsRNA. The pools of small interfering RNAs derived from dsRNA produced by these systems were validated and shown to efficiently decrease the expression of both exogenous and endogenous targets.

Major histocompatibility complex and coronary artery disease: Special emphasis on Chlamydia pneumoniae, and periodontitis

Most of the genes in the MHC region are involveed in adaptive and innate immunity, with essential function in inflammatory reactions and in protection against infections. These genes might serve as a candidate region for infection and inflammation associated diseases. CAD is an inflammatory disease. The present set of studies was performed to assess whether the MHC region harbors genetic markers for CAD, and whether these genetic markers explain the CAD risk factors: e.g., C. pneumoniae, periodontitis, and periodontal pathogens. Study I was performed using two separate patient materials and age- and sex-matched healthy controls, categorizing them into two independent studies: the HTx and ACS studies. Both studies consistently showed the HLA-A3– B35– DR1 (35 ancestral haplotype) haplotype as a susceptible MHC genetic marker for CAD. HLA-DR1 alone was associated not only with CAD, but also with CAD risk factor diseases, e.g., diabetes mellitus, and hyperlipidemia. The ACS study further showed the HLA-B*07 and -DRB1*15 -related haplotype as a protective MHC haplotype for CAD. Study II showed that patients with CAD showed signs of chronic C. pneumoniae infection when compared to age- and sex-matched healthy controls. HLA-B*35 or -related haplotypes associated with the C. pneumoniae infection markers. Among these haplotype carriers, males and smokers associated with elevated C. pneumoniae infection markers. Study III showed that CAD patients with periodontitis had elevated serum markers of P. gingivalis and occurrence of the pathogen in saliva. LTA+496C strongly associated with periodontitis, while HLA-DRB1*01 with periodontitis and with the elevated serum antibodies of P. gingivalis. Study IV showed that the increased level of C3/C4 ratio was a new risk factor and was associated with recurrent cardiovascular end-points. The increased C3 and decreased C4 concentrations in serum explained the increased level of the C3/C4 ratio. Both the higher than cut-off value (4.53) and the highest quartile of the C3/C4 ratio were also associated with worst survival, increased end-points, and C4 null alleles. The presence of C4 null alleles associated with decreased serum C4 concentration, and increased C3/C4 ratio. In conclusion, the present studies show that the CAD susceptibility haplotype (HLA-A3− B35− DR1 -related haplotypes, Study I) partially explains the development of CAD in patients possessing several recognized and novel risk factors: diabetes mellitus, increased LDL, smoking, C4B*Q0, C. pneumnoiae, periodontitis, P. gingivalis, and complement C3/C4 ratio (Study II, III, and IV).

Complex trait of acute pancreatitis : Studies of candidate genes and adipokines

Acute pancreatitis (AP) is a common disease. Mild disease resolves spontaneously in a few days. Severe forms of the disease can lead to local complications, necrosis, and abscesses in and around the pancreas. Systemic inflammation in severe AP is associated with distant organ failures. The aim of this study is to identify genetically determined prognostic factors involved in the clinical features of AP. The study employs a candidate-gene approach, and the genes are involved in trysinogen activation in the initiation phase of the disease, as well as in the systemic inflammation as the disease proceeds. The last study examines adipokines, fat-derived hormones characterized with the capacity to modify inflammation. SPINK 1 is a gene coding trypsin activation inhibitor. Mutations N34S and P55N were determined by minisequencing methods in 371 AP patients and in 459 controls. The mutation N34S was more common in AP patients (7.8%) than in controls (2.6%). This suggests that SPINK 1 gene mutation N34S is a risk factor for AP. In the fourth study, in 12 matched pairs of patients with severe and mild AP, levels of adipokines, adiponectin, and leptin were evaluated. Plasma adipokine levels did not differ between patients with mild and severe AP. The results suggest that in AP, adipokine plasma levels are not factors predisposing to organ failures. This study identified the SPINK 1 mutation N34S to be a risk factor for AP in the general population. As AP is a multifactorial disease, and extensive genetic heterogeneity is likely, further identification of genetic factors in the disease requires larger future studies with more advanced genetic study models. Further identification of the patient characteristics associated with organ failures offers another direction of the study to achieve more detailed understanding of the severe form of AP.