Homogeneous model theory of metric structures

This thesis studies homogeneous classes of complete metric spaces. Over the past few decades model theory has been extended to cover a variety of nonelementary frameworks. Shelah introduced the abstact elementary classes (AEC) in the 1980s as a common framework for the study of nonelementary classes. Another direction of extension has been the development of model theory for metric structures. This thesis takes a step in the direction of combining these two by introducing an AEC-like setting for studying metric structures. To find balance between generality and the possibility to develop stability theoretic tools, we work in a homogeneous context, thus extending the usual compact approach. The homogeneous context enables the application of stability theoretic tools developed in discrete homogeneous model theory. Using these we prove categoricity transfer theorems for homogeneous metric structures with respect to isometric isomorphisms. We also show how generalized isomorphisms can be added to the class, giving a model theoretic approach to, e.g., Banach space isomorphisms or operator approximations. The novelty is the built-in treatment of these generalized isomorphisms making, e.g., stability up to perturbation the natural stability notion. With respect to these generalized isomorphisms we develop a notion of independence. It behaves well already for structures which are omega-stable up to perturbation and coincides with the one from classical homogeneous model theory over saturated enough models. We also introduce a notion of isolation and prove dominance for it.

Finitary Abstract Elementary Classes

The research in model theory has extended from the study of elementary classes to non-elementary classes, i.e. to classes which are not completely axiomatizable in elementary logic. The main theme has been the attempt to generalize tools from elementary stability theory to cover more applications arising in other branches of mathematics. In this doctoral thesis we introduce finitary abstract elementary classes, a non-elementary framework of model theory. These classes are a special case of abstract elementary classes (AEC), introduced by Saharon Shelah in the 1980's. We have collected a set of properties for classes of structures, which enable us to develop a 'geometric' approach to stability theory, including an independence calculus, in a very general framework. The thesis studies AEC's with amalgamation, joint embedding, arbitrarily large models, countable Löwenheim-Skolem number and finite character. The novel idea is the property of finite character, which enables the use of a notion of a weak type instead of the usual Galois type. Notions of simplicity, superstability, Lascar strong type, primary model and U-rank are inroduced for finitary classes. A categoricity transfer result is proved for simple, tame finitary classes: categoricity in any uncountable cardinal transfers upwards and to all cardinals above the Hanf number. Unlike the previous categoricity transfer results of equal generality the theorem does not assume the categoricity cardinal being a successor. The thesis consists of three independent papers. All three papers are joint work with Tapani Hyttinen.

Mathematical models on the impact of noise and dyadic molecular structures on the properties of a cardiac myocyte

In cardiac myocytes (heart muscle cells), coupling of electric signal known as the action potential to contraction of the heart depends crucially on calcium-induced calcium release (CICR) in a microdomain known as the dyad. During CICR, the peak number of free calcium ions (Ca) present in the dyad is small, typically estimated to be within range 1-100. Since the free Ca ions mediate CICR, noise in Ca signaling due to the small number of free calcium ions influences Excitation-Contraction (EC) coupling gain. Noise in Ca signaling is only one noise type influencing cardiac myocytes, e.g., ion channels playing a central role in action potential propagation are stochastic machines, each of which gates more or less randomly, which produces gating noise present in membrane currents. How various noise sources influence macroscopic properties of a myocyte, how noise is attenuated and taken advantage of are largely open questions. In this thesis, the impact of noise on CICR, EC coupling and, more generally, macroscopic properties of a cardiac myocyte is investigated at multiple levels of detail using mathematical models. Complementarily to the investigation of the impact of noise on CICR, computationally-efficient yet spatially-detailed models of CICR are developed. The results of this thesis show that (1) gating noise due to the high-activity mode of L-type calcium channels playing a major role in CICR may induce early after-depolarizations associated with polymorphic tachycardia, which is a frequent precursor to sudden cardiac death in heart failure patients; (2) an increased level of voltage noise typically increases action potential duration and it skews distribution of action potential durations toward long durations in cardiac myocytes; and that (3) while a small number of Ca ions mediate CICR, Excitation-Contraction coupling is robust against this noise source, partly due to the shape of ryanodine receptor protein structures present in the cardiac dyad.

Tannakian Formalism Applied to the Category of Mixed Hodge Structures

Many problems in analysis have been solved using the theory of Hodge structures. P. Deligne started to treat these structures in a categorical way. Following him, we introduce the categories of mixed real and complex Hodge structures. Category of mixed Hodge structures over the field of real or complex numbers is a rigid abelian tensor category, and in fact, a neutral Tannakian category. Therefore it is equivalent to the category of representations of an affine group scheme. The direct sums of pure Hodge structures of different weights over real or complex numbers can be realized as a representation of the torus group, whose complex points is the Cartesian product of two punctured complex planes. Mixed Hodge structures turn out to consist of information of a direct sum of pure Hodge structures of different weights and a nilpotent automorphism. Therefore mixed Hodge structures correspond to the representations of certain semidirect product of a nilpotent group and the torus group acting on it.

Mining Sequential Data – in Search of Segmental Structures

Segmentation is a data mining technique yielding simplified representations of sequences of ordered points. A sequence is divided into some number of homogeneous blocks, and all points within a segment are described by a single value. The focus in this thesis is on piecewise-constant segments, where the most likely description for each segment and the most likely segmentation into some number of blocks can be computed efficiently. Representing sequences as segmentations is useful in, e.g., storage and indexing tasks in sequence databases, and segmentation can be used as a tool in learning about the structure of a given sequence. The discussion in this thesis begins with basic questions related to segmentation analysis, such as choosing the number of segments, and evaluating the obtained segmentations. Standard model selection techniques are shown to perform well for the sequence segmentation task. Segmentation evaluation is proposed with respect to a known segmentation structure. Applying segmentation on certain features of a sequence is shown to yield segmentations that are significantly close to the known underlying structure. Two extensions to the basic segmentation framework are introduced: unimodal segmentation and basis segmentation. The former is concerned with segmentations where the segment descriptions first increase and then decrease, and the latter with the interplay between different dimensions and segments in the sequence. These problems are formally defined and algorithms for solving them are provided and analyzed. Practical applications for segmentation techniques include time series and data stream analysis, text analysis, and biological sequence analysis. In this thesis segmentation applications are demonstrated in analyzing genomic sequences.

Naiset ja naisten puheet kirkolliskokouksen naispappeuskeskusteluissa vuosina 1974-1987

Women and women s words in discussions about the ordination of women in the General Synod between 1974 and 1987. In 1986, the General Synod of the Evangelical Lutheran Church in Finland approved the ordination of women. Prior to that decision, a considerable amount of discussion and debate took place about this renewal in both the Synod and the general public. The different points of view had divided the church and the people, and had placed the church under pressure to resolve the issue as soon as possible. At the same time, the changing climate in people s attitudes toward the church and the changing position of women in society clearly weighed in on this matter. The research material consists of the speeches about the ordination of women given by the women representatives in the General Synod of the Evangelical Lutheran Church in Finland between the years 1974 and 1987. The aim is to determine why these representatives wanted to ordain women as pastors, what kind of women pastors they wanted to have in the congregations, and what they wanted to change in the church through this renewal. The basic methods of the analysis include discourse analysis as well as the new rhetorics and some concepts used by Pierre Bourdieu. A framework, which I named rhetoric patterning, was developed to interpret the results. This framework has facilitated the identification of three effective discourses in the studied argumentation: the folk church discourse, the pastor image discourse and the church image discourse. According to the opinions of the women representatives, the concept of change turned out to be a very decisive factor as the church sought a way to reach its members. To maintain a good and modern image seemed very important for the church to be able to perform its task in the modern era. The women representatives presented the situation of the church in terms of contextual theology and took seriously the membership of all those baptized into the church. They were therefore ready to take into account the opinion of all church members. The problem was that even though the ordination of women was established, the fixed mental schemes of the people and the strong power structures of the church remained untouched. Women were allowed into a new area of church life, but with certain publicly pronounced and unconsciously recognized conditions. Did this change really mean greater equality between women and men, as was intended? Key words: ordination of women, General Synod, contextualization, discourse analysis.

Regional Integration and the State : The Changing Nature of Sovereignty in Southern Africa and Europe

The study explores the role of the state in regional integration processes. The question is approached through theoretical discussion and two case-studies - SADC (Southern African Development Community) and the EU. The main research question of the study is, what are the possibilities and problems of the integration process in Southern Africa and how do they differ from the possibilities and problems of the integration process in Europe. The undelrying question of the study is why do states decide to participate in an integration process where they have to limit their sovereignty. Review of the theoretical discussion of the integration studies shows that the integration process is affected by several factors on different levels of the international system. But the state plays a central role in integration processes - integration processes are inititated and carried on by the participatig states. The European integration process shows that the interests of the state can change over time. At the beginning of the integration process, the objective was to strengthen participating states. Later EU member states have decided that it is in their interest to deepen the process even if it has meant limitation of their sovereignty. The determinant factor has been that the member states have considered it to be in their interst to deepen the process. In Southern Africa the integration process is only at the beginning. SADC aims to establish a free trade area by 2008. The biggest challenge is how to implement the integration process so that it benefits all member states in a region that is economically dominated by South Africa. In practice this can be achieved through establishment of corrective mechanisms, which ensure equitable distribution of benefits. This would require deeper integration and South Africa to adapt responsibility towards its regional partners. African integration processes in general have not been as successful as for example the EU. African states have been reluctant to limit their sovereignty in favour of regional organisations.This can be explained by the differences between European and African states. The EU member states have been democracies while African states have been characterised by concentration of power in the executive branch. Furthermore the political systems in Africa have been characterised by vertical clientelist reltionships. As a result it has not been in the interest of the political elite to limit the state sovereignty in favour of regional organisations. In recent years SADC has been relatively succesful in its integration process and reforms, but a lot remains to be done before the implementation of the free trade area can be succesful. The institutional structure and treaties of SADC differ from the structures of the EU. Member states are the main actors of the integration processes. Their differences are reflected in the process and produce different kinds of integration in different parts of the world.

Cellular Membranes as a Playground for Semliki Forest Virus Replication Complex

All positive-strand RNA viruses utilize cellular membranes for the assembly of their replication complexes, which results in extensive membrane modification in infected host cells. These alterations act as structural and functional scaffolds for RNA replication, providing protection for the viral double-stranded RNA against host defences. It is known that different positive-strand RNA viruses alter different cellular membranes. However, the origin of the targeted membranes, the mechanisms that direct replication proteins to specific membranes and the steps in the formation of the membrane bound replication complex are not completely understood. Alphaviruses (including Semliki Forest virus, SFV), members of family Togaviridae, replicate their RNA in association with membranes derived from the endosomal and lysosomal compartment, inducing membrane invaginations called spherules. Spherule structures have been shown to be the specific sites for RNA synthesis. Four replication proteins, nsP1-nsP4, are translated as a polyprotein (P1234) which is processed autocatalytically and gives rise to a membrane-bound replication complex. Membrane binding is mediated via nsP1 which possesses an amphipathic α-helix (binding peptide) in the central region of the protein. The aim of this thesis was to characterize the association of the SFV replication complex with cellular membranes and the modification of the membranes during virus infection. Therefore, it was necessary to set up the system for determining which viral components are needed for inducing the spherules. In addition, the targeting of the replication complex, the formation site of the spherules and their intracellular trafficking were studied in detail. The results of current work demonstrate that mutations in the binding peptide region of nsP1 are lethal for virus replication and change the localization of the polyprotein precursor P123. The replication complex is first targeted to the plasma membrane where membrane invaginations, spherules, are induced. Using a specific regulated endocytosis event the spherules are internalized from the plasma membrane in neutral carrier vesicles and transported via an actin-and microtubule-dependent manner to the pericentriolar area. Homotypic fusions and fusions with pre-existing acidic organelles lead to the maturation of previously described cytopathic vacuoles with hundreds of spherules on their limiting membranes. This work provides new insights into the membrane binding mechanism of SFV replication complex and its role in the virus life cycle. Development of plasmid-driven system for studying the formation of the replication complex described in this thesis allows various applications to address different steps in SFV life cycle and virus-host interactions in the future. This trans-replication system could be applied for many different viruses. In addition, the current work brings up new aspects of membranes and cellular components involved in SFV replication leading to further understanding in the formation and dynamics of the membrane-associated replication complex.

Characterization of the molecular components and function of BARE-1, Hin-Mu and Mu transposition machineries

Transposable elements, transposons, are discrete DNA segments that are able to move or copy themselves from one locus to another within or between their host genome(s) without a requirement for DNA homology. They are abundant residents in virtually all the genomes studied, for instance, the genomic portion of TEs is approximately 3% in Saccharomyces cerevisiae, 45% in humans, and apparently more than 70% in some plant genomes such as maize and barley. Transposons plays essential role in genome evolution, in lateral transfer of antibiotic resistance genes among bacteria and in life cycle of certain viruses such as HIV-1 and bacteriophage Mu. Despite the diversity of transposable elements they all use a fundamentally similar mechanism called transpositional DNA recombination (transposition) for the movement within and between the genomes of their host organisms. The DNA breakage and joining reactions that underlie their transposition are chemically similar in virtually all known transposition systems. The similarity of the reactions is also reflected in the structure and function of the catalyzing enzymes, transposases and integrases. The transposition reactions take place within the context of a transposition machinery, which can be particularly complex, as in the case of the VLP (virus like particle) machinery of retroelements, which in vivo contains RNA or cDNA and a number of element encoded structural and catalytic proteins. Yet, the minimal core machinery required for transposition comprises a multimer of transposase or integrase proteins and their binding sites at the element DNA ends only. Although the chemistry of DNA transposition is fairly well characterized, the components and function of the transposition machinery have been investigated in detail for only a small group of elements. This work focuses on the identification, characterization, and functional studies of the molecular components of the transposition machineries of BARE-1, Hin-Mu and Mu. For BARE-1 and Hin-Mu transpositional activity has not been shown previously, whereas bacteriophage Mu is a general model of transposition. For BARE-1, which is a retroelement of barley (Hordeum vulgare), the protein and DNA components of the functional VLP machinery were identified from cell extracts. In the case of Hin-Mu, which is a Mu-like prophage in Haemophilus influenzae Rd genome, the components of the core machinery (transposase and its binding sites) were characterized and their functionality was studied by using an in vitro methodology developed for Mu. The function of Mu core machinery was studied for its ability to use various DNA substrates: Hin-Mu end specific DNA substrates and Mu end specific hairpin substrates. The hairpin processing reaction by MuA was characterized in detail. New information was gained of all three machineries. The components or their activity required for functional BARE-1 VLP machinery and retrotransposon life cycle were present in vivo and VLP-like structures could be detected. The Hin-Mu core machinery components were identified and shown to be functional. The components of the Mu and Hin-Mu core machineries were partially interchangeable, reflecting both evolutionary conservation and flexibility within the core machineries. The Mu core machinery displayed surprising flexibility in substrate usage, as it was able to utilize Hin-Mu end specific DNA substrates and to process Mu end DNA hairpin substrates. This flexibility may be evolutionarily and mechanistically important.

Stress responses of Gram-positive bacteria to cationic antimicrobial peptides

As the resistance of bacteria to conventional antibiotics has become an increasing problem, new antimicrobial drugs are urgently needed. One possible source of new antibacterial agents is a group of cationic antimicrobial peptides (CAMPs) produced by practically all living organisms. These peptides are typically small, amphipathic and positively charged and contain well defined a-helical or b-sheet secondary structures. The main antibacterial action mechanism of CAMPs is considered to be disruption of the cell membrane, but other targets of CAMPs also exist. Some bacterial species have evolved defence mechanisms against the harmful effects of CAMPs. One of the most effective defence mechanisms is reduction of the net negative charge of bacterial cell surfaces. Global analysis of gene expression of two Gram-positive bacteria, Bacillus subtilis and Staphylococcus aureus, was used to further study the stress responses induced by different types of CAMPs. B. subtilis cells were treated with sublethal concentrations of a-helical peptide LL-37, b-sheet peptide protegrin 1 or synthetic analogue poly-L-lysine, and the changes in gene expression were studied using DNA macroarrays. In the case of S. aureus, three different a-helical peptides were selected for the transcriptome analyses: temporin L, ovispirin-1 and dermaseptin K4-S4(1-16). Transcriptional changes caused by peptide stress were examined using oligo DNA microarrays. The transcriptome analysis revealed two main cell signalling mechanisms mediating CAMP stress responses in Gram-positive bacteria: extracytoplasmic function (ECF)sigma factors and two-component systems (TCSs). In B. subtilis, ECF sigma factors sigW and sigM as well as TCS LiaRS responded to the cell membrane disruption caused by CAMPs. In S. aureus, CAMPs caused a similar stress response to antibiotics interfering in cell wall synthesis, and TCS VraSR was strongly activated. All of these transcriptional regulators are known to respond to several compounds other than CAMPs interfering with cell envelope integrity, suggesting that they sense cell envelope stress in general. Among the most strongly induced genes were yxdLM (in B. subtilis) and vraDE (in S. aureus) encoding homologous ABC transporters. Transcription of yxdLM and vraDE operons is controlled by TCSs YxdJK and ApsRS, respectively. These TCSs seemed to be responsible for the direct recognition of CAMPs. The yxdLM operon was specifically induced by LL-37, but its role in CAMP resistance remained unclear. VraDE was proven to be a bacitracin transporter. We also showed that the net positive charge of the cell wall affects the signalrecognition of different TCSs responding to cell envelope stress. Inactivation of the Dlt system responsible for the D-alanylation of teichoic acids had a strong and differential effect on the activity of the studied TCSs, depending on their functional role in cells and the stimuli they sense.

The Molecular Basis of Hydrolethalus Syndrome

Hydrolethalus syndrome (HLS) is a severe fetal malformation syndrome that is inherited by an autosomal recessive manner. HLS belongs to the Finnish disease heritage, an entity of rare diseases that are more prevalent in Finland than in other parts of the world. The phenotypic spectrum of the syndrome is wide and it is characterized by several developmental abnormalities, including hydrocephalus and absent midline structures in the brain, abnormal lobation of the lungs, polydactyly as well as micrognathia and other craniofacial anomalies. Polyhydramnios are relatively frequent during pregnancy. HLS can nowadays be effectively identified by ultrasound scan already at the end of the first trimester of pregnancy. One of the main goals in this study was to identify and characterize the gene defect underlying HLS. The defect was found from a previously unknown gene that was named HYLS1. Identification of the gene defect made it possible to confirm the HLS diagnosis genetically, an aspect that provides valuable information for the families in which a fetus is suspected to have HLS. Neuropathological findings of mutation confirmed HLS cases were described for the first time in detail in this study. Also, detailed general pathological findings were described. Since HYLS1 was an unknown gene with no relatives in the known gene families, many functional studies were performed in order to unravel the function of the gene and of the protein it codes for. Studies showed, for example, that the subcellular localization of the HYLS1 protein was different when the normal and the defective forms were compared. In addition, HYLS1 was shown to possess transactivation potential which was significantly diminished in the defective form. According to the results of this study it can be stated that HYLS1 most likely participates in transcriptional regulation and also in the regulation of cholesterol metabolism and that the function of HYLS1 is critical for normal fetal development.

Population structure and evolution in the ant Plagiolepis pygmaea and its two social parasites Plagiolepis xene and Plagiolepis grassei

Social behaviour affects dispersal of animals and is an important modifier of genetic population structures. The female sex is often philopatric, which maintains coancestry within the breeding groups and promotes cooperative behaviours. This enables also inclusive fitness returns from altruism and explains why some individuals sacrifice personal reproduction for the good of others in social insects such as ants. However, reduced dispersal and population substructuring at the level of colonies may also entail inbreeding, loss of genetic diversity, and vulnerability. In addition, the most vulnerable ants are species that are evolved to parasitize colonies of other ants, and which compromise between abilities to disperse and the efficiency to parasitize the host. On the other hand, certain social organisations of ant colonies may facilitate a species to disperse outside its natural range and become a pest. Altogether, knowledge on genetic structuring of ant populations, as well as the evolution of their life histories can contribute to conservation biology and population management. The aim of this thesis was to investigate population structures and phylogenetic evolution of the ant Plagiolepis pygmaea and its two obligatory, workerless social parasites (inquilines) P. xene and P. grassei with genetic markers and DNA sequence data. The results support the general assumption that populations of inquiline parasites are highly fragmented and genetically vulnerable. Comparison of the two parasites suggests that differences in their relative abundance may follow from their interaction with the host, i.e. how well the species is adapted to reproduce in the host colonies. The results also indicate that the most recent free living ancestor to these two parasite species is their common host. This is considered to provide evidence for the controversial issue of sympatric speciation. Further, given that the level of adaptations to parasitic life history depends on the evolutionary time since the free-living ancestor, the results establish a link between species rarity and its evolutionary age. The populations of the host species P. pygmaea displayed significantly reduced dispersal both among the females (queens) and males, and high levels of inbreeding which may enhance worker altruism. In addition, the queens were found to mate with multiple males. Given the high relatedness between the queens and their mates, this occurs probably for non-genetic reasons, e.g. without benefits associated in genetically more diverse offspring. The results hence caution that the contribution of non-genetic factors to the prevailing mating patterns and genetic population structures should not be underestimated.

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.