Topological Quantum Computation - An Analysis of an Anyon Model Based on Quantum Double Symmetries

There exists various suggestions for building a functional and a fault-tolerant large-scale quantum computer. Topological quantum computation is a more exotic suggestion, which makes use of the properties of quasiparticles manifest only in certain two-dimensional systems. These so called anyons exhibit topological degrees of freedom, which, in principle, can be used to execute quantum computation with intrinsic fault-tolerance. This feature is the main incentive to study topological quantum computation. The objective of this thesis is to provide an accessible introduction to the theory. In this thesis one has considered the theory of anyons arising in two-dimensional quantum mechanical systems, which are described by gauge theories based on so called quantum double symmetries. The quasiparticles are shown to exhibit interactions and carry quantum numbers, which are both of topological nature. Particularly, it is found that the addition of the quantum numbers is not unique, but that the fusion of the quasiparticles is described by a non-trivial fusion algebra. It is discussed how this property can be used to encode quantum information in a manner which is intrinsically protected from decoherence and how one could, in principle, perform quantum computation by braiding the quasiparticles. As an example of the presented general discussion, the particle spectrum and the fusion algebra of an anyon model based on the gauge group S_3 are explicitly derived. The fusion algebra is found to branch into multiple proper subalgebras and the simplest one of them is chosen as a model for an illustrative demonstration. The different steps of a topological quantum computation are outlined and the computational power of the model is assessed. It turns out that the chosen model is not universal for quantum computation. However, because the objective was a demonstration of the theory with explicit calculations, none of the other more complicated fusion subalgebras were considered. Studying their applicability for quantum computation could be a topic of further research.

Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

Mitochondrial Malfunction in Tumor Formation and Neuromuscular Diseases : Consequences of defects in fumarate hydratase and in the respiratory chain

The mitochondrion is an organelle of outmost importance, and the mitochondrial network performs an array of functions that go well beyond ATP synthesis. Defects in mitochondrial performance lead to diseases, often affecting nervous system and muscle. Although many of these mitochondrial diseases have been linked to defects in specific genes, the molecular mechanisms underlying the pathologies remain unclear. The work in this thesis aims to determine how defects in mitochondria are communicated within - and interpreted by - the cells, and how this contributes to disease phenotypes. Fumarate hydratase (FH) is an enzyme of the citrate cycle. Recessive defects in FH lead to infantile mitochondrial encephalopathies, while dominant mutations predispose to tumor formation. Defects in succinate dehydrogenase (SDH), the enzyme that precedes FH in the citrate cycle, have also been described. Mutations in SDH subunits SDHB, SDHC and SDHD are associated with tumor predisposition, while mutations in SDHA lead to a characteristic mitochondrial encephalopathy of childhood. Thus, the citrate cycle, via FH and SDH, seems to have essential roles in mitochondrial function, as well as in the regulation of processes such as cell proliferation, differentiation or death. Tumor predisposition is not a typical feature of mitochondrial energy deficiency diseases. However, defects in citrate cycle enzymes also affect mitochondrial energy metabolism. It is therefore necessary to distinguish what is specific for defects in citrate cycle, and thus possibly associated with the tumor phenotype, from the generic consequences of defects in mitochondrial aerobic metabolism. We used primary fibroblasts from patients with recessive FH defects to study the cellular consequences of FH-deficiency (FH-). Similarly to the tumors observed in FH- patients, these fibroblasts have very low FH activity. The use of primary cells has the advantage that they are diploid, in contrast with the aneuploid tumor cells, thereby enabling the study of the early consequences of FH- in diploid background, before tumorigenesis and aneuploidy. To distinguish the specific consequences of FH- from typical consequences of defects in mitochondrial aerobic metabolism, we used primary fibroblasts from patients with MELAS (mitochondrial encephalopathy with lactic acidosis and stroke-like episodes) and from patients with NARP (neuropathy, ataxia and retinitis pigmentosa). These diseases also affect mitochondrial aerobic metabolism but are not known to predispose to tumor formation. To study in vivo the systemic consequences of defects in mitochondrial aerobic metabolism, we used a transgenic mouse model of late-onset mitochondrial myopathy. The mouse contains a transgene with an in-frame duplication of a segment of Twinkle, the mitochondrial replicative helicase, whose defects underlie the human disease progressive external ophthalmoplegia. This mouse model replicates the phenotype in the patients, particularly neuronal degeneration, mitochondrial myopathy, and subtle decrease of respiratory chain activity associated with mtDNA deletions. Due to the accumulation of mtDNA deletions, the mouse was named deletor. We first studied the consequences of FH- and of respiratory chain defects for energy metabolism in primary fibroblasts. To further characterize the effects of FH- and respiratory chain malfunction in primary fibroblasts at transcriptional level, we used expression microarrays. In order to understand the in vivo consequences of respiratory chain defects in vivo, we also studied the transcriptional consequences of Twinkle defects in deletor mice skeletal muscle, cerebellum and hippocampus. Fumarate accumulated in the FH- homozygous cells, but not in the compound heterozygous lines. However, virtually all FH- lines lacked cytoplasmic FH. Induction of glycolysis was common to FH-, MELAS and NARP fibroblasts. In deletor muscle glycolysis seemed to be upregulated. This was in contrast with deletor cerebellum and hippocampus, where mitochondrial biogenesis was in progress. Despite sharing a glycolytic pattern in energy metabolism, FH- and respiratory chain defects led to opposite consequences in redox environment. FH- was associated with reduced redox environment, while MELAS and NARP displayed evidences of oxidative stress. The deletor cerebellum had transcriptional induction of antioxidant defenses, suggesting increased production of reactive oxygen species. Since the fibroblasts do not represent the tissues where the tumors appear in FH- patients, we compared the fibroblast array data with the data from FH- leiomyomas and normal myometrium. This allowed the determination of the pathways and networks affected by FH-deficiency in primary cells that are also relevant for myoma formation. A key pathway regulating smooth muscle differentiation, SRF (serum response factor)-FOS-JUNB, was found to be downregulated in FH- cells and in myomas. While in the deletor mouse many pathways were affected in a tissue-specific basis, like FGF21 induction in the deletor muscle, others were systemic, such as the downregulation of ALAS2-linked heme synthesis in all deletor tissues analyzed. However, interestingly, even a tissue-specific response of FGF21 excretion could elicit a global starvation response. The work presented in this thesis has contributed to a better understanding of mitochondrial stress signalling and of pathways interpreting and transducing it to human pathology.

Cellular Cholesterol Accumulation and Egress from Endosomal Compartments

One of the most important factors determining the development of atherosclerosis is the amount of LDL particles in the circulation. In general, LDL particles are clinically regarded as “bad cholesterol” since these particles get entrapped within the vascular wall, leading to atherosclerosis. Circulating HDL particles are conversely regarded as “good cholesterol” because of their ability to transport cholesterol from peripheral tissues to the liver for secretion as bile salts. Once inside the artery wall LDL particles are engulfed by macrophages, resulting in macrophage foam cells. If the macrophage foam cells are not able to efflux the cholesterol back into the bloodstream, the excessive cholesterol ultimately leads to cell death, and the deposition of cellular debris within the atherosclerotic lesion. The cells ability to secrete cholesterol is mainly dependent on the ABCA1 transporter (ATP-binding cassette transporter A1) which transfers cellular cholesterol to extracellular apoA-I (apolipoprotein A-I) particles, leading to the generation of nascent HDL particles. The process of atherosclerotic plaque development is therefore to a large extent a cellular one, in which the capacity of the macrophages in handling the excessive cholesterol load determines the progression of lesion development. In this work we have studied the cellular mechanisms that regulate the trafficking of LDL-derived cholesterol from endosomal compartments to other parts of the cell. As a basis for the study we have utilized cells from patients with Niemann-Pick type C disease, a genetic disorder resulting from mutations in the NPC1 and NPC2 genes. In these cells, cholesterol is entrapped within the endosomal compartment, and is not available for efflux. By identifying proteins that bypass the cholesterol trafficking defect, we were able to identify the small GTPase Rab8 as an important protein involved in ABCA1 dependent cholesterol efflux. In the study, we show that Rab8 regulates cholesterol efflux in human macrophages by facilitating intracellular cholesterol transport, as well as by regulating the plasma membrane availability of ABCA1. Collectively, these results give new insight in to atherosclerotic lesion development and intracellular cholesterol processing.

LKB1 tumor suppression in Peutz-Jeghers Syndrome

Kasvainten, ajatellaan syntyvän yksittäisen solun perimän mutaatioista, jonka seurauksena tuon solun kasvu häiriintyy. Ruoansulatuskanavan polyyppien syntyä käytetään usein mallina siitä, miten nämä epiteelisoluun kerääntyvät mutaatiot aiheuttavat asteittain pahenevan kasvuhäiriön. Peutz–Jeghersin oireyhtymä (PJS) on perinnöllinen polypoosisyndrooma, jossa oireita aiheuttavat erityisesti maha-suolikanavan hamartomatoottiset polyypit. Noin puolella PJS potilaista havaitaan mutaatioita LKB1 kasvunrajoite geenissä. Hiirille joilta toinen Lkb1 alleeli on poistettu (Lkb1+/-) kehittyy PJS-tyypin maha-suolikanavan polyyppeja, joissa on epiteelin liikakasvun lisäksi merkittävä sileälihaskomponentti, aivan kuten PJS polyypeissa. Kuten myös muissa ruoansulatuskanavan polypooseissa, sekä PJS että hiirten polyypeissa Cyclo-oxygenaasi-2:n (COX-2) määrä on usein kohonnut. PJS-polyyppien kehittymisen molekulaarinen mekanismi on kuitenkin selvittämättä. Koska vain osa PJS potilaista kantaa LKB1 mutaatioita, mutaatiot jossakin toisessa lokuksessa saattaisivat selittää osan PJS tapauksista. Jotta PJS:n geneettinen tausta selviäisi, seulottiin kolmen LKB1:n kanssa interaktoivan proteiinin (BRG1, STRADα ja MO25α) geenit PJS potilaista joilla ei ole havaittu LKB1 mutaatioita. Yhdessäkään tutkituista geeneistä ei havaittu tautia aiheuttavia mutaatioita. Näiden kolmen geenin pois sulkeminen, ja uusien menetelmien ansiosta kasvanut havaittujen Lkb1 mutaatioden määrä viittaavat LKB1:n olevan useimpien PJS tapausten taustalla. COX-2:n estäjien käyttö on tehokkaasti vähentänyt polyyppien määrää familiaarisessa adenomatoottisessa polypoosissa. Tästä johtuen COX-2:n eston tehokkuutta tutkittiin PJS polypoosissa. PJS-tyypin polypoosin havaittin pienenevän merkittävästi Lkb1+/- hiirissä, joilta oli lisäksi poistettu toinen tai molemmat COX-2:n alleeleista. Lisäksi farmakologinen COX-2:n esto Celecoxib:lla vähensi polypoosia tehokkaasti. Näin ollen COX-2:n eston tehokkuutta tutkittiin seuraavaksi PJS potilaissa. Kuuden kuukauden Celecoxib hoidon jälkeen polypoosin havaittiin vähentyneen merkittävästi osalla potilaista (2/6). Nämä tulokset osoittavat COX-2:n roolin PJS-polyyppien kehityksessä, ja viittaavat COX-2:n eston vähentävän polypoosia. Kasvunrajoitegeenin klassisen määritelmän mukaan kasvaimen kehitys vaatii perinnöllisen mutaation lisäksi geenin toisenkin alleelin mutaation, mutta PJS-polyyppien häiriintyneestä epiteelistä ei kuitenkaan systemaattisesti löydy toista LKB1:n mutaatiota. Havainto johti tutkimukseen, jossa selvitettiin voisiko LKB1:n kasvun rajoitus välittyäkin epäsuorasti tukikudokseksi ajatelluista sileälihassoluista. Tätä tutkittiin kehittämällä poistogeeninen hiirimalli jossa Lkb1 on mutatoitunut vain sileälihassoluissa. Näille hiirille kehittyi polyyppeja, jotka ovat kaikin tavoin PJS-polyyppien kaltaisia. Lkb1:n menettäneiden solujen havaittiin tuottavan vähemmän transformoivaa kasvutekijä beetaa (TGFß), joka aiheutti solujen välisen viestinnän heikentymisen ja mahdollisesti viereisten epiteelisolujen liikakasvun. Vastaava häiriö havaittiin myös PJS-potilaiden polyypeissa, mikä viittaa siihen, että potilaillakin sileälihassolujen häiriö on polyyppien taustalla. Havainto suuntaa täten hoitokohteiden etsintää ja osoittaa että LKB1 toimii kasvunrajoittajana epätyypillisellä tavalla pitäen naapurisolujen kasvun kurissa.

Pharmacogenetic Variation at CYP2D6, CYP2C9, and CYP2C19: Population Genetic and Forensic Aspects

Pharmacogenetics deals with genetically determined variation in drug response. In this context, three phase I drug-metabolizing enzymes, CYP2D6, CYP2C9, and CYP2C19, have a central role, affecting the metabolism of about 20-30% of clinically used drugs. Since genes coding for these enzymes in human populations exhibit high genetic polymorphism, they are of major pharmacogenetic importance. The aims of this study were to develop new genotyping methods for CYP2D6, CYP2C9, and CYP2C19 that would cover the most important genetic variants altering the enzyme activity, and, for the first time, to describe the distribution of genetic variation at these loci on global and microgeographic scales. In addition, pharmacogenetics was applied to a postmortem forensic setting to elucidate the role of genetic variation in drug intoxications, focusing mainly on cases related to tricyclic antidepressants, which are commonly involved in fatal drug poisonings in Finland. Genetic variability data were obtained by genotyping new population samples by the methods developed based on PCR and multiplex single-nucleotide primer extension reaction, as well as by collecting data from the literature. Data consisted of 138, 129, and 146 population samples for CYP2D6, CYP2C9, and CYP2C19, respectively. In addition, over 200 postmortem forensic cases were examined with respect to drug and metabolite concentrations and genotypic variation at CYP2D6 and CYP2C19. The distribution of genetic variation within and among human populations was analyzed by descriptive statistics and variance analysis and by correlating the genetic and geographic distances using Mantel tests and spatial autocorrelation. The correlation between phenotypic and genotypic variation in drug metabolism observed in postmortem cases was also analyzed statistically. The genotyping methods developed proved to be informative, technically feasible, and cost-effective. Detailed molecular analysis of CYP2D6 genetic variation in a global survey of human populations revealed that the pattern of variation was similar to those of neutral genomic markers. Most of the CYP2D6 diversity was observed within populations, and the spatial pattern of variation was best described as clinal. On the other hand, genetic variants of CYP2D6, CYP2C9, and CYP2C19 associated with altered enzymatic activity could reach extremely high frequencies in certain geographic regions. Pharmacogenetic variation may also be significantly affected by population-specific demographic histories, as seen within the Finnish population. When pharmacogenetics was applied to a postmortem forensic setting, a correlation between amitriptyline metabolic ratios and genetic variation at CYP2D6 and CYP2C19 was observed in the sample material, even in the presence of confounding factors typical for these cases. In addition, a case of doxepin-related fatal poisoning was shown to be associated with a genetic defect at CYP2D6. Each of the genes studied showed a distinct variation pattern in human populations and high frequencies of altered activity variants, which may reflect the neutral evolution and/or selective pressures caused by dietary or environmental exposure. The results are relevant also from the clinical point of view since the genetic variation at CYP2D6, CYP2C9, and CYP2C19 already has a range of clinical applications, e.g. in cancer treatment and oral anticoagulation therapy. This study revealed that pharmacogenetics may also contribute valuable information to the medicolegal investigation of sudden, unexpected deaths.

Molecular and clinical characteristics of tricarboxylic acid cycle-associated tumors

Hereditary leiomyomatosis and renal cell cancer (HLRCC) is a rare, dominantly inherited tumor predisposition syndrome characterized by benign cutaneous and uterine (ULM) leiomyomas, and sometimes renal cell cancer (RCC). A few cases of uterine leiomyosarcoma (ULMS) have also been reported. Mutations in a nuclear gene encoding fumarate hydratase (FH), an enzyme of the mitochondrial tricarboxylic acid cycle (TCA cycle), underlie HLRCC. As a recessive condition, germline mutations in FH predispose to a neurological defect, FH deficiency (FHD). Hereditary paragangliomatosis (HPGL) is a dominant disorder associated with paragangliomas and pheochromocytomas. Inherited mutations in three genes encoding subunits of succinate dehydrogenase (SDH), also a TCA cycle enzyme, predispose to HPGL. Both FH and SDH seem to act as tumor suppressors. One of the consequences of the TCA cycle defect is abnormal activation of HIF1 pathway ( pseudohypoxia ) in the HLRCC and HPGL tumors. HIF1 drives transcription of genes encoding e.g. angiogenetic factors which can facilitate tumor growth. Recently hypoxia/HIF1 has been suggested to be one of the causes of genetic instability as well. One of the aims of this study was to broaden the clinical definers of HLRCC. To determine the cancer risk and to identify possible novel tumor types associated with FH mutations eight Finnish HLRCC/FHD families were extensively evaluated. The extension of the pedigrees and the Finnish Cancer Registry based tumor search yielded genealogical and cancer data of altogether 868 individuals. The standardized incidence ratio-based comparison of HLRCC/FHD family members with general Finnish population revealed 6.5-fold risk for RCC. Moreover, risk for ULMS was highly increased. However, according to the recent and more stringent diagnosis criteria of ULMS many of the HLRCC uterine tumors previously considered malignant are at present diagnosed as atypical or proliferative ULMs (with a low risk of recurrence). Thus, the formation of ULMS (as presently defined) in HLRCC appears to be uncommon. Though increased incidence was not observed, interestingly the genetic analyses suggested possible association of breast and bladder cancer with loss of FH. Moreover, cancer cases were exceptionally detected in an FHD family. Another clinical finding was the conventional (clear cell) type RCC of a young Spanish HLRCC patient. Conventional RCC is distinct from the types previously observed in this syndrome but according to these results, FH mutation may underlie some of young conventional cancer cases. Secondly, the molecular pathway from defective TCA cycle to tumor formation was intended to clarify. Since HLRCC and HPGL tumors display abnormally activated HIF1, the hypothesis on the link between HIF1/hypoxia and genetic instability was of interest to study in HLRCC and HPGL tumor material. HIF1α (a subunit of HIF1) stabilization was confirmed in the majority of the specimens. However, no repression of MSH2, a protein of DNA mismatch repair system, or microsatellite instability (MSI), an indicator of genetic instability, was observed. Accordingly, increased instability seems not to play a role in the tumorigenesis of pseudohypoxic TCA cycle-deficient tumors. Additionally, to study the putative alternative functions of FH, a recently identified alternative FH transcript (FHv) was characterized. FHv was found to contain instead of exon 1, an alternative exon 1b. Differential subcellular distribution, lack of FH enzyme activity, low mRNA expression compared to FH, and induction by cellular stress suggest FHv to have a role distinct from FH, for example in apoptosis or survival. However, the physiological significance of FHv requires further elucidation.

Molecular classification of familial colorectal and endometrial carcinoma

Hereditary nonpolyposis colorectal cancer (HNPCC) is the most common known clearly hereditary cause of colorectal and endometrial cancer (CRC and EC). Dominantly inherited mutations in one of the known mismatch repair (MMR) genes predispose to HNPCC. Defective MMR leads to an accumulation of mutations especially in repeat tracts, presenting microsatellite instability. HNPCC is clinically a very heterogeneous disease. The age at onset varies and the target tissue may vary. In addition, families that fulfill the diagnostic criteria for HNPCC but fail to show any predisposing mutation in MMR genes exist. Our aim was to evaluate the genetic background of familial CRC and EC. We performed comprehensive molecular and DNA copy number analyses of CRCs fulfilling the diagnostic criteria for HNPCC. We studied the role of five pathways (MMR, Wnt, p53, CIN, PI3K/AKT) and divided the tumors into two groups, one with MMR gene germline mutations and the other without. We observed that MMR proficient familial CRC consist of two molecularly distinct groups that differ from MMR deficient tumors. Group A shows paucity of common molecular and chromosomal alterations characteristic of colorectal carcinogenesis. Group B shows molecular features similar to classical microsatellite stable tumors with gross chromosomal alterations. Our finding of a unique tumor profile in group A suggests the involvement of novel predisposing genes and pathways in colorectal cancer cohorts not linked to MMR gene defects. We investigated the genetic background of familial ECs. Among 22 families with clustering of EC, two (9%) were due to MMR gene germline mutations. The remaining familial site-specific ECs are largely comparable with HNPCC associated ECs, the main difference between these groups being MMR proficiency vs. deficiency. We studied the role of PI3K/AKT pathway in familial ECs as well and observed that PIK3CA amplifications are characteristic of familial site-specific EC without MMR gene germline mutations. Most of the high-level amplifications occurred in tumors with stable microsatellites, suggesting that these tumors are more likely associated with chromosomal rather than microsatellite instability and MMR defect. The existence of site-specific endometrial carcinoma as a separate entity remains equivocal until predisposing genes are identified. It is possible that no single highly penetrant gene for this proposed syndrome exists, it may, for example be due to a combination of multiple low penetrance genes. Despite advances in deciphering the molecular genetic background of HNPCC, it is poorly understood why certain organs are more susceptible than others to cancer development. We found that important determinants of the HNPCC tumor spectrum are, in addition to different predisposing germline mutations, organ specific target genes and different instability profiles, loss of heterozygosity at MLH1 locus, and MLH1 promoter methylation. This study provided more precise molecular classification of families with CRC and EC. Our observations on familial CRC and EC are likely to have broader significance that extends to sporadic CRC and EC as well.

Effects of seed origin latitude on the timing of height growth cessation and field performance of silver birch

The aim of this thesis was to increase our knowledge about the effects of seed origin on the timing of height growth cessation and field performance of silver birch from different latitudes, with special attention paid to the browsing damage by moose in young birch plantations. The effect of seed origin latitude and sowing time on timing of height growth cessation of first-year seedlings was studied in a greenhouse experiment with seven seed origins (lat. 58º - 67ºN). Variation in critical night length (CNL) for 50 % bud set within two latitudinally distant stands (60º and 67ºN) was studied in three phytotron experiments. Browsing by moose on 5-11 -year-old silver birch saplings from latitudinally different seed origins (53º - 67ºN) was studied in a field experiment in southern Finland. Yield and stem quality of 22-year-old silver birch trees of Baltic, Finnish and Russian origin (54º - 63ºN) and the effect of latitudinal seed transfers were studied in two provenance trials at Tuusula, southern and Viitasaari, central Finland. The timing of height growth cessation depended systematically on latitude of seed origin and sowing date. The more northern the seed origin, the earlier the growth cessation and the shorter the growth period. Later sowing dates delayed growth cessation but also shortened the growth period. The mean CNL of the southern ecotype was longer, 6.3 ± 0.2 h (95 % confidence interval), than that of the northern ecotype, 3.1 ± 0.3 h. Within-ecotype variance of the CNL was higher in the northern ecotype (0.484 h2) than in the southern ecotype (0.150 h2). Browsing by moose decreased with increasing latitude of seed origin and sapling height. Origins transferred from more southern latitudes were more heavily browsed than the more northern native ones. Southern Finnish seed origins produced the highest volume per unit area in central Finland (lat. 63º11'N). Estonian and north Latvian stand seed origins, and the southern Finnish plus tree origins, were the most productive ones in southern Finland (lat. 60º21'N). Latitudinal seed transfer distance had a significant effect on survival, stem volume/ha and proportion of trees with a stem defect. The relationship of both survival and stem volume/ha to the latitudinal seed transfer distance was curvilinear. Volume was increased by transferring seed from ca. 2 degrees of latitude from the south. A longer transfer from the south, and transfer from the north, decreased the yield. The proportion of trees with a stem defect increased linearly in relation to the latitudinal seed transfer distance from the south.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Luonnollisten lukujen joukon määriteltävyys funktioalgebroissa

Let X be a topological space and K the real algebra of the reals, the complex numbers, the quaternions, or the octonions. The functions form X to K form an algebra T(X,K) with pointwise addition and multiplication. We study first-order definability of the constant function set N' corresponding to the set of the naturals in certain subalgebras of T(X,K). In the vocabulary the symbols Constant, +, *, 0', and 1' are used, where Constant denotes the predicate defining the constants, and 0' and 1' denote the constant functions with values 0 and 1 respectively. The most important result is the following. Let X be a topological space, K the real algebra of the reals, the compelex numbers, the quaternions, or the octonions, and R a subalgebra of the algebra of all functions from X to K containing all constants. Then N' is definable in , if at least one of the following conditions is true. (1) The algebra R is a subalgebra of the algebra of all continuous functions containing a piecewise open mapping from X to K. (2) The space X is sigma-compact, and R is a subalgebra of the algebra of all continuous functions containing a function whose range contains a nonempty open set of K. (3) The algebra K is the set of reals or the complex numbers, and R contains a piecewise open mapping from X to K and does not contain an everywhere unbounded function. (4) The algebra R contains a piecewise open mapping from X to the set of the reals and function whose range contains a nonempty open subset of K. Furthermore R does not contain an everywhere unbounded function.

Bending the Rules of Cell Protrusions : Molecular Mechanisms and Biological Roles of Inverse-BAR Proteins in Cell Morphogenesis

Plasma membrane adopts myriad of different shapes to carry out essential cellular processes such as nutrient uptake, immunological defence mechanisms and cell migration. Therefore, the details how different plasma membrane structures are made and remodelled are of the upmost importance. Bending of plasma membrane into different shapes requires substantial amount of force, which can be provided by the actin cytoskeleton, however, the molecules that regulate the interplay between the actin cytoskeleton and plasma membrane have remained elusive. Recent findings have placed new types of effectors at sites of plasma membrane remodelling, including BAR proteins, which can directly bind and deform plasma membrane into different shapes. In addition to their membrane-bending abilities, BAR proteins also harbor protein domains that intimately link them to the actin cytoskeleton. The ancient BAR domain fold has evolved into at least three structurally and functionally different sub-groups: the BAR, F-BAR and I-BAR domains. This thesis work describes the discovery and functional characterization of the Inverse-BAR domains (I-BARs). Using synthetic model membranes, we have shown that I-BAR domains bind and deform membranes into tubular structures through a binding-surface composed of positively charged amino acids. Importantly, the membrane-binding surface of I-BAR domains displays an inverse geometry to that of the BAR and F-BAR domains, and these structural differences explain why I-BAR domains induce cell protrusions whereas BAR and most F-BAR domains induce cell invaginations. In addition, our results indicate that the binding of I-BAR domains to membranes can alter the spatial organization of phosphoinositides within membranes. Intriguingly, we also found that some I-BAR domains can insert helical motifs into the membrane bilayer, which has important consequences for their membrane binding/bending functions. In mammals there are five I-BAR domain containing proteins. Cell biological studies on ABBA revealed that it is highly expressed in radial glial cells during the development of the central nervous system and plays an important role in the extension process of radial glia-like C6R cells by regulating lamellipodial dynamics through its I-BAR domain. To reveal the role of these proteins in the context of animals, we analyzed MIM knockout mice and found that MIM is required for proper renal functions in adult mice. MIM deficient mice displayed a severe urine concentration defect due to defective intercellular junctions of the kidney epithelia. Consistently, MIM localized to adherens junctions in cultured kidney epithelial cells, where it promoted actin assembly through its I-BAR andWH2 domains. In summary, this thesis describes the mechanism how I-BAR proteins deform membranes and provides information about the biological role of these proteins, which to our knowledge are the first proteins that have been shown to directly deform plasma membrane to make cell protrusions.

Pathogenicity, functional significance and clinical phenotype of mismatch repair gene MSH2 variants found in cancer patients

DNA ja siinä sijaitsevat geenit ohjaavat kaikkea solujen toimintaa. DNA-molekyyleihin kuitenkin kertyy mutaatioita sekä ympäristön vaikutuksen, että solujen oman toiminnan tuloksena. Mikäli virheitä ei korjata, saattaa tuloksena olla solun muuttuminen syöpäsoluksi. Soluilla onkin käytössä useita DNA-virheiden korjausmekanismeja, joista yksi on ns. mismatch repair (MMR). MMR vastaa DNA:n kahdentumisessa syntyvien virheiden korjauksesta. Periytyvät mutaatiot geeneissä, jotka vastaavat MMR-proteiinien rakentamisesta, aiheuttavat ongelmia DNA:n korjauksessa ja altistavat kantajansa periytyvälle ei-polypoottiselle paksusuolisyöpäoireyhtymälle (hereditary nonpolyposis colorectal cancer, HNPCC). Yleisimmin mutatoituneet MMR-geenit ovat MLH1 ja MSH2. HNPCC periytyy vallitsevasti, eli jo toiselta vanhemmalta peritty geenivirhe altistaa syövälle. MMR-geenivirheen kantaja sairastuu syöpään elämänsä aikana suurella todennäköisyydellä, ja sairastumisikä on vain noin 40 vuotta. Syövälle altistavan geenivirheen löytäminen mutaation kantajilta on hyvin tärkeää, sillä säännöllinen seuranta mahdollistaa kehittymässä olevan kasvaimen havaitsemisen ja poistamisen jo aikaisessa vaiheessa. Tämän on osoitettu alentavan syöpäkuolleisuutta merkittävästi. Varma tieto altistuksen alkuperästä on tärkeä myös niille syöpäsuvun jäsenille, jotka eivät kanna kyseistä mutaatiota. Syövälle altistavien mutaatioiden ohella MMR-geeneistä löydetään säännöllisesti muutoksia, jotka ovat normaalia henkilöiden välistä geneettistä vaihtelua, eikä niiden oleteta lisäävän syöpäaltistusta. Altistavien mutaatioiden erottaminen näistä neutraaleista variaatioista on vaikeaa, mutta välttämätöntä altistuneiden tehokkaan seurannan varmistamiseksi. Tässä väitöskirjassa tutkittiin 18:a MSH2 -geenin mutaatiota. Mutaatiot oli löydetty perheistä, joissa esiintyi paljon syöpiä, mutta niiden vaikutus DNA:n korjaustehoon ja syöpäaltistukseen oli epäselvä. Työssä tutkittiin kunkin mutaation vaikutusta MSH2-proteiinin normaaliin toimintaan, ja tuloksia verrattiin potilaiden ja sukujen kliinisiin tietoihin. Tutkituista mutaatiosta 12 aiheutti puutteita MMR-korjauksessa. Nämä mutaatiot tulkittiin syövälle altistaviksi. Analyyseissä normaalisti toimineet 4 mutaatiota eivät todennäköisesti ole syynä syövän syntyyn kyseisillä perheillä. Tulkinta jätettiin avoimeksi 2 mutaation kohdalla. Tutkimuksesta hyötyivät suoraan kuvattujen mutaatioiden kantajaperheet, joiden geenivirheen syöpäaltistuksesta saatiin tietoa, mahdollistaen perinnöllisyysneuvonnan ja seurannan kohdentamisen sitä tarvitseville. Työ selvensi myös mekanismeja, joilla mutatoitunut MSH2-proteiini voi menettää toimintakykynsä.

U12-type Spliceosome: Localization and Effects of Splicing Efficiency on Gene Expression

The removal of non-coding sequences, introns, is an essential part of messenger RNA processing. In most metazoan organisms, the U12-type spliceosome processes a subset of introns containing highly conserved recognition sequences. U12-type introns constitute less than 0,5% of all introns and reside preferentially in genes related to information processing functions, as opposed to genes encoding for metabolic enzymes. It has previously been shown that the excision of U12-type introns is inefficient compared to that of U2-type introns, supporting the model that these introns could provide a rate-limiting control for gene expression. The low efficiency of U12-type splicing is believed to have important consequences to gene expression by limiting the production of mature mRNAs from genes containing U12-type introns. The inefficiency of U12-type splicing has been attributed to the low abundance of the components of the U12-type spliceosome in cells, but this hypothesis has not been proven. The aim of the first part of this work was to study the effect of the abundance of the spliceosomal snRNA components on splicing. Cells with a low abundance of the U12-type spliceosome were found to inefficiently process U12-type introns encoded by a transfected construct, but the expression levels of endogenous genes were not found to be affected by the abundance of the U12-type spliceosome. However, significant levels of endogenous unspliced U12-type intron-containing pre-mRNAs were detected in cells. Together these results support the idea that U12-type splicing may limit gene expression in some situations. The inefficiency of U12-type splicing has also promoted the idea that the U12-type spliceosome may control gene expression, limiting the mRNA levels of some U12-type intron-containing genes. While the identities of the primary target genes that contain U12-type introns are relatively well known, little has previously been known about the downstream genes and pathways potentially affected by the efficiency of U12-type intron processing. Here, the effects of U12-type splicing efficiency on a whole organism were studied in a Drosophila line with a mutation in an essential U12-type spliceosome component. Genes containing U12-type introns showed variable gene-specific responses to the splicing defect, which points to variation in the susceptibility of different genes to changes in splicing efficiency. Surprisingly, microarray screening revealed that metabolic genes were enriched among downstream effects, and that the phenotype could largely be attributed to one U12-type intron-containing mitochondrial gene. Gene expression control by the U12-type spliceosome could thus have widespread effects on metabolic functions in the organism. The subcellular localization of the U12-type spliceosome components was studied as a response to a recent dispute on the localization of the U12-type spliceosome. All components studied were found to be nuclear indicating that the processing of U12-type introns occurs within the nucleus, thus clarifying a question central to the field. The results suggest that the U12-type spliceosome can limit the expression of genes that contain U12-type introns in a gene-specific manner. Through its limiting role in pre-mRNA processing, the U12-type splicing activity can affect specific genetic pathways, which in the case of Drosophila are involved in metabolic functions.

From actin monomers to bundles: The roles of twinfilin and α-actinin in Drosophila melanogaster development

The actin cytoskeleton is essential for a large variety of cell biological processes. Actin exists in either a monomeric or a filamentous form, and it is very important for many cellular functions that the local balance between these two actin populations is properly regulated. A large number of proteins participate in the regulation of actin dynamics in the cell, and twinfilin, one of the proteins examined in this thesis, belongs to this category. The second level of regulation involves proteins that crosslink or bundle actin filaments, thereby providing the cell with a certain shape. α-Actinin, the second protein studied, mainly acts as an actin crosslinking protein. Both proteins are conserved in organisms ranging from yeast to mammals. In this thesis, the roles of twinfilin and α-actinin in development were examined using Drosophila melanogaster as a model organism. Twinfilin is an actin monomer binding protein that is structurally related to cofilin. In vitro, twinfilin reduces actin polymerisation by sequestering actin monomers. The Drosophila twinfilin (twf) gene was identified and found to encode a protein functionally similar to yeast and mammalian twinfilins. A strong hypomorphic twf mutation was identified, and flies homozygous for this allele were viable and fertile. The adult twf mutant flies displayed reduced viability, a rough eye phenotype and severely malformed bristles. The shape of the adult bristle is determined by the actin bundles that are regularly spaced around the perimeter of the developing pupal bristles. Examination of the twf pupal bristles revealed an increased level of filamentous actin, which in turn resulted in splitting and displacement of the actin bundles. The bristle defect was rescued by twf overexpression in developing bristles. The Twinfilin protein was localised at sites of actin filament assembly, where it was required to limit actin polymerisation. A genetic interaction between twinfilin and twinstar (the gene encoding Cofilin) was detected, consistent with the model predicting that both proteins act to limit the amount of filamentous actin. α-Actinin has been implicated in several diverse cell biological processes. In Drosophila, the only function for α-actinin yet known is in the organisation of the muscle sarcomere. Muscle and non-muscle cells utilise different α-actinin isoforms, which in Drosophila are produced by alternative splicing of a single gene. In this work, novel α-actinin deletion alleles, including ActnΔ233, were generated, which specifically disrupted the transcript encoding the non-muscle α-actinin isoform. Nevertheless, ActnΔ233 homozygous mutant flies were viable and fertile with no obvious defects. By comparing α-actinin protein distribution in wild type and ActnΔ233 mutant animals, it could be concluded that non-muscle α-actinin is the only isoform expressed in young embryos, in the embryonic central nervous system and in various actin-rich structures of the ovarian germline cells. In the ActnΔ233 mutant, α-actinin was detected not only in muscle tissue, but also in embryonic epidermal cells and in certain follicle cell populations in the ovaries. The population of α-actinin protein present in non-muscle cells of the ActnΔ233 mutant is referred to as FC-α-actinin (Follicle Cell). The follicular epithelium in the Drosophila ovary is a well characterised model system for studies on patterning and morphogenesis. Therefore, α-actinin expression, regulation and function in this tissue were further analysed. Examination of the α-actinin localisation pattern revealed that the basal actin fibres of the main body follicle cells underwent an organised remodelling during the final stages of oogenesis. This involved the assembly of a transient adhesion site in the posterior of the cell, in which α-actinin and Enabled (Ena) accumulated. Follicle cells genetically manipulated to lack all α-actinin isoforms failed to remodel their cytoskeleton and translocate Ena to the posterior of the cell, while the actin fibres as such were not affected. Neither was epithelial morphogenesis disrupted. The reorganisation of the basal actin cytoskeleton was also disturbed following ectopic expression of Decapentaplegic (Dpp) or as a result of a heat shock. At late oogenesis, the main body follicle cells express both non-muscle α-actinin and FC-α-actinin, while the dorsal anterior follicle cells express only non-muscle α-actinin. The dorsal anterior cells are patterned by the Dpp and Epidermal growth factor receptor (EGFR) signalling pathways, and they will ultimately secrete the dorsal appendages of the egg. Experiments involving ectopic activation of EGFR and Dpp signalling showed that FC-α-actinin is negatively regulated by combined EGFR and Dpp signalling. Ubiquitous overexpression of the adult muscle-specific α-actinin isoform induced the formation of aberrant actin bundles in migrating follicle cells that did not normally express FC-α-actinin, provided that the EGFR signalling pathway was activated in the cells. Taken together, this work contributes new data to our knowledge of α-actinin function and regulation in Drosophila. The cytoskeletal remodelling shown to depend on α-actinin function provides the first evidence that α-actinin has a role in the organisation of the cytoskeleton in a non-muscle tissue. Furthermore, the cytoskeletal remodelling constitutes a previously undescribed morphogenetic event, which may provide us with a model system for in vivo studies on adhesion dynamics in Drosophila.