On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Lymphatic vessels in health and disease: Role of the VEGF-C/VEGFR-3 pathway and the transcription factor FOXC2

The circulatory system consists of two vessel types, which act in concert but significantly differ from each other in several structural and functional aspects as well as in mechanisms governing their development. The blood vasculature transports oxygen, nutrients and cells to tissues whereas the lymphatic vessels collect extravasated fluid, macromolecules and cells of the immune system and return them back to the blood circulation. Understanding the molecular mechanisms behind the developmental and functional regulation of the lymphatic system long lagged behind that of the blood vasculature. Identification of several markers specific for the lymphatic endothelium, and the discovery of key factors controlling the development and function of the lymphatic vessels have greatly facilitated research in lymphatic biology over the past few years. Recognition of the crucial importance of lymphatic vessels in certain pathological conditions, most importantly in tumor metastasis, lymphedema and inflammation, has increased interest in this vessel type, for so long overshadowed by its blood vascular cousin. VEGF-C (Vascular Endothelial Growth Factor C) and its receptor VEGFR-3 are essential for the development and maintenance of embryonic lymphatic vasculature. Furthermore, VEGF-C has been shown to be upregulated in many tumors and its expression found to positively correlate with lymphatic metastasis. Mutations in the transcription factor FOXC2 result in lymphedema-distichiasis (LD), which suggests a role for FOXC2 in the regulation of lymphatic development or function. This study was undertaken to obtain more information about the role of the VEGF-C/VEGFR-3 pathway and FOXC2 in regulating lymphatic development, growth, function and survival in physiological as well as in pathological conditions. We found that the silk-like carboxyterminal propeptide is not necessary for the lymphangiogenic activity of VEGF-C, but enhances it, and that the aminoterminal propeptide mediates binding of VEGF-C to the neuropilin-2 coreceptor, which we suggest to be involved in VEGF-C signalling via VEGFR-3. Furthermore, we found that overexpression of VEGF-C increases tumor lymphangiogenesis and intralymphatic tumor growth, both of which could be inhibited by a soluble form of VEGFR-3. These results suggest that blocking VEGFR-3 signalling could be used for prevention of lymphatic tumor metastasis. This might prove to be a safe treatment method for human cancer patients, since inhibition of VEGFR-3 activity had no effect on the normal lymphatic vasculature in adult mice, though it did lead to regression of lymphatic vessels in the postnatal period. Interestingly, in contrast to VEGF-C, which induces lymphangiogenesis already during embryonic development, we found that the related VEGF-D promotes lymphatic vessel growth only after birth. These results suggest, that the lymphatic vasculature undergoes postnatal maturation, which renders it independent of ligand induced VEGFR-3 signalling for survival but responsive to VEGF-D for growth. Finally, we show that FOXC2 is necessary for the later stages of lymphatic development by regulating the morphogenesis of lymphatic valves, as well as interactions of the lymphatic endothelium with vascular mural cells, in which it cooperates with VEGFR-3. Furthermore, our study indicates that the absence of lymphatic valves, abnormal association of lymphatic capillaries with mural cells and an increased amount of basement membrane underlie the pathogenesis of LD. These findings have given new insight into the mechanisms of normal lymphatic development, as well as into the pathogenesis of diseases involving the lymphatic vasculature. They also reveal new therapeutic targets for the prevention and treatment of tumor metastasis and lymphatic vascular failure in certain forms of lymphedema. Several interesting questions were posed that still need to be addressed. Most importantly, the mechanism of VEGF-C promoted tumor metastasis and the molecular nature of the postnatal lymphatic vessel maturation remain to be elucidated.

Folding and Selective Exit of Reporter Proteins from the Yeast Endoplasmic Reticulum

The present study analyses the traffic of Hsp150 fusion proteins through the endoplasmic reticulum (ER) of yeast cells, from their post-translational translocation and folding to their exit from the ER via a selective COPI-independent pathway. The reporter proteins used in the present work are: Hsp150p, an O-glycosylated natural secretory protein of Saccharomyces cerevisiae, as well as fusion proteins consisting of a fragment of Hsp150 that facilitates in the yeast ER proper folding of heterologous proteins fused to it. It is thought that newly synthesized polypeptides are kept in an unfolded form by cytosolic chaperones to facilitate the post-translational translocation across the ER membrane. However, beta-lactamase, fused to the Hsp150 fragment, folds in the cytosol into bioactive conformation. Irreversible binding of benzylpenicillin locked beta-lactamase into a globular conformation, and prevented the translocation of the fusion protein. This indicates that under normal conditions the beta-lactamase portion unfolds for translocation. Cytosolic machinery must be responsible for the unfolding. The unfolding is a prerequisite for translocation through the Sec61 channel into the lumen of the ER, where the polypeptide is again folded into a bioactive and secretion-competent conformation. Lhs1p is a member of the Hsp70 family, which functions in the conformational repair of misfolded proteins in the yeast ER. It contains Hsp70 motifs, thus it has been thought to be an ATPase, like other Hsp70 members. In order to understand its activity, authentic Lhs1p and its recombinant forms expressed in E. coli, were purified. However, no ATPase activity of Lhs1p could be detected. Nor could physical interaction between Lhs1p and activators of the ER Hsp70 chaperone Kar2p, such as the J-domain proteins Sec63p, Scj1p, and Jem1p and the nucleotide exchange factor Sil1p, be demonstrated. The domain structure of Lhs1p was modelled, and found to consist of an ATPase-like domain, a domain resembling the peptide-binding domain (PBD) of Hsp70 proteins, and a C-terminal extension. Crosslinking experiments showed that Lhs1p and Kar2p interact. The interacting domains were the C-terminal extension of Lhs1p and the ATPase domain of Kar2p, and this interaction was independent of ATPase activity of Kar2p. A model is presented where the C-terminal part of Lhs1p forms a Bag-like 3 helices bundle that might serve in the nucleotide exchange function for Kar2p in translocation and folding of secretory proteins in the ER. Exit of secretory proteins in COPII-coated vesicles is believed to be dependent of retrograde transport from the Golgi to the ER in COPI-coated vesicles. It is thought that receptors escaping to the Golgi must be recycled back to the ER exit sites to recruit cargo proteins. We found that Hsp150 leaves the ER even in the absence of functional COPI-traffic from the Golgi to the ER. Thus, an alternative, COPI-independent ER exit pathway must exists, and Hsp150 is recruited to this route. The region containing the signature guiding Hsp150 to this alternative pathway was mapped.

Role of HMGB1 in cells of the circulation

The matrix of blood is a liquid plasma that transports molecules and blood cells within vessels lined by endothelial cells. High-mobility group B1 (HMGB1) is a protein expressed in blood cells. Under normal circumstances, HMGB1 is virtually absent from plasma, but during inflammation or trauma its level in plasma is increased. In resting and quiescent cells, HMGB1 is usually localized in the intracellular compartment, with the exception of motile cells that express HMGB1 on their outer surface to mediate cell migration. During cell transformation or immune cell activation HMGB1 can be actively secreted outside of the cell. Further, when a cell is damaged, HMGB1 can passively leak into extracellular environment. Extracellular HMGB1 can then participate in regulation of the immune response and under some conditions it can mediate lethality in systemic inflammatory response. The aim of this study was to evaluate the expression and functions of HMGB1 in cells of the vascular system and to investigate the prognostic value of circulating HMGB1 in severe sepsis and septic shock. HMGB1 was detected in platelets, leukocytes, and endothelial cells. HMGB1 was released from platelets and leukocytes, and it was found to mediate their adhesive and migratory functions. During severe infections the plasma levels of HMGB1 were elevated; however, no direct correlation with lethality was found. Further, the analysis of proinflammatory mechanisms suggested that HMGB1 forms complexes with other molecules to activate the immune system. In conclusion, HMGB1 is expressed in the cells of the vascular system, and it participates in inflammatory mechanisms by activating platelets and leukocytes and by mediating monocyte migration.

The high- and low-activity forms of human plasma phospholipid transfer protein (PLTP)

Plasma phospholipid transfer protein (PLTP) plays a crucial role in high-density lipoprotein (HDL) metabolism and reverse cholesterol transport (RCT). It mediates the generation of pre-beta-HDL particles, enhances the cholesterol efflux from peripheral cells to pre-beta-HDL, and metabolically maintains the plasma HDL levels by facilitating the transfer of post-lipolytic surface remnants of triglyceride-rich lipoproteins to HDL. In addition to the antiatherogenic properties, recent findings indicate that PLTP has also proatherogenic characteristics, and that these opposite characteristics of PLTP are dependent on the site of PLTP expression and action. In human plasma, PLTP exists in a high-activity (HA-PLTP) and a low-activity form (LA-PLTP), which are associated with macromolecular complexes of different size and composition. The aims of this thesis were to isolate the two PLTP forms from human plasma, to characterize the molecular complexes in which the HA- and LA-PLTP reside, and to study the interactions of the PLTP forms with apolipoproteins (apo) and the ability of apolipoproteins to regulate PLTP activity. In addition, we aimed to study the distribution of the two PLTP forms in a Finnish population sample as well as to find possible regulatory factors for PLTP by investigating the influence of lipid and glucose metabolism on the balance between the HA- and LA-PLTP. For these purposes, an enzyme-linked immunosorbent assay (ELISA) capable of determining the serum total PLTP concentration and quantitating the two PLTP forms separately was developed. In this thesis, it was demonstrated that the HA-PLTP isolated from human plasma copurified with apoE, whereas the LA-PLTP formed a complex with apoA-I. The separation of these two PLTP forms was carried out by a dextran sulfate (DxSO4)-CaCl2 precipitation of plasma samples before the mass determination. A similar immunoreactivity of the two PLTP forms in the ELISA could be reached after a partial sample denaturation by SDS. Among normolipidemic Finnish individuals, the mean PLTP mass was 6.6 +/- 1.5 mg/l and the mean PLTP activity 6.6 +/- 1.7 umol/ml/h. Of the serum PLTP concentration, almost 50% represented HA-PLTP. The results indicate that plasma HDL levels could regulate PLTP concentration, while PLTP activity could be regulated by plasma triglyceride-rich very low-density lipoprotein (VLDL) concentration. Furthermore, new evidence is presented that PLTP could also play a role in glucose metabolism. Finally, both PLTP forms were found to interact with apoA-I, apoA-IV, and apoE. In addition, both apoE and apoA-IV, but not apoA-I, were capable of activating the LA-PLTP. These findings suggest that the distribution of the HA- and LA-PLTP in human plasma is subject to dynamic regulation by apolipoproteins.

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.

Neuromagnetic studies on cortical somatosensory functions in infants and children : Normal development and effect of early brain lesions

Until recently, objective investigation of the functional development of the human brain in vivo was challenged by the lack of noninvasive research methods. Consequently, fairly little is known about cortical processing of sensory information even in healthy infants and children. Furthermore, mechanisms by which early brain insults affect brain development and function are poorly understood. In this thesis, we used magnetoencephalography (MEG) to investigate development of cortical somatosensory functions in healthy infants, very premature infants at risk for neurological disorders, and adolescents with hemiplegic cerebral palsy (CP). In newborns, stimulation of the hand activated both the contralateral primary (SIc) and secondary somatosensory cortices (SIIc). The activation patterns differed from those of adults, however. Some of the earliest SIc responses, constantly present in adults, were completely lacking in newborns and the effect of sleep stage on SIIc responses differed. These discrepancies between newborns and adults reflect the still developmental stage of the newborns’ somatosensory system. Its further maturation was demonstrated by a systematic transformation of the SIc response pattern with age. The main early adult­like components were present by age two. In very preterm infants, at term age, the SIc and SIIc were activated at similar latencies as in healthy fullterm newborns, but the SIc activity was weaker in the preterm group. The SIIc response was absent in four out of the six infants with brain lesions of the underlying hemisphere. Determining the prognostic value of this finding remains a subject for future studies, however. In the CP adolescents with pure subcortical lesions, contrasting their unilateral symptoms, the SIc responses of both hemispheres differed from those of controls: For example the distance between SIc representation areas for digits II and V was shorter bilaterally. In four of the five CP patients with cortico­subcortical brain lesions, no normal early SIc responses were evoked by stimulation of the palsied hand. The varying differences in neuronal functions, underlying the common clinical symptoms, call for investigation of more precisely designed rehabilitation strategies resting on knowledge about individual functional alterations in the sensorimotor networks.

Immune mechanisms in atherosclerosis; Focus on the role of the complement system

Atherosclerosis is an inflammatory disease characterized by accumulation of lipids in the inner layer of the arterial wall. During atherogenesis, various structures that are recognized as non-self by the immune system, such as modified lipoproteins, are deposited in the arterial wall. Accordingly, atherosclerotic lesions and blood of humans and animals with atherosclerotic lesions show signs of activation of both innate and adaptive immune responses. Although immune attack is initially a self-protective reaction, which is meant to destroy or remove harmful agents, a chronic inflammatory state in the arterial wall accelerates atherosclerosis. Indeed, various modulations of the immune system of atherosclerosis-prone animals have provided us with convincing evidence that immunological mechanisms play an important role in the pathogenesis of atherosclerosis. This thesis focuses on the role of complement system, a player of the innate immunity, in atherosclerosis. Complement activation via any of the three different pathways (classical, alternative, lectin) proceeds as a self-amplifying cascade, which leads to the generation of opsonins, anaphylatoxins C3a and C5a, and terminal membrane-attack complex (MAC, C5b-9), all of which regulate the inflammatory response and act in concert to destroy their target structures. To prevent uncontrolled complement activation or its attack against normal host cells, complement needs to be under strict control by regulatory proteins. The complement system has been shown to be activated in atherosclerotic lesions, modified lipoproteins and immune complexes containing oxLDL, for instance, being its activators. First, we investigated the presence and role of complement regulators in human atherosclerotic lesions. We found that inhibitors of the classical and alternative pathways, C4b-binding protein and factor H, respectively, were present in atherosclerotic lesions, where they localized in the superficial proteoglycan-rich layer. In addition, both inhibitors were found to bind to arterial proteoglycans in vitro. Immunohistochemical stainings revealed that, in the superficial layer of the intima, complement activation had been limited to the C3 level, whereas in the deeper intimal layers, complement activation had proceeded to the terminal C5b-9 level. We were also able to show that arterial proteoglycans inhibit complement activation in vitro. These findings suggested to us that the proteoglycan-rich layer of the arterial intima contains matrix-bound complement inhibitors and forms a protective zone, in which complement activation is restricted to the C3 level. Thus, complement activation is regulated in atherosclerotic lesions, and the extracellular matrix is involved in this process. Next, we studied whether the receptors for the two complement derived effectors, anaphylatoxins C3a and C5a, are expressed in human coronary atherosclerotic lesions. Our results of immunohistochemistry and RT-PCR analysis showed that, in contrast to normal intima, C3aR and C5aR were highly expressed in atherosclerotic lesions. In atherosclerotic plaques, the principal cells expressing both C3aR and C5aR were macrophages. Moreover, T cells expressed C5aR, and a small fraction of them also expressed C3aR, mast cells expressed C5aR, whereas endothelial cells and subendothelial smooth muscle cells expressed both C3aR and C5aR. These results suggested that intimal cells can respond to and become activated by complement-derived anaphylatoxins. Finally, we wanted to learn, whether oxLDL-IgG immune complexes, activators of the classical complement pathway, could have direct cellular effects in atherogenesis. Thus, we tested whether oxLDL-IgG immune complexes affect the survival of human monocytes, the precursors of macrophages, which are the most abundant inflammatory cell type in atherosclerotic lesions. We found that OxLDL-IgG immune complexes, in addition to transforming monocytes into foam cells, promoted their survival by decreasing their spontaneous apoptosis. This effect was mediated by cross-linking Fc receptors with ensuing activation of Akt-dependent survival signaling. Our finding revealed a novel mechanism by which oxLDL-IgG immune complexes can directly affect the accumulation of monocyte-macrophages in human atherosclerotic lesions and thus play a role in atherogenesis.

Development of Novel Assays for Measuring Different Molecular Forms of Prostate Specific Antigen

Prostate cancer (PCa) is the most commonly diagnosed non-skin cancer and second leading cause of cancer-related death of men in developed countries. Measurement of prostate specific antigen (PSA) is a very sensitive method for diagnosing and monitoring of prostate cancer (PCa), but the specificity needs improvement. Measurements of different molecular forms of PSA have been shown to improve differentiation between PCa and benign prostatic diseases. However, accurate measurement of some isoforms has not been achieved in previous assays. The aim of the present study was to develop new assays that reliably measure enzymatically active PSA, PSA-α1-chymotryposin (PSA-ACT) and PSA-α1-protease inhibitor (PSA-API), and to evaluate their diagnostic value. Double-label immunofluorometric assays using a novel monoclonal antibody (MAb) and another antibody to either free PSA (fPSA) or total PSA (tPSA) were developed and used to measure PSA-ACT and fPSA or tPSA at the same time. These assays provide enough sensitivity for measurement of PSA-ACT in sera with low PSA levels. The results obtained confirmed that proportion of PSA-ACT to tPSA (%PSA-ACT) was as useful as proportion of fPSA to tPSA (%fPSA) for discrimination between PCa and benign prostatic hyperplasia (BPH). We developed an immunoassay for detection of PSA-API based on proximity ligation, which improved assay sensitivity 10-fold compared with conventional assays. Our results confirmed previous findings that the PSA-API level is somewhat lower in men with than without PCa, and the combination of %fPSA and proportion of PSA-API to tPSA (%PSA-API) provides diagnostic improvement compared with either method alone. Assays based on this principle should be applicable to other immunoassays in which the nonspecific background is a problem. An immunopeptidometric sandwich assay (IPMA) was developed to measure the enzymatically active PSA. This assay showed high specificity, but sensitivity was not good enough for measurement of PSA concentrations in the gray zone, 2-10 µg/L, in which tPSA does not efficiently differentiate between PCa and BPH. We further developed a solid-phase proximity ligation immunoassay, which provided a 10-fold improvement in sensitivity. This proof of concept study shows that peptides reacting with proteins are potentially useful for sensitive and specific measurement of protein variants for which specific MAbs cannot be obtained.