Perineuronale Netze (PN) sind eine spezialisierte Form der neuronalen extrazellulären Matrix. Es wird vermutet, dass sie neuroprotektive Eigenschaften besitzen und die von ihnen umschlossenen Neurone gegenüber Degeneration schützen. Mehrere Studien untersuchten bereits die PN in Zusammenhang mit der Pathologie der Alzheimer-Erkrankung. Für die Frontotemporalen Demenzen, die nach der Alzheimer-Erkrankung und der vaskulären Demenz zu den häufigsten dementiellen Erkrankungen gehören, ist die Beziehung von PN und Tau-Protein (TP)-Pathologie noch nicht untersucht worden. Die Dissertation beschäftigt sich mit der Korrelation von netztragenden Neuronen mit TP-Pathologie in einem Mausmodel der Frontotemporalen Demenz mit Parkinsonismus des Chromosoms 17 (FTDP-17). Sie geht der Frage nach, ob netztragende Neuronen vor Degeneration und intrazellulären Ablagerungen von verändertem TP, in Form von Hyperphosphorylierungen (HP) und Neurofibrillären Tangles (NFT), geschützt sind. Mit Hilfe immunhistochemischer Fluoreszenzmarkierung und Western Blot wurden die Gehirne transgener Mäuse mit der P301L-Mutation des TP im Alter von drei und achteinhalb Monaten untersucht. Dabei wurden sechs Hirnregionen ausgewählt: Primärer Somatosensorischer Kortex (PSC), Entorhinaler Kortex (EC), Hippokampus (Hipp), Pars magnocellularis des Nucleus ruber (NR-m), Pars reticulata der Substantia nigra (SN-r) und Motorischer Trigeminuskern (Mo5). Die Untersuchungen zeigen, dass die PN bei der FTDP-17 die Neurone nicht explizit vor TP-Pathologie schützen. Jedoch kommt es zu keiner signifikanten Reduktion der netztragenden Zellen im Altersgang, sodass eine neuroprotektive Funktion der PN weiterhin vermutet werden kann.

M. Niemann-Pick Typ C (NPC) ist eine juvenile Demenz mit intrazellulärer Anreicherung von freiem Cholesterin, M. Alzheimer (AD) eine senile Demenz, die mit einem Polymorphismus im Gen des Cholesterintransportproteins Apolipoprotein E (ApoE) assoziiert ist. Bei beiden Erkrankungen treten im Gehirn zahlreiche neurofibrilläre Tangles (NFT), bestehend aus Protein Tau, auf. Es sollte mit einer für freies Cholesterin spezifischen Filipin-Färbung herausgefunden werden, ob sich bei beiden Erkrankungen der Cholesteringehalt Tangle-tragender Neurone von dem Tangle-freier unterscheidet. Zur Verfügung standen diverse Teile aus dem Zentralen Nervensystem von 5 NPC- und Gyri temporales superficiales von 9 AD-Fällen. In Material von 3 NPC-Fällen und 1 AD-Fall fanden sich intraneuronale, mit Tangles assoziierte Cholesterinakkumulationen. In 3 AD-Fällen fanden sich außerdem Cholesterinakkumulationen in Assoziation mit Senilen Plaques. Der Cholesteringehalt Tangle-tragender Neurone war in 6 Regionen der NPC-Fälle und in 3 AD-Fällen erhöht. Für alle Neuronenpaare der AD-Fälle insgesamt ergab sich ein erhöhter Cholesteringehalt des Tangle-tragenden Neurons. Cholesterinspeicherung im NPC-Hirn könnte über oxidativen Stress oder eine Veränderung der cholesterinabhängigen Signaltransduktion zur Tangle-Bildung führen. Argumente für die Unterstützung der Tangle-Bildung durch Cholesterin über oxidativen Stress und veränderte Signaltransduktion in AD werden angeführt. Diese Untersuchung erlaubt, neue Hypothesen zu gemeinsamen Mechanismen der Tangle-Entstehung in AD und NPC zu formulieren. / Niemann-Pick type C disease (NPC) is a juvenile dementia with intracellular accumulation of free cholesterol, whereas Alzheimer s disease (AD) is a senile dementia associated with a gene polymorphism of a cholesterol transport protein, apolipoprotein E (apoE). In both conditions, there are abundant neurofibrillary tangles (NFT) in brain, consisting of protein tau. This study addresses the issue whether cholesterol content of tangle-bearing neurons is the same compared to tangle-free neurons, in both diseases. For this purpose, staining with the free cholesterol-specific fluorochrome filipin was used. Several CNS tissue specimen of 5 NPC cases and superior temporal gyri of 9 AD cases were available. In 3 NPC cases and 1 AD case, intraneuronal cholesterol accumulation were found associated with neurofibrillary tangles. Furthermore, cholesterol accumulations were found associated with senile plaques in 3 AD cases. Cholesterol content of tangle-bearing neurons was increased in 6 regions of the NPC cases and in 3 AD cases. For all neurons analysed in AD, the tangle-bearing neuron showed more cholesterol than the adjacent tangle-free neuron. Cholesterol storage in NPC brain could lead to neurofibrillary degeneration by enhancing oxidative stress or by alterating cholesterol-dependent signal transduction. Cholesterol accumulation in AD neurons could lead to neurofibrillary degeneration by the same mechanisms. This study allows the creation of new hypotheses concerning common mechanisms of neurofibrillary degeneration in both Niemann-Pick type C and Alzheimer s diseases.

Perineuronale Netze (PN) sind eine spezialisierte Form der neuronalen extrazellulären Matrix. Es wird vermutet, dass sie neuroprotektive Eigenschaften besitzen und die von ihnen umschlossenen Neurone gegenüber Degeneration schützen. Mehrere Studien untersuchten bereits die PN in Zusammenhang mit der Pathologie der Alzheimer-Erkrankung. Für die Frontotemporalen Demenzen, die nach der Alzheimer-Erkrankung und der vaskulären Demenz zu den häufigsten dementiellen Erkrankungen gehören, ist die Beziehung von PN und Tau-Protein (TP)-Pathologie noch nicht untersucht worden. Die Dissertation beschäftigt sich mit der Korrelation von netztragenden Neuronen mit TP-Pathologie in einem Mausmodel der Frontotemporalen Demenz mit Parkinsonismus des Chromosoms 17 (FTDP-17). Sie geht der Frage nach, ob netztragende Neuronen vor Degeneration und intrazellulären Ablagerungen von verändertem TP, in Form von Hyperphosphorylierungen (HP) und Neurofibrillären Tangles (NFT), geschützt sind. Mit Hilfe immunhistochemischer Fluoreszenzmarkierung und Western Blot wurden die Gehirne transgener Mäuse mit der P301L-Mutation des TP im Alter von drei und achteinhalb Monaten untersucht. Dabei wurden sechs Hirnregionen ausgewählt: Primärer Somatosensorischer Kortex (PSC), Entorhinaler Kortex (EC), Hippokampus (Hipp), Pars magnocellularis des Nucleus ruber (NR-m), Pars reticulata der Substantia nigra (SN-r) und Motorischer Trigeminuskern (Mo5). Die Untersuchungen zeigen, dass die PN bei der FTDP-17 die Neurone nicht explizit vor TP-Pathologie schützen. Jedoch kommt es zu keiner signifikanten Reduktion der netztragenden Zellen im Altersgang, sodass eine neuroprotektive Funktion der PN weiterhin vermutet werden kann.

Pan, Tak Yin. / Thesis submitted in: November 2007. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references. / Abstracts in English and Chinese. / Acknowledgements --- p.i / Abstract (English) --- p.ii / Abstract (Chinese) --- p.iv / Content --- p.v / Abbreviations --- p.x / List of Figures --- p.xi / List of Tables --- p.xii / Chapter Chapter 1: --- Introduction --- p.1 / Chapter 1.1 --- Alzheimer's Disease --- p.1 / Chapter 1.1.1 --- Cholinergic hypothesis --- p.2 / Chapter 1.1.2 --- p-amyloid hypothesis --- p.2 / Chapter 1.1.3 --- Taupathy hypothesis --- p.3 / Chapter 1.1.4 --- Current therapies --- p.4 / Chapter 1.2 --- Proteins Involved in Alzhemer's Disease --- p.5 / Chapter 1.2.1 --- Acetylcholinesterase (AChE) --- p.5 / Chapter 1.2.2 --- p-amyloid --- p.6 / Chapter 1.2.3 --- Paired helical filaments (PHF) --- p.7 / Chapter 1.2.4 --- Protein kinases --- p.8 / Chapter 1.2.4.1 --- Glycogen synthase kinase-3 (GSK-3) --- p.9 / Chapter 1.2.4.2 --- Cyclin-dependent kinase-5 (CDK-5) --- p.9 / Chapter 1.2.5 --- Protein phosphatase (PP) --- p.10 / Chapter 1.2.5.1 --- Protein phosphatase 1 (PP-1) --- p.11 / Chapter 1.2.5.2 --- Protein phosphatise 2A (PP-2A) --- p.12 / Chapter 1.2.5.3 --- Protein phosphatise 2B (PP-2B) --- p.13 / Chapter 1.2.6 --- Apoptotic and Anti-apoptotic proteins --- p.14 / Chapter 1.2.6.1 --- Caspase-3 --- p.15 / Chapter 1.2.6.2 --- Bcl-2 --- p.15 / Chapter 1.3 --- Flavonoids --- p.16 / Chapter 1.3.1 --- Biosynthesis of flavonoids --- p.17 / Chapter 1.3.2 --- Biological functions of flavonoids in plants --- p.18 / Chapter 1.3.3 --- Beneficial effects of flavonoids on human health --- p.19 / Chapter Chapter 2: --- Materials and Methods --- p.20 / Chapter 2.1 --- Differentiation of SHSY-5Y cells --- p.20 / Chapter 2.1.1 --- SHSY-5Y cell culture --- p.20 / Chapter 2.1.2 --- Counting cells --- p.20 / Chapter 2.1.3 --- Retinoic acid differentiation --- p.21 / Chapter 2.2 --- Western blot analysis --- p.21 / Chapter 2.2.1 --- Extraction of proteins from mammalian cells --- p.21 / Chapter 2.2.2 --- Sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) --- p.22 / Chapter 2.2.3 --- Semi-dry protein transfer to nitrocellulose membrane --- p.23 / Chapter 2.2.4. --- Membrane blocking and immunostaining --- p.24 / Chapter 2.3 --- MTT assay --- p.25 / Chapter 2.4 --- Hoechst 33342 Nuclei staining --- p.25 / Chapter 2.5 --- Cell cycle analysis --- p.25 / Chapter 2.5.1 --- Ethanol fixation --- p.25 / Chapter 2.5.2 --- Propidium iodide staining --- p.26 / Chapter 2.6 --- Annexin V-FITC & Propidium iodide staining --- p.26 / Chapter 2.7 --- DNA fragmentation analysis --- p.26 / Chapter 2.7.1 --- Phenol/Chloroform extraction of DNA --- p.26 / Chapter 2.7.2 --- Ethanol precipitation of DNA --- p.27 / Chapter 2.7.3 --- Agarose gel electrophoresis of DNA --- p.27 / Chapter 2.8 --- Proteomic analysis --- p.28 / Chapter 2.8.1 --- First dimension: isoelectric focusing --- p.28 / Chapter 2.8.2 --- Second dimension: SDS PAGE --- p.29 / Chapter 2.8.3 --- Gel staining --- p.30 / Chapter 2.8.3.1 --- Silver staining --- p.30 / Chapter 2.8.3.2 --- SYBRO Ruby staining --- p.31 / Chapter 2.8.4 --- Gel scanning and image analysis --- p.31 / Chapter 2.8.5 --- ln-gel digestion --- p.32 / Chapter 2.8.6 --- Zip Tip for desalting the digested sample --- p.33 / Chapter 2.8.7 --- Protein identification with mass spectrometry and database search --- p.33 / Chapter Chapter 3: --- Characterization of Okadaic acid-induced tail hyperphosphorylation in SHSY-5Y cells --- p.35 / Chapter 3.1 --- Introduction --- p.35 / Chapter 3.2 --- Objectives --- p.37 / Chapter 3.3 --- Results --- p.38 / Chapter 3.3.1 --- Differentiation of SH-SY5Y cell --- p.38 / Chapter 3.3.2 --- Changes of protein expression after okadaic acid treatment --- p.40 / Chapter 3.3.3 --- Neurite Retraction Induced by okadaic acid --- p.42 / Chapter 3.3.4 --- Okadaic acid-induced Cell Death measured by MTT assay --- p.44 / Chapter 3.3.5 --- Hoechst 33342 Nuclei Staining --- p.44 / Chapter 3.3.6 --- Cell cycle analysis by propidium iodide staining --- p.47 / Chapter 3.3.7 --- Early Apoptotic cells detection by Annexin V/PI staini --- p.49 / Chapter 3.3.8 --- DNA fragmentation --- p.51 / Chapter 3.4 --- Discussion --- p.53 / Chapter Chapter 4: --- Flavonoids screening for protecting neuronal death by preventing tau hyperphosphorylation --- p.57 / Chapter 4.1 --- Introduction --- p.57 / Chapter 4.2 --- Objectives --- p.58 / Chapter 4.3 --- Tested flavonoids --- p.59 / Chapter 4.4 --- Results --- p.60 / Chapter 4.4.1 --- Toxicity of flavonoids --- p.60 / Chapter 4.4.2 --- Effects of flavonoid pre-treatment on OA-induced neu retractions and cell death --- p.62 / Chapter 4.4.3 --- Western blot analysis --- p.65 / Chapter 4.4.4 --- The effect of different concentrations of hesperidin or OA treatment --- p.70 / Chapter 4.4.5 --- Proteomic analysis --- p.74 / Chapter 4.5 --- Discussion --- p.78 / Chapter Chapter 5: --- General Discussion --- p.82 / References

Tauopathies are a group of neurodegenerative diseases characterized by the abnormal deposition of the protein tau, a microtubule stabilizing protein. Under normal physiological conditions tau is a highly soluble protein that is not prone to aggregation. In disease states alterations to tau lead to enhanced fibril formation and aggregation, eventually forming neurofibrillary tangles (NFTs). The exact cause for NFT deposition is unknown, but increased post-translational modifications and mutations to the tau gene can increase tangle formation. Tauopathic brains are stuck in a detrimental cycle, with cellular dysfunction contributing to the development of tau pathology and the development of tau pathology contributing to cellular dysfunction. The exact mechanisms by which each part of the cycle contributes to the other are still being explored. To investigate the unique contributions of each part of this cycle we utilized two separate models of tauopathy: one chronic and one acute. Overall this project provides novel insight into the role of pathological tau as both a cause, and a consequence, of cellular dysfunction. To understand how development of tau pathology contributes to cellular dysfunction we studied chronic disease models. Using human brain tissue we found that under normal conditions tau associates with ribosomes but that this interaction is enhanced in Alzheimer’s disease brains. We then used in vitro and in vivo models of tauopathy to show that this association causes a decrease in protein synthesis. Finally, we show that wild type tau and mutant tau reduce protein translation to similar levels. To understand how general cellular dysfunction contributes to development of pathology we used an acute model of tauopathy through traumatic brain injury (TBI). We injured rTg4510 tau transgenic mice at different ages to investigate the effect of TBI on tau fibrillization (2 month old) and the effect of TBI on tau already in NFTs (4.5 month old). In 2 month old mice, we found that tau hyperphosphorylation was decreased at 24 hours and increased at 7 days post injury, and that tau oligomerization was decreased at 24 hours post injury. We also found that tau fibrillization was not increased after 24 hours or 7 days post injury. In 4.5 month old mice, we found that TBI did not increase or decrease tangle counts in the brain, but we did qualitatively observe decreased variability within groups. Overall these studies contribute novel understanding of tau’s role in different disease states. We identified a functional consequence of the interaction between tau and ribosomes, and demonstrated that a single head impact did not increase tau fibril formation within 7 days of injury. While human diseases associated with TBI show neurofibrillary tangle deposition, we have yet to recreate that aspect of the disease in research models of TBI. Our findings support the need for further investigation into the nuances of tau in disease, especially following TBI.

Doctor of Philosophy / This thesis presents a study of the cyclotomic BMW algebras, introduced by Haring-Oldenburg as a generalization of the BMW (Birman-Murakami-Wenzl) algebras related to the cyclotomic Hecke algebras of type G(k,1,n) (also known as Ariki-Koike algebras) and type B knot theory involving affine/cylindrical tangles. The motivation behind the definition of the BMW algebras may be traced back to an important problem in knot theory; namely, that of classifying knots (and links) up to isotopy. The algebraic definition of the BMW algebras uses generators and relations originally inspired by the Kauffman link invariant. They are intimately connected with the Artin braid group of type A, Iwahori-Hecke algebras of type A, and with many diagram algebras, such as the Brauer and Temperley-Lieb algebras. Geometrically, the BMW algebra is isomorphic to the Kauffman Tangle algebra. The representations and the cellularity of the BMW algebra have now been extensively studied in the literature. These algebras also feature in the theory of quantum groups, statistical mechanics, and topological quantum field theory. In view of these relationships between the BMW algebras and several objects of "type A", several authors have since naturally generalized the BMW algberas for other types of Artin groups. Motivated by knot theory associated with the Artin braid group of type B, Haring-Oldenburg introduced the cyclotomic BMW algebras B_n^k as a generalization of the BMW algebras such that the Ariki-Koike algebra h_{n,k} is a quotient of B_n^k, in the same way the Iwahori-Hecke algebra of type A is a quotient of the BMW algebra. In this thesis, we investigate the structure of these algebras and show they have a topological realization as a certain cylindrical analogue of the Kauffman Tangle algebra. In particular, they are shown to be R-free of rank k^n (2n-1)!! and bases that may be explicitly described both algebraically and diagrammatically in terms of cylindrical tangles are obtained. Unlike the BMW and Ariki-Koike algebras, one must impose extra so-called "admissibility conditions" on the parameters of the ground ring in order for these results to hold. This is due to potential torsion caused by the polynomial relation of order k imposed on one of the generators of B_n^k. It turns out that the representation theory of B_2^k is crucial in determining these conditions precisely. The representation theory of B_2^k is analysed in detail in a joint preprint with Wilcox in [45] (http://arxiv.org/abs/math/0611518). The admissibility conditions and a universal ground ring with admissible parameters are given explicitly in Chapter 3. The admissibility conditions are also closely related to the existence of a non-degenerate Markov trace function of B_n^k which is then used together with the cyclotomic Brauer algebras in the linear independency arguments contained in Chapter 4. Furthermore, in Chapter 5, we prove the cyclotomic BMW algebras are cellular, in the sense of Graham and Lehrer. The proof uses the cellularity of the Ariki-Koike algebras (Graham-Lehrer [16] and Dipper-James-Mathas [8]) and an appropriate "lifting" of a cellular basis of the Ariki-Koike algebras into B_n^k, which is compatible with a certain anti-involution of B_n^k. When k = 1, the results in this thesis specialize to those previously established for the BMW algebras by Morton-Wasserman [30], Enyang [9], and Xi [47]. REMARKS: During the writing of this thesis, Goodman and Hauschild-Mosley also attempt similar arguments to establish the freeness and diagram algebra results mentioned above. However, they withdrew their preprints ([14] and [15]), due to issues with their generic ground ring crucial to their linear independence arguments. A similar strategy to that proposed in [14], together with different trace maps and the study of rings with admissible parameters in Chapter 3, is used in establishing linear independency of our basis in Chapter 4. Since the submission of this thesis, new versions of these preprints have been released in which Goodman and Hauschild-Mosley use alternative topological and Jones basic construction theory type arguments to establish freeness of B_n^k and an isomorphism with the cyclotomic Kauffman Tangle algebra. However, they require their ground rings to be an integral domain with parameters satisfying the (slightly stronger) admissibility conditions introduced by Wilcox and the author in [45]. Also, under these conditions, Goodman has obtained cellularity results. Rui and Xu have also obtained freeness and cellularity results when k is odd, and later Rui and Si for general k, under the assumption that \delta is invertible and using another stronger condition called "u-admissibility". The methods and arguments employed are strongly influenced by those used by Ariki, Mathas and Rui [3] for the cyclotomic Nazarov-Wenzl algebras and involve the construction of seminormal representations; their preprints have recently been released on the arXiv. It should also be noted there are slight differences between the definitions of cyclotomic BMW algebras and ground rings used, as explained partly above. Furthermore, Goodman and Rui-Si-Xu use a weaker definition of cellularity, to bypass a problem discovered in their original proofs relating to the anti-involution axiom of the original Graham-Lehrer definition. This Ph.D. thesis, completed at the University of Sydney, was submitted September 2007 and passed December 2007.

The aging brain is prone to the development of pathology and dementia. With a rapidly growing elderly population diagnoses of neurodegenerative diseases, such as Alzheimer’s disease (AD), frontotemporal dementia (FTD), and Parkinson’s disease are on the rise. Additionally, diabetes and obesity are linked to an increased risk of dementia. The convergence of this increasingly aged population with the obesity and diabetes epidemic give rise to new concerns regarding the future of prevention and treatment of neurodegenerative diseases. Our lab has previously shown that leptin, an adipokine involved in signaling satiety to the hypothalamus, can modulate the generation of the amyloid beta (Aβ) peptide (a toxic peptide associated with neurologic disease) and attenuate hyperphosphorylation of the tau protein (another peptide prone to forming large insoluble structures causing neurodegeneration). From these studies we have elucidated that leptin resistant mice (which develop severe obesity and type-2 diabetes mellitus) with knock-in mutations for the amyloid precursor protein (APP) and presenilin-1 (PS1) genes develop extensive vascular pathology and cognitive impairments. Interestingly, these mice do not display increased levels of amyloid deposition in the brain. Additionally, increased tau phosphorylation occurs in these mice with leptin resistance. As a follow up to this study db mice were transduced, via adeno-associated virus, with the tau P301L mutant to induce the development of tangle pathology. These mice displayed no cognitive deficits, yet they displayed increases in both tau phosphorylation and tangle count within the hippocampus. Collectively, these studies indicate leptin resistance, obesity, and type-2 diabetes mellitus promote the development of cerebrovascular and neurofibrillary tangle pathologies associated with neurodegeneration and dementia. These observations open many previously unexplored avenues for developing novel therapeutics to treat these devastating diseases.

Doctor of Philosophy / This thesis presents a study of the cyclotomic BMW algebras, introduced by Haring-Oldenburg as a generalization of the BMW (Birman-Murakami-Wenzl) algebras related to the cyclotomic Hecke algebras of type G(k,1,n) (also known as Ariki-Koike algebras) and type B knot theory involving affine/cylindrical tangles. The motivation behind the definition of the BMW algebras may be traced back to an important problem in knot theory; namely, that of classifying knots (and links) up to isotopy. The algebraic definition of the BMW algebras uses generators and relations originally inspired by the Kauffman link invariant. They are intimately connected with the Artin braid group of type A, Iwahori-Hecke algebras of type A, and with many diagram algebras, such as the Brauer and Temperley-Lieb algebras. Geometrically, the BMW algebra is isomorphic to the Kauffman Tangle algebra. The representations and the cellularity of the BMW algebra have now been extensively studied in the literature. These algebras also feature in the theory of quantum groups, statistical mechanics, and topological quantum field theory. In view of these relationships between the BMW algebras and several objects of "type A", several authors have since naturally generalized the BMW algberas for other types of Artin groups. Motivated by knot theory associated with the Artin braid group of type B, Haring-Oldenburg introduced the cyclotomic BMW algebras B_n^k as a generalization of the BMW algebras such that the Ariki-Koike algebra h_{n,k} is a quotient of B_n^k, in the same way the Iwahori-Hecke algebra of type A is a quotient of the BMW algebra. In this thesis, we investigate the structure of these algebras and show they have a topological realization as a certain cylindrical analogue of the Kauffman Tangle algebra. In particular, they are shown to be R-free of rank k^n (2n-1)!! and bases that may be explicitly described both algebraically and diagrammatically in terms of cylindrical tangles are obtained. Unlike the BMW and Ariki-Koike algebras, one must impose extra so-called "admissibility conditions" on the parameters of the ground ring in order for these results to hold. This is due to potential torsion caused by the polynomial relation of order k imposed on one of the generators of B_n^k. It turns out that the representation theory of B_2^k is crucial in determining these conditions precisely. The representation theory of B_2^k is analysed in detail in a joint preprint with Wilcox in [45] (http://arxiv.org/abs/math/0611518). The admissibility conditions and a universal ground ring with admissible parameters are given explicitly in Chapter 3. The admissibility conditions are also closely related to the existence of a non-degenerate Markov trace function of B_n^k which is then used together with the cyclotomic Brauer algebras in the linear independency arguments contained in Chapter 4. Furthermore, in Chapter 5, we prove the cyclotomic BMW algebras are cellular, in the sense of Graham and Lehrer. The proof uses the cellularity of the Ariki-Koike algebras (Graham-Lehrer [16] and Dipper-James-Mathas [8]) and an appropriate "lifting" of a cellular basis of the Ariki-Koike algebras into B_n^k, which is compatible with a certain anti-involution of B_n^k. When k = 1, the results in this thesis specialize to those previously established for the BMW algebras by Morton-Wasserman [30], Enyang [9], and Xi [47]. REMARKS: During the writing of this thesis, Goodman and Hauschild-Mosley also attempt similar arguments to establish the freeness and diagram algebra results mentioned above. However, they withdrew their preprints ([14] and [15]), due to issues with their generic ground ring crucial to their linear independence arguments. A similar strategy to that proposed in [14], together with different trace maps and the study of rings with admissible parameters in Chapter 3, is used in establishing linear independency of our basis in Chapter 4. Since the submission of this thesis, new versions of these preprints have been released in which Goodman and Hauschild-Mosley use alternative topological and Jones basic construction theory type arguments to establish freeness of B_n^k and an isomorphism with the cyclotomic Kauffman Tangle algebra. However, they require their ground rings to be an integral domain with parameters satisfying the (slightly stronger) admissibility conditions introduced by Wilcox and the author in [45]. Also, under these conditions, Goodman has obtained cellularity results. Rui and Xu have also obtained freeness and cellularity results when k is odd, and later Rui and Si for general k, under the assumption that \delta is invertible and using another stronger condition called "u-admissibility". The methods and arguments employed are strongly influenced by those used by Ariki, Mathas and Rui [3] for the cyclotomic Nazarov-Wenzl algebras and involve the construction of seminormal representations; their preprints have recently been released on the arXiv. It should also be noted there are slight differences between the definitions of cyclotomic BMW algebras and ground rings used, as explained partly above. Furthermore, Goodman and Rui-Si-Xu use a weaker definition of cellularity, to bypass a problem discovered in their original proofs relating to the anti-involution axiom of the original Graham-Lehrer definition. This Ph.D. thesis, completed at the University of Sydney, was submitted September 2007 and passed December 2007.

Les mécanismes physiopathologiques liés aux maladies neurodégénératives restent encore largement méconnus. Deux processus semblent être particulièrement en cause dans les phénomènes de neurodégénérescence : la neurotoxicité par afflux massif de calcium due à une activation excessive des récepteurs NMDA (GluN) et la neurotoxicité par déstabilisation du cytosquelette du neurone par le biais de la phosphorylation anormale de la protéine tau. L'imagerie moléculaire par le biais de la tomographie par émission de positons (TEP) et de radiotraceurs, en étudiant les mécanismes moléculaires in vivo, permet de détecter et quantifier ces phénomènes. Ce travail a eu pour objet d'étudier un dérivé de la mémantine, un antagoniste des GluN se fixant sur un site intra-canal accessible uniquement lorsque ces récepteurs sont activés ce qui en fait donc un vecteur d'imagerie intéressant pour étudier leur activation. Nous avons mis au point la synthèse d'un nouveau radiotraceur dérivé de la mémantine : la [18F]-FNM (Fluoroéthylnormémantine). Il s'agit d'une synthèse par substitution nucléophile d'un groupement tosylate par du [18F], suivie d'une hydrolyse acide. Cette synthèse est reproductible avec un rendement de 10%, son activité spécifique est > 355 GBq/µmol. Chez le rat, le traceur passe la barrière hémato-encéphalique et sa distribution cérébrale est bien corrélée avec la localisation des GluN (r=0.622, p<0.0001). Sa cinétique de fixation (40 minutes) est compatible avec son utilisation en TEP. En ce qui concerne les tauopathies, la protéine tau stabilise l'organisation microtubulaire. Lors d'une phosphorylation anormale, l'interaction avec les microtubules diminue et les protéines tau vont s'accumuler en formant des Paires de Filaments en Hélice (PHF). Nous avons optimisé la radiosynthèse de l' [18F]-AV1451 ciblant les PHF. Notre rendement de synthèse est de 30% et l'activité spécifique du traceur > 10 GBq/µmol. Nous avons réalisé des autoradiographies sur des coupes de cerveaux atteints de tauopathie et nous avons constaté la capacité du traceur à différencier les coupes saines des coupes malades. La production de cet outil dans notre centre va nous permettre d'étudier la présence de PHF chez le marmouset, un primate particulièrement intéressant dans l'étude du vieillissement. Nous avons donc réalisé la synthèse de deux radiotraceurs innovants : la [18F]-FNM et le [18F]-AV1451, les synthèses sont reproductibles et les rendements compatibles avec des productions de doses en recherche pré-clinique et clinique. / The pathophysiological mechanisms associated with neurodegenerative diseases remain largely unknown. Two processes appear to be particularly involved in the phenomena of neurodegeneration: neurotoxicity induced by massive influx of calcium caused by excessive activation of NMDA receptors (GluN) and neurotoxicity by destabilization of neuron cytoskeleton through abnormal protein tau phosphorylation. Molecular imaging through positron emission tomography (PET) and radiotracers, by studying the molecular mechanisms in vivo, allows to detect and quantify these phenomena. This work was intended to study a memantine derivative, a GluN antagonist. We chose to develop a ligand that selectively binds to the ion channel in the open and active state which therefore makes it an interesting vector to study their overactivation. We have developed the synthesis of a new memantine analogue radiotracer: the [18F]-FNM (Fluoroéthylnormémantine). This is a synthesis by nucleophilic substitution of a tosylate with [18F], followed by acid hydrolysis. This synthesis is reproducible with a yield of 10%, its specific activity was> 355 GBq / µmol. In rats, the tracer cross the blood-brain barrier and brain distribution correlates well with the location of GluN (r = 0.622, p <0.0001). The binding kinetics (40 minutes) is compatible with its use in PET. Regarding tauopathies, the tau protein stabilizes microtubule organization. During abnormal phosphorylation, interaction with microtubules and tau proteins decreases and tau will accumulate to form Paired helical Filament (PHF). We optimized the radiosynthesis of [18F] AV1451 targeting 3 tau PHF. Our yield of synthesis is 30% and the specific activity of the tracer> 10 GBq / µmol. We made autoradiography on brains sections and have shown tracer ability to differentiate healthy and pathological slices. This tool will allow us to study the presence of PHF in marmosets, a particularly interesting primate in the study of aging. So we performed the synthesis of two innovative radiotracers: the [18F]-FNM and [18F]-AV1451, syntheses are reproducible and yields compatible with doses manufacturing in pre-clinical and clinical research.

Knot theory is the mathematical study of knots. In this thesis we study knots and one of its applications in DNA. Knot theory sits in the mathematical field of topology and naturally this is where the work begins. Topological concepts such as topological spaces, homeomorphisms, and homology are considered. Thereafter knot theory, and in particular, knot theoretical invariants are examined, aiming to provide insights into why it is difficult to answer the question "How can we tell knots appart?". In knot theory invariants such as the bracket polynomial, the Jones polynomial and tricolorability are considered as well as other helpful results like Seifert surfaces. Lastly knot theory is applied to DNA, where it will shed light on how certain enzymes interact with the genome.