A Thesis submitted to The University of Arizona College of Medicine - Phoenix in partial fulfillment of the requirements for the Degree of Doctor of Medicine. / Objective: Formed visual hallucinations are a common phenomenon in neurodegenerative disorders such as Parkinson’s Disease (PD), Alzheimer’s disease (AD) and Dementia with Lewy bodies (DLB). While Lewy‐type alpha‐synucleinopathy (LTSis the hallmark neuropathological finding in PD and DLB, amyloid plaques and neurofibrillary tangles are the pathological finding in AD. Previous research has linked complex or formed visual hallucinations (VH) to LTS in neocortical and limbic areas in patients with PD and DLB. As VH also occur in Alzheimer’s disease, and AD pathology often co‐occurs with LTS, we questioned whether this pathology might also be linked to VH. Methods: We performed a semi‐quantitative neuropathological study across brainstem, limbic, and cortical structures in subjects with a documented clinical history of VH and a clinicopathological diagnosis of Parkinson’s disease (PD), Alzheimer’s disease (AD), or dementia with Lewy bodies (DLB). 173 subjects – including 50 with VH and 123 without VH – were selected from the Arizona Study of Aging and Neurodegenerative Disorders. Clinical variables examined included the Mini‐mental State Exam, Hoehn & Yahr stage, and total dopaminergic medication dose. Neuropathological variables examined included total and regional LTS and plaque and tangle densities. Results: A significant relationship was found between the density of LTS and the presence of VH in all diagnostic groups. Plaque and tangle densities also were associated with VH in PD (p=.003 for plaque and p=.004 for tangles), but not in AD, where densities were high regardless of the presence of hallucinations.. Conclusion: Plaques and tangles as well as LTS may contribute to the pathogenesis of VH. Incident VH may be a clinical indicator of underlying pathological events: the development of plaques and tangles in patients with PD, and LTS in patients with AD.

Proteins play a vital role in all organic life. The structure of a protein is directly related to its function. Hence, how they fold and what they fold into is of great interest. Given the spontaneous manner in which many proteins fold, one would not expect complicated structures like knots to occur in native states. Nevertheless, current research has shown that proteins do indeed contain local knots; some with as many as 6 crossings. In general, the role of knots in proteins and how they are formed is not completely understood. This thesis develops models of protein knotting by using knot theory and tangles. Mathematically, a knot is just a topological embedding of a circle in Euclidean 3-space, R3, or the unit 3-sphere, S3. A tangle is defined as a pair, (B, T), where B is a 3-dimensional ball and T is a set of disjoint arcs properly embedded in B. We begin with 2-string tangles and use the tangle calculus developed by Ernst and Sumners to set up tangle equations. In this model the strings of the 2-tangles represent the protein chain. Solutions to these 2-string tangle equations are then found. Motivated by the hypothesized folding pathway of the knotted protein DehI, a more complicated 3-string tangle model is developed. It is hypothesized that a terminal end of the protein is threaded through two loops. In the proposed model, the threading of a terminal end of the protein through two loops is translated into a Γ;-move on 3-string tangles. A Γ;-move is a special type of 3-string tangle replacement. The 3-braids are utilized as a subset of 3-string tangles to find solutions in a limited case. Additionally, tangle models give insight into how to make specific knot types in proteins. We finish with a general result by proving that any knot of unknotting number 2 can be unknotted by the Γ;-move. With these models we determine which knots are the most biologically possible to occur in proteins.

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This thesis introduces a new quantity called loop number, and shows the conditions in which loop numbers become knot invariants. For a given knot diagram D, one can traverse the knot diagram and count the number of loops created by the traversal. The number of loops recorded depends on the starting point in the diagram D and on the traversal direction. Looking at the minimum or maximum number of loops over all starting points and directions, one can define two positive integers as loop numbers of the diagram D. In this thesis, the conditions under which these loop numbers become knot invariants are identified. In particular, the thesis answers the question when these numbers are invariant under flypes in the diagram D.

Alzheimer's disease (AD) is characterised by memory loss, insidious cognitive decline, profound neurodegeneration, and the extracellular accumulation of amyloid-beta (Aβ) peptide in senile plaques and intracellular accumulation of tau in neurofibrillary tangles. Synaptic dysfunction and loss is the strongest pathological correlate of cognitive decline in AD with increasing evidence implicating neuropathological forms of both amyloid-beta and tau protein in this process. A large amount of evidence suggests that oligomeric forms of Aβ, associated with senile plaques, are toxic to synapses but the precise localisation of Aβ and which forms are synaptotoxic remain unknown. Using the high-resolution technique, array tomography, this thesis characterised the synaptic localisation of different forms of Aβ oligomers in a mouse model of amyloidopathy. These results show that different oligomeric Aβ species are present in both presynapses and postsynapses. This study highlights the potential of array tomography for rapid testing of aggregation state specific Aβ antibodies in brain tissue. Following these results, the presence of tau at synapses was examined. Despite the knowledge that tau spreads through defined synaptic circuits, it is currently unknown whether synapse loss occurs before the accumulation of tau or as a consequence. To address this, array tomography was used to examine a mouse model in which mutant P301L human tau is expressed primarily in the entorhinal cortex (rTgTauEC). It has previously been shown that rTgTauEC mice exhibit neuronal loss in the entorhinal cortex and synapse density loss in the middle molecular layer (MML) of the dentate gyrus at 24 months of age. The density of tau-expressing and total presynapses, and the spread of tau into the postsynapse in the MML of 3-6, 9, and 18 month old mice were examined. No loss of synapse density was observed in the MML up to 18 months of age, even in axons expressing tau. Despite the maintenance of synapse density, we see spread of human tau from presynaptic terminals to postsynaptic compartments in the MML at very early ages. This indicates that the spread of tau through neural circuits is not due to the degeneration of axon terminals and is an early feature of the disease process. Following examination of both synaptic amyloid-beta and tau in separate models, this thesis then examined how these two proteins may be synergistically working together to drive synaptic pathology. To investigate this a novel mouse model was used in which amyloid-beta deposits are present in combination with non-mutated human tau expression (APP/PS1 + hTau). These results suggested that the addition of human tau expression does not increase plaque associated synapse loss, neither does it increase the proportion of synapses colocalising with amyloid-beta. Similarly the presence of human tau at individual postsynapses was not enhanced in the presence of oligomeric Aβ. Surprisingly, intact long-term recognition memory was observed in APP/PS1 + hTau mice. However a hyperactive phenotype was detected in these mice that could be prevented upon tau suppression. This suggests a synergistic relationship may exist in the presentation of this phenotype. Finally in the last part of this thesis, synapses from post-mortem human Alzheimer's disease and age-matched controls were investigated. It has previously been suggested that both amyloid-beta and tau can interfere with mitochondrial transport to the synapse and mitochondrial function. For this reason the presence of synaptic mitochondria at both the presynapse and postsynapse was determined in order to investigate any alteration in the diseased state. A reduction in the proportion of presynapses with multiple mitochondria present was detected in anterior/posterior transverse temporal cortex (BA41/42). This was not observed in dorsolateral prefrontal cortex (BA46), suggesting either a selective vulnerability of the former brain region or a selective resistance of the latter brain region, to mitochondrial depletion at the synapse. The findings presented in this thesis demonstrate that when investigated in isolation, pathological forms of amyloid-beta are present at a subset of synapses where they may contribute to toxicity, whilst the spread of tau protein is an early feature of the disease process and occurs prior to overt synapse loss. This thesis also explores the proposed synergistic relationship between amyloid-beta and tau using a novel mouse model and human post-mortem brain tissue. Since these two proteins both have been implicated in synaptic dysfunction, investigating Aβ and tau in new mouse models and human brain tissue will be instrumental in furthering our understanding of mechanisms and features of synaptotoxicity that could be important therapeutic targets.

The traditional skein relation for the Alexander polynomial involves an oriented knot, K+, with a distinguished positive crossing; a knot K−, obtained by changing the distinguished positive crossing of K+ to a negative crossing; and a link K0, the orientation preserving resolution of the distinguished crossing. We refer to (K+,K−,K0) as the oriented skein triple. A tangle is defined as a pair (B, t) of a 3-dimensional ball B and a collection of disjoint, simple, properly embedded arcs, denoted t. DeWitt Sumners and Claus Ernst developed the tangle model which uses the mathematics of tangles to model DNA-protein binding. The protein is seen as the 3-ball and the DNA bound by the protein as properly embedded curves in the 3-ball. Topoisomerases are proteins that break one segment of DNA allowing a DNA segment to pass through before resealing the break. Effectively, the action of these proteins can be modeled as K− ↔ K+. Recombinases are proteins that cut two segments of DNA and recombine them in some manner. While recombinase local action varies, most are mathematically equivalent to a resolution, i.e. K± ↔ K0. The oriented triple is now viewed as K− = circular DNA substrate, K+ = product of topoisomerase action, K0 = product of recombinase action. The theorem stated in this dissertation gives a relationship between two 2-bridge knots, K+ and K−, that differ by a crossing change and a link, K0 created from the oriented resolution of that crossing. We apply this theorem to difference topology experiments using topoisomerase proteins to study SMC proteins. In recent years, link homology theories have become a popular invariant to develop and study. One such invariant knot Floer homology, was constructed by Peter Ozsváth, Zoltán Szabó, and independently Jacob Rasmussen, denoted by HFK. It is also a refinement of a classical invariant, the Alexander polynomial. The study of DNA knots and links are of great interest to molecular biologists as they are present in many cellular process. The variety of experimentally observed DNA knots and links makes separating and categorizing these molecules a critical issue. Thus, knowing the knot Floer homology will provide restrictions on knotted and linked products of protein action. We give a summary of the combinatorial version of knot Floer homology from known work, providing a worked out example. The thesis ends with reviewing knot Floer homology properties of three particular sub-families of biologically relevant links known as (2, p)- torus links, clasp knots and 3-strand pretzel links.

A hybrid molecular dynamics/multiparticle collision dynamics algorithm was constructed to model the pressure-driven flow of a compressible fluid through a nanoscopic channel of square cross-sectional area, as well as the effect of this flow on the configuration of a polymer chain that was tethered to the surface of this nanochannel. In the process of simulating channel flow, a new adiabatic partial slip boundary condition was created as well as a modified source/sink inlet and outlet boundary condition that could maintain a specified pressure gradient across the channel without the large entrance effects typically associated with these algorithms. The results of the flow simulations were contrasted with the results from a series solution to the Navier-Stokes equation for isothermal compressible flow, and showed excellent agreement with the results from the series solution when slip-boundary conditions were applied. A finitely extendible non-linear elastic spring and bead polymer chain was used to simulate the effect of flow on the polymer chain configuration under poor solvent and θ solvent conditions. Under θ solvent conditions, the cyclical dynamics that have been previousy observed for tethered polymer chains in pure shear flows were noted, however they were restricted to the end of the polymer chain. Under poor solvent conditions, the polymer adopted a metastable helix configuration as it collapsed to a globule state. The study also examined interchain and intrachain entanglements in polymers using the granny knot and overhand knot. The mechanisms by which these tangles untied themselves were determined. At low flow rates, the tangles unravelled by the end of the chain migrating through the loops of the tangle. At high flow rates, the tangles behaved like an entrained object as they reptated towards the end of the chain.

A hybrid molecular dynamics/multiparticle collision dynamics algorithm was constructed to model the pressure-driven flow of a compressible fluid through a nanoscopic channel of square cross-sectional area, as well as the effect of this flow on the configuration of a polymer chain that was tethered to the surface of this nanochannel. In the process of simulating channel flow, a new adiabatic partial slip boundary condition was created as well as a modified source/sink inlet and outlet boundary condition that could maintain a specified pressure gradient across the channel without the large entrance effects typically associated with these algorithms. The results of the flow simulations were contrasted with the results from a series solution to the Navier-Stokes equation for isothermal compressible flow, and showed excellent agreement with the results from the series solution when slip-boundary conditions were applied. A finitely extendible non-linear elastic spring and bead polymer chain was used to simulate the effect of flow on the polymer chain configuration under poor solvent and θ solvent conditions. Under θ solvent conditions, the cyclical dynamics that have been previousy observed for tethered polymer chains in pure shear flows were noted, however they were restricted to the end of the polymer chain. Under poor solvent conditions, the polymer adopted a metastable helix configuration as it collapsed to a globule state. The study also examined interchain and intrachain entanglements in polymers using the granny knot and overhand knot. The mechanisms by which these tangles untied themselves were determined. At low flow rates, the tangles unravelled by the end of the chain migrating through the loops of the tangle. At high flow rates, the tangles behaved like an entrained object as they reptated towards the end of the chain.

The accumulation of the microtubule associated protein tau has been implicated in several neurological disorders; however, its interaction with chaperones along its normal degradation pathway remains largely uncharacterized at single residue resolution. In this study, nuclear magnetic resonance (NMR) spectroscopy was used to probe the interaction between tau, the molecular chaperone Hsp90, and the immunophilin FKBP51. Resonance intensity changes were observed for specific residues in the heteronuclear single quantum coherence (HSQC) spectra of 15N-labeled tau in the presence of Hsp90 and/or FKBP51. Analysis of the HSQC spectra identified the two hydrophobic hexapeptide motifs located at residues V275 - K280 and V306 - K311 in tau's C-terminal assembly domain as the sites of an interaction with both Hsp90 and FKBP51. Resonances that show reduced intensities did not experience line broadening, which suggests that slow chemical exchange is occurring with a bound conformation that is not observable due to the molecular weight of the complex. We have also investigated the role of the PPIase domain alone in binding to tau and found that specific residues within the PPIase active site experience significant reductions in intensity upon addition of tau. The experimental data is collectively used to propose a structural model for ternary complex formation between tau, Hsp90, and FKBP51.

There is an urgent need for the development of new therapeutic strategies for Alzheimer's disease (AD). The dual-specificity tyrosine phosphorylation-regulated kinase-1A (Dyrk1a) is a protein kinase that phosphorylates the amyloid precursor protein (APP) and tau and thus represents a link between two key proteins involved in AD pathogenesis. Furthermore, Dyrk1a is upregulated in postmortem human brains, and high levels of Dyrk1a are associated with mental retardation. Here, we sought to determine the effects of Dyrk1 inhibition on AD-like pathology developed by 3xTg-AD mice, a widely used animal model of AD. We dosed 10-month-old 3xTg-AD and nontransgenic (NonTg) mice with a Dyrk1 inhibitor (Dyrk1-inh) or vehicle for eight weeks. During the last three weeks of treatment, we tested the mice in a battery of behavioral tests. The brains were then analyzed for the pathological markers of AD. We found that chronic Dyrk1 inhibition reversed cognitive deficits in 3xTg-AD mice. These effects were associated with a reduction in amyloid-beta (Ab) and tau pathology. Mechanistically, Dyrk1 inhibition reduced APP and insoluble tau phosphorylation. The reduction in APP phosphorylation increased its turnover and decreased Ab levels. These results suggest that targeting Dyrk1 could represent a new viable therapeutic approach for AD.