Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function

AMS Subj. Classification: MSC2010: 11F72, 11M36, 58J37

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Calculating the derivative of piecewise functions

Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners’ knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions.

Protein modification and phospholipid oxidation

Phospholipid oxidation can generate reactive and electrophilic products that are capable of modifying proteins, especially at cysteine, lysine and histidine residues. Such lipoxidation reactions are known to alter protein structure and function, both with gain of function and loss of activity effects. As well as potential importance in the redox regulation of cell behaviour, lipoxidation products in plasma could also be useful biomarkers for stress conditions. Although studies with antibodies suggested the occurrence of lipoxidation adducts on ApoB-100, these products had not previously been characterized at a molecular level. We have developed new mass spectrometry-based approaches to detect and locate adducts of oxidized phospholipids in plasma proteins, as well as direct oxidation modifications of proteins, which avoid some of the problems typically encountered with database search engines leading to erroneous identifications of oxidative PTMs. This approach uses accurate mass extracted ion chromatograms (XICs) of fragment ions from peptides containing oxPTMs, and allows multiple modifications to be examined regardless of the protein that contains them. For example, a reporter ion at 184.074 Da/e corresponding to phosphocholine indicated the presence of oxidized phosphatidylcholine adducts, while 2 reporter ions at 100.078 and 82.025 Da/e were selective for allysine. ApoB-100-oxidized phospholipid adducts were detected even in healthy human samples, as well as LDL from patients with inflammatory disease. Lipidomic studies showed that more than 350 different species of lipid were present in LDL, and were altered in disease conditions. LDL clearly represents a very complex carrier system and one that offers a rich source of information about systemic conditions, with potential as indicators of oxidative damage in ageing or inflammatory diseases.

Fiber Scaffolds of Poly (glycerol-dodecanedioate) and its Derivative via Electrospinning for Neural Tissue Engineering

Peripheral nerves have demonstrated the ability to bridge gaps of up to 6 mm. Peripheral Nerve System injury sites beyond this range need autograft or allograft surgery. Central Nerve System cells do not allow spontaneous regeneration due to the intrinsic environmental inhibition. Although stem cell therapy seems to be a promising approach towards nerve repair, it is essential to use the distinct three-dimensional architecture of a cell scaffold with proper biomolecule embedding in order to ensure that the local environment can be controlled well enough for growth and survival. Many approaches have been developed for the fabrication of 3D scaffolds, and more recently, fiber-based scaffolds produced via the electrospinning have been garnering increasing interest, as it offers the opportunity for control over fiber composition, as well as fiber mesh porosity using a relatively simple experimental setup. All these attributes make electrospun fibers a new class of promising scaffolds for neural tissue engineering. Therefore, the purpose of this doctoral study is to investigate the use of the novel material PGD and its derivative PGDF for obtaining fiber scaffolds using the electrospinning. The performance of these scaffolds, combined with neural lineage cells derived from ESCs, was evaluated by the dissolvability test, Raman spectroscopy, cell viability assay, real time PCR, Immunocytochemistry, extracellular electrophysiology, etc. The newly designed collector makes it possible to easily obtain fibers with adequate length and integrity. The utilization of a solvent like ethanol and water for electrospinning of fibrous scaffolds provides a potentially less toxic and more biocompatible fabrication method. Cell viability testing demonstrated that the addition of gelatin leads to significant improvement of cell proliferation on the scaffolds. Both real time PCR and Immunocytochemistry analysis indicated that motor neuron differentiation was achieved through the high motor neuron gene expression using the metabolites approach. The addition of Fumaric acid into fiber scaffolds further promoted the differentiation. Based on the results, this newly fabricated electrospun fiber scaffold, combined with neural lineage cells, provides a potential alternate strategy for nerve injury repair.

Total phospholipid fatty acid concentrations structrures of ODP Hole 191-1179 samples (Table 1)

Sediment samples ranging from 0.05 to 278 m below sea floor (mbsf) at a Northwest Pacific deep-water (5564 mbsl) site (ODP Leg 191, Site 1179) were analyzed for phospholipid fatty acids (PLFAs). Total PLFA concentrations decreased by a factor of three over the first meter of sediment and then decreased at a slower rate to approximately 30 mbsf. The sharp decrease over the first meter corresponds to the depth of nitrate and Mn(IV) reduction as indicated by pore water chemistry. PLFA-based cell numbers at site 1179 had a similar depth profile as that for Acridine orange direct cell counts previously made on ODP site 1149 sediments which have a similar water depth and lithology. The mole percentage of straight chain saturated PLFAs increases with depth, with a large shift between the 0.95 and 3.95 mbsf samples. PLFA stable carbon isotope ratios were determined for sediments from 0.05 to 4.53 mbsf and showed a general trend toward more depleted d13C values with depth. Both of these observations may indicate a shift in the bacterial community with depth across the different redox zones inferred from pore water chemistry data. The PLFA 10me16:0, which has been attributed to the bacterial genera Desulfobacter in many marine sediments, showed the greatest isotopic depletion, decreasing from -20 to -35 per mil over the first meter of sediment. Pore water chemistry suggested that sulfate reduction was absent or minimal over this same sediment interval. However, 10me16:0 has been shown to be produced by recently discovered anaerobic ammonium oxidizing (anammox) bacteria which are known chemoautotrophs. The increasing depletion in d13C of 10me16:0 with the unusually lower concentration of ammonium and linear decrease of nitrate concentration is consistent with a scenario of anammox bacteria mediating the oxidation of ammonium via nitrite, an intermediate of nitrate reduction.

A transatlantic case: the derivative action as a corporate governance tool

The derivative action as a minority shareholder protection device seems to be almost a dead-letter law in the British Isles as compared with the United States. Whether it can or should be revived through legislative reform and judicial interpretation presents us with important governance questions at first instance, but also raises questions regarding the importance of law, as distinct from non-legally enforceable norms, to the development of corporate governance systems, in particular regarding the director-shareholder relationship.

Phospholipid fatty acid and quinone composition of sediments from ODP Leg 205 sites

Assessing the habitability of deep-sea sediments undergoing compaction, compression, and subduction at convergent margins adds to our understanding of the limits of the terrestrial biosphere. In this work, we report exploratory biomarker data on sediments obtained at Ocean Drilling Program (ODP) Sites 1253, 1254, and 1255 during drilling at the Costa Rica subduction trench and forearc sedimentary wedge. The samples selected for postcruise biomarker analyses were located within intervals of potentially enhanced fluid flow within the décollement and sedimentary wedge fault zones (Sites 1254 and 1255) and within basal carbonates at the reference site (Site 1253). The passage of fluids that are geochemically distinct from ambient interstitial water provides a disequilibrium setting that may enhance habitability. Biomarker data show low levels of microbial biomass in subseafloor sediments sampled at the Costa Rica convergent margin as deep as ~370 meters below seafloor.

Targeting treatment resistant breast cancer stem cells with FKBPL and its peptide derivative, AD-01

FKBPL and its peptide derivative, AD-01, have already demonstrated well-established inhibitory effects on breast cancer growth and CD44 dependent anti-angiogenic activity1, 2, 3. Since breast cancer stem cells (BCSCs) are CD44 positive, we wanted to explore if AD-01 could specifically target BCSCs. FKBPL stable overexpression or AD-01 treatment were highly effective at reducing the BCSC population measured by inhibiting mammosphere forming efficiency (MFE) in cell lines and primary breast cancer samples from both solid breast tumours and pleural effusions. Flow cytometry, to assess the ESA+/CD44+/CD24- subpopulation, validated these results. The ability of AD-01 to inhibit the self-renewal capacity of BCSCs was confirmed across three generations of mammospheres, where mammospheres were completely eradicated by the third generation (p<0.001). Clonogenic assays suggested that AD-01 mediated BCSC differentiation, with a significant decrease in the number of holoclones and an associated increase in meroclones/paraclones. In support of this, the stem cell markers, Nanog and Oct4 were significantly reduced following AD-01 treatment, whilst transfection of FKBPL-targeted siRNAs led to an increase in these markers and in mammosphere forming potential, highlighting the endogenous role of FKBPL in stem cell signalling. The clinical relevance of this was confirmed using a publically available microarray data set (GSE7390), where, high FKBPL and low Nanog expression were independently associated with improved overall survival in breast cancer patients (log rank test p=0.03; hazard ratio=3.01). When AD-01 was combined with other agents, we observed synergistic activity with the Notch inhibitor, DAPT and AD-01 was also able to abrogate a chemo- and radiotherapy induced enrichment in BCSCs. Importantly, using ‘gold standard’ in vivo limiting dilution assays we demonstrated a delay in tumour initiation and reoccurrence in AD-01 treated xenografts. In summary, AD-01 appears to have dual anti-angiogenic and anti-BCSC activity which will be advantageous as this agent enters clinical trial.

Erythrocyte Phospholipid Molecular Species and Fatty Acids of Down Syndrome Children Compared with Non-affected Siblings

The majority of children with Down syndrome (DS) develop Alzheimer's disease (AD) at an early age. Although long-chain n-3 fatty acids (FA) are protective of neurodegeneration, little is known about the FA status in DS. In the present study, we aimed to investigate whether children with DS presented altered plasma and erythrocyte membrane phospholipids (PL) FA composition, when compared with their non-affected siblings. Venous blood samples were analysed for plasma and erythrocyte membrane FA composition by TLC followed by GC techniques. Lipid molecular species were determined by electrospray ionisation/tandem MS (ESI-MS/MS). FA analysis measured by standard GC showed an increased concentration of MUFA and a decreased concentration of plasmalogens in major PL fractions, but there were no differences in the concentrations of arachidonic acid or DHA. However, as identified by ESI-MS/MS, children with DS had increased levels of the following erythrocyte PL molecular species: 16 : 0–16 : 0, 16 : 0–18 : 1 and 16 : 0–18 : 2n-6, with reduced levels of 16 : 0–20 : 4n-6 species. Children with DS presented significantly higher levels of MUFA in both plasma and erythrocyte membrane, as well as higher levels of saturated and monounsaturated molecular species. Of interest was the almost double proportion of 16 : 0–18 : 2n-6 and nearly half the proportion of 16 : 0–20 : 4n-6 of choline phosphoacylglycerol species in children with DS compared with their non-affected siblings. These significant differences were only revealed by ESI-MS/MS and were not observed in the GC analysis. Further investigations are needed to explore molecular mechanisms and to test the association between the pathophysiology of DS and the risk of AD.

Interactions of Cytochrome P450 3A4 with Phospholipid Bilayer Nanodiscs

Thesis (Ph.D.)--University of Washington, 2016-08