Application of real and functional analysis to solve boundary value problems

This thesis is about using appropriate tools in functional analysis arid classical analysis to tackle the problem of existence and uniqueness of nonlinear partial differential equations. There being no unified strategy to deal with these equations, one approaches each equation with an appropriate method, depending on the characteristics of the equation. The correct setting of the problem in appropriate function spaces is the first important part on the road to the solution. Here, we choose the setting of Sobolev spaces. The second essential part is to choose the correct tool for each equation. In the first part of this thesis (Chapters 3 and 4) we consider a variety of nonlinear hyperbolic partial differential equations with mixed boundary and initial conditions. The methods of compactness and monotonicity are used to prove existence and uniqueness of the solution (Chapter 3). Finding a priori estimates is the main task in this analysis. For some types of nonlinearity, these estimates cannot be easily obtained, arid so these two methods cannot be applied directly. In this case, we first linearise the equation, using linear recurrence (Chapter 4). In the second part of the thesis (Chapter 5), by using an appropriate tool in functional analysis (the Sobolev Imbedding Theorem), we are able to improve previous results on a posteriori error estimates for the finite element method of lines applied to nonlinear parabolic equations. These estimates are crucial in the design of adaptive algorithms for the method, and previous analysis relies on, what we show to be, unnecessary assumptions which limit the application of the algorithms. Our analysis does not require these assumptions. In the last part of the thesis (Chapter 6), staying with the theme of choosing the most suitable tools, we show that using classical analysis in a proper way is in some cases sufficient to obtain considerable results. We study in this chapter nonexistence of positive solutions to Laplace's equation with nonlinear Neumann boundary condition. This problem arises when one wants to study the blow-up at finite time of the solution of the corresponding parabolic problem, which models the heating of a substance by radiation. We generalise known results which were obtained by using more abstract methods.

Functional analysis of the sheep Wilson disease protein (sATP7B) in CHO cells

In this study we investigated the function of the sheep orthologue of ATP7B (sATP7B), the protein affected in the human copper toxicosis disorder Wilson disease. Two forms of sATP7B are found in the sheep, a ‘normal’ form and one with an alternate N terminus, both of which were expressed in CHO-K1 cells. Cells expressing either form of sATP7B were more resistant to copper than the parental CHO-K1 cells. Subcellular localisation studies showed that both forms of sATP7B were similarly located in the trans-Golgi network (TGN). When the extracellular copper concentration was increased, each form of sATP7B redistributed to a punctate, vesicular compartment that extended throughout the cytoplasm. Both forms of sATP7B recycled to the perinuclear location within one hour when the cells were subsequently incubated in basal medium. After treatment of cells with bafilomycin A1 sATP7B accumulated in cytoplasmic vesicles, implying that ATP7B continuously recycles via the endocytic pathway. These results suggest that both forms of sATP7B are functional copper-transport proteins and that the intracellular location and trafficking of the sheep protein within the cell also appears normal.

Functional analysis of natriuretic peptide receptors in the bladder of the toad, bufo marinus

This study aimed to localize and characterize natriuretic peptide binding sites in the urinary bladder of Bufo marinus and to then examine the effect of natriuretic peptides on the bladder vascular tone and water reabsorption in isolated perfused bladder preparations. Specific ¹²⁵I-rat atrial natriuretic peptide (¹²⁵I-rANP) binding sites were present on blood vessels, muscle, and epithelium. In tissue sections and/or isolated membranes, the binding was completely displaced by frog ANP, rat ANP, and porcine C-type natriuretic peptide (CNP; membranes only). However, a reduction in binding was observed after incubation with ¹²⁵I-rANP and 1 μM of the natriuretic peptide receptor-C (NPR-C) ligand C-ANF, but residual binding remained suggesting the presence of two distinct binding sites. Electrophoresis of bladder membranes cross-linked to ¹²⁵I-rANP identified two bands at approximately 70 and 140 kDa that correspond to the monomeric mass of NPR-C and the guanylate cyclase receptors, respectively. Furthermore, the presence of natriuretic peptide receptor-A and NPR-C mRNA in the bladder was demonstrated with reverse transcription–polymerase chain reaction. In addition, rat ANP, frog ANP, and porcine CNP stimulated a significant increase in cGMP generation in bladder membrane preparations, which indicated the presence of guanylate cyclase-linked receptors. In perfused bladder preparations, arginine vasotocin increased perfusion pressure and water permeability. The infusion of frog ANP or porcine CNP failed to alter perfusion pressure or water reabsorption in the presence or absence of arginine vasotocin. This study identified a well-developed natriuretic peptide receptor system in the urinary bladder of B. marinus but the function of the receptors remains unclear.

Toad atrial natriuretic peptide : cDNA cloning and functional analysis in isolated perfused kidneys

Complementary DNA (cDNA) encoding Bufo marinus (toad) preproatrial natriuretic peptide (preproANP) was isolated by reverse-transcription polymerase chain reaction. Sequence analysis of toad preproANP cDNA revealed an open reading frame of 150 amino acid residues, which shared 72% and 66% identity with Rana catesbeiana and Xenopus laevis preproANP, respectively. The deduced amino acid sequence of toad ANP that corresponded to ANP 1–24 of R. catesbeiana and Rana ridibunda was identical, but it differed by four residues from that of X. laevis. ANP mRNA transcripts were also shown to be expressed in the toad kidney. Subsequently, the effect of frog ANP (1–24) on renal function in toad was examined using a perfused kidney preparation. The arterial infusion of frog ANP caused a dose-dependent decrease in the arterial perfusion pressure that was associated with an increase in the glomerular filtration rate (GFR) and a renal natriuresis and diuresis. The renal natriuresis and diuresis resulted predominantly from an increased GFR rather than from direct tubular effects. This study demonstrates that ANP can regulate renal function, which suggests it may be involved in overall fluid volume regulation.

Functional analysis of yeast snoRNA and snRNA 3' end formation mediated by uncoupling of cleavage and polyadenylation

Many nuclear and nucleolar small RNAs are accumulated as nonpolyadenylated species and require 3′-end processing for maturation. Here, we show that several genes coding for box C/D and H/ACA snoRNAs and for the U5 and U2 snRNAs contain sequences in their 3′ portions which direct cleavage of primary transcripts without being polyadenylated. Genetic analysis of yeasts with mutations in different components of the pre-mRNA cleavage and polyadenylation machinery suggests that this mechanism of 3"-end formation requires cleavage factor IA (CF IA) but not cleavage and polyadenylation factor activity. However, in vitro results indicate that other factors participate in the reaction besides CF IA. Sequence analysis of snoRNA genes indicated that they contain conserved motifs in their 3" noncoding regions, and mutational studies demonstrated their essential role in 3"-end formation. We propose a model in which CF IA functions in cleavage and polyadenylation of pre-mRNAs and, in combination with a different set of factors, in 3"-end formation of nonpolyadenylated polymerase II transcripts.

Functional analysis of the leading malaria vaccine candidate AMA-1 reveals an essential role for the cytoplasmic domain in the invasion process

A key process in the lifecycle of the malaria parasite Plasmodium falciparum is the fast invasion of human erythrocytes. Entry into the host cell requires the apical membrane antigen 1 (AMA-1), a type I transmembrane protein located in the micronemes of the merozoite. Although AMA-1 is evolving into the leading blood-stage malaria vaccine candidate, its precise role in invasion is still unclear. We investigate AMA-1 function using live video microscopy in the absence and presence of an AMA-1 inhibitory peptide. This data reveals a crucial function of AMA-1 during the primary contact period upstream of the entry process at around the time of moving junction formation. We generate a Plasmodium falciparum cell line that expresses a functional GFP-tagged AMA-1. This allows the visualization of the dynamics of AMA-1 in live parasites. We functionally validate the ectopically expressed AMA-1 by establishing a complementation assay based on strain-specific inhibition. This method provides the basis for the functional analysis of essential genes that are refractory to any genetic manipulation. Using the complementation assay, we show that the cytoplasmic domain of AMA-1 is not required for correct trafficking and surface translocation but is essential for AMA-1 function. Although this function can be mimicked by the highly conserved cytoplasmic domains of P. vivax and P. berghei, the exchange with the heterologous domain of the microneme protein EBA-175 or the rhoptry protein Rh2b leads to a loss of function. We identify several residues in the cytoplasmic tail that are essential for AMA-1 function. We validate this data using additional transgenic parasite lines expressing AMA-1 mutants with TY1 epitopes. We show that the cytoplasmic domain of AMA-1 is phosphorylated. Mutational analysis suggests an important role for the phosphorylation in the invasion process, which might translate into novel therapeutic strategies.

Functional analysis of Plasmodium falciparum merozoite antigens : implications for erythrocyte invasion and vaccine development

Malaria is a major human health problem and is responsible for over 2 million deaths per year. It is caused by a number of species of the genus Plasmodium, and Plasmodium falciparum is the causative agent of the most lethal form. Consequently, the development of a vaccine against this parasite is a priority. There are a number of stages of the parasite life cycle that are being targeted for the development of vaccines. Important candidate antigens include proteins on the surface of the asexual merozoite stage, the form that invades the host erythrocyte. The development of methods to manipulate the genome of Plasmodium species has enabled the construction of gain-of-function and loss-of-function mutants and provided new strategies to analyse the role of parasite proteins. This has provided new information on the role of merozoite antigens in erythrocyte invasion and also allows new approaches to address their potential as vaccine candidates.

Functional analysis of proteins involved in Plasmodium falciparum merozoite invasion of red blood cells

Plasmodium falciparum causes the most lethal form of malaria in humans and is responsible for over two million deaths per year. The development of a vaccine against this parasite is an urgent priority and potential protein targets include those on the surface of the asexual merozoite stage, the form that invades the host erythrocyte. The development of methods to transfect P. falciparum has enabled the construction of gain-of-function and loss-of-function mutants and provided new strategies to analyse the role of parasite proteins. In this review, we describe the use of this technology to examine the role of merozoite antigens in erythrocyte invasion and to address their potential as vaccine candidates.

Functional analysis of a Type-I ribosome inactivating protein balsamin from Momordica balsamina with anti-microbial and DNase activity

Ribosome inactivating proteins (RIPs) have received considerable attention in biomedical research because of their unique activities towards tumor and virus-infected cells. We extracted balsamin, a type-I RIP, from Momordica balsamina. In the present study, a detailed investigation on DNase activity, antioxidant capacity and antibacterial activity was conducted using purified balsamin. DNase-like activity of balsamin towards plasmid DNA was pH, incubation time and temperature dependent. Moreover, the presence of Mg(2+) (10-50 mM) influenced the DNA cleavage activity. Balsamin also demonstrated reducing power and a capacity to scavenge free radicals in a dose dependent manner. Furthermore, the protein exhibited antibacterial activity against Staphylococcus aureus, Salmonella enterica, Staphylococcus epidermidis and Escherichia coli, which suggests potential utility of balsamin as a nutraceutical.

Typography and the branding of culture: a systemic functional analysis of typography’s performance in branding cultural festivals in Australia

This paper offers a social semiotic analysis of logotypes used to brand cultural festivals in 21st century Australia. A contemporary method is explored that suits the significant role typography performs within this context and offers a contribution to design research and the festival scape that not only engages with the artefacts of design but with the conceptualization of designed meaning in visual culture. Branding is a vital part of the festival space and relies on typography to establish the symbolic values and representations of urban freedoms; rich histories, cultured places, playfulness and stimulation that seek to subvert our daily existence while performing the task of engaging local, national, and international visitors and participants. However, professional practices demonstrated in the design, media and arts industries have far outpaced the extent to which this phenomenon has been written about in the academic or public realm. This paper addresses this shortfall and offers the foundation for a systemic functional method in the decoding of typography in visual culture

Mutation analysis of the Menkes gene

Menkes disease is a copper deficiency caused by mutations in the Menkes gene, which encodes a copper-transporting protein. This study identified the causative mutations in several Menkes patients, which provided a diagnostic test for relatives and identified critical regions of the Menkes protein. Further regions were identified through functional analysis of mutations introduced by in vitro mutagenesis.

Role assessment of GIS analysis and its reliability while ranking urban sustainability using scenarios specific to regional climate, community and culture

Urban Sustainability expresses the level of conservation of a city while living a town or consuming its urban resources, but the measurement of urban sustainability depends on what are considered important indicators of conservation besides the permitted levels of consumption in accordance with adopted criteria. This criterion should have common factors that are shared for all the members tested or cities to be evaluated as in this particular case for Abu Dhabi, but also have specific factors that are related to the geographic place, community and culture, that is the measures of urban sustainability specific to a middle east climate, community and culture where GIS Vector and Raster analysis have a role or add a value in urban sustainability measurements or grading are considered herein. Scenarios were tested using various GIS data types to replicate urban history (ten years period), current status and expected future of Abu Dhabi City setting factors to climate, community needs and culture. The useful Vector or Raster GIS data sets that are related to every scenario where selected and analysed in the sense of how and how much it can benefit the urban sustainability ranking in quantity and quality tests, this besides assessing the suitable data nature, type and format, the important topology rules to be considered, the useful attributes to be added, the relationships which should be maintained between data types of a geo- database, and specify its usage in a specific scenario test, then setting weights to each and every data type representing some elements of a phenomenon related to urban suitability factor. The results of assessing the role of GIS analysis provided data collection specifications such as the measures of accuracy reliable to a certain type of GIS functional analysis used in an urban sustainability ranking scenario tests. This paper reflects the prior results of the research that is conducted to test the multidiscipline evaluation of urban sustainability using different indicator metrics, that implement vector GIS Analysis and Raster GIS analysis as basic tools to assist the evaluation and increase of its reliability besides assessing and decomposing it, after which a hypothetical implementation of the chosen evaluation model represented by various scenarios was implemented on the planned urban sustainability factors for a certain period of time to appraise the expected future grade of urban sustainability and come out with advises associated with scenarios for assuring gap filling and relative high urban future sustainability. The results this paper is reflecting are concentrating on the elements of vector and raster GIS analysis that assists the proper urban sustainability grading within the chosen model, the reliability of spatial data collected; analysis selected and resulted spatial information. Starting from selecting some important indicators to comprise the model which include regional culture, climate and community needs an example of what was used is Energy Demand & Consumption (Cooling systems). Thus, this factor is related to the climate and it‟s regional specific as the temperature varies around 30-45 degrees centigrade in city areas, GIS 3D Polygons of building data used to analyse the volume of buildings, attributes „building heights‟, estimate the number of floors from the equation, following energy demand was calculated and consumption for the unit volume, and compared it in scenario with possible sustainable energy supply or using different environmental friendly cooling systems this is followed by calculating the cooling system effects on an area unit selected to be 1 sq. km, combined with the level of greenery area, and open space, as represented by parks polygons, trees polygons, empty areas, pedestrian polygons and road surface area polygons. (initial measures showed that cooling system consumption can be reduced by around 15 -20 % with a well-planned building distributions, proper spaces and with using environmental friendly products and building material, temperature levels were also combined in the scenario extracted from satellite images as interpreted from thermal bands 3 times during the period of assessment. Other examples of the assessment of GIS analysis to urban sustainability took place included Waste Productivity, some effects of greenhouse gases measured by the intensity of road polygons and closeness to dwelling areas, industry areas as defined from land use land cover thematic maps produced from classified satellite images then vectors were created to take part in defining their role within the scenarios. City Noise and light intensity assessment was also investigated, as the region experiences rapid development and noise is magnified due to construction activities, closeness of the airports, and highways. The assessment investigated the measures taken by urban planners to reduce degradation or properly manage it. Finally as a conclusion tables were presented to reflect the scenario results in combination with GIS data types, analysis types, and the level of GIS data reliability to measure the sustainability level of a city related to cultural and regional demands.

Paraoxonase (PON)1 Q192R functional genotypes and PON1 Q192R genotype by smoking interactions are risk factors for the metabolic syndrome, but not overweight or obesity

Background The metabolic syndrome (MetS) is a complex of multiple risk factors that contribute to the onset of cardiovascular disorder, including lowered levels of high-density lipoprotein (HDL) and abdominal obesity. Smoking, mood disorders, and oxidative stress are associated with the MetS. Paraoxonase (PON)1 is an antioxidant bound to HDL, that is under genetic control by functional polymorphisms in the PON1 Q192R coding sequence. Aims and methods This study aimed to delineate the associations of the MetS with plasma PON1 activity, PON1 Q192R genotypes, smoking, and mood disorders (major depression and bipolar disorder), while adjusting for HDL cholesterol, body mass index, age, gender, and sociodemographic data. We measured plasma PON1 activity and serum HDL cholesterol and determined PON1 Q192R genotypes through functional analysis in 335 subjects, consisting of 97 with and 238 without MetS. The severity of nicotine dependence was measured using the Fagerström Nicotine Dependence Scale. Results PON1 Q192R functional genotypes and PON1 Q192R genotypes by smoking interactions were associated with the MetS. The QQ and QR genotypes were protective against MetS while smoking increased metabolic risk in QQ carriers only. There were no significant associations between PON1 Q192R genotypes and smoking by genotype interactions and obesity or overweight, while body mass index significantly increased MetS risk. Smoking and especially severe nicotine dependence are significantly associated with the MetS although these effects were no longer significant after considering the effects of the smoking by PON1 Q192R genotype interaction. The MetS was not associated with mood disorders, major depression or bipolar disorder. Discussion PON1 Q192R genotypes and genotypes by smoking interactions are risk factors for the MetS that together with lowered HDL and increased body mass and age contribute to the MetS.